diff --git a/-dE4T4oBgHgl3EQfDwsm/content/2301.04871v1.pdf b/-dE4T4oBgHgl3EQfDwsm/content/2301.04871v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..d6ede5c586ea2288c84834be6999be5f9f78974a
--- /dev/null
+++ b/-dE4T4oBgHgl3EQfDwsm/content/2301.04871v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e8b6f1def5a202979203791c8fd4a1293f29f54abd6c4ad57aff640038c7db5c
+size 426096
diff --git a/-dE4T4oBgHgl3EQfDwsm/vector_store/index.pkl b/-dE4T4oBgHgl3EQfDwsm/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..ba97c6cf0ee610b94117be1856dbbe01cf37d405
--- /dev/null
+++ b/-dE4T4oBgHgl3EQfDwsm/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b6e6eeeeac62fe14354fb1a255af153e3c649b98d6ce03d4ad6e2da3fd47b5a1
+size 139634
diff --git a/.gitattributes b/.gitattributes
index 6fbdca4170bf6a3cd95e001e9b93c8773f4c6add..f1669a3db941197f2023f0d4faaa5f562a5f893f 100644
--- a/.gitattributes
+++ b/.gitattributes
@@ -2050,3 +2050,87 @@ PNFOT4oBgHgl3EQf4TQo/content/2301.12949v1.pdf filter=lfs diff=lfs merge=lfs -tex
 s9AzT4oBgHgl3EQfPfs9/content/2301.01183v1.pdf filter=lfs diff=lfs merge=lfs -text
 m9E3T4oBgHgl3EQfKgnW/content/2301.04355v1.pdf filter=lfs diff=lfs merge=lfs -text
 m9E3T4oBgHgl3EQfKgnW/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+d9E1T4oBgHgl3EQfeAT4/content/2301.03203v1.pdf filter=lfs diff=lfs merge=lfs -text
+2tFQT4oBgHgl3EQfGDUx/content/2301.13243v1.pdf filter=lfs diff=lfs merge=lfs -text
+htE3T4oBgHgl3EQf4Quq/content/2301.04771v1.pdf filter=lfs diff=lfs merge=lfs -text
+z9AzT4oBgHgl3EQfRPsg/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+2tFQT4oBgHgl3EQfGDUx/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+F9E0T4oBgHgl3EQfRAC9/content/2301.02202v1.pdf filter=lfs diff=lfs merge=lfs -text
+KtAyT4oBgHgl3EQf6Prq/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+OdE2T4oBgHgl3EQfrAj4/content/2301.04046v1.pdf filter=lfs diff=lfs merge=lfs -text
+LdAyT4oBgHgl3EQf6fqP/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+UdE0T4oBgHgl3EQflgEz/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+X9E5T4oBgHgl3EQfdQ8b/content/2301.05609v1.pdf filter=lfs diff=lfs merge=lfs -text
+pNE3T4oBgHgl3EQf7wtN/content/2301.04801v1.pdf filter=lfs diff=lfs merge=lfs -text
+CdE2T4oBgHgl3EQf9AmF/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+BdAzT4oBgHgl3EQf___2/content/2301.01958v1.pdf filter=lfs diff=lfs merge=lfs -text
+ZNE5T4oBgHgl3EQfdw-l/content/2301.05614v1.pdf filter=lfs diff=lfs merge=lfs -text
+ytAzT4oBgHgl3EQfCvqr/content/2301.00965v1.pdf filter=lfs diff=lfs merge=lfs -text
+OdE2T4oBgHgl3EQfrAj4/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+v9AzT4oBgHgl3EQfsf3v/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+btFPT4oBgHgl3EQfBDTK/content/2301.12984v1.pdf filter=lfs diff=lfs merge=lfs -text
+ddE1T4oBgHgl3EQfLQO1/content/2301.02975v1.pdf filter=lfs diff=lfs merge=lfs -text
+vdFPT4oBgHgl3EQfOTSJ/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+btAyT4oBgHgl3EQf-PpJ/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+pNE3T4oBgHgl3EQf7wtN/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+X9E5T4oBgHgl3EQfdQ8b/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+ttE1T4oBgHgl3EQf3wUi/content/2301.03492v1.pdf filter=lfs diff=lfs merge=lfs -text
+y9AyT4oBgHgl3EQfbPc2/content/2301.00257v1.pdf filter=lfs diff=lfs merge=lfs -text
+WtE2T4oBgHgl3EQfDga8/content/2301.03626v1.pdf filter=lfs diff=lfs merge=lfs -text
+pdE0T4oBgHgl3EQfqgHp/content/2301.02555v1.pdf filter=lfs diff=lfs merge=lfs -text
+UtE1T4oBgHgl3EQfawTU/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+S9FKT4oBgHgl3EQfkC7A/content/2301.11848v1.pdf filter=lfs diff=lfs merge=lfs -text
+HNAyT4oBgHgl3EQfS_eb/content/2301.00097v1.pdf filter=lfs diff=lfs merge=lfs -text
+btAyT4oBgHgl3EQf-PpJ/content/2301.00888v1.pdf filter=lfs diff=lfs merge=lfs -text
+y9AyT4oBgHgl3EQfbPc2/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+oNE0T4oBgHgl3EQfqQFw/content/2301.02550v1.pdf filter=lfs diff=lfs merge=lfs -text
+L9FLT4oBgHgl3EQfMi8T/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+lNE2T4oBgHgl3EQfdwfJ/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+S9FKT4oBgHgl3EQfkC7A/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+ltE5T4oBgHgl3EQfHQ5_/content/2301.05438v1.pdf filter=lfs diff=lfs merge=lfs -text
+F9E0T4oBgHgl3EQfRAC9/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+c9FJT4oBgHgl3EQfRiy-/content/2301.11496v1.pdf filter=lfs diff=lfs merge=lfs -text
+fdE5T4oBgHgl3EQfhQ8n/content/2301.05639v1.pdf filter=lfs diff=lfs merge=lfs -text
+fdE5T4oBgHgl3EQfhQ8n/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+s9E2T4oBgHgl3EQf1wgV/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+ltE5T4oBgHgl3EQfHQ5_/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+ZNE5T4oBgHgl3EQfdw-l/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+pNAzT4oBgHgl3EQfOfvU/content/2301.01168v1.pdf filter=lfs diff=lfs merge=lfs -text
+ttE1T4oBgHgl3EQf3wUi/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+59FKT4oBgHgl3EQf-y48/content/2301.11959v1.pdf filter=lfs diff=lfs merge=lfs -text
+oNE0T4oBgHgl3EQfqQFw/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+itE2T4oBgHgl3EQfIAZX/content/2301.03674v1.pdf filter=lfs diff=lfs merge=lfs -text
+59FKT4oBgHgl3EQf-y48/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+UtE1T4oBgHgl3EQfawTU/content/2301.03166v1.pdf filter=lfs diff=lfs merge=lfs -text
+HNAyT4oBgHgl3EQfS_eb/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+FtAyT4oBgHgl3EQf5Poe/content/2301.00799v1.pdf filter=lfs diff=lfs merge=lfs -text
+BdAzT4oBgHgl3EQf___2/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+CNE2T4oBgHgl3EQfRwe0/content/2301.03785v1.pdf filter=lfs diff=lfs merge=lfs -text
+pdE0T4oBgHgl3EQfqgHp/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+2dAzT4oBgHgl3EQfDvol/content/2301.00980v1.pdf filter=lfs diff=lfs merge=lfs -text
+VNE0T4oBgHgl3EQf2wJn/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+c9FJT4oBgHgl3EQfRiy-/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+mNE1T4oBgHgl3EQfOAOw/content/2301.03010v1.pdf filter=lfs diff=lfs merge=lfs -text
+jNAyT4oBgHgl3EQfx_lt/content/2301.00676v1.pdf filter=lfs diff=lfs merge=lfs -text
+A9E4T4oBgHgl3EQf5A6T/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+ytAzT4oBgHgl3EQfCvqr/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+XNE2T4oBgHgl3EQfYgch/content/2301.03854v1.pdf filter=lfs diff=lfs merge=lfs -text
+lNE2T4oBgHgl3EQfdwfJ/content/2301.03910v1.pdf filter=lfs diff=lfs merge=lfs -text
+WtE2T4oBgHgl3EQfDga8/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+A9E4T4oBgHgl3EQf5A6T/content/2301.05319v1.pdf filter=lfs diff=lfs merge=lfs -text
+aNA0T4oBgHgl3EQfF__0/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+XNE2T4oBgHgl3EQfYgch/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+X9AyT4oBgHgl3EQf9foH/content/2301.00873v1.pdf filter=lfs diff=lfs merge=lfs -text
+btFPT4oBgHgl3EQfBDTK/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+T9E3T4oBgHgl3EQfaQqr/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+htE3T4oBgHgl3EQf4Quq/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+cNE0T4oBgHgl3EQfWQCi/content/2301.02276v1.pdf filter=lfs diff=lfs merge=lfs -text
+aNA0T4oBgHgl3EQfF__0/content/2301.02042v1.pdf filter=lfs diff=lfs merge=lfs -text
+FtE4T4oBgHgl3EQfHAzF/content/2301.04900v1.pdf filter=lfs diff=lfs merge=lfs -text
+7dE2T4oBgHgl3EQfPQbU/content/2301.03758v1.pdf filter=lfs diff=lfs merge=lfs -text
+cdE5T4oBgHgl3EQffg9z/content/2301.05627v1.pdf filter=lfs diff=lfs merge=lfs -text
+-dE4T4oBgHgl3EQfDwsm/content/2301.04871v1.pdf filter=lfs diff=lfs merge=lfs -text
+1NAyT4oBgHgl3EQfofhG/content/2301.00507v1.pdf filter=lfs diff=lfs merge=lfs -text
+FtE4T4oBgHgl3EQfHAzF/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+pNAzT4oBgHgl3EQfOfvU/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+T9E3T4oBgHgl3EQfaQqr/content/2301.04505v1.pdf filter=lfs diff=lfs merge=lfs -text
diff --git a/1NAyT4oBgHgl3EQfofhG/content/2301.00507v1.pdf b/1NAyT4oBgHgl3EQfofhG/content/2301.00507v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..82fa2672f50eb284bf980ab3e98fc2bb37c998b0
--- /dev/null
+++ b/1NAyT4oBgHgl3EQfofhG/content/2301.00507v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4c488e0b9d4e943ff59f1648c5faf90e8876105f77224f5d5d67542b5ff8fcff
+size 229268
diff --git a/1NAyT4oBgHgl3EQfofhG/vector_store/index.pkl b/1NAyT4oBgHgl3EQfofhG/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..91ee5c4a7df452ec8e02aa0aa778ffe689392739
--- /dev/null
+++ b/1NAyT4oBgHgl3EQfofhG/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ae778cea3f10ac0093a583cd7c9e573989024a2e095889c650089865a7ce8356
+size 80484
diff --git a/2dAzT4oBgHgl3EQfDvol/content/2301.00980v1.pdf b/2dAzT4oBgHgl3EQfDvol/content/2301.00980v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..601871bbc1a84ddfd1852c0490b47179b7b814d9
--- /dev/null
+++ b/2dAzT4oBgHgl3EQfDvol/content/2301.00980v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:164ec6d21fa77ac37c4a89fb8afc5d4495825da9e71998b3e34d0fb89b0fc5f8
+size 282183
diff --git a/2dAzT4oBgHgl3EQfDvol/vector_store/index.pkl b/2dAzT4oBgHgl3EQfDvol/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..487dd83df734b6dd580d2fa7f8ca9c5fd6ae3a5b
--- /dev/null
+++ b/2dAzT4oBgHgl3EQfDvol/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:cc247f7cc828a1d9cb1c271d36da3f923500293c2e3b8e06f8f82fe0741b4fa1
+size 118429
diff --git a/2tFQT4oBgHgl3EQfGDUx/content/2301.13243v1.pdf b/2tFQT4oBgHgl3EQfGDUx/content/2301.13243v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..894b1907a62feb919e2408e2bad923ae08184ab4
--- /dev/null
+++ b/2tFQT4oBgHgl3EQfGDUx/content/2301.13243v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:bd2406dc103db5bb607377b5ebac79963ba4ae695e53588d0eef0bb284c09d00
+size 690989
diff --git a/2tFQT4oBgHgl3EQfGDUx/vector_store/index.faiss b/2tFQT4oBgHgl3EQfGDUx/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..95098f7c793cab64a3b21e8c236093a76be8427b
--- /dev/null
+++ b/2tFQT4oBgHgl3EQfGDUx/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5d449761694772d0bddbf3f97e729218921530a181e6307007afa6a4bb38c553
+size 3080237
diff --git a/49FAT4oBgHgl3EQfFRw-/content/tmp_files/2301.08426v1.pdf.txt b/49FAT4oBgHgl3EQfFRw-/content/tmp_files/2301.08426v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..18001726d5c07e7be76a00f780b5d0d1917899df
--- /dev/null
+++ b/49FAT4oBgHgl3EQfFRw-/content/tmp_files/2301.08426v1.pdf.txt
@@ -0,0 +1,1916 @@
+η-pairing on bipartite and non-bipartite lattices
+Yutaro Misu1, Shun Tamura2, Yukio Tanaka2 and Shintaro Hoshino1
+1Department of Physics, Saitama University, Saitama 338-8570, Japan
+2Department of Applied Physics, Nagoya University, Nagoya 464-8603, Japan
+(Dated: January 23, 2023)
+The η-pairing is a type of Cooper pairing state in which the phase of the superconducting order
+parameter is aligned in a staggered manner, in contrast to the usual BCS superconductors with a
+spatially uniform phase. In this study, we search for a characteristic η-pairing state in a triangular
+lattice where a simple staggered alignment of the phase is not possible. As an example, we consider
+the attractive Hubbard model on both the square and triangular lattices under strong external
+Zeeman field.
+Using the mean-field approximation, we have identified several η-pairing states.
+Additionally, we have examined the electromagnetic stability of the pairing state by calculating the
+Meissner kernel. Odd-frequency pairing plays a crucial role in achieving diamagnetic response if the
+electrons experience a staggered superconducting phase during the propagation of current.
+I.
+INTRODUCTION
+The diversity of superconducting phenomena has been
+attracting continued attention.
+The superconducting
+state of matter is characterized by the properties of
+Cooper pairs, which can be classified based on their
+space-time and spin structures.
+With regard to their
+space structure, Cooper pairs are typically classified as
+s-wave, p-wave, or d-wave pairs depending on their rel-
+ative coordinate structure. As for their center-of-mass
+coordinate, while it is usually assumed to be zero in
+most superconductors, it is possible to consider the exis-
+tence of a finite center-of-mass momentum. One example
+of this is the Flude-Ferrell-Larkin-Ovchinnikov (FFLO)
+state [1, 2], in which the Cooper pair has a small but finite
+center-of-mass momentum under the influence of a mag-
+netic field. More generally, the magnitude of the center-
+of-mass momentum can be larger and of the order of the
+reciprocal lattice vector ∼ π/a, where a is a lattice con-
+stant. This type of pairing state is known as η-pairing,
+a concept first proposed by C. N. Yang, which forms a
+staggered alignment of the superconducting phase on a
+bipartite lattice [3]. The spatially modulating order pa-
+rameter is known also as the pair density wave, and has
+been discussed in relation to cuprate superconductors [4].
+The actual realization of the η-pairing has been pro-
+posed for the correlated electron systems such as the at-
+tractive Hubbard (AH) model with the magnetic field
+[5], the single- and two-channel Kondo lattices [6, 7], the
+Penson-Kolb model [8], and also the non-equilibrium sit-
+uation [9–14].
+Since the phase of the superconducting
+order parameter can be regarded as the XY spin, the η-
+pairing is analogous to an antiferromagnetic state of the
+XY spin model.
+Hence, the η-pairing state should be
+strongly dependent on the underlying lattice structure
+and we naively expect a variety of the η-pairing state
+if we consider the geometrically frustrated lattice such
+as the triangular lattice since the simple staggered state
+cannot be realized.
+In this paper, we deal with the AH model on the non-
+bipartite lattice in order to search for possible new su-
+perconducting states depending on the feature of the
+non-bipartite lattice structure in equilibrium.
+Already
+in the normal state without superconductivity, it has
+been pointed out that the non-bipartite lattice generates
+a non-trivial state of matter. For example in the Kondo
+lattice, a partial-Kondo-screening, which has a coexisting
+feature of Kondo spin-singlet and antiferromagnetism, is
+realized [15]. Also in the AH model at half-filling, charge-
+density-wave (CDW) is suppressed due to the frustration
+effect [16]. The η-pairing that appears in a photodoped
+Hubbard model on the triangular lattice has been studied
+recently [14]. In the equilibrium situation, the properties
+of the AH model have been studied on bipartite lattices
+[5], but the model on a non-bipartite lattice has not been
+explored.
+As shown in the rest of this paper, there are several
+types of η-pairings on the triangular lattice of the AH
+model under the Zeeman field.
+One of the η-pairing
+states is regarded as a 120◦-N´eel state.
+Since the rel-
+ative phase between the nearest neighbor sites is neither
+parallel nor anti-parallel, the inter-atomic Josephson cur-
+rent is spontaneously generated. This state can also be
+regarded as a staggered flux state, where the flux is cre-
+ated by the atomic-scale superconducting loop current.
+While the staggered flux state has been studied so far
+[17–23], the staggered flux in this paper is induced by
+the Josephson effect associated with superconductivity
+and has a different origin.
+For the analysis of the AH model, we employ the mean-
+field approximation in this paper. It has been suggested
+that a simple η-pairing shows a paramagnetic Meissner
+state [24]. Hence it is necessary to investigate the electro-
+magnetic stability of the solution for superconductivity.
+We evaluate the Meissner kernel whose sign corresponds
+to the diamagnetic (minus) or paramagnetic (plus) re-
+sponse of the whole system, where the physically sta-
+ble state should show diamagnetism. We confirm that
+if the mean-field η-pairing state has the lowest energy
+compared to the other ordered states, the calculation of
+the Meissner kernel shows the diamagnetic response. It
+is also notable that the odd-frequency pairing amplitude,
+which has an odd functional form with respect to the fre-
+quency [6, 25–30], can contribute to the diamagnetism in
+arXiv:2301.08426v1  [cond-mat.supr-con]  20 Jan 2023
+
+2
+the η-pairing state. This is in contrast to the usual super-
+conductivity with the uniform phase where the conven-
+tional even-frequency pairing contributes to the diamag-
+netism. It has been shown that the odd-frequency pairing
+induced at the edge, interface or junctions [31–36] shows
+a paramagnetic response [37–41]. In this paper, by con-
+trast, we consider the odd-frequency pairing realized in
+bulk, which shows a qualitatively different behavior.
+This paper is organized as follows.
+We explain the
+model and method for the AH model in Sec. II, and the
+Meissner kernel in Sec. III. The numerical results for the
+AH model are shown in Sec. IV, and we summarize the
+paper in Sec. V.
+II.
+ATTRACTIVE HUBBARD MODEL
+A.
+Hamiltonian
+We consider the Hamiltonian of the AH model with
+magnetic field h which induce Zeeman effect only (Zee-
+man field) :
+H = −t
+�
+⟨i,j⟩σ
+c†
+iσcjσ + H.c. + U
+�
+i
+ni↑ni↓
+− µ
+�
+i
+ni − h ·
+�
+i
+si,
+(1)
+where c†
+iσ and ciσ are the creation and annihilation op-
+erators of the i-th site with spin σ, respectively.
+The
+symbol ⟨i, j⟩ represents a pair of the nearest-neighbor
+sites.
+Here, the parameter t is the nearest-neighbor
+single-electron hopping integral. U (= −|U|) is the on-
+site attractive interaction. The spin operator is defined
+as si =
+1
+2
+�
+σσ′ c†
+iστσσ′ciσ′, where τ is the Pauli ma-
+trix, and the number operator of electrons is denoted as
+ni = ni↑ + ni↓ = �
+σ c†
+iσciσ. The electron concentration
+is controlled by adjusting the chemical potential µ.
+The AH model has been successfully used to elucidate
+several important and fundamental issues in supercon-
+ductors [42]. The model on a bipartite lattice at half fill-
+ing is theoretically mapped onto the repulsive Hubbard
+model by the following partial particle-hole transforma-
+tion [43]
+c†
+i↑ → c†
+i↑, c†
+i↓ → ci↓eiQ·Ri.
+(2)
+The reciprocal vector Q satisfies the condition eiQ·Ri =
+(−1)i that takes ±1 depending on Ri belonging to A or
+B sublattice on the bipartite lattice. Then, the η-pairing
+appears in the region that corresponds to a ferromagnet
+with transverse magnetization in the repulsive model [5].
+In a mean-field theory, the phase diagram for the repul-
+sive Hubbard model without the magnetic field is shown
+in the left panel of Fig. 1 [44]. From this figure, we find
+that the ferromagnet is located in the regime where the
+repulsive interaction U > 0 is large and the electron con-
+centration is not half-filled. Hence, the η-pairing phase
+nc
+t
+|U|
+m
+0
+1
+0
+1
+PM
+AFM
+FM
+FF
+BCS
+-pairing
+η
+Repulsive Hubbard (
+)
+U > 0
+Attractive Hubbard (
+)
+U < 0
+h = 0
+nc = 1.0
+Spin-polarized 
+normal state
+FIG. 1.
+Sketches of the phase diagrams for the repulsive
+Hubbard model [44] (left panel) and AH model (right panel).
+nc is the electron concentration and m is the magnetization.
+When the interaction |U| is large, the ground state in the re-
+pulsive Hubbard model is ferromagnet (FM), while the ground
+state in the AH model is η-pairing.
+is located in the regime where the attractive interaction
+U < 0 is large and the magnetization is finite. The phase
+diagram of the AH model at half filling is shown in the
+right panel of Fig. 1. In principle, an attractive interac-
+tion large enough to realize η-pairing could be realized in
+artificial cold atom systems [45].
+The Cooper pair is formed by the two electrons
+with (k ↑,
+− k + q ↓) where q is the center-of-mass
+momentum. The FFLO state and the η-pairing are dis-
+tinguished by the magnitude of |q|.
+In η-pairing, the
+center-of-mass momentum of the Cooper pair is the or-
+der of the reciprocal lattice vector, while the momentum
+of the FFLO state is much smaller and the spatial mod-
+ulation is slowly-varying compared to the atomic scale.
+Although the large center-of-mass momentum is usually
+not energetically favorable, a strong attractive interac-
+tion can make it stable.
+B.
+Mean-field theory
+By applying the mean-field approximation, we obtain
+the mean-field Hamiltonian
+HMF = −t
+�
+⟨i,j⟩σ
+c†
+iσcjσ + H.c. − µ
+�
+i
+ni − h ·
+�
+i
+si
+−
+�
+i
+�
+vini + Hi · si − ∆ic†
+i↑c†
+i↓ − ∆∗
+i ci↓ci↑
+�
+.
+(3)
+
+3
+The order parameters are given by the self-consistent
+equations
+vi ≡ |U|
+2 ⟨ni⟩,
+(4)
+∆i ≡ −|U|⟨ci↓ci↑⟩,
+(5)
+mi = 1
+2
+�
+σσ′
+⟨c†
+iστσσ′ciσ′⟩,
+Hi =
+− 2|U|mi,
+(6)
+where ⟨A⟩ = Tr
+�
+Ae−HMF/T �
+/Tr
+�
+e−HMF/T �
+is a quan-
+tum statistical average with the mean-field Hamiltonian
+and T is temperature.
+∆i is the order parameter for
+s-wave singlet superconductivity (pair potential).
+The
+phase θi ∈ [0, 2π) of the pair potential ∆i = |∆i|eiθi is
+dependent on the site index and will be represented by
+the arrow in a two-dimensional space. The mean-fields
+for the charge and spin are given by vi and Hi, respec-
+tively, at each site. The derivation of the self-consistent
+equations is summarized in Appendix A. We will consider
+the AH model both on the two-dimensional square and
+triangular lattices.
+III.
+MEISSNER KERNEL FOR A GENERAL
+TIGHT-BINDING LATTICE
+A.
+Definition
+As we explained in Sec. I, it is necessary to calculate
+the Meissner kernel to determine whether the mean-field
+solution for η-pairing is electromagnetically stable. In the
+tight-binding model, the electromagnetic field appears as
+Peierls phase:
+Hkin = −t
+�
+⟨i,j⟩σ
+eiAijc†
+iσcjσ + H.c..
+(7)
+The Meissner effect is examined by the weak external or-
+bital magnetic field applied perpendicular to the plane,
+while the η-pairing is stabilized only under a strong Zee-
+man field. In order to make these compatible, we apply
+the Zeeman field parallel to the plane h = (h, 0, 0), which
+does not create the orbital motion of the tight-binding
+electrons.
+Thus, the weak magnetic field that triggers
+the Meissner effect is applied perpendicular to the plane
+in addition to the in-plane magnetic field.
+While the
+out-of-plane Zeeman effect is also induced by the weak
+additional field, it is neglected since the dominant Zee-
+man field already exists by the strong in-plane magnetic
+field.
+Let us formulate the Meissner response kernel on a
+general tight-binding model. We apply the formulation in
+Refs. [46–48] to the present case with sublattice degrees
+of freedom. The current density operator between two
+sites is defined as
+jij = ∂Hkin
+∂Aij
+ˆδij
+= −it
+�
+σ
+�
+c†
+iσcjσeiAij − c†
+jσciσe−iAij�
+ˆδij,
+(8)
+where δij = Ri − Rj is the inter-site lattice vector be-
+tween i-th and j-th sites, and hat (ˆ) symbol means a unit
+vector. In the linear response theory, the current oper-
+ator which appears as a response to the static magnetic
+field in equilibrium is written as
+jij ≃ −it
+�
+σ
+(c†
+iσcjσ − c†
+jσciσ)ˆδij
++ t
+�
+σ
+(c†
+iσcjσ + c†
+jσciσ)ˆδijAij
+≡ jpara
+ij
++ jdia
+ij .
+(9)
+The first term is called the paramagnetic term and the
+second term is diamagnetic.
+The Fourier-transformed
+paramagnetic and diamagnetic current density operators
+are written as jpara(q) and jdia(q). The linear response
+kernel is then defined by ⟨jν(q)⟩ = �
+µ Kνµ(q)Aµ(q),
+where ν, µ = x, y is the direction. We evaluate the ker-
+nel Kνµ(q → 0) ≡ Kνµ when investigating the stability
+of superconductivity. This is called the Meissner kernel,
+which is proportional to the superfluid density.
+The Meissner kernel is separated into paramagnetic
+and diamagnetic terms as Kνµ = (Kpara)νµ + (Kdia)νµ.
+The paramagnetic kernel is given by
+(Kpara)νµ = 1
+N
+� 1/T
+0
+dτ⟨jpara
+ν
+(q = 0, τ)jpara
+µ
+(q = 0)⟩,
+(10)
+where N = �
+i 1 is the number of sites. The Heisenberg
+representation with the imaginary time τ is defined as
+A(τ) = eHτAe−Hτ. The form of the diamagnetic kernel
+is obvious from Eq. (9).
+We note that if the sign of the Meissner kernel K is
+negative, the superconducting state is electromagneti-
+cally stable and is also called a diamagnetic Meissner
+state, which expels magnetic flux. On the other hand, if
+the sign is positive, the superconducting state is called
+the paramagnetic Meissner state, which attracts mag-
+netic flux. For a stable thermodynamic superconducting
+state, the negative value of K is required.
+B.
+Method of evaluation
+The actual evaluation of the kernels is performed based
+on the wave-vector representation.
+Here, the physical
+quantities are described by the operator cα
+kσ where α dis-
+tinguishes the sublattice. Note that the Brillouin zone is
+
+4
+folded by �
+α 1 times. The diamagnetic kernel is rewrit-
+ten as
+(Kdia)νµ = 1
+N
+�
+α,β
+�
+kσ
+�
+m−1
+kαβ
+�
+νµ ⟨cα†
+kσcβ
+kσ⟩.
+(11)
+The inverse mass tensor m−1
+kαβ, which reflects the char-
+acteristics of the lattice shape, are given by
+�
+m−1
+kαβ
+�
+νµ ≡ t
+�
+⟨iα,jβ⟩
+�
+ˆδiαjβ
+�
+ν
+�
+ˆδiαjβ
+�
+µ e−ik·Riαjβ ,
+(12)
+where iα is the i-th unit cell with sublattice α.
+The
+symbol ⟨iα, jβ⟩ represents a pair of the nearest-neighbor
+sites and Riαjβ is the vector between the unit lattice with
+the i-th sublattice α and the unit lattice with the j-th
+sublattice β.
+The paramagnetic term has the form of a current-
+current correlation function. We can calculate this term
+by using the Green’s function matrix
+ˇGk(τ) ≡ −⟨Tτψk(τ)ψ†
+k⟩
+(13)
+where ψk = (cα
+k↑, cα†
+−k↓, · · · )T is the Nambu-spinor. Tτ is
+time-ordering operator regrading τ. Each component of
+the Green’s function matrix is given by the diagonal and
+off-diagonal Green’s functions:
+Gαβ
+σσ′(k, τ) ≡ −⟨Tτcα
+kσ(τ)cβ†
+kσ′⟩,
+(14)
+¯Gαβ
+σσ′(k, τ) ≡ −⟨Tτcα†
+kσ(τ)cβ
+k′σ′⟩,
+(15)
+F αβ
+σσ′(k, τ) ≡ −⟨Tτcα
+kσ(τ)cβ
+−kσ′⟩,
+(16)
+F αβ†
+σσ′ (k, τ) ≡ −⟨Tτcα†
+−kσ(τ)cβ†
+kσ′⟩.
+(17)
+The anomalous part of Green’s function [Eq. (16)] is also
+called the pair amplitude. The paramagnetic kernel in
+Eq. (10) can be divided into the normal (G) and anoma-
+lous (F) Green’s function contributions as
+(Kpara)νµ = − 1
+N
+� � 1/T
+0
+dτ (vkαβ)ν · (vkα′β′)µ ×
+�
+¯Gαβ′
+σσ′(k, τ)Gα′β
+σσ′(k, τ) + ¯Gαβ′
+σσ′(−k, τ)Gα′β
+σσ′(−k, τ)
+�
+− 1
+N
+� � 1/T
+0
+dτ (vkαβ)ν · (v−kα′β′)µ ×
+�
+F βα†
+σ′σ (k, −τ)F α′β′
+σ,σ′ (k, τ) + F βα†
+σ′σ (−k, −τ)F α′β′
+σ,σ′ (−k, τ)
+�
+≡ KG
+para + KF
+para.
+(18)
+The summation � is performed over the indices which appears only in the right-hand side. The velocity vector vkαβ
+is defined by
+(vkαβ)ν ≡ t
+�
+⟨iα,jβ⟩
+�
+ˆδiαjβ
+�
+ν e−ik·Riαjβ .
+(19)
+In order to perform the integral with respect to τ in Eq. (18), we define the Fourier-transformed Green’s function as
+gk(iωn) ≡
+� 1/T
+0
+dτgk(τ)eiωnτ,
+(20)
+where gk represents one of Eqs. (14)-(17) and ωn = (2n + 1)πT is fermionic Mastubara frequency. Moreover, the
+Fourier-transformed Green’s function matrix is given by using the matrix representation of mean-field Hamiltonian
+Eq. (3) as
+ˇGk(iωn) =
+�
+iωnˇ1 − ˇHMF
+k
+�−1 = ˇUk
+�
+iωnˇ1 − ˇΛk
+�−1 ˇU †
+k,
+(21)
+where ˇΛk and ˇUk are, respectively, a diagonal eigenvalue matrix and a unitary matrix satisfying ˇU † ˇHMF
+k
+ˇU = ˇΛk =
+diag(λk1, λk2, . . .). From Eq. (21), Kpara can be calculated as
+(Kpara)νµ = − 1
+N
+� �
+(vkαβ)ν · (vkα′β′)µ Uβ′σ′,ασ
+kp
+Uα′σ,βσ′
+kp′
++ (vkαβ)ν · (v−kα′β′)µ Uβσ′,ασ
+kp
+Uα′σ,β′σ′
+kp′
+� f (λkp) − f (λkp′)
+λkp − λkp′
++ c.c.
+(22)
+where f(λkp) =
+1
+eλkp/T +1 is the Fermi-Dirac distribution function and we have defined the coefficient Uασ,βσ′
+kp
+≡
+� ˇUk
+�
+ασ,p
+�
+ˇU †
+k
+�
+p,βσ′.
+The anomalous part of Eq. (18) KF
+para is further de-
+composed into the contributions KEFP and KOFP from
+
+5
+the even-frequency pair (EFP) and odd-frequency pair
+(OFP) amplitudes defined by
+F EFP(k, iωn) ≡ F(k, iωn) + F(k, −iωn)
+2
+,
+(23)
+F OFP(k, iωn) ≡ F(k, iωn) − F(k, −iωn)
+2
+.
+(24)
+Then, we obtain KEFP and KOFP by using Eqs. (23) and
+(24) as
+KEFP,OFP
+νµ
+= − 1
+2N
+�
+k
+�
+αβα′β′
+(vkαβ)ν · (v−kα′β′)µ
+×
+�
+σσ′
+�
+pp′
+Uβσ′,ασ
+kp
+Uα′σ,βσ′
+kp′
+×
+�f (λkp) − f (λkp′)
+λkp − λkp′
+∓ f (λkp) − f (−λkp′)
+λkp + λkp′
+�
++ c.c.,
+(25)
+where the minus (−) sign in the square bracket is taken
+for EFP contribution and the plus (+) for OFP pairing.
+These quantities are numerically calculated as shown in
+the next section. Note that the cross term of the EFP
+and OFP terms of Green’s functions vanishes after the
+summation with respect to the Matsubara frequency.
+C.
+Paramagnetic Meissner response of a simple
+η-pairing state
+Before we show the results of the AH model, let us show
+that a simple η-pairing state leads to the paramagnetic
+response which would not arise from thermodynamically
+stable states [24, 49]. We consider the simple bipartite
+lattice with staggered ordering vector Q. The anomalous
+contribution to the Meissner kernel may be written as [49]
+KF
+para,xx = −T
+�
+nkk′σσ′
+vx
+kvx
+k′F ∗
+σ′σ(k′, k, iωn)Fσσ′(k, k′, iωn).
+(26)
+This contribution must be negative (diamagnetic re-
+sponse) in order to dominate over the paramagnetic con-
+tribution. For a purely η-pairing state, we assume the
+relation Fσσ′(k, k′) = Fσσ′(k)δk′,−k−Q, and obtain
+KF
+para,xx = −T
+�
+nkσσ′
+(vx
+k)2F ∗
+σ′σ(k, iωn)Fσσ′(k, iωn), (27)
+where we have used vx
+−k−Q = vx
+k valid for square lat-
+tice, which is in contrast to the relation vx
+−k = −vx
+k
+for the uniform pairing with additional minus sign [24].
+We separate the spin-singlet and triplet parts as Fσσ′ =
+Fsiτ y
+σσ′ + Ft · (τiτ y)σσ′, and then obtain
+KF
+para,xx = 2T
+�
+nk
+(vx
+k)2�
+|Fs(k, iωn)|2 − |Ft(k, iωn)|2�
+.
+(28)
+If we consider the simple η-pairing with only spin-singlet
+part (Ft = 0), it leads to the paramagnetic response
+(positive).
+Thus, a simple s-wave spin-singlet η-pairing is unlikely
+realized as a stable state. On the other hand, in the AH
+model with magnetic field, the spin-triplet pair contribu-
+tion is substantially generated by the Zeeman field, which
+plays an important role for the diamagnetic response as
+shown below.
+IV.
+NUMERICAL RESULT FOR AH MODEL
+A.
+Square lattice
+1.
+Prerequisites
+Let us begin with the analysis of the AH model on
+the square lattice. We consider the two-sublattice struc-
+ture to describe the staggered ordered phase such as a
+η-pairing. While the superconducting states in the at-
+tractive model are interpreted in terms of the magnetic
+phases of the repulsive model by the particle-hole trans-
+formation in Eq. (2), the response functions such as the
+Meissner kernel are specific to the attractive model and
+have not been explored.
+In the following, we choose the band width W = 1
+as the unit of energy.
+We fix the value of the attrac-
+tive interaction U = −1.375. The electron concentration
+is fixed as nc = 1, and the temperature is taken to be
+T = 1.0 × 10−3 unless otherwise specified. We will in-
+vestigate the change of the Meissner kernel for η-pairing
+as a function of magnetic field strength h = |h|. In this
+paper, the mean-field solutions are calculated using the
+60 × 60 mesh in k-space. The result of the Meissner ker-
+nel for η-pairings is calculated with the mesh 300 × 300.
+We also checked that the behaviors remain qualitatively
+unchanged when these numbers are increased. The self-
+consistent equations in Eqs. (4)-(6) are computed by
+using an iterative method.
+In the following subsec-
+tion IV A 2, we restrict ourselves to the analysis of two-
+sublattice mean-field solutions, and in IV A 3, we exam-
+ine the solutions when the two-sublattice constraint is
+relaxed.
+2.
+Two-sublattice solution
+Before investigating the electromagnetic stability, we
+clarify the regime where the η-pairing becomes the
+ground state. In this paper, we assume that the inter-
+nal energy in Eq. (1) is approximately equal to the free
+energy in the low temperature region. The upper panel
+of Fig. 2 shows the internal energy of several ordered
+states measured from the normal-state energy as a func-
+tion of the Zeeman field h. Here, the η-pairing solution
+is obtained by solving the self-consistent equation with
+imposing the constraint of the staggered phase of the pair
+
+6
+0.0 0.25 0.5 0.75 1.0 1.25 1.5 1.75 2.0 2.25 2.5
+h
+−3.0
+−2.5
+−2.0
+−1.5
+−1.0
+−0.5
+0.0
+Ei − Enormal
+BCS
+CDW
+Normal
+η-pairing
+0.0 0.25 0.5 0.75 1.0 1.25 1.5 1.75 2.0 2.25 2.5
+0.00
+0.04
+0.08
+D0
+FIG. 2.
+(Upper panel) Magnetic-field dependence of the
+internal energy for each state measured from the normal state
+in the square lattice model. (Lower plane) Density of state
+(DOS) at zero energy D0 for each state.
+−1.5
+−1.0
+−0.5
+0.0
+0.5
+1.0
+1.5
+ω
+0.0
+0.1
+0.2
+D(ω)
+h = 1.25
+h = 1.375
+h = 1.5
+FIG. 3. Density of states for the η-pairing around magnetic
+filed h = 1.375 in the square lattice model.
+Here D(ω) is
+normalized as
+�
+dωD(ω) = 1.
+amplitude. A constraint is also used for the calculation
+of the other types of order parameters. Our calculations
+have not found any ordered states other than the types
+shown in Fig. 2 even when a random initial condition is
+employed.
+We determine the thermodynamically stable ground
+state by comparing the internal energies. In low magnetic
+fields, BCS and CDW are degenerated ground states. On
+the other hand, we find that the η-pairing becomes the
+ground state in the magnetic field located in 1.063 < h <
+1.875. The η-pairing solution itself is found in the wider
+regime although the internal energy is not the lowest one.
+It has been known that the attractive Hubbard model
+under a magnetic field also shows the FFLO state [50],
+but this possibility cannot be considered when we take
+the two-sublattice condition. This point will be revisited
+in the next subsection where the two-sublattice condition
+is relaxed.
+The lower panel of Fig. 2 shows the density of
+state (DOS) at the Fermi level for each state. The re-
+sult indicates that there is no energy gap in the η-pairing
+state, in contrast to the conventional BCS pairing state.
+There exists the regime where the DOS at the Fermi
+level for η-pairing is larger than that of normal metal
+(1.25 ≲ h ≲ 1.5). This is due to the van-Hove singular-
+ity of the square lattice model as shown in FIG. 3. We
+also perform the calculation for the cubic lattice where
+the van-Hove singularity is absent at zero energy and con-
+firm in this case that the DOS is smaller than the normal
+state (see Appendix B).
+The stability of the η-pairing depends upon the mag-
+nitude of the magnetic field as seen in the Meissner re-
+sponse kernel K (= Kxx = Kyy) (green symbol) in
+Fig. 4(a).
+The contributions from the paramagnetic
+(Kpara, positive) and diamagnetic (Kdia, negative) parts
+are also separately plotted in the figure. In the regime
+with h ≤ 1.125 and 1.75 ≤ h, the η-pairing is electromag-
+netically unstable, while it is stable in 1.125 < h < 1.75.
+In Fig. 4, the yellow shaded rectangle indicates the regime
+where the η-pairing becomes the ground state as seen
+from Fig. 2. We find a narrow region where η-pairing is
+regarded as the ground state but is not an electromagnet-
+ically stable state around h = 1.125. From these results,
+we see that the η-pairing is not necessarily electromag-
+netically stable even if it becomes the ground state in
+a two-sublattice calculation. As we shall see later, the
+simple η-pairing in this narrow regime does not necessar-
+ily exist if we relax the two-sublattice condition of the
+mean-field solution.
+We also show in Fig. 4(a) the contributions from the
+even- and odd-frequency pairs defined in Eqs. (23) and
+(24). The negative sign of the kernel, which means the re-
+sponse is diamagnetic, is partly due to the odd-frequency
+component of the pair amplitude, (KOFP < 0).
+This
+is in contrast to the FFLO state whose Meissner ker-
+nel is also negative due to the even-frequency component
+[51]. Hence, it implies that the mechanism of the dia-
+magnetism is different between the FFLO and η-pairing
+states.
+In
+addition
+to
+the
+Meissner
+kernel,
+we
+calcu-
+late the local pair amplitudes which are shown in
+FIG. 4(b).
+Here the left- and right-panels represent
+the spin-triplet and spin-singlet components of the lo-
+cal pair amplitude, respectively. The triplet component
+�
+σσ′(τ µiτ y)σσ′Fσσ′(iωn) with µ = x has a finite imagi-
+nary part and zero real part, which represents the odd-
+frequency pair. The other µ = y, z components are zero.
+On the other hand, the singlet component has a finite real
+part and zero imaginary part and is the even-frequency
+pair. We can see that the maximum value of the spin-
+triplet component of the pair amplitude is largest at the
+magnetic field h = 1.375, where the magnitude of KOFP
+is largest. It is also notable that the magnitude of the
+odd-frequency pair amplitude correlates with the magni-
+tude of DOS at zero energy as seen by comparing Figs. 3
+and 4.
+We comment on the singular behavior of KOFP at the
+magnetic field h = 1.375, although it does not affect the
+total Meissner kernel K. This anomalous feature is re-
+lated to the van Hove singularity of the DOS at zero
+energy as shown in FIG. 3, which shows a sharp peak at
+the Fermi level.
+
+7
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+h
+-1.0
+-0.5
+0.0
+0.5
+1.0
+K
+Kdia
+Kpara
+K
+KEFP
+KOFP
+(a)
+(b)
+<latexit sha1_base64="hwzoaSF0Y+Oi/TJGH/A
+8l7Sl9vw=">AD0HichVO5TsNAEH3BnOEIR4NEg4iQKFC0QZxdEA0lVwCJIGSbTbKL9kbFIQioEW08A
++IH+EHKPgEagoaCmY35lIUM5bt2TfvjWd2x1bgiEgy9pLqMrp7ev6B9KDQ8MjmdGx8f3Ir4c2L9q+4e
+HlhlxR3i8KIV0+GEQctO1H5g1TZU/OCMh5HwvT15HvBj16x4oixsUxK0U2qejGZjmbnfysZNFbFv+
+WKqEk7hw0YdLjg8SPIdmIjoOkIeDAFhx7gLCRP6DhHE2nS1onFiWESWqNnhVZHMerRWuWMtNqmrzh0h6
+Scxix7Zg/sjT2xR/bKPjrmutA5VC3n9LZaWh6cZG4md9/Vbn0lqj+qBJrlihjVdcqPZAI6oLW+s7KxW
+nQr0Jila13qKYRbiTsEuK5SbG/3Y+39ZTZ2WFdtktKpPq/FPFYpbI18m8n6fX1LNEa1djSbx1M429Kz5
+xA4SuV8d/+am9ayvKVv6nux2Z38hl1/OLW4vZgvrV62p78cUZjBHk72CAjaxhSJlLuMWd7g3doyGcWlct
+6hdqfhPmcAfM24+AbMryxg=</latexit>}Eq. (25)
+°3
+°2
+°1
+0
+1
+2
+3
+!n
+0.0
+0.6
+1.2
+1.8
+2.4
+3.0
+3.6
+4.2
+4.8
+5.4
+6.0
+6.6
+Re[F " #(i!n) ° F # "(i!n)]/
+p
+2
+2.0
+1.875
+1.75
+1.625
+1.5
+1.375
+1.25
+1.125
+1.0
+0.875
+0.75
+0.625
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+h
+-1.0
+-0.5
+0.0
+0.5
+1.0
+K
+Kdia
+Kpara
+K
+KEFP
+KOFP
+OFP
+EFP
+°3
+°2
+°1
+0
+1
+2
+3
+!n
+0.0
+0.6
+1.2
+1.8
+2.4
+3.0
+3.6
+4.2
+4.8
+5.4
+6.0
+6.6
+Im[F # #(i!n) ° F " "(i!n)]/
+p
+2
+FIG. 4.
+(a) Magnetic field dependence of the Meissner ker-
+nel K(= Kxx = Kyy) for the η-pairing on the square lattice.
+The yellow shaded rectangle indicates the range where the
+η-pairing becomes the ground state in two-sublattice calcula-
+tion. The number of the wavenumber k is taken as 300×300.
+(b) Matsubara frequency dependence of the local pair ampli-
+tude at several magnetic fields. The left panel represents the
+imaginary part of [F↓↓(iωn) − F↑↑(iωn)] /
+√
+2, and the right
+panel represents the real part of [F↑↓(iωn) − F↓↑(iωn)] /
+√
+2.
+The values of the pair amplitudes are shifted by 0.6 at each
+magnetic field for visual clarity, and the gray-dotted lines are
+the zero axes for each magnetic field.
+3.
+Beyond two-sublattice
+In order to clarify the stable ordered state where the
+Meissner kernel is positive (paramagnetic), we investi-
+gate mean-field solutions on finite-sized lattice where the
+two-sublattice condition is not imposed.
+We have nu-
+merically solved the Eqs. (4)-(6) self-consistently by us-
+ing the mean-field solutions of the η-pairing obtained for
+two-sublattice as an initial condition.
+Figure 5 shows the spatial distribution of the phase of
+the gap function when the number of sites is 8 × 8. At
+h = 0.5 in (a), where the η-pairing is not a ground state,
+the uniform BCS pairing state is realized as expected.
+With increasing the magnetic field, the longer-periodicity
+structures are found as shown in Figs. 5(b), (c) and (d).
+At h = 1.375 in (c), where the η-pairing solution has the
+lowest energy and the electromagnetic response is well
+diamagnetic, we obtain the staggered alignment of the
+(a) h = 0.5
+(d) h = 1.875
+(c) h = 1.375
+(b) h = 1.125
+FIG. 5.
+Spatial distribution of the phase of the supercon-
+ducting order parameter at several magnetic fields. The cal-
+culation is performed on the finite-sized lattice (8 × 8) with
+open boundary condition. Small black dots are lattice points
+and red arrows indicate the phase of the pair potential for
+each lattice point.
+phases. When the parameters are close to the edges of
+the yellow-highlighted region in Fig. 4, the complex struc-
+tures are formed as shown in (b) and (d). The behavior
+in (b) is interpreted as due to the competing effect where
+the simple uniform and staggered phases are energetically
+close to each other.
+We also investigate the case with the other choice of pa-
+rameters: U = −1.25 and h = 1.25. In this case, we find
+the staggered flux state where the phase of pair poten-
+tial is characterized by 90◦-N´eel ordering as in Fig. 6(a).
+This ordered state cannot be described in the mean-field
+theory with two sublattices.
+Owing to a non-colinear
+90◦-N´eel ordering vector, the spontaneous clockwise or
+counterclockwise loop currents arise by the inter-atomic
+Josephson effect. The current density is calculated by
+jij = −it
+�
+σ
+⟨c†
+iσcjσ − c†
+jσciσ⟩
+(29)
+which is identical to the expression of the paramagnetic
+current in the linear response theory. We can also evalu-
+ate the flux for each plaquette, which is define by
+Φ =
+�
+(i,j)∈plaquette
+jij
+(30)
+This expression is similar to the flux
+�
+C
+j ·ds =
+�
+S
+b·dS
+(j = ∇ × b) defined in a continuum system, where b is
+a flux density. The flux is aligned in a staggered manner
+
+8
+(a)
+(b)
+Current
+Magnetic flux
+FIG. 6. (a) Spatial distribution of the phase of the supercon-
+ducting order parameter for the η-pairing with 90◦-N´eel state
+on the finite-sized lattice under open boundary conditions.
+(b) Spatial distributions of the spontaneous loop current and
+the flux defined on each plaquette. The color of vectors dis-
+plays the magnitude of current, and the color of dots in each
+plaquette indicates the value of the magnetic flux defined in
+Eq. (30).
+on a dual lattice as indicated in Fig. 6(b). The staggered
+flux originating from the normal part has been studied
+before [20–23], while the staggered flux shown in Fig. 6(b)
+has a different origin: it arises from the superconductiv-
+ity associated with the off-diagonal part in the Nambu
+representation.
+We also comment on a feedback effect to the electro-
+magnetic field from the supercurrent.
+Since the char-
+acteristic length scale for the magnetic field in layered
+superconductor becomes long [52], each magnetic flux on
+the plaquette is smeared out with this length. Hence we
+expect that the net magnetic field is not created from the
+staggered superconducting flux.
+B.
+Triangular lattice
+1.
+Mean-field solution
+Now we search for the η-pairing reflecting the charac-
+teristics of a geometrically frustrated triangular lattice
+at the half-filling (nc = 1.0). We choose the parameters
+U = −1.83 and T = 1.0 × 10−3. We consider the cases of
+two- and three-sublattice structures. For a usual antifer-
+romagnet, the typical ordered state in the two-sublattice
+case has a stripe pattern, while in the three-sublattice
+case we expect a 120◦-N´eel state. Below we study the
+superconducting η-pairing phases within the mean-field
+theory.
+We have found the four types of superconducting states
+reflecting the characteristics of the triangular lattice,
+which are referred to as the η-pairing I, II, III, and IV.
+The schematic pictures for these four states are shown
+in Fig. 7(a), where the arrow indicates the phase of the
+superconducting order parameter at each site. We make
+a few general remarks: the three-sublattice structure is
+assumed for I, II, III, while the two sublattice is employed
+0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6
+0.0
+0.5
+1.0
+0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6
+0.0
+0.5
+1.0
+1.5
+ni, mi
+nA
+nB
+nC
+mA
+mB
+mC
+0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6
+0.0
+0.5
+1.0
+ni, mi
+nA
+nB
+mA
+mB
+(a)
+(b)
+<latexit sha1_base64="HLHSkuiSo7OABq7I/GuoPhNC6Lg=">AD5XichVNa9tAEH20tRxmsRJCR6MTWFHhKzLmT3hx6SW8pqe2AbYykbOTF+kJaBxth6LnQW8m19Njkj/QP9NCf0HMOufTQ2bXzYyVEZJm37w3mtkdWaErYsn
+Yn0zWHi0+Di3lF9+srK6VljfqMdBP7J5zQ7cIDq2zJi7wuc1KaTLj8OIm57l8obVe6/ijTMexSLwP8lhyNue6fjiVNimJKhT2GxFXvKh1Y1D0+bJdrnCvVF91CmUWJlpK846lYlTwsQOg/VMCy2cICNPjxw+JDkuzAR09VEBQwhYW0khEXkCR3nGCFP2j6xODFMQnv0dGjVnKA+rVXOWKt+opLd0TKIl6y3+wnu2K/2CX7y/7NzZXoHKqWIb2tsZaHnbUvz46uH1R59Jbo3qlSa5Y4xZ6uVDtoUZUF7bWz1cqjkO9CYp2td6imEW4m7JLiuWlxqc735rpab7SoV02Ce3q0xo8UIXi
+9siXqbz75dWc0xrT6NpPLWzAz1rAbHDVO5Nx/e5eT3r75S9uZ3sWaf+ulx5W975uFOq7n8eT30Oz/ECr2iyd1HFAQ5Ro8wJfuACl4ZjfDW+GedjajYz+VOeYsqM7/8B8nDTJg=</latexit>IV
+<latexit sha1_base64="0lzRl8Ev1iYodM/0b/A8BMLCw=">AD5XichVNb9NAEH2paSmhtAmoEhKXqFGlHm
+i0qQot1S9kFsQzYeURJHtbp1V/CV7g1JZkTgjcau4Io6QP8If4MBP4MyBSw+d3YR+KIo7lu3ZN+NZ3bHVuiKWDL2O7NkPFhebj6KPt47cn6Ri7/tBEHw8jmdTtwg6hlmTF3hc/rUkiXt8KIm57l8qY1OFbx5gcexSLwT+R5yLue6fji
+TNimJKiX2+xEXlLt9OPQtHmyWypzb1wd93JFVmLaCvNOeYUMbNakM90MEpAtgYwgOHD0m+CxMxXW2UwRAS1kVCWESe0HGOMbKkHRKLE8MkdEBPh1btGerTWuWMtdqmr7h0R6QsYJv9Yt/ZX/aTdgfdrkwV6JzqFrO6W1NtTzsbXx6/v7
+fvSqP3hL9G1VqzRJnONS1Cqo91Ijqwtb6xUrFcag3QdG+1lsUswh3U3ZJsbzU+N3OX871tFjp0C6bhPb1aY3uqUJxB+TLVN7t80urOa1p9E0ntrZkZ61gNhKvd/x7e5WT3rb5S9up7seaexVyq/Lu2/2y9Wj5Op34VL7CFHZrsA1TwF
+jXUKXOCb/iBieEYn40L48uUupSZ/SnPcMeMr1fF9NMZ</latexit>II
+<latexit sha1_base64="+wPFmdUeKb1/4PbXkIuITbQNFGw=">AD9HichVO7TuNAFD3BPEJ4BWiQaBABiQKiCe
+LZUDHQgCSARFthmSUfySPUGgKBI130C32mKFhGjZL9gfoOATt6ChoI7k/CMYq5l+8651zfO3NtBY6IJGOPiS6ju6e3L9mfGhgcGh5Jj47tR34tHnB9h0/PLTMiDvC4wUpMPg5CbruXwA6u6oeIHZzyMhO/tyYuAH7tm2ROnwjYl
+QaX0TDF061vFShSYNq8vZHPcbXxdNkrpDMsybVPtTq7lZNCybX80UQRJ/BhowYXHB4k+Q5MRHQdIQeGgLBj1AkLyRM6ztFAirQ1YnFimIRW6Vm1VEL9WitckZabdNXHLpDUk5hlj2w3+w/+8tu2D/23DFXedQtVzQ2pqeVAauZrYfp
+W5dJbovKuiq1Z4hRrulZBtQcaUV3YWt9ZqThl6k1QtKL1FsUswp2YXVIsNzb+ufP5tp46K8u0yahFX1a59UobhV8mUs7+P5xdUc0drVaBxP7ey5njWf2Es97Xj9yUnvV1Zctvk93u7C9mcyvZpZ2lTP7HZXPqk5jENOZosleRxya2U
+aDMV7jDPf4YZ8a18dP41aR2JVp/yjg+mXH7AkDw2R4=</latexit>III
+<latexit sha1_base64="1D3cNDco74HVKDqoxdioDUzCYmY=">AD1HichVPLSsNAFD01Pmp960ZwIxbBhZSp+N
+wpbnSnaKtgRZI4tmPzIplKpQqCuHEhbvUPxB/xB1z4Ca5duHhnWl9URpvSHLn3HNu7p25sQJHRJKxl0Sb0d7R2ZXsTvX09vUPDA4N5yO/Eto8Z/uOH+5aZsQd4fGcFNLhu0HITdy+I5VXlXxnRMeRsL3tuVpwPds+iJI2GbkqB8IXRr
+6+cHg2mWYdrGm51sw0mjYRv+UKAg7hw0YFLjg8SPIdmIjo2kMWDAFh+6gRFpIndJzjHCnSVojFiWESWqZnkVZ7DdSjtcoZabVNX3HoDk5jkn2zB7YG3tij+yVfbTMVdM5VC2n9LbqWh4cDFyPbr3/q3LpLVH6UcXWLHGERV2roNoDjag
+ubK1vrVScIvUmKFrSeotiFuFOzC4plhsb/9v5dFNPrZVF2mWT0JI+reo/VShumXwZy/t9fnE1R7R2NRrHUztb1bPmEzuI5X51/Jub0rO+pGzue7KbnfxMJjufmd2cTS+vXNSnPokxTGCKJnsBy1jDBnKU+Ri3uMO9kTfOjEvjqk5tSzT+l
+BH8MePmE+ykzOM=</latexit>I
+A
+B
+C
+<latexit sha1_base64="pw/0hoI9HJeFkpOwH0i+6Zr/+zU=">AD1nichVM7TwJBEB
+4H4gPRBsTGyMxsTBkMT47lMYSo+glYMzducCGe+VuMRCsTEmVsZW/4Dxj/gHLPwJ1hY2Fs4up0Ix1zudvab79ub2Z3VXZP5nJD3SFQZGR0bj03EJ6emZxKzybkT36l7Bi0Yjul4q
+751GQ2LXDGTaq6HtUs3aSnei0n4qeX1POZYx/zpkvPLK1iszIzNI6QWvKs1n7uqH0+myJpIm2p38kETgoCyzvJSAlKcAEOGFAHCyjYwNE3QMfnyJkgICL2Bm0EPQYzJOoQ1x1NaRZ
+GhIVrDbwVnxQC1cS7W9KXawL+Y+HqoXIV8kaeySd5JS/kg3wPXKsl1xC5NHUO1rqnifuFo6+hqosHDlU/1WhOXMow47MlWHurkREFYbUD1YKTgVrYxitSr2OMR1xM2SXBMsKjfdWvt
+ZX02BlBXdZQ7QqT6sxJAvBraHPQ3nd5xeWs49zS6JhPLGzDdlrDrLdUO5vxd3cuOz1XWGbf53d75yspzNb6Y3DjVR27rT9TFYhGVYxc7ehiwcQB4KsqMf4BGeFW5Um6U2w41Ggluyj
+z0mHL/AygEzY=</latexit>BCS
+<latexit sha1_base64="0lzRl8Ev1iYodM/0b/A8BMLCw=">AD5XichVNb9NAEH
+2paSmhtAmoEhKXqFGlHmi0qQot1S9kFsQzYeURJHtbp1V/CV7g1JZkTgjcau4Io6QP8If4MBP4MyBSw+d3YR+KIo7lu3ZN+NZ3bHVuiKWDL2O7NkPFhebj6KPt47cn6Ri7/tBEHw8
+jmdTtwg6hlmTF3hc/rUkiXt8KIm57l8qY1OFbx5gcexSLwT+R5yLue6fjiTNimJKiX2+xEXlLt9OPQtHmyWypzb1wd93JFVmLaCvNOeYUMbNakM90MEpAtgYwgOHD0m+CxMxXW2UwR
+AS1kVCWESe0HGOMbKkHRKLE8MkdEBPh1btGerTWuWMtdqmr7h0R6QsYJv9Yt/ZX/aTdgfdrkwV6JzqFrO6W1NtTzsbXx6/v7fvSqP3hL9G1VqzRJnONS1Cqo91Ijqwtb6xUrFcag3Qd
+G+1lsUswh3U3ZJsbzU+N3OX871tFjp0C6bhPb1aY3uqUJxB+TLVN7t80urOa1p9E0ntrZkZ61gNhKvd/x7e5WT3rb5S9up7seaexVyq/Lu2/2y9Wj5Op34VL7CFHZrsA1TwFjXUKX
+OCb/iBieEYn40L48uUupSZ/SnPcMeMr1fF9NMZ</latexit>II
+<latexit sha1_base64="1D3cNDco74HVKDqoxdioDUzCYmY=">AD1HichVPLSsNAFD
+01Pmp960ZwIxbBhZSp+NwpbnSnaKtgRZI4tmPzIplKpQqCuHEhbvUPxB/xB1z4Ca5duHhnWl9URpvSHLn3HNu7p25sQJHRJKxl0Sb0d7R2ZXsTvX09vUPDA4N5yO/Eto8Z/uOH+5aZs
+Qd4fGcFNLhu0HITdy+I5VXlXxnRMeRsL3tuVpwPds+iJI2GbkqB8IXRr6+cHg2mWYdrGm51sw0mjYRv+UKAg7hw0YFLjg8SPIdmIjo2kMWDAFh+6gRFpIndJzjHCnSVojFiWESWq
+ZnkVZ7DdSjtcoZabVNX3HoDk5jkn2zB7YG3tij+yVfbTMVdM5VC2n9LbqWh4cDFyPbr3/q3LpLVH6UcXWLHGERV2roNoDjagubK1vrVScIvUmKFrSeotiFuFOzC4plhsb/9v5dFNPrZ
+VF2mWT0JI+reo/VShumXwZy/t9fnE1R7R2NRrHUztb1bPmEzuI5X51/Jub0rO+pGzue7KbnfxMJjufmd2cTS+vXNSnPokxTGCKJnsBy1jDBnKU+Ri3uMO9kTfOjEvjqk5tSzT+lBH8Me
+PmE+ykzOM=</latexit>I
+<latexit sha1_base64="1D3cNDco74HVKDqoxdioDUzCYmY=">AD1HichVPLSsNAFD01Pmp960ZwIxbBhZSp+NwpbnSnaKtgRZI4tmPzIplKpQqCuHEhbvUPxB/xB1z4Ca5duHh
+nWl9URpvSHLn3HNu7p25sQJHRJKxl0Sb0d7R2ZXsTvX09vUPDA4N5yO/Eto8Z/uOH+5aZsQd4fGcFNLhu0HITdy+I5VXlXxnRMeRsL3tuVpwPds+iJI2GbkqB8IXRr6+cHg2mWYdrGm51sw0mjYRv+UKAg7hw0YFLjg8SPIdmIjo2kMWDAFh+6gRFpIndJzjHCnSVojFiWESWqZnkVZ7DdSjtcoZabVNX3HoDk5jkn2zB7YG3tij+yVfbTMVdM5VC2n9LbqWh4cDFyPbr3/
+q3LpLVH6UcXWLHGERV2roNoDjagubK1vrVScIvUmKFrSeotiFuFOzC4plhsb/9v5dFNPrZVF2mWT0JI+reo/VShumXwZy/t9fnE1R7R2NRrHUztb1bPmEzuI5X51/Jub0rO+pGzue7KbnfxMJjufmd2cTS+vXNSnPokxTGCKJnsBy1jDBnKU+Ri3uMO9kTfOjEvjqk5tSzT+lBH8MePmE+ykzOM=</latexit>I
+0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6
+h
+°0.05
+0.00
+0.05
+Ei ° E¥°pairing I
+<latexit sha1_base64="HLHSkuiSo7OABq7I/GuoPhNC6Lg=">AD5XichVNa9tAEH20tRx
+msRJCR6MTWFHhKzLmT3hx6SW8pqe2AbYykbOTF+kJaBxth6LnQW8m19Njkj/QP9NCf0HMOufTQ2bXzYyVEZJm37w3mtkdWaErYsnYn0zWHi0+Di3lF9+srK6VljfqMdBP7J5zQ7cIDq2zJi7wuc1
+KaTLj8OIm57l8obVe6/ijTMexSLwP8lhyNue6fjiVNimJKhT2GxFXvKh1Y1D0+bJdrnCvVF91CmUWJlpK846lYlTwsQOg/VMCy2cICNPjxw+JDkuzAR09VEBQwhYW0khEXkCR3nGCFP2j6xODFMQnv0
+dGjVnKA+rVXOWKt+opLd0TKIl6y3+wnu2K/2CX7y/7NzZXoHKqWIb2tsZaHnbUvz46uH1R59Jbo3qlSa5Y4xZ6uVDtoUZUF7bWz1cqjkO9CYp2td6imEW4m7JLiuWlxqc735rpab7SoV02Ce3q0xo
+8UIXi9siXqbz75dWc0xrT6NpPLWzAz1rAbHDVO5Nx/e5eT3r75S9uZ3sWaf+ulx5W975uFOq7n8eT30Oz/ECr2iyd1HFAQ5Ro8wJfuACl4ZjfDW+GedjajYz+VOeYsqM7/8B8nDTJg=</latexit>IV
+0.0
+1.8
+3.6
+5.4
+7.2
+9.0
+10.8
+12.6
+14.4
+16.2
+18.0
+19.8
+21.6
+23.4
+°3
+°2
+°1
+0
+Ei ° Enormal
+BCS
+normal
+¥-pairing I
+¥-pairing IV
+¥-pairing III
+¥-pairing II
+(c)
+0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6
+h
+°0.05
+0.00
+0.05
+Ei ° E¥°pairing I
+0.0
+1.8
+3.6
+5.4
+7.2
+9.0
+10.8
+12.6
+14.4
+16.2
+18.0
+19.8
+21.6
+23.4
+°3
+°2
+°1
+0
+Ei ° Enormal
+BCS
+normal
+¥-pairing I
+¥-pairing IV
+¥-pairing III
+¥-pairing II
+-pairing II
+η
+-pairing IV
+η
+0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6
+h
+°0.05
+0.00
+0.05
+Ei ° E¥°pairing I
+0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6
+0.0
+0.5
+1.0
+1.5
+ni, mi
+nA
+nB
+nC
+mA
+mB
+mC
+0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6
+0.0
+0.5
+1.0
+1.5
+ni, mi
+nA
+nB
+nC
+mA
+mB
+mC
+0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6
+0.0
+0.5
+1.0
+ni, mx
+i
+0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6
+0.0
+0.5
+1.0
+ni, mx
+i
+0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6
+0.0
+0.5
+1.0
+ni, mx
+i
+x
+y
+FIG. 7.
+(a) Schematics for the four η-pairings in the tri-
+angular lattice model. The arrows indicate the phase of the
+pair potential. The size of the circles shows the amount of
+the electron density for each sublattice. (b) Magnetic field
+dependence of the internal energies measured from the nor-
+mal state (upper panel). The lower panel shows the inter-
+nal energy measured from the η-pairing I. (c) Magnetic field
+dependence of the number of electrons and magnetization on
+each sublattice for the η-pairing II (upper panel) and IV (lower
+panel).
+for IV. The type-I has a non-colinear structure, and in the
+other η-pairings the vectors are aligned in a colinear man-
+ner. We also note that CDW accompanies the η-pairings
+II and III, where the number of local filling is indicated
+by the size of the filled circle symbols in Fig. 7(a).
+Figure 7(b) shows the internal energy of the ordered
+states measured from the normal state (Upper panel) and
+from the η-pairing I (Lower panel). From the lower panel
+of Fig. 7(b), we can identify the ground state. With in-
+creasing the magnetic field, the ground state changes as
+BCS → η-pairing II→ η-pairing I → η-pairing IV→ η-
+pairing I → normal. Figure 7(c) shows the particle den-
+
+9
+(a)
+(b)
+Iloop
+h
+0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6
+h
+-0.2
+-0.1
+0.0
+0.1
+Iloop
+FIG. 8. (a) Schematic picture of the staggered flux state on
+the triangular lattice. The straight arrows display the phase
+of the pair potential at each site, and the circle arrows indicate
+the staggered loop current. (b) Magnetic field dependence of
+the magnitude of loop current. The yellow shaded rectangle
+indicates the range where the η-pairing I becomes the ground
+state.
+sity and x-direction magnetization mx
+i of each sublattice
+for η-pairing II (Upper panel) and η-pairing IV (Lower
+panel). The values of my
+i and mz
+i are zero because the
+Zeeman field h is applied along the x-direction. Below,
+we explain the characteristic features for each η-pairing
+state.
+η-pairing-I state.— The η-pairing I has 120◦ N´eel or-
+dering vector (Green pentagon in Fig. 7(b)). The spon-
+taneous supercurrent appears in this non-colinear state
+as schematically shown in Fig. 8(a). This superconduct-
+ing state forms a staggered flux state, where the flux is
+aligned on a honeycomb dual lattice, which is similar to
+the η-pairing with 90◦-N´eel ordering vector on the square
+lattice shown in Fig. 6(b). Figure 8(b) displays the val-
+ues of spontaneous loop current density as a function of
+the magnetic field.
+η-pairing-II state.— The η-pairing II has the struc-
+ture with up-up-down colinear phases plus CDW (Red
+hexagon in Fig. 7(b)). There is the relation nA = nB <
+nC for the electron filling at each sublattice shown in
+Fig. 7(c).
+We note that this site-dependent feature is
+characteristic for the II (and IV) state. The phases of the
+pair potential at A and B sublattices are “ferromagnetic”,
+while the phase at C sublattice is “antiferromagnetic”.
+The resulting ordered state is regarded as the emergence
+of the honeycomb lattice formed by equivalent A and B
+sublattices.
+η-pairing-III state.— This is the η-pairing with a stag-
+gered ordering vector and CDW (Magenta square in
+Fig. 7(b)).
+The order parameter ∆ at C sublattice is
+zero, but the others (A,B) are finite. The electron-rich
+sublattices A and B form a simple bipartite η-pairing
+state on an emergent honeycomb lattice. Since this state
+does not become a ground state anywhere for the present
+choice of U = −1.83, we do not further investigate this
+state in the following.
+η-pairing-IV state.— This is the η-pairing with a sim-
+ple stripe alignment (Cyan rhombus in Fig. 7(b)). This
+η-pairing is accompanied by CDW around h = 1.9 shown
+0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6
+h
+°1.5
+°1.0
+°0.5
+0.0
+0.5
+1.0
+1.5
+Kxx, Kyy
+(a) -pairing Ⅰ
+η
+Eq. (25)
+0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6
+h
+-1.5
+-1.0
+-0.5
+0.0
+0.5
+1.0
+1.5
+Kxx, Kyy
+(b) -pairing Ⅱ
+η
+0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6
+h
+°1.5
+°1.0
+°0.5
+0.0
+0.5
+1.0
+1.5
+Kyy
+0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6
+h
+°1.5
+°1.0
+°0.5
+0.0
+0.5
+1.0
+1.5
+Kxx
+(c1) -pairing Ⅳ
+η
+(c2) -pairing Ⅳ
+η
+0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6
+h
+°1.5
+°1.0
+°0.5
+0.0
+0.5
+1.0
+1.5
+Kyy
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+h
+-1.0
+-0.5
+0.0
+0.5
+1.0
+K
+Kdia
+Kpara
+K
+KEFP
+KOFP
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+h
+-1.0
+-0.5
+0.0
+0.5
+1.0
+K
+Kdia
+Kpara
+K
+KEFP
+KOFP
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+h
+-1.0
+-0.5
+0.0
+0.5
+1.0
+K
+Kdia
+Kpara
+K
+KEFP
+KOFP
+<latexit sha1_base64="hwzoaSF0Y+Oi/TJGH
+/A8l7Sl9vw=">AD0HichVO5TsNAEH3BnOEIR4NEg4iQKFC0QZxdEA0lVwCJIGSbTbKL9kbFIQio
+EW08A+IH+EHKPgEagoaCmY35lIUM5bt2TfvjWd2x1bgiEgy9pLqMrp7ev6B9KDQ8MjmdGx8f3Ir4c
+2L9q+4eHlhlxR3i8KIV0+GEQctO1H5g1TZU/OCMh5HwvT15HvBj16x4oixsUxK0U2qejGZjmb
+nfysZNFbFv+WKqEk7hw0YdLjg8SPIdmIjoOkIeDAFhx7gLCRP6DhHE2nS1onFiWESWqNnhVZHMer
+RWuWMtNqmrzh0h6Scxix7Zg/sjT2xR/bKPjrmutA5VC3n9LZaWh6cZG4md9/Vbn0lqj+qBJrlihjV
+dcqPZAI6oLW+s7KxWnQr0Jila13qKYRbiTsEuK5SbG/3Y+39ZTZ2WFdtktKpPq/FPFYpbI18m8n
+6fX1LNEa1djSbx1M429Kz5xA4SuV8d/+am9ayvKVv6nux2Z38hl1/OLW4vZgvrV62p78cUZjBHk72C
+AjaxhSJlLuMWd7g3doyGcWlct6hdqfhPmcAfM24+AbMryxg=</latexit>}
+FIG. 9. Magnetic field dependence of the Meissner kernels
+Kxx and Kyy for the η-pairings I, II, IV on the triangular lat-
+tice. The yellow shaded rectangle indicates the regime where
+each η-pairing becomes the ground state. The symbols are
+the same as those in Fig. 4(a). For the η-pairing IV, Kxx and
+Kyy are separately plotted in (c1) and (c2).
+in Fig. 7(c). As shown below, this stripe phase show an
+anisotropic behavior in linear response coefficients, while
+the other η-pairing states are isotropic.
+2.
+Meissner response
+Now we discuss the Meissner response. Figure 9(a,b,c)
+shows the Meissner kernels Kxx, Kyy for the η-pairing I,
+II and IV. The yellow-highlighted parts indicate the re-
+gion where each η-pairing becomes the ground state as
+identified from Fig. 7(b).
+The result for the η-pairing
+III is not shown because it does not become a ground
+state at U = −1.83. We confirm that the Meissner re-
+sponse is basically diamagnetic if the η-pairing becomes
+the ground state as shown in Figs. 9(a,b,c). Thus the en-
+ergetic stability and diamagnetic response are reasonably
+correlated. In the following, we discuss the properties of
+the Meissner kernel for each state.
+The Meissner kernels for both η-pairing I and η-pairing
+II shown in Figs. 9(a) and (b) satisfy the relation Kxx =
+Kyy, which means an isotropic linear response. For the η-
+pairing I, the Meissner kernel becomes positive in the re-
+gions h < 1.2, 1.95 < h < 2.12, while the kernel becomes
+negative in the ground state region (Fig. 9(a)). Although
+the local current density is finite for the η-pairing I state,
+it does not affect the expression of the Meissner kernel in
+Eq. (10) since the total current j(q = 0) is zero.
+Next we disucuss the η-pairing IV state. The Meiss-
+
+10
+ner kernel jumps at h = 1.8 due to the emergence of
+the CDW order parameter as shown in Fig. 9(c1,c2). It
+is notable that the η-pairing IV with the stripe pattern
+shows a difference between x and y directions as shown
+in Figs. 9(c1,c2), respectively. This characteristic behav-
+ior can be intuitively understood from Fig. 7(a), where
+the current along the x-axis flows with experiencing a
+staggered pair potential, whereas the current in the y-
+direction feels an uniform pair potential. In the Meissner
+response, Kxx shows a characteristic behavior of the η-
+pairing, while Kyy is qualitatively the same as the kernel
+of BCS. Thus, as shown in Fig. 9(c1), the diamagnetic
+response in the x-axis direction is related to to the odd-
+frequency pair, whereas the diamagnetic response in the
+y-axis direction, shown in Fig. 9(c2), is related to even-
+frequency pair.
+V.
+SUMMARY AND OUTLOOK
+We have studied the square and the triangular lattice
+of the attractive Hubbard model by using the mean-field
+theory.
+Several types of η-pairing have been found in
+the triangular lattice where a simple bipartite pattern
+is not allowed.
+Using the formulation of the Meissner
+kernel for a general tight-binding lattice, we have inves-
+tigated the electromagnetic stability of η-pairings. We
+have confirmed that the electromagnetic stability of the
+η-pairing correlates with the internal energy. In a narrow
+parameter range, we also find that the η-pairing state can
+show an unphysical paramagnetic response if we assume
+the two or three sublattice structure in the mean-field
+calculation.
+In this case, another solution with longer
+periodicity needs to be sought.
+When the current path experiences the staggered
+phase of the superconducting order parameter, the odd-
+frequency component of the pair amplitude contributes
+to the diamagnetic response. This is in contrast to the
+conventional BCS case in which the even-frequency com-
+ponent of the pair amplitude contributes to the diamag-
+netism.
+We have further clarified that one of the η-
+pairing states on the triangular lattice has a stripe pat-
+tern and shows an anisotropic Meissner response. In this
+case, the odd-frequency pair contributes diamagnetically
+or paramagnetically depending on the direction of cur-
+rent.
+We comment on some issues which are not explored in
+this paper. We expect that the η-pairing without a simple
+staggered phase will appear on pyrochlore, kagome and
+quasicrystalline lattice, whose phase-alignment could be
+qualitatively different from the triangular lattice. In ad-
+dition, there is another model that shows η-pairing in
+equilibrium. A two-channel Kondo lattice (TCKL) is an
+example of a model in which η-pairing appears even in
+the absence of a Zeeman field [24]. Our preliminary cal-
+culation for the TCKL shows a number of ordered states
+which have similar energies.
+These additional studies
+provide more insight into the exotic superconductivity
+(a)
+(b)
+(c)
+°1
+0
+1
+!n
+0.0
+0.6
+1.2
+1.8
+2.4
+3.0
+3.6
+4.2
+4.8
+5.4
+6.0
+Re[F " #(i!n) ° F # "(i!n)]/
+p
+2
+h=1.417
+h=1.375
+h=1.333
+h=1.25
+h=1.167
+h=1.083
+h=1.0
+h=0.917
+h=0.833
+h=0.75
+h=0.667
+°0.2°0.1 0.0
+0.1
+0.2
+!n
+0.0
+0.6
+1.2
+1.8
+2.4
+3.0
+3.6
+4.2
+4.8
+5.4
+6.0
+Re[F " #(i!n) ° F # "(i!n)]/
+p
+2
+1.417
+1.375
+1.333
+1.25
+1.167
+1.083
+1.0
+0.917
+0.833
+0.75
+0.667
+°1.0 °0.5
+0.0
+0.5
+1.0
+!
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+1.2
+1.4
+1.6
+1.8
+2.0
+D¥°pairing ° Dnormal
+°0.2°0.1 0.0
+0.1
+0.2
+!n
+0.0
+0.6
+1.2
+1.8
+2.4
+3.0
+3.6
+4.2
+4.8
+5.4
+6.0
+Im[F # #(i!n) ° F " "(i!n)]/
+p
+2
+FIG. 10. (a) The difference between the DOSs of the η-pairing
+and normal states in the cubic lattice model. The values of
+the DOS are shifted by 0.2 for each magnetic field, and the
+gray dotted lines are the zero axes for each magnetic field.
+We also show the Matsubara frequency dependence of (b) the
+imaginary part of [F↓↓(iωn) − F↑↑(iωn)] /
+√
+2 and (c) the real
+part of [F↑↓(iωn) − F↓↑(iωn)] /
+√
+2 for each magnetic field. The
+values of the pair amplitudes are shifted by 0.6.
+characteristic for the η-pairing.
+ACKNOWLEDGEMENT
+This work was supported by KAKENHI Grants No.
+18H01176, No. 19H01842, and No. 21K03459.
+Appendix A: Self-consistent equations in mean-field
+theory
+We derive self-consistent equations for the general in-
+teracting Hamiltonian. Let us begin with the Hamilto-
+nian
+H =
+�
+12
+ε12c†
+1c2 +
+�
+1234
+U1234c†
+1c†
+2c4c3
+(A1)
+where site-spin indices are written as 1 = (i1, σ1). The
+mean-field Hamiltonian is introduced as
+HMF =
+�
+12
+�
+E12c†
+1c2 + ∆12c†
+1c†
+2 + ∆∗
+12c2c1
+�
+.
+(A2)
+We assume ⟨H ⟩ = ⟨HMF⟩ where the statistical average
+is taken with HMF. Then the self-consistent equation is
+obtained as
+E12 = ∂⟨H ⟩
+∂⟨c†
+1c2⟩
+= ε12 +
+�
+34
+(U1324 + U3142 − U1342 − U3124)⟨c†
+3c4⟩
+(A3)
+∆12 = ∂⟨H ⟩
+∂⟨c†
+1c†
+2⟩
+=
+�
+34
+U1234⟨c4c3⟩
+(A4)
+
+11
+where the Wick’s theorem is used for the derivation. Al-
+though the variational principle for the free energy also
+gives the same equation, the above formalism gives a sim-
+ple procedure to derive the self-consistent equations.
+Appendix B: Attractive Hubbard model on Cubic
+lattice
+We analyze the η-pairing on the cubic lattice, whose
+DOS does not have a van Hove singularity near zero en-
+ergy. Here we choose the parameter U = −1.375 and
+the electron concentration is half-filled. As a result, the
+DOS for the η-pairing around zero energy for each mag-
+netic filed on the cubic lattice is smaller than the DOS of
+the normal state as shown in Fig. 10(a). For reference,
+we also show in Figs.
+10(b) and (c) the pair amplitude
+similar to Fig. 4(b) in the main text. In addition, the
+odd-frequency pair amplitude increases when DOS near
+zero energy is enhanced as seen from Figs. 10(a) and (b).
+[1] P. Fulde and R. A. Ferrell, Phys. Rev. 135, A550 (1964).
+[2] A. I. Larkin and Y. N. Ovchinnikov, Zh. Eksp. Teor. Fiz.
+47, 1136 (1964).
+[3] C. N. Yang, Phys. Rev. Lett. 63, 2144 (1989).
+[4] For a review, see, D.F. Agterberg, J.C.S. Davis, S.D.
+Edkins, E. Fradkin, D.J. Van Harlingen, S.A. Kivelson,
+P.A. Lee, L. Radzihovsky, J.M. Tranquada, and Y. Wang,
+Ann. Rev. Condens. Matter Phys., 11, 231 (2020).
+[5] R. R. P. Singh and R. T. Scalettar, Phys. Rev. Lett. 66,
+3203 (1991).
+[6] P. Coleman, E. Miranda, and A. Tsvelik, Phys. Rev. Lett.
+70, 2960 (1993).
+[7] S. Hoshino and Y. Kuramoto, Phys. Rev. Lett. 112,
+167204 (2014).
+[8] W. R. Czart, K. J. Kapcia, R. Micnas, S. Robaszkiewicz,
+Physica A: Statistical Mechanics and its Applications.
+585, 126403 (2022)
+[9] T. Kaneko, T. Shirakawa, S. Sorella, and S. Yunoki,
+Phys. Rev. Lett. 122, 077002 (2019).
+[10] P. Werner, J. Li, D. Golez and M. Eckstein, Phys. Rev.
+B 100, 155130 (2019).
+[11] J. Li, D. Golez, P. Werner, and M. Eckstein, Phys. Rev.
+B 102, 165136 (2020).
+[12] M. Nakagawa,
+N. Tsuji,
+N. Kawakami,
+M. Ueda,
+arXiv:2103.13624 (2021).
+[13] X. M. Yang and Z. Song, Phys. Rev. B 105, 195132
+(2022).
+[14] L. Jiajun, M. M¨uller, A. J. Kim, A. M. L¨auchli, and P.
+Werner, arXiv:2202.10176 (2022).
+[15] Y. Motome, K. Nakamikawa, Y. Yamaji, and M. Uda-
+gawa, Phys. Rev. Lett. 105, 036403 (2010).
+[16] R. R. dos Santos Phys. Rev. B 48, 3976 (1993).
+[17] I. Affleck and J. B. Marston, Phys. Rev. B 37, 3774
+(1988).
+[18] S. Chakravarty, R. B. Laughlin, D. K. Morr, and C.
+Nayak, Phys. Rev. B 63, 094503 (2001).
+[19] D. K. Morr, Phys. Rev. Lett. 89, 106401 (2002).
+[20] S. Zhou and Z. Wang, Phys. Rev. B 70, 020501(R)
+(2004).
+[21] H. Yokoyama, S. Tamura, and M. Ogata, J. Phys. Soc.
+Jpn. 85, 124707 (2016).
+[22] K. Kobayashi, H. Yokoyama, and Y. Toga, J. Phys.:
+Conf. Ser. 1054, 012016 (2018).
+[23] S. Fukuda, K. Yamazaki, H. Tsuchiura, and M. Ogata,
+J. Phys.: Conf. Ser. 1293, 012026 (2019).
+[24] S. Hoshino, Phys. Rev. B 90, 115154 (2014).
+[25] V.L. Berezinskii, ZhETF Pis Red. 20, 628 (1974), [JETP
+Lett. 20, 287 (1974)].
+[26] T. R. Kirkpatrick and D. Belitz, Phys. Rev. Lett. 66,
+1533 (1991).
+[27] A. Balatsky and E. Abrahams, Phys. Rev. B 45, 13125
+(1992).
+[28] Y. Tanaka, M. Sato, and N. Nagaosa, J. Phys. Soc. Jpn.
+81, 011013 (2012).
+[29] J. Linder and A.V. Balatsky, Rev. Mod. Phys. 91, 045005
+(2019).
+[30] J. Cayao, C. Triola and M. Black-Schaffer, Eur. Phys. J.:
+Spec. Top. 229, 545 (2020)
+[31] H. Walter, W. Prusseit, R. Semerad, H. Kinder, W. Ass-
+mann, H. Huber, H. Burkhardt, D. Rainer, and J. A.
+Sauls, Phys. Rev. Lett. 80, 3598 (1998).
+[32] Y. Tanaka, Y. Asano, A. A. Golubov, and S. Kashiwaya,
+Phys. Rev. B 72, 140503 (2005).
+[33] F. S. Bergeret, A. F. Volkov, and K. B. Efetov, Rev. Mod.
+Phys. 77, 1321 (2005).
+[34] Ya. V. Fominov, Y. Tanaka, Y. Asano, and M. Eschrig,
+Phys. Rev. B 91, 144514 (2015)
+[35] Y. Tanaka and A. A. Golubov, Phys. Rev. Lett. 98,
+037003 (2007)
+[36] Y. Tanaka, Y. Tanuma, and A. A. Golubov, Phys. Rev.
+B 76, 054522 (2007)
+[37] S. Higashitani, J. Phys. Soc. Jpn. 66, 2556 (1997).
+[38] T. Yokoyama, Y. Tanaka, and N. Nagaosa, Phys. Rev.
+Lett. 106, 246601 (2011).
+[39] S.-I. Suzuki and Y. Asano, Phys. Rev. B 91, 214510
+(2015).
+[40] A. Di Bernardo, Z. Salman, X. L. Wang, M. Amado, M.
+Egilmez, M. G. Flokstra, A. Suter, S. L. Lee, J. H. Zhao,
+T. Prokscha, E. Morenzoni, M. G. Blamire, J. Linder,
+and J. W. A. Robinson, Phys. Rev. X 5, 041021 (2015).
+[41] J. A. Krieger, A. Pertsova, S. R. Giblin, M. Dbeli, T.
+Prokscha, C. W. Schneider, A. Suter, T. Hesjedal, A. V.
+Balatsky, and Z. Salman, Phys. Rev. Lett. 125, 026802
+(2020).
+[42] R. Micnas, J. Ranninger, and S. Robaszkiewicz, Rev.
+Mod. Phys. 62, 113 (1990).
+[43] H. Shiba, Prog. Theor. Phys. 48, 2171 (1972).
+
+12
+[44] Y. Claveau, B. Arnaud, S. D. Matteo, Eur. J. Phys. 35,
+035023 (2014).
+[45] I. Bloch, J. Dalibard, and W. Zwerger, Rev. Mod. Phys.
+80, 885 (2008).
+[46] D.J. Scalapino, S. R. White, and S. C. Zhang, Phys. Rev.
+Lett. 68, 2830 (1992).
+[47] D. J. Scalapino, S. R. White, and S. C. Zhang, Phys.
+Rev. B 47, 7995 (1993).
+[48] T. Kostyrko, R. Micnas, and K. A. Chao, Phys. Rev. B
+49, 6158 (1994).
+[49] S. Hoshino, K. Yada, and Y. Tanaka, Phys. Rev. B 93,
+224511 (2016).
+[50] A. Tsuruta, S. Hyodo, and K. Miyake, J. Phys. Soc. Jpn.
+83, 063706 (2014).
+[51] D. Chakraborty and A. M. Black-Schaffer, Phys. Rev. B
+106, 024511 (2022).
+[52] J. Pearl, App. Phys. Lett. 5, 65 (1964).
+
diff --git a/49FAT4oBgHgl3EQfFRw-/content/tmp_files/load_file.txt b/49FAT4oBgHgl3EQfFRw-/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b78fbf3f4355b1781796f2325f78234c91429355
--- /dev/null
+++ b/49FAT4oBgHgl3EQfFRw-/content/tmp_files/load_file.txt
@@ -0,0 +1,1534 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf,len=1533
+page_content='η-pairing on bipartite and non-bipartite lattices  Yutaro Misu1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Shun Tamura2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Yukio Tanaka2 and Shintaro Hoshino1  1Department of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Saitama University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Saitama 338-8570,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Japan  2Department of Applied Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Nagoya University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Nagoya 464-8603,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Japan  (Dated: January 23,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 2023)  The η-pairing is a type of Cooper pairing state in which the phase of the superconducting order  parameter is aligned in a staggered manner,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' in contrast to the usual BCS superconductors with a  spatially uniform phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' In this study, we search for a characteristic η-pairing state in a triangular  lattice where a simple staggered alignment of the phase is not possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' As an example, we consider  the attractive Hubbard model on both the square and triangular lattices under strong external  Zeeman field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Using the mean-field approximation, we have identified several η-pairing states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Additionally, we have examined the electromagnetic stability of the pairing state by calculating the  Meissner kernel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Odd-frequency pairing plays a crucial role in achieving diamagnetic response if the  electrons experience a staggered superconducting phase during the propagation of current.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  INTRODUCTION  The diversity of superconducting phenomena has been  attracting continued attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  The superconducting  state of matter is characterized by the properties of  Cooper pairs, which can be classified based on their  space-time and spin structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  With regard to their  space structure, Cooper pairs are typically classified as  s-wave, p-wave, or d-wave pairs depending on their rel-  ative coordinate structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' As for their center-of-mass  coordinate, while it is usually assumed to be zero in  most superconductors, it is possible to consider the exis-  tence of a finite center-of-mass momentum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' One example  of this is the Flude-Ferrell-Larkin-Ovchinnikov (FFLO)  state [1, 2], in which the Cooper pair has a small but finite  center-of-mass momentum under the influence of a mag-  netic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' More generally, the magnitude of the center-  of-mass momentum can be larger and of the order of the  reciprocal lattice vector ∼ π/a, where a is a lattice con-  stant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' This type of pairing state is known as η-pairing,  a concept first proposed by C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Yang, which forms a  staggered alignment of the superconducting phase on a  bipartite lattice [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The spatially modulating order pa-  rameter is known also as the pair density wave, and has  been discussed in relation to cuprate superconductors [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  The actual realization of the η-pairing has been pro-  posed for the correlated electron systems such as the at-  tractive Hubbard (AH) model with the magnetic field  [5], the single- and two-channel Kondo lattices [6, 7], the  Penson-Kolb model [8], and also the non-equilibrium sit-  uation [9–14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Since the phase of the superconducting  order parameter can be regarded as the XY spin, the η-  pairing is analogous to an antiferromagnetic state of the  XY spin model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Hence, the η-pairing state should be  strongly dependent on the underlying lattice structure  and we naively expect a variety of the η-pairing state  if we consider the geometrically frustrated lattice such  as the triangular lattice since the simple staggered state  cannot be realized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  In this paper, we deal with the AH model on the non-  bipartite lattice in order to search for possible new su-  perconducting states depending on the feature of the  non-bipartite lattice structure in equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Already  in the normal state without superconductivity, it has  been pointed out that the non-bipartite lattice generates  a non-trivial state of matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' For example in the Kondo  lattice, a partial-Kondo-screening, which has a coexisting  feature of Kondo spin-singlet and antiferromagnetism, is  realized [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Also in the AH model at half-filling, charge-  density-wave (CDW) is suppressed due to the frustration  effect [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The η-pairing that appears in a photodoped  Hubbard model on the triangular lattice has been studied  recently [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' In the equilibrium situation, the properties  of the AH model have been studied on bipartite lattices  [5], but the model on a non-bipartite lattice has not been  explored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  As shown in the rest of this paper, there are several  types of η-pairings on the triangular lattice of the AH  model under the Zeeman field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  One of the η-pairing  states is regarded as a 120◦-N´eel state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Since the rel-  ative phase between the nearest neighbor sites is neither  parallel nor anti-parallel, the inter-atomic Josephson cur-  rent is spontaneously generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' This state can also be  regarded as a staggered flux state, where the flux is cre-  ated by the atomic-scale superconducting loop current.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  While the staggered flux state has been studied so far  [17–23], the staggered flux in this paper is induced by  the Josephson effect associated with superconductivity  and has a different origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  For the analysis of the AH model, we employ the mean-  field approximation in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' It has been suggested  that a simple η-pairing shows a paramagnetic Meissner  state [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Hence it is necessary to investigate the electro-  magnetic stability of the solution for superconductivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  We evaluate the Meissner kernel whose sign corresponds  to the diamagnetic (minus) or paramagnetic (plus) re-  sponse of the whole system, where the physically sta-  ble state should show diamagnetism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' We confirm that  if the mean-field η-pairing state has the lowest energy  compared to the other ordered states, the calculation of  the Meissner kernel shows the diamagnetic response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' It  is also notable that the odd-frequency pairing amplitude,  which has an odd functional form with respect to the fre-  quency [6, 25–30], can contribute to the diamagnetism in  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='08426v1  [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='supr-con]  20 Jan 2023  2  the η-pairing state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' This is in contrast to the usual super-  conductivity with the uniform phase where the conven-  tional even-frequency pairing contributes to the diamag-  netism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' It has been shown that the odd-frequency pairing  induced at the edge, interface or junctions [31–36] shows  a paramagnetic response [37–41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' In this paper, by con-  trast, we consider the odd-frequency pairing realized in  bulk, which shows a qualitatively different behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  This paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  We explain the  model and method for the AH model in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' II, and the  Meissner kernel in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The numerical results for the  AH model are shown in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' IV, and we summarize the  paper in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  ATTRACTIVE HUBBARD MODEL  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Hamiltonian  We consider the Hamiltonian of the AH model with  magnetic field h which induce Zeeman effect only (Zee-  man field) :  H = −t  �  ⟨i,j⟩σ  c†  iσcjσ + H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' + U  �  i  ni↑ni↓  − µ  �  i  ni − h ·  �  i  si,  (1)  where c†  iσ and ciσ are the creation and annihilation op-  erators of the i-th site with spin σ, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  The  symbol ⟨i, j⟩ represents a pair of the nearest-neighbor  sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Here, the parameter t is the nearest-neighbor  single-electron hopping integral.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' U (= −|U|) is the on-  site attractive interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The spin operator is defined  as si =  1  2  �  σσ′ c†  iστσσ′ciσ′, where τ is the Pauli ma-  trix, and the number operator of electrons is denoted as  ni = ni↑ + ni↓ = �  σ c†  iσciσ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The electron concentration  is controlled by adjusting the chemical potential µ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  The AH model has been successfully used to elucidate  several important and fundamental issues in supercon-  ductors [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The model on a bipartite lattice at half fill-  ing is theoretically mapped onto the repulsive Hubbard  model by the following partial particle-hole transforma-  tion [43]  c†  i↑ → c†  i↑, c†  i↓ → ci↓eiQ·Ri.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  (2)  The reciprocal vector Q satisfies the condition eiQ·Ri =  (−1)i that takes ±1 depending on Ri belonging to A or  B sublattice on the bipartite lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Then, the η-pairing  appears in the region that corresponds to a ferromagnet  with transverse magnetization in the repulsive model [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  In a mean-field theory, the phase diagram for the repul-  sive Hubbard model without the magnetic field is shown  in the left panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 1 [44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' From this figure, we find  that the ferromagnet is located in the regime where the  repulsive interaction U > 0 is large and the electron con-  centration is not half-filled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Hence, the η-pairing phase  nc  t  |U|  m  0  1  0  1  PM  AFM  FM  FF  BCS  pairing  η  Repulsive Hubbard (  )  U > 0  Attractive Hubbard (  )  U < 0  h = 0  nc = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  Spin-polarized  normal state  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Sketches of the phase diagrams for the repulsive  Hubbard model [44] (left panel) and AH model (right panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  nc is the electron concentration and m is the magnetization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  When the interaction |U| is large, the ground state in the re-  pulsive Hubbard model is ferromagnet (FM), while the ground  state in the AH model is η-pairing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  is located in the regime where the attractive interaction  U < 0 is large and the magnetization is finite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The phase  diagram of the AH model at half filling is shown in the  right panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' In principle, an attractive interac-  tion large enough to realize η-pairing could be realized in  artificial cold atom systems [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  The Cooper pair is formed by the two electrons  with (k ↑,  − k + q ↓) where q is the center-of-mass  momentum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The FFLO state and the η-pairing are dis-  tinguished by the magnitude of |q|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  In η-pairing, the  center-of-mass momentum of the Cooper pair is the or-  der of the reciprocal lattice vector, while the momentum  of the FFLO state is much smaller and the spatial mod-  ulation is slowly-varying compared to the atomic scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Although the large center-of-mass momentum is usually  not energetically favorable, a strong attractive interac-  tion can make it stable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Mean-field theory  By applying the mean-field approximation, we obtain  the mean-field Hamiltonian  HMF = −t  �  ⟨i,j⟩σ  c†  iσcjσ + H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' − µ  �  i  ni − h ·  �  i  si  −  �  i  �  vini + Hi · si − ∆ic†  i↑c†  i↓ − ∆∗  i ci↓ci↑  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  (3)  3  The order parameters are given by the self-consistent  equations  vi ≡ |U|  2 ⟨ni⟩,  (4)  ∆i ≡ −|U|⟨ci↓ci↑⟩,  (5)  mi = 1  2  �  σσ′  ⟨c†  iστσσ′ciσ′⟩,  Hi =  − 2|U|mi,  (6)  where ⟨A⟩ = Tr  �  Ae−HMF/T �  /Tr  �  e−HMF/T �  is a quan-  tum statistical average with the mean-field Hamiltonian  and T is temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  ∆i is the order parameter for  s-wave singlet superconductivity (pair potential).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  The  phase θi ∈ [0, 2π) of the pair potential ∆i = |∆i|eiθi is  dependent on the site index and will be represented by  the arrow in a two-dimensional space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The mean-fields  for the charge and spin are given by vi and Hi, respec-  tively, at each site.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The derivation of the self-consistent  equations is summarized in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' We will consider  the AH model both on the two-dimensional square and  triangular lattices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  MEISSNER KERNEL FOR A GENERAL  TIGHT-BINDING LATTICE  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Definition  As we explained in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' I, it is necessary to calculate  the Meissner kernel to determine whether the mean-field  solution for η-pairing is electromagnetically stable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' In the  tight-binding model, the electromagnetic field appears as  Peierls phase:  Hkin = −t  �  ⟨i,j⟩σ  eiAijc†  iσcjσ + H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='.  (7)  The Meissner effect is examined by the weak external or-  bital magnetic field applied perpendicular to the plane,  while the η-pairing is stabilized only under a strong Zee-  man field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' In order to make these compatible, we apply  the Zeeman field parallel to the plane h = (h, 0, 0), which  does not create the orbital motion of the tight-binding  electrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Thus, the weak magnetic field that triggers  the Meissner effect is applied perpendicular to the plane  in addition to the in-plane magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  While the  out-of-plane Zeeman effect is also induced by the weak  additional field, it is neglected since the dominant Zee-  man field already exists by the strong in-plane magnetic  field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Let us formulate the Meissner response kernel on a  general tight-binding model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' We apply the formulation in  Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' [46–48] to the present case with sublattice degrees  of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The current density operator between two  sites is defined as  jij = ∂Hkin  ∂Aij  ˆδij  = −it  �  σ  �  c†  iσcjσeiAij − c†  jσciσe−iAij�  ˆδij,  (8)  where δij = Ri − Rj is the inter-site lattice vector be-  tween i-th and j-th sites, and hat (ˆ) symbol means a unit  vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' In the linear response theory, the current oper-  ator which appears as a response to the static magnetic  field in equilibrium is written as  jij ≃ −it  �  σ  (c†  iσcjσ − c†  jσciσ)ˆδij  + t  �  σ  (c†  iσcjσ + c†  jσciσ)ˆδijAij  ≡ jpara  ij  + jdia  ij .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  (9)  The first term is called the paramagnetic term and the  second term is diamagnetic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  The Fourier-transformed  paramagnetic and diamagnetic current density operators  are written as jpara(q) and jdia(q).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The linear response  kernel is then defined by ⟨jν(q)⟩ = �  µ Kνµ(q)Aµ(q),  where ν, µ = x, y is the direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' We evaluate the ker-  nel Kνµ(q → 0) ≡ Kνµ when investigating the stability  of superconductivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' This is called the Meissner kernel,  which is proportional to the superfluid density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  The Meissner kernel is separated into paramagnetic  and diamagnetic terms as Kνµ = (Kpara)νµ + (Kdia)νµ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  The paramagnetic kernel is given by  (Kpara)νµ = 1  N  � 1/T  0  dτ⟨jpara  ν  (q = 0, τ)jpara  µ  (q = 0)⟩,  (10)  where N = �  i 1 is the number of sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The Heisenberg  representation with the imaginary time τ is defined as  A(τ) = eHτAe−Hτ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The form of the diamagnetic kernel  is obvious from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' (9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  We note that if the sign of the Meissner kernel K is  negative, the superconducting state is electromagneti-  cally stable and is also called a diamagnetic Meissner  state, which expels magnetic flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' On the other hand, if  the sign is positive, the superconducting state is called  the paramagnetic Meissner state, which attracts mag-  netic flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' For a stable thermodynamic superconducting  state, the negative value of K is required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Method of evaluation  The actual evaluation of the kernels is performed based  on the wave-vector representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Here, the physical  quantities are described by the operator cα  kσ where α dis-  tinguishes the sublattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Note that the Brillouin zone is  4  folded by �  α 1 times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The diamagnetic kernel is rewrit-  ten as  (Kdia)νµ = 1  N  �  α,β  �  kσ  �  m−1  kαβ  �  νµ ⟨cα†  kσcβ  kσ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  (11)  The inverse mass tensor m−1  kαβ, which reflects the char-  acteristics of the lattice shape, are given by  �  m−1  kαβ  �  νµ ≡ t  �  ⟨iα,jβ⟩  �  ˆδiαjβ  �  ν  �  ˆδiαjβ  �  µ e−ik·Riαjβ ,  (12)  where iα is the i-th unit cell with sublattice α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  The  symbol ⟨iα, jβ⟩ represents a pair of the nearest-neighbor  sites and Riαjβ is the vector between the unit lattice with  the i-th sublattice α and the unit lattice with the j-th  sublattice β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  The paramagnetic term has the form of a current-  current correlation function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' We can calculate this term  by using the Green’s function matrix  ˇGk(τ) ≡ −⟨Tτψk(τ)ψ†  k⟩  (13)  where ψk = (cα  k↑, cα†  −k↓, · · · )T is the Nambu-spinor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Tτ is  time-ordering operator regrading τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Each component of  the Green’s function matrix is given by the diagonal and  off-diagonal Green’s functions:  Gαβ  σσ′(k, τ) ≡ −⟨Tτcα  kσ(τ)cβ†  kσ′⟩,  (14)  ¯Gαβ  σσ′(k, τ) ≡ −⟨Tτcα†  kσ(τ)cβ  k′σ′⟩,  (15)  F αβ  σσ′(k, τ) ≡ −⟨Tτcα  kσ(τ)cβ  −kσ′⟩,  (16)  F αβ†  σσ′ (k, τ) ≡ −⟨Tτcα†  −kσ(τ)cβ†  kσ′⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  (17)  The anomalous part of Green’s function [Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' (16)] is also  called the pair amplitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The paramagnetic kernel in  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' (10) can be divided into the normal (G) and anoma-  lous (F) Green’s function contributions as  (Kpara)νµ = − 1  N  � � 1/T  0  dτ (vkαβ)ν · (vkα′β′)µ ×  �  ¯Gαβ′  σσ′(k, τ)Gα′β  σσ′(k, τ) + ¯Gαβ′  σσ′(−k, τ)Gα′β  σσ′(−k, τ)  �  − 1  N  � � 1/T  0  dτ (vkαβ)ν · (v−kα′β′)µ ×  �  F βα†  σ′σ (k, −τ)F α′β′  σ,σ′ (k, τ) + F βα†  σ′σ (−k, −τ)F α′β′  σ,σ′ (−k, τ)  �  ≡ KG  para + KF  para.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  (18)  The summation � is performed over the indices which appears only in the right-hand side.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The velocity vector vkαβ  is defined by  (vkαβ)ν ≡ t  �  ⟨iα,jβ⟩  �  ˆδiαjβ  �  ν e−ik·Riαjβ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  (19)  In order to perform the integral with respect to τ in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' (18), we define the Fourier-transformed Green’s function as  gk(iωn) ≡  � 1/T  0  dτgk(τ)eiωnτ,  (20)  where gk represents one of Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' (14)-(17) and ωn = (2n + 1)πT is fermionic Mastubara frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Moreover, the  Fourier-transformed Green’s function matrix is given by using the matrix representation of mean-field Hamiltonian  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' (3) as  ˇGk(iωn) =  �  iωnˇ1 − ˇHMF  k  �−1 = ˇUk  �  iωnˇ1 − ˇΛk  �−1 ˇU †  k,  (21)  where ˇΛk and ˇUk are, respectively, a diagonal eigenvalue matrix and a unitary matrix satisfying ˇU † ˇHMF  k  ˇU = ˇΛk =  diag(λk1, λk2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' From Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' (21), Kpara can be calculated as  (Kpara)νµ = − 1  N  � �  (vkαβ)ν · (vkα′β′)µ Uβ′σ′,ασ  kp  Uα′σ,βσ′  kp′  + (vkαβ)ν · (v−kα′β′)µ Uβσ′,ασ  kp  Uα′σ,β′σ′  kp′  � f (λkp) − f (λkp′)  λkp − λkp′  + c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  (22)  where f(λkp) =  1  eλkp/T +1 is the Fermi-Dirac distribution function and we have defined the coefficient Uασ,βσ′  kp  ≡  � ˇUk  �  ασ,p  �  ˇU †  k  �  p,βσ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  The anomalous part of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' (18) KF  para is further de-  composed into the contributions KEFP and KOFP from  5  the even-frequency pair (EFP) and odd-frequency pair  (OFP) amplitudes defined by  F EFP(k, iωn) ≡ F(k, iωn) + F(k, −iωn)  2  ,  (23)  F OFP(k, iωn) ≡ F(k, iωn) − F(k, −iωn)  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  (24)  Then, we obtain KEFP and KOFP by using Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' (23) and  (24) as  KEFP,OFP  νµ  = − 1  2N  �  k  �  αβα′β′  (vkαβ)ν · (v−kα′β′)µ  ×  �  σσ′  �  pp′  Uβσ′,ασ  kp  Uα′σ,βσ′  kp′  ×  �f (λkp) − f (λkp′)  λkp − λkp′  ∓ f (λkp) − f (−λkp′)  λkp + λkp′  �  + c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=',  (25)  where the minus (−) sign in the square bracket is taken  for EFP contribution and the plus (+) for OFP pairing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  These quantities are numerically calculated as shown in  the next section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Note that the cross term of the EFP  and OFP terms of Green’s functions vanishes after the  summation with respect to the Matsubara frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Paramagnetic Meissner response of a simple  η-pairing state  Before we show the results of the AH model, let us show  that a simple η-pairing state leads to the paramagnetic  response which would not arise from thermodynamically  stable states [24, 49].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' We consider the simple bipartite  lattice with staggered ordering vector Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The anomalous  contribution to the Meissner kernel may be written as [49]  KF  para,xx = −T  �  nkk′σσ′  vx  kvx  k′F ∗  σ′σ(k′, k, iωn)Fσσ′(k, k′, iωn).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  (26)  This contribution must be negative (diamagnetic re-  sponse) in order to dominate over the paramagnetic con-  tribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' For a purely η-pairing state, we assume the  relation Fσσ′(k, k′) = Fσσ′(k)δk′,−k−Q, and obtain  KF  para,xx = −T  �  nkσσ′  (vx  k)2F ∗  σ′σ(k, iωn)Fσσ′(k, iωn), (27)  where we have used vx  −k−Q = vx  k valid for square lat-  tice, which is in contrast to the relation vx  −k = −vx  k  for the uniform pairing with additional minus sign [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  We separate the spin-singlet and triplet parts as Fσσ′ =  Fsiτ y  σσ′ + Ft · (τiτ y)σσ′, and then obtain  KF  para,xx = 2T  �  nk  (vx  k)2�  |Fs(k, iωn)|2 − |Ft(k, iωn)|2�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  (28)  If we consider the simple η-pairing with only spin-singlet  part (Ft = 0), it leads to the paramagnetic response  (positive).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Thus, a simple s-wave spin-singlet η-pairing is unlikely  realized as a stable state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' On the other hand, in the AH  model with magnetic field, the spin-triplet pair contribu-  tion is substantially generated by the Zeeman field, which  plays an important role for the diamagnetic response as  shown below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  NUMERICAL RESULT FOR AH MODEL  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Square lattice  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Prerequisites  Let us begin with the analysis of the AH model on  the square lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' We consider the two-sublattice struc-  ture to describe the staggered ordered phase such as a  η-pairing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' While the superconducting states in the at-  tractive model are interpreted in terms of the magnetic  phases of the repulsive model by the particle-hole trans-  formation in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' (2), the response functions such as the  Meissner kernel are specific to the attractive model and  have not been explored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  In the following, we choose the band width W = 1  as the unit of energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  We fix the value of the attrac-  tive interaction U = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='375.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The electron concentration  is fixed as nc = 1, and the temperature is taken to be  T = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 × 10−3 unless otherwise specified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' We will in-  vestigate the change of the Meissner kernel for η-pairing  as a function of magnetic field strength h = |h|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' In this  paper, the mean-field solutions are calculated using the  60 × 60 mesh in k-space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The result of the Meissner ker-  nel for η-pairings is calculated with the mesh 300 × 300.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  We also checked that the behaviors remain qualitatively  unchanged when these numbers are increased.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The self-  consistent equations in Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' (4)-(6) are computed by  using an iterative method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  In the following subsec-  tion IV A 2, we restrict ourselves to the analysis of two-  sublattice mean-field solutions, and in IV A 3, we exam-  ine the solutions when the two-sublattice constraint is  relaxed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Two-sublattice solution  Before investigating the electromagnetic stability, we  clarify the regime where the η-pairing becomes the  ground state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' In this paper, we assume that the inter-  nal energy in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' (1) is approximately equal to the free  energy in the low temperature region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The upper panel  of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 2 shows the internal energy of several ordered  states measured from the normal-state energy as a func-  tion of the Zeeman field h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Here, the η-pairing solution  is obtained by solving the self-consistent equation with  imposing the constraint of the staggered phase of the pair  6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='25 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='75 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='25 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  h  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  Ei − Enormal  BCS  CDW  Normal  η-pairing  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='25 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='75 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='25 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='08  D0  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  (Upper panel) Magnetic-field dependence of the  internal energy for each state measured from the normal state  in the square lattice model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' (Lower plane) Density of state  (DOS) at zero energy D0 for each state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  ω  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2  D(ω)  h = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='25  h = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='375  h = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Density of states for the η-pairing around magnetic  filed h = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='375 in the square lattice model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Here D(ω) is  normalized as  �  dωD(ω) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  amplitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' A constraint is also used for the calculation  of the other types of order parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Our calculations  have not found any ordered states other than the types  shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 2 even when a random initial condition is  employed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  We determine the thermodynamically stable ground  state by comparing the internal energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' In low magnetic  fields, BCS and CDW are degenerated ground states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' On  the other hand, we find that the η-pairing becomes the  ground state in the magnetic field located in 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='063 < h <  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='875.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The η-pairing solution itself is found in the wider  regime although the internal energy is not the lowest one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  It has been known that the attractive Hubbard model  under a magnetic field also shows the FFLO state [50],  but this possibility cannot be considered when we take  the two-sublattice condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' This point will be revisited  in the next subsection where the two-sublattice condition  is relaxed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  The lower panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 2 shows the density of  state (DOS) at the Fermi level for each state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The re-  sult indicates that there is no energy gap in the η-pairing  state, in contrast to the conventional BCS pairing state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  There exists the regime where the DOS at the Fermi  level for η-pairing is larger than that of normal metal  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='25 ≲ h ≲ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' This is due to the van-Hove singular-  ity of the square lattice model as shown in FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' We  also perform the calculation for the cubic lattice where  the van-Hove singularity is absent at zero energy and con-  firm in this case that the DOS is smaller than the normal  state (see Appendix B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  The stability of the η-pairing depends upon the mag-  nitude of the magnetic field as seen in the Meissner re-  sponse kernel K (= Kxx = Kyy) (green symbol) in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 4(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  The contributions from the paramagnetic  (Kpara, positive) and diamagnetic (Kdia, negative) parts  are also separately plotted in the figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' In the regime  with h ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='125 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='75 ≤ h, the η-pairing is electromag-  netically unstable, while it is stable in 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='125 < h < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 4, the yellow shaded rectangle indicates the regime  where the η-pairing becomes the ground state as seen  from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' We find a narrow region where η-pairing is  regarded as the ground state but is not an electromagnet-  ically stable state around h = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='125.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' From these results,  we see that the η-pairing is not necessarily electromag-  netically stable even if it becomes the ground state in  a two-sublattice calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' As we shall see later, the  simple η-pairing in this narrow regime does not necessar-  ily exist if we relax the two-sublattice condition of the  mean-field solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  We also show in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 4(a) the contributions from the  even- and odd-frequency pairs defined in Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' (23) and  (24).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The negative sign of the kernel, which means the re-  sponse is diamagnetic, is partly due to the odd-frequency  component of the pair amplitude, (KOFP < 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  This  is in contrast to the FFLO state whose Meissner ker-  nel is also negative due to the even-frequency component  [51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Hence, it implies that the mechanism of the dia-  magnetism is different between the FFLO and η-pairing  states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  In  addition  to  the  Meissner  kernel,  we  calcu-  late the local pair amplitudes which are shown in  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 4(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Here the left- and right-panels represent  the spin-triplet and spin-singlet components of the lo-  cal pair amplitude, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The triplet component  �  σσ′(τ µiτ y)σσ′Fσσ′(iωn) with µ = x has a finite imagi-  nary part and zero real part, which represents the odd-  frequency pair.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The other µ = y, z components are zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  On the other hand, the singlet component has a finite real  part and zero imaginary part and is the even-frequency  pair.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' We can see that the maximum value of the spin-  triplet component of the pair amplitude is largest at the  magnetic field h = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='375, where the magnitude of KOFP  is largest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' It is also notable that the magnitude of the  odd-frequency pair amplitude correlates with the magni-  tude of DOS at zero energy as seen by comparing Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 3  and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  We comment on the singular behavior of KOFP at the  magnetic field h = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='375, although it does not affect the  total Meissner kernel K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' This anomalous feature is re-  lated to the van Hove singularity of the DOS at zero  energy as shown in FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 3, which shows a sharp peak at  the Fermi level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  h  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='K  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='Kdia  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='Kpara  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='K  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='KEFP  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='KOFP  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='(a)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='(b)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='<latexit sha1_base64="hwzoaSF0Y+Oi/TJGH/A  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8l7Sl9vw=">AD0HichVO5TsNAEH3BnOEIR4NEg4iQKFC0QZxdEA0lVwCJIGSbTbKL9kbFIQioEW08A  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='+IH+EHKPgEagoaCmY35lIUM5bt2TfvjWd2x1bgiEgy9pLqMrp7ev6B9KDQ8MjmdGx8f3Ir4c2L9q+4e  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='HlhlxR3i8KIV0+GEQctO1H5g1TZU/OCMh5HwvT15HvBj16x4oixsUxK0U2qejGZjmbnfysZNFbFv+  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='WKqEk7hw0YdLjg8SPIdmIjoOkIeDAFhx7gLCRP6DhHE2nS1onFiWESWqNnhVZHMerRWuWMtNqmrzh0h6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='Scxix7Zg/sjT2xR/bKPjrmutA5VC3n9LZaWh6cZG4md9/Vbn0lqj+qBJrlihjVdcqPZAI6oLW+s7KxW  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='nQr0Jila13qKYRbiTsEuK5SbG/3Y+39ZTZ2WFdtktKpPq/FPFYpbI18m8n6fX1LNEa1djSbx1M429Kz5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='xA4SuV8d/+am9ayvKVv6nux2Z38hl1/OLW4vZgvrV62p78cUZjBHk72CAjaxhSJlLuMWd7g3doyGcWlct  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6hdqfhPmcAfM24+AbMryxg=</latexit>}Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' (25)  °3  °2  °1  0  1  2  3  !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='n  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6  Re[F " #(i!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='n) ° F # "(i!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='n)]/  p  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='875  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='75  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='625  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='375  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='25  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='125  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='875  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='625  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  h  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  K  Kdia  Kpara  K  KEFP  KOFP  OFP  EFP  °3  °2  °1  0  1  2  3  !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='n  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6  Im[F # #(i!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='n) ° F " "(i!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='n)]/  p  2  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  (a) Magnetic field dependence of the Meissner ker-  nel K(= Kxx = Kyy) for the η-pairing on the square lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  The yellow shaded rectangle indicates the range where the  η-pairing becomes the ground state in two-sublattice calcula-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The number of the wavenumber k is taken as 300×300.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  (b) Matsubara frequency dependence of the local pair ampli-  tude at several magnetic fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The left panel represents the  imaginary part of [F↓↓(iωn) − F↑↑(iωn)] /  √  2, and the right  panel represents the real part of [F↑↓(iωn) − F↓↑(iωn)] /  √  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  The values of the pair amplitudes are shifted by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6 at each  magnetic field for visual clarity, and the gray-dotted lines are  the zero axes for each magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Beyond two-sublattice  In order to clarify the stable ordered state where the  Meissner kernel is positive (paramagnetic), we investi-  gate mean-field solutions on finite-sized lattice where the  two-sublattice condition is not imposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  We have nu-  merically solved the Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' (4)-(6) self-consistently by us-  ing the mean-field solutions of the η-pairing obtained for  two-sublattice as an initial condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Figure 5 shows the spatial distribution of the phase of  the gap function when the number of sites is 8 × 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' At  h = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5 in (a), where the η-pairing is not a ground state,  the uniform BCS pairing state is realized as expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  With increasing the magnetic field, the longer-periodicity  structures are found as shown in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 5(b), (c) and (d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  At h = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='375 in (c), where the η-pairing solution has the  lowest energy and the electromagnetic response is well  diamagnetic, we obtain the staggered alignment of the  (a) h = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  (d) h = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='875  (c) h = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='375  (b) h = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='125  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Spatial distribution of the phase of the supercon-  ducting order parameter at several magnetic fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The cal-  culation is performed on the finite-sized lattice (8 × 8) with  open boundary condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Small black dots are lattice points  and red arrows indicate the phase of the pair potential for  each lattice point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' When the parameters are close to the edges of  the yellow-highlighted region in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 4, the complex struc-  tures are formed as shown in (b) and (d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The behavior  in (b) is interpreted as due to the competing effect where  the simple uniform and staggered phases are energetically  close to each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  We also investigate the case with the other choice of pa-  rameters: U = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='25 and h = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' In this case, we find  the staggered flux state where the phase of pair poten-  tial is characterized by 90◦-N´eel ordering as in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 6(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  This ordered state cannot be described in the mean-field  theory with two sublattices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Owing to a non-colinear  90◦-N´eel ordering vector, the spontaneous clockwise or  counterclockwise loop currents arise by the inter-atomic  Josephson effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The current density is calculated by  jij = −it  �  σ  ⟨c†  iσcjσ − c†  jσciσ⟩  (29)  which is identical to the expression of the paramagnetic  current in the linear response theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' We can also evalu-  ate the flux for each plaquette, which is define by  Φ =  �  (i,j)∈plaquette  jij  (30)  This expression is similar to the flux  �  C  j ·ds =  �  S  b·dS  (j = ∇ × b) defined in a continuum system, where b is  a flux density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The flux is aligned in a staggered manner  8  (a)  (b)  Current  Magnetic flux  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' (a) Spatial distribution of the phase of the supercon-  ducting order parameter for the η-pairing with 90◦-N´eel state  on the finite-sized lattice under open boundary conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  (b) Spatial distributions of the spontaneous loop current and  the flux defined on each plaquette.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The color of vectors dis-  plays the magnitude of current, and the color of dots in each  plaquette indicates the value of the magnetic flux defined in  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' (30).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  on a dual lattice as indicated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 6(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The staggered  flux originating from the normal part has been studied  before [20–23], while the staggered flux shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 6(b)  has a different origin: it arises from the superconductiv-  ity associated with the off-diagonal part in the Nambu  representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  We also comment on a feedback effect to the electro-  magnetic field from the supercurrent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Since the char-  acteristic length scale for the magnetic field in layered  superconductor becomes long [52], each magnetic flux on  the plaquette is smeared out with this length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Hence we  expect that the net magnetic field is not created from the  staggered superconducting flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Triangular lattice  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Mean-field solution  Now we search for the η-pairing reflecting the charac-  teristics of a geometrically frustrated triangular lattice  at the half-filling (nc = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' We choose the parameters  U = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='83 and T = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 × 10−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' We consider the cases of  two- and three-sublattice structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' For a usual antifer-  romagnet, the typical ordered state in the two-sublattice  case has a stripe pattern, while in the three-sublattice  case we expect a 120◦-N´eel state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Below we study the  superconducting η-pairing phases within the mean-field  theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  We have found the four types of superconducting states  reflecting the characteristics of the triangular lattice,  which are referred to as the η-pairing I, II, III, and IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  The schematic pictures for these four states are shown  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 7(a), where the arrow indicates the phase of the  superconducting order parameter at each site.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' We make  a few general remarks: the three-sublattice structure is  assumed for I, II, III, while the two sublattice is employed  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  ni, mi  nA  nB  nC  mA  mB  mC  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  ni,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' mi  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='nA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='nB  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='mA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='mB  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='(a)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='(b)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='<latexit sha1_base64="HLHSkuiSo7OABq7I/GuoPhNC6Lg=">AD5XichVNa9tAEH20tRxmsRJCR6MTWFHhKzLmT3hx6SW8pqe2AbYykbOTF+kJaBxth6LnQW8m19Njkj/QP9NCf0HMOufTQ2bXzYyVEZJm37w3mtkdWaErYsn  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='Yn0zWHi0+Di3lF9+srK6VljfqMdBP7J5zQ7cIDq2zJi7wuc1KaTLj8OIm57l8obVe6/ijTMexSLwP8lhyNue6fjiVNimJKhT2GxFXvKh1Y1D0+bJdrnCvVF91CmUWJlpK846lYlTwsQOg/VMCy2cICNPjxw+JDkuzAR09VEBQwhYW0khEXkCR3nGCFP2j6xODFMQnv0dGjVnKA+rVXOWKt+opLd0TKIl6y3+wnu2K/2CX7y/7NzZXoHKqWIb2tsZaHnbUvz46uH1R59Jbo3qlSa5Y4xZ6uVDtoUZUF7bWz1cqjkO9CYp2td6imEW4m7JLiuWlxqc735rpab7SoV02Ce3q0xo8UIXi  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='9siXqbz75dWc0xrT6NpPLWzAz1rAbHDVO5Nx/e5eT3r75S9uZ3sWaf+ulx5W975uFOq7n8eT30Oz/ECr2iyd1HFAQ5Ro8wJfuACl4ZjfDW+GedjajYz+VOeYsqM7/8B8nDTJg=</latexit>IV  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='<latexit sha1_base64="0lzRl8Ev1iYodM/0b/A8BMLCw=">AD5XichVNb9NAEH2paSmhtAmoEhKXqFGlHm  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='i0qQot1S9kFsQzYeURJHtbp1V/CV7g1JZkTgjcau4Io6QP8If4MBP4MyBSw+d3YR+KIo7lu3ZN+NZ3bHVuiKWDL2O7NkPFhebj6KPt47cn6Ri7/tBEHw8jmdTtwg6hlmTF3hc/rUkiXt8KIm57l8qY1OFbx5gcexSLwT+R5yLue6fji  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='TNimJKiX2+xEXlLt9OPQtHmyWypzb1wd93JFVmLaCvNOeYUMbNakM90MEpAtgYwgOHD0m+CxMxXW2UwRAS1kVCWESe0HGOMbKkHRKLE8MkdEBPh1btGerTWuWMtdqmr7h0R6QsYJv9Yt/ZX/aTdgfdrkwV6JzqFrO6W1NtTzsbXx6/v7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='fvSqP3hL9G1VqzRJnONS1Cqo91Ijqwtb6xUrFcag3QdG+1lsUswh3U3ZJsbzU+N3OX871tFjp0C6bhPb1aY3uqUJxB+TLVN7t80urOa1p9E0ntrZkZ61gNhKvd/x7e5WT3rb5S9up7seaexVyq/Lu2/2y9Wj5Op34VL7CFHZrsA1TwF  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='jXUKXOCb/iBieEYn40L48uUupSZ/SnPcMeMr1fF9NMZ</latexit>II  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='<latexit sha1_base64="+wPFmdUeKb1/4PbXkIuITbQNFGw=">AD9HichVO7TuNAFD3BPEJ4BWiQaBABiQKiCe  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='LZUDHQgCSARFthmSUfySPUGgKBI130C32mKFhGjZL9gfoOATt6ChoI7k/CMYq5l+8651zfO3NtBY6IJGOPiS6ju6e3L9mfGhgcGh5Jj47tR34tHnB9h0/PLTMiDvC4wUpMPg5CbruXwA6u6oeIHZzyMhO/tyYuAH7tm2ROnwjYl  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='QaX0TDF061vFShSYNq8vZHPcbXxdNkrpDMsybVPtTq7lZNCybX80UQRJ/BhowYXHB4k+Q5MRHQdIQeGgLBj1AkLyRM6ztFAirQ1YnFimIRW6Vm1VEL9WitckZabdNXHLpDUk5hlj2w3+w/+8tu2D/23DFXedQtVzQ2pqeVAauZrYfp  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='W5dJbovKuiq1Z4hRrulZBtQcaUV3YWt9ZqThl6k1QtKL1FsUswp2YXVIsNzb+ufP5tp46K8u0yahFX1a59UobhV8mUs7+P5xdUc0drVaBxP7ey5njWf2Es97Xj9yUnvV1Zctvk93u7C9mcyvZpZ2lTP7HZXPqk5jENOZosleRxya2U  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='aDMV7jDPf4YZ8a18dP41aR2JVp/yjg+mXH7AkDw2R4=</latexit>III  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='<latexit sha1_base64="1D3cNDco74HVKDqoxdioDUzCYmY=">AD1HichVPLSsNAFD01Pmp960ZwIxbBhZSp+N  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='wpbnSnaKtgRZI4tmPzIplKpQqCuHEhbvUPxB/xB1z4Ca5duHhnWl9URpvSHLn3HNu7p25sQJHRJKxl0Sb0d7R2ZXsTvX09vUPDA4N5yO/Eto8Z/uOH+5aZsQd4fGcFNLhu0HITdy+I5VXlXxnRMeRsL3tuVpwPds+iJI2GbkqB8IXRr  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6+cHg2mWYdrGm51sw0mjYRv+UKAg7hw0YFLjg8SPIdmIjo2kMWDAFh+6gRFpIndJzjHCnSVojFiWESWqZnkVZ7DdSjtcoZabVNX3HoDk5jkn2zB7YG3tij+yVfbTMVdM5VC2n9LbqWh4cDFyPbr3/q3LpLVH6UcXWLHGERV2roNoDjag  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='ubK1vrVScIvUmKFrSeotiFuFOzC4plhsb/9v5dFNPrZVF2mWT0JI+reo/VShumXwZy/t9fnE1R7R2NRrHUztb1bPmEzuI5X51/Jub0rO+pGzue7KbnfxMJjufmd2cTS+vXNSnPokxTGCKJnsBy1jDBnKU+Ri3uMO9kTfOjEvjqk5tSzT+l  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='BH8MePmE+ykzOM=</latexit>I  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='A  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='B  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='C  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='<latexit sha1_base64="pw/0hoI9HJeFkpOwH0i+6Zr/+zU=">AD1nichVM7TwJBEB  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4H4gPRBsTGyMxsTBkMT47lMYSo+glYMzducCGe+VuMRCsTEmVsZW/4Dxj/gHLPwJ1hY2Fs4up0Ix1zudvab79ub2Z3VXZP5nJD3SFQZGR0bj03EJ6emZxKzybkT36l7Bi0Yjul4q  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='751GQ2LXDGTaq6HtUs3aSnei0n4qeX1POZYx/zpkvPLK1iszIzNI6QWvKs1n7uqH0+myJpIm2p38kETgoCyzvJSAlKcAEOGFAHCyjYwNE3QMfnyJkgICL2Bm0EPQYzJOoQ1x1NaRZ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='GhIVrDbwVnxQC1cS7W9KXawL+Y+HqoXIV8kaeySd5JS/kg3wPXKsl1xC5NHUO1rqnifuFo6+hqosHDlU/1WhOXMow47MlWHurkREFYbUD1YKTgVrYxitSr2OMR1xM2SXBMsKjfdWvt  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='ZX02BlBXdZQ7QqT6sxJAvBraHPQ3nd5xeWs49zS6JhPLGzDdlrDrLdUO5vxd3cuOz1XWGbf53d75yspzNb6Y3DjVR27rT9TFYhGVYxc7ehiwcQB4KsqMf4BGeFW5Um6U2w41Ggluyj  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='z0mHL/AygEzY=</latexit>BCS  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='<latexit sha1_base64="0lzRl8Ev1iYodM/0b/A8BMLCw=">AD5XichVNb9NAEH  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2paSmhtAmoEhKXqFGlHmi0qQot1S9kFsQzYeURJHtbp1V/CV7g1JZkTgjcau4Io6QP8If4MBP4MyBSw+d3YR+KIo7lu3ZN+NZ3bHVuiKWDL2O7NkPFhebj6KPt47cn6Ri7/tBEHw8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='jmdTtwg6hlmTF3hc/rUkiXt8KIm57l8qY1OFbx5gcexSLwT+R5yLue6fjiTNimJKiX2+xEXlLt9OPQtHmyWypzb1wd93JFVmLaCvNOeYUMbNakM90MEpAtgYwgOHD0m+CxMxXW2UwR  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='AS1kVCWESe0HGOMbKkHRKLE8MkdEBPh1btGerTWuWMtdqmr7h0R6QsYJv9Yt/ZX/aTdgfdrkwV6JzqFrO6W1NtTzsbXx6/v7fvSqP3hL9G1VqzRJnONS1Cqo91Ijqwtb6xUrFcag3Qd  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='G+1lsUswh3U3ZJsbzU+N3OX871tFjp0C6bhPb1aY3uqUJxB+TLVN7t80urOa1p9E0ntrZkZ61gNhKvd/x7e5WT3rb5S9up7seaexVyq/Lu2/2y9Wj5Op34VL7CFHZrsA1TwFjXUKX  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='OCb/iBieEYn40L48uUupSZ/SnPcMeMr1fF9NMZ</latexit>II  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='<latexit sha1_base64="1D3cNDco74HVKDqoxdioDUzCYmY=">AD1HichVPLSsNAFD  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='01Pmp960ZwIxbBhZSp+NwpbnSnaKtgRZI4tmPzIplKpQqCuHEhbvUPxB/xB1z4Ca5duHhnWl9URpvSHLn3HNu7p25sQJHRJKxl0Sb0d7R2ZXsTvX09vUPDA4N5yO/Eto8Z/uOH+5aZs  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='Qd4fGcFNLhu0HITdy+I5VXlXxnRMeRsL3tuVpwPds+iJI2GbkqB8IXRr6+cHg2mWYdrGm51sw0mjYRv+UKAg7hw0YFLjg8SPIdmIjo2kMWDAFh+6gRFpIndJzjHCnSVojFiWESWq  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='ZnkVZ7DdSjtcoZabVNX3HoDk5jkn2zB7YG3tij+yVfbTMVdM5VC2n9LbqWh4cDFyPbr3/q3LpLVH6UcXWLHGERV2roNoDjagubK1vrVScIvUmKFrSeotiFuFOzC4plhsb/9v5dFNPrZ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='VF2mWT0JI+reo/VShumXwZy/t9fnE1R7R2NRrHUztb1bPmEzuI5X51/Jub0rO+pGzue7KbnfxMJjufmd2cTS+vXNSnPokxTGCKJnsBy1jDBnKU+Ri3uMO9kTfOjEvjqk5tSzT+lBH8Me  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='PmE+ykzOM=</latexit>I  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='<latexit sha1_base64="1D3cNDco74HVKDqoxdioDUzCYmY=">AD1HichVPLSsNAFD01Pmp960ZwIxbBhZSp+NwpbnSnaKtgRZI4tmPzIplKpQqCuHEhbvUPxB/xB1z4Ca5duHh  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='nWl9URpvSHLn3HNu7p25sQJHRJKxl0Sb0d7R2ZXsTvX09vUPDA4N5yO/Eto8Z/uOH+5aZsQd4fGcFNLhu0HITdy+I5VXlXxnRMeRsL3tuVpwPds+iJI2GbkqB8IXRr6+cHg2mWYdrGm51sw0mjYRv+UKAg7hw0YFLjg8SPIdmIjo2kMWDAFh+6gRFpIndJzjHCnSVojFiWESWqZnkVZ7DdSjtcoZabVNX3HoDk5jkn2zB7YG3tij+yVfbTMVdM5VC2n9LbqWh4cDFyPbr3/  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='q3LpLVH6UcXWLHGERV2roNoDjagubK1vrVScIvUmKFrSeotiFuFOzC4plhsb/9v5dFNPrZVF2mWT0JI+reo/VShumXwZy/t9fnE1R7R2NRrHUztb1bPmEzuI5X51/Jub0rO+pGzue7KbnfxMJjufmd2cTS+vXNSnPokxTGCKJnsBy1jDBnKU+Ri3uMO9kTfOjEvjqk5tSzT+lBH8MePmE+ykzOM=</latexit>I  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6  h  °0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='05  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='Ei ° E¥°pairing I  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='<latexit sha1_base64="HLHSkuiSo7OABq7I/GuoPhNC6Lg=">AD5XichVNa9tAEH20tRx  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='msRJCR6MTWFHhKzLmT3hx6SW8pqe2AbYykbOTF+kJaBxth6LnQW8m19Njkj/QP9NCf0HMOufTQ2bXzYyVEZJm37w3mtkdWaErYsnYn0zWHi0+Di3lF9+srK6VljfqMdBP7J5zQ7cIDq2zJi7wuc1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='KaTLj8OIm57l8obVe6/ijTMexSLwP8lhyNue6fjiVNimJKhT2GxFXvKh1Y1D0+bJdrnCvVF91CmUWJlpK846lYlTwsQOg/VMCy2cICNPjxw+JDkuzAR09VEBQwhYW0khEXkCR3nGCFP2j6xODFMQnv0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='dGjVnKA+rVXOWKt+opLd0TKIl6y3+wnu2K/2CX7y/7NzZXoHKqWIb2tsZaHnbUvz46uH1R59Jbo3qlSa5Y4xZ6uVDtoUZUF7bWz1cqjkO9CYp2td6imEW4m7JLiuWlxqc735rpab7SoV02Ce3q0xo  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8UIXi9siXqbz75dWc0xrT6NpPLWzAz1rAbHDVO5Nx/e5eT3r75S9uZ3sWaf+ulx5W975uFOq7n8eT30Oz/ECr2iyd1HFAQ5Ro8wJfuACl4ZjfDW+GedjajYz+VOeYsqM7/8B8nDTJg=</latexit>IV  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4  °3  °2  °1  0  Ei ° Enormal  BCS  normal  ¥-pairing I  ¥-pairing IV  ¥-pairing III  ¥-pairing II  (c)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6  h  °0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='05  Ei ° E¥°pairing I  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4  °3  °2  °1  0  Ei ° Enormal  BCS  normal  ¥-pairing I  ¥-pairing IV  ¥-pairing III  ¥-pairing II  pairing II  η  pairing IV  η  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6  h  °0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='05  Ei ° E¥°pairing I  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  ni, mi  nA  nB  nC  mA  mB  mC  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  ni, mi  nA  nB  nC  mA  mB  mC  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  ni, mx  i  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  ni, mx  i  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  ni, mx  i  x  y  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  (a) Schematics for the four η-pairings in the tri-  angular lattice model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The arrows indicate the phase of the  pair potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The size of the circles shows the amount of  the electron density for each sublattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' (b) Magnetic field  dependence of the internal energies measured from the nor-  mal state (upper panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The lower panel shows the inter-  nal energy measured from the η-pairing I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' (c) Magnetic field  dependence of the number of electrons and magnetization on  each sublattice for the η-pairing II (upper panel) and IV (lower  panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  for IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The type-I has a non-colinear structure, and in the  other η-pairings the vectors are aligned in a colinear man-  ner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' We also note that CDW accompanies the η-pairings  II and III, where the number of local filling is indicated  by the size of the filled circle symbols in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 7(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Figure 7(b) shows the internal energy of the ordered  states measured from the normal state (Upper panel) and  from the η-pairing I (Lower panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' From the lower panel  of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 7(b), we can identify the ground state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' With in-  creasing the magnetic field, the ground state changes as  BCS → η-pairing II→ η-pairing I → η-pairing IV→ η-  pairing I → normal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Figure 7(c) shows the particle den-  9  (a)  (b)  Iloop  h  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6  h  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='1  Iloop  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' (a) Schematic picture of the staggered flux state on  the triangular lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The straight arrows display the phase  of the pair potential at each site, and the circle arrows indicate  the staggered loop current.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' (b) Magnetic field dependence of  the magnitude of loop current.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The yellow shaded rectangle  indicates the range where the η-pairing I becomes the ground  state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  sity and x-direction magnetization mx  i of each sublattice  for η-pairing II (Upper panel) and η-pairing IV (Lower  panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The values of my  i and mz  i are zero because the  Zeeman field h is applied along the x-direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Below,  we explain the characteristic features for each η-pairing  state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  η-pairing-I state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='— The η-pairing I has 120◦ N´eel or-  dering vector (Green pentagon in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 7(b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The spon-  taneous supercurrent appears in this non-colinear state  as schematically shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 8(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' This superconduct-  ing state forms a staggered flux state, where the flux is  aligned on a honeycomb dual lattice, which is similar to  the η-pairing with 90◦-N´eel ordering vector on the square  lattice shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 6(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Figure 8(b) displays the val-  ues of spontaneous loop current density as a function of  the magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  η-pairing-II state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='— The η-pairing II has the struc-  ture with up-up-down colinear phases plus CDW (Red  hexagon in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 7(b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' There is the relation nA = nB <  nC for the electron filling at each sublattice shown in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 7(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  We note that this site-dependent feature is  characteristic for the II (and IV) state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The phases of the  pair potential at A and B sublattices are “ferromagnetic”,  while the phase at C sublattice is “antiferromagnetic”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  The resulting ordered state is regarded as the emergence  of the honeycomb lattice formed by equivalent A and B  sublattices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  η-pairing-III state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='— This is the η-pairing with a stag-  gered ordering vector and CDW (Magenta square in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 7(b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  The order parameter ∆ at C sublattice is  zero, but the others (A,B) are finite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The electron-rich  sublattices A and B form a simple bipartite η-pairing  state on an emergent honeycomb lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Since this state  does not become a ground state anywhere for the present  choice of U = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='83, we do not further investigate this  state in the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  η-pairing-IV state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='— This is the η-pairing with a sim-  ple stripe alignment (Cyan rhombus in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 7(b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' This  η-pairing is accompanied by CDW around h = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='9 shown  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6  h  °1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  °1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  °0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  Kxx, Kyy  (a) -pairing Ⅰ  η  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' (25)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6  h  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  Kxx, Kyy  (b) -pairing Ⅱ  η  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6  h  °1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  °1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  °0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  Kyy  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6  h  °1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  °1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  °0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  Kxx  (c1) -pairing Ⅳ  η  (c2) -pairing Ⅳ  η  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6  h  °1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  °1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  °0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  Kyy  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  h  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  K  Kdia  Kpara  K  KEFP  KOFP  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  h  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  K  Kdia  Kpara  K  KEFP  KOFP  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  h  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='K  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='Kdia  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='Kpara  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='K  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='KEFP  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='KOFP  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='<latexit sha1_base64="hwzoaSF0Y+Oi/TJGH  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='/A8l7Sl9vw=">AD0HichVO5TsNAEH3BnOEIR4NEg4iQKFC0QZxdEA0lVwCJIGSbTbKL9kbFIQio  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='EW08A+IH+EHKPgEagoaCmY35lIUM5bt2TfvjWd2x1bgiEgy9pLqMrp7ev6B9KDQ8MjmdGx8f3Ir4c  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2L9q+4eHlhlxR3i8KIV0+GEQctO1H5g1TZU/OCMh5HwvT15HvBj16x4oixsUxK0U2qejGZjmb  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='nfysZNFbFv+WKqEk7hw0YdLjg8SPIdmIjoOkIeDAFhx7gLCRP6DhHE2nS1onFiWESWqNnhVZHMer  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='RWuWMtNqmrzh0h6Scxix7Zg/sjT2xR/bKPjrmutA5VC3n9LZaWh6cZG4md9/Vbn0lqj+qBJrlihjV  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='dcqPZAI6oLW+s7KxWnQr0Jila13qKYRbiTsEuK5SbG/3Y+39ZTZ2WFdtktKpPq/FPFYpbI18m8n  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6fX1LNEa1djSbx1M429Kz5xA4SuV8d/+am9ayvKVv6nux2Z38hl1/OLW4vZgvrV62p78cUZjBHk72C  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='AjaxhSJlLuMWd7g3doyGcWlct6hdqfhPmcAfM24+AbMryxg=</latexit>}  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Magnetic field dependence of the Meissner kernels  Kxx and Kyy for the η-pairings I, II, IV on the triangular lat-  tice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The yellow shaded rectangle indicates the regime where  each η-pairing becomes the ground state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The symbols are  the same as those in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 4(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' For the η-pairing IV, Kxx and  Kyy are separately plotted in (c1) and (c2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 7(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' As shown below, this stripe phase show an  anisotropic behavior in linear response coefficients, while  the other η-pairing states are isotropic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Meissner response  Now we discuss the Meissner response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Figure 9(a,b,c)  shows the Meissner kernels Kxx, Kyy for the η-pairing I,  II and IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The yellow-highlighted parts indicate the re-  gion where each η-pairing becomes the ground state as  identified from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 7(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  The result for the η-pairing  III is not shown because it does not become a ground  state at U = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' We confirm that the Meissner re-  sponse is basically diamagnetic if the η-pairing becomes  the ground state as shown in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 9(a,b,c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Thus the en-  ergetic stability and diamagnetic response are reasonably  correlated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' In the following, we discuss the properties of  the Meissner kernel for each state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  The Meissner kernels for both η-pairing I and η-pairing  II shown in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 9(a) and (b) satisfy the relation Kxx =  Kyy, which means an isotropic linear response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' For the η-  pairing I, the Meissner kernel becomes positive in the re-  gions h < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='95 < h < 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='12, while the kernel becomes  negative in the ground state region (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 9(a)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Although  the local current density is finite for the η-pairing I state,  it does not affect the expression of the Meissner kernel in  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' (10) since the total current j(q = 0) is zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Next we disucuss the η-pairing IV state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The Meiss-  10  ner kernel jumps at h = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8 due to the emergence of  the CDW order parameter as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 9(c1,c2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' It  is notable that the η-pairing IV with the stripe pattern  shows a difference between x and y directions as shown  in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 9(c1,c2), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' This characteristic behav-  ior can be intuitively understood from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 7(a), where  the current along the x-axis flows with experiencing a  staggered pair potential, whereas the current in the y-  direction feels an uniform pair potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' In the Meissner  response, Kxx shows a characteristic behavior of the η-  pairing, while Kyy is qualitatively the same as the kernel  of BCS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Thus, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 9(c1), the diamagnetic  response in the x-axis direction is related to to the odd-  frequency pair, whereas the diamagnetic response in the  y-axis direction, shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 9(c2), is related to even-  frequency pair.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  SUMMARY AND OUTLOOK  We have studied the square and the triangular lattice  of the attractive Hubbard model by using the mean-field  theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Several types of η-pairing have been found in  the triangular lattice where a simple bipartite pattern  is not allowed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Using the formulation of the Meissner  kernel for a general tight-binding lattice, we have inves-  tigated the electromagnetic stability of η-pairings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' We  have confirmed that the electromagnetic stability of the  η-pairing correlates with the internal energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' In a narrow  parameter range, we also find that the η-pairing state can  show an unphysical paramagnetic response if we assume  the two or three sublattice structure in the mean-field  calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  In this case, another solution with longer  periodicity needs to be sought.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  When the current path experiences the staggered  phase of the superconducting order parameter, the odd-  frequency component of the pair amplitude contributes  to the diamagnetic response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' This is in contrast to the  conventional BCS case in which the even-frequency com-  ponent of the pair amplitude contributes to the diamag-  netism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  We have further clarified that one of the η-  pairing states on the triangular lattice has a stripe pat-  tern and shows an anisotropic Meissner response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' In this  case, the odd-frequency pair contributes diamagnetically  or paramagnetically depending on the direction of cur-  rent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  We comment on some issues which are not explored in  this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' We expect that the η-pairing without a simple  staggered phase will appear on pyrochlore, kagome and  quasicrystalline lattice, whose phase-alignment could be  qualitatively different from the triangular lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' In ad-  dition, there is another model that shows η-pairing in  equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' A two-channel Kondo lattice (TCKL) is an  example of a model in which η-pairing appears even in  the absence of a Zeeman field [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Our preliminary cal-  culation for the TCKL shows a number of ordered states  which have similar energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  These additional studies  provide more insight into the exotic superconductivity  (a)  (b)  (c)  °1  0  1  !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='n  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  Re[F " #(i!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='n) ° F # "(i!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='n)]/  p  2  h=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='417  h=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='375  h=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='333  h=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='25  h=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='167  h=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='083  h=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  h=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='917  h=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='833  h=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='75  h=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='667  °0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2°0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2  !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='n  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  Re[F " #(i!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='n) ° F # "(i!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='n)]/  p  2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='417  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='375  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='333  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='25  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='167  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='083  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='917  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='833  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='667  °1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0 °0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  D¥°pairing ° Dnormal  °0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2°0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2  !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='n  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='8  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='4  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='0  Im[F # #(i!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='n) ° F " "(i!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='n)]/  p  2  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' (a) The difference between the DOSs of the η-pairing  and normal states in the cubic lattice model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The values of  the DOS are shifted by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='2 for each magnetic field, and the  gray dotted lines are the zero axes for each magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  We also show the Matsubara frequency dependence of (b) the  imaginary part of [F↓↓(iωn) − F↑↑(iωn)] /  √  2 and (c) the real  part of [F↑↓(iωn) − F↓↑(iωn)] /  √  2 for each magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The  values of the pair amplitudes are shifted by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  characteristic for the η-pairing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  ACKNOWLEDGEMENT  This work was supported by KAKENHI Grants No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  18H01176, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 19H01842, and No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 21K03459.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Appendix A: Self-consistent equations in mean-field  theory  We derive self-consistent equations for the general in-  teracting Hamiltonian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Let us begin with the Hamilto-  nian  H =  �  12  ε12c†  1c2 +  �  1234  U1234c†  1c†  2c4c3  (A1)  where site-spin indices are written as 1 = (i1, σ1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' The  mean-field Hamiltonian is introduced as  HMF =  �  12  �  E12c†  1c2 + ∆12c†  1c†  2 + ∆∗  12c2c1  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  (A2)  We assume ⟨H ⟩ = ⟨HMF⟩ where the statistical average  is taken with HMF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Then the self-consistent equation is  obtained as  E12 = ∂⟨H ⟩  ∂⟨c†  1c2⟩  = ε12 +  �  34  (U1324 + U3142 − U1342 − U3124)⟨c†  3c4⟩  (A3)  ∆12 = ∂⟨H ⟩  ∂⟨c†  1c†  2⟩  =  �  34  U1234⟨c4c3⟩  (A4)  11  where the Wick’s theorem is used for the derivation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Al-  though the variational principle for the free energy also  gives the same equation, the above formalism gives a sim-  ple procedure to derive the self-consistent equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Appendix B: Attractive Hubbard model on Cubic  lattice  We analyze the η-pairing on the cubic lattice, whose  DOS does not have a van Hove singularity near zero en-  ergy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Here we choose the parameter U = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='375 and  the electron concentration is half-filled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' As a result, the  DOS for the η-pairing around zero energy for each mag-  netic filed on the cubic lattice is smaller than the DOS of  the normal state as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 10(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' For reference,  we also show in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  10(b) and (c) the pair amplitude  similar to Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 4(b) in the main text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' In addition, the  odd-frequency pair amplitude increases when DOS near  zero energy is enhanced as seen from Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 10(a) and (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [1] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Fulde and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Ferrell, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 135, A550 (1964).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [2] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Larkin and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Ovchinnikov, Zh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Eksp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Teor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Fiz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  47, 1136 (1964).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [3] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Yang, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 63, 2144 (1989).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [4] For a review, see, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Agterberg, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Davis, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Edkins, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Fradkin, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Van Harlingen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Kivelson,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Lee, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Radzihovsky, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Tranquada, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Wang,  Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Condens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Matter Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=', 11, 231 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [5] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Singh and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Scalettar, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 66,  3203 (1991).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [6] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Coleman, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Miranda, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Tsvelik, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  70, 2960 (1993).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [7] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Hoshino and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Kuramoto, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 112,  167204 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [8] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Czart, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Kapcia, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Micnas, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Robaszkiewicz,  Physica A: Statistical Mechanics and its Applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  585, 126403 (2022)  [9] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Kaneko, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Shirakawa, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Sorella, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Yunoki,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 122, 077002 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [10] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Werner, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Li, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Golez and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Eckstein, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  B 100, 155130 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [11] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Li, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Golez, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Werner, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Eckstein, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  B 102, 165136 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [12] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Nakagawa,  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Tsuji,  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Kawakami,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Ueda,  arXiv:2103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='13624 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [13] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Yang and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Song, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' B 105, 195132  (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [14] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Jiajun, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' M¨uller, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Kim, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' L¨auchli, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Werner, arXiv:2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='10176 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [15] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Motome, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Nakamikawa, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Yamaji, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Uda-  gawa, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 105, 036403 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [16] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' dos Santos Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' B 48, 3976 (1993).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [17] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Affleck and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Marston, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' B 37, 3774  (1988).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [18] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Chakravarty, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Laughlin, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Morr, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Nayak, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' B 63, 094503 (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [19] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Morr, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 89, 106401 (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [20] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Zhou and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Wang, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' B 70, 020501(R)  (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [21] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Yokoyama, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Tamura, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Ogata, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Jpn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 85, 124707 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [22] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Kobayashi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Yokoyama, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Toga, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' :  Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 1054, 012016 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [23] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Fukuda, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Yamazaki, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Tsuchiura, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Ogata,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' : Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 1293, 012026 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [24] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Hoshino, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' B 90, 115154 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [25] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Berezinskii, ZhETF Pis Red.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 20, 628 (1974), [JETP  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 20, 287 (1974)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [26] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Kirkpatrick and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Belitz, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 66,  1533 (1991).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [27] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Balatsky and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Abrahams, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' B 45, 13125  (1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [28] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Tanaka, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Sato, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Nagaosa, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Jpn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  81, 011013 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [29] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Linder and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Balatsky, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 91, 045005  (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [30] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Cayao, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Triola and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Black-Schaffer, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=':  Spec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Top.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 229, 545 (2020)  [31] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Walter, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Prusseit, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Semerad, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Kinder, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Ass-  mann, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Huber, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Burkhardt, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Rainer, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Sauls, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 80, 3598 (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [32] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Tanaka, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Asano, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Golubov, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Kashiwaya,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' B 72, 140503 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [33] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Bergeret, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Volkov, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Efetov, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 77, 1321 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [34] Ya.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Fominov, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Tanaka, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Asano, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Eschrig,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' B 91, 144514 (2015)  [35] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Tanaka and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Golubov, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 98,  037003 (2007)  [36] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Tanaka, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Tanuma, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Golubov, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  B 76, 054522 (2007)  [37] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Higashitani, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Jpn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 66, 2556 (1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [38] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Yokoyama, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Tanaka, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Nagaosa, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 106, 246601 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [39] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='-I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Suzuki and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Asano, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' B 91, 214510  (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [40] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Di Bernardo, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Salman, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Wang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Amado, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Egilmez, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Flokstra, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Suter, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Zhao,  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Prokscha, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Morenzoni, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Blamire, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Linder,  and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Robinson, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' X 5, 041021 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [41] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Krieger, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Pertsova, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Giblin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Dbeli, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Prokscha, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Schneider, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Suter, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Hesjedal, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Balatsky, and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Salman, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 125, 026802  (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [42] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Micnas, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Ranninger, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Robaszkiewicz, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 62, 113 (1990).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [43] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Shiba, Prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 48, 2171 (1972).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  12  [44] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Claveau, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Arnaud, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Matteo, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 35,  035023 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [45] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Bloch, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Dalibard, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Zwerger, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  80, 885 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [46] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Scalapino, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' White, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Zhang, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 68, 2830 (1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [47] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Scalapino, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' White, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Zhang, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' B 47, 7995 (1993).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [48] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Kostyrko, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Micnas, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Chao, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' B  49, 6158 (1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [49] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Hoshino, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Yada, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Tanaka, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' B 93,  224511 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [50] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Tsuruta, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Hyodo, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Miyake, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Jpn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  83, 063706 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [51] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Chakraborty and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Black-Schaffer, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' B  106, 024511 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content='  [52] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Pearl, App.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
+page_content=' 5, 65 (1964).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FAT4oBgHgl3EQfFRw-/content/2301.08426v1.pdf'}
diff --git a/4dFAT4oBgHgl3EQflx3j/content/tmp_files/2301.08620v1.pdf.txt b/4dFAT4oBgHgl3EQflx3j/content/tmp_files/2301.08620v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..cfb8514ab9166e0452fb268c0d5093c7d7654bc0
--- /dev/null
+++ b/4dFAT4oBgHgl3EQflx3j/content/tmp_files/2301.08620v1.pdf.txt
@@ -0,0 +1,1060 @@
+Adjoint-based Identification of Sound Sources for
+Sound Reinforcement and Source Localization
+Mathias Lemke and Lewin Stein
+Institut f¨ur Str¨omungsmechanik und Technische Akustik,
+Technische Universit¨at Berlin, Germany
+mathias.lemke@tnt.tu-berlin.de
+Abstract. The identification of sound sources is a common problem in
+acoustics. Different parameters are sought, among these are signal and
+position of the sources. We present an adjoint-based approach for sound
+source identification, which employs computational aeroacoustic tech-
+niques. Two different applications are presented as a proof-of-concept:
+optimization of a sound reinforcement setup and the localization of (mov-
+ing) sound sources.
+Keywords: Computational Aeroacoustics, Adjoint Equations, Source
+Identification, Sound Reinforcement, Source Localization
+1
+Introduction
+A common issue in acoustics is the identification of fixed or moving sound
+sources. In general, several parameters have to be determined; among these are
+the source signal and the position of the sources. This general problem occurs
+in many applications, from environmental to industrial acoustics.
+In this contribution, we discuss an adjoint-based approach for sound source
+identification. The time-domain method is based on the (adjoint) Euler equa-
+tions, which are solved by means of computational aeroacoustic techniques (CAA).
+The approach allows considering complex base flows, such as non-homogeneous
+base flow, thermal stratification as well as complex geometries.
+Adjoint-based methods have been used in the field of fluid mechanics for
+decades. They have proven to be an effective approach for the analysis of flow
+configurations and determining optimal model parameters in various applications
+[7]. Adjoint-based techniques are used to optimize flow configurations by means
+of geometry modifications [9] or for active flow control applications [1]. They are
+applied for the analysis and optimization of reactive flow configurations [13,12]
+and data assimilation applications [23,14,8]. Furthermore, they are employed in
+the field of aeroacoustics [4,20] and sound reinforcement applications [15,21].
+Here, we restrict ourselves to two applications from the areas of sound re-
+inforcement and sound source localization with generic setups as a proof-of-
+concept.
+In the context of sound reinforcement, line arrays are used for the synthesis of
+sound fields. The identification of the geometric arrangement and the electronic
+arXiv:2301.08620v1  [cs.SD]  20 Jan 2023
+
+2
+Mathias Lemke et al.
+drive of the loudspeaker cabinets to optimally (re-)produce a sound field is an
+ill-posed, inverse problem. Typically frequency domain approaches are employed
+[3,22].
+For the localization of moving and non-moving sound sources, usually, micro-
+phone array methods like beam-forming are used. Depending on the specific task,
+different algorithms, working in the time domain or in the frequency domain,
+are applied. See [16] for a recent overview.
+The manuscript is organized as follows: In Sec. 2, the adjoint approach is in-
+troduced, and the adjoint Euler equations are derived. After a short description
+of the numerical implementation in Sec. 3, the derived framework is employed for
+an application in the context of sound reinforcement in Sec. 4. The applicability
+of the approach for localization of sound sources is discussed in Sec. 5.
+2
+Adjoint Approach
+2.1
+General Adjoint Equations
+Adjoint equations can be derived in different ways, e.g., the continuous or the
+discrete approach. Despite different discretizations, the approaches are consistent
+and applicable, see [7] for a discussion. In addition, automatic differentiation
+techniques are used to create adjoint codes from existing simulation programs.
+Recently, a mode-based approach to derive adjoint operators was presented [19]
+as an enhancement of a direct operator construction method [12].
+Here, the adjoint equations are introduced in a discrete manner. A matrix-
+vector notation is used, in which the vector space is the full solution in space
+and time. The section is based on [7,11].
+In general, the adjoint equations arise by a scalar-valued objective function
+J, which is defined by the user and encodes the target of the analysis, e.g., an
+optimization. It is given by the scalar product between a weight vector g and a
+system state vector q
+J = gTq.
+(1)
+The system state q is the solution of the governing system
+Aq = s
+(2)
+with A as governing operator and s as right-hand side forcing. In order to opti-
+mize J by means of s in terms of a brute-force approach, the governing equation
+has to be solved for all possible s.
+Instead, to reduce the computational effort, the adjoint equation can be used
+ATq∗ = g,
+(3)
+with the adjoint variable q∗.
+With
+J = gTq =
+�
+ATq∗�T q = q∗TAq = q∗Ts
+(4)
+
+Adjoint Sound
+3
+a formulation is found, which enables the computation of the objective J without
+solving the governing system for every possible s. With the solution of the adjoint
+equation, the objective can be calculated by a scalar product. Thus, the adjoint
+approach enables efficient computation of gradients for J with respect to s.
+2.2
+Adjoint Euler equations for Acoustic Applications
+The section is based on [11,21]. The objective function J is defined in space and
+time with dΩ = dxidt in the whole computational domain:
+J = 1
+2
+�� �
+q − qtarget�2 dΩ.
+(5)
+The variable q contains the full state q = [ϱ, uj, p] of the system governed by the
+Euler equations. Therein, ϱ denotes the density, uj the velocity in the direction
+xj, and p the pressure.
+For the following aeroacoustic analyses the evaluation of the objective func-
+tion is restricted to the pressure, resulting in
+J = 1
+2
+�� �
+p − ptarget�2 σ dΩ.
+(6)
+The additional weight σ(xi, t) defines where and when the objective is evalu-
+ated. In general, the objective function has to be supplemented by a regular-
+ization term, which is omitted here for the sake of clarity. The target ptarget is
+application-specific. For optimization tasks, as presented in Sec. 4, it is defined
+corresponding to a desired sound field, e.g., optimal listening experience for the
+auditorium of an open-air concert. For the source localization application pre-
+sented in Sec. 5, the target pressure is defined by microphone measurements.
+The microphone positions are included by means of the weight function σ. In
+both cases, a minimum of J is desired.
+This minimum is to be achieved under the constraint that the Euler equa-
+tions
+∂t
+�
+�
+ϱ
+ϱuj
+p
+γ−1
+�
+� + ∂xi
+�
+�
+ϱui
+ϱuiuj + pδij
+uipγ
+γ−1
+�
+� − ui∂xi
+�
+�
+0
+0
+p
+�
+� =
+�
+�
+0
+0
+sp
+�
+� ,
+with γ as heat capacity ratio, are fulfilled. The summation convention applies.
+For details on the formulation, in particular, the reformulation of the energy
+equation in terms of pressure, see [13].
+To ease the derivation, the above system of partial differential equations is
+abbreviated by
+E(q) = s.
+(7)
+The terms s = [0, 0, sp] on the right side of the Euler equations character-
+ize monopole sound sources, which allow controlling the system state, respec-
+tively, the solution of the equations. In general, also mass and momentum source
+
+4
+Mathias Lemke et al.
+terms could be considered. The overall goal is to obtain a solution of the Euler
+equations, which reduces the objective (6) by adapting s. An optimization of s
+corresponds to an optimization of the loudspeakers’ output signals.
+To use the adjoint approach for optimizing s, the objective function (6) and
+the governing system (7) have to be linearized. This results in
+δJ =
+�� �
+q − qtarget�
+σ
+�
+��
+�
+=g
+δpdΩ,
+(8)
+and
+Elinδq = δs.
+(9)
+The weight g = (q − qtarget)σ encodes the difference between the current numer-
+ical solution and the target field. Here, it is evaluated only in terms of pressure,
+as discussed above. Combining the linearized system and the objective in a La-
+grangian manner leads to
+δJ = gTδq − q∗T (Elinδq − δs)
+�
+��
+�
+=0
+(10)
+= q∗Tδs + δqT �
+g − ET
+linq∗�
+.
+Please note, the spatial and temporal integrals are not shown for the sake of
+simplicity.
+The desired adjoint equation E∗ = ET
+lin results from demanding
+g − ET
+linq∗ = 0,
+(11)
+with q∗ = [ϱ∗, u∗
+j, p∗] as adjoint state variable.
+For a detailed derivation of the adjoint Euler equations see [11]. They are
+given by
+∂tq∗ = ˜A
+�
+−(Bi)T∂xiq∗ − ∂xi(Ci)Tq∗ + ˜Ci∂xic − g
+�
+(12)
+with ˜A =
+�
+AT�−1 and ˜Ci as resorting
+q∗
+αδCi
+αβ∂xicβ = q∗
+αδqκ
+∂Ci
+αβ
+∂qκ
+∂xicβ
+(13)
+abbreviated as δqκ ˜Ci
+κβ∂xicβ. The matrices A, Bi and Ci are given in the ap-
+pendix.
+Finally, the change of the objective function is given by
+δJ = q∗Tδs.
+(14)
+Thus, the solution of the adjoint equation can be interpreted as gradient of J
+with respect to the source terms s
+∇sJ = q∗.
+(15)
+Initial and boundary conditions of the adjoint Euler equations as well as the
+derivation of the adjoint compressible Navier-Stokes equations are discussed in
+[11].
+
+Adjoint Sound
+5
+sources
+initial guess
+s0=0
+solution
+Euler equations
+N(q, sn) 
+target
+qtarget
+solution adjoint
+Euler equations
+N*(q,q*,Δ q)
+gradient
+q*
+sources
+update sn+1
+Δ q = q ­ qtarget
+optimal
+s
+source
+positions
+p
+convergence
+loop 1
+Fig. 1. Iterative procedure for the determination of an optimal s. Computationally
+intensive steps are marked in gray. The first gradient provides information on (optimal)
+source positions, see Sec. 5 for a detailed discussion.
+2.3
+Iterative Process
+The adjoint-based gradient is employed in an iterative manner. First, the Euler
+equations (7) are solved forward in time, usually with s0 = 0. Subsequently,
+the adjoint equations (12) are calculated backward in time, deploying the direct
+solution and g. Based on the adjoint solution, the gradient ∇sJ is determined
+and used to update the source distribution sn by means of a steepest gradient
+approach:
+sn+1 = sn + α∇sJ,
+(16)
+with α denoting an appropriate step size and n the iteration number. The gradi-
+ent is calculated for the whole computing region and the entire simulation time.
+For the determination of sound sources with a known position, the gradient is
+evaluated only there. The procedure is repeated, using the current sn, until a
+suitable convergence criterion is reached. Typically, for acoustic problems, con-
+vergence is reached within or less 20 loops.
+The identification of global optima is not ensured as the proposed technique
+optimizes to local extrema only. The computational costs of the approach are
+independent of the number of sources and their arrangement. However, they
+depend on the size and resolution of the computational domain in space and
+time, defined by the considered frequency range. The computational problem is
+fully parallelizable.
+2.4
+Source Localization
+In particular, when s0 = 0 holds, the first adjoint solution contains information
+on the position of the sources. By the pointwise summation of the absolute
+adjoint sensitivities p∗ in the spatial domain over all computed time steps
+¯p =
+tn=end
+�
+tn=0
+|p∗|,
+(17)
+
+6
+Mathias Lemke et al.
+the positions featuring maximum impact on the objective function can be iden-
+tified by means of maxima of ¯p. These correspond to the most likely (monopole)
+source locations. Thus, the adjoint solution allows the localization of sound
+sources, see Sec. 5. A subsequent iterative adaptation of the sources can be
+interpreted as adjoint-based monopole synthesis.
+3
+Adjoint CAA framework
+The set of governing equations (7) is implemented by means of a new MPI-
+parallelized Fortran program. The discretization is realized by a finite difference
+time domain approach (FDTD). For the spatial derivatives, a compact scheme
+of 6th order is employed [10]. The corresponding linear system of equations is
+solved by BLAS routines using an LU-decomposition. For the time-wise inte-
+gration, the standard explicit Runge-Kutta-scheme of fourth-order is used.
+To ensure stability, a compact filter is employed [5]. Boundaries are treated by
+characteristic boundary conditions [18]. The MPI implementation is realized by
+collective communication via all2all v. The parallelization strategy is found to
+be efficient for the governing equations (7), see Fig. 2, and comparable to other
+implementations using collective communication, e.g. [17].
+Thus, the code is prepared to handle large scale problems, e.g., open-air festi-
+val sites in the context of sound reinforcement applications or source localization
+for vehicle aeroacoustics in wind tunnels. However, the examples presented in
+the following are computed using a single workstation or a few cluster nodes.
+Fig. 2. (Left) Strong scaling behaviour. The overall number of grid points is kept
+constant while increasing the number of MPI processes. Nearly linear scaling is found.
+(Right) Weak scaling behaviour. The number of grid points on each process is kept
+constant while increasing the number of MPI processes. An admissible reduction of the
+parallelization efficiency is found.
+The adjoint equations are solved using the same discretization. A detailed
+discussion on the adjoint initial- and characteristic boundary conditions can be
+found in [11].
+
+8
+speedup
+6
+4
+caa
+2
+--ideal
+400
+1200
+2000
+2800
+3600
+MPl processesefficiency
+0.9
+0.8
+caa
+.--ideal
+0.7
+40
+80
+160
+320
+640
+1280 2560
+MPl processesAdjoint Sound
+7
+4
+Application I: Sound Reinforcement
+This section presents a test case regarding the optimization of sound reinforce-
+ment setups. The overall goal is to identify optimal drives (amplitude and phase)
+for given loudspeakers in order to synthesise a desired sound field. The loudspeak-
+ers are approximated by means of monopole sources, which is feasible for low
+frequencies.
+The spatial domain under consideration is 1.6 × 1.6 × 1.6 m3. The domain
+is resolved by 197 × 197 × 99 equidistantly distributed points. The time step,
+and by this, the sampling rate, is given by 48 kHz, corresponding to a CFL-
+condition smaller than 1. The computational time span considered is 31.25 ms.
+The reference values for density and pressure correspond to a speed of sound
+of 343 m/s. All boundaries are treated as non-reflecting. In addition, a sponge
+layer is applied at all boundaries.
+For the test case reference signals for five sources, located in a curved ar-
+rangement in the center x1-x2 plane, are predefined. The signals are charac-
+terised by different amplitudes and phase delays resulting in a steered sound
+field, see Fig. 3 (left). In order to investigate the frequency band 1-3 kHz, a
+corresponding logarithmic sine-sweep is specified as the reference signal. Using
+this setup, a reference sound field is computed by a Complex Directivity Point
+Source (CDPS) algorithm [2]. The resulting reference sound field serves as the
+target for the adjoint-based framework, with the aim to identify the reference
+signals (amplitudes and phases) based on the reference target sound field only.
+After 15 iterative loops of the adjoint framework, the objective function is
+reduced to nearly 3% with respect to the initial solution with s = 0, see Fig. 3
+(right). The general features of the target reference sound field are captured, see
+Fig. 4. A detailed spectral analysis of the occurring deviations at two selected
+microphone positions, presented in Fig. 4, show amplitude deviations less than
+1 dB within the confidence interval from 1.3 to 2.7 kHz. The normalized phase
+derivations, with respect to 2π, are in the limits of -0.07 to 0.07.
+A discussion on how to derive optimal electronic drives from the adjoint-
+based signals s is given in [21]. Therein, the capability of the approach to consider
+complex base flows by means of wind and temperature stratification is shown.
+5
+Application II: Source Localization
+In this section, the localization of fixed and moving sound sources is shown. Two
+generic setups serve as a proof of concept. For the first setup with four stationary
+sound sources and the second setup with a moving source, it is shown that the
+adjoint-based approach is able to identify the sources and track their path in
+case of moving.
+In both cases, the measurements are provided by a reference computation
+with predefined sound sources. Synthetic microphone signals are extracted from
+this reference solution. A spatially discrete planar array with 64 microphones is
+used. The general setup is based on the array benchmark test case B7 provided
+
+8
+Mathias Lemke et al.
+Fig. 3. (Left) Sound reinforcement setup including a selected time step of the CDPS-
+based reference sound field shown at the center x1-x2 plane of the computational do-
+main. The five monopole speakers in a curved arrangement are denoted by (*). Different
+driving functions (in amplitude and phase) for the speaker result in a steered sound
+field. The area/volume marked by the dashed line corresponds to the spatial weight σ
+in the objective function. Please note, the employed CDPS technique for computing
+the reference sound field does not provide reliable solutions near the source positions;
+therefore, p′
+ref is discontinuous for x1 = [0.32, 0.62] m. (Right) Progress of the objective
+function with a logarithmic y-axis. Convergence is reached. The objective is reduced
+by nearly two orders of magnitude with respect to the initial guess s = 0.
+Fig. 4. Reference target (left) and resulting optimized (right) sound field at t = 15.63
+ms for the center x1-x2 plane. The general features of the reference field are (re-)
+captured. The influence of the employed sponge layer in the adjoint-based sound field
+is visible. The dashed line encodes the spatial weight σ within the objective function.
+The marked positions correspond to synthetic microphone positions x1,2 = [1.1, 1.1]
+and x1,2 = [0.8, 0.8] which are used for spectral analysis, see text for details.
+
+1.5
+0.8
+米‘
+speaker
+0.6
+0.4
+a
+m
+0.
+8
+0
+d-
+0.5
+0.P
+-0.4
+0.5
+1
+1.5
+X, /m1
+0.5
+0.25
+r/
+0.1
+0.05
+0.02
+5
+10
+15
+iteration1.5
+0.5
+1
+a
+P
+0
++
+ref
+p
+0.5
+-0.5
+0.5
+1
+1.5
+X, / m1.5
+0.5
+1
+a
+P
+0
++
+opt
+2
+p
+0.5
+-0.5
+0.5
+1
+1.5Adjoint Sound
+9
+Fig. 5. (Left) Normalized amplitude difference between resulting optimized and refer-
+ence target sound field at selected microphone positions, see Fig. 4. (Right) Normalized
+phase difference between resulting optimized and reference target sound field at the
+selected microphone positions.
+by the Brandenburg university of technology, see [6]. Modifications are discussed
+below. An example in which experimental data are used is shown in [11].
+The spatial domain under consideration is 1.7 × 1.7 × 1.25 m3. The domain
+is resolved by 240 × 240 × 176 equidistantly distributed points. The time step,
+and by this, the sampling rate of the microphone measurements, is given by
+53.33 kHz, corresponding to a CFL-condition smaller than 1. In both cases, no
+base flow is considered. The reference values for density and pressure correspond
+to a speed of sound of 343 m/s. The spiral-like microphone array is located at
+x3 = 0 m and centered in the corresponding plane. The spatial distribution of
+the microphones is described in more detail in [6]. All boundaries are treated as
+non-reflecting. In addition, a sponge layer is applied at all boundaries.
+5.1
+Four sources
+As in the array benchmark test case B7 four monopole sources are located in
+the x1-x2-plane at x3 = 0.75 m, see Fig. 6 (left). For the reference computation,
+the original benchmark source signals are replaced by incoherent random sig-
+nals, frequency-band limited between 750 and 2500 Hz, see Fig. 6 (right). The
+computational time span is 14.06 ms.
+Using a corresponding reference forcing s = �
+i si a simulation of the Euler
+equations (7) is carried out. From the results, discrete microphone signals are
+extracted, see Fig. 7 (left), which are the result of the superposition of all sources
+and the associated signals.
+The 64 signals are encoded in the objective function J (6) using the spatial
+weight σ. To avoid an unstable discrete forcing of the adjoint equations, σ is
+chosen as Gauss-distribution with a half-width of 2∆x for each microphone
+position. After determining the solution of the direct equations with an initial
+guess for s = 0, here, constant environmental conditions for all time steps, the
+
+mic 1
+B
+0.4
+mic 2
+ta
+0.2
+p
+opt
+0
+-0.2
+-0.4
+-0.6
+1500
+2000
+2500
+f /Hz0.1
+mic 1
+mic 2
+2π
+0.05
+tar
+0
+opt
+-0.05
+-0.1
+1500
+2000
+2500
+f / Hz10
+Mathias Lemke et al.
+Fig. 6. (Left) Acoustic setup for source localization of four sources (*) by 64 micro-
+phones (o) located in the planes x3 = 0.75 m respectively x3 = 0 m. (Right) Normalized
+signals si of the four reference sources, shown for the whole computational time.
+adjoint equations are solved backwards in time. From the resulting gradient, the
+source positions can be derived, as discussed before. That way, the reference
+source positions are identified, see Fig. 7 (right).
+Fig. 7. (Left) Captured pressure signal at the center microphone in the array. The
+initial silence results from the distance between the sources and the array. (Right) Re-
+sulting pointwise summation of the absolute adjoint sensitivities p∗ (17). The reference
+source positions (∗) are recovered.
+Please note, the analysis is based on the first adjoint-based gradient only.
+The required computational time for the analysis is less than 15 min on a 16
+core workstation. Iterative optimization of s might improve the results.
+5.2
+Single moving source
+Again, the aforementioned test case B7 from [6] serves as a base for the following
+test setup. The planar microphone array is located in the same plane (x3 = 0) but
+
+米
+米
+0.5
+米
+米
+8
+00
+0
+8
+0
+0
+0
+0
+00
+00
+00
+00
+0
+0
+0
+0
+0
+00
+0
+0.
+00
+00
+0
+0
+0
+00
+8
+0.5
+0.5
+0
+0
+-0.5
+-0.5
+×2 /m
+X, / mS
+(normalized)
+0.5
+S
+2
+S
+1
+3
+.
+S
+0
+4
+..
+: i
+11
+-0.5
+11
+S
+II
+.....
+11
+二
+-1
+2
+6
+10
+14
+t/ mscenter mic
+0.1
+a
+P
+8
+d-(
+p
+-0.1
+2
+6
+10
+14
+t/msref. sources
+0.5
+0.8
+(normalized)
+0.6
+米
+米
+0
+*
+米
+0.4
+p
+-0.5
+0.2
+-0.5
+0
+0.5
+/ mAdjoint Sound
+11
+scaled by a factor of 0.8, resulting in smaller distances between the microphones.
+The incoherent sources are replaced by a single source with a harmonic 2 kHz
+reference signal. The source is moving in the x1-x2-plane, see Fig. 8 (left). The
+movement is described by an acceleration and deceleration, taking place along
+the x1 axis. It starts at the beginning of the computational time and ends with
+the simulation after 8.44 ms. The highest speed of the movement is reached
+midway.
+Again a reference solution provides synthetic microphone signals, which are
+encoded in the objective function. Using constant environmental conditions as
+solution of the direct equations (s0 = 0), the adjoint equations are solved. Eval-
+uation of the adjoint sensitivity p∗ over time at the reference source position
+provides information of the reference signal, see Fig. 8 (right). The phase of
+the reference signal is determined with very good agreement. The amplitude
+shows deviations at the beginning and end of the simulation. The influence of
+the directional characteristic of the used microphone array is presumed.
+Fig. 8. (Left) Acoustic setup for source localization of a single moving source (*) by
+means of 64 microphones (o) located in the planes x3 = 0.75 m, respectively x3 = 0
+m. The movement of the source is visualized by it waypoints, chosen with a constant
+time interval. (Right) Normalized adjoint-based sensitivity p∗ at the reference source
+positions over time in comparison to the reference forcing. See text for a detailed
+discussion.
+Besides, the identification of the source signal also its position might be
+tracked. In Fig. 9 the adjoint-based sensitivity p∗ is shown for the plane x3 = 0.75
+m for different time steps. Occurring maxima give rise to the actual sound source
+position, besides its signal.
+Again, the analysis is based on the first adjoint-based gradient only. The
+required computational time for the analysis is less than 10 min on 8 cluster
+nodes with 8 cores each.
+
+m
+0.5
+0
+0
+CD
+0
+000
+00
+0
+00
+0
+8
+0
+00
+0.5
+0.5
+0
+0
+-0.5
+-0.5
+m
+m
+25 二 1
+I 
+0.5
+(normalized)
+?
+P-0.5
+adjoint-based
+4
+--- reference
+-
+1!
+2
+4
+6
+8
+t/ms12
+Mathias Lemke et al.
+Fig. 9. Normalized adjoint-based sensitivity p∗ at the plane x3 = 0.75 for different
+time steps. The reference source location is marked by (*) in a white circle. In the
+inset, the normalized reference signal is shown.
+
+t= 3.88125 / ms
+0.5
+0.5
+(normalized)
+m
+0
+0
++
+p
+-0.5
+-0.5
+/
+米
+3.5
+4
+4.5
+t / ms
+-0.5
+0
+0.5
+, / mt= 3.99375/ ms
+0.5
+0.5
+(normalized)
+m
+0
+0
+/
++
+米
+p
+-0.5
+-0.5
+3.5
+4
+4.5
+t / ms
+-0.5
+0
+0.5
+X, / mt= 4.12500 / ms
+0.5
+0.5
+(normalized)
+m
+0
+0
+/
+*
+米
+p
+-0.5
+-0.5
+3.5
+4
+4.5
+t / ms
+-0.5
+0
+0.5
+_ / mt= 4.25625 / ms
+0.5
+0.5
+(normalized)
+m
+0
+0
+/
+p
+-0.5
+-0.5
+3.6
+44.4
+4.8
+t / ms
+-0.5
+0
+0.5
+_ /mAdjoint Sound
+13
+6
+Summary
+An adjoint-based framework for the identification of sound sources is presented.
+It is shown that the approach is able to determine (optimal) source signals and
+to track moving sources.
+By design, the time-domain approach allows the consideration of base flows,
+such as velocity profiles and temperature stratification, and complex geometries,
+which will be the focus of the upcoming work. The first results that take into
+account a complex base flow in the context of sound reinforcement are shown in
+[21].
+Acknowledgments
+The authors gratefully acknowledge financial support by the Deutsche Forschungs-
+gemeinschaft (DFG) within the project LE 3888/2-1.
+We thank Florian Straube (Audio Communication Group, TU Berlin) for
+defining the target sound field for the sound reinforcement test case.
+References
+1. A. Carnarius, F. Thiele, E. ¨Ozkaya, A. Nemili, and N. Gauger. Optimal control of
+unsteady flows using a discrete and a continuous adjoint approach. In D. H¨omberg
+and F. Tr¨oltzsch, editors, System Modeling and Optimization, volume 391 of IFIP
+Advances in Information and Communication Technology, pages 318–327. Springer
+Berlin Heidelberg, 2013.
+2. S. Feistel. Modeling the radiation of modern sound reinforcement systems in high
+resolution, volume 19. Logos Verlag Berlin GmbH, 2014.
+3. S. Feistel, M. Sempf, K. K¨ohler, and H. Schmalle. Adapting loudspeaker array
+radiation to the venue using numerical optimization of FIR filters. In Proc. of the
+135th Audio Eng. Soc. Conv., New York, number #8937, 2013.
+4. J. B. Freund. Adjoint-based optimization for understanding and suppressing jet
+noise. Journal of Sound and Vibration, 330(17):4114 – 4122, 2011.
+5. D. V. Gaitonde and M. R. Visbal. Pade-type higher-order boundary filters for the
+navier-stokes equations. AIAA Journal, 38:2103–2112, Nov. 2000.
+6. T. Geyer. https://www.b-tu.de/fg-akustik/lehre/aktuelles/arraybenchmark. last
+seen 12. Dec. 2019.
+7. M. Giles and N. Pierce. An introduction to the adjoint approach to design. Flow,
+Turbulence and Combustion, 65:393–415, 2000.
+8. J. Gray, M. Lemke, J. Reiss, C. Paschereit, J. Sesterhenn, and J. Moeck. A compact
+shock-focusing geometry for detonation initiation: Experiments and adjoint-based
+variational data assimilation. Combustion and Flame, 183:144 – 156, 2017.
+9. A. Jameson. Optimum aerodynamic design using cfd and control theory. AIAA
+paper, 1729:124–131, 1995.
+10. S. K. Lele. Compact finite difference schemes with spectral-like resolution. Journal
+of Computational Physics, 103(1):16 – 42, 1992.
+11. M. Lemke. Adjoint based data assimilation in compressible flows with application to
+pressure determination from PIV data. PhD thesis, Technische Universit¨at Berlin,
+2015.
+
+14
+Mathias Lemke et al.
+12. M. Lemke, L. Cai, J. Reiss, H. Pitsch, and J. Sesterhenn. Adjoint-based sensitiv-
+ity analysis of quantities of interest of complex combustion models. Combustion
+Theory and Modelling, 23(1):180–196, 2019.
+13. M. Lemke, J. Reiss, and J. Sesterhenn.
+Adjoint based optimisation of reactive
+compressible flows. Combustion and Flame, 161(10):2552 – 2564, 2014.
+14. M. Lemke and J. Sesterhenn.
+Adjoint-based pressure determination from PIV
+data in compressible flows — validation and assessment based on synthetic data.
+European Journal of Mechanics - B/Fluids, 58:29 – 38, 2016.
+15. M. Lemke, F. Straube, F. Schultz, J. Sesterhenn, and S. Weinzierl. Adjoint-based
+time domain sound reinforcement. In Audio Engineering Society Conference: 2017
+AES International Conference on Sound Reinforcement – Open Air Venues, Aug
+2017. featured in Ramsey, F. (2017): ’Sound Reinforcement in the Open Air.’ In:
+J. Audio Eng. Soc., vol. 65, no. 12, pp. 1051 - 1055 (December).
+16. R. Merino-Mart´ınez, P. Sijtsma, M. Snellen, T. Ahlefeldt, J. Antoni, C. J. Bahr,
+D. Blacodon, D. Ernst, A. Finez, S. Funke, T. F. Geyer, S. Haxter, G. Herold,
+X. Huang, W. M. Humphreys, Q. Lecl`ere, A. Malgoezar, U. Michel, T. Padois,
+A. Pereira, C. Picard, E. Sarradj, H. Siller, D. G. Simons, and C. Spehr. A review
+of acoustic imaging methods using phased microphone arrays. CEAS Aeronautical
+Journal, 10(1):197–230, Mar 2019.
+17. D. Pekurovsky. P3dfft: A framework for parallel computations of fourier transforms
+in three dimensions. SIAM Journal on Scientific Computing, 34(4):C192–C209,
+2012.
+18. T. Poinsot and S. Lele. Boundary conditions for direct simulations of compressible
+viscous flows. Journal Computational Physics, 101:104–129, 1992.
+19. J. Reiss, M. Lemke, and J. Sesterhenn. Mode-based derivation of adjoint equations
+- a lazy man’s approach. on ArXiv, 2018.
+20. J. Schulze, P. Schmid, and J. Sesterhenn.
+Iterative optimization based on an
+objective functional in frequency-space with application to jet-noise cancellation.
+Journal of Computational Physics, 230(15):6075 – 6098, 2011.
+21. L. Stein, F. Straube, J. Sesterhenn, S. Weinzierl, and M. Lemke. Adjoint-based
+optimization of sound reinforcement including non-uniform flow. The Journal of
+the Acoustical Society of America, 146(3):1774–1785, 2019.
+22. A. Thompson and J. Luzarraga. Drive granularity for straight and curved loud-
+speaker arrays. Proc. of the Inst. of Acoustics, 35(2):210–218, 2013.
+23. Y. Yang, C. Robinson, D. Heitz, and E. M´emin. Enhanced ensemble-based 4dvar
+scheme for data assimilation. Computers & Fluids, 115:201 – 210, 2015.
+A
+Appendix
+A.1
+Adjoint equations
+As stated above, linearization of the governing Euler equations with respect to
+all state variables by q = q0 + δq results in
+∂tAδq + ∂xiBiδq + Ci∂xiδq + δCi∂xic = δs.
+(18)
+Again, the summation convention applies. The corresponding linearization ma-
+trices are
+
+Adjoint Sound
+15
+A =
+�
+�����
+1 0 0 0
+0
+u1 ρ 0 0
+0
+u2 0 ρ 0
+0
+u3 0 0 ρ
+0
+0 0 0 0
+1
+γ−1
+�
+�����
+,
+B1 =
+�
+�����
+u1
+ρ
+0
+0
+0
+u2
+1
+2ρu1
+0
+0
+1
+u1u2 ρu2 ρu1
+0
+0
+u1u3 ρu3
+0 ρu1
+0
+0
+γp
+γ−1
+0
+0
+γu1
+γ−1
+�
+�����
+,
+B2 =
+�
+�����
+u2
+0
+ρ
+0
+0
+u1u2 ρu2 ρu1
+0
+0
+u2
+2
+0 2ρu2
+0
+1
+u2u3
+0
+ρu3 ρu2
+0
+0
+0
+γp
+γ−1
+0
+γu2
+γ−1
+�
+�����
+,
+B3 =
+�
+�����
+u3
+0
+0
+ρ
+0
+u1u3 ρu3
+0
+ρu1
+0
+u2u3
+0 ρu3 ρu2
+0
+u2
+3
+0
+0 2ρu3
+1
+0
+0
+0
+γp
+γ−1
+γu3
+γ−1
+�
+�����
+,
+Ci =
+�
+�����
+0 0 0 0
+0
+0 0 0 0
+0
+0 0 0 0
+0
+0 0 0 0
+0
+0 0 0 0 −ui
+�
+�����
+,
+δCi =
+�
+�����
+0 0 0 0
+0
+0 0 0 0
+0
+0 0 0 0
+0
+0 0 0 0
+0
+0 0 0 0 −δui
+�
+�����
+.
+The full adjoint Navier-Stokes equations, in particular, the friction terms,
+are derived and discussed in [11]. The two-dimensional adjoint Euler equations
+can be found in [15].
+status: draft for review
+last modified: January 23, 2023 by (ML)
+
diff --git a/4dFAT4oBgHgl3EQflx3j/content/tmp_files/load_file.txt b/4dFAT4oBgHgl3EQflx3j/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c664231167bd13df68ad5656a172a2678143810b
--- /dev/null
+++ b/4dFAT4oBgHgl3EQflx3j/content/tmp_files/load_file.txt
@@ -0,0 +1,643 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf,len=642
+page_content='Adjoint-based Identification of Sound Sources for  Sound Reinforcement and Source Localization  Mathias Lemke and Lewin Stein  Institut f¨ur Str¨omungsmechanik und Technische Akustik,  Technische Universit¨at Berlin, Germany  mathias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='lemke@tnt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='tu-berlin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='de  Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The identification of sound sources is a common problem in  acoustics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Different parameters are sought, among these are signal and  position of the sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' We present an adjoint-based approach for sound  source identification, which employs computational aeroacoustic tech-  niques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Two different applications are presented as a proof-of-concept:  optimization of a sound reinforcement setup and the localization of (mov-  ing) sound sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  Keywords: Computational Aeroacoustics, Adjoint Equations, Source  Identification, Sound Reinforcement, Source Localization  1  Introduction  A common issue in acoustics is the identification of fixed or moving sound  sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' In general, several parameters have to be determined;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' among these are  the source signal and the position of the sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' This general problem occurs  in many applications, from environmental to industrial acoustics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  In this contribution, we discuss an adjoint-based approach for sound source  identification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The time-domain method is based on the (adjoint) Euler equa-  tions, which are solved by means of computational aeroacoustic techniques (CAA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  The approach allows considering complex base flows, such as non-homogeneous  base flow, thermal stratification as well as complex geometries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  Adjoint-based methods have been used in the field of fluid mechanics for  decades.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' They have proven to be an effective approach for the analysis of flow  configurations and determining optimal model parameters in various applications  [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Adjoint-based techniques are used to optimize flow configurations by means  of geometry modifications [9] or for active flow control applications [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' They are  applied for the analysis and optimization of reactive flow configurations [13,12]  and data assimilation applications [23,14,8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Furthermore, they are employed in  the field of aeroacoustics [4,20] and sound reinforcement applications [15,21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  Here, we restrict ourselves to two applications from the areas of sound re-  inforcement and sound source localization with generic setups as a proof-of-  concept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  In the context of sound reinforcement, line arrays are used for the synthesis of  sound fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The identification of the geometric arrangement and the electronic  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='08620v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='SD]  20 Jan 2023  2  Mathias Lemke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  drive of the loudspeaker cabinets to optimally (re-)produce a sound field is an  ill-posed, inverse problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Typically frequency domain approaches are employed  [3,22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  For the localization of moving and non-moving sound sources, usually, micro-  phone array methods like beam-forming are used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Depending on the specific task,  different algorithms, working in the time domain or in the frequency domain,  are applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' See [16] for a recent overview.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  The manuscript is organized as follows: In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' 2, the adjoint approach is in-  troduced, and the adjoint Euler equations are derived.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' After a short description  of the numerical implementation in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' 3, the derived framework is employed for  an application in the context of sound reinforcement in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The applicability  of the approach for localization of sound sources is discussed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  2  Adjoint Approach  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='1  General Adjoint Equations  Adjoint equations can be derived in different ways, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=', the continuous or the  discrete approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Despite different discretizations, the approaches are consistent  and applicable, see [7] for a discussion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' In addition, automatic differentiation  techniques are used to create adjoint codes from existing simulation programs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  Recently, a mode-based approach to derive adjoint operators was presented [19]  as an enhancement of a direct operator construction method [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  Here, the adjoint equations are introduced in a discrete manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' A matrix-  vector notation is used, in which the vector space is the full solution in space  and time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The section is based on [7,11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  In general, the adjoint equations arise by a scalar-valued objective function  J, which is defined by the user and encodes the target of the analysis, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=', an  optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' It is given by the scalar product between a weight vector g and a  system state vector q  J = gTq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  (1)  The system state q is the solution of the governing system  Aq = s  (2)  with A as governing operator and s as right-hand side forcing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' In order to opti-  mize J by means of s in terms of a brute-force approach, the governing equation  has to be solved for all possible s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  Instead, to reduce the computational effort, the adjoint equation can be used  ATq∗ = g,  (3)  with the adjoint variable q∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  With  J = gTq =  �  ATq∗�T q = q∗TAq = q∗Ts  (4)  Adjoint Sound  3  a formulation is found, which enables the computation of the objective J without  solving the governing system for every possible s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' With the solution of the adjoint  equation, the objective can be calculated by a scalar product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Thus, the adjoint  approach enables efficient computation of gradients for J with respect to s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='2  Adjoint Euler equations for Acoustic Applications  The section is based on [11,21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The objective function J is defined in space and  time with dΩ = dxidt in the whole computational domain:  J = 1  2  �� �  q − qtarget�2 dΩ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  (5)  The variable q contains the full state q = [ϱ, uj, p] of the system governed by the  Euler equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Therein, ϱ denotes the density, uj the velocity in the direction  xj, and p the pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  For the following aeroacoustic analyses the evaluation of the objective func-  tion is restricted to the pressure, resulting in  J = 1  2  �� �  p − ptarget�2 σ dΩ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  (6)  The additional weight σ(xi, t) defines where and when the objective is evalu-  ated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' In general, the objective function has to be supplemented by a regular-  ization term, which is omitted here for the sake of clarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The target ptarget is  application-specific.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' For optimization tasks, as presented in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' 4, it is defined  corresponding to a desired sound field, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=', optimal listening experience for the  auditorium of an open-air concert.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' For the source localization application pre-  sented in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' 5, the target pressure is defined by microphone measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  The microphone positions are included by means of the weight function σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' In  both cases, a minimum of J is desired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  This minimum is to be achieved under the constraint that the Euler equa-  tions  ∂t  �  �  ϱ  ϱuj  p  γ−1  �  � + ∂xi  �  �  ϱui  ϱuiuj + pδij  uipγ  γ−1  �  � − ui∂xi  �  �  0  0  p  �  � =  �  �  0  0  sp  �  � ,  with γ as heat capacity ratio, are fulfilled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The summation convention applies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  For details on the formulation, in particular, the reformulation of the energy  equation in terms of pressure, see [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  To ease the derivation, the above system of partial differential equations is  abbreviated by  E(q) = s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  (7)  The terms s = [0, 0, sp] on the right side of the Euler equations character-  ize monopole sound sources, which allow controlling the system state, respec-  tively, the solution of the equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' In general, also mass and momentum source  4  Mathias Lemke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  terms could be considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The overall goal is to obtain a solution of the Euler  equations, which reduces the objective (6) by adapting s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' An optimization of s  corresponds to an optimization of the loudspeakers’ output signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  To use the adjoint approach for optimizing s, the objective function (6) and  the governing system (7) have to be linearized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' This results in  δJ =  �� �  q − qtarget�  σ  �  ��  �  =g  δpdΩ,  (8)  and  Elinδq = δs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  (9)  The weight g = (q − qtarget)σ encodes the difference between the current numer-  ical solution and the target field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Here, it is evaluated only in terms of pressure,  as discussed above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Combining the linearized system and the objective in a La-  grangian manner leads to  δJ = gTδq − q∗T (Elinδq − δs)  �  ��  �  =0  (10)  = q∗Tδs + δqT �  g − ET  linq∗�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  Please note, the spatial and temporal integrals are not shown for the sake of  simplicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  The desired adjoint equation E∗ = ET  lin results from demanding  g − ET  linq∗ = 0,  (11)  with q∗ = [ϱ∗, u∗  j, p∗] as adjoint state variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  For a detailed derivation of the adjoint Euler equations see [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' They are  given by  ∂tq∗ = ˜A  �  −(Bi)T∂xiq∗ − ∂xi(Ci)Tq∗ + ˜Ci∂xic − g  �  (12)  with ˜A =  �  AT�−1 and ˜Ci as resorting  q∗  αδCi  αβ∂xicβ = q∗  αδqκ  ∂Ci  αβ  ∂qκ  ∂xicβ  (13)  abbreviated as δqκ ˜Ci  κβ∂xicβ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The matrices A, Bi and Ci are given in the ap-  pendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  Finally, the change of the objective function is given by  δJ = q∗Tδs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  (14)  Thus, the solution of the adjoint equation can be interpreted as gradient of J  with respect to the source terms s  ∇sJ = q∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  (15)  Initial and boundary conditions of the adjoint Euler equations as well as the  derivation of the adjoint compressible Navier-Stokes equations are discussed in  [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  Adjoint Sound  5  sources  initial guess  s0=0  solution  Euler equations  N(q, sn)  target  qtarget  solution adjoint  Euler equations  N*(q,q*,Δ q)  gradient  q*  sources  update sn+1  Δ q = q \xad qtarget  optimal  s  source  positions  p  convergence  loop 1  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Iterative procedure for the determination of an optimal s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Computationally  intensive steps are marked in gray.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The first gradient provides information on (optimal)  source positions, see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' 5 for a detailed discussion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='3  Iterative Process  The adjoint-based gradient is employed in an iterative manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' First, the Euler  equations (7) are solved forward in time, usually with s0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Subsequently,  the adjoint equations (12) are calculated backward in time, deploying the direct  solution and g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Based on the adjoint solution, the gradient ∇sJ is determined  and used to update the source distribution sn by means of a steepest gradient  approach:  sn+1 = sn + α∇sJ,  (16)  with α denoting an appropriate step size and n the iteration number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The gradi-  ent is calculated for the whole computing region and the entire simulation time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  For the determination of sound sources with a known position, the gradient is  evaluated only there.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The procedure is repeated, using the current sn, until a  suitable convergence criterion is reached.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Typically, for acoustic problems, con-  vergence is reached within or less 20 loops.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  The identification of global optima is not ensured as the proposed technique  optimizes to local extrema only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The computational costs of the approach are  independent of the number of sources and their arrangement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' However, they  depend on the size and resolution of the computational domain in space and  time, defined by the considered frequency range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The computational problem is  fully parallelizable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='4  Source Localization  In particular, when s0 = 0 holds, the first adjoint solution contains information  on the position of the sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' By the pointwise summation of the absolute  adjoint sensitivities p∗ in the spatial domain over all computed time steps  ¯p =  tn=end  �  tn=0  |p∗|,  (17)  6  Mathias Lemke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  the positions featuring maximum impact on the objective function can be iden-  tified by means of maxima of ¯p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' These correspond to the most likely (monopole)  source locations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Thus, the adjoint solution allows the localization of sound  sources, see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' A subsequent iterative adaptation of the sources can be  interpreted as adjoint-based monopole synthesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  3  Adjoint CAA framework  The set of governing equations (7) is implemented by means of a new MPI-  parallelized Fortran program.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The discretization is realized by a finite difference  time domain approach (FDTD).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' For the spatial derivatives, a compact scheme  of 6th order is employed [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The corresponding linear system of equations is  solved by BLAS routines using an LU-decomposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' For the time-wise inte-  gration, the standard explicit Runge-Kutta-scheme of fourth-order is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  To ensure stability, a compact filter is employed [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Boundaries are treated by  characteristic boundary conditions [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The MPI implementation is realized by  collective communication via all2all v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The parallelization strategy is found to  be efficient for the governing equations (7), see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' 2, and comparable to other  implementations using collective communication, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  Thus, the code is prepared to handle large scale problems, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=', open-air festi-  val sites in the context of sound reinforcement applications or source localization  for vehicle aeroacoustics in wind tunnels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' However, the examples presented in  the following are computed using a single workstation or a few cluster nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' (Left) Strong scaling behaviour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The overall number of grid points is kept  constant while increasing the number of MPI processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Nearly linear scaling is found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  (Right) Weak scaling behaviour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The number of grid points on each process is kept  constant while increasing the number of MPI processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' An admissible reduction of the  parallelization efficiency is found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  The adjoint equations are solved using the same discretization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' A detailed  discussion on the adjoint initial- and characteristic boundary conditions can be  found in [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  8  speedup  6  4  caa  2  --ideal  400  1200  2000  2800  3600  MPl processesefficiency  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='8  caa  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='--ideal  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='7  40  80  160  320  640  1280 2560  MPl processesAdjoint Sound  7  4  Application I: Sound Reinforcement  This section presents a test case regarding the optimization of sound reinforce-  ment setups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The overall goal is to identify optimal drives (amplitude and phase)  for given loudspeakers in order to synthesise a desired sound field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The loudspeak-  ers are approximated by means of monopole sources, which is feasible for low  frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  The spatial domain under consideration is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='6 × 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='6 × 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='6 m3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The domain  is resolved by 197 × 197 × 99 equidistantly distributed points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The time step,  and by this, the sampling rate, is given by 48 kHz, corresponding to a CFL-  condition smaller than 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The computational time span considered is 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='25 ms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  The reference values for density and pressure correspond to a speed of sound  of 343 m/s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' All boundaries are treated as non-reflecting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' In addition, a sponge  layer is applied at all boundaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  For the test case reference signals for five sources, located in a curved ar-  rangement in the center x1-x2 plane, are predefined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The signals are charac-  terised by different amplitudes and phase delays resulting in a steered sound  field, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' 3 (left).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' In order to investigate the frequency band 1-3 kHz, a  corresponding logarithmic sine-sweep is specified as the reference signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Using  this setup, a reference sound field is computed by a Complex Directivity Point  Source (CDPS) algorithm [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The resulting reference sound field serves as the  target for the adjoint-based framework, with the aim to identify the reference  signals (amplitudes and phases) based on the reference target sound field only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  After 15 iterative loops of the adjoint framework, the objective function is  reduced to nearly 3% with respect to the initial solution with s = 0, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' 3  (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The general features of the target reference sound field are captured, see  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' A detailed spectral analysis of the occurring deviations at two selected  microphone positions, presented in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' 4, show amplitude deviations less than  1 dB within the confidence interval from 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='3 to 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='7 kHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The normalized phase  derivations, with respect to 2π, are in the limits of -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='07 to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  A discussion on how to derive optimal electronic drives from the adjoint-  based signals s is given in [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Therein, the capability of the approach to consider  complex base flows by means of wind and temperature stratification is shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  5  Application II: Source Localization  In this section, the localization of fixed and moving sound sources is shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Two  generic setups serve as a proof of concept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' For the first setup with four stationary  sound sources and the second setup with a moving source, it is shown that the  adjoint-based approach is able to identify the sources and track their path in  case of moving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  In both cases, the measurements are provided by a reference computation  with predefined sound sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Synthetic microphone signals are extracted from  this reference solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' A spatially discrete planar array with 64 microphones is  used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The general setup is based on the array benchmark test case B7 provided  8  Mathias Lemke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' (Left) Sound reinforcement setup including a selected time step of the CDPS-  based reference sound field shown at the center x1-x2 plane of the computational do-  main.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The five monopole speakers in a curved arrangement are denoted by (*).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Different  driving functions (in amplitude and phase) for the speaker result in a steered sound  field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The area/volume marked by the dashed line corresponds to the spatial weight σ  in the objective function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Please note, the employed CDPS technique for computing  the reference sound field does not provide reliable solutions near the source positions;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  therefore, p′  ref is discontinuous for x1 = [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='32, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='62] m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' (Right) Progress of the objective  function with a logarithmic y-axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Convergence is reached.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The objective is reduced  by nearly two orders of magnitude with respect to the initial guess s = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Reference target (left) and resulting optimized (right) sound field at t = 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='63  ms for the center x1-x2 plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The general features of the reference field are (re-)  captured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The influence of the employed sponge layer in the adjoint-based sound field  is visible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The dashed line encodes the spatial weight σ within the objective function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  The marked positions correspond to synthetic microphone positions x1,2 = [1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='1, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='1]  and x1,2 = [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='8, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='8] which are used for spectral analysis, see text for details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='8  米‘  speaker  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='4  a  m  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  8  0  d-  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='P  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  X, /m1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='25  r/  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='02  5  10  15  iteration1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  1  a  P  0  +  ref  p  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  X, / m1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  1  a  P  0  +  opt  2  p  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5Adjoint Sound  9  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' (Left) Normalized amplitude difference between resulting optimized and refer-  ence target sound field at selected microphone positions, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' (Right) Normalized  phase difference between resulting optimized and reference target sound field at the  selected microphone positions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  by the Brandenburg university of technology, see [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Modifications are discussed  below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' An example in which experimental data are used is shown in [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  The spatial domain under consideration is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='7 × 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='7 × 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='25 m3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The domain  is resolved by 240 × 240 × 176 equidistantly distributed points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The time step,  and by this, the sampling rate of the microphone measurements, is given by  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='33 kHz, corresponding to a CFL-condition smaller than 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' In both cases, no  base flow is considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The reference values for density and pressure correspond  to a speed of sound of 343 m/s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The spiral-like microphone array is located at  x3 = 0 m and centered in the corresponding plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The spatial distribution of  the microphones is described in more detail in [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' All boundaries are treated as  non-reflecting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' In addition, a sponge layer is applied at all boundaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='1  Four sources  As in the array benchmark test case B7 four monopole sources are located in  the x1-x2-plane at x3 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='75 m, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' 6 (left).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' For the reference computation,  the original benchmark source signals are replaced by incoherent random sig-  nals, frequency-band limited between 750 and 2500 Hz, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' 6 (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The  computational time span is 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='06 ms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  Using a corresponding reference forcing s = �  i si a simulation of the Euler  equations (7) is carried out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' From the results, discrete microphone signals are  extracted, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' 7 (left), which are the result of the superposition of all sources  and the associated signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  The 64 signals are encoded in the objective function J (6) using the spatial  weight σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' To avoid an unstable discrete forcing of the adjoint equations, σ is  chosen as Gauss-distribution with a half-width of 2∆x for each microphone  position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' After determining the solution of the direct equations with an initial  guess for s = 0, here, constant environmental conditions for all time steps, the  mic 1  B  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='4  mic 2  ta  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='2  p  opt  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='6  1500  2000  2500  f /Hz0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='1  mic 1  mic 2  2π  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='05  tar  0  opt  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='1  1500  2000  2500  f / Hz10  Mathias Lemke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' (Left) Acoustic setup for source localization of four sources (*) by 64 micro-  phones (o) located in the planes x3 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='75 m respectively x3 = 0 m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' (Right) Normalized  signals si of the four reference sources, shown for the whole computational time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  adjoint equations are solved backwards in time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' From the resulting gradient, the  source positions can be derived, as discussed before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' That way, the reference  source positions are identified, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' 7 (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' (Left) Captured pressure signal at the center microphone in the array.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The  initial silence results from the distance between the sources and the array.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' (Right) Re-  sulting pointwise summation of the absolute adjoint sensitivities p∗ (17).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The reference  source positions (∗) are recovered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  Please note, the analysis is based on the first adjoint-based gradient only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  The required computational time for the analysis is less than 15 min on a 16  core workstation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Iterative optimization of s might improve the results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='2  Single moving source  Again, the aforementioned test case B7 from [6] serves as a base for the following  test setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The planar microphone array is located in the same plane (x3 = 0) but  米  米  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  米  米  8  00  0  8  0  0  0  0  00  00  00  00  0  0  0  0  0  00  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  00  00  0  0  0  00  8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  0  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  ×2 /m  X, / mS  (normalized)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  S  2  S  1  3  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  S  0  4  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='.  : i  11  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  11  S  II  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  11  二  1  2  6  10  14  t/ mscenter mic  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='1  a  P  8  d-(  p  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='1  2  6  10  14  t/msref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' sources  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='8  (normalized)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='6  米  米  0 米  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='4  p  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  / mAdjoint Sound  11  scaled by a factor of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='8, resulting in smaller distances between the microphones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  The incoherent sources are replaced by a single source with a harmonic 2 kHz  reference signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The source is moving in the x1-x2-plane, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' 8 (left).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The  movement is described by an acceleration and deceleration, taking place along  the x1 axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' It starts at the beginning of the computational time and ends with  the simulation after 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='44 ms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The highest speed of the movement is reached  midway.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  Again a reference solution provides synthetic microphone signals, which are  encoded in the objective function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Using constant environmental conditions as  solution of the direct equations (s0 = 0), the adjoint equations are solved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Eval-  uation of the adjoint sensitivity p∗ over time at the reference source position  provides information of the reference signal, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' 8 (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The phase of  the reference signal is determined with very good agreement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The amplitude  shows deviations at the beginning and end of the simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The influence of  the directional characteristic of the used microphone array is presumed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' (Left) Acoustic setup for source localization of a single moving source (*) by  means of 64 microphones (o) located in the planes x3 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='75 m, respectively x3 = 0  m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The movement of the source is visualized by it waypoints, chosen with a constant  time interval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' (Right) Normalized adjoint-based sensitivity p∗ at the reference source  positions over time in comparison to the reference forcing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' See text for a detailed  discussion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  Besides, the identification of the source signal also its position might be  tracked.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' 9 the adjoint-based sensitivity p∗ is shown for the plane x3 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='75  m for different time steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Occurring maxima give rise to the actual sound source  position, besides its signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  Again, the analysis is based on the first adjoint-based gradient only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The  required computational time for the analysis is less than 10 min on 8 cluster  nodes with 8 cores each.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  m  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  0  0  CD  0  000  00  0  00  0  8  0  00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  0  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  m  m  25 二 1  I  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  (normalized)  ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  P-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  adjoint-based  4  --- reference 1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  2  4  6  8  t/ms12  Mathias Lemke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Normalized adjoint-based sensitivity p∗ at the plane x3 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='75 for different  time steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The reference source location is marked by (*) in a white circle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' In the  inset, the normalized reference signal is shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  t= 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='88125 / ms  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  (normalized)  m  0  0  +  p  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  /  米  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  4  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  t / ms  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  , / mt= 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='99375/ ms  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  (normalized)  m  0  0  /  +  米  p  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  4  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  t / ms  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  X, / mt= 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='12500 / ms  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  (normalized)  m  0  0  / 米  p  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  4  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  t / ms  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  _ / mt= 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='25625 / ms  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  (normalized)  m  0  0  /  p  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='6  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='4  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='8  t / ms  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='5  _ /mAdjoint Sound  13  6  Summary  An adjoint-based framework for the identification of sound sources is presented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  It is shown that the approach is able to determine (optimal) source signals and  to track moving sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  By design, the time-domain approach allows the consideration of base flows,  such as velocity profiles and temperature stratification, and complex geometries,  which will be the focus of the upcoming work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The first results that take into  account a complex base flow in the context of sound reinforcement are shown in  [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  Acknowledgments  The authors gratefully acknowledge financial support by the Deutsche Forschungs-  gemeinschaft (DFG) within the project LE 3888/2-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  We thank Florian Straube (Audio Communication Group, TU Berlin) for  defining the target sound field for the sound reinforcement test case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  References  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Carnarius, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Thiele, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' ¨Ozkaya, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Nemili, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Gauger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Optimal control of  unsteady flows using a discrete and a continuous adjoint approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' In D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' H¨omberg  and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Tr¨oltzsch, editors, System Modeling and Optimization, volume 391 of IFIP  Advances in Information and Communication Technology, pages 318–327.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Springer  Berlin Heidelberg, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Feistel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Modeling the radiation of modern sound reinforcement systems in high  resolution, volume 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Logos Verlag Berlin GmbH, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Feistel, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Sempf, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' K¨ohler, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Schmalle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Adapting loudspeaker array  radiation to the venue using numerical optimization of FIR filters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' In Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' of the  135th Audio Eng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Conv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=', New York, number #8937, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Freund.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Adjoint-based optimization for understanding and suppressing jet  noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Journal of Sound and Vibration, 330(17):4114 – 4122, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Gaitonde and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Visbal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Pade-type higher-order boundary filters for the  navier-stokes equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' AIAA Journal, 38:2103–2112, Nov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Geyer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='b-tu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='de/fg-akustik/lehre/aktuelles/arraybenchmark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' last  seen 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Giles and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Pierce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' An introduction to the adjoint approach to design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Flow,  Turbulence and Combustion, 65:393–415, 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Gray, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Lemke, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Reiss, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Paschereit, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Sesterhenn, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Moeck.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' A compact  shock-focusing geometry for detonation initiation: Experiments and adjoint-based  variational data assimilation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Combustion and Flame, 183:144 – 156, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Jameson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Optimum aerodynamic design using cfd and control theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' AIAA  paper, 1729:124–131, 1995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Lele.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Compact finite difference schemes with spectral-like resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Journal  of Computational Physics, 103(1):16 – 42, 1992.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Lemke.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Adjoint based data assimilation in compressible flows with application to  pressure determination from PIV data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' PhD thesis, Technische Universit¨at Berlin,  2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  14  Mathias Lemke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Lemke, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Cai, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Reiss, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Pitsch, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Sesterhenn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Adjoint-based sensitiv-  ity analysis of quantities of interest of complex combustion models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Combustion  Theory and Modelling, 23(1):180–196, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Lemke, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Reiss, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Sesterhenn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  Adjoint based optimisation of reactive  compressible flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Combustion and Flame, 161(10):2552 – 2564, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Lemke and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Sesterhenn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  Adjoint-based pressure determination from PIV  data in compressible flows — validation and assessment based on synthetic data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  European Journal of Mechanics - B/Fluids, 58:29 – 38, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Lemke, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Straube, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Schultz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Sesterhenn, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Weinzierl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Adjoint-based  time domain sound reinforcement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' In Audio Engineering Society Conference: 2017  AES International Conference on Sound Reinforcement – Open Air Venues, Aug  2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' featured in Ramsey, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' (2017): ’Sound Reinforcement in the Open Air.’ In:  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Audio Eng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' 65, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' 12, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' 1051 - 1055 (December).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Merino-Mart´ınez, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Sijtsma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Snellen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Ahlefeldt, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Antoni, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Bahr,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Blacodon, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Ernst, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Finez, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Funke, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Geyer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Haxter, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Herold,  X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Huang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Humphreys, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Lecl`ere, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Malgoezar, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Michel, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Padois,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Pereira, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Picard, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Sarradj, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Siller, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Simons, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Spehr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' A review  of acoustic imaging methods using phased microphone arrays.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' CEAS Aeronautical  Journal, 10(1):197–230, Mar 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Pekurovsky.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' P3dfft: A framework for parallel computations of fourier transforms  in three dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' SIAM Journal on Scientific Computing, 34(4):C192–C209,  2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Poinsot and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Lele.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Boundary conditions for direct simulations of compressible  viscous flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Journal Computational Physics, 101:104–129, 1992.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Reiss, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Lemke, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Sesterhenn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Mode-based derivation of adjoint equations  a lazy man’s approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' on ArXiv, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Schulze, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Schmid, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Sesterhenn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  Iterative optimization based on an  objective functional in frequency-space with application to jet-noise cancellation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  Journal of Computational Physics, 230(15):6075 – 6098, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Stein, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Straube, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Sesterhenn, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Weinzierl, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Lemke.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Adjoint-based  optimization of sound reinforcement including non-uniform flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The Journal of  the Acoustical Society of America, 146(3):1774–1785, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Thompson and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Luzarraga.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Drive granularity for straight and curved loud-  speaker arrays.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' of the Inst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' of Acoustics, 35(2):210–218, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Yang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Robinson, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Heitz, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' M´emin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Enhanced ensemble-based 4dvar  scheme for data assimilation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' Computers & Fluids, 115:201 – 210, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  A  Appendix  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='1  Adjoint equations  As stated above, linearization of the governing Euler equations with respect to  all state variables by q = q0 + δq results in  ∂tAδq + ∂xiBiδq + Ci∂xiδq + δCi∂xic = δs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  (18)  Again, the summation convention applies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The corresponding linearization ma-  trices are  Adjoint Sound  15  A =  �  �����  1 0 0 0  0  u1 ρ 0 0  0  u2 0 ρ 0  0  u3 0 0 ρ  0  0 0 0 0  1  γ−1  �  �����  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  B1 =  �  �����  u1  ρ  0  0  0  u2  1  2ρu1  0  0  1  u1u2 ρu2 ρu1  0  0  u1u3 ρu3  0 ρu1  0  0  γp  γ−1  0  0  γu1  γ−1  �  �����  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  B2 =  �  �����  u2  0  ρ  0  0  u1u2 ρu2 ρu1  0  0  u2  2  0 2ρu2  0  1  u2u3  0  ρu3 ρu2  0  0  0  γp  γ−1  0  γu2  γ−1  �  �����  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  B3 =  �  �����  u3  0  0  ρ  0  u1u3 ρu3  0  ρu1  0  u2u3  0 ρu3 ρu2  0  u2  3  0  0 2ρu3  1  0  0  0  γp  γ−1  γu3  γ−1  �  �����  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  Ci =  �  �����  0 0 0 0  0  0 0 0 0  0  0 0 0 0  0  0 0 0 0  0  0 0 0 0 −ui  �  �����  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  δCi =  �  �����  0 0 0 0  0  0 0 0 0  0  0 0 0 0  0  0 0 0 0  0  0 0 0 0 −δui  �  �����  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  The full adjoint Navier-Stokes equations, in particular, the friction terms,  are derived and discussed in [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content=' The two-dimensional adjoint Euler equations  can be found in [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
+page_content='  status: draft for review  last modified: January 23, 2023 by (ML)' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dFAT4oBgHgl3EQflx3j/content/2301.08620v1.pdf'}
diff --git a/4tE4T4oBgHgl3EQfbgyP/content/tmp_files/2301.05074v1.pdf.txt b/4tE4T4oBgHgl3EQfbgyP/content/tmp_files/2301.05074v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4beb6a9aa75f1a2ccef77f5532da6c5091611630
--- /dev/null
+++ b/4tE4T4oBgHgl3EQfbgyP/content/tmp_files/2301.05074v1.pdf.txt
@@ -0,0 +1,351 @@
+Identification of light leptons and pions in the electromagnetic calorimeter of Belle II
+Anja Novosela,b, Abtin Narimani Charanc, Luka ˇSanteljb,a, Torben Ferberd, Peter Kriˇzanb,a, Boˇstjan Golobe,a
+aJoˇzef Stefan Institute, Ljubljana, Slovenia
+bFaculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia
+cDeutsches Elektronen-Synchrotron (DESY), Hamburg, Germany
+dKarlsruhe Institute of Technology (KIT) , Karlsruhe, Germany
+eUniversity of Nova Gorica, Nova Gorica, Slovenia
+Abstract
+The paper discusses new method for electron/pion and muon/pion separation in the Belle II detector at transverse momenta below
+0.7 GeV/c, which is essential for efficient measurements of semi-leptonic decays of B mesons with tau lepton in the final state. The
+method is based on the analysis of patterns in the electromagnetic calorimeter by using a Convolutional Neural Network (CNN).
+Keywords: Electromagnetic calorimeter, Particle identification, Convolutional Neural Network
+1. Introduction
+Searches for New Physics at the intensity frontier are based
+on very precise measurements of rare processes within the Stan-
+dard Model. Of particular interest, because of persistent hints of
+Lepton Flavour Universality (LFU) violation, are semi-leptonic
+decays of B mesons, e.g. decays mediated by the b → cτ+ντ
+transitions with a tau lepton in the final state and decays in-
+volving b → sµ+µ− and b → se+e− transitions. In decays with
+tau lepton in the final state, the tau lepton must be reconstructed
+from its long-lived decay products, for example from the decays
+τ− → µ−¯νµντ or τ− → e−¯νeντ. In the Belle II experiment [1, 2],
+the momentum spectrum of light leptons from tau decays is
+rather soft, a sizable fraction being below 0.7 GeV/c. One of
+the crucial steps in the analysis of these decays is identifying
+low momenta light leptons (e or µ) from hadronic background
+(mostly π). The simplest baseline feature for separating elec-
+trons from other charged particles (muons and pions) is E/p,
+the ratio between the energy measured in the electromagnetic
+calorimeter and the reconstructed momentum of topologically
+matched charged track. This variable provides an excellent sep-
+aration for particles with p > 1 GeV/c, but due to increased en-
+ergy losses from bremsstrahlung for low momentum electrons,
+the separation is less distinct [3]. Muons are identified in the
+KL and muon system. However, its efficiency is very poor for
+low momentum muons that are out of acceptance of the ded-
+icated sub-detector. Other sub-detectors designed for particle
+identification, the time of propagation detector and the aerogel
+ring-imaging Cherenkov detector, are not able to provide effi-
+cient µ/π separation in this momentum range because at low
+momenta multiple scattering in the material of the detector as
+well as the material in front of it blurs the pattern considerably.
+Our main goal is to improve the identification of low momen-
+tum leptons using the information of energy deposition in the
+electromagnetic calorimeter in a form of images. As a classifier
+we are using a Convolutional Neural Network (CNN), a power-
+ful machine learning technique designed for working with two-
+dimensional images. Using CNN on the images allows us to ac-
+cess the information on the shape of the energy deposition with-
+out depending on cluster reconstruction or track-cluster match-
+ing.
+In what follows, we will describe the electromagnetic
+calorimeter of Belle II, discuss the analysis of simulated pion,
+muon and electron patterns in the electromagnetic calorimeter,
+and present the results.
+2. Electromagnetic calorimeter of Belle II
+The Belle II detector is a large-solid-angle magnetic spec-
+trometer designed to reconstruct the products of collisions pro-
+duced by the SuperKEKB collider. The detector consists of
+several sub-detectors arranged around the interaction point in
+cylindrical geometry: the innermost Vertex Detector (VXD)
+used for reconstructing decay vertices, a combination of the
+Pixel Detector (PXD) and Silicon Vertex Detector (SVD); the
+Central Drift Chamber (CDC) is the main tracking system; the
+Time of Propagation (TOP) detector in the barrel region and
+the Aerogel Ring-Imaging Cherenkov detector (ARICH) in the
+forward endcap region are used for hadron identification; the
+Electromagnetic Calorimeter (ECL) is used to measure the en-
+ergy of photons and electrons and the outermost K-Long and
+Muon (KLM) detector detects muons and neutral K0
+L mesons
+[1].
+The sub-detector relevant for this work is the ECL, more
+specifically its central barrel region barrel region which con-
+sists of 6624 CsI(Tl) scintillation crystals, covering the po-
+lar angle region 32.2◦ < θ < 128.7◦ with respect to the
+beam axis. A solenoid surrounding the calorimeter generates
+a uniform 1.5 T magnetic field filling its inner volume [2].
+We are mainly interested in the transverse momentum range
+0.28 < pT < 0.7 GeV/c, where the minimal pT threshold en-
+sures the tracks are within the ECL barrel region acceptance.
+Preprint submitted to Nucl. Instr. Meth. A
+January 13, 2023
+arXiv:2301.05074v1  [hep-ex]  12 Jan 2023
+
+Currently, two methods for the particle identification in the ECL
+are available. The first method relies exclusively on the ratio
+of the energy deposited by a charged particle in the ECL and
+the reconstructed momentum of topologically matched charged
+track, E/p. While for electrons this variable enables powerful
+discrimination, as electrons completely deposit their energy in
+the ECL, the µ/π separation is strongly limited, especially for
+low-momentum particles with a broader E/p distribution as can
+be seen on Fig. 1. The second method uses Boosted Decision
+Trees (BDT) with several expert-engineered observables char-
+acterising the shower shape in the ECL [4].
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+1.2
+E/p [c]
+0
+2
+4
+6
+8
+Events (normalised / (0.02 c))
+Belle II Simulation, ECL barrel, 0.28 
+ pT < 0.7 GeV/c
+e
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+1.2
+E/p [c]
+0
+1
+2
+3
+4
+5
+Events (normalised / (0.02 c))
+Belle II Simulation, ECL barrel, 0.28 
+ pT < 0.7 GeV/c
+Figure 1: Distribution of E/p for simulated single particle candidates: e
+(green), µ (red) and π (blue) for 0.28 ≤ pT < 0.7 GeV/c in the ECL barrel
+region.
+3. Analysis of the patterns in the electromagnetic calorime-
+ter
+Our proposed method to improve the identification of low-
+momentum leptons is to exploit the specific patterns in the spa-
+tial distribution of energy deposition in the ECL crystals us-
+ing a Convolutional Neural Network (CNN)1. The images are
+consistent with the 11 x 11 neighbouring crystals around the
+entry point of the extrapolated track into the ECL, where each
+pixel corresponds to an individual ECL crystal and pixel inten-
+sity to the energy deposited by charged particle in the crystal.
+Examples of the obtained images are shown on Fig. 2. While
+electrons generate electromagnetic showers depositing the ma-
+jority of their energy in the ECL, the dominant interaction in
+CsI(Tl) for muons and pions in the aforementioned transverse-
+momentum range is ionization. Besides, pions can strongly in-
+teract with nuclei producing less localized images compared to
+muons [5].
+Energy [GeV]
+0.00
+0.02
+0.04
+0.06
+0.08
+0.10
+0.00
+0.02
+0.04
+0.06
+0.08
+0.10
+0.00
+0.02
+0.04
+0.06
+0.08
+0.10
+Belle II Simulation, ECL barrel, 0.28 
+ pT <  0.7 GeV/c
+Figure 2: Examples of simulated energy depositions and the average over 80000
+images for e (left), µ (middle) and π (right).
+For each binary classification we generated 1.5 × 106 events
+using the Belle II Analysis Software Framework [6], where the
+1CNN is built using TensorFlow software available from tensorflow.org.
+data set consists of the same number of signal (e or µ) and back-
+ground (π) events with uniformly distributed transverse mo-
+menta, polar angle and azimuthal angle. The two data sets were
+split on the train-validation-test set as 70 − 10 − 20% and we
+use the same CNN architecture for e/π and µ/π case. As an
+input to the convolutional layers we use 11 x 11 images. Before
+fully connected layers we add the information about pT and θID,
+where the later represents an integer number corresponding to
+the location of the ECL crystal and is in the network imple-
+mented as an embedding. To perform a binary classification,
+we have 1 neuron in the output layer with a sigmoid activation
+function that outputs the signal probability that the image was
+produced by a lepton.
+4. Performance
+To validate the performance of a binary classifier we use
+a Receiver Operating Characteristic (ROC) curve by plotting
+true positive rate (µ or e efficiency) against the false positive
+rate (π mis-ID rate). As the reference for the existing ECL
+information, we use the log-likelihood difference, a powerful
+discriminator between the competing hypotheses, defined as
+∆LLECL = log LECL
+e,µ
+− log LECL
+π
+based only on E/p [3] and
+BDT ECL using the shower-shape information from the ECL,
+thoroughly described in [4]. The ROC curves obtained by these
+three methods are shown on Fig. 3 for e/π and on Fig. 4 for µ/π
+classification.
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+ mis-ID rate
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+e efficiency
+Belle II Simulation, ECL barrel, 0.28 
+ pT < 0.5 GeV/c
+LLECL (AUC: 89.34)
+BDT ECL (AUC: 94.12)
+CNN (AUC: 99.35)
+0.0
+0.1
+0.6
+0.7
+0.8
+0.9
+1.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+ mis-ID rate
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+e efficiency
+Belle II Simulation, ECL barrel, 0.5 
+ pT < 0.7 GeV/c
+LLECL (AUC: 98.58)
+BDT ECL (AUC: 99.25)
+CNN (AUC: 99.86)
+0.0
+0.1
+0.6
+0.7
+0.8
+0.9
+1.0
+Figure 3: The performance of three different classifiers for e/π based on only
+ECL information: ∆LLECL, BDT ECL, and ∆LLCNN.
+2
+
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+ mis-ID rate
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+ efficiency
+Belle II Simulation, ECL barrel, 0.28 
+ pT < 0.5 GeV/c
+LLECL (AUC: 69.02)
+BDT ECL (AUC: 86.50)
+CNN (AUC: 93.56)
+0.0
+0.1
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+ mis-ID rate
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+ efficiency
+Belle II Simulation, ECL barrel, 0.5 
+ pT < 0.7 GeV/c
+LLECL (AUC: 69.65)
+BDT ECL (AUC: 79.89)
+CNN (AUC: 84.94)
+0.0
+0.1
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Figure 4: The performance of three different classifiers for µ/π based on only
+ECL information: ∆LLECL, BDT ECL, and ∆LLCNN.
+Looking at the shapes of ROC curves and the Area Under the
+Curve (AUC) values, it is evident that the CNN outperforms
+the existing classifiers, ∆LLECL and BDT ECL for both e/π and
+µ/π. The performance of the CNN drops with increasing mo-
+mentum as the path in the ECL gets shorter and the specific
+patterns in the images become less evident.
+5. Summary and outlook
+We can conclude there is more information in the ECL that is
+currently used for particle identification. We saw that the sep-
+aration between low-momentum light leptons and pions can be
+improved using a CNN on the ECL images. The newly pro-
+posed method looks very promising and worthwhile to be fur-
+ther developed. A comparison of the method presented in this
+article to a novel BDT-based analysis is a subject of a forthcom-
+ing publication [7].
+6. Acknowledgements
+We thank Anˇze Zupanc for his support with ideas and ad-
+vice in the early stages of the project. This work was supported
+by the following funding sources: European Research Coun-
+cil, Horizon 2020 ERC-Advanced Grant No. 884719; BMBF,
+DFG, HGF (Germany); Slovenian Research Agency research
+grants No. J1-9124, J1-4358 and P1-0135 (Slovenia).
+References
+[1] T. Abe et al., KEK Report 2010-1 (2010)
+[2] I. Adachi et al., Nucl. Instrum. Meth. A 907 (2018)
+[3] E. Kou et al., PTEP, Volume 2019, Issue 12, 123C01 (2019)
+[4] M. Milesi, J. Tan, P. Urquijo, EPJ Web of Conferences 245, 06023 (2020)
+[5] S. Longo, J. M. Roney et al., Nucl. Instrum. Meth. A 982 (2020)
+[6] T. Kuhr, C. Pulvermacher, M. Ritter et al., Comput Softw Big Sci 3, 1
+(2019)
+[7] M. Milesi et al., in preparation for Nucl. Instrum. Meth. A
+3
+
diff --git a/4tE4T4oBgHgl3EQfbgyP/content/tmp_files/load_file.txt b/4tE4T4oBgHgl3EQfbgyP/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8d4e5c0667b8d09c89850c5641fc8372bdfee9f0
--- /dev/null
+++ b/4tE4T4oBgHgl3EQfbgyP/content/tmp_files/load_file.txt
@@ -0,0 +1,273 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf,len=272
+page_content='Identification of light leptons and pions in the electromagnetic calorimeter of Belle II  Anja Novosela,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='b,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Abtin Narimani Charanc,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Luka ˇSanteljb,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='a,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Torben Ferberd,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Peter Kriˇzanb,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='a,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Boˇstjan Golobe,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='a  aJoˇzef Stefan Institute,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Ljubljana,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Slovenia  bFaculty of Mathematics and Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' University of Ljubljana,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Ljubljana,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Slovenia  cDeutsches Elektronen-Synchrotron (DESY),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Hamburg,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Germany  dKarlsruhe Institute of Technology (KIT) ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Karlsruhe,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Germany  eUniversity of Nova Gorica,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Nova Gorica,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Slovenia  Abstract  The paper discusses new method for electron/pion and muon/pion separation in the Belle II detector at transverse momenta below  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='7 GeV/c, which is essential for efficient measurements of semi-leptonic decays of B mesons with tau lepton in the final state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' The  method is based on the analysis of patterns in the electromagnetic calorimeter by using a Convolutional Neural Network (CNN).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='  Keywords: Electromagnetic calorimeter, Particle identification, Convolutional Neural Network  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Introduction  Searches for New Physics at the intensity frontier are based  on very precise measurements of rare processes within the Stan-  dard Model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Of particular interest, because of persistent hints of  Lepton Flavour Universality (LFU) violation, are semi-leptonic  decays of B mesons, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' decays mediated by the b → cτ+ντ  transitions with a tau lepton in the final state and decays in-  volving b → sµ+µ− and b → se+e− transitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' In decays with  tau lepton in the final state, the tau lepton must be reconstructed  from its long-lived decay products, for example from the decays  τ− → µ−¯νµντ or τ− → e−¯νeντ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' In the Belle II experiment [1, 2],  the momentum spectrum of light leptons from tau decays is  rather soft, a sizable fraction being below 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='7 GeV/c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' One of  the crucial steps in the analysis of these decays is identifying  low momenta light leptons (e or µ) from hadronic background  (mostly π).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' The simplest baseline feature for separating elec-  trons from other charged particles (muons and pions) is E/p,  the ratio between the energy measured in the electromagnetic  calorimeter and the reconstructed momentum of topologically  matched charged track.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' This variable provides an excellent sep-  aration for particles with p > 1 GeV/c, but due to increased en-  ergy losses from bremsstrahlung for low momentum electrons,  the separation is less distinct [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Muons are identified in the  KL and muon system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' However, its efficiency is very poor for  low momentum muons that are out of acceptance of the ded-  icated sub-detector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Other sub-detectors designed for particle  identification, the time of propagation detector and the aerogel  ring-imaging Cherenkov detector, are not able to provide effi-  cient µ/π separation in this momentum range because at low  momenta multiple scattering in the material of the detector as  well as the material in front of it blurs the pattern considerably.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='  Our main goal is to improve the identification of low momen-  tum leptons using the information of energy deposition in the  electromagnetic calorimeter in a form of images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' As a classifier  we are using a Convolutional Neural Network (CNN), a power-  ful machine learning technique designed for working with two-  dimensional images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Using CNN on the images allows us to ac-  cess the information on the shape of the energy deposition with-  out depending on cluster reconstruction or track-cluster match-  ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='  In what follows, we will describe the electromagnetic  calorimeter of Belle II, discuss the analysis of simulated pion,  muon and electron patterns in the electromagnetic calorimeter,  and present the results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Electromagnetic calorimeter of Belle II  The Belle II detector is a large-solid-angle magnetic spec-  trometer designed to reconstruct the products of collisions pro-  duced by the SuperKEKB collider.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' The detector consists of  several sub-detectors arranged around the interaction point in  cylindrical geometry: the innermost Vertex Detector (VXD)  used for reconstructing decay vertices, a combination of the  Pixel Detector (PXD) and Silicon Vertex Detector (SVD);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' the  Central Drift Chamber (CDC) is the main tracking system;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' the  Time of Propagation (TOP) detector in the barrel region and  the Aerogel Ring-Imaging Cherenkov detector (ARICH) in the  forward endcap region are used for hadron identification;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' the  Electromagnetic Calorimeter (ECL) is used to measure the en-  ergy of photons and electrons and the outermost K-Long and  Muon (KLM) detector detects muons and neutral K0  L mesons  [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='  The sub-detector relevant for this work is the ECL, more  specifically its central barrel region barrel region which con-  sists of 6624 CsI(Tl) scintillation crystals, covering the po-  lar angle region 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='2◦ < θ < 128.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='7◦ with respect to the  beam axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' A solenoid surrounding the calorimeter generates  a uniform 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='5 T magnetic field filling its inner volume [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='  We are mainly interested in the transverse momentum range  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='28 < pT < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='7 GeV/c, where the minimal pT threshold en-  sures the tracks are within the ECL barrel region acceptance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='  Preprint submitted to Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Instr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Meth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' A  January 13, 2023  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='05074v1  [hep-ex]  12 Jan 2023  Currently, two methods for the particle identification in the ECL  are available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' The first method relies exclusively on the ratio  of the energy deposited by a charged particle in the ECL and  the reconstructed momentum of topologically matched charged  track, E/p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' While for electrons this variable enables powerful  discrimination, as electrons completely deposit their energy in  the ECL, the µ/π separation is strongly limited, especially for  low-momentum particles with a broader E/p distribution as can  be seen on Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' The second method uses Boosted Decision  Trees (BDT) with several expert-engineered observables char-  acterising the shower shape in the ECL [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='2  E/p [c]  0  2  4  6  8  Events (normalised / (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='02 c))  Belle II Simulation, ECL barrel, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='28  pT < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='7 GeV/c  e  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='2  E/p [c]  0  1  2  3  4  5  Events (normalised / (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='02 c))  Belle II Simulation, ECL barrel, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='28  pT < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='7 GeV/c  Figure 1: Distribution of E/p for simulated single particle candidates: e  (green), µ (red) and π (blue) for 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='28 ≤ pT < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='7 GeV/c in the ECL barrel  region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Analysis of the patterns in the electromagnetic calorime-  ter  Our proposed method to improve the identification of low-  momentum leptons is to exploit the specific patterns in the spa-  tial distribution of energy deposition in the ECL crystals us-  ing a Convolutional Neural Network (CNN)1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' The images are  consistent with the 11 x 11 neighbouring crystals around the  entry point of the extrapolated track into the ECL, where each  pixel corresponds to an individual ECL crystal and pixel inten-  sity to the energy deposited by charged particle in the crystal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='  Examples of the obtained images are shown on Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' While  electrons generate electromagnetic showers depositing the ma-  jority of their energy in the ECL, the dominant interaction in  CsI(Tl) for muons and pions in the aforementioned transverse-  momentum range is ionization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Besides, pions can strongly in-  teract with nuclei producing less localized images compared to  muons [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='  Energy [GeV]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='10  Belle II Simulation, ECL barrel, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='28  pT <  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='7 GeV/c  Figure 2: Examples of simulated energy depositions and the average over 80000  images for e (left), µ (middle) and π (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='  For each binary classification we generated 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='5 × 106 events  using the Belle II Analysis Software Framework [6], where the  1CNN is built using TensorFlow software available from tensorflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='org.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='  data set consists of the same number of signal (e or µ) and back-  ground (π) events with uniformly distributed transverse mo-  menta, polar angle and azimuthal angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' The two data sets were  split on the train-validation-test set as 70 − 10 − 20% and we  use the same CNN architecture for e/π and µ/π case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' As an  input to the convolutional layers we use 11 x 11 images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Before  fully connected layers we add the information about pT and θID,  where the later represents an integer number corresponding to  the location of the ECL crystal and is in the network imple-  mented as an embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' To perform a binary classification,  we have 1 neuron in the output layer with a sigmoid activation  function that outputs the signal probability that the image was  produced by a lepton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Performance  To validate the performance of a binary classifier we use  a Receiver Operating Characteristic (ROC) curve by plotting  true positive rate (µ or e efficiency) against the false positive  rate (π mis-ID rate).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' As the reference for the existing ECL  information, we use the log-likelihood difference, a powerful  discriminator between the competing hypotheses, defined as  ∆LLECL = log LECL  e,µ  − log LECL  π  based only on E/p [3] and  BDT ECL using the shower-shape information from the ECL,  thoroughly described in [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' The ROC curves obtained by these  three methods are shown on Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' 3 for e/π and on Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' 4 for µ/π  classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='0  mis-ID rate  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='0  e efficiency  Belle II Simulation, ECL barrel, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='28  pT < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='5 GeV/c  LLECL (AUC: 89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='34)  BDT ECL (AUC: 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='12)  CNN (AUC: 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='35)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='0  mis-ID rate  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='0  e efficiency  Belle II Simulation, ECL barrel, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='5  pT < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='7 GeV/c  LLECL (AUC: 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='58)  BDT ECL (AUC: 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='25)  CNN (AUC: 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='86)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='0  Figure 3: The performance of three different classifiers for e/π based on only  ECL information: ∆LLECL, BDT ECL, and ∆LLCNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='  2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='0  mis-ID rate  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='0  efficiency  Belle II Simulation, ECL barrel, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='28  pT < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='5 GeV/c  LLECL (AUC: 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='02)  BDT ECL (AUC: 86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='50)  CNN (AUC: 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='56)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='0  mis-ID rate  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='0  efficiency  Belle II Simulation, ECL barrel, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='5  pT < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='7 GeV/c  LLECL (AUC: 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='65)  BDT ECL (AUC: 79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='89)  CNN (AUC: 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='94)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='0  Figure 4: The performance of three different classifiers for µ/π based on only  ECL information: ∆LLECL, BDT ECL, and ∆LLCNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='  Looking at the shapes of ROC curves and the Area Under the  Curve (AUC) values, it is evident that the CNN outperforms  the existing classifiers, ∆LLECL and BDT ECL for both e/π and  µ/π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' The performance of the CNN drops with increasing mo-  mentum as the path in the ECL gets shorter and the specific  patterns in the images become less evident.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Summary and outlook  We can conclude there is more information in the ECL that is  currently used for particle identification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' We saw that the sep-  aration between low-momentum light leptons and pions can be  improved using a CNN on the ECL images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' The newly pro-  posed method looks very promising and worthwhile to be fur-  ther developed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' A comparison of the method presented in this  article to a novel BDT-based analysis is a subject of a forthcom-  ing publication [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Acknowledgements  We thank Anˇze Zupanc for his support with ideas and ad-  vice in the early stages of the project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' This work was supported  by the following funding sources: European Research Coun-  cil, Horizon 2020 ERC-Advanced Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' 884719;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' BMBF,  DFG, HGF (Germany);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Slovenian Research Agency research  grants No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' J1-9124, J1-4358 and P1-0135 (Slovenia).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content='  References  [1] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Abe et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=', KEK Report 2010-1 (2010)  [2] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Adachi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=', Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Instrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Meth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' A 907 (2018)  [3] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Kou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=', PTEP, Volume 2019, Issue 12, 123C01 (2019)  [4] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Milesi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Tan, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Urquijo, EPJ Web of Conferences 245, 06023 (2020)  [5] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Longo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Roney et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=', Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Instrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Meth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' A 982 (2020)  [6] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Kuhr, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Pulvermacher, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Ritter et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=', Comput Softw Big Sci 3, 1  (2019)  [7] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Milesi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=', in preparation for Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Instrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' Meth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
+page_content=' A  3' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tE4T4oBgHgl3EQfbgyP/content/2301.05074v1.pdf'}
diff --git a/59FKT4oBgHgl3EQf-y48/content/2301.11959v1.pdf b/59FKT4oBgHgl3EQf-y48/content/2301.11959v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..a53cc095757d8ed4736d8b38485dfcadaa87981d
--- /dev/null
+++ b/59FKT4oBgHgl3EQf-y48/content/2301.11959v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e2e1dae6b272ef9f8334d1c8b18be33af5ffc0dab3b26ad751b93b590f19dfb4
+size 324157
diff --git a/59FKT4oBgHgl3EQf-y48/vector_store/index.faiss b/59FKT4oBgHgl3EQf-y48/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..8abaad5d550327c780f80af600b769bf3cb4bb7e
--- /dev/null
+++ b/59FKT4oBgHgl3EQf-y48/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:650ae78b74b7b55fab783f55fbe9125d134508d6198160848666a13f7146613a
+size 3145773
diff --git a/59FKT4oBgHgl3EQf-y48/vector_store/index.pkl b/59FKT4oBgHgl3EQf-y48/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..0a5a1e69a05becec218fb174bdd26f246a93b0e9
--- /dev/null
+++ b/59FKT4oBgHgl3EQf-y48/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:71a2aed0c6421367c97016241cbe17a1e599dcd255f64095ff900417af1df870
+size 134762
diff --git a/5NAzT4oBgHgl3EQfEPrI/content/tmp_files/2301.00991v1.pdf.txt b/5NAzT4oBgHgl3EQfEPrI/content/tmp_files/2301.00991v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9ff6ce825e5a42af91c52ed8f7db59a11e933d49
--- /dev/null
+++ b/5NAzT4oBgHgl3EQfEPrI/content/tmp_files/2301.00991v1.pdf.txt
@@ -0,0 +1,1821 @@
+MNRAS 000, 1–14 (2021)
+Preprint 4 January 2023
+Compiled using MNRAS LATEX style file v3.0
+Multi-wavelength study of TeV blazar 1ES 1218+304 using
+gamma-ray, X-ray and optical observations
+Rishank Diwan,1⋆ Raj Prince,2 Aditi Agarwal,3 Debanjan Bose,4† Pratik Majumdar,5
+Aykut Özdönmez,6 Sunil Chandra,7,8 Rukaiya Khatoon,8 Ergün Ege,9
+1Laboratory for Space Research, The University of Hong Kong, 405B Cyberport 4, 100 Cyberport Road, Cyberport, Hong Kong
+2Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland
+3 Raman Research Institute, C. V. Raman Avenue, Sadashivanagar, Bengaluru - 560080, India
+4 S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata-700106
+5 Saha Institute of Nuclear Physics, a CI of Homi Bhabha National Institute, Kolkata 700064, West Bengal, India
+6 Ataturk University, Faculty of Science, Department of Astronomy and Space Science, 25240, Yakutiye, Erzurum
+7 South African Astronomical Observatory, Observatory Road, Observatory, Cape Town 7925, South Africa
+8 Center for Space Research, North-West University, Potchefstroom, 2520, South Africa
+9 Istanbul University, Faculty of Science, Department of Astronomy and Space Sciences, 34116, Beyazıt, Istanbul, Turkey
+Accepted XXX. Received YYY; in original form ZZZ
+ABSTRACT
+We report the multi-wavelength study for a high-synchrotron-peaked BL Lac 1ES 1218+304 using near-simultaneous
+data obtained during the period from January 1, 2018, to May 31, 2021 (MJD 58119-59365) from various instruments
+including Fermi-LAT, Swift-XRT, AstroSat, and optical from Swift-UVOT & TUBITAK observatory in Turkey. The
+source was reported to be flaring in TeV γ-ray during 2019 but no significant variation in Fermi-LAT is observed. A
+minute scale variability is seen in SXT light curve suggesting a compact emission region for their variability. However,
+Hour’s scale variability is observed in the γ-ray light curve. A "softer-when-brighter" trend is observed in γ-ray and an
+opposite trend is seen in X-ray suggesting both emissions are produced via two different processes as expected from an
+HBL source. We have chosen the two epochs in January 2019 to study and compare their physical parameters. A joint
+fit of SXT and LAXPC provides a great constraint on the synchrotron peak roughly estimated to be ∼2.68×1017 Hz.
+A clear shift in the synchrotron peak is observed from 1017−18 to 1020 Hz revealing its extreme nature or behaving like
+an EHBL-type source. The optical observation provides color-index variation as "blue-when-brighter". The broadband
+SED is fitted with a single-zone SSC model and their parameters are discussed in the context of a TeV blazar and
+possible mechanism behind the broadband emission.
+Key words:
+galaxies: active – galaxies: jets – gamma-rays: galaxies – radiation mechanisms: non-thermal – BL
+Lacertae objects: individual: 1ES 1218+304
+1 INTRODUCTION
+Active galactic nuclei (AGN) host a supermassive black hole
+(SMBH) at the center which accretes matter from the sur-
+rounding. The matters are in Keplerian orbit and fall into
+the SMBH via an accretion disk. The mechanism proposed
+in Blandford & Znajek (1977) suggests that the magnetic
+field lines from the accretion disk get twisted and collimated
+due to the high spin of SMBH and eject the matter through
+a bipolar jet perpendicular to the accretion disk plane. Later,
+the AGNs were classified based on how they are viewed
+commonly known as the AGN unification scheme (Urry &
+Padovani 1995). Blazars are a subclass of active galactic nu-
+clei that have their relativistic jet pointed to the observer.
+⋆ E-mail: rishank2610@gmail.com
+† E-mail: debaice@gmail.com
+They are characterized by rapid variability from hours to
+days’ timescales across all wavelengths, high polarization, and
+superluminal jet speeds. Blazars can be further subdivided
+into two classes: flat spectrum radio quasars (FSRQs) and
+BL Lacertae (BL Lac) objects. The broad-band continuum
+spectra of blazars are dominated by non-thermal emission.
+The spectral energy distribution of blazars is characterized
+by a double hump structure: the first hump is generally at-
+tributed to the synchrotron radiation in the radio to X-ray
+bands whereas there is intense debate about the origin of
+the second hump. The commonly accepted emission mech-
+anism is via inverse Compton scattering of the low-energy
+photons by high-energy electrons in the system from GeV
+to TeV energies. There are alternative scenarios proposed
+by several authors which involve hadronic interactions pro-
+ducing neutral pions. These pions decay to generate photons
+in the GeV-TeV energies (Mannheim 1993; Aharonian 2000;
+© 2021 The Authors
+arXiv:2301.00991v1  [astro-ph.HE]  3 Jan 2023
+
+2
+R. Diwan et al.
+Böttcher et al. 2013). The BL Lac-type sources are further
+subdivided into three main classes depending on the position
+of their low-energy peak. If the synchrotron peak is observed
+at < 1014Hz, those BL Lacs are called low-frequency peaked
+BL Lacs (LBLs). If the synchrotron peak is observed be-
+tween 1014Hz and 1015Hz, then they are called intermediate-
+frequency peaked BL Lacs (IBLs). Finally, BL Lacs with syn-
+chrotron peak ≥ 1015Hz is called high-frequency peaked BL
+Lacs (HBLs). There is also a newly defined class of ultra-
+high-frequency peaked BL Lacs (UHBLs) with the spectral
+peak of the second bump (high energy peak) in the SED lo-
+cated at an energy of 1 TeV or above. These blazars are also
+known as "extreme blazars" or EHBLs. (Abdo et al. 2010).
+Multiwavelength observation of blazars is a very important
+tool for investigating the various properties of the blazars and
+the jet. For example, the shortest variability timescale allows
+one to put strong constraints on the size of the emission re-
+gion of the blazar. The location of the emission region along
+the jet axis is another challenging problem in blazar physics.
+Many studies have been done in the past to locate the emis-
+sion region, in some cases, it has been found that the emission
+happens very close to the SMBH within the broad-line region
+(BLR) (Prince 2020; Prince et al. 2021). However, in some
+studies, it has been proposed to be at higher distances be-
+yond the broad-line region (Cao & Wang 2013; Nalewajko
+et al. 2014; Barat et al. 2022). The break or curvature in the
+γ-ray spectrum above 10-20 GeV suggests the emission region
+within the BLR as the BLR is opaque to high energy pho-
+tons above 10 GeV ( Liu & Bai 2006). The cross-correlation
+studies among the various wavebands are another way to lo-
+cate the emission region along the jet axis. In many studies,
+it has been reported that simultaneous broadband emissions
+generally have a co-spatial origin. However, in some cases, a
+significant time lag has been reported strongly suggesting the
+different locations for the different emissions (Prince 2019).
+In the first case scenario, one zone emission model is favored
+to explain the broadband SED, and in the later case, the
+multi-zone emission model is preferred (Prince et al. 2019).
+The production of high-energy γ-rays in blazar suggests an
+acceleration of charged particles to very high energy and
+many models have been proposed to explain the acceleration.
+The most accepted mechanisms are the diffusive shock accel-
+eration (Schlickeiser 1989a,b) and the magnetic re-connection
+(Shukla & Mannheim 2020). In many studies shock accelera-
+tion has been favored which also demands the emission region
+close to the SMBH within the BLR because the shocks are
+produced and are strong at the base of the jet. On the other
+hand, the magnetic reconnection happens due to external per-
+turbation and hence demands the jet to be less collimated i.e.
+the emission region is farther from the base.
+In this paper, we report on a multiwavelength study of the
+TeV blazar 1ES1218+304 to understand the broadband prop-
+erties of the source. It is located at a redshift, z = 0.182 with
+R.A. = 12 21 26.3 (hh mm ss), Dec = +30 11 29 (dd mm ss).
+It has been observed in TeV energy with VERITAS (Fortin
+2008, Acciari et al. 2009) and MAGIC (Albert et al. 2006,
+Lombardi et al. 2011) and are part of TeV Catalog1.
+The paper is arranged in the following way. We discuss the
+multiwavelength observations and the data analysis proce-
+1 http://tevcat.uchicago.edu/
+dures from different instruments used in this study in Section
+2. In section 3, we have discussed the results from Astrosat
+alone and the broadband light curves and spectral energy dis-
+tributions at length. In Section 4 we summarise and discussed
+the important findings in the context of blazar physics and
+eventually conclude our work in Section 5.
+2 MULTIWAVELENGTH OBSERVATIONS,
+DATA ANALYSIS AND DATA REDUCTION
+The following section describes the data analysis technique
+used to generate a multi-waveband light curve. In the sub-
+sections, we provide a description of the data analysis tech-
+nique of γ-ray data collected from Fermi-Lat. X-ray, and
+UV-optical data were collected from Swift-XRT and Swift-
+UVOT. Also, soft X-ray and hard X-ray data were collected
+from AstroSat-SXT and AstroSat-LAXPC, respectively and
+Optical Data from TUBITAK National Observatory.
+2.1 Fermi-LAT γ-ray Observatory
+Large Area Telescope (LAT) is a gamma-ray telescope placed
+on Fermi gamma-ray space observatory2 which was launched
+in 2008. It has a working energy range of 20 MeV to 1
+TeV with a field of view of 2.4 Sr (Atwood et al. 2009).
+The orbital period of the telescope is around ∼ 96 mins
+in each hemisphere and covers the entire sky in total ∼ 3
+hr. Blazar 1ES 1218+304 is continuously being monitored
+since 2008. In this study, we have analyzed the data from
+1st January 2018 - 31st May 2021 when the source was
+reported to be flaring in gamma-ray (January 2019). The
+analysis was performed using Fermipy v0.17.43(Wood et al.
+2021) and the standard Fermi tools software (Fermitools
+v1.2.23)4 between 0.3-300 GeV. A 15◦ circular region was
+chosen around the source to extract the photon events with
+evclass=128 and evtype=3 and the time intervals were re-
+stricted using ‘(DATA_QUAL>0)&&(LAT_CONFIG==1)’
+as recommended by the Fermi-LAT team in the fermitools
+documentation. The source model file was generated using
+the Fermi 4FGL catalog (Abdollahi et al. 2020) and the back-
+ground gamma-ray emission was taken care of by using the
+gll_iem_V07.fits file along with the isotropic background
+emission by using the iso_P8R3_SOURCE_V2_v1.txt file. In
+addition, the zenith angle cut was chosen as 90◦ to reduce the
+contamination from the Earth limb’s γ-ray. The source and
+background were modeled by the binned Likelihood method.
+Initially, the spectral parameters of all the sources were kept
+free to optimize the γ-ray emission from them. Eventually,
+we generated the γ-ray light curves for 7, 15, and 30 days
+of binning for our scientific purpose. To extract lightcurve
+and perform spectral fitting normalization of the sources only
+within 2◦ of ROI were kept free, and the rest of the param-
+eters and other source models were frozen, except that of
+Source of Interest, in this case, blazar 1ES 1218+304 and a
+high flux source 4FGL J1217.9+3007, with an offset of 0.753◦
+from 1ES 1218+304, which constitutes to 10 parameters for
+2 https://fermi.gsfc.nasa.gov/
+3 Fermipy webpage
+4 Fermtools Github page
+MNRAS 000, 1–14 (2021)
+
+Multi-wavelength study of 1ES 1218+304
+3
+likelihood analysis. PowerLaw model was used for the source
+as given below:
+dN(E)
+dE
+= No ×
+� E
+Eo
+�−α
+(1)
+where Eo and No are the scale factor and the prefactor, re-
+spectively provided in the 4FGL catalog and α is the spectral
+index.
+2.2 AstroSat
+On January 03, 2019 MAGIC reported a gamma-ray activ-
+ity and detection of very high energy γ ray from blazar 1ES
+1218+304 (Mirzoyan 2019). Later, VERITAS also detected a
+γ-ray flare from this source (Mukherjee & VERITAS Collab-
+oration 2019). Following these two events, we proposed a tar-
+get of opportunity proposal in India’s first space-based multi-
+wavelength observatory, AstroSat5. Observations were car-
+ried out from 17th to 20th January with a soft-Xray telescope
+(SXT) and large area X-ray proportional counter (LAXPC).
+2.2.1 SXT
+The SXT working energy range is 0.3-7.0 keV and the ob-
+servation was performed with photon counting mode (PC).
+The level-1 data was downloaded from the webpage and fur-
+ther reduction was performed with the latest SXT pipeline,
+sxtpipeline1.4b (Release Date: 2019-01-04). It produces
+the cleaned level-2 data products which were used for fur-
+ther analysis (Singh et al. 2016, Singh et al. 2017). The ob-
+servations were done in various orbits and therefore it was
+merged together with the help of SXTEVTMERGERTOOL. The
+X-ray light curve is extracted using XSELECT with a circular
+region of 16′ centered on the source. The energy selection
+of 0.3-7.0 keV was applied in XSELECT itself using the chan-
+nel filtering through pha_cutoff filter. The source spectrum
+was extracted for 0.3-7.0 keV energy range and the back-
+ground spectrum file was used provided by the AstroSat
+SkyBkg_comb_EL3p5_Cl_Rd16p0_v01.pha. The spectrum was
+grouped in GRPPHA in order to have good photon statistics in
+each bin. The ancillary response file (arf) was generated using
+sxtARFModule and the RMF file (sxt_pc_mat_g0to12.rmf)
+was provided by the SXT-POC (Payload Operation Cen-
+ter) team. Eventually, the X-ray spectra from 0.3-7.0 KeV
+with proper background and response files were loaded in
+XSPEC and fitted with the simple absorbed power-law and
+log-parabola spectral models with the correction of ISM ab-
+sorption model at NH = 1.91×1020 cm−2 (HI4PI Collabora-
+tion et al. 2016).
+2.2.2 LAXPC
+LAXPC works in the hard X-ray energy range from 3.0-80.0
+keV (Yadav et al. 2016) consisting of three identical detec-
+tors namely LAXPC10, LAXPC20, and LAXPC30. Unfor-
+tunately, LAXPC 10 was operating at a lower gain during
+the time of observation period. Also, the LAXPC30 detec-
+tor has a gain instability issue caused by substantial gas
+5 https://www.isro.gov.in/AstroSat.html
+leakage. Therefore, we used only LAXPC20 for the analy-
+sis, and the corresponding results are presented here. The
+Level-1 data were processed using the LaxpcSoft package
+available in AstroSat Science Support Cell (ASSC)6. We
+generated the Level-2 combined event file using the com-
+mand laxpc_make_event. During the data processing, a
+good time interval was applied to exclude the time inter-
+vals corresponding to the Earth occultation periods, SAA
+passage, and standard elevation angle screening criteria
+by using the laxpc_make_stdgti tool. Finally, the tools
+laxpc_make_spectra and laxpc_make_lightcurve were used
+to produce the spectra and lightcurve of the source, using the
+gti file. We restricted the spectra to the energy range of
+4-20 keV since the background dominates the spectra above
+this energy. In the spectral analysis, a 3% systematic un-
+certainty was added to the data. The obtained lightcurve is
+not background subtracted, therefore we estimated the back-
+ground following the faint source routine (Misra et al. 2021).
+However, due to insignificant variations observed in the ex-
+tracted lightcurve from LAXPC20, we did not use them in
+our study.
+2.3 The Neil Gehrels Swift Observatory
+Simultaneous to AstroSat, blazar 1ES 1218+304 was also ob-
+served in X-ray with Swift-XRT and in optical-UV by Swift-
+UVOT telescopes7. It provides a unique opportunity to have
+simultaneous broadband light curves and spectrum which is
+important to decipher the cause behind the flare and the
+broadband emission.
+2.3.1 XRT
+X-ray telescope (XRT) works in an energy range between 0.3-
+10.0 keV. Multiple observations were done during this period
+with an average of 2ks exposure. We have analyzed the data
+following the standard Swift xrtpipeline and the details can
+be found on Swift webpage8. The cleaned event files were pro-
+duced and a circular region of 10” was chosen for the source
+and background around the source and away from the source.
+Tool XSELECT was used to extract the source light curve and
+the spectrum. The spectrum was binned by using the tool
+GRPPHA to have a sufficient number of counts in each bin. A
+proper ancillary response file (ARF) and the redistribution
+matrix files (RMF) were used to model the X-ray spectra in
+XSPEC. A simple unabsorbed power law was used to fit the X-
+ray 0.3-10.0 keV spectra and extract the X-ray flux. The soft
+X-ray (below 1 keV) is prone to go through interstellar ab-
+sorption in Milky-way and hence a correction is applied with
+NH = 1.91×1020 cm−2 (HI4PI Collaboration et al. 2016).
+2.3.2 UVOT
+Having an ultraviolet-optical telescope has the advantage of
+getting simultaneous observations to X-ray. UVOT has six
+filters namely U, B, and V in optical and W1, M2, and W2
+in the ultraviolet band. The image files were opened in DS9
+6 http://astrosat-ssc.iucaa.in
+7 https://swift.gsfc.nasa.gov/
+8 https://www.swift.ac.uk/analysis/xrt/
+MNRAS 000, 1–14 (2021)
+
+4
+R. Diwan et al.
+Table 1. Best fit spectral parameters of 1ES 1218+304 from SXT observations of 17-20 January 2019. X-ray flux is presented in the unit
+(erg cm−2 s−1). The spectrum is fitted with both the power-law and log-parabola models. In the last row, we show the joint fit of the
+SXT and LAXPC spectrum. We also added a 3% systematic in the fit as suggested by the AstroSat team. The parameters are compared
+for free and fixed NH (HI4PI Collaboration et al. 2016) values. The overall fit provide better fit with free NH.
+Model
+Parameters
+Value
+Power-law
+Fixed nH
+Free nH
+TBabs
+NH(1022cm−2)
+0.0191
+0.057±0.005
+Index
+Γ
+1.95±0.01
+2.11±0.02
+Flux
+F0.3−10.0 keV
+(1.427 ± 0.004) × 10−10
+(1.474 ± 0.006) × 10−10
+χ2/dof
+777/434
+595.75/433
+Logparabola
+TBabs
+NH(1022cm−2)
+0.0191
+0.075±0.014
+Index
+α
+1.90±0.02
+2.21±0.08
+β
+0.28±0.04
+0.15±0.11
+Flux
+F0.3−10.0 keV
+(1.300 ± 0.009) × 10−10
+(1.585 ± 0.037) × 10−10
+χ2/dof
+642.28/433
+590.55/432
+Logparabola
+joint fit
+SXT + LAXPC
+TBabs
+NH(1022cm−2)
+0.0191
+0.042±0.010
+Index
+α
+1.85±0.02
+1.98±0.06
+β
+0.33±0.03
+0.22±0.06
+Norm
+0.0262±0.0002
+0.0281 ± 0.0009
+Constant factor
+-
+0.96±0.04
+0.96±0.04
+χ2/dof
+601.16/402
+587.72/401
+software and the source and background region of 5" and 10"
+were selected around the source and away from the source,
+respectively. The task UVOTSOURCE has been used to get the
+magnitudes which were later corrected for galactic reddening,
+E(B-V)=0.0176 (Schlafly & Finkbeiner 2011) and converted
+into the fluxes using zero points and the conversion factor
+(Giommi et al. 2006).
+2.4 Optical
+The optical observations of our source were performed in the
+Johnson BVRI bands using the three ground-based facilities
+in Turkey, namely, 0.6m RC robotic (T60) and the 1.0m RC
+(T100) telescopes at TUBITAK National Observatory, and
+0.5m RC telescope at Ataturk University in Turkey. Techni-
+cal details of these telescopes are explained in Agarwal et al.
+(2022). The standard data reduction of all CCD frames, i.e.
+the bias subtraction, twilight flat-fielding, and cosmic-ray re-
+moval, was done as mentioned in (Agarwal et al. 2019a).
+2.5 Archival
+We have used the archival optical data from ASAS-SN (All-
+Sky Automated Survey for Supernovae) (Shappee et al. 2014;
+Kochanek et al. 2017).We have also used long-term high flux
+observation in UV/Optical range from NASA/IPAC Extra-
+galactic Database (NED)9 for providing the reference points
+in our SED analysis. We have also extracted the NuSTAR
+SED data points from (Sahakyan 2020) and plotted them
+alongside our SED analysis.
+9 https://ned.ipac.caltech.edu/
+3 RESULTS
+In this section, we provide the main results of our work using
+the above broadband observations. We have explained various
+characteristics of broadband light curves and spectral energy
+distributions.
+3.1 Astrosat results
+Astrosat observations in SXT and LAXPC were done dur-
+ing 17-20 January 2019 after two weeks of TeV detection.
+We have produced the SXT light curve and the spectrum
+as shown in Figure 1 and Figure 2 for 0.3-7.0 keV energy
+band. The source appears to be variable on a short-time
+scale and the corresponding fractional variability and vari-
+ability time is estimated in section 3.2. A spectrum is ex-
+tracted in the energy range of 0.3-7 keV and fitted with the
+power law and log-parabola models. The best-fit parame-
+ters are presented in Table 1. We started with a power-law
+with fixed hydrogen column density, NH = 0.0191×1020 cm−2
+and ended up getting χ2/dof = 777/434 with photon spec-
+tral index, Γ = 1.95±0.01 and 0.3-7 keV flux, F0.3−7keV =
+(14.27±0.04)×10−11 ergs/cm2/s. Next, we keep NH as a free
+parameter and the best fit value is estimated as 0.057±0.005
+in units of 1020 cm−2. The χ2/dof has improved to 595.75/433
+and the spectral index was found to be 2.11±0.02 with almost
+the same 0.3-7 keV flux. We repeat the same procedure with
+the log parabola model and with both the cases of fixed and
+free NH and it gives a better fit than the power law. With
+the free NH parameter we achieved a better fit with χ2/dof
+= 590.55/432 compared to the power-law case. The best-fit
+spectral index is 2.21±0.08 a bit softer than the power-law
+index. The details about the other parameters are provided
+in Table 1.
+MNRAS 000, 1–14 (2021)
+
+Multi-wavelength study of 1ES 1218+304
+5
+0
+20000
+40000
+60000
+80000
+100000 120000
+Time(s)
+1.6
+1.7
+1.8
+1.9
+2.0
+2.1
+2.2
+2.3
+Counts/sec
+SXT 0.3-7.0 keV
+Figure 1. AstroSat-SXT light curve for energy 0.3-7.0 keV. The
+bin size is taken as 856 sec.
+We could not get a good light curve in LAXPC but ex-
+tracted the spectrum from 4-20 keV. The SXT and LAXPC
+spectra are jointly fitted with Power law and Log-parabola
+models. In the case of the Power-law, we get the χ2/dof
+= 948.46/403 and 623.25/402 for fixed and free NH val-
+ues. In both cases, the reduced-χ2 is much higher than
+the case of Log-parabola (Table 1) and hence not pur-
+sued further. For the joint fit, we used the total model as
+constant*tbabs*logpar. The constant factor is fixed at 1.0
+for data group 1 and kept as a free parameter for data group
+2. The best fit value for the constant factor is 0.96±0.04 for
+both fixed and free NH. The overall reduced-χ2 is improved
+when the NH is free and it is estimated as 4.2±1.0 (×1020
+cm−2), almost two times higher than the fixed NH value. Fig-
+ure 3 shows the best fit plot with a log-parabola model. We
+found that the spectral index, α, and the curvature parame-
+ter, β are a bit different during fixed and free NH. The math-
+ematical representation of the log-parabolic model is given
+as,
+F(E) = K(E/E1)(−α+βlog(E/E1))ph cm−2 s−1 keV,
+(2)
+where K is the normalization and the E1 is the reference
+energy fixed at 1 keV. Using the best-fit parameters of the
+log-parabola model we can estimate the location of the syn-
+chrotron peak, which is given as Ep = E1 10(2−α)/2β keV.
+For α=1.98 and β=0.22, the Ep is estimated as 1.11 keV or
+2.68×1017 Hz. The peak of the synchrotron emission is mostly
+constrained by the X-ray as shown in Figure 3 which peaks
+at ∼ 2.68×1017 Hz.
+3.2 Broadband Light curves
+We have collected the γ-ray data between 2018 to 2021. The
+source was found to be in a flaring state in γ-ray during Jan
+2019. Simultaneous observation in Swift-XRT and UVOT
+also confirms the flaring behavior in X-ray as well as in
+optical-UV. On 02 January 2019 source was reported to be
+flaring in very high energy gamma-ray by MAGIC (Mirzoyan
+2019) which was followed by VERITAS (Mukherjee &
+VERITAS Collaboration 2019) and observation was done on
+4, 5, and 6 January 2019 show high flux state above 100 GeV
+and the corresponding period is marked by light pink color
+in Figure 4. We identify this period as Flare A. In X-ray
+10−3
+0.01
+0.1
+1
+normalized counts s−1 keV−1
+1
+0.5
+2
+5
+0.5
+1
+1.5
+2
+2.5
+ratio
+Energy (keV)
+Figure 2. The 0.3 - 7.0 keV energy spectrum of 1ES 1218+304
+fitted with Logparabola spectral model with free galactic absorp-
+tion. The SXT data were taken during the period 17-20 January
+2019.
+10−10
+2×10−11
+5×10−11
+ν Fν (ergs cm−2 s−1)
+1017
+1018
+2×1017
+5×1017
+2×1018
+1
+1.5
+2
+ratio
+Energy (Hz)
+Figure 3. The joint SXT (red) and LAXPC (blue) spectra are
+modeled together. The SXT energy range is taken as 0.3 - 7.0
+keV and LAXPC is taken from 3.0-20.0 keV. The joint spectra are
+fitted with a log parabola spectral model. Both spectra were taken
+simultaneously during the period of 17-20 January 2019.
+and optical source was reported to be historically bright
+with flux around ∼ 2×10−10 erg cm−2 s−1 in X-ray and
+with R band flux 2.35±0.05 mJy (Ramazani et al. 2019).
+We also proposed this source in India’s first space mission,
+AstroSat for broadband observation. Our observation was
+done between 17-20 January 2019. This period is marked
+as a vertical green line in Figure 4 and identified as Flare
+B. The first two panels of Figure 4 represent the long-term
+γ-ray (GeV) light curve and corresponding photon spectral
+index. The source is not very bright in Fermi-LAT but a
+clear variability in the flux is seen. Panel 3 & 4 represent the
+long-term Swift-XRT light curve and corresponding photon
+spectral index. A clear X-ray brightening during Jan 2019 is
+observed. During this period, we do not have many optical
+observations (panel 5), and hence it’s difficult to comment
+on the flux level. However, in UV (W1, M2, W2) bands
+(panel 6) high flux state is observed corresponding to TeV
+and X-ray activity. In panel 7, we show the archival optical
+data from ASAS-SN, and no short time scale variability
+MNRAS 000, 1–14 (2021)
+
+6
+R. Diwan et al.
+is seen. We also have optical data from the ground-based
+observatory (panel 5) which covers the last part of the light
+curve showing a nice variation from a high flux state to a low
+flux state, suggesting a long-term variation in optical bands.
+3.3 Variability Study
+In general, blazar shows significant variability during the flar-
+ing period. The properties of these flares can depend on var-
+ious factors like particle injection, particle acceleration, and
+energy dissipation in the jets of the blazars. To study this in-
+trinsic property we calculate the Fractional Variability Am-
+plitude (Fvar) from the multi-wavelength light curve of the
+source. The relation given in (Vaughan et al. 2003) is used to
+determine the fractional variability (Fvar)
+Fvar =
+�
+S2 − E2
+F 2
+(3)
+err(Fvar) =
+�
+�
+�
+�
+��
+1
+2N
+E2
+F 2Fvar
+�2
++
+��
+E2
+N
+1
+F
+�2
+(4)
+where S2 is the variance of the light curve, F is the aver-
+age flux, E2 is the mean of the squared error in the flux
+measurements and N is the number of flux points in a light
+curve. We have estimated the Fvar for all the light curves
+and the corresponding values are tabulated in Table 2. We
+found that the source is more variable in UV followed by X-
+ray and gamma-ray. We also plot the Fvar with respect to
+the corresponding frequency in Figure 5. A similar behavior
+is also seen for another TeV blazar 1ES 1727+502 for one of
+the states (Prince et al. 2022). In past studies, it has also
+been argued that the variability pattern resembles the shape
+of the broadband SED seen in blazar if the source is observed
+from radio to very high energy gamma-ray. One of the best
+examples is Mrk 421 which is also a TeV source, where the
+variability pattern during its two flaring states resembles the
+blazar SED (Aleksić et al. 2015a,b). A long-term study, using
+10 yrs data, is done on 1ES 1218+304 by Singh et al. (2019)
+using the multi-wavelength data from radio to γ-ray and the
+Fvar estimated on long-term period is different from what we
+have found in our study. Singh et al. (2019) have found that
+source is more variable in radio at 15 GHz followed by X-ray
+and then optical-UV and γ-ray.
+The timescale of variability is yet another important pa-
+rameter that sets the bound on the size of the emission re-
+gion. Doubling/Halving timescales are calculated for all time
+bins from MJD 58119 to 59365 for the 7-day binned γ-ray
+light curve. The formula used is:
+F(t2) = F(t1) × 2(t2−t1)/Td
+(5)
+Here F(t1) and F(t2) are the fluxes measured at time t1
+and t2, respectively. Td is the flux doubling/halving time
+scale. The fastest doubling/halving time (Tf) in γ-ray was
+found to be 0.396 days. The value for tvar can be given by
+tvar = ln(2)×Tf which is 0.275 days or 6.6 hours. The hour’s
+scale variability is very common in blazar suggesting a com-
+pact emitting region close to the central supermassive black
+hole.
+Waveband
+Fvar
+err(Fvar)
+Fermi γ-ray
+0.2601
+0.0964
+AstroSat-SXT X-ray
+0.0421
+0.0058
+Swift X-ray
+0.5074
+0.01513
+W1
+0.9448
+0.0006
+W2
+0.6805
+0.0005
+M2
+0.9448
+0.0007
+U
+0.0242
+3.3185E-05
+V
+0.0147
+0.0002
+B
+0.0171
+0.0002
+R
+0.0144
+6.5188E-05
+I
+0.0120
+8.2755E-05
+Table 2.
+Fractional variability amplitude (Fvar) parameter for
+the blazar 1ES 1218+304 from optical to HE γ-rays using observa-
+tions during January 1, 2018 - May 31, 2021 (MJD 58119-59365)
+with different instruments.
+Using the same equation we also calculate the time-scale vari-
+ability for the 856 sec binned AstroSat SXT light curve shown
+in Figure 1. The flux doubling/halving time is estimated as
+Tf = 1848.645 sec and the tvar is 1281.29 sec (1.2 ksec) or
+21.35 minutes. A similar flux variability time of 1.1 ksec is
+also estimated for Mrk 421 in SXT light curve by Chatter-
+jee et al. (2021). Considering the fact that 1ES 1218+304
+is a high synchrotron peaked blazar the X-ray will explain
+the synchrotron emission. As argued by many authors that
+the variability time can be associated with the characteristic
+time scale in the system. Here, we consider that the X-ray
+variability timescale can be linked with the radiation cooling
+time scale due to synchrotron only. Under this assumption
+the cooling time can be the fast X-ray variability time and
+can be defined as (Rybicki & Lightman 1979),
+tcool ≃ 7.74 × 108 (1 + z)
+δ
+B−2γ−1 sec.
+(6)
+Where, B is the strength of the magnetic field in Gauss and
+tcool is the synchrotron cooling timescale in seconds. Follow-
+ing Rybicki & Lightman (1979), We can also derive the char-
+acteristic frequency of the electron population responsible for
+the synchrotron emission at the peak frequency,
+νch,e = 4.2 × 106
+δ
+(1 + z)Bγ2 Hz.
+(7)
+Using the above two equations, we eliminate the γ since it
+changes with different states and derives a single equation
+given as,
+B3δ ≃ 2.5(1 + z)(νch,e/1018)−1τ −2
+d .
+(8)
+Using the above equation we derive the magnetic field
+strength for Doppler factor, δ, =30 and variability time scale
+of 1.2 ksec and it is found to be 0.1 G. The strength of the
+magnetic field derived from the broadband SED modeling is
+a factor lower than this estimated value. This discrepancy
+could be because of the many assumptions made in deriving
+the eqn (7) or due to the degeneracy in the SED modeling.
+3.4 Flux-Index Correlation
+We computed flux-index correlation for the γ-ray and X-ray
+data to study index hardening/softening. The flux vs index
+plot is shown in Figure 6 with γ-ray on the upper panel and
+MNRAS 000, 1–14 (2021)
+
+Multi-wavelength study of 1ES 1218+304
+7
+0
+1
+2
+3
+4
+5
+Flux0.3
+300 GeV
+1.0
+1.5
+2.0
+2.5
+Index
+0.5
+1.0
+1.5
+2.0
+Flux0.3
+10 KeV
+1.5
+2.0
+2.5
+3.0
+Index
+15.0
+15.5
+16.0
+16.5
+17.0
+Optical (mag)
+U
+B
+V
+R
+I
+15.5
+16.0
+16.5
+17.0
+17.5
+UV (mag)
+W1
+M2
+W2
+58200
+58400
+58600
+58800
+59000
+59200
+MJD
+14
+15
+16
+17
+Optical (mag)
+ASAS-SN
+Figure 4. Multi-wavelength light curve of 1ES 1218+304 from January 2018 to May 2021. 7-day binned γ-ray flux are presented in units
+of 10−8 ph cm−2 s−1, and X-ray fluxes are in units of 10−10 erg cm−2 s−1. The vertical red line represents the Flare period from 5-7
+January 2019 and the vertical green line represents the Flare period from 15-20 January 2019. This period also includes the data from
+AstroSat for the period 17-20 January 2019. We identify these periods as Flare A and Flare B.
+X-ray on the lower panel. In the case of γ-ray, we have taken
+data points with TS≥16. We also observe a positive corre-
+lation between the flux and index, with Pearson correlation
+coefficient, R = 0.644 and p-value ≈ 0. The trend follows
+the linear function with slope = 0.212. In contrast to the
+above plot, X-ray data shows an inverse trend i.e; a negative
+correlation between flux and index, with Pearson correlation
+coefficient, R = -0.748 and p-value ≈ 0. It can also be fit-
+ted by a linear function with a slope = -0.423. This plot
+shows two contrasting trends, we can see the ’harder-when-
+brighter’ trend in the X-ray energy range and the ’softer-
+when-brighter’ trend in the γ-ray energy range. A similar
+trend is also observed for one of the TeV blazar 1ES 1727+502
+(Prince et al. 2022). One of the possible explanations for hav-
+ing different trends in X-ray and gamma-ray is that they are
+produced via two different processes. For BL Lac-type sources
+such as 1ES 1218+304, it is well-known that the X-rays are
+produced by the synchrotron process and γ-rays are produced
+via the inverse-Compton process. A long-term study done by
+Singh et al. (2019) also found a mild harder-when-brighter
+MNRAS 000, 1–14 (2021)
+
+8
+R. Diwan et al.
+1016
+1018
+1020
+1022
+1024
+1026
+Frequency (Hz)
+0.0
+0.2
+0.4
+0.6
+0.8
+Fractional Variability amplitude
+Gamma-ray
+SWIFT X-ray
+Optical
+SWIFT-UV
+AstroSat SXT
+Figure 5. Fractional variability for various wavebands is plotted
+with respect to their frequency.
+0
+1
+2
+3
+4
+5
+6
+7
+Photon Flux (10
+8 ph cm
+2 sec
+1)
+1.0
+1.5
+2.0
+2.5
+3.0
+Index
+-ray
+r= 0.644, p-value= 1.04×10
+11
+0.25
+0.50
+0.75
+1.00
+1.25
+1.50
+1.75
+2.00
+Flux_(0.3-10 KeV) (10
+10 erg cm
+2 sec
+1)
+1.6
+1.8
+2.0
+2.2
+2.4
+2.6
+2.8
+3.0
+Index
+X-ray
+r= -0.748, p-value= 1.139×10
+5
+Figure 6. Scatter plot for the correlation between flux and index of
+the blazar 1ES 1218+304. The top plot represents the 7-day binned
+Fermi-Lat data. The slope is positive and the Person correlation
+coefficient is 0.644. The bottom plot represents Swift-XRT data
+for Flux (0.3-10 KeV) vs Photon Index. The slope is negative and
+the Pearson correlation coefficient is -0.748, it follows an inverse
+trend as the γ-ray data. The orange line is a linear fit for reference.
+trend in X-rays using almost 10 yrs of data. The average
+spectral index is estimated as 1.99±0.16 which is consistent
+with our estimated value as ∼2.0. These results are also con-
+sistent with the long-term study done by Wierzcholska &
+Wagner (2016) where they found the average photon spec-
+tral index as ∼2.0±0.01 for different values of galactic ab-
+sorption taken from different models. A recent study done by
+Sahakyan (2020) estimated the average photon spectral index
+≥2 for the period considering from 2008 to 2020. The spec-
+tra can be even harder during the bright state as 1.60±0.05
+which is consistent with our result (see Figure 6).
+103
+104
+105
+Energy (MeV)
+10
+6
+10
+5
+10
+4
+E2 dN
+dE [MeV cm
+2 s
+1]
+Likelihood Fit
+5-7 Jan
+15-20 Jan
+Total Time Period
+Figure 7. The γ-ray SED extracted for both the period and fit-
+ted with power-law using the Likelihood fit method. The fitting
+parameters are discussed in the corresponding Section 3.5.
+3.5 Fermi-LAT γ-ray spectral fitting
+The process for data extraction and fitting is provided in
+subsection 2.1. We have used the fermipy to extract the γ-
+ray SED for the two periods (5-7 and 15-20 January 2019).
+The SEDs are then fitted with a simple power law spectral
+model. We noticed that the spectra are very hard and still
+increasing with energy suggesting the involvement of high-
+energy particles in their production. The fitted parameters
+are given in Table 3 and the spectral index for period A
+(Γ=1.55±0.23) and B (Γ=1.54±0.19) are much harder than
+the average power law index, (Γ=1.75±0.03) for the total pe-
+riod. The harder spectra suggest that the IC peak is even at
+higher energy which is clearly seen in broadband SED model-
+ing. A study by Costamante et al. (2018) also shows a harder
+gamma-ray spectrum for many TeV blazar. A harder gamma-
+ray spectrum is also seen in another TeV extreme blazar. In-
+cluding the TeV data in broadband SED Aguilar-Ruiz et al.
+(2022) modeled the SED for six such sources with a two-
+zone emission model. Few new EHBL types sources are also
+discovered with the MAGIC telescope and the Fermi-LAT
+gamma-ray spectra were found to be very hard for all the
+sources suggesting an extreme location of the second SED
+peak above 100 GeV energy range (Acciari et al. 2020). A
+long-term gamma-ray spectral index was also estimated for
+1ES 1218+304 by Singh et al. (2019) and they found it to
+be harder with 1.67±0.05, similar to our estimated value. Sa-
+hakyan (2020) also estimated the γ-ray spectra averaged over
+∼11.7 years which found to be 1.71±0.02 mostly consistent
+with above discussed results. These values are also consistent
+with the long-term average photon spectral index reported in
+the recent 4FGL catalog.
+3.6 Color-Magnitude Variations
+The color-magnitude relation helps us understand the differ-
+ent variability scenarios of the blazar. Fluctuations in optical
+flux are often followed by spectral changes. Therefore study-
+ing the color-magnitude (CM) relationship can further shed
+light on the dominant emission mechanisms in the blazar.
+To obtain a better understanding of the CM relation for our
+source, we fit a linear plot (CI = m V +c) between the color
+MNRAS 000, 1–14 (2021)
+
+Multi-wavelength study of 1ES 1218+304
+9
+Parameter
+Flare A
+Flare B
+Whole Time Period
+Units
+Spectral Index (α)
+-1.547 ± 0.230
+-1.540 ± 0.191
+-1.745 ± 0.030
+-
+Flux (F0.3−300GeV )
+3.306
+3.063
+1.310
+10−8× photon(s) cm−2 s−1
+Prefactor (N0)
+9.538 ± 3.633
+8.902 ± 2.796
+2.966 ± 0.122
+10−13× photon(s) cm−2 s−1 MeV−1
+TS
+43.497
+48.297
+2913.496
+-
+Table 3. Best fit spectral parameters of 1ES 1218+304 from Fermi-Lat observations using equation 1 for two flaring periods 58488-58490
+MJD (Flare A), 58498-58503 MJD (Flare B) and whole time period MJD 58119-59365.
+15.6
+15.8
+16.0
+16.2
+16.4
+16.6
+(B+V)/2
+0.25
+0.50
+0.75
+1.00
+1.25
+1.50
+1.75
+2.00
+Color Indices
+B-V + 1.3
+B-I
+R-I + 0.2
+V-R
+Figure 8. Colour magnitude plot for 1ES 1218+304. The various
+color indices are plotted against (B+V)/2.
+indices (CI) and (B+V)/2 magnitude. We then estimate the
+fit values, i.e., slope (m), constant (c), along with the corre-
+lation coefficient (r) and the respective null hypothesis prob-
+ability (p) using two methods, Pearson and Spearman, as
+listed in Table 4. The generated CM plots are shown in Fig-
+ure 8. Offsets of 1.3 and 0.2 are used for (B-V) and (R-I).
+A positive slope with p < 0.05 implies a bluer-when-brighter
+(BWB) trend or a redder-when-fainter trend (Agarwal et al.
+2021) while a negative slope indicates a redder-when-brighter
+trend (RWB). As evident from Table 4, a significant BWB is
+dominant during our observation period for all possible color
+indices, namely; (B-V), (B-I), (R-I), and (V-R). Blazars, in
+general, display BWB from their quasi-simultaneous optical
+observations (Ghosh et al. 2000; Agarwal et al. 2015; Gupta
+et al. 2016a).
+The BWB trend can be attributed to the process of elec-
+tron acceleration to higher energies at the shock front, fol-
+lowed by losing energy by radiative cooling while propagat-
+ing away (Kirk et al. 1998). On the other hand, the opposite
+trend of redder when brighter is observed more commonly
+in FSRQs due to the contribution of bluer thermal emission
+from the accretion disc (Villata et al. 2006). In addition to
+BWB and RWB trends, other optical studies have revealed
+cycle or loop-like trends (Agarwal et al. 2021), a mixed trend
+where BWB is dominant during higher state while RWB dur-
+ing the fainter state, or a stable-when-brighter (SWB) which
+is no significant color-magnitude correlation in the data at
+any timescale (Gupta et al. 2016b; Isler et al. 2017; Negi
+et al. 2022; Agarwal et al. 2022). However, due to the lack
+of simultaneous observations for a larger sample of blazars,
+color-magnitude trends are still a topic of debate.
+3.7 Broadband SED modeling
+The broadband SED modeling in blazar is used to un-
+derstand the simultaneous multi-wavelength emission from
+the source along with the possible physical mechanism re-
+sponsible for broadband flaring event. Simultaneous multi-
+wavelength SEDs were generated for two time periods, which
+overlapped with proposed flaring periods. The model fit-
+ting was done using a publicly available code JetSet10 (Tra-
+macere et al. 2009, 2011, 2020; Massaro, E. et al. 2006).
+Broadband emission of BL Lac sources like 1ES 1218+304 is
+better explained by the one-zone Synchrotron-Self Compton
+(SSC) model. Leptonic models assume that relativistic lep-
+tons (mostly electrons and positrons) interact with the mag-
+netic field in the emission region and produce synchrotron
+photons in the frequency region of radio to soft-X-ray or the
+first hump of the SED. The emission in the frequency region
+of X-ray to γ-ray or the second hump of the SED is pro-
+duced by inverse Compton (IC) scattering of a photon popu-
+lation further classified into synchrotron-self Compton (SSC)
+or external Compton (EC) categories based on the source
+of the seed photons. In the case of SSC models (Ghisellini
+1993; Maraschi et al. 1992) relativistic electrons up-scatter
+the same synchrotron photons which they have produced in
+the magnetic field. The model assumes a spherically sym-
+metric blob of radius (R) in the emission region, surrounded
+by relativistic particles accelerated by the magnetic field (B).
+The blob makes an angle θ with the observer and moves along
+the jet with the bulk Lorentz factor Γ, affecting emission re-
+gion by the beaming factor δ = 1/Γ(1 − β cos θ). The blob
+is filled with a relativistic population of electrons following
+an empirical lepton distribution relation and the power law
+with an exponential cut-off (PLEC) distribution of particles
+is assumed:
+Ne(γ) = N0γ−αexp(−γ/γcut)
+(9)
+where γcut is the highest energy cut-off in the electron spec-
+trum. We see that the optical/UV measurements are higher
+than the non-thermal emission from the jet predicted by
+the SSC model. We also see high flux points in UV/optical
+range from the long-term observation of 1ES 1218+304, from
+NASA/IPAC Extragalactic Database (NED)11. These obser-
+vations suggest that the stellar emission from the host galaxy
+of the source is dominant at optical/UV frequencies. In order
+to accurately account for this emission due to the host galaxy,
+we have added the host galaxy component during modeling
+the SED using JetSet. Modeling of blazar 1ES 1218+304 is
+based on the SSC model in reference to equation 9. Results
+10 https://jetset.readthedocs.io/en/latest/
+11 https://ned.ipac.caltech.edu/
+MNRAS 000, 1–14 (2021)
+
+10
+R. Diwan et al.
+Colour
+In-
+dices
+Slope
+Intercept
+Pearson
+Coeffi-
+cient
+Pearson
+P-value
+Spearman
+Coeffi-
+cient
+Spearman
+P-value
+(B-V)
+0.216
+±
+0.024
+−3.152
+±
+0.390
+0.752
+7.88E-
+13
+0.774
+6.33E-
+14
+(B-I)
+0.446
+±
+0.031
+−6.002
+±
+0.506
+0.893
+1.15E-
+19
+0.928
+6.06E-
+24
+(R-I)
+0.156
+±
+0.019
+−1.982
+±
+0.317
+0.550
+1.67E-
+05
+0.734
+2.65E-
+10
+(V-R)
+0.085
+±
+0.018
+−1.070
+±
+0.292
+0.745
+1.52E-
+10
+0.787
+2.77E-
+12
+Table 4. Colour magnitude fitting and correlations coefficient.
+2
+0
+2
+4
+6
+8
+10
+12
+14
+log(E) (eV)
+12
+14
+16
+18
+20
+22
+24
+26
+28
+log( )  (Hz)
+14
+13
+12
+11
+10
+9
+8
+log( F  )  (erg cm
+2  s
+1)
+  -Sync
+  -SSC
+host_galaxy
+Total SED
+FERMI
+SWIFT UVOT
+SWIFT XRAY
+archived
+Nustar
+Figure 9. Broadband SED Modelling for 5-7 January 2019 (Flare
+A). Optical data are fitted with the host galaxy template available
+in JetSet. Archival NuSTAR data are also plotted in cyan color
+which does not match with the current state X-ray spectral shape.
+Due to the hard X-ray spectral index, the synchrotron peak is
+shifted to higher energy (∼1020 Hz) compared to the synchrotron
+peak location (1017−18 Hz) during 15-20 January as constrained
+by AstroSat observation in Figure 3 and also visible in Figure 10.
+for the SSC model are shown in Figure 9 and Figure 10 for
+Flare A and Flare B. The model parameters are given in table
+5.
+3.7.1 The constraint on Doppler factor
+We can calculate the minimum value of the Doppler factor
+using the detection of high-energy photons from the source.
+This calculation assumes the optical depth, τγγ(Eh), of the
+highest energy photon, Eh, to γγ interaction is 1. The formula
+for calculating the minimum value of the Doppler factor is
+δmin =
+�σtd2
+l (1 + z)2fϵEh
+4tvarmec4
+�1/6
+(10)
+where σt is the Thomson scattering cross-section for the elec-
+tron (6.65 × 10−25cm2), dl is the luminosity distance of the
+source, fϵ is the X-ray flux in 0.3-10 KeV energy range, Eh
+is the highest energy photon, tvar is the observed variability
+time. For 1ES 1218+304, z=0.182, dl is 924 Mpc and tvar is
+0.275 days. Using the value of highest energy photon Eh =
+162.822 GeV for Flare A and 278.132 GeV for Flare B, and
+fϵ = 1.94 × 10−10 for Flare A and 1.55 × 10−10 for Flare B,
+2.5
+0.0
+2.5
+5.0
+7.5
+10.0
+12.5
+log(E) (eV)
+12
+14
+16
+18
+20
+22
+24
+26
+28
+log( )  (Hz)
+14
+13
+12
+11
+10
+9
+log( F  )  (erg cm
+2  s
+1)
+  -Sync
+  -SSC
+host_galaxy
+Total SED
+FERMI
+SWIFT UVOT
+archived
+Nustar
+AstroSat-SXT
+SWIFT XRAY
+Figure 10. The plot is the same as Figure 8 but for 15-20 January
+2019 (Flare B). Here also the archival NuSTAR spectrum does
+not match the current state X-ray spectral shape which suggests
+that the NuSTAR spectrum was taken in low-flux states. Here the
+synchrotron peak is decided by both the XRT and SXT spectra
+plotted on top of each other which peaks at roughly ∼2.68×1017
+Hz as estimated in section 3.1 using AstroSat data.
+we get the δmin value to be 13.725 for Flare A and 14.455 for
+Flare B.
+3.7.2 The size of emission region
+The information on the size and location of the emission re-
+gion is very important for performing the SED modeling. The
+variability time scale estimated from the γ-ray light curve is
+used to estimate the size of the emission region. The radius
+R can be estimated by using the equation,
+R = cδmintvar/(1 + z),
+(11)
+where R is estimated to be 8.27 − 8.71 × 1015cm, using the
+δmin calculated in the previous section, and tvar is calculated
+in section 3.3. During SED modeling we have used the values
+1.06 × 1016 cm for Flare A and 1.40 × 1016 cm for Flare B.
+The location of the emission region along the jet axis from
+the supermassive black hole can also be estimated from the
+variability time assuming a spherical emission region by using
+the expression d ∼ 2cΓ2tvar/(1+z). Using the Lorentz factor,
+Γ = δmin and tvar = 0.275 days and z = 0.182, the location is
+estimated to be, d ∼ 2×1017 cm. To optimize the broadband
+SED modeling, we have fixed the location of the emission
+region to 1.0 × 1017 cm along the jet axis.
+MNRAS 000, 1–14 (2021)
+
+Multi-wavelength study of 1ES 1218+304
+11
+Sr. No.
+Model Parameters
+Unit
+Flare A
+Flare B
+5-7 Jan
+15-20 Jan
+1.
+γmin
+-
+88.342
+5.9990
+2.
+γmax
+-
+6.3346 × 107
+6.2115 × 107
+3.
+γcut
+-
+2.8153 × 107
+6.2216 × 105
+4.
+RH
+1017cm
+1.0
+1.0
+5.
+R
+1016cm
+1.0658
+1.4
+6.
+α
+-
+1.482500
+1.530156
+7.
+N
+cm−3
+85.34312
+37.58231
+8.
+B
+G
+2.7378 × 10−3
+1.3035 × 10−2
+9.
+z
+-
+0.182
+0.182
+10.
+δ
+-
+15.97827
+30.30340
+11.
+Ue
+erg cm−3
+3.470401
+4.179746 × 10−2
+12.
+UB
+erg cm−3
+2.982449 × 10−7
+6.760266 × 10−6
+13.
+Pe
+erg s−1
+9.460334 × 1045
+7.081457 × 1044
+14.
+PB
+erg s−1
+8.130172 × 1038
+1.145346 × 1041
+15.
+Pjet
+erg s−1
+1.060629 × 1046
+7.370064 × 1044
+16.
+Reduced Chi-Squared
+-
+1.079990
+2.707362
+Host Galaxy
+17.
+nuFnu_p_host
+erg cm−2 s−1
+-10.373
+-10.373
+18.
+nu_scale
+Hz
+0.496
+0.493
+Table 5. [1-3] Minimum, maximum and cut Lorentz factor of injected electron spectrum [4] The position of the region [5] The size of
+emission region [6] Spectral Index [7] Particle density [8] Magnetic field [9] Red Shift [10] Doppler factor [11] Electron energy density [12]
+Magnetic field energy density [13] Jet power in electrons [14] Jet power in magnetic field [15] Total jet power
+3.7.3 Jet Power
+We have estimated the power carried by individual compo-
+nents (leptons, protons, and magnetic fields) and the total
+jet power. The total power of the jet was estimated using
+Pjet = πR2Γ2c(U ′
+e + U ′
+p + U ′
+B)
+(12)
+Here Γ is the bulk Lorentz factor. U ′
+e, U ′
+p, U ′
+B are the energy
+densities of electrons-positrons, cold protons and the mag-
+netic field respectively in the co-moving jet’s frame (primed
+quantities are in the co-moving jet frame while unprimed
+quantities are in the observer frame). The power in leptons
+is given by
+Pe = 3Γ2c
+4R
+� Emin
+Emax
+EQ(E)dE
+(13)
+where Q(E) is the injected particle spectrum. The integration
+limits, Emin and Emax are calculated by multiplying the min-
+imum and maximum Lorentz factor (γmin and γmax) of the
+electrons with the rest-mass energy of the electron respec-
+tively. The power in the magnetic field is calculated using
+PB = R2Γ2cB2
+8
+(14)
+where B is the magnetic field strength obtained from the
+SED modeling. The energy densities for electron-positron and
+magnetic field for both Flare events were returned by our
+model. The energy density for cold proton was not estimated
+as it was too small. We calculated Pe, PB which are the power
+carried by the leptons and the magnetic field respectively. The
+total power Pjet ≈ Pe + PB along with the power of the in-
+dividual components has been mentioned in Table 5. The jet
+is dominated by the lepton’s power and its value decreases
+for the second flare period. The luminosities have been com-
+puted for a pure electron/positron jet since the proton con-
+tent is not well known, and can be considered as the lower
+limit. The absolute jet power Ljet ≃ 1×1046ergs−1 for Flare
+A and is below the Eddington luminosity for a 5.6 × 108M⊙
+black hole mass (LEdd = 7.3 × 1046ergs−1) estimated from
+the properties of the host galaxy in the optical band (Rüger
+et al. 2010). For Flare B, Ljet ≃ 7.37 × 1044ergs−1 is signifi-
+cantly below the LEdd.
+3.7.4 Broadband emission during flaring states
+We choose two flaring periods during the month of January
+2019, MJD 58488-58490 (5-7 January 2019, Fig 9) and MJD
+58498-58503 (15-20 January 2019, Fig 10) were modeled with
+a one-zone leptonic scenario. The modeled parameters are
+mentioned in Table 5. The model parameters inferred from
+this fitting suggest that Flare A had more activity compared
+to Flare B. Although the γmax and α are almost the same for
+both the flares inferring that there was very little variability
+in VHE γ-ray band, we see from Table 5 that γmin, γcut have
+significantly higher values for Flare A compared to Flare B,
+which may be due to the flaring seen in the X-ray band. The
+magnetic field (B) for Flare A (2.73×10−3) is also less than
+that of Flare B (1.30×10−2). During the fitting of SED, we
+kept RH and δ as free parameters. We find that the value of
+RH is close to the value we calculate using equation 11. We
+also calculate the minimum doppler factor δmin between the
+range (13.725-14.455), but during the SED modeling, we find
+that for Flare A δ = 15.98 and for Flare B it is much higher δ
+= 30.30 then the calculated value. It suggests that variation
+in δ could be one of the reasons for different flux states.
+During these flares, the optical-UV emission is dominated
+MNRAS 000, 1–14 (2021)
+
+12
+R. Diwan et al.
+by thermal emission from the host galaxy and hence has been
+modeled using the host galaxy model using JetSet. It is also
+seen that the X-ray data is better explained by synchrotron
+radiation of electrons. The SSC component of SED model-
+ing dominates above 1020 Hz (∼ 1 MeV) and it is useful in
+describing the data up to the VHE γ-ray band.
+4 SUMMARY AND DISCUSSIONS
+In our work, we present the multi-wavelength study of HBL
+blazar 1ES 1218+304 from 1st January 2018 to 31st March
+2021 (58119-59365), which also include the high flux event in
+VHE γ-rays detected by both MAGIC and VERITAS obser-
+vatories during January 2019. This high flux rate was also
+seen in Swift-XRT and UVOT instruments. Hence we di-
+vided our SED analysis into two flaring periods 5-7 Jan-
+uary 2019 and 15-20 January 2019 for simultaneous multi-
+wavelength observation of 1ES 1218+304. The fastest vari-
+ability timescale was found to be 0.275 days from analyzing
+the γ-ray light curve, constraining the size of the emission
+region to 8.27 − 8.71 × 1015 cm, which came out to be higher
+than previous modeling results (Rüger et al. 2010, Sahakyan
+2020, Singh et al. 2019) but comparable to SED modeled
+results in our case, see Table 5. The location of the emis-
+sion region is estimated to be d ∼ 2 × 1017cm was similar
+to that used for SED modeling. The highest energy photon
+detected was 278.132 GeV which arrived during Flare B. We
+can also see the ’harder-when-brighter’ trend in the X-ray en-
+ergy range and the ’softer-when-brighter’ trend in the γ-ray
+energy range.
+The broadband SED modeling of the source was repro-
+duced by a leptonic simple one-zone SSC model with the
+electron energy distribution described by a Power-law with
+an exponential cut-off (PLEC) function. Parameters like the
+magnetic field, injected electron spectrum, and minimum and
+maximum energy of injected electrons have been optimized
+to get a good fit to the SEDs data points. So this study sug-
+gests that a single-zone model can also be good enough to
+explain the multi-waveband emissions from 1ES 1218+304.
+The optical and UV emissions from the source are found to
+be dominated by the stellar thermal emissions from the host
+galaxy and can be modeled using the JetSet code by a simple
+blackbody approximation (Rüger et al. 2010).
+Costamante et al. (2018) argued that the broadband SED
+modeling in hard-TeV blazar can be explained by the one-
+zone SSC model at the expense of extreme electron ener-
+gies with very low radiative efficiency. The maximum elec-
+tron Lorentz factor estimated in their modeling for all the six
+sources is orders of 107 which is consistent with our results
+for 1ES 1218+304. The other modeling parameters such as
+the size of the emission region, magnetic field strength, and
+the magnetization parameters (UB/Ue) are very similar to
+our SED modeling result for 1ES 1218+304. In our case, the
+UB/Ue = 10−4 - 10−6 and in Costamante et al. (2018) it order
+of 10−2 - 10−5. Similar results were also obtained by Kauf-
+mann et al. (2011) where they model the broadband SED of
+extreme TeV source 1ES 0229+200. The magnetic field and
+the magnetization parameter (10−5) are consistent with our
+results for 1ES 1218+304. But their model requires a narrow
+electron energy distribution with γmin ∼ 105 to γmax ∼ 107
+rather than the broad energy range obtained in our study,
+Costamante et al. (2018), and Acciari et al. (2020).
+Acciari et al. (2020) have observed ten new TeV sources
+with MAGIC from 2010 to 2017 for a total period of 262
+hours and the simultaneous X-ray observations confirm that
+out of 10, 8 sources are of extreme nature. Their γ-SED
+was found to be very hard between 1.4 to 1.9. Blazar 1ES
+1218+304 is also an extreme TeV blazar and in our study, the
+gamma-ray SED is found to be 1.5 consistent with the above
+TeV sources. They have modeled all the sources with a sin-
+gle zone conical-jet SSC model. Additionally, they also used
+the proton-synchrotron and a leptonic scenario with a struc-
+tured jet. They also argue that all the model provides a good
+fit to the broadband SED but the individual parameters in
+each model differ substantially. Comparing their SSC model
+results to our SSC modeling the maximum electron energy is
+consistent. The electron spectral index in our case is harder
+than their results and also the magnetic field in our case is
+much smaller. The estimated Lorentz factor is more or less
+consistent with the Γ used for all the sources in their study.
+In their recent work Aguilar-Ruiz et al. (2022) have modeled
+the six well-known extreme BL Lac sources with a lepto-
+hadronic two-zone emission model to explain the broadband
+SED. In another study, Zech & Lemoine (2021) have shown
+that the broadband SED of extreme BL Lac sources can be
+explained by considering the co-acceleration of electrons and
+protons on internal or recollimation shocks inside the rela-
+tivistic jet. Sahakyan (2020) has modeled the average state
+of 1ES 1218+304 with one-zone SSC model. The parameter
+estimated in their study is mostly consistent with ours. How-
+ever, our study focuses on the smaller period including two
+flaring events. During the flaring event (15-20 Jan) the mag-
+netic field and the magnetization parameters are estimated
+as 1.30×10−2 Gauss and ∼10−4 which is comparable to the
+value for the same parameters estimated by modeling the av-
+erage state of the source in Sahakyan (2020). However, the
+Doppler factor required in Sahakyan (2020) is much higher
+than the Doppler factor needed to fit the flaring state in our
+case. Singh et al. (2019) also modeled the average broadband
+SED collected for almost 10 years with a one-zone SSC model.
+The required γmin, γmax and Doppler factor are consistent
+with our result but the size of the emission region is one order
+of magnitude smaller than ours, and also the magnetic field
+estimated in their model is much higher than what we found.
+The difference in some of the parameters could be because
+they modeled the average SED and in our case, we are more
+focused on a short period of time. The optical-UV SED is
+mostly off to the general trend of broadband SED of blazar
+and hence in both cases is fitted with a host-galaxy contri-
+bution. Singh et al. (2019) used a specific model to fit the
+host-galaxy and estimated the black hole mass of the source,
+however, in JetSet we can not include a specific model, and
+hence host-galaxy is fitted as a free parameter.
+The above discussion suggests that the known extreme BL
+Lac sources are very less in number and need careful attention
+and more broadband study to exactly quantify their nature
+and the physical emission mechanism.
+MNRAS 000, 1–14 (2021)
+
+Multi-wavelength study of 1ES 1218+304
+13
+5 CONCLUSIONS
+In this work, we present the long-term study of the blazar
+1ES 1218+304 using 3.5 years of near-simultaneous multi-
+wavelength data from Fermi-LAT, SWIFT-XRT, SWIFT-
+UVOT, AstroSat, and TUBITAK observations taken between
+January 1, 2018, and March 31, 2021. This study explores the
+broadband temporal and spectral behavior of the source dur-
+ing flaring states. The main results of our study are provided
+below:
+• During the month of January 2019, VHE γ-rays detected
+by both MAGIC and VERITAS observatory. This high flux
+state was also seen in Fermi, Swift-XRT, and UVOT instru-
+ments. The fractional variability estimated across the wave-
+bands suggests that UV is more variable followed by X-ray,
+γ-ray, and optical.
+• The fast flux variability in γ-ray is calculated to be
+0.275 days, the size of the emission region is estimated to
+be ∼8×1015 cm, and the emission region is located at a dis-
+tance of ∼ 2 × 1017 cm. A "harder-when-brighter" trend was
+seen in X-ray whereas a "softer-when-brighter" trend was in
+γ-ray. The γ-ray emission from 1ES 1218+304 can also be
+described by a power law with a spectral index of ∼ 1.745.
+• The Astrosat SXT light curve reveals a minute scale of
+variability of the order of 20 minutes and the X-ray spectrum
+is well fitted with both power-law and the log parabola mod-
+els. However, the LP provides a better fit. A joint fit with the
+LAXPC spectrum provides a great constrain on the location
+of synchrotron peak roughly around 2.68×1017Hz.
+• As seen in many other TeV blazars, a shift in syn-
+chrotron peak is observed from one state to another state
+from ∼1017−18 Hz to ∼1020 suggesting an extreme nature of
+the source.
+• The broadband SED modeling of the source is repro-
+duced by a one-zone leptonic SSC model with the electron
+energy distribution described by a Power-law with an expo-
+nential cut-off (PLEC) function. We also find that the Opti-
+cal/UV emissions from the source are dominated by the stel-
+lar thermal emissions from the host galaxy which are modeled
+by a simple blackbody approximation (Rüger et al. 2010) us-
+ing JetSet. The JetSet code uses an approximation of the host
+galaxy model to help fit the SED modeling. We need more
+precise and dedicated observation in the UV/Optical band
+for a better understanding of the host galaxy.
+• 1ES 1218+304 is also an important source for obser-
+vations within the upcoming high-energy ground-based tele-
+scopes like CTA (Cherenkov Telescope Array)12 observatory
+to establish the link beyond the GeV energy range, in the
+realm of TeV γ-ray emission and MeV-GeV emission mea-
+sured from the Fermi-LAT and its extreme blazar behavior.
+ACKNOWLEDGEMENTS
+D. Bose acknowledges the support of Ramanujan Fellowship-
+SB/S2/RJN-038/2017. R. Prince is grateful for the support of
+the Polish Funding Agency National Science Centre, project
+2017/26/A/ST9/-00756 (MAESTRO 9) and MNiSW grant
+DIR/WK/2018/12. This work made use of Fermi telescope
+12 https://www.cta-observatory.org
+data and the Fermitool package obtained through the Fermi
+Science Support Center (FSSC) provided by NASA. This
+work also made use of publicly available packages JetSet, Fer-
+mipy, and PSRESP. This publication uses the data from the
+AstroSat mission of the Indian Space Research Organisation
+(ISRO), archived at the Indian Space Science Data Centre
+(ISSDC). This work has used the data from the Soft X-ray
+Telescope (SXT) developed at TIFR, Mumbai, and the SXT
+POC at TIFR is thanked for verifying and releasing the data
+via the ISSDC data archive and providing the necessary soft-
+ware tools. We thank the LAXPC Payload Operation Center
+(POC) at TIFR, Mumbai for providing the necessary soft-
+ware tools. We have also made use of the software provided
+by the High Energy Astrophysics Science Archive Research
+Center (HEASARC), which is a service of the Astrophysics
+Science Division at NASA/GSFC.
+DATA AVAILABILITY
+For this work, we have used data from the Fermi-LAT, Swift-
+XRT, Swift-UVOT, and AstroSat which are available in the
+public domain. We have also used optical data collected by
+the TUBITAK telescope. This optical data was given to us
+on request. Details are given in Section 2.
+REFERENCES
+Abdo A. A., et al., 2010, The Astrophysical Journal, 716, 30
+Abdollahi S., et al., 2020, The Astrophysical Journal Supplement
+Series, 247, 33
+Abhir J., Joseph J., Patel S. R., Bose D., 2021a, MNRAS, 501,
+2504
+Abhir J., Prince R., Joseph J., Bose D., Gupta N., 2021b, ApJ,
+915, 26
+Acciari V. A., et al., 2009, ApJ, 695, 1370
+Acciari V. A., et al., 2020, ApJS, 247, 16
+Agarwal A., et al., 2015, MNRAS, 451, 3882
+Agarwal A., et al., 2019a, MNRAS, 488, 4093
+Agarwal A., et al., 2019b, Monthly Notices of the Royal Astronom-
+ical Society, 488, 4093
+Agarwal A., et al., 2021, A&A, 645, A137
+Agarwal A., Pandey A., Özdönmez A., Ege E., Kumar Das A.,
+Karakulak V., 2022, ApJ, 933, 42
+Aguilar-Ruiz E., Fraija N., Galván-Gámez A., Benítez E., 2022,
+MNRAS, 512, 1557
+Aharonian F. A., 2000, New Astron., 5, 377
+Albert J., et al., 2006, ApJ, 642, L119
+Aleksić J., et al., 2015a, A&A, 576, A126
+Aleksić J., et al., 2015b, A&A, 578, A22
+Atwood W. B., et al., 2009, ApJ, 697, 1071
+Barat S., Chatterjee R., Mitra K., 2022, Monthly Notices of the
+Royal Astronomical Society, 515, 1655
+Blandford R. D., Znajek R. L., 1977, MNRAS, 179, 433
+Bose D., Chitnis V. R., Majumdar P., Acharya B. S., 2022, The
+European Physical Journal Special Topics, 231, 3
+Böttcher M., Reimer A., Sweeney K., Prakash A., 2013, ApJ, 768,
+54
+Cao G., Wang J.-C., 2013, Monthly Notices of the Royal Astro-
+nomical Society, 436, 2170
+Chatterjee R., et al., 2021, arXiv e-prints, p. arXiv:2102.00919
+Costamante L., Bonnoli G., Tavecchio F., Ghisellini G., Taglia-
+ferri G., Khangulyan D., 2018, Monthly Notices of the Royal
+Astronomical Society, 477, 4257
+MNRAS 000, 1–14 (2021)
+
+14
+R. Diwan et al.
+Feng
+Q.,
+VERITAS
+Collaboration
+2022,
+in
+37th
+Interna-
+tional Cosmic Ray Conference. p. 802 (arXiv:2108.05333),
+doi:10.22323/1.395.0802
+Fortin P., 2008, in Aharonian F. A., Hofmann W., Rieger F.,
+eds, American Institute of Physics Conference Series Vol. 1085,
+American Institute of Physics Conference Series. pp 565–568
+(arXiv:0810.0301), doi:10.1063/1.3076735
+Ghisellini G., 1993, Advances in Space Research, 13, 587
+Ghosh K. K., Ramsey B. D., Sadun A. C., Soundararajaperumal
+S., 2000, ApJS, 127, 11
+Giommi P., et al., 2006, A&A, 456, 911
+Gupta A. C., et al., 2016a, MNRAS, 458, 1127
+Gupta A. C., et al., 2016b, Monthly Notices of the Royal Astro-
+nomical Society, 458, 1127
+HI4PI Collaboration et al., 2016, A&A, 594, A116
+Isler J. C., Urry C. M., Coppi P., Bailyn C., Brady M., MacPherson
+E., Buxton M., Hasan I., 2017, ApJ, 844, 107
+Kaufmann S., Wagner S. J., Tibolla O., Hauser M., 2011, A&A,
+534, A130
+Kirk J. G., Rieger F. M., Mastichiadis A., 1998, A&A, 333, 452
+Kochanek C. S., et al., 2017, PASP, 129, 104502
+Liu H. T., Bai J. M., 2006, The Astrophysical Journal, 653, 1089
+Lombardi S., Lindfors E., Becerra Gonzalez J., Colin P., Sitarek
+J., Stamerra A., 2011, arXiv e-prints, p. arXiv:1110.6786
+Mannheim K., 1993, A&A, 269, 67
+Maraschi L., Ghisellini G., Celotti A., 1992, ApJ, 397, L5
+Massaro, E. Tramacere, A. Perri, M. Giommi, P. Tosti, G. 2006,
+A&A, 448, 861
+Mirzoyan R., 2019, The Astronomer’s Telegram, 12354, 1
+Misra R., Roy J., Yadav J. S., 2021, Journal of Astrophysics and
+Astronomy, 42, 55
+Mukherjee R., VERITAS Collaboration 2019, The Astronomer’s
+Telegram, 12360, 1
+Nalewajko K., Begelman M. C., Sikora M., 2014, The Astrophysi-
+cal Journal, 789, 161
+Negi V., Joshi R., Chand K., Chand H., Wiita P., Ho L. C., Singh
+R. S., 2022, MNRAS, 510, 1791
+Prince R., 2019, ApJ, 871, 101
+Prince R., 2020, The Astrophysical Journal, 890, 164
+Prince R., Majumdar P., Gupta N., 2017, The Astrophysical Jour-
+nal, 844, 62
+Prince R., Gupta N., Nalewajko K., 2019, ApJ, 883, 137
+Prince R., Khatoon R., Stalin C. S., 2021, MNRAS, 502, 5245
+Prince R., Khatoon R., Majumdar P., Czerny B., Gupta N., 2022,
+Monthly Notices of the Royal Astronomical Society, 515, 2633
+Priya S., Prince R., Agarwal A., Bose D., Özdönmez A., Ege E.,
+2022, Monthly Notices of the Royal Astronomical Society, 513,
+2239
+Ramazani V. F., Bonneli G., Cerruti M., 2019, The Astronomer’s
+Telegram, 12365, 1
+Rybicki G. B., Lightman A. P., 1979, Radiative processes in astro-
+physics
+Rüger M., Spanier F., Mannheim K., 2010, Monthly Notices of the
+Royal Astronomical Society, 401, 973
+Sahakyan N., 2020, MNRAS, 496, 5518
+Schlafly E. F., Finkbeiner D. P., 2011, The Astrophysical Journal,
+737, 103
+Schlickeiser R., 1989a, ApJ, 336, 243
+Schlickeiser R., 1989b, ApJ, 336, 264
+Shappee B. J., et al., 2014, ApJ, 788, 48
+Shukla A., Mannheim K., 2020, Nature Communications, 11, 4176
+Singh K. P., et al., 2016, in den Herder J.-W. A., Takahashi T.,
+Bautz M., eds, Society of Photo-Optical Instrumentation Engi-
+neers (SPIE) Conference Series Vol. 9905, Space Telescopes and
+Instrumentation 2016: Ultraviolet to Gamma Ray. p. 99051E,
+doi:10.1117/12.2235309
+Singh K. P., et al., 2017, Journal of Astrophysics and Astronomy,
+38, 29
+Singh K. K., Bisschoff B., van Soelen B., Tolamatti A., Marais
+J. P., Meintjes P. J., 2019, Monthly Notices of the Royal As-
+tronomical Society, 489, 5076
+Sun S.-S., Li H.-L., Yang X., Lü J., Xu D.-W., Wang J., 2021,
+Research in Astronomy and Astrophysics, 21, 197
+Tramacere A., 2020, JetSeT: Numerical modeling and SED fit-
+ting tool for relativistic jets, Astrophysics Source Code Library,
+record ascl:2009.001 (ascl:2009.001)
+Tramacere A., Giommi P., Perri M., Verrecchia F., Tosti G., 2009,
+A&A, 501, 879
+Tramacere A., Massaro E., Taylor A. M., 2011, ApJ, 739, 66
+Urry C. M., Padovani P., 1995, PASP, 107, 803
+Vaughan S., Edelson R., Warwick R. S., Uttley P., 2003, MNRAS,
+345, 1271
+Villata M., et al., 2006, A&A, 453, 817
+Wierzcholska A., Wagner S. J., 2016, Monthly Notices of the Royal
+Astronomical Society, 458, 56
+Wood M., Caputo R., Charles E., Di Mauro M., Magill J.,
+Perkins J. S., Fermi-LAT Collaboration 2021, in 35th In-
+ternational
+Cosmic
+Ray
+Conference
+(ICRC2017).
+p.
+824
+(arXiv:1707.09551), doi:10.22323/1.301.0824
+Yadav J. S., et al., 2016, in den Herder J.-W. A., Takahashi T.,
+Bautz M., eds, Society of Photo-Optical Instrumentation Engi-
+neers (SPIE) Conference Series Vol. 9905, Space Telescopes and
+Instrumentation 2016: Ultraviolet to Gamma Ray. p. 99051D,
+doi:10.1117/12.2231857
+Zech A., Lemoine M., 2021, A&A, 654, A96
+This paper has been typeset from a TEX/LATEX file prepared by
+the author.
+MNRAS 000, 1–14 (2021)
+
diff --git a/5NAzT4oBgHgl3EQfEPrI/content/tmp_files/load_file.txt b/5NAzT4oBgHgl3EQfEPrI/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f267ca245daacabeee29328df70311e3e81f9e8c
--- /dev/null
+++ b/5NAzT4oBgHgl3EQfEPrI/content/tmp_files/load_file.txt
@@ -0,0 +1,1369 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf,len=1368
+page_content='MNRAS 000, 1–14 (2021)  Preprint 4 January 2023  Compiled using MNRAS LATEX style file v3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0  Multi-wavelength study of TeV blazar 1ES 1218+304 using  gamma-ray, X-ray and optical observations  Rishank Diwan,1⋆ Raj Prince,2 Aditi Agarwal,3 Debanjan Bose,4† Pratik Majumdar,5  Aykut Özdönmez,6 Sunil Chandra,7,8 Rukaiya Khatoon,8 Ergün Ege,9  1Laboratory for Space Research, The University of Hong Kong, 405B Cyberport 4, 100 Cyberport Road, Cyberport, Hong Kong  2Center for Theoretical Physics, Polish Academy of Sciences, Al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Lotników 32/46, 02-668 Warsaw, Poland  3 Raman Research Institute, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Raman Avenue, Sadashivanagar, Bengaluru - 560080, India  4 S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Bose National Centre for Basic Sciences,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Block-JD,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Sector-III,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Salt Lake,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Kolkata-700106  5 Saha Institute of Nuclear Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' a CI of Homi Bhabha National Institute,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Kolkata 700064,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' West Bengal,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' India  6 Ataturk University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Faculty of Science,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Department of Astronomy and Space Science,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 25240,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Yakutiye,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Erzurum  7 South African Astronomical Observatory,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Observatory Road,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Observatory,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Cape Town 7925,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' South Africa  8 Center for Space Research,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' North-West University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Potchefstroom,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2520,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' South Africa  9 Istanbul University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Faculty of Science,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Department of Astronomy and Space Sciences,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 34116,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Beyazıt,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Istanbul,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Turkey  Accepted XXX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Received YYY;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' in original form ZZZ  ABSTRACT  We report the multi-wavelength study for a high-synchrotron-peaked BL Lac 1ES 1218+304 using near-simultaneous  data obtained during the period from January 1, 2018, to May 31, 2021 (MJD 58119-59365) from various instruments  including Fermi-LAT, Swift-XRT, AstroSat, and optical from Swift-UVOT & TUBITAK observatory in Turkey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The  source was reported to be flaring in TeV γ-ray during 2019 but no significant variation in Fermi-LAT is observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' A  minute scale variability is seen in SXT light curve suggesting a compact emission region for their variability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' However,  Hour’s scale variability is observed in the γ-ray light curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' A "softer-when-brighter" trend is observed in γ-ray and an  opposite trend is seen in X-ray suggesting both emissions are produced via two different processes as expected from an  HBL source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' We have chosen the two epochs in January 2019 to study and compare their physical parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' A joint  fit of SXT and LAXPC provides a great constraint on the synchrotron peak roughly estimated to be ∼2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='68×1017 Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  A clear shift in the synchrotron peak is observed from 1017−18 to 1020 Hz revealing its extreme nature or behaving like  an EHBL-type source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The optical observation provides color-index variation as "blue-when-brighter".' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The broadband  SED is fitted with a single-zone SSC model and their parameters are discussed in the context of a TeV blazar and  possible mechanism behind the broadband emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  Key words:  galaxies: active – galaxies: jets – gamma-rays: galaxies – radiation mechanisms: non-thermal – BL  Lacertae objects: individual: 1ES 1218+304  1 INTRODUCTION  Active galactic nuclei (AGN) host a supermassive black hole  (SMBH) at the center which accretes matter from the sur-  rounding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The matters are in Keplerian orbit and fall into  the SMBH via an accretion disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The mechanism proposed  in Blandford & Znajek (1977) suggests that the magnetic  field lines from the accretion disk get twisted and collimated  due to the high spin of SMBH and eject the matter through  a bipolar jet perpendicular to the accretion disk plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Later,  the AGNs were classified based on how they are viewed  commonly known as the AGN unification scheme (Urry &  Padovani 1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Blazars are a subclass of active galactic nu-  clei that have their relativistic jet pointed to the observer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  ⋆ E-mail: rishank2610@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='com  † E-mail: debaice@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='com  They are characterized by rapid variability from hours to  days’ timescales across all wavelengths, high polarization, and  superluminal jet speeds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Blazars can be further subdivided  into two classes: flat spectrum radio quasars (FSRQs) and  BL Lacertae (BL Lac) objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The broad-band continuum  spectra of blazars are dominated by non-thermal emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  The spectral energy distribution of blazars is characterized  by a double hump structure: the first hump is generally at-  tributed to the synchrotron radiation in the radio to X-ray  bands whereas there is intense debate about the origin of  the second hump.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The commonly accepted emission mech-  anism is via inverse Compton scattering of the low-energy  photons by high-energy electrons in the system from GeV  to TeV energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' There are alternative scenarios proposed  by several authors which involve hadronic interactions pro-  ducing neutral pions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' These pions decay to generate photons  in the GeV-TeV energies (Mannheim 1993;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Aharonian 2000;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  © 2021 The Authors  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='00991v1  [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='HE]  3 Jan 2023  2  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Diwan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  Böttcher et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The BL Lac-type sources are further  subdivided into three main classes depending on the position  of their low-energy peak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' If the synchrotron peak is observed  at < 1014Hz, those BL Lacs are called low-frequency peaked  BL Lacs (LBLs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' If the synchrotron peak is observed be-  tween 1014Hz and 1015Hz, then they are called intermediate-  frequency peaked BL Lacs (IBLs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Finally, BL Lacs with syn-  chrotron peak ≥ 1015Hz is called high-frequency peaked BL  Lacs (HBLs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' There is also a newly defined class of ultra-  high-frequency peaked BL Lacs (UHBLs) with the spectral  peak of the second bump (high energy peak) in the SED lo-  cated at an energy of 1 TeV or above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' These blazars are also  known as "extreme blazars" or EHBLs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' (Abdo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  Multiwavelength observation of blazars is a very important  tool for investigating the various properties of the blazars and  the jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' For example, the shortest variability timescale allows  one to put strong constraints on the size of the emission re-  gion of the blazar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The location of the emission region along  the jet axis is another challenging problem in blazar physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  Many studies have been done in the past to locate the emis-  sion region, in some cases, it has been found that the emission  happens very close to the SMBH within the broad-line region  (BLR) (Prince 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Prince et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' However, in some  studies, it has been proposed to be at higher distances be-  yond the broad-line region (Cao & Wang 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Nalewajko  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Barat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The break or curvature in the  γ-ray spectrum above 10-20 GeV suggests the emission region  within the BLR as the BLR is opaque to high energy pho-  tons above 10 GeV ( Liu & Bai 2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The cross-correlation  studies among the various wavebands are another way to lo-  cate the emission region along the jet axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' In many studies,  it has been reported that simultaneous broadband emissions  generally have a co-spatial origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' However, in some cases, a  significant time lag has been reported strongly suggesting the  different locations for the different emissions (Prince 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  In the first case scenario, one zone emission model is favored  to explain the broadband SED, and in the later case, the  multi-zone emission model is preferred (Prince et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  The production of high-energy γ-rays in blazar suggests an  acceleration of charged particles to very high energy and  many models have been proposed to explain the acceleration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  The most accepted mechanisms are the diffusive shock accel-  eration (Schlickeiser 1989a,b) and the magnetic re-connection  (Shukla & Mannheim 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' In many studies shock accelera-  tion has been favored which also demands the emission region  close to the SMBH within the BLR because the shocks are  produced and are strong at the base of the jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' On the other  hand, the magnetic reconnection happens due to external per-  turbation and hence demands the jet to be less collimated i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  the emission region is farther from the base.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  In this paper, we report on a multiwavelength study of the  TeV blazar 1ES1218+304 to understand the broadband prop-  erties of the source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' It is located at a redshift, z = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='182 with  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' = 12 21 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3 (hh mm ss), Dec = +30 11 29 (dd mm ss).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  It has been observed in TeV energy with VERITAS (Fortin  2008, Acciari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2009) and MAGIC (Albert et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2006,  Lombardi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2011) and are part of TeV Catalog1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  The paper is arranged in the following way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' We discuss the  multiwavelength observations and the data analysis proce-  1 http://tevcat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='uchicago.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='edu/  dures from different instruments used in this study in Section  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' In section 3, we have discussed the results from Astrosat  alone and the broadband light curves and spectral energy dis-  tributions at length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' In Section 4 we summarise and discussed  the important findings in the context of blazar physics and  eventually conclude our work in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  2 MULTIWAVELENGTH OBSERVATIONS,  DATA ANALYSIS AND DATA REDUCTION  The following section describes the data analysis technique  used to generate a multi-waveband light curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' In the sub-  sections, we provide a description of the data analysis tech-  nique of γ-ray data collected from Fermi-Lat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' X-ray, and  UV-optical data were collected from Swift-XRT and Swift-  UVOT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Also, soft X-ray and hard X-ray data were collected  from AstroSat-SXT and AstroSat-LAXPC, respectively and  Optical Data from TUBITAK National Observatory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='1 Fermi-LAT γ-ray Observatory  Large Area Telescope (LAT) is a gamma-ray telescope placed  on Fermi gamma-ray space observatory2 which was launched  in 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' It has a working energy range of 20 MeV to 1  TeV with a field of view of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='4 Sr (Atwood et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  The orbital period of the telescope is around ∼ 96 mins  in each hemisphere and covers the entire sky in total ∼ 3  hr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Blazar 1ES 1218+304 is continuously being monitored  since 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' In this study, we have analyzed the data from  1st January 2018 - 31st May 2021 when the source was  reported to be flaring in gamma-ray (January 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The  analysis was performed using Fermipy v0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='43(Wood et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  2021) and the standard Fermi tools software (Fermitools  v1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='23)4 between 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3-300 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' A 15◦ circular region was  chosen around the source to extract the photon events with  evclass=128 and evtype=3 and the time intervals were re-  stricted using ‘(DATA_QUAL>0)&&(LAT_CONFIG==1)’  as recommended by the Fermi-LAT team in the fermitools  documentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The source model file was generated using  the Fermi 4FGL catalog (Abdollahi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2020) and the back-  ground gamma-ray emission was taken care of by using the  gll_iem_V07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='fits file along with the isotropic background  emission by using the iso_P8R3_SOURCE_V2_v1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='txt file.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' In  addition, the zenith angle cut was chosen as 90◦ to reduce the  contamination from the Earth limb’s γ-ray.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The source and  background were modeled by the binned Likelihood method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  Initially, the spectral parameters of all the sources were kept  free to optimize the γ-ray emission from them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Eventually,  we generated the γ-ray light curves for 7, 15, and 30 days  of binning for our scientific purpose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' To extract lightcurve  and perform spectral fitting normalization of the sources only  within 2◦ of ROI were kept free, and the rest of the param-  eters and other source models were frozen, except that of  Source of Interest, in this case, blazar 1ES 1218+304 and a  high flux source 4FGL J1217.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='9+3007, with an offset of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='753◦  from 1ES 1218+304, which constitutes to 10 parameters for  2 https://fermi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='gsfc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='nasa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='gov/  3 Fermipy webpage  4 Fermtools Github page  MNRAS 000, 1–14 (2021)  Multi-wavelength study of 1ES 1218+304  3  likelihood analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' PowerLaw model was used for the source  as given below:  dN(E)  dE  = No ×  � E  Eo  �−α  (1)  where Eo and No are the scale factor and the prefactor, re-  spectively provided in the 4FGL catalog and α is the spectral  index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='2 AstroSat  On January 03, 2019 MAGIC reported a gamma-ray activ-  ity and detection of very high energy γ ray from blazar 1ES  1218+304 (Mirzoyan 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Later, VERITAS also detected a  γ-ray flare from this source (Mukherjee & VERITAS Collab-  oration 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Following these two events, we proposed a tar-  get of opportunity proposal in India’s first space-based multi-  wavelength observatory, AstroSat5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Observations were car-  ried out from 17th to 20th January with a soft-Xray telescope  (SXT) and large area X-ray proportional counter (LAXPC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='1 SXT  The SXT working energy range is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3-7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0 keV and the ob-  servation was performed with photon counting mode (PC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  The level-1 data was downloaded from the webpage and fur-  ther reduction was performed with the latest SXT pipeline,  sxtpipeline1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='4b (Release Date: 2019-01-04).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' It produces  the cleaned level-2 data products which were used for fur-  ther analysis (Singh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2016, Singh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The ob-  servations were done in various orbits and therefore it was  merged together with the help of SXTEVTMERGERTOOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The  X-ray light curve is extracted using XSELECT with a circular  region of 16′ centered on the source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The energy selection  of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3-7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0 keV was applied in XSELECT itself using the chan-  nel filtering through pha_cutoff filter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The source spectrum  was extracted for 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3-7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0 keV energy range and the back-  ground spectrum file was used provided by the AstroSat  SkyBkg_comb_EL3p5_Cl_Rd16p0_v01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='pha.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The spectrum was  grouped in GRPPHA in order to have good photon statistics in  each bin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The ancillary response file (arf) was generated using  sxtARFModule and the RMF file (sxt_pc_mat_g0to12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='rmf)  was provided by the SXT-POC (Payload Operation Cen-  ter) team.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Eventually, the X-ray spectra from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3-7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0 KeV  with proper background and response files were loaded in  XSPEC and fitted with the simple absorbed power-law and  log-parabola spectral models with the correction of ISM ab-  sorption model at NH = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='91×1020 cm−2 (HI4PI Collabora-  tion et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='2 LAXPC  LAXPC works in the hard X-ray energy range from 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0-80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0  keV (Yadav et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2016) consisting of three identical detec-  tors namely LAXPC10, LAXPC20, and LAXPC30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Unfor-  tunately, LAXPC 10 was operating at a lower gain during  the time of observation period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Also, the LAXPC30 detec-  tor has a gain instability issue caused by substantial gas  5 https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='isro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='gov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='in/AstroSat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='html  leakage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Therefore, we used only LAXPC20 for the analy-  sis, and the corresponding results are presented here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The  Level-1 data were processed using the LaxpcSoft package  available in AstroSat Science Support Cell (ASSC)6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' We  generated the Level-2 combined event file using the com-  mand laxpc_make_event.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' During the data processing, a  good time interval was applied to exclude the time inter-  vals corresponding to the Earth occultation periods, SAA  passage, and standard elevation angle screening criteria  by using the laxpc_make_stdgti tool.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Finally, the tools  laxpc_make_spectra and laxpc_make_lightcurve were used  to produce the spectra and lightcurve of the source, using the  gti file.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' We restricted the spectra to the energy range of  4-20 keV since the background dominates the spectra above  this energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' In the spectral analysis, a 3% systematic un-  certainty was added to the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The obtained lightcurve is  not background subtracted, therefore we estimated the back-  ground following the faint source routine (Misra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  However, due to insignificant variations observed in the ex-  tracted lightcurve from LAXPC20, we did not use them in  our study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3 The Neil Gehrels Swift Observatory  Simultaneous to AstroSat, blazar 1ES 1218+304 was also ob-  served in X-ray with Swift-XRT and in optical-UV by Swift-  UVOT telescopes7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' It provides a unique opportunity to have  simultaneous broadband light curves and spectrum which is  important to decipher the cause behind the flare and the  broadband emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='1 XRT  X-ray telescope (XRT) works in an energy range between 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3-  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0 keV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Multiple observations were done during this period  with an average of 2ks exposure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' We have analyzed the data  following the standard Swift xrtpipeline and the details can  be found on Swift webpage8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The cleaned event files were pro-  duced and a circular region of 10” was chosen for the source  and background around the source and away from the source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  Tool XSELECT was used to extract the source light curve and  the spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The spectrum was binned by using the tool  GRPPHA to have a sufficient number of counts in each bin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' A  proper ancillary response file (ARF) and the redistribution  matrix files (RMF) were used to model the X-ray spectra in  XSPEC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' A simple unabsorbed power law was used to fit the X-  ray 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3-10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0 keV spectra and extract the X-ray flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The soft  X-ray (below 1 keV) is prone to go through interstellar ab-  sorption in Milky-way and hence a correction is applied with  NH = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='91×1020 cm−2 (HI4PI Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='2 UVOT  Having an ultraviolet-optical telescope has the advantage of  getting simultaneous observations to X-ray.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' UVOT has six  filters namely U, B, and V in optical and W1, M2, and W2  in the ultraviolet band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The image files were opened in DS9  6 http://astrosat-ssc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='iucaa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='in  7 https://swift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='gsfc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='nasa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='gov/  8 https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='swift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='uk/analysis/xrt/  MNRAS 000, 1–14 (2021)  4  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Diwan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Best fit spectral parameters of 1ES 1218+304 from SXT observations of 17-20 January 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' X-ray flux is presented in the unit  (erg cm−2 s−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The spectrum is fitted with both the power-law and log-parabola models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' In the last row, we show the joint fit of the  SXT and LAXPC spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' We also added a 3% systematic in the fit as suggested by the AstroSat team.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The parameters are compared  for free and fixed NH (HI4PI Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2016) values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The overall fit provide better fit with free NH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  Model  Parameters  Value  Power-law  Fixed nH  Free nH  TBabs  NH(1022cm−2)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0191  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='057±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='005  Index  Γ  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='95±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='01  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='11±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='02  Flux  F0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3−10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0 keV  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='427 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='004) × 10−10  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='474 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='006) × 10−10  χ2/dof  777/434  595.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='75/433  Logparabola  TBabs  NH(1022cm−2)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0191  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='075±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='014  Index  α  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='90±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='02  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='21±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='08  β  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='28±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='15±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='11  Flux  F0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3−10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0 keV  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='300 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='009) × 10−10  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='585 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='037) × 10−10  χ2/dof  642.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='28/433  590.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='55/432  Logparabola  joint fit  SXT + LAXPC  TBabs  NH(1022cm−2)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0191  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='042±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='010  Index  α  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='85±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='02  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='98±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='06  β  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='33±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='22±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='06  Norm  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0262±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0002  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0281 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0009  Constant factor 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='96±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='96±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='04  χ2/dof  601.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='16/402  587.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='72/401  software and the source and background region of 5" and 10"  were selected around the source and away from the source,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The task UVOTSOURCE has been used to get the  magnitudes which were later corrected for galactic reddening,  E(B-V)=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0176 (Schlafly & Finkbeiner 2011) and converted  into the fluxes using zero points and the conversion factor  (Giommi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='4 Optical  The optical observations of our source were performed in the  Johnson BVRI bands using the three ground-based facilities  in Turkey, namely, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='6m RC robotic (T60) and the 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0m RC  (T100) telescopes at TUBITAK National Observatory, and  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='5m RC telescope at Ataturk University in Turkey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Techni-  cal details of these telescopes are explained in Agarwal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The standard data reduction of all CCD frames, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  the bias subtraction, twilight flat-fielding, and cosmic-ray re-  moval, was done as mentioned in (Agarwal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2019a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='5 Archival  We have used the archival optical data from ASAS-SN (All-  Sky Automated Survey for Supernovae) (Shappee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  Kochanek et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='We have also used long-term high flux  observation in UV/Optical range from NASA/IPAC Extra-  galactic Database (NED)9 for providing the reference points  in our SED analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' We have also extracted the NuSTAR  SED data points from (Sahakyan 2020) and plotted them  alongside our SED analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  9 https://ned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='ipac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='caltech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='edu/  3 RESULTS  In this section, we provide the main results of our work using  the above broadband observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' We have explained various  characteristics of broadband light curves and spectral energy  distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='1 Astrosat results  Astrosat observations in SXT and LAXPC were done dur-  ing 17-20 January 2019 after two weeks of TeV detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  We have produced the SXT light curve and the spectrum  as shown in Figure 1 and Figure 2 for 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3-7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0 keV energy  band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The source appears to be variable on a short-time  scale and the corresponding fractional variability and vari-  ability time is estimated in section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' A spectrum is ex-  tracted in the energy range of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3-7 keV and fitted with the  power law and log-parabola models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The best-fit parame-  ters are presented in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' We started with a power-law  with fixed hydrogen column density, NH = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0191×1020 cm−2  and ended up getting χ2/dof = 777/434 with photon spec-  tral index, Γ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='95±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='01 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3-7 keV flux, F0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3−7keV =  (14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='27±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='04)×10−11 ergs/cm2/s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Next, we keep NH as a free  parameter and the best fit value is estimated as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='057±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='005  in units of 1020 cm−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The χ2/dof has improved to 595.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='75/433  and the spectral index was found to be 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='11±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='02 with almost  the same 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3-7 keV flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' We repeat the same procedure with  the log parabola model and with both the cases of fixed and  free NH and it gives a better fit than the power law.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' With  the free NH parameter we achieved a better fit with χ2/dof  = 590.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='55/432 compared to the power-law case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The best-fit  spectral index is 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='21±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='08 a bit softer than the power-law  index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The details about the other parameters are provided  in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  MNRAS 000, 1–14 (2021)  Multi-wavelength study of 1ES 1218+304  5  0  20000  40000  60000  80000  100000 120000  Time(s)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='7  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='9  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3  Counts/sec  SXT 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3-7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0 keV  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' AstroSat-SXT light curve for energy 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3-7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0 keV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The  bin size is taken as 856 sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  We could not get a good light curve in LAXPC but ex-  tracted the spectrum from 4-20 keV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The SXT and LAXPC  spectra are jointly fitted with Power law and Log-parabola  models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' In the case of the Power-law, we get the χ2/dof  = 948.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='46/403 and 623.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='25/402 for fixed and free NH val-  ues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' In both cases, the reduced-χ2 is much higher than  the case of Log-parabola (Table 1) and hence not pur-  sued further.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' For the joint fit, we used the total model as  constant*tbabs*logpar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The constant factor is fixed at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0  for data group 1 and kept as a free parameter for data group  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The best fit value for the constant factor is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='96±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='04 for  both fixed and free NH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The overall reduced-χ2 is improved  when the NH is free and it is estimated as 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='2±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0 (×1020  cm−2), almost two times higher than the fixed NH value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Fig-  ure 3 shows the best fit plot with a log-parabola model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' We  found that the spectral index, α, and the curvature parame-  ter, β are a bit different during fixed and free NH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The math-  ematical representation of the log-parabolic model is given  as,  F(E) = K(E/E1)(−α+βlog(E/E1))ph cm−2 s−1 keV,  (2)  where K is the normalization and the E1 is the reference  energy fixed at 1 keV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Using the best-fit parameters of the  log-parabola model we can estimate the location of the syn-  chrotron peak, which is given as Ep = E1 10(2−α)/2β keV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  For α=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='98 and β=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='22, the Ep is estimated as 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='11 keV or  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='68×1017 Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The peak of the synchrotron emission is mostly  constrained by the X-ray as shown in Figure 3 which peaks  at ∼ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='68×1017 Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='2 Broadband Light curves  We have collected the γ-ray data between 2018 to 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The  source was found to be in a flaring state in γ-ray during Jan  2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Simultaneous observation in Swift-XRT and UVOT  also confirms the flaring behavior in X-ray as well as in  optical-UV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' On 02 January 2019 source was reported to be  flaring in very high energy gamma-ray by MAGIC (Mirzoyan  2019) which was followed by VERITAS (Mukherjee &  VERITAS Collaboration 2019) and observation was done on  4, 5, and 6 January 2019 show high flux state above 100 GeV  and the corresponding period is marked by light pink color  in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' We identify this period as Flare A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' In X-ray  10−3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='1  1  normalized counts s−1 keV−1  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='5  2  5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='5  ratio  Energy (keV)  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3 - 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0 keV energy spectrum of 1ES 1218+304  fitted with Logparabola spectral model with free galactic absorp-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The SXT data were taken during the period 17-20 January  2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  10−10  2×10−11  5×10−11  ν Fν (ergs cm−2 s−1)  1017  1018  2×1017  5×1017  2×1018  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='5  2  ratio  Energy (Hz)  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The joint SXT (red) and LAXPC (blue) spectra are  modeled together.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The SXT energy range is taken as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3 - 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0  keV and LAXPC is taken from 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0-20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0 keV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The joint spectra are  fitted with a log parabola spectral model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Both spectra were taken  simultaneously during the period of 17-20 January 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  and optical source was reported to be historically bright  with flux around ∼ 2×10−10 erg cm−2 s−1 in X-ray and  with R band flux 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='35±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='05 mJy (Ramazani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  We also proposed this source in India’s first space mission,  AstroSat for broadband observation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Our observation was  done between 17-20 January 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' This period is marked  as a vertical green line in Figure 4 and identified as Flare  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The first two panels of Figure 4 represent the long-term  γ-ray (GeV) light curve and corresponding photon spectral  index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The source is not very bright in Fermi-LAT but a  clear variability in the flux is seen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Panel 3 & 4 represent the  long-term Swift-XRT light curve and corresponding photon  spectral index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' A clear X-ray brightening during Jan 2019 is  observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' During this period, we do not have many optical  observations (panel 5), and hence it’s difficult to comment  on the flux level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' However, in UV (W1, M2, W2) bands  (panel 6) high flux state is observed corresponding to TeV  and X-ray activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' In panel 7, we show the archival optical  data from ASAS-SN, and no short time scale variability  MNRAS 000, 1–14 (2021)  6  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Diwan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  is seen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' We also have optical data from the ground-based  observatory (panel 5) which covers the last part of the light  curve showing a nice variation from a high flux state to a low  flux state, suggesting a long-term variation in optical bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3 Variability Study  In general, blazar shows significant variability during the flar-  ing period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The properties of these flares can depend on var-  ious factors like particle injection, particle acceleration, and  energy dissipation in the jets of the blazars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' To study this in-  trinsic property we calculate the Fractional Variability Am-  plitude (Fvar) from the multi-wavelength light curve of the  source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The relation given in (Vaughan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2003) is used to  determine the fractional variability (Fvar)  Fvar =  �  S2 − E2  F 2  (3)  err(Fvar) =  �  �  �  �  ��  1  2N  E2  F 2Fvar  �2  +  ��  E2  N  1  F  �2  (4)  where S2 is the variance of the light curve, F is the aver-  age flux, E2 is the mean of the squared error in the flux  measurements and N is the number of flux points in a light  curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' We have estimated the Fvar for all the light curves  and the corresponding values are tabulated in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' We  found that the source is more variable in UV followed by X-  ray and gamma-ray.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' We also plot the Fvar with respect to  the corresponding frequency in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' A similar behavior  is also seen for another TeV blazar 1ES 1727+502 for one of  the states (Prince et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' In past studies, it has also  been argued that the variability pattern resembles the shape  of the broadband SED seen in blazar if the source is observed  from radio to very high energy gamma-ray.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' One of the best  examples is Mrk 421 which is also a TeV source, where the  variability pattern during its two flaring states resembles the  blazar SED (Aleksić et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2015a,b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' A long-term study, using  10 yrs data, is done on 1ES 1218+304 by Singh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' (2019)  using the multi-wavelength data from radio to γ-ray and the  Fvar estimated on long-term period is different from what we  have found in our study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Singh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' (2019) have found that  source is more variable in radio at 15 GHz followed by X-ray  and then optical-UV and γ-ray.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  The timescale of variability is yet another important pa-  rameter that sets the bound on the size of the emission re-  gion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Doubling/Halving timescales are calculated for all time  bins from MJD 58119 to 59365 for the 7-day binned γ-ray  light curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The formula used is:  F(t2) = F(t1) × 2(t2−t1)/Td  (5)  Here F(t1) and F(t2) are the fluxes measured at time t1  and t2, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Td is the flux doubling/halving time  scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The fastest doubling/halving time (Tf) in γ-ray was  found to be 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='396 days.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The value for tvar can be given by  tvar = ln(2)×Tf which is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='275 days or 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='6 hours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The hour’s  scale variability is very common in blazar suggesting a com-  pact emitting region close to the central supermassive black  hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  Waveband  Fvar  err(Fvar)  Fermi γ-ray  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='2601  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0964  AstroSat-SXT X-ray  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0421  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0058  Swift X-ray  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='5074  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='01513  W1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='9448  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0006  W2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='6805  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0005  M2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='9448  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0007  U  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0242  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3185E-05  V  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0147  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0002  B  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0171  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0002  R  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0144  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='5188E-05  I  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0120  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='2755E-05  Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  Fractional variability amplitude (Fvar) parameter for  the blazar 1ES 1218+304 from optical to HE γ-rays using observa-  tions during January 1, 2018 - May 31, 2021 (MJD 58119-59365)  with different instruments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  Using the same equation we also calculate the time-scale vari-  ability for the 856 sec binned AstroSat SXT light curve shown  in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The flux doubling/halving time is estimated as  Tf = 1848.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='645 sec and the tvar is 1281.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='29 sec (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='2 ksec) or  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='35 minutes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' A similar flux variability time of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='1 ksec is  also estimated for Mrk 421 in SXT light curve by Chatter-  jee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Considering the fact that 1ES 1218+304  is a high synchrotron peaked blazar the X-ray will explain  the synchrotron emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' As argued by many authors that  the variability time can be associated with the characteristic  time scale in the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Here, we consider that the X-ray  variability timescale can be linked with the radiation cooling  time scale due to synchrotron only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Under this assumption  the cooling time can be the fast X-ray variability time and  can be defined as (Rybicki & Lightman 1979),  tcool ≃ 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='74 × 108 (1 + z)  δ  B−2γ−1 sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  (6)  Where, B is the strength of the magnetic field in Gauss and  tcool is the synchrotron cooling timescale in seconds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Follow-  ing Rybicki & Lightman (1979), We can also derive the char-  acteristic frequency of the electron population responsible for  the synchrotron emission at the peak frequency,  νch,e = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='2 × 106  δ  (1 + z)Bγ2 Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  (7)  Using the above two equations, we eliminate the γ since it  changes with different states and derives a single equation  given as,  B3δ ≃ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='5(1 + z)(νch,e/1018)−1τ −2  d .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  (8)  Using the above equation we derive the magnetic field  strength for Doppler factor, δ, =30 and variability time scale  of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='2 ksec and it is found to be 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='1 G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The strength of the  magnetic field derived from the broadband SED modeling is  a factor lower than this estimated value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' This discrepancy  could be because of the many assumptions made in deriving  the eqn (7) or due to the degeneracy in the SED modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='4 Flux-Index Correlation  We computed flux-index correlation for the γ-ray and X-ray  data to study index hardening/softening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The flux vs index  plot is shown in Figure 6 with γ-ray on the upper panel and  MNRAS 000, 1–14 (2021)  Multi-wavelength study of 1ES 1218+304  7  0  1  2  3  4  5  Flux0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3  300 GeV  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='5  Index  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0  Flux0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3  10 KeV  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0  Index  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='5  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='5  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0  Optical (mag)  U  B  V  R  I  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='5  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='5  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='5  UV (mag)  W1  M2  W2  58200  58400  58600  58800  59000  59200  MJD  14  15  16  17  Optical (mag)  ASAS-SN  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Multi-wavelength light curve of 1ES 1218+304 from January 2018 to May 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 7-day binned γ-ray flux are presented in units  of 10−8 ph cm−2 s−1, and X-ray fluxes are in units of 10−10 erg cm−2 s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The vertical red line represents the Flare period from 5-7  January 2019 and the vertical green line represents the Flare period from 15-20 January 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' This period also includes the data from  AstroSat for the period 17-20 January 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' We identify these periods as Flare A and Flare B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  X-ray on the lower panel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' In the case of γ-ray, we have taken  data points with TS≥16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' We also observe a positive corre-  lation between the flux and index, with Pearson correlation  coefficient, R = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='644 and p-value ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The trend follows  the linear function with slope = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' In contrast to the  above plot, X-ray data shows an inverse trend i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='e;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' a negative  correlation between flux and index, with Pearson correlation  coefficient, R = -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='748 and p-value ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' It can also be fit-  ted by a linear function with a slope = -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='423.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' This plot  shows two contrasting trends, we can see the ’harder-when-  brighter’ trend in the X-ray energy range and the ’softer-  when-brighter’ trend in the γ-ray energy range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' A similar  trend is also observed for one of the TeV blazar 1ES 1727+502  (Prince et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' One of the possible explanations for hav-  ing different trends in X-ray and gamma-ray is that they are  produced via two different processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' For BL Lac-type sources  such as 1ES 1218+304, it is well-known that the X-rays are  produced by the synchrotron process and γ-rays are produced  via the inverse-Compton process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' A long-term study done by  Singh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' (2019) also found a mild harder-when-brighter  MNRAS 000, 1–14 (2021)  8  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Diwan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  1016  1018  1020  1022  1024  1026  Frequency (Hz)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='8  Fractional Variability amplitude  Gamma-ray  SWIFT X-ray  Optical  SWIFT-UV  AstroSat SXT  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Fractional variability for various wavebands is plotted  with respect to their frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  0  1  2  3  4  5  6  7  Photon Flux (10  8 ph cm  2 sec  1)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0  Index  ray  r= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='644, p-value= 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='04×10  11  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='75  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='00  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='25  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='50  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='75  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='00  Flux_(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3-10 KeV) (10  10 erg cm  2 sec  1)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='8  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='6  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='8  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0  Index  X-ray  r= -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='748, p-value= 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='139×10  5  Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Scatter plot for the correlation between flux and index of  the blazar 1ES 1218+304.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The top plot represents the 7-day binned  Fermi-Lat data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The slope is positive and the Person correlation  coefficient is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='644.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The bottom plot represents Swift-XRT data  for Flux (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3-10 KeV) vs Photon Index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The slope is negative and  the Pearson correlation coefficient is -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='748, it follows an inverse  trend as the γ-ray data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The orange line is a linear fit for reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  trend in X-rays using almost 10 yrs of data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The average  spectral index is estimated as 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='99±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='16 which is consistent  with our estimated value as ∼2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' These results are also con-  sistent with the long-term study done by Wierzcholska &  Wagner (2016) where they found the average photon spec-  tral index as ∼2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='01 for different values of galactic ab-  sorption taken from different models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' A recent study done by  Sahakyan (2020) estimated the average photon spectral index  ≥2 for the period considering from 2008 to 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The spec-  tra can be even harder during the bright state as 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='60±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='05  which is consistent with our result (see Figure 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  103  104  105  Energy (MeV)  10  6  10  5  10  4  E2 dN  dE [MeV cm  2 s  1]  Likelihood Fit  5-7 Jan  15-20 Jan  Total Time Period  Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The γ-ray SED extracted for both the period and fit-  ted with power-law using the Likelihood fit method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The fitting  parameters are discussed in the corresponding Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='5 Fermi-LAT γ-ray spectral fitting  The process for data extraction and fitting is provided in  subsection 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' We have used the fermipy to extract the γ-  ray SED for the two periods (5-7 and 15-20 January 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  The SEDs are then fitted with a simple power law spectral  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' We noticed that the spectra are very hard and still  increasing with energy suggesting the involvement of high-  energy particles in their production.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The fitted parameters  are given in Table 3 and the spectral index for period A  (Γ=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='55±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='23) and B (Γ=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='54±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='19) are much harder than  the average power law index, (Γ=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='75±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='03) for the total pe-  riod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The harder spectra suggest that the IC peak is even at  higher energy which is clearly seen in broadband SED model-  ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' A study by Costamante et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' (2018) also shows a harder  gamma-ray spectrum for many TeV blazar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' A harder gamma-  ray spectrum is also seen in another TeV extreme blazar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' In-  cluding the TeV data in broadband SED Aguilar-Ruiz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  (2022) modeled the SED for six such sources with a two-  zone emission model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Few new EHBL types sources are also  discovered with the MAGIC telescope and the Fermi-LAT  gamma-ray spectra were found to be very hard for all the  sources suggesting an extreme location of the second SED  peak above 100 GeV energy range (Acciari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' A  long-term gamma-ray spectral index was also estimated for  1ES 1218+304 by Singh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' (2019) and they found it to  be harder with 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='67±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='05, similar to our estimated value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Sa-  hakyan (2020) also estimated the γ-ray spectra averaged over  ∼11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='7 years which found to be 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='71±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='02 mostly consistent  with above discussed results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' These values are also consistent  with the long-term average photon spectral index reported in  the recent 4FGL catalog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='6 Color-Magnitude Variations  The color-magnitude relation helps us understand the differ-  ent variability scenarios of the blazar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Fluctuations in optical  flux are often followed by spectral changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Therefore study-  ing the color-magnitude (CM) relationship can further shed  light on the dominant emission mechanisms in the blazar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  To obtain a better understanding of the CM relation for our  source, we fit a linear plot (CI = m V +c) between the color  MNRAS 000, 1–14 (2021)  Multi-wavelength study of 1ES 1218+304  9  Parameter  Flare A  Flare B  Whole Time Period  Units  Spectral Index (α)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='547 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='230  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='540 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='191  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='745 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='030 Flux (F0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3−300GeV )  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='306  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='063  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='310  10−8× photon(s) cm−2 s−1  Prefactor (N0)  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='538 ± 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='633  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='902 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='796  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='966 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='122  10−13× photon(s) cm−2 s−1 MeV−1  TS  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='497  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='297  2913.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='496 Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Best fit spectral parameters of 1ES 1218+304 from Fermi-Lat observations using equation 1 for two flaring periods 58488-58490  MJD (Flare A), 58498-58503 MJD (Flare B) and whole time period MJD 58119-59365.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='6  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='8  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='2  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='4  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='6  (B+V)/2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='75  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='00  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='25  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='50  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='75  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='00  Color Indices  B-V + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3  B-I  R-I + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='2  V-R  Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Colour magnitude plot for 1ES 1218+304.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The various  color indices are plotted against (B+V)/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  indices (CI) and (B+V)/2 magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' We then estimate the  fit values, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', slope (m), constant (c), along with the corre-  lation coefficient (r) and the respective null hypothesis prob-  ability (p) using two methods, Pearson and Spearman, as  listed in Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The generated CM plots are shown in Fig-  ure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Offsets of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='2 are used for (B-V) and (R-I).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  A positive slope with p < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='05 implies a bluer-when-brighter  (BWB) trend or a redder-when-fainter trend (Agarwal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  2021) while a negative slope indicates a redder-when-brighter  trend (RWB).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' As evident from Table 4, a significant BWB is  dominant during our observation period for all possible color  indices, namely;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' (B-V), (B-I), (R-I), and (V-R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Blazars, in  general, display BWB from their quasi-simultaneous optical  observations (Ghosh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2000;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Agarwal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Gupta  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2016a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  The BWB trend can be attributed to the process of elec-  tron acceleration to higher energies at the shock front, fol-  lowed by losing energy by radiative cooling while propagat-  ing away (Kirk et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' On the other hand, the opposite  trend of redder when brighter is observed more commonly  in FSRQs due to the contribution of bluer thermal emission  from the accretion disc (Villata et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' In addition to  BWB and RWB trends, other optical studies have revealed  cycle or loop-like trends (Agarwal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2021), a mixed trend  where BWB is dominant during higher state while RWB dur-  ing the fainter state, or a stable-when-brighter (SWB) which  is no significant color-magnitude correlation in the data at  any timescale (Gupta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2016b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Isler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Negi  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Agarwal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' However, due to the lack  of simultaneous observations for a larger sample of blazars,  color-magnitude trends are still a topic of debate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='7 Broadband SED modeling  The broadband SED modeling in blazar is used to un-  derstand the simultaneous multi-wavelength emission from  the source along with the possible physical mechanism re-  sponsible for broadband flaring event.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Simultaneous multi-  wavelength SEDs were generated for two time periods, which  overlapped with proposed flaring periods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The model fit-  ting was done using a publicly available code JetSet10 (Tra-  macere et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2009, 2011, 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Massaro, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  Broadband emission of BL Lac sources like 1ES 1218+304 is  better explained by the one-zone Synchrotron-Self Compton  (SSC) model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Leptonic models assume that relativistic lep-  tons (mostly electrons and positrons) interact with the mag-  netic field in the emission region and produce synchrotron  photons in the frequency region of radio to soft-X-ray or the  first hump of the SED.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The emission in the frequency region  of X-ray to γ-ray or the second hump of the SED is pro-  duced by inverse Compton (IC) scattering of a photon popu-  lation further classified into synchrotron-self Compton (SSC)  or external Compton (EC) categories based on the source  of the seed photons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' In the case of SSC models (Ghisellini  1993;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Maraschi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 1992) relativistic electrons up-scatter  the same synchrotron photons which they have produced in  the magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The model assumes a spherically sym-  metric blob of radius (R) in the emission region, surrounded  by relativistic particles accelerated by the magnetic field (B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  The blob makes an angle θ with the observer and moves along  the jet with the bulk Lorentz factor Γ, affecting emission re-  gion by the beaming factor δ = 1/Γ(1 − β cos θ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The blob  is filled with a relativistic population of electrons following  an empirical lepton distribution relation and the power law  with an exponential cut-off (PLEC) distribution of particles  is assumed:  Ne(γ) = N0γ−αexp(−γ/γcut)  (9)  where γcut is the highest energy cut-off in the electron spec-  trum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' We see that the optical/UV measurements are higher  than the non-thermal emission from the jet predicted by  the SSC model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' We also see high flux points in UV/optical  range from the long-term observation of 1ES 1218+304, from  NASA/IPAC Extragalactic Database (NED)11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' These obser-  vations suggest that the stellar emission from the host galaxy  of the source is dominant at optical/UV frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' In order  to accurately account for this emission due to the host galaxy,  we have added the host galaxy component during modeling  the SED using JetSet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Modeling of blazar 1ES 1218+304 is  based on the SSC model in reference to equation 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Results  10 https://jetset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='readthedocs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='io/en/latest/  11 https://ned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='ipac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='caltech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='edu/  MNRAS 000, 1–14 (2021)  10  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Diwan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  Colour  In-  dices  Slope  Intercept  Pearson  Coeffi-  cient  Pearson  P-value  Spearman  Coeffi-  cient  Spearman  P-value  (B-V)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='216  ±  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='024  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='152  ±  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='390  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='752  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='88E-  13  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='774  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='33E-  14  (B-I)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='446  ±  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='031  −6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='002  ±  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='506  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='893  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='15E-  19  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='928  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='06E-  24  (R-I)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='156  ±  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='019  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='982  ±  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='317  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='550  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='67E-  05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='734  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='65E-  10  (V-R)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='085  ±  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='018  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='070  ±  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='292  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='745  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='52E-  10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='787  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='77E-  12  Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Colour magnitude fitting and correlations coefficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  2  0  2  4  6  8  10  12  14  log(E) (eV)  12  14  16  18  20  22  24  26  28  log( )  (Hz)  14  13  12  11  10  9  8  log( F  )  (erg cm  2  s  1)  Sync  SSC  host_galaxy  Total SED  FERMI  SWIFT UVOT  SWIFT XRAY  archived  Nustar  Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Broadband SED Modelling for 5-7 January 2019 (Flare  A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Optical data are fitted with the host galaxy template available  in JetSet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Archival NuSTAR data are also plotted in cyan color  which does not match with the current state X-ray spectral shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  Due to the hard X-ray spectral index, the synchrotron peak is  shifted to higher energy (∼1020 Hz) compared to the synchrotron  peak location (1017−18 Hz) during 15-20 January as constrained  by AstroSat observation in Figure 3 and also visible in Figure 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  for the SSC model are shown in Figure 9 and Figure 10 for  Flare A and Flare B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The model parameters are given in table  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='1 The constraint on Doppler factor  We can calculate the minimum value of the Doppler factor  using the detection of high-energy photons from the source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  This calculation assumes the optical depth, τγγ(Eh), of the  highest energy photon, Eh, to γγ interaction is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The formula  for calculating the minimum value of the Doppler factor is  δmin =  �σtd2  l (1 + z)2fϵEh  4tvarmec4  �1/6  (10)  where σt is the Thomson scattering cross-section for the elec-  tron (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='65 × 10−25cm2), dl is the luminosity distance of the  source, fϵ is the X-ray flux in 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3-10 KeV energy range, Eh  is the highest energy photon, tvar is the observed variability  time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' For 1ES 1218+304, z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='182, dl is 924 Mpc and tvar is  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='275 days.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Using the value of highest energy photon Eh =  162.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='822 GeV for Flare A and 278.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='132 GeV for Flare B, and  fϵ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='94 × 10−10 for Flare A and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='55 × 10−10 for Flare B,  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='5  log(E) (eV)  12  14  16  18  20  22  24  26  28  log( )  (Hz)  14  13  12  11  10  9  log( F  )  (erg cm  2  s  1)  Sync  SSC  host_galaxy  Total SED  FERMI  SWIFT UVOT  archived  Nustar  AstroSat-SXT  SWIFT XRAY  Figure 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The plot is the same as Figure 8 but for 15-20 January  2019 (Flare B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Here also the archival NuSTAR spectrum does  not match the current state X-ray spectral shape which suggests  that the NuSTAR spectrum was taken in low-flux states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Here the  synchrotron peak is decided by both the XRT and SXT spectra  plotted on top of each other which peaks at roughly ∼2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='68×1017  Hz as estimated in section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='1 using AstroSat data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  we get the δmin value to be 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='725 for Flare A and 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='455 for  Flare B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='2 The size of emission region  The information on the size and location of the emission re-  gion is very important for performing the SED modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The  variability time scale estimated from the γ-ray light curve is  used to estimate the size of the emission region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The radius  R can be estimated by using the equation,  R = cδmintvar/(1 + z),  (11)  where R is estimated to be 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='27 − 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='71 × 1015cm, using the  δmin calculated in the previous section, and tvar is calculated  in section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' During SED modeling we have used the values  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='06 × 1016 cm for Flare A and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='40 × 1016 cm for Flare B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  The location of the emission region along the jet axis from  the supermassive black hole can also be estimated from the  variability time assuming a spherical emission region by using  the expression d ∼ 2cΓ2tvar/(1+z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Using the Lorentz factor,  Γ = δmin and tvar = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='275 days and z = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='182, the location is  estimated to be, d ∼ 2×1017 cm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' To optimize the broadband  SED modeling, we have fixed the location of the emission  region to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0 × 1017 cm along the jet axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  MNRAS 000, 1–14 (2021)  Multi-wavelength study of 1ES 1218+304  11  Sr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  Model Parameters  Unit  Flare A  Flare B  5-7 Jan  15-20 Jan  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  γmin 88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='342  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='9990  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  γmax 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3346 × 107  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='2115 × 107  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  γcut 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='8153 × 107  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='2216 × 105  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  RH  1017cm  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  R  1016cm  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0658  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='4  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  α 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='482500  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='530156  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  N  cm−3  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='34312  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='58231  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  B  G  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='7378 × 10−3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3035 × 10−2  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  z 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='182  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='182  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  δ 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='97827  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='30340  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  Ue  erg cm−3  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='470401  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='179746 × 10−2  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  UB  erg cm−3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='982449 × 10−7  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='760266 × 10−6  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  Pe  erg s−1  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='460334 × 1045  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='081457 × 1044  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  PB  erg s−1  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='130172 × 1038  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='145346 × 1041  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  Pjet  erg s−1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='060629 × 1046  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='370064 × 1044  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  Reduced Chi-Squared 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='079990  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='707362  Host Galaxy  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  nuFnu_p_host  erg cm−2 s−1  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='373  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='373  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  nu_scale  Hz  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='496  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='493  Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' [1-3] Minimum, maximum and cut Lorentz factor of injected electron spectrum [4] The position of the region [5] The size of  emission region [6] Spectral Index [7] Particle density [8] Magnetic field [9] Red Shift [10] Doppler factor [11] Electron energy density [12]  Magnetic field energy density [13] Jet power in electrons [14] Jet power in magnetic field [15] Total jet power  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3 Jet Power  We have estimated the power carried by individual compo-  nents (leptons, protons, and magnetic fields) and the total  jet power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The total power of the jet was estimated using  Pjet = πR2Γ2c(U ′  e + U ′  p + U ′  B)  (12)  Here Γ is the bulk Lorentz factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' U ′  e, U ′  p, U ′  B are the energy  densities of electrons-positrons, cold protons and the mag-  netic field respectively in the co-moving jet’s frame (primed  quantities are in the co-moving jet frame while unprimed  quantities are in the observer frame).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The power in leptons  is given by  Pe = 3Γ2c  4R  � Emin  Emax  EQ(E)dE  (13)  where Q(E) is the injected particle spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The integration  limits, Emin and Emax are calculated by multiplying the min-  imum and maximum Lorentz factor (γmin and γmax) of the  electrons with the rest-mass energy of the electron respec-  tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The power in the magnetic field is calculated using  PB = R2Γ2cB2  8  (14)  where B is the magnetic field strength obtained from the  SED modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The energy densities for electron-positron and  magnetic field for both Flare events were returned by our  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The energy density for cold proton was not estimated  as it was too small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' We calculated Pe, PB which are the power  carried by the leptons and the magnetic field respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The  total power Pjet ≈ Pe + PB along with the power of the in-  dividual components has been mentioned in Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The jet  is dominated by the lepton’s power and its value decreases  for the second flare period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The luminosities have been com-  puted for a pure electron/positron jet since the proton con-  tent is not well known, and can be considered as the lower  limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The absolute jet power Ljet ≃ 1×1046ergs−1 for Flare  A and is below the Eddington luminosity for a 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='6 × 108M⊙  black hole mass (LEdd = 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3 × 1046ergs−1) estimated from  the properties of the host galaxy in the optical band (Rüger  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' For Flare B, Ljet ≃ 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='37 × 1044ergs−1 is signifi-  cantly below the LEdd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='4 Broadband emission during flaring states  We choose two flaring periods during the month of January  2019, MJD 58488-58490 (5-7 January 2019, Fig 9) and MJD  58498-58503 (15-20 January 2019, Fig 10) were modeled with  a one-zone leptonic scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The modeled parameters are  mentioned in Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The model parameters inferred from  this fitting suggest that Flare A had more activity compared  to Flare B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Although the γmax and α are almost the same for  both the flares inferring that there was very little variability  in VHE γ-ray band, we see from Table 5 that γmin, γcut have  significantly higher values for Flare A compared to Flare B,  which may be due to the flaring seen in the X-ray band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The  magnetic field (B) for Flare A (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='73×10−3) is also less than  that of Flare B (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='30×10−2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' During the fitting of SED, we  kept RH and δ as free parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' We find that the value of  RH is close to the value we calculate using equation 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' We  also calculate the minimum doppler factor δmin between the  range (13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='725-14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='455), but during the SED modeling, we find  that for Flare A δ = 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='98 and for Flare B it is much higher δ  = 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='30 then the calculated value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' It suggests that variation  in δ could be one of the reasons for different flux states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  During these flares, the optical-UV emission is dominated  MNRAS 000, 1–14 (2021)  12  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Diwan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  by thermal emission from the host galaxy and hence has been  modeled using the host galaxy model using JetSet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' It is also  seen that the X-ray data is better explained by synchrotron  radiation of electrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The SSC component of SED model-  ing dominates above 1020 Hz (∼ 1 MeV) and it is useful in  describing the data up to the VHE γ-ray band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  4 SUMMARY AND DISCUSSIONS  In our work, we present the multi-wavelength study of HBL  blazar 1ES 1218+304 from 1st January 2018 to 31st March  2021 (58119-59365), which also include the high flux event in  VHE γ-rays detected by both MAGIC and VERITAS obser-  vatories during January 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' This high flux rate was also  seen in Swift-XRT and UVOT instruments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Hence we di-  vided our SED analysis into two flaring periods 5-7 Jan-  uary 2019 and 15-20 January 2019 for simultaneous multi-  wavelength observation of 1ES 1218+304.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The fastest vari-  ability timescale was found to be 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='275 days from analyzing  the γ-ray light curve, constraining the size of the emission  region to 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='27 − 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='71 × 1015 cm, which came out to be higher  than previous modeling results (Rüger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2010, Sahakyan  2020, Singh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2019) but comparable to SED modeled  results in our case, see Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The location of the emis-  sion region is estimated to be d ∼ 2 × 1017cm was similar  to that used for SED modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The highest energy photon  detected was 278.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='132 GeV which arrived during Flare B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' We  can also see the ’harder-when-brighter’ trend in the X-ray en-  ergy range and the ’softer-when-brighter’ trend in the γ-ray  energy range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  The broadband SED modeling of the source was repro-  duced by a leptonic simple one-zone SSC model with the  electron energy distribution described by a Power-law with  an exponential cut-off (PLEC) function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Parameters like the  magnetic field, injected electron spectrum, and minimum and  maximum energy of injected electrons have been optimized  to get a good fit to the SEDs data points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' So this study sug-  gests that a single-zone model can also be good enough to  explain the multi-waveband emissions from 1ES 1218+304.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  The optical and UV emissions from the source are found to  be dominated by the stellar thermal emissions from the host  galaxy and can be modeled using the JetSet code by a simple  blackbody approximation (Rüger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  Costamante et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' (2018) argued that the broadband SED  modeling in hard-TeV blazar can be explained by the one-  zone SSC model at the expense of extreme electron ener-  gies with very low radiative efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The maximum elec-  tron Lorentz factor estimated in their modeling for all the six  sources is orders of 107 which is consistent with our results  for 1ES 1218+304.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The other modeling parameters such as  the size of the emission region, magnetic field strength, and  the magnetization parameters (UB/Ue) are very similar to  our SED modeling result for 1ES 1218+304.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' In our case, the  UB/Ue = 10−4 - 10−6 and in Costamante et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' (2018) it order  of 10−2 - 10−5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Similar results were also obtained by Kauf-  mann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' (2011) where they model the broadband SED of  extreme TeV source 1ES 0229+200.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The magnetic field and  the magnetization parameter (10−5) are consistent with our  results for 1ES 1218+304.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' But their model requires a narrow  electron energy distribution with γmin ∼ 105 to γmax ∼ 107  rather than the broad energy range obtained in our study,  Costamante et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' (2018), and Acciari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  Acciari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' (2020) have observed ten new TeV sources  with MAGIC from 2010 to 2017 for a total period of 262  hours and the simultaneous X-ray observations confirm that  out of 10, 8 sources are of extreme nature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Their γ-SED  was found to be very hard between 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='4 to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Blazar 1ES  1218+304 is also an extreme TeV blazar and in our study, the  gamma-ray SED is found to be 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='5 consistent with the above  TeV sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' They have modeled all the sources with a sin-  gle zone conical-jet SSC model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Additionally, they also used  the proton-synchrotron and a leptonic scenario with a struc-  tured jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' They also argue that all the model provides a good  fit to the broadband SED but the individual parameters in  each model differ substantially.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Comparing their SSC model  results to our SSC modeling the maximum electron energy is  consistent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The electron spectral index in our case is harder  than their results and also the magnetic field in our case is  much smaller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The estimated Lorentz factor is more or less  consistent with the Γ used for all the sources in their study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  In their recent work Aguilar-Ruiz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' (2022) have modeled  the six well-known extreme BL Lac sources with a lepto-  hadronic two-zone emission model to explain the broadband  SED.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' In another study, Zech & Lemoine (2021) have shown  that the broadband SED of extreme BL Lac sources can be  explained by considering the co-acceleration of electrons and  protons on internal or recollimation shocks inside the rela-  tivistic jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Sahakyan (2020) has modeled the average state  of 1ES 1218+304 with one-zone SSC model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The parameter  estimated in their study is mostly consistent with ours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' How-  ever, our study focuses on the smaller period including two  flaring events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' During the flaring event (15-20 Jan) the mag-  netic field and the magnetization parameters are estimated  as 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='30×10−2 Gauss and ∼10−4 which is comparable to the  value for the same parameters estimated by modeling the av-  erage state of the source in Sahakyan (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' However, the  Doppler factor required in Sahakyan (2020) is much higher  than the Doppler factor needed to fit the flaring state in our  case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Singh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' (2019) also modeled the average broadband  SED collected for almost 10 years with a one-zone SSC model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  The required γmin, γmax and Doppler factor are consistent  with our result but the size of the emission region is one order  of magnitude smaller than ours, and also the magnetic field  estimated in their model is much higher than what we found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  The difference in some of the parameters could be because  they modeled the average SED and in our case, we are more  focused on a short period of time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The optical-UV SED is  mostly off to the general trend of broadband SED of blazar  and hence in both cases is fitted with a host-galaxy contri-  bution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Singh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' (2019) used a specific model to fit the  host-galaxy and estimated the black hole mass of the source,  however, in JetSet we can not include a specific model, and  hence host-galaxy is fitted as a free parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  The above discussion suggests that the known extreme BL  Lac sources are very less in number and need careful attention  and more broadband study to exactly quantify their nature  and the physical emission mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  MNRAS 000, 1–14 (2021)  Multi-wavelength study of 1ES 1218+304  13  5 CONCLUSIONS  In this work, we present the long-term study of the blazar  1ES 1218+304 using 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='5 years of near-simultaneous multi-  wavelength data from Fermi-LAT, SWIFT-XRT, SWIFT-  UVOT, AstroSat, and TUBITAK observations taken between  January 1, 2018, and March 31, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' This study explores the  broadband temporal and spectral behavior of the source dur-  ing flaring states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The main results of our study are provided  below:  During the month of January 2019, VHE γ-rays detected  by both MAGIC and VERITAS observatory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' This high flux  state was also seen in Fermi, Swift-XRT, and UVOT instru-  ments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The fractional variability estimated across the wave-  bands suggests that UV is more variable followed by X-ray,  γ-ray, and optical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  The fast flux variability in γ-ray is calculated to be  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='275 days, the size of the emission region is estimated to  be ∼8×1015 cm, and the emission region is located at a dis-  tance of ∼ 2 × 1017 cm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' A "harder-when-brighter" trend was  seen in X-ray whereas a "softer-when-brighter" trend was in  γ-ray.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The γ-ray emission from 1ES 1218+304 can also be  described by a power law with a spectral index of ∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='745.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  The Astrosat SXT light curve reveals a minute scale of  variability of the order of 20 minutes and the X-ray spectrum  is well fitted with both power-law and the log parabola mod-  els.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' However, the LP provides a better fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' A joint fit with the  LAXPC spectrum provides a great constrain on the location  of synchrotron peak roughly around 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='68×1017Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  As seen in many other TeV blazars, a shift in syn-  chrotron peak is observed from one state to another state  from ∼1017−18 Hz to ∼1020 suggesting an extreme nature of  the source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  The broadband SED modeling of the source is repro-  duced by a one-zone leptonic SSC model with the electron  energy distribution described by a Power-law with an expo-  nential cut-off (PLEC) function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' We also find that the Opti-  cal/UV emissions from the source are dominated by the stel-  lar thermal emissions from the host galaxy which are modeled  by a simple blackbody approximation (Rüger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2010) us-  ing JetSet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' The JetSet code uses an approximation of the host  galaxy model to help fit the SED modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' We need more  precise and dedicated observation in the UV/Optical band  for a better understanding of the host galaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  1ES 1218+304 is also an important source for obser-  vations within the upcoming high-energy ground-based tele-  scopes like CTA (Cherenkov Telescope Array)12 observatory  to establish the link beyond the GeV energy range, in the  realm of TeV γ-ray emission and MeV-GeV emission mea-  sured from the Fermi-LAT and its extreme blazar behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  ACKNOWLEDGEMENTS  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Bose acknowledges the support of Ramanujan Fellowship-  SB/S2/RJN-038/2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Prince is grateful for the support of  the Polish Funding Agency National Science Centre, project  2017/26/A/ST9/-00756 (MAESTRO 9) and MNiSW grant  DIR/WK/2018/12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' This work made use of Fermi telescope  12 https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='cta-observatory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='org  data and the Fermitool package obtained through the Fermi  Science Support Center (FSSC) provided by NASA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' This  work also made use of publicly available packages JetSet, Fer-  mipy, and PSRESP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' This publication uses the data from the  AstroSat mission of the Indian Space Research Organisation  (ISRO), archived at the Indian Space Science Data Centre  (ISSDC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' This work has used the data from the Soft X-ray  Telescope (SXT) developed at TIFR, Mumbai, and the SXT  POC at TIFR is thanked for verifying and releasing the data  via the ISSDC data archive and providing the necessary soft-  ware tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' We thank the LAXPC Payload Operation Center  (POC) at TIFR, Mumbai for providing the necessary soft-  ware tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' We have also made use of the software provided  by the High Energy Astrophysics Science Archive Research  Center (HEASARC), which is a service of the Astrophysics  Science Division at NASA/GSFC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  DATA AVAILABILITY  For this work, we have used data from the Fermi-LAT, Swift-  XRT, Swift-UVOT, and AstroSat which are available in the  public domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' We have also used optical data collected by  the TUBITAK telescope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' This optical data was given to us  on request.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Details are given in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  REFERENCES  Abdo A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2010, The Astrophysical Journal, 716, 30  Abdollahi S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2020, The Astrophysical Journal Supplement  Series, 247, 33  Abhir J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Joseph J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Patel S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Bose D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2021a, MNRAS, 501,  2504  Abhir J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Prince R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Joseph J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Bose D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Gupta N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2021b, ApJ,  915, 26  Acciari V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2009, ApJ, 695, 1370  Acciari V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2020, ApJS, 247, 16  Agarwal A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2015, MNRAS, 451, 3882  Agarwal A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2019a, MNRAS, 488, 4093  Agarwal A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2019b, Monthly Notices of the Royal Astronom-  ical Society, 488, 4093  Agarwal A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2021, A&A, 645, A137  Agarwal A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Pandey A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Özdönmez A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Ege E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Kumar Das A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=',  Karakulak V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2022, ApJ, 933, 42  Aguilar-Ruiz E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Fraija N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Galván-Gámez A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Benítez E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2022,  MNRAS, 512, 1557  Aharonian F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2000, New Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 5, 377  Albert J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2006, ApJ, 642, L119  Aleksić J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2015a, A&A, 576, A126  Aleksić J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2015b, A&A, 578, A22  Atwood W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2009, ApJ, 697, 1071  Barat S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Chatterjee R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Mitra K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2022, Monthly Notices of the  Royal Astronomical Society, 515, 1655  Blandford R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Znajek R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 1977, MNRAS, 179, 433  Bose D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Chitnis V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Majumdar P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Acharya B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2022, The  European Physical Journal Special Topics, 231, 3  Böttcher M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Reimer A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Sweeney K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Prakash A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2013, ApJ, 768,  54  Cao G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Wang J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2013, Monthly Notices of the Royal Astro-  nomical Society, 436, 2170  Chatterjee R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2021, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' arXiv:2102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='00919  Costamante L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Bonnoli G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Tavecchio F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Ghisellini G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Taglia-  ferri G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Khangulyan D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2018, Monthly Notices of the Royal  Astronomical Society, 477, 4257  MNRAS 000, 1–14 (2021)  14  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Diwan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  Feng  Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=',  VERITAS  Collaboration  2022,  in  37th  Interna-  tional Cosmic Ray Conference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 802 (arXiv:2108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='05333),  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='22323/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='395.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0802  Fortin P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2008, in Aharonian F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Hofmann W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Rieger F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=',  eds, American Institute of Physics Conference Series Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 1085,  American Institute of Physics Conference Series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' pp 565–568  (arXiv:0810.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0301), doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='3076735  Ghisellini G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 1993, Advances in Space Research, 13, 587  Ghosh K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Ramsey B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Sadun A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Soundararajaperumal  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2000, ApJS, 127, 11  Giommi P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2006, A&A, 456, 911  Gupta A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2016a, MNRAS, 458, 1127  Gupta A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2016b, Monthly Notices of the Royal Astro-  nomical Society, 458, 1127  HI4PI Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2016, A&A, 594, A116  Isler J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Urry C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Coppi P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Bailyn C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Brady M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', MacPherson  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Buxton M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Hasan I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2017, ApJ, 844, 107  Kaufmann S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Wagner S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Tibolla O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Hauser M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2011, A&A,  534, A130  Kirk J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Rieger F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Mastichiadis A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 1998, A&A, 333, 452  Kochanek C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2017, PASP, 129, 104502  Liu H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Bai J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2006, The Astrophysical Journal, 653, 1089  Lombardi S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Lindfors E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Becerra Gonzalez J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Colin P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Sitarek  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Stamerra A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2011, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' arXiv:1110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='6786  Mannheim K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 1993, A&A, 269, 67  Maraschi L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Ghisellini G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Celotti A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 1992, ApJ, 397, L5  Massaro, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Tramacere, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Perri, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Giommi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' Tosti, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 2006,  A&A, 448, 861  Mirzoyan R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2019, The Astronomer’s Telegram, 12354, 1  Misra R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Roy J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Yadav J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2021, Journal of Astrophysics and  Astronomy, 42, 55  Mukherjee R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', VERITAS Collaboration 2019, The Astronomer’s  Telegram, 12360, 1  Nalewajko K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Begelman M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Sikora M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2014, The Astrophysi-  cal Journal, 789, 161  Negi V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Joshi R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Chand K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Chand H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Wiita P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Ho L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Singh  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2022, MNRAS, 510, 1791  Prince R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2019, ApJ, 871, 101  Prince R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2020, The Astrophysical Journal, 890, 164  Prince R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Majumdar P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Gupta N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2017, The Astrophysical Jour-  nal, 844, 62  Prince R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Gupta N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Nalewajko K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2019, ApJ, 883, 137  Prince R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Khatoon R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Stalin C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2021, MNRAS, 502, 5245  Prince R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Khatoon R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Majumdar P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Czerny B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Gupta N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2022,  Monthly Notices of the Royal Astronomical Society, 515, 2633  Priya S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Prince R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Agarwal A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Bose D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Özdönmez A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Ege E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=',  2022, Monthly Notices of the Royal Astronomical Society, 513,  2239  Ramazani V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Bonneli G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Cerruti M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2019, The Astronomer’s  Telegram, 12365, 1  Rybicki G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Lightman A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 1979, Radiative processes in astro-  physics  Rüger M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Spanier F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Mannheim K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2010, Monthly Notices of the  Royal Astronomical Society, 401, 973  Sahakyan N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2020, MNRAS, 496, 5518  Schlafly E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Finkbeiner D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2011, The Astrophysical Journal,  737, 103  Schlickeiser R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 1989a, ApJ, 336, 243  Schlickeiser R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 1989b, ApJ, 336, 264  Shappee B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2014, ApJ, 788, 48  Shukla A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Mannheim K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2020, Nature Communications, 11, 4176  Singh K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2016, in den Herder J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Takahashi T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=',  Bautz M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', eds, Society of Photo-Optical Instrumentation Engi-  neers (SPIE) Conference Series Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 9905, Space Telescopes and  Instrumentation 2016: Ultraviolet to Gamma Ray.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 99051E,  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='1117/12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='2235309  Singh K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2017, Journal of Astrophysics and Astronomy,  38, 29  Singh K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Bisschoff B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', van Soelen B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Tolamatti A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Marais  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Meintjes P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2019, Monthly Notices of the Royal As-  tronomical Society, 489, 5076  Sun S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Li H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Yang X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Lü J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Xu D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Wang J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2021,  Research in Astronomy and Astrophysics, 21, 197  Tramacere A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2020, JetSeT: Numerical modeling and SED fit-  ting tool for relativistic jets, Astrophysics Source Code Library,  record ascl:2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='001 (ascl:2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='001)  Tramacere A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Giommi P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Perri M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Verrecchia F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Tosti G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2009,  A&A, 501, 879  Tramacere A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Massaro E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Taylor A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2011, ApJ, 739, 66  Urry C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Padovani P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 1995, PASP, 107, 803  Vaughan S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Edelson R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Warwick R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Uttley P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2003, MNRAS,  345, 1271  Villata M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2006, A&A, 453, 817  Wierzcholska A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Wagner S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2016, Monthly Notices of the Royal  Astronomical Society, 458, 56  Wood M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Caputo R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Charles E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Di Mauro M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Magill J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=',  Perkins J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Fermi-LAT Collaboration 2021, in 35th In-  ternational  Cosmic  Ray  Conference  (ICRC2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  824  (arXiv:1707.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='09551), doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='22323/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='0824  Yadav J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2016, in den Herder J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Takahashi T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=',  Bautz M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', eds, Society of Photo-Optical Instrumentation Engi-  neers (SPIE) Conference Series Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 9905, Space Telescopes and  Instrumentation 2016: Ultraviolet to Gamma Ray.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=' 99051D,  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='1117/12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='2231857  Zech A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', Lemoine M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content=', 2021, A&A, 654, A96  This paper has been typeset from a TEX/LATEX file prepared by  the author.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
+page_content='  MNRAS 000, 1–14 (2021)' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQfEPrI/content/2301.00991v1.pdf'}
diff --git a/5dAyT4oBgHgl3EQfQPaq/content/tmp_files/2301.00042v1.pdf.txt b/5dAyT4oBgHgl3EQfQPaq/content/tmp_files/2301.00042v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..06ae9c459dfa87031000e489b988700a2d04d5c0
--- /dev/null
+++ b/5dAyT4oBgHgl3EQfQPaq/content/tmp_files/2301.00042v1.pdf.txt
@@ -0,0 +1,3502 @@
+Fundamental Limits to Expressive Capacity of Finitely Sampled Qubit-Based Systems
+Fangjun Hu,1, ∗ Gerasimos Angelatos,1, ∗ Saeed A. Khan,1 Marti Vives,1, 2 Esin T¨ureci,3
+Leon Bello,1 Graham E. Rowlands,4 Guilhem J. Ribeill,4 and Hakan E. T¨ureci1
+1Department of Electrical and Computer Engineering, Princeton University, Princeton, NJ 08544, USA
+2Q-CTRL, Santa Monica, CA 90401, USA
+3Department of Computer Science, Princeton University, Princeton, NJ 08544, USA
+4Raytheon BBN, Cambridge, MA 02138, USA
+(Dated: January 3, 2023)
+The expressive capacity for learning with quantum systems is fundamentally limited by the quantum sampling
+noise incurred during measurement. While studies suggest that noise limits the resolvable capacity of quantum
+systems, its precise impact on learning remains an open question. We develop a framework for quantifying
+the expressive capacity of qubit-based systems from finite numbers of projective measurements, and calculate
+a tight bound on the expressive capacity and the corresponding accuracy limit that we compare to experiments
+on superconducting quantum processors. We uncover the native function set a finitely-sampled quantum system
+can approximate, called eigentasks. We then demonstrate how low-noise eigentasks improve performance for
+tasks such as classification in a way that is robust to noise and overfitting. We also present experimental and
+numerical analyses suggesting that entanglement enhances learning capacity by reducing noise in eigentasks.
+Our results are broadly relevant to quantum machine learning and sensing applications.
+I.
+INTRODUCTION
+Learning with quantum systems is a promising application
+of near-term quantum processors, with several recent demon-
+strations in both quantum machine learning (QML) [1–5] and
+quantum sensing [6–8]. A broad class of such data-driven ap-
+plications proceed by embedding data into the evolution of
+a quantum system, where the embedding, dynamics, and ex-
+tracted outputs via measurement are all governed by a set of
+general parameters θ. Depending on the learning scheme, dif-
+ferent components of this general framework may be trained
+for optimal performance of a given task. Irrespective of the
+scheme, however, the fundamental role of the quantum sys-
+tem is that of a high-dimensional feature generator. Given
+inputs u, a set of frequencies for the occurrence of different
+measurement outcomes act as a feature vector to learn a func-
+tion f(u) that minimizes the chosen loss function (see Fig. 1).
+The relationship between the physical structure of the model
+and the function classes that can be expressed with high accu-
+racy, referred to as expressivity, is a fundamental question of
+basic importance to the success of quantum models. Recent
+results have begun to shed light on this important question
+and provide guidance on the choice of parameterized quantum
+models [9–16]. Yet when it comes to experimental implemen-
+tations, the presence of noise is found to substantially curtail
+theoretical expectations for performance [1–3].
+Given an input u to a general dynamical system, we de-
+fine its Expressive Capacity (EC) as a measure of the accu-
+racy with which K linearly independent functions {f(u)} of
+the input can be constructed from K readout features. This is
+a suitable generalization to noisy systems of the Information
+∗ These two authors contributed equally
+Processing Capacity introduced in Ref. [17]. A central chal-
+lenge in determining the EC for quantum systems is the fun-
+damentally stochastic nature of measurement outcomes. Even
+when technical noise due to system parameter fluctuations is
+minimized as in an error-corrected quantum computer, there
+is a fundamental level of noise, the quantum sampling noise
+(QSN), which cannot be eliminated in learning with quantum
+systems. QSN therefore sets a fundamental limit to the EC
+of any physical system. Although QSN is well-understood
+theoretically, a formulation of its impact on learning is a chal-
+lenging task as it is strongly determined by the quantum state
+of the system relative to the measurement basis, and is highly
+correlated when entanglement is present. Consequently, the
+impact of QSN is often ignored [18–21] (with a few excep-
+tions [14, 22]), even though it can place strong constraints on
+practical optimization [23] and performance [22]. In this ar-
+ticle, we develop a mathematical framework to quantify the
+EC that exactly accounts for the structure of QSN, providing
+a tight bound for an L-qubit system under S measurements,
+and illustrate how a mathematical framework for its quantifi-
+cation can guide experimental design for QML applications.
+Our work goes beyond simply defining the EC as a figure of
+merit, however. In particular, we offer a methodology to iden-
+tify the native function set that is most accurately realizable
+by a given encoding under finite sampling. Equivalently, we
+show that this defines a construction of measured features that
+is optimally robust to noise in readout, thereby revealing how
+such a quantum system can be optimally employed for learn-
+ing tasks. Finally, while the strength of the EC lies in its gener-
+ality, we provide numerical examples that suggest that higher
+EC is typically indicative of improved performance on spe-
+cific QML tasks. As such, the EC provides a metric whose op-
+timization can be targeted for improved learning performance
+in a task-agnostic and parameter-independent manner.
+This strategy for defining the noise-constrained EC natu-
+arXiv:2301.00042v1  [quant-ph]  30 Dec 2022
+
+2
+Entangled 
+system
+Increased
+sampling
+Product
+system
+Input
+         dimensional 
+    input domain
+Output            under finite sampling
+Feature generator
+(a)
+(b)
+Individual function capacity:
+Function approximation
+features
+(Probabilities)
+Quantum system
+Quantum annealers
+Quantum Neural Networks/
+Variatonal Quantum Algorithms
+Quantum Kernel Methods
+Target:
+Learned Estimate:
+Learned linear weights 
+e.g.    -Qubit system
+Computational basis measurement
+FIG. 1. (a) Representation of the learning framework considered in
+this work – inputs u are transformed to a set of outputs via a feature
+generator, here implemented using a finitely-sampled quantum sys-
+tem as shown in (b). Inputs are encoded in the state of a quantum
+system via a general quantum channel U. Information is extracted
+from the quantum system via projective measurements in the com-
+putational basis. The geometric structure of the quantum sampling
+noise in the high-dimensional measured feature space can strongly
+depend on the encoding, and the degree of entanglement generated
+upon parametric evolution. The learning scheme discussed in the
+present work optimally leverages the geometric structure of corre-
+lated noise.
+This framework describes a wide range of practical
+quantum systems, from quantum circuits used in QML, to quantum
+annealers exhibiting continuous evolution, and beyond, all defined by
+general parameters θ. As shown in (a), learned estimates for desired
+functions are constructed via a trained linear estimator ˜w applied to
+K measured observables ¯
+X of the quantum system, with a resolu-
+tion limited by quantum sampling noise with finite shots S. Capacity
+then quantifies the error in the approximation of a target function via
+this scheme.
+rally focuses on accessible noisy output features under a spec-
+ified measurement scheme, as opposed to unmeasured degrees
+of freedom.
+This makes the EC an efficiently-computable
+quantity in practice, as we demonstrate using both numerical
+simulations and experiments on IBM Quantum’s supercon-
+ducting multi-qubit processors [24]. Our work also identifies
+enhancement in measurable quantum correlations as a general
+principle to increase the EC of quantum systems under finite
+sampling.
+II.
+LEARNING WITH QUANTUM SYSTEMS
+The most general approach to learning from data using a
+generic quantum system is depicted schematically in Fig. 1.
+A table with symbols and abbreviations used in the text can
+be found in Appendix A. For concreteness, we detail a specific
+realization for L-qubit systems that are measured projectively,
+which will be analyzed in the remainder of this work. Any
+learning scheme begins with embedding the data u through a
+quantum channel parameterized by θ acting on a known initial
+state, ˆρ(u; θ) = U(u; θ)ˆρ0. For an L-qubit quantum system,
+for example, we consider ˆρ0 = |0⟩⟨0|⊗L.
+Any computation must be performed using outputs ex-
+tracted from the quantum system via measurements in a
+specified basis parameterized by K operators { ˆ
+Mk}, k =
+0, · · · , K − 1. For a projectively measured L-qubit system,
+the measurement basis is defined by the K = 2L projectors
+ˆ
+Mk = |bk⟩⟨bk| corresponding to measurement of bitstrings
+bk. A single measurement or “shot” yields a discrete out-
+come b(s)(u) for each observable: if the outcome of shot s
+is state k, then b(s)(u) ← bk. Measured features are then
+constructed by ensemble-averaging over S repeated shots:
+¯Xk(u) = 1/S �
+s δ(b(s)(u), bk). Hence ¯Xk(u) in this case
+is the measured frequency of occurrence of the bitstring bk in
+S repetitions of the experiment with the same input u. These
+measured features are formally random variables that are un-
+biased estimators of the expected value of the corresponding
+observable as computed from ˆρ(u): explicitly,
+limS→∞ ¯Xk(u) ≡ xk(u) = Tr{ ˆ
+Mk ˆρ(u; θ)},
+(1)
+so that xk is the quantum mechanical probability of occur-
+rence of the kth bitstring.
+In QML theory, it is standard to consider the limit S → ∞,
+and to thus use expected features {xk(u)} for learning. How-
+ever, for any practical implementation, measured features
+{ ¯Xk(u)} must be constructed under finite S, in which case
+their fundamentally quantum-stochastic nature can no longer
+be ignored.
+This quantum sampling noise, like any other
+source of noise, can unsurprisingly limit the EC. Completely
+unlike classical noise sources however, the statistics of quan-
+tum sampling noise are strongly determined by the state of
+the quantum system itself. This leads to a rich noise structure
+that changes dramatically based on, for example, the entan-
+glement of the generated quantum state, as depicted in Fig. 1.
+In this work, we exactly account for this structure of quantum
+sampling noise to quantify its fundamental impact on EC. By
+further leveraging the complexity and quantum state depen-
+dence of sampling noise, we provide a practical, experimen-
+tally applicable methodology that maximizes the capacity for
+learning functions using finitely-sampled quantum systems,
+and also avoids overfitting in ML tasks.
+We begin by observing that ¯
+X are samples from a multino-
+mial distribution with S trials and K = 2L categories, which
+can be decomposed into their expected value and an input-
+dependent sampling noise:
+¯
+X(u) = x(u) +
+1
+√
+S
+ζ(u),
+(2)
+where ζ(u) is a zero-mean random vector obeying multino-
+mial statistics.
+As discussed in Appendix B and C, what
+makes quantum systems special is the fundamental relation-
+ship between the noise ζ(u) and the ‘signal’ x(u).
+Pre-
+cisely, the covariance Σ(u) of ζ(u) depends on the gen-
+erated quantum state:
+Σkk′(u)
+=
+Tr{ ˆ
+Mk ˆ
+Mk′ ˆρ(u)} −
+Tr{ ˆ
+Mk ˆρ(u)}Tr{ ˆ
+Mk′ ˆρ(u)}. This quantum covariance of the
+measured observables therefore comprises non-linear func-
+tions of the signal x(u) itself; at a given S, we will show
+that this allows for more information to be extracted from sys-
+tems with more quantum correlations between observables.
+Note that ζ can be straightforwardly modified to include other
+
+3
+noise sources, such as gate or measurement errors (see Ap-
+pendix B 2), with 1/
+√
+S then interpreted as a general noise
+strength. However our focus here remains on quantum sam-
+pling noise and its fundamental role in learning with quantum
+systems.
+The use of such a quantum system for the learning of func-
+tions under finite sampling is then depicted schematically in
+Fig. 1. For a target function f(u), an approximation fW (u)
+is obtained via a linear (for reasons clarified shortly) esti-
+mator applied to readout features under finite S, fW (u) =
+W · ¯
+X(u), where
+¯
+X = ( ¯X0, . . . , ¯XK−1)T .
+To quantify
+the fidelity of this approximation, we introduce the capac-
+ity [14, 17, 20] to construct the target function as the minimum
+achievable (normalized) mean squared error between the tar-
+get and its estimate:
+C[f] = 1 − min
+W ∈RK
+Eu[|f(u) − fW (u)|2]
+Eu[|f(u)|2]
+.
+(3)
+In the above, Eu refers to the expected value with respect to an
+input distribution p(u) over a compact input domain, which
+can be continuous or discrete: Eu[f] ≡
+�
+du p(u)f(u) ≃
+1
+N
+�
+n f(u(n)) for i.i.d. sampling obeying u(n) ∼ p(u) for
+all n ∈ [N].
+Minimizing error in the approximation of
+f(u) by fW (u) over the input domain to determine capac-
+ity thus requires finding ˜w = argminW Eu[|f − fW (u)|2]
+(via a resource-efficient pseudoinverse). This capacity is con-
+structed such that 0 ≤ C[f] ≤ 1.
+The choice of a linear estimator and a mean squared er-
+ror loss function may appear restrictive at first glance, but the
+generality of our formalism averts such limitations. For ex-
+ample, the use of a linear estimator applied directly to readout
+features precludes classical nonlinear post-processing of mea-
+surements; however, this is simply to ensure the calculated
+capacity is a measure of the quantum system itself, and not of
+a classical nonlinear layer. Importantly, our formalism is gen-
+eral enough to incorporate such processing in a calculation
+of capacity, via a simple redefinition of readout features ¯
+X.
+Hence the use of a linear estimator does not necessarily lose
+generality. Secondly, while higher-order loss functions may
+be used, the mean squared loss effectively describes the Tay-
+lor expansion of a wide range of loss functions (see Appendix
+C 5).
+To extend the notion of capacity to a task-independent mea-
+sure of the expressivity of a physical system, we can eval-
+uate the function capacity over a complete orthonormal set
+of basis functions {fℓ}ℓ∈N, equipped with the inner product
+⟨fℓ, fℓ′⟩p =
+� 1
+−1 fℓ(u)fℓ′(u)p(u)du = δℓℓ′. The total Ex-
+pressive Capacity (EC) is then CT ≡ �∞
+ℓ=0 C[fℓ], which ef-
+fectively quantifies how many linearly-independent functions
+can be expressed from a linear combination of { ¯Xk(u)}. Our
+main result, which is proven in Appendix C 4, is that the EC
+for an L-qubit system whose readout features are stochastic
+variables of the form of Eq. (2) is given by
+CT (θ) = Tr
+��
+G + 1
+S V
+�−1
+G
+�
+=
+K
+�
+k=1
+1
+1 + β2
+k(θ)/S . (4)
+The first equality is written in terms of the expected feature
+Gram and covariance matrices G ≡ Eu[xxT ] and V ≡
+Eu[Σ] respectively; we later demonstrate that these expected
+quantities can be accurately estimated under finite S sam-
+pling.
+The second equality expresses the total capacity in
+a finite-dimensional linear space, in terms of the eigenval-
+ues {β2
+k}k∈[K] satisfying the generalized eigenvalue prob-
+lem Vr(k) = β2
+kGr(k). Inspecting this expression, we first
+note that it is independent of the particular set {fℓ}ℓ∈N cho-
+sen, which would have required an evaluation over an infi-
+nite set of functions and its numerical evaluation therefore
+would be subject to inaccuracies due to truncation [17]. In-
+stead, CT can be interpreted as the sum of capacities to con-
+struct K individual functions living in an otherwise infinite-
+dimensional function space; the identity of these special func-
+tions is closely connected with the generalized eigenvectors
+{r(k)}, and will be clarified shortly. Secondly, in the absence
+of noise, limS→∞ CT = Rank{G} = K = 2L, provided no
+special symmetries exist (see Appendix C 6). Such theoreti-
+cal exponential growth in expressive capacity with L is often-
+cited as a motivator for ML on quantum systems [14, 20, 25].
+From the perspective of infinite-shot capacity, this also im-
+plies that all L-qubit systems with K measured features are
+equivalent, regardless of encoding. Such universality has also
+been pointed out for classical dynamical systems subject to
+zero input and output noise [17].
+However, our expression for CT is also valid for any noisy
+physical system, corresponding to finite S.
+In particular,
+Eq. (4) shows that the EC of a qubit-based physical system
+satisfies CT ≤ K at finite S, and can be fully characterized in
+terms of the spectrum {β2
+k}, which is ultimately determined
+by parameters θ governing the physical system and embed-
+ding via the Gram (G) and covariance (V) matrices. Related
+characterizations of noise-constrained capacity have been at-
+tempted for Gaussian quantum systems [22], but to our knowl-
+edge no precise formulation exists that also encompasses non-
+Gaussian systems such as qubit systems. Furthermore, from
+the perspective of capacity, what makes one embedding or
+physical system different from another is simply its ability to
+accurately express functions in the presence of noise. Our
+expression for CT thus provides a general, comprehensive,
+and straightforward metric to assess and compare this capac-
+ity across physical systems and their associated embedding
+under finite S.
+Furthermore, via the associated eigenvectors {r(k)}, our
+analysis uncovers a finite set of orthogonal functions native
+to a particular encoding that is maximally resolvable through
+S measurements. This set of K orthonormal functions, the
+eigentasks y(k)(u) = �
+j r(k)
+j
+xj(u), can be estimated from
+measured readout features as described in Appendix D 1. The
+eigentasks characterize an ordered set of functions that can be
+constructed with mean squared error β2
+k/S, leading to a natu-
+ral interpretation of β2
+k as noise-to-signal (NSR) eigenvalues,
+determined by fundamental sampling noise. As we will show,
+this experimentally extractable information can be utilized for
+optimal learning (with minimal degrees of freedom) with a
+noisy quantum system.
+
+4
+III.
+EXPERIMENTAL RESULTS
+To demonstrate the above results in practice, we now show
+how the spectrum {β2
+k}, the EC, and eigentasks can all be
+computed for real quantum devices in the presence of param-
+eter fluctuations and device noise.
+We emphasize at the outset that our approach for quantify-
+ing the EC of a quantum system is very general, and can be
+applied to a variety of quantum system models. For practical
+reasons, we perform experiments on IBM Quantum (IBMQ)
+processors, whose dynamics is described by a parameterized
+quantum circuit containing single and two-qubit gates. How-
+ever, as an example of the general validity of our approach,
+in Appendix E we compute the EC for L-qubit quantum an-
+nealers via numerical simulations, governed by the markedly
+different model of continuous-time Hamiltonian dynamics.
+On IBMQ devices, resource limitations restrict our compu-
+tation of EC to 1D inputs u that are uniformly distributed,
+p(u)
+=
+Unif[−1, 1], see Fig. 2(a).
+We emphasize that
+this analysis can be straightforwardly extended to multi-
+dimensional and arbitrarily-distributed inputs given suitable
+hardware resources, without modifying the form of the Gram
+and covariance matrices.
+We are only now required to specify the model of the L-
+qubit system in Eq. (1), which has been left completely gen-
+eral thus far. The specific ansatz we consider is tailored to
+be natively implementable on IBMQ processors; more gen-
+eral ansatz can also be considered (see Appendix B). It con-
+sists of τ ∈ N repetitions of the same input-dependent circuit
+block depicted in Fig. 2(a). The block itself is of the form
+Rx(θx/2)W(J)Rz(θz + θIu)Rx(θx/2), where Rx/z are
+Pauli-rotations applied qubit-wise, e.g. Rz = �
+l Rz(θz
+l +
+θI
+l u).
+The entangling gate acts between physically con-
+nected qubits in the device and can be written as W(J) =
+�
+⟨l,l′⟩ exp{−i J
+2 ˆσz
+l ˆσz
+l′}.
+Note that for this ansatz, the choice J = 0 (mod π) yields
+either W = ˆI or ˆσz ⊗ ˆσz, both of which ensure ˆρ(u) is a prod-
+uct state and measured features are simply products of uncor-
+related individual qubit observables – equivalent to a noisy
+classical system. Starting from this product system (PS), tun-
+ing the coupling J ̸= 0 (mod π) provides a controllable pa-
+rameter to realize an entangled system (ES). This control en-
+ables us to address a natural question regarding EC of quan-
+tum systems under finite S: what is the dependence of EC
+and realizable eigentasks on J, and hence on quantum corre-
+lations?
+This calculation of EC requires extracting measured fea-
+tures from the quantum circuit under input u, one example of
+which is shown for the IBMQ ibmq perth device in Fig. 2(a),
+for S = 214. For comparison, we also show ideal-device
+simulations (no device noise), where slight deviations are ob-
+served. The agreement with the experimental feature is im-
+proved when the effects of gate and readout errors, and qubit
+relaxation are included, hereafter referred to as “device noise”
+simulations, highlighting the non-negligible role of device er-
++
++
++ C-NOT
++
++
++
++
++
++
++
++
+Input
+ES
+PS
+Order
+(a)
+(b)
+(c)
+Shots
+Coupling
+IBM Perth
+Output
+Experiment
+Experiment
+Simulations
+Simulations
+Estimate
+Calculate
+Device encoding
+Device encoding
+Device noise
+Device noise
+Ideal
+Ideal
+Mean over 8 random 
+encodings: device noise 
+Mean over 8 random 
+encodings: ideal
+Ideal sim.
+Device noise
+sim.
+Experiment
+FIG. 2.
+(a) IBMQ Perth device and quantum circuit schematic for
+EC calculation, and classification task in Fig. 3. Here τ = 3 lay-
+ers, and random qubit rotation parameters are θx/z
+l
+∼ Unif[0, 2π]
+and θI
+l ∼ Unif[0, 10π]. On the right, the specific feature plotted is
+¯
+X1(u) = P000001(u) for S = 214 shots. (b) Left panel: Device
+NSR spectrum β2
+k for ES, J = π/2 (blue crosses) and PS, J = 0
+(brown diamonds). Ideal (solid) and device noise (dashed) simula-
+tions are also shown. Note the agreement between device and simu-
+lation, along with distortion from more direct exponential growth in
+β2
+k with k in the ideal case, due to device errors. Right panel: CT
+vs. S calculated from the left panel. At a given S, the CT can be
+approximated by performing the indicated sum over all β2
+k < S. (c)
+EC (top panel) and ETC (lower panel) under S = 214 from the IBM
+device, and device noise simulations (dashed peach). Average met-
+rics over 8 random encodings for device noise (solid peach) and ideal
+(solid gray) simulations are also shown. The S → ∞ EC of these
+encodings always attains the max{CT } = 64, indicated in dashed
+red.
+rors.
+The measured features under finite S are used to estimate
+the Gram and covariance matrices (see Appendix D), and to
+thus solve the eigenproblem for NSR eigenvalues {β2
+k}. Typ-
+ical NSR spectra computed for two random encodings on the
+device are shown in Fig. 2(b), for J = 0 (PS) and J = π/2
+(ES), together with spectra from device noise simulations,
+with which they agree well. We note that at lower k, the device
+NSR eigenvalues are larger than those from ideal simulations,
+due to device noise contributions. For larger k, device results
+deviate from the pure exponential increase (with order) seen in
+ideal simulations. The deviation is captured by device noise
+simulations and can therefore be attributed to device errors.
+The NSR spectra therefore can serve as effective diagnostic
+tools for quantum processors and encoding schemes. More
+examples will be provided later in the discussion.
+The NSR spectra can be used to directly compute the EC of
+the corresponding quantum device for finite S, via Eq. (4). As
+a rule of thumb, at a given S only NSR eigenvalues β2
+k ≲ S
+contribute substantially to the EC. An NSR spectrum with a
+flatter slope therefore has more NSR eigenvalues below S,
+
+0
+1
+2
+3
+4
+5
+65
+which gives rise to a higher capacity. Fig. 2(b) shows that the
+ES generally exhibits an NSR spectrum with a flatter slope
+than the PS, yielding a larger capacity for function approxi-
+mation across all sampled S.
+To more precisely quantify the role of entanglement and
+quantum correlations in EC, we introduce the expected total
+correlation (ETC) of the measured state over the input domain
+of u [26, 27],
+¯T = Eu
+� L
+�
+l=1
+S(ˆρM
+l (u)) − S(ˆρM(u))
+�
+,
+(5)
+where
+ˆρM
+is
+the
+measured
+state:
+ˆρM(u)
+≡
+�
+k ˆρkk(u) |bk⟩⟨bk| and S is the von Neumann entropy (see
+Appendix G). We now compute EC and ETC using S = 214
+in Fig. 2(c) as a function of J, together with both ideal and
+device noise simulations of the same. We note that product
+states by definition have ¯T = 0 [28]; this is seen in ideal
+simulations for J = 0 (mod π). However, the actual device
+retains a small amount of correlation at this operating point,
+which is reproduced by device noise simulations. This can be
+attributed to gate or measurement errors as well as cross-talk,
+especially relevant for the transmon-based IBMQ platform
+with a parasitic always-on ZZ coupling.
+With increasing J, ¯T increases and peaks around J ∼
+π/2 (mod π); interestingly, CT also peaks for the same cou-
+pling range. From the analogous plot of EC, we clearly see
+that at finite S, increased ETC appears directly correlated
+with higher EC. We have observed very similar behaviour us-
+ing completely different models of quantum systems (see Ap-
+pendix Fig. 5 [29, 30]). This indicates the utility of enhancing
+quantum correlations as a means of improving the general ex-
+pressivity of quantum systems.
+However, we see that at finite S, even with increased quan-
+tum correlations, the maximum EC is still substantially lower
+than the upper bound of K = 64. Note that this remains true
+even for ideal simulations, and over several random encod-
+ings, so the underperformance cannot be attributed to device
+noise or poor ansatz choice respectively. These results clearly
+indicate that the resulting sampling noise at finite S is the fun-
+damental limitation for QML applications on this particular
+IBM device, rather than other types of noise sources and er-
+rors.
+IV.
+A ROBUST APPROACH TO LEARNING
+While we have demonstrated the EC as an efficiently-
+computable metric of general expressivity of a noisy quantum
+system, some important practical questions arise. First, does
+the general EC metric have implications for practical perfor-
+mance on specific QML tasks? Secondly, given the limiting –
+and unavoidable – nature of correlated sampling noise, does
+the EC provide any insights on optimal learning using a par-
+ticular noisy quantum system and the associated embedding?
+Input
+Target
+Distinguish inputs from 
+Class 1 vs. Class 2
+ES
+ES
+PS
+PS
+Input
+Eigentasks
+,
+(a)
+(b)
+(c)
+Increasing noise
+Learning with
+     
+eigentasks
+Class 1
+Training
+Testing
+Class 2
+Equiv. to learning 
+likelihood function
+,
+FIG. 3.
+(a) Device eigentasks for ES (left) and PS (right), con-
+structed from noisy features at S = 210 and S = 214. (b) Clas-
+sification demonstration on IBMQ Perth. Binary distributions to be
+classified over the input domain are shown. (c) The classification
+task can be cast as learning the likelihood function separating the
+two distributions; this target function is shown in the upper panel.
+Lower panels show the trained estimate of this target using outputs
+from the ES and PS respectively, using KL = 36 eigentasks with
+S = 214.
+Our formulation addresses both these important questions
+naturally, as we now discuss. Beyond being a simple figure of
+merit, we show in the Appendix C that the EC is precisely the
+sum of capacities to approximate a particular set of orthogonal
+functions native to the given noisy quantum system: the eigen-
+tasks. Crucially, these eigentasks ¯y(k)(u) = � r(k)
+j
+¯Xj(u) can
+be directly estimated from a noisy quantum system via the
+generalized eigenvectors {r(k)}, and are ordered by their as-
+sociated NSR {β2
+k}. We show a selection of estimated eigen-
+tasks from IBMQ, for an ES (J = 5π/3) and PS (J = 0) in
+Fig. 3(a). For both systems, the increase in noise with eigen-
+task order is apparent when comparing two sampling values,
+S = 210 and S = 214. Furthermore, for any order k, eigen-
+tasks for the PS are visibly noisier than the ES; this is con-
+sistent with NSR eigenvalues for PS being larger than those
+for ES, as seen in Fig. 2(b). This ability to more accurately
+resolve eigentasks provides a complementary perspective on
+the higher expressive capacity of ES in comparison to PS.
+The resolvable eigentasks of a finitely-sampled quantum
+system are intimately related to its performance at specific
+QML applications. To demonstrate this result, we consider
+a concrete application: a binary classification task that is
+not linearly-separable. Samples u(n), n ∈ [N], obeying the
+same distribution p(u) for u ∈ [−1, 1] as considered for the
+EC evaluation, are separated into two classes, as depicted in
+Fig. 3(b). A selection of Ntrain = 150 total samples - with
+equal numbers from each class - are input to the IBMQ device,
+and readout features ¯
+X(u(n)) are extracted using S = 214
+shots.
+A linear estimator applied to these features is then
+trained using logistic regression to learn the class label associ-
+ated with each input. Finally, the trained IBMQ device is used
+to predict class labels of Ntest = 150 distinct input samples
+for testing.
+This task can equivalently be cast as one of learning the
+likelihood function that discriminates the two input distribu-
+
+6
+Classification accuracy
+Testing
+ Classification accuracy
+No. of eigentasks used for learning,
+(a)
+(b)
+ES
+PS
+Coupling
+Experiment
+Simulations
+Device encoding
+Device encoding
+Testing
+NSR Cutoff
+Mean over 
+8 random encodings
+Overfitting
+Overfitting
+Training
+FIG. 4. (a) Training (light) and testing (dark) accuracy for an ES and
+PS in blue and brown respectively, as a function of number of eigen-
+tasks used in learning. The optimal test set performance is found near
+the NSR cutoff Kc(S) (dash-dotted lines) informed by the quantum
+system’s NSR spectra. In all figures, the IBMQ Perth device is sam-
+pled with S = 214, and the training and test sets consist of 150 ran-
+dom points. (b) Testing set classification accuracy as a function of
+J for our optimal learning method. The average of simulated encod-
+ings is shown in solid peach, and the horizontal line shows the best
+performance of a software neural network with KL = 36 parameters
+for comparison.
+tions, shown in Fig. 3(c), with minimum error. The set of up
+to KL eigentasks ¯y(k)(u), where KL ≤ K, serves as the na-
+tive basis of readout features used to approximate any target
+function using the quantum system. The noisier eigentasks of
+the PS therefore limit the accuracy with which it can be used
+to learn the target, in comparison to the ES. This is clear from
+the learned estimates shown in Fig. 3(c), using an equal num-
+ber of KL = 36 eigentasks to ensure a fair comparison. The
+higher approximation capacity translates to improved classi-
+fication performance, as we show via the training and testing
+classification accuracy in Fig. 4(a) for both ES and PS. We
+plot both as a function of the number of eigentasks KL used
+for learning, from which it is clear that the maximum testing
+accuracy using the ES exceeds that of the PS.
+However, using eigentasks ordered by NSR reveals even
+more about learning using noisy quantum systems, and pro-
+vides a path towards optimal learning. While intuition sug-
+gests that using more eigentasks can only be beneficial,
+weights learned when training with noisier eigentasks may
+not generalize well to unseen samples. For example, using
+all eigentasks (KL = K) yields a test accuracy far lower than
+that found in training. The observed deviation is a distinct
+signature of overfitting: the optimized estimator learns noise
+in the training set, and thus loses generalizability in testing.
+Crucially, an optimal number of eigentasks clearly emerges,
+around KL ≃ Kc(S) = maxk{β2
+k < S}, for which the NSR
+eigenvalue is closest to S. Eigentasks k > Kc typically con-
+tribute more ‘noise’ to the function approximation task than
+‘signal’. Excluding these eigentasks therefore limits overfit-
+ting without adversely impacting performance.
+Fig. 4(b) also shows the classification accuracy as J is var-
+ied, where we highlight the striking similarity with Fig. 2(c):
+encodings with larger quantum correlations and thus higher
+expressive capacity will perform generically better on learn-
+ing tasks in the presence of noise, because they generate a
+larger set of eigentasks that can be resolved at a given sam-
+pling S. The NSR spectra and eigentasks therefore provide
+a natural truncation scheme to maximise testing accuracy,
+avoiding overfitting without any additional regularization (see
+also Appendix H and I).
+V.
+DISCUSSION
+We have developed a straightforward approach to quan-
+tify the expressive capacity of any qubit-based system in the
+presence of fundamental sampling noise.
+Our analysis is
+built upon an underlying framework that determines the native
+function set that can be most robustly realized by a finitely-
+sampled quantum system: its eigentasks. We use this frame-
+work to introduce a methodology for optimal learning using
+noisy quantum systems, which centers around identifying the
+minimal number of eigentasks required for a given learning
+task. The resulting learning methodology is resource-efficient
+and robust to overfitting. We demonstrate that eigentasks can
+be efficiently estimated from experiments on real devices us-
+ing a limited number of training points and finite shots. We
+also demonstrate across two distinct qubit evolution ans¨atze
+that the presence of measured quantum correlations enhances
+expressive capacity. Our work has direct application to the
+design of circuits for learning with qubit-based systems. In
+particular, we propose the optimization of expressive capacity
+as a meaningful goal for the design of quantum circuits with
+finite measurement resources.
+ACKNOWLEDGEMENT
+This research was developed with funding from the
+DARPA contract HR00112190072, AFOSR award FA9550-
+20-1-0177, and AFOSR MURI award FA9550-22-1-0203.
+The views, opinions, and findings expressed are solely the au-
+thors and not the U.S. government.
+[1] E. Grant, M. Benedetti, S. Cao, A. Hallam, J. Lockhart, V. Sto-
+jevic, A. G. Green, and S. Severini, Hierarchical quantum clas-
+sifiers, npj Quantum Information 4, 1 (2018).
+[2] V. Havl´ıˇcek, A. D. C´orcoles, K. Temme, A. W. Harrow, A. Kan-
+dala, J. M. Chow, and J. M. Gambetta, Supervised learning with
+quantum-enhanced feature spaces, Nature 567, 209 (2019).
+[3] F. Tacchino, P. Barkoutsos, C. Macchiavello, I. Tavernelli,
+D. Gerace, and D. Bajoni, Quantum implementation of an arti-
+ficial feed-forward neural network, Quantum Science and Tech-
+nology 5, 044010 (2020).
+[4] J. Chen, H. I. Nurdin, and N. Yamamoto, Temporal Informa-
+tion Processing on Noisy Quantum Computers, Physical Re-
+view Applied 14, 024065 (2020).
+
+7
+[5] Y. Suzuki, Q. Gao, K. C. Pradel, K. Yasuoka, and N. Yamamoto,
+Natural quantum reservoir computing for temporal information
+processing, Scientific Reports 12, 1353 (2022).
+[6] J. J. Meyer, Fisher Information in Noisy Intermediate-Scale
+Quantum Applications, Quantum 5, 539 (2021).
+[7] Z. Ma, P. Gokhale, T.-X. Zheng, S. Zhou, X. Yu, L. Jiang,
+P. Maurer, and F. T. Chong, Adaptive Circuit Learning for
+Quantum Metrology, arXiv:2010.08702 [quant-ph] (2021).
+[8] C. D. Marciniak, T. Feldker, I. Pogorelov, R. Kaubruegger,
+D. V. Vasilyev, R. van Bijnen, P. Schindler, P. Zoller, R. Blatt,
+and T. Monz, Optimal metrology with programmable quantum
+sensors, Nature 603, 604–609 (2022).
+[9] S. Sim, P. D. Johnson, and A. Aspuru-Guzik, Expressibility
+and Entangling Capability of Parameterized Quantum Circuits
+for Hybrid Quantum-Classical Algorithms, Advanced Quantum
+Technologies 2, 1900070 (2019).
+[10] R. LaRose and B. Coyle, Robust data encodings for quantum
+classifiers, Phys. Rev. A 102, 032420 (2020).
+[11] M. Schuld, R. Sweke, and J. J. Meyer, Effect of data encod-
+ing on the expressive power of variational quantum-machine-
+learning models, Physical Review A 103, 032430 (2021).
+[12] A. Abbas, D. Sutter, C. Zoufal, A. Lucchi, A. Figalli, and
+S. Woerner, The power of quantum neural networks, Nature
+Computational Science 1, 403–409 (2021).
+[13] Y. Wu, J. Yao, P. Zhang, and H. Zhai, Expressivity of quantum
+neural networks, Phys. Rev. Research 3, L032049 (2021).
+[14] L. G. Wright and P. L. McMahon, The Capacity of Quantum
+Neural Networks, arXiv:1908.01364 [quant-ph] (2019).
+[15] Y. Du, M.-H. Hsieh, T. Liu, and D. Tao, Expressive power of
+parametrized quantum circuits, Physical Review Research 2,
+033125 (2020).
+[16] Z. Holmes, K. Sharma, M. Cerezo, and P. J. Coles, Connect-
+ing ansatz expressibility to gradient magnitudes and barren
+plateaus, PRX Quantum 3, 010313 (2022).
+[17] J. Dambre, D. Verstraeten, B. Schrauwen, and S. Massar, Infor-
+mation Processing Capacity of Dynamical Systems, Scientific
+Reports 2, 514 (2012).
+[18] K. Fujii and K. Nakajima, Harnessing Disordered-Ensemble
+Quantum Dynamics for Machine Learning, Physical Review
+Applied 8, 024030 (2017).
+[19] M. Benedetti, E. Lloyd, S. Sack, and M. Fiorentini, Parame-
+terized quantum circuits as machine learning models, Quantum
+Science and Technology 4, 043001 (2019).
+[20] R. Mart´ınez-Pe˜na, J. Nokkala, G. L. Giorgi, R. Zambrini, and
+M. C. Soriano, Information processing capacity of spin-based
+quantum reservoir computing systems, Cognitive Computation
+(2020).
+[21] M. Schuld and F. Petruccione, Machine Learning with Quan-
+tum Computers, Quantum Science and Technology (Springer
+International Publishing, 2021).
+[22] J. Garc´ıa-Beni, G. L. Giorgi, M. C. Soriano, and R. Zam-
+brini, Scalable photonic platform for real-time quantum reser-
+voir computing, arXiv:2207.14031 [quant-ph] (2022).
+[23] A. Arrasmith, M. Cerezo, P. Czarnik, L. Cincio, and P. J. Coles,
+Effect of barren plateaus on gradient-free optimization, Quan-
+tum 5, 558 (2021).
+[24] IBM Quantum, https://quantum-computing.ibm.com (2022).
+[25] W. D. Kalfus, G. J. Ribeill, G. E. Rowlands, H. K. Krovi, T. A.
+Ohki, and L. C. G. Govia, Hilbert space as a computational
+resource in reservoir computing, Physical Review Research 4,
+033007 (2022).
+[26] V. Vedral, The role of relative entropy in quantum information
+theory, Reviews of Modern Physics 74, 197 (2002).
+[27] K. Modi, T. Paterek, W. Son, V. Vedral, and M. Williamson,
+Unified view of quantum and classical correlations, Physical
+Review Letters 104, 080501 (2010).
+[28] M. A. Nielsen and I. Chuang, Quantum computation and quan-
+tum information (Cambridge University Press, 2010).
+[29] V. Giovannetti, S. Lloyd, and L. Maccone, Quantum metrology,
+Physical Review Letters 96, 010401 (2006).
+[30] R. Mart´ınez-Pe˜na, G. L. Giorgi, J. Nokkala, M. C. Soriano, and
+R. Zambrini, Dynamical phase transitions in quantum reservoir
+computing, Phys. Rev. Lett. 127, 100502 (2021).
+
+8
+Appendix A: Table of Symbols and Abbreviations
+Abbreviations
+NISQ
+Noisy Intermediate Scale Quantum
+(Q)ML
+(Quantum) Machine Learning
+QSN
+Quantum Sampling Noise
+VQC
+Variational Quantum Circuits
+PS
+Product System
+ES
+Entangled System
+EC
+Total Expressive Capacity, CT
+ETC
+Expected Total Correlation, ¯T
+Symbols and notation
+S
+Number of shots
+N
+Number of inputs
+L
+Number of qubits
+K
+≡ 2L, number of measured features
+u
+Input
+θ
+Quantum system parameters
+ˆρ
+Generated quantum state
+ˆ
+Mk
+Measured observable
+W
+Output weights (can be untrained)
+˜w
+Optimal learned output weights on S-finite readout data
+L
+Loss function
+bk
+Label for eigenstate of ˆ
+Mk
+b(s)
+Measurement outcome for shot s
+xk
+Expected features Tr{ ˆ
+Mk ˆρ}
+X(s)
+k
+Observed bit in shot s
+¯
+Xk
+Empirical observed feature 1/S �
+s δ(b(s), bk)
+ζk
+Noise part in ¯
+Xk
+G
+Gram matrix of expected features {xk}
+V
+Expected covariance matrix of random variable X(s)
+k (u)
+R
+Noise-to-Signal matrix
+β2
+k
+Eigen-NSR
+y(k)
+Principal feature
+r(k)
+Combination coefficients in y(k) = �
+k′ r(k)
+k′ xk′
+¯y(k)
+≡ �
+k′ r(k)
+k′ ¯
+Xk′, noisy eigentask
+ξ(k)
+≡ �
+k′ r(k)
+k′ ζk′, noise part in ¯y(k)
+ˆOk
+≡ �
+k′ r(k)
+k′ |bk′⟩⟨bk′|, optimal measurement basis
+ˆρM
+≡ �
+k ˆρkk(u) |bk⟩⟨bk|, post-measurement state
+Kc(S)
+Cutoff index where β2
+k reaches S
+�
+( · )N
+Quantity obtained from finite N sampling data
+�
+( · )
+Large N limit, that is limN→∞ �
+( · )N
+TABLE I. Table of notations.
+Appendix B: Feature maps using quantum systems
+1.
+Details of input encodings into quantum systems
+In the main text, we introduce the idea of encoding inputs into the state of a quantum system via a parameterized quantum
+channel, reproduced below:
+ˆρ(u; θ) = U(u; θ)ˆρ0
+(B1)
+Our analysis of EC presented in this work does not depend on the precise details of the quantum channel U. For practical
+calculations, however, we have to consider concrete models, about which we provide more details in this section.
+
+9
+To describe these models, we begin by first limiting to 1-D inputs as analyzed in the main text; generalizations to multi-
+dimensional inputs u are straightforward. Then, we write Eq. (B1) in the form
+ˆρ(u; θ) = B(u; θ)ˆρ0B†(u; θ)
+(B2)
+In the main text, we have considered a model for dynamics of an L-qubit quantum system that is natively implementable on
+modern quantum computing platforms: namely the ansatz of quantum circuits with single and two-qubit gates. In this case,
+which we refer to as the circuit ansatz (or C-ansatz for short), the operator B(u; θ) takes the precise form
+B(u; θ) =
+�
+Rx
+�θx
+2
+�
+W(J)Rz
+�
+θz + θIu
+�
+Rx
+�θx
+2
+��τ
+(C-ansatz)
+(B3)
+For completeness, we recall that Rx/z are Pauli-rotations applied qubit-wise, e.g. Rz = �
+l Rz(θz
+l + θI
+l u), while the entangling
+gate acts between physically connected qubits in the device and can be written as W(J) = �
+⟨l,l′⟩ exp{−i J
+2 ˆσz
+l ˆσz
+l′}. We empha-
+size here again that τ ∈ N+ is an integer, representing the number of repeated blocks in the C-ansatz encoding. We note that
+the actual operations implemented on IBMQ processors also include dynamics due to noise, gate, and measurement errors. As
+discussed in the main text, the EC of a quantum system can be computed in the presence of these more general dynamics, and is
+sensitive to the limitations introduced by them.
+An alternative ansatz which we analyze in this SI, is where the operator B(u; θ) describes continuous Hamiltonian dynamics.
+This ansatz is relevant to computation with general quantum devices, such as quantum annealers and more generally quantum
+simulators. In this case, which we refer to as the Hamiltonian ansatz (or H-ansatz for short),
+B(u; θ) = exp{−i ˆH(u)t}, ˆH(u) = ˆH0 + u · ˆH1
+(H-ansatz)
+(B4)
+Here t is a continuous parameter defining the evolution time; and ˆH0 = �L
+l,l′ J⟨l,l′⟩ˆσz
+l ˆσz
+l′ + �L
+l=1 hx
+l ˆσx
+l + �L
+l=1 hz
+l ˆσz
+l and
+ˆH1 = �L
+l=1 hI
+l ˆσz
+l . The transverse x-field strength hx
+l = ¯hx + εx
+l and longitudinal z-drive strength hz,I
+l
+= ¯hz,I + εz,I
+l
+are all
+randomly chosen and held fixed for a given realization of the quantum system,
+εx,z,I
+l
+∼ hx,z,I
+rms N(0, 1),
+(B5)
+where N(0, 1) defines the standard normal distribution with zero mean and unit variance. We consider nearest-neighbor inter-
+actions Jl,l′, which can be constant Jl,l′ ≡ J, or drawn from Jl,l′ ∼ Unif[0, Jmax], where Unif[a, b] is a uniform distribution
+with non-zero density within [a, b].
+As an aside, we note that the C-ansatz quantum channel described by Eq. (B3) can be considered a Trotterization-inspired
+implementation of the H-ansatz in Eq. (B4). In particular, if we set θx/z/I = hx/z/I∆ · τ, where t = ∆ · τ, and consider the
+limit ∆ → 0 while keeping t fixed, Eq. (B3) corresponds to a Trotterized implementation of Eq. (B4). This correspondence is
+chosen for practical reasons, but is not necessary in our analysis.
+The parameterized quantum channel characterizes how information is injected into the quantum system and processed by it;
+however, to probe information from the quantum system, one must apply an appropriate and feasible quantum measurement.
+For extract information efficiently, we consider a wide family of observable ˆ
+Mk: the only restriction of these observables is
+that they must be a product of local observables, ˆ
+Mk = ˆo1 ⊗ · · · ⊗ ˆoL, which mutually commute with each other (meaning
+they are are simultaneously measurable). We consider two general schemes. The first one is the probability representation
+ˆol ∈ {|0⟩⟨0| , |1⟩⟨1|}, while the second is the spin moments representation, ˆol ∈ {ˆI, ˆσz}; the former representation is used
+throughout the main text. We will show below that these two readout schemes are equivalent up to a unitary transformation.
+2.
+Extracting output features under finite sampling: expressions for features and covariances
+Following evolution of the quantum system under the input-dependent Hamiltonian given by Eq. (B4), we extract certain
+measurable observables that are used as outputs for any learning task. The form of observables is again chosen for compliance
+with measurement protocols native to near-term quantum computing implementations: we consider Pauli z basis measurements
+only (although this can be generalized easily). This means our algorithm has access only to diagonal terms in ˆρ(u). We abbreviate
+vectors ⃗Mk, ⃗ρ(u) ∈ RK such that ( ⃗Mk′)k = ( ˆ
+Mk′)kk and (⃗ρ(u))k = ˆρ(u)kk. Then one can check for {+1, −1} readout:
+⃗Mk · ⃗Mk′ = Kδjj′, and the readout features can be expressed into dot product form xk(u) = Tr
+�
+ˆ
+Mk ˆρ(u)
+�
+= ⃗Mk · ⃗ρ(u). In
+
+10
+QRC, we hope to make full use of all functions in family {(⃗ρ(u))k}k∈[K] as readout features. The collection of all readout
+features
+x(u) =
+�
+�
+�
+�
+x0(u)
+x1(u)
+...
+xK−1(u)
+�
+�
+�
+� =
+�
+�
+�
+�
+�
+⃗M T
+0
+⃗M T
+1...
+⃗M T
+K−1
+�
+�
+�
+�
+� ⃗ρ(u) =: U⃗ρ(u),
+(B6)
+The orthonormality of { ⃗Mk}k∈[K] implies that U is unitary up to an overall constant (in fact, U =
+�
+1
+1
+1 −1
+�⊗L
+is the
+Hadamard matrix [28]). This unitarity implies that the above transformation is information-preserving. In particularly, this
+guarantees the ability to reconstruct the diagonal QRC density matrix elements (via tomography), ⃗ρ(u) = U −1x(u), simply
+computing the required inverse via the numerically-robust relationship U −1 = 1
+K U T .
+If each qubit has a readout error ϵ, that is, it will flip |0⟩ ↔ |1⟩. Then the transition probability of reading out |bk′⟩ from |bk⟩
+will be ϵd(bk,bk′)(1 − ϵ)L−d(bk,bk′) where d(bk, bk′) is the Hamming distance between bk and bk′. Thus, readout errors can
+furthermore be mathematically modeled by one more transition matrix (more precisely, a stochastic matrix):
+x(u) = U
+�
+1 − ϵ
+ϵ
+ϵ
+1 − ϵ
+�⊗L
+⃗ρ(u).
+(B7)
+The covariance of the X(u) ∈ {+1, −1}L (the random features for individual shot S = 1) can also be expressed easily:
+V[X(u)] = U
+�
+diag(⃗ρ(u)) − ⃗ρ(u) · ⃗ρ(u)T �
+U T
+(B8)
+where diag(⃗v) is a diagonal matrix that has the elements of ⃗v as entries. To prove this expression, it suffices to verify that the
+second order moments are entries
+V[X(u)]k1k2 ≡ Tr
+�
+ˆ
+Mk1 ˆ
+Mk2 ˆρ(u)
+�
+=
+K−1
+�
+k=0
+( ˆ
+Mk1 ˆ
+Mk2)kk ˆρkk(u) =
+K−1
+�
+k=0
+(U)k1k (U)k2k ˆρkk(u) =
+�
+Udiag (⃗ρ(u)) U T �
+k1k2 .
+(B9)
+Appendix C: Information capacity with quantum sampling noise
+1.
+Definition of capacity for quantum systems with sampling noise
+The function approximation universality (which will be formally stated in Appendix I), as a basic requirement of most neural
+network model can be made concrete by defining a metric to quantify how well a given quantum system (generalizable to any
+dynamical system) approximates general functions. Suppose an arbitrary probability distribution p(u) for a random (scalar)
+variable u defined in [−1, 1]. This naturally defines a function space L2
+p([−1, 1]) containing all functions f : [−1, 1] → R with
+� 1
+−1 f 2(u)p(u)du < ∞. The space is equipped with the inner product structure ⟨f1, f2⟩p =
+� 1
+−1 f1(u)f2(u)p(u)du. A standard
+way to check the ability of fitting nonlinear functions by a physical system is the information processing capacity [17],
+C[fℓ] = 1 −
+min
+Wℓ∈RK
+� 1
+−1
+��K−1
+k=0 Wℓkxk(u) − fℓ(u)
+�2
+p(u)du
+� 1
+−1 fℓ(u)2p(u)du
+,
+(C1)
+where functions fℓ(u) are orthogonal target functions ⟨fℓ, fℓ′⟩p =
+� 1
+−1 fℓ(u)fℓ′(u)p(u)du = 0 for ℓ ̸= ℓ′. The total expressive
+capacity is computing the limitation CT ≡ �∞
+ℓ=0 C[fℓ], capturing the ability of what type of function the linear combination of
+physical system readout features can produce. Dambre’s argument claims that the total capacity must be upper bounded by the
+number of features CT ≤ K.
+While Dambre’s result is quite general [17], it neglects the limitations due to noise in readout features, a fact that is unavoidable
+when using quantum systems in the presence of finite computational and measurement resources. In this appendix section, we
+will focus on the impact of fundamental quantum readout noise on this upper bound under finite sampling S. Given u and S,
+
+11
+the quantum readout features ¯Xk(u) = 1
+S
+�S
+s=1 X(s)
+k (u) are stochastic variables (where X(s)
+k
+∈ {−1, +1} are binary random
+values). The expectation vector and covariance matrix of ¯
+X(u) can be expressed in terms of ⃗ρ(u), the diagonal entries of the
+density matrix (see Eq. (B8))
+E[ ¯
+X(u)] ≡ x(u) = U⃗ρ(u),
+(C2)
+E[ ¯
+X(u) ¯
+XT (u)] − E[ ¯
+X(u)]E[ ¯
+X(u)]T ≡ 1
+S Σ(u) = 1
+S U
+�
+diag (⃗ρ(u)) − ⃗ρ(u) · ⃗ρ(u)T �
+U T .
+(C3)
+The dependence of readout features xk(u) on the input u can always be written in the form of a Taylor expansion,
+xk(u) =
+∞
+�
+j=0
+(T)kjuj
+(C4)
+where we define the transfer matrix T(θ) ≡ T ∈ RK×∞ that depends on the density matrix ˆρ(u), and in particular on
+parameters θ characterizing the quantum system.
+To determine the optimal capacity to compute an arbitrary normalized function f(u) = �∞
+j=0(Y)juj using the noisy readout
+features ¯
+X(u) extracted from the quantum system, we need to find an optimal W such that
+C[f] = 1 −
+minW
+� 1
+−1
+��K−1
+k=0 Wk ¯Xk(u) − f(u)
+�2
+p(u)du
+� 1
+−1 f(u)2p(u)du
+(C5)
+By expanding the numerator of the right-hand side for a given, finite number of shots S, we find
+� 1
+−1
+f(u)2p(u)du −
+� 1
+−1
+�K−1
+�
+k=0
+Wk ¯Xk(u) − f(u)
+�2
+p(u)du
+= −
+K−1
+�
+k1=0
+K−1
+�
+k2=0
+Wk1Wk2
+� 1
+−1
+¯Xk(u) ¯Xk2(u)p(u)du + 2
+K−1
+�
+k=0
+Wk
+� 1
+−1
+¯Xk(u)f(u)p(u)du
+≈ − 1
+N
+K−1
+�
+k1=0
+K−1
+�
+k2=0
+Wk1Wk2
+N
+�
+n=1
+¯Xk1(u(n)) ¯Xk2(u(n)) + 2
+N
+K−1
+�
+k=0
+Wk
+N
+�
+n=1
+¯Xk(u(n))f(u(n)).
+(C6)
+where we have approximated the integral over the input domain by a finite sum in the limit of a large number of inputs N.
+Next, note that if n ̸= n′, then Xk1(u(n)) and Xk2(u(n′)) are independent random variables (thought not necessarily identically
+distributed). The sums over N on the right hand side are therefore sums of bounded independent random variables. In the
+limit of large N ≫ 1, the deviation between stochastic realizations of these sums and their expectation values is exponentially
+suppressed, as determined by the Hoeffding inequality. Then, with large probability, the sums over N may be replaced by their
+expectation values,
+� 1
+−1
+f(u)2p(u)du −
+� 1
+−1
+�K−1
+�
+k=0
+Wk ¯Xk(u) − f(u)
+�2
+p(u)du
+≈ − 1
+N
+K−1
+�
+k1=0
+K−1
+�
+k2=0
+Wk1Wk2
+N
+�
+n=1
+E[ ¯Xk1(u(n)) ¯Xk2(u(n))] + 2
+N
+K−1
+�
+k=0
+Wk
+N
+�
+n=1
+E[ ¯Xk(u(n))f(u(n))]
+= − 1
+N
+K−1
+�
+k1=0
+K−1
+�
+k2=0
+Wk1Wk2
+N
+�
+n=1
+�
+xk1(u(n))xk2(u(n)) + 1
+S Σ(u(n))k1k2
+�
++ 2
+N
+K−1
+�
+k=0
+Wk
+N
+�
+n=1
+xk(u(n))f(u(n))
+≈ −
+K−1
+�
+k1=0
+K−1
+�
+k2=0
+Wk1Wk2
+� 1
+−1
+�
+xk1(u)xk2(u) + 1
+S Σ(u)k1k2
+�
+p(u)du + 2
+K−1
+�
+k=0
+Wk
+� 1
+−1
+xk(u)f(u)p(u)du.
+(C7)
+The first approximation above comes from the Hoeffding inequality, where terms that are dropped are proportional to 1/
+√
+N.
+In going from the second to the third line, we have used Eq. (C3). The final expression is obtained by rewriting sums over u as
+integrals, with an error proportional to 1/
+√
+N once more. Thus we can say the original integral in Eq. (C5) is approximately
+equal to Eq. (C7) to O(1/
+√
+N).
+
+12
+The first term in Eq. (C7) does not depend explicitly on the function f(u) being constructed, and introduces quantities that are
+determined entirely by the response of the quantum system of interest to inputs over the entire domain of u. In particular, we
+introduce the Gram matrix G ∈ RK×K as
+(G)k1k2 =
+� 1
+−1
+xk1(u)xk2(u)p(u)du =
+∞
+�
+j1=0
+∞
+�
+j2=0
+(T)k1j1
+�� 1
+−1
+uj1+j2p(u)du
+�
+(T)k2j2 ≡ (TΛTT )k1k2
+(C8)
+where in the second line we have also introduced the generalized Hilbert matrix Λ ∈ R∞×∞ as
+(Λ)j1j2 =
+� 1
+−1
+uj1+j2p(u)du.
+(C9)
+Secondly, we introduce the noise matrix V ∈ RK×K,
+(V)k1k2 =
+� 1
+−1
+Σ(u)k1k2 p(u)du =
+� 1
+−1
+(xk(u) − xk1(u)xk2(u))p(u)du ≡ (D)k1k2 − (G)k1k2
+(C10)
+for index k satisfying ˆ
+Mk = ˆ
+Mk1 ˆ
+Mk2. Here we have also introduced the second-order-moment matrix D ∈ RK×K such that
+(D)k1k2 =
+� 1
+−1 xk(u)p(u)du. Then, the noise matrix simply defines the covariance of readout features, and is therefore given
+by V = D − G.
+The second term in Eq. (C7) depends on f(u) and can be simplified using the Λ matrix as well,
+� 1
+−1
+xk(u)f(u)p(u)du =
+∞
+�
+j1=0
+∞
+�
+j2=0
+(T)kj1
+�� 1
+−1
+uj1+j2p(u)du
+�
+(Y)j2 = (TΛY)k.
+(C11)
+With these definitions, Eq. (C5) can be compactly written in matrix form as a Tikhonov regularization problem:
+C[f] = max
+W
+�
+−W T �
+TΛTT + 1
+S V
+�
+W + 2W T TΛY
+YT ΛY
+�
+= 1 − min
+W
+�
+�
+�
+���Λ
+1
+2 TT W − Λ
+1
+2 Y
+���
+2
++ 1
+S W T VW
+YT ΛY
+�
+�
+� .
+(C12)
+The least-squares form ensures that the optimal value (argmin) �
+w of W has closed form
+�
+w =
+�
+TΛTT + 1
+S V
+�−1
+TΛY.
+(C13)
+Substituting w into the expression for C, we obtain the optimal capacity with which a function f can be constructed, which
+takes the form of a generalized Rayleigh quotient
+C[f] = YT ΛTT �
+G + 1
+S V
+�−1 TΛY
+YT ΛY
+.
+(C14)
+2.
+Eigentasks
+Eq. (C14) defines the optimal capacity of approximating an arbitrary function f(u) = �∞
+j=0(Y)juj. We can therefore
+naturally ask which functions f maximise this optimal capacity. To this end, we first note that the denominator of Eq. (C14) is
+simply a normalization factor that can be absorbed into the definition of the function f(u) being approximated, without loss of
+generality. More precisely, we consider:
+⟨f, f⟩p = 1 =
+�
+Λ
+1
+2 Y
+�T �
+Λ
+1
+2 Y
+�
+= YT ΛY.
+(C15)
+Then, we can rewrite the optimal capacity from Eq. (C17) as
+C[f] = YT Λ
+1
+2
+�
+QΛ
+1
+2 Y
+�
+(C16)
+
+13
+Here we have defined the matrix Q ∈ R∞×∞ as
+Q = B
+�
+I + 1
+S R
+�−1
+BT ,
+(C17)
+by introducing the matrix square root of G = G
+1
+2 G
+1
+2 , where G
+1
+2 ∈ RK×K. Then, R = G− 1
+2 VG− 1
+2 becomes the noise-to-
+signal matrix, while the matrix B is given by
+B = Λ
+1
+2 TT G− 1
+2 ,
+(C18)
+The decomposition in Eq. (C17) may be verified by direct substitution into Eq. (C16). The ability to calculate matrix powers and
+in particular the inverse of G requires constraints on its rank, which we show are satisfied in Appendix C 6.
+We now consider the measure-independent part of the eigenvectors of Q, indexed Y(k), satisfying the standard eigenvalue
+problem:
+Q
+�
+Λ
+1
+2 Y(k)�
+= CkΛ
+1
+2 Y(k).
+(C19)
+where k = 0, · · · , K − 1. From Eq. (C16), it is clear that these eigenvectors have a particular meaning. Consider the function
+y(k)(u) defined by the eigenvector Y(k), namely
+y(k)(u) =
+∞
+�
+j=0
+Y(k)
+j
+uj,
+(C20)
+which we will refer to from now on as eigentasks. Suppose we wish to construct the function y(k)(u) using outputs obtained
+from the physical system defined by Q in the S → ∞ limit (namely, with deterministic outputs). At a first glance, before
+we dive into solving the eigenproblem Eq.(C19), we do not know any relationship between y(k) and x(u).The rest part of this
+subsection is aiming to prove that y(k) must be a specific linear combination of features x(u). Then, the physical system’s
+capacity for this construction is simply given by the corresponding eigenvalue Ck, as may be seen by substituting Eq. (C19)
+into Eq. (C16). Formally, the y(k)(u) serves as the critical point (or stationary point) of the generalized Rayleigh quotient in
+Eq. (C14). Consequently, the function that is constructed with largest capacity then corresponds to the nontrivial eigenvector
+with largest eigenvalue.
+To obtain these eigentasks, we must solve the eigenproblem defined by Eq. (C19). Here, the representation of Q in Eq. (C17)
+becomes useful, as we will see that the eigensystem of Q is related closely to that of the noise-to-signal matrix R. In particular,
+we first define the eigenproblem of R,
+R
+�
+G
+1
+2 r(k)�
+= β2
+kG
+1
+2 r(k)
+(C21)
+with NSR eigenvalues β2
+k and corresponding eigenvectors r(k), which satisfy the orthogonality relation r(k′)T Gr(k) = δk,k′.
+Here the r(k) is equivalent to be defined as the solution to generalized eigen-problem:
+Vr(k) = β2
+kGr(k).
+(C22)
+This is because Vr(k) = G
+1
+2 RG
+1
+2 r(k) = β2
+kG
+1
+2 G
+1
+2 r(k) = β2
+kGr(k). The prefactor G
+1
+2 is introduced for later convenience.
+Eq. (C21) then allows us to define the related eigenproblem
+�
+I + 1
+S R
+�−1
+G
+1
+2 r(k) =
+�
+1 + β2
+k
+S
+�−1
+G
+1
+2 r(k)
+(C23)
+Next, we note that Q is related to the matrix in brackets above via a generalized similarity transformation defined by B,
+Eq. (C17). In particular, BT B = G− 1
+2 GG− 1
+2 = I ∈ RK×K, while we remark that BBT ̸= I since it is in R∞×∞. This
+connection allow us to show that
+Q
+�
+BG
+1
+2 r(k)�
+= B
+�
+I + 1
+S R
+�−1
+BT BG
+1
+2 r(k) =
+1
+1 + β2
+k/S BG
+1
+2 r(k).
+(C24)
+Comparing with Eq. (C19), we can now simply read off both the eigenvalues and eigenvectors of Q,
+Ck =
+1
+1+β2
+k/S
+Λ
+1
+2 Y(k) = BG
+1
+2 r(k)
+�
+=⇒ Y(k) = TT r(k)
+(C25)
+
+14
+where we have used the definition of B from Eq. (C18). The functions defined by the eigenvectors Y(k) are automatically
+orthonormalized:
+�
+y(k1), y(k2)�
+p =
+�
+Λ
+1
+2 Y(k1)�T�
+Λ
+1
+2 Y(k2)�
+= r(k1)T G
+1
+2 BT BG
+1
+2 r(k2) = r(k1)T Gr(k2) = δk1k2.
+(C26)
+3.
+Noisy eigentasks from readout features
+We can now also discuss the interpretation of {β2
+k} for a physical system - in this case a quantum circuit - for which {r(k)} are
+known. Consider a single run of the quantum system under finite shots S, which yields a single instance of the readout features
+¯
+X(u). We can simply read off that an noisy version of the kth eigentask, ¯y(k)(u) can be constructed as
+¯y(k)(u) =
+K−1
+�
+k′=0
+r(k)
+k′ ¯Xk′(u)
+(C27)
+which is equivalent to requiring the output weights W = r(k).The corresponding set of noisy function is also orthogonal, this
+is because Vr(k) = β2
+kGr(k) implies r(k)T Vr(k′) = β2
+kδk,k′ and hence
+�
+¯y(k1), ¯y(k2)�
+p = r(k1)T
+�
+G + 1
+S V
+�
+r(k2) =
+�
+1 + β2
+k
+S
+�
+δk1k2
+(C28)
+This equation can be further decomposed into two parts. Let the linear transformation of noise ξ(u) by defining ξ(k)(u) =
+�K−1
+k=0 r(k)
+k′ ζk′(u)
+Eu[y(k1)y(k2)] =
+�
+y(k1), y(k2)�
+p = r(k1)T Gr(k2) = δk1k2,
+(C29)
+Eu[ξ(k1)ξ(k2)] =
+�
+ξ(k1), ξ(k2)�
+p = 1
+S r(k1)T Vr(k2) = β2
+k1
+S δk1k2.
+(C30)
+It means that the combination {r(k) ∈ RK}k∈[K] not only produces orthogonal eigentasks {y(k)(u)} for signal, but also induces
+a set of orthogonal noise functions {ξ(k)(u)}.
+If the quantum circuit can be run multiple times for a given S, multiple instances of ¯
+X(u) can be obtained, from each of
+which an estimate of the kth eigentask ¯y(k)(u) can be constructed. The expectation value of these estimates then simply yields
+E[¯y(k)(u)] =
+K−1
+�
+k′=0
+r(k)
+k′ E[ ¯Xk′(u)] =
+K−1
+�
+k′=0
+r(k)
+k′ xk′(u) = y(k)(u)
+(C31)
+If we have access to only a single instance of ¯
+X(u), however, and thus only one estimate ¯y(k)(u) (as y(k)(u) and ¯y(k)(u)
+depicted in Fig. 7), it is useful to know the expected error in this estimate. This error can be extracted from Eq. (C12). In
+particular, requiring Y(k) = TT r(k), we have
+���Λ
+1
+2 TT r(k) − Λ
+1
+2 Y(k)���
+2
++ 1
+S r(k)T Vr(k)
+Y(k)T ΛY(k)
+= 1
+S r(k)T Vr(k) = β2
+k
+S .
+(C32)
+This mean squared error in using ¯y(k)(u) to estimate y(k)(u) over the domain of u decreases to zero for S → ∞ as expected,
+since the noise in ¯
+X decreases with S. However, β2
+k defines the S-independent contribution to the error. In particular, this
+indicates that at a given S, certain functions with lowers NSR eigenvalues β2
+k may be better approximated using this physical
+system than others. We present in Fig. 7 the measured features ¯
+X, the eigentasks y and their S-finite version ¯y in a 6-qubit
+Hamiltonian based system. The associated eigen-NSR spectrum, expressive capacity, and total correlations are also depicted for
+both ES J ̸= 0 and PS J = 0.
+
+15
+4.
+Expressive capacity
+Given an arbitrary set of complete orthonormal basis functions fℓ(u) = �∞
+j=0(Yℓ)juj,
+⟨fℓ, fℓ′⟩p =
+�
+Λ
+1
+2 Yℓ
+�T �
+Λ
+1
+2 Yℓ′
+�
+= δℓℓ′.
+(C33)
+The total capacity is independent of the basis choice
+CT (S) =
+∞
+�
+ℓ=0
+C[fℓ] =
+∞
+�
+ℓ=0
+YT
+ℓ Λ
+1
+2
+�
+Λ
+1
+2 TT
+�
+TΛTT + 1
+S V
+�−1
+TΛ
+1
+2
+�
+Λ
+1
+2 Yℓ
+= Tr
+�
+Λ
+1
+2 TT
+�
+TΛTT + 1
+S V
+�−1
+TΛ
+1
+2
+�
+= Tr
+��
+G + 1
+S V
+�−1
+G
+�
+=
+K−1
+�
+k=0
+1
+1 + β2
+k
+S
+.
+(C34)
+5.
+Estimation in case of nonlinear functions after linear output layer
+Usually, instead of taking the linear transformation W · ¯
+X, the training process can involve some complicated nonlinear
+activation functions or classical kernel, which may also be fed into a non-quadratic nonlinear loss function afterwards. These
+two processes can be unified to be σNL( ¯
+X(u)) with any smooth function σNL. In this subsection, we show how to translate our
+result obtaining from quadratic nonlinear function Eq. (C5) into a more general loss function with form of
+L = Eu[σNL( ¯
+X)]
+(C35)
+Now let us first transform all noisy measured features { ¯Xk} into the naturally orthogonal basis of signal {y(k)} and noise {ξ(k)}.
+¯Xk′(u) ≡
+K−1
+�
+k=0
+Γk′k(y(k)(u) + ξ(k)(u)),
+(C36)
+such transformation of Γ ∈ RK×K must uniquely exist, this is because all K of {r(k)} are linearly independent. Recall
+Eq. (C30) claims that Eu[ξ(k)] = 0 and Eu[ξ(k)ξ(k′)] = β2
+kδkk′/S, we can deal with the nonlinearity by taking the quadratic
+expansion, where , we get
+L = Eu[σNL( ¯
+X)] = Eu[σNL(Γ¯y)] = Eu
+�
+σNL
+��
+k
+Γ0,k(y(k) + ξ(k)), · · · ,
+�
+k
+ΓK−1,k(y(k) + ξ(k))
+��
+≈ Eu[σNL(Γy)] +
+K−1
+�
+k=0
+Eu
+�∂σNL
+∂y(k) ξ(k)
+�
++ 1
+2
+K−1
+�
+k1=0
+K−1
+�
+k2=0
+Eu
+�
+∂2σNL
+∂y(k1)∂y(k2) ξ(k1)ξ(k2)
+�
+= Eu[σNL(Γy)] + 1
+2
+K−1
+�
+k1=0
+K−1
+�
+k2=0
+Eu
+�
+∂2σNL
+∂y(k1)∂y(k2) ξ(k1)ξ(k2)
+�
+,
+(C37)
+where the first order terms vanish due to Hoeffding inequality again. We then make a further approximation of Eq. (C37) by
+replacing the ξ(k1)ξ(k2) with its u-average Eu[ξ(k1)ξ(k2)] = δk1k2β2
+k1/S:
+L ≈ Eu[σNL(Γy)] +
+K−1
+�
+k=0
+β2
+k
+S · Eu
+� ∂2σNL
+(∂y(k))2
+�
+.
+(C38)
+In fact, any of the second terms can be further simplified by chain rule: L ≈ Eu[σNL(Γy)] + �
+k
+β2
+k
+S · Eu[(ΓT ∇2
+xσNLΓ)kk].
+The approximation in Eq. (C38) is rough, but it still gives us a sufficient reason to do the following manipulation: for optimized
+L , the dependence on y(k) with β2
+k/S > 1 will be strongly suppressed in large-N limit, hence we can pre-exclude the eigentasks
+whose β2
+k/S > 1.
+Let us use one typical example, the widely used logistic regression in classification, to illustrate our argument here. As what
+we will introduce in Appendix I, the target function is the conditional probability distribution f(u) := Pr[u ∈ C1|u] in such
+
+16
+classification model (see Eq. (I4)), and then there is one more layer of softmax and cross-entropy function acting on linear
+map L = Eu[H(f(u), σ(W · ¯
+X(u)))] where σ is sigmoid function (e.g. softmax function σ(z) = 1/(1 + exp(−z))), and
+H(p, q) = −p ln q − (1 − p) ln(1 − q) is the cross-entropy. Especially, any linear combination of { ¯Xk} can be translated into
+linear combination
+W · ¯
+X(u) ≡
+K−1
+�
+k=0
+Ωk · (y(k)(u) + ξ(k)(u)),
+(C39)
+Again, such vector Ω = ΓT W must also uniquely exist.
+For any σNL = g(W · x), one always have ΓT ∇2
+xσNLΓ =
+g′′(Ω · y)ΩT Ω:
+L ≈ Eu[H(f, σ(Ω · y))] +
+�K−1
+�
+k=0
+β2
+k
+S Ω2
+k
+�
+· Eu[σ(Ω · y)(1 − σ(Ω · y))] .
+(C40)
+It helps us read from the prefactor β2
+k/S induces a natural regularization on Ωk in loss function, in addition to the S-infinity
+term limS→∞ L = Eu[H(f, σ(Ω · y))]. We will leave the detailed discussion of this important application in Appendix H and
+Appendix I.
+6.
+Proof that the Gram matrix G is full rank
+Recall that before we analytically find the eigenvectors of Q, we first show that the matrix G is invertible. It comes from that
+all K readout features {xk(u)}k∈[K] being linear independent is entirely equivalent to the full-rankness of the corresponding
+Gram matrix Rank(G) = K. Thanks to the linearity of readout, we can show such linear independence by contradiction.
+Suppose on the contrary there exists coefficients {ck}k∈[K] such that
+K−1
+�
+k=0
+ckxk(u) = Tr
+��K−1
+�
+k=0
+ck ˆ
+Mk
+�
+U(u)ˆρ0
+�
+= 0.
+(C41)
+However, this means that the quantum observable �K−1
+k=0 ck ˆ
+Mk is a zero-expectation readout-qubit quantity for any state U(u)ˆρ0
+under arbitrary input u, which is impossible. This shows the linear independence. Furthermore, we then argue that it ensures G
+has no non-trivial null space. This is because that any {ck}k∈[K] will satisfy
+K
+�
+k1,k2=1
+ck1ck2(G)k1,k2 =
+� 1
+−1
+� K
+�
+k1=1
+ck1xk1(u)
+�� K
+�
+k2=1
+ck2xk2(u)
+�
+p(u)du =
+�K−1
+�
+k=0
+ckxk,
+K−1
+�
+k=0
+ckxk
+�
+p
+.
+(C42)
+where the RHS is the norm of function �K−1
+k=0 ckxk(u). The summation �K
+k1,k2=1 ck1ck2(G)k1,k2 = 0 vanishes if and only
+if function �K−1
+k=0 ckxk(u) is a zero function. That is why the linear independence of features {ck}k∈[K] is equivalent to that
+symmetric matrix G has no zero eigenvalues, namely Rank(G) = K. Numerically speaking, this relation always holds in
+general as long as assuming this is for the case where N ≫ K.
+7.
+Simplifying the noise-to-signal matrix and its eigenproblem
+We have shown that the problem of obtaining the eigentasks for a generic quantum system, and deducing its expressive
+capacity under finite measurement resources, can be reduced simply to solving the eigenproblem of its noise-to-signal matrix
+R, Eq. (C21). Note that constructing R = G− 1
+2 VG− 1
+2 requires computing the inverse of G. However, G can have small
+(although always nonzero) eigenvalues, especially for larger systems, rendering it ill-conditioned and making the computation
+of R numerically unstable. Fortunately, certain simplifications can be made to derive an equivalent eigenproblem that is much
+easier to solve.
+To begin, we first note that so far, we have placed no requirements on the specific form of measurement operators { ˆ
+Mk}, and
+thus the readout features xk(u) = Tr{ ˆ
+Mk ˆρ(u)} are also unspecified. Our analysis thus far holds for any set of measurement
+operators that describe a complete set of commuting observables. However, specific choices of measurement operators can
+
+17
+simplify the form of the matrices G and V involved. In particular, if one chooses ˆ
+Mk to be the projections onto the computational
+basis, ˆ
+Mk = |bk⟩ ⟨bk|, then according to Eq. (B8), by setting U = I we have x(u) ≡ ⃗ρ(u), which we refer to as the probability
+representation of readout features. Practically, the probability representation is native to measurement schemes in contemporary
+quantum processors, and therefore minimizes the required post-processing of readout features obtained from a real device. More
+importantly, although it is related to any other readout feature representation via a unitary transformation, the strength of the
+probability representation lies in the fact that it renders the second-order moment matrix D diagonal. In particular,
+(D)k1k2 =
+� �K−1
+k=0 (G)kk1, if k1 = k2
+0,
+if k1 ̸= k2
+(in probability representation of readout features)
+(C43)
+Using V = D − G, we can rewrite the eigenproblem for R,
+R
+�
+G
+1
+2 r(k)�
+= β2
+kG
+1
+2 r(k)
+=⇒ G− 1
+2 (D − G)G− 1
+2
+�
+G
+1
+2 r(k)�
+= β2
+kG
+1
+2 r(k)
+=⇒ G−1Dr(k) = (1 + β2
+k)r(k)
+(C44)
+Finally, considering the inverse of the matrix on the left hand side, we obtain the simplified eigenproblem for the matrix D−1G,
+D−1Gr(k) = (1 + β2
+k)−1r(k) ≡ αkr(k),
+(C45)
+which shares eigenvectors with R, and whose eigenvalues are a simple transformation of the NSR eigenvalues β2
+k. Impor-
+tantly, constructing D−1G no longer requires calculating any powers of G, and when further choosing readout features in the
+probability representation, it relies only on the inversion of a simple diagonal matrix D.
+The matrix D−1G has significance in spectral graph theory, when interpreting the Gram matrix G as the adjacency matrix of
+a weighted graph. This connection is elaborated upon in Appendix C 8.
+8.
+Connections to spectral graph theory
+Let us have a small digression to the graphic theoretic meaning of G and D−1G. Now we consider a weighted graph with
+adjacency matrix G. In spectral graph theory, the matrix D−1G is exactly the random walk matrix associated with graph G, and
+then the second order matrix D happens to be the degree matrix of this graph since (D)kk = �K−1
+k′=0(G)kk′. Then the eigentask
+combination coefficient r(k) is precisely the right eigenvector of random walk matrix. Another concept associated with a graph
+is I − D− 1
+2 GD− 1
+2 , the normalized Laplacian matrix of G, while the matrix D− 1
+2 GD− 1
+2 is always referred to be normalized
+adjacency matrix in many literatures. The eigenproblem of normalized adjacency matrix can also be solved easily, because
+D− 1
+2 GD− 1
+2
+�
+D
+1
+2 r(k)�
+= D
+1
+2 D−1Gr(k) = αk
+�
+D
+1
+2 r(k)�
+.
+(C46)
+From perspective of spectral graph theory, roughly speaking, a reservoir with stronger ability to resist noise are those who has
+more “bottlenecks” in graph G’s connectivity. The extreme case is supposing that αk = 1 (or 1 − αk = 0) for all k. According
+the basic conclusion in spectral graph theory, the normalized Laplacian matrix has K zero eigenvalues iff the graph G is fully
+disconnected. This gives us the condition when noisy information capacity obtain its upper bound K: there exists a partition
+{Domk}k∈[K] of domain Dom = [−1, 1] such that ˆρkk(u) = 1 iff u ∈ Domk.
+Appendix D: Spectral analysis based on finite statistics
+While Eq. (C45) is a numerically simpler eigenproblem to solve than Eq. (C21), it still requires the approximation of G (recall
+that D can be obtained from G) from readout features ¯
+X(u) under finite sampling, due to the finiteness of shots S, the number
+of input points N, and also the number of realizations of readout features for a given S. In what follows, we show how an
+approximation �GN of G can be constructed from finitely-sampled readout features, as relevant for practical quantum devices.
+Secondly, we also describe an approach to obtain the eigentasks y(k)(u) and corresponding NSR eigenvalues β2
+k that avoids
+explicit construction of the Gram matrix, and is thus even more numerically robust.
+
+18
+1.
+Approximating eigentasks and NSR eigenvalues under finite S and N
+For practical computations, readout features ¯
+X(u) from the quantum system for finite S can be computed for a discrete set
+of u(n) ∈ [−1, 1] for n = 1, . . . , N. Labelling the corresponding readout features ¯
+X(u(n)), we can define the regression matrix
+constructed from these readout features,
+�FN ≡ ( ¯
+X(u(1)), ¯
+X(u(2)), · · · , ¯
+X(u(N)))T =
+�
+�
+�
+¯X0(u(1)) · · ·
+¯XK−1(u(1))
+...
+...
+¯X0(u(N)) · · ·
+¯XK−1(u(N))
+�
+�
+� .
+(D1)
+Here, �FN ∈ RN×K, with subscript N indicating its construction from a finite set of N inputs, is a random matrix due to the
+stochasticity of readout features; in particular it can be written as:
+�FN = FN +
+1
+√
+S
+Z(FN)
+(D2)
+where (FN)nk = E[ ¯Xk(u(n))] = xk(u(n)), and Z is the centered multinomial stochastic process, so that E[�FN] = FN.
+Using this regression matrix �FN, we can obtain an estimation of the Gram matrix and second order moment matrix, which
+we denote �GN and �DN, and whose matrix elements are defined via
+( �GN)k1k2 ≡ 1
+N
+N
+�
+n=1
+¯Xk1(u(n)) ¯Xk2(u(n)) = 1
+N (�FT
+N �FN)k1k2 ≈
+� 1
+−1
+¯Xk1(u) ¯Xk2(u)p(u)du,
+(D3)
+( �DN)k1k2 ≡ δk1,k2
+1
+N
+N
+�
+n=1
+¯Xk1(u(n)) ≈ δk1,k2
+� 1
+−1
+¯Xk1(u)p(u)du.
+(D4)
+While the quantities �GN and �DN are computed from stochastic readout features, their stochastic contributions are suppressed
+in the large N limit by the Hoeffding inequality for sums of bounded stochastic variables. In particular, we can define their
+deterministic limit for N → ∞, according to Eq. (C7), as
+�G ≡ lim
+N→∞
+1
+N (�FT
+N �FN)k1k2 = G + 1
+S V = G + 1
+S (D − G),
+(D5)
+�D ≡ lim
+N→∞
+�DN = D.
+(D6)
+Inverting the above expressions allow us to express the Gram matrix G and second-order moment matrix D in terms of the
+estimates �G and �D computed using a finite number of shots S,
+G =
+S
+S − 1
+�G −
+1
+S − 1
+�D,
+(D7)
+D = �D.
+(D8)
+We see that to lowest order in 1
+S , G ≈ �G and D ≈ �D, which is what one might expect naively. However, we clearly see that
+the estimation of G can be improved by including a higher-order correction in 1
+S . This contribution arises due to the highly-
+correlated nature of noise and signal for quantum systems: we are able to estimate the noise matrix �G and �D using knowledge
+of the readout features, and correct for the contribution to �G and �D that arises from this noise matrix. We will see that this
+contribution will be important in more accurately approximating quantities of interest derived from G, D.
+To this end, we recall that our ultimate aim is not just to estimate G and D, but to solve the eigenproblem of Eq. (C45). Using
+the above relation, we can then establish �D−1 �G = S−1
+S D−1G + 1
+S I, and write Eq. (C45) in a form entirely in terms of �G and
+�D,
+D−1Gr(k) = (1 + β2
+k)−1r(k),
+=⇒ �D−1 �Gr(k) =
+�S − 1
+S
+(1 + β2
+k)−1 + 1
+S
+�
+r(k).
+(D9)
+
+19
+5
+10
+15
+20
+25
+30
+Order k
+100
+101
+102
+103
+104
+105
+Eigen-NSRs β2
+k
+β2
+k, S → ∞
+˜β2
+N,k, S = 102
+˜β2
+k, S = 102
+S· ˜β2
+N,k
+(S−1)− ˜β2
+N,k, S = 102
+S = 102
+FIG. 5. Eigen-analysis in L = 5 H-ansatz system by taking S = 102 shots on each of N = 104 samples, with true eigen-NSRs β2
+k (black),
+S-finite sampled ˜β2
+N,k (blue) and corrected (S · ˜β2
+N,k)/((S − 1) − ˜β2
+N,k) (purple). ˜β2
+k, the large N limit of ˜β2
+N,k is also plotted in red for
+comparison. The data correction is necessary since all ˜β2
+N,k are below the S = 102, and the corrected data show much better performance
+even if β2
+k ≫ S. The estimated line (in purple) are cutoff at k = 25 since all sampled ˜β2
+N,k after that are larger the S − 1 so that they are not
+correctable.
+Note that the final form is conveniently another eigenproblem, now for the finite-S matrix �D−1 �G:
+�D−1 �G˜r(k) = (1 + ˜β2
+k)−1˜r(k) ≡ ˜αk ˜r(k),
+(D10)
+whose eigenvalues and eigenvectors can be easily related to the desired eigenvalues β2
+k and eigenvectors r(k) of Eq. (C45).
+Following some algebra, we find:
+β2
+k =
+S
+(S − 1) − ˜β2
+k
+· ˜β2
+k = ˜β2
+k +
+∞
+�
+j=1
+˜β2
+k
+�
+1 + ˜β2
+k
+�j � 1
+S
+�j
+,
+(D11)
+r(k) = ˜r(k).
+(D12)
+From Eq. (D11), we see that to lowest order in 1
+S , β2
+k ≈ ˜β2
+k. However, this expression also supplies corrections to higher orders
+in 1
+S , which are non-negligible even for β2
+k < S, as we see in example of Fig. 5. In contrast, the estimated eigenvectors ˜r(k) to
+any order in 1
+S equal the desired eigenvectors r(k) without any corrections.
+Of course, in practice we do not have access to the matrices �G and �D, as these are only defined precisely in the limit
+where N → ∞. However, for large enough N, we can approximate these matrices to lowest order by their finite N values,
+�G = �GN + O
+� 1
+N
+�
+and �D = �DN + O
+� 1
+N
+�
+. Then, the eigenproblem in Eq. (D10) can be expressed in the final form,
+�D−1
+N �GN ˜r(k)
+N = (1 + ˜β2
+N,k)−1˜r(k)
+N ≡ ˜αN,k ˜r(k)
+N ,
+(D13)
+where the eigenvalues ˜β2
+N,k, ˜αN,k and eigenvectors ˜r(k)
+N in the large N limit must satisfy
+lim
+N→∞
+˜β2
+N,k = ˜β2
+k,
+lim
+N→∞ ˜αN,k = ˜αk,
+lim
+N→∞ ˜r(k)
+N = ˜r(k) ≡ r(k).
+(D14)
+Here the invertibility of the empirically-computed matrix �DN required for Eq. (D13) is numerically checked, based on which
+we can establish a better numerical method in Appendix D 2.
+Eq. (D13) represents the eigenproblem whose eigenvalues ˜β2
+N,k and eigenvectors ˜r(k)
+N we actually calculate. For large enough
+N and under finite S, we can use these as valid approximations to the eigenvalues and eigenvectors of Eq. (D10). This finally
+enables us to directly estimate the N, S → ∞ quantities β2
+k and r(k) using Eqs. (D11), (D12):
+β2
+k ≈
+S · ˜β2
+N,k
+(S − 1) − ˜β2
+N,k
+= 1 − ˜αN,k
+˜αN,k − 1
+S
+,
+(D15)
+r(k) ≈ ˜r(k)
+N .
+(D16)
+
+20
+0
+5
+10
+15
+−1
+0
+1
+Coefficient r(k)
+r(1): β2
+1 = 0.0 v.s. ˜r(1)
+N :
+1−˜αN,1
+˜αN,1−1/S = 0.0
+Eigenvector of D−1G
+Eigenvector of ˜D−1
+N ˜GN
+0
+5
+10
+15
+−0.25
+0.00
+0.25
+r(2): β2
+2 = 4.656 v.s. ˜r(2)
+N :
+1−˜αN,2
+˜αN,2−1/S = 4.663
+0
+5
+10
+15
+−0.5
+0.0
+r(3): β2
+3 = 5.898 v.s. ˜r(3)
+N :
+1−˜αN,3
+˜αN,3−1/S = 6.03
+0
+5
+10
+15
+0.0
+0.5
+r(4): β2
+4 = 12.661 v.s. ˜r(4)
+N :
+1−˜αN,4
+˜αN,4−1/S = 12.824
+0
+5
+10
+15
+0.0
+0.5
+Coefficient r(k)
+r(5): β2
+5 = 17.548 v.s. ˜r(5)
+N :
+1−˜αN,5
+˜αN,5−1/S = 17.571
+0
+5
+10
+15
+−0.5
+0.0
+0.5
+r(6): β2
+6 = 21.166 v.s. ˜r(6)
+N :
+1−˜αN,6
+˜αN,6−1/S = 22.382
+0
+5
+10
+15
+−0.5
+0.0
+r(7): β2
+7 = 29.809 v.s. ˜r(7)
+N :
+1−˜αN,7
+˜αN,7−1/S = 30.513
+0
+5
+10
+15
+−0.5
+0.0
+r(8): β2
+8 = 51.107 v.s. ˜r(8)
+N :
+1−˜αN,8
+˜αN,8−1/S = 51.635
+0
+5
+10
+15
+−0.5
+0.0
+0.5
+Coefficient r(k)
+r(9): β2
+9 = 69.874 v.s. ˜r(9)
+N :
+1−˜αN,9
+˜αN,9−1/S = 71.21
+0
+5
+10
+15
+−0.5
+0.0
+0.5
+r(10): β2
+10 = 111.001 v.s. ˜r(10)
+N :
+1−˜αN,10
+˜αN,10−1/S = 109.021
+0
+5
+10
+15
+0.0
+0.5
+r(11): β2
+11 = 151.254 v.s. ˜r(11)
+N :
+1−˜αN,11
+˜αN,11−1/S = 144.208
+0
+5
+10
+15
+−0.5
+0.0
+0.5
+r(12): β2
+12 = 248.423 v.s. ˜r(12)
+N :
+1−˜αN,12
+˜αN,12−1/S = 233.445
+0
+5
+10
+15
+Index k′ of r(k)
+k′
+0.0
+0.5
+Coefficient r(k)
+r(13): β2
+13 = 333.471 v.s. ˜r(13)
+N :
+1−˜αN,13
+˜αN,13−1/S = 348.828
+0
+5
+10
+15
+Index k′ of r(k)
+k′
+−0.5
+0.0
+r(14): β2
+14 = 416.321 v.s. ˜r(14)
+N :
+1−˜αN,14
+˜αN,14−1/S = 409.548
+0
+5
+10
+15
+Index k′ of r(k)
+k′
+−0.5
+0.0
+0.5
+r(15): β2
+15 = 655.346 v.s. ˜r(15)
+N :
+1−˜αN,15
+˜αN,15−1/S = 743.085
+0
+5
+10
+15
+Index k′ of r(k)
+k′
+−0.5
+0.0
+0.5
+r(16): β2
+16 = 2191.863 v.s. ˜r(16)
+N :
+1−˜αN,16
+˜αN,16−1/S = 1945.381
+FIG. 6. Estimating NSR eigenvalues and corresponding eigentask coefficients under finite statistics (N = 300, S = 1000) in a 4-qubit
+H-encoding system, and comparison with theoretical value for N → ∞, S → ∞.
+It is clear that the approximation of β2
+k to lowest order will be an underestimate, as the contribution of order 1
+S is positive. In
+Fig. 6, we plot the estimated eigenvectors ˜r(k)
+N computed under finite statistics (N = 300, S = 1000, where these two numbers
+are relevant for IBM quantum processors) in H-encoding, together with the N, S → ∞ eigenvectors r(k), and the estimated
+eigenvalues.
+2.
+Gram matrix-free construction to approximate eigentasks and NSR eigenvalues
+If we consider Eq. (D13) and multiply through by D
+− 1
+2
+N , the resulting equation can be written as an equivalent eigenproblem,
+1
+N
+�D
+− 1
+2
+N �FT
+N �FN �D
+− 1
+2
+N
+�
+�D
+1
+2
+N ˜r(k)
+N
+�
+= ˜αN,k
+�
+�D
+− 1
+2
+N ˜r(k)
+N
+�
+(D17)
+where we have also written �GN =
+1
+N �FT
+N �FN as in the previous section. Note that as written above, the eigenproblem is
+entirely equivalent to obtaining the singular value decomposition of the matrix
+1
+√
+N �D
+− 1
+2
+N �FT
+N. This particular normalization factor
+1
+√
+N �D
+− 1
+2
+N
+is different from the standard z-score of principal components analysis. To obtain the combination coefficients r(k),
+let t(k) ∈ RK be the left singular vector of
+1
+√
+N �D
+− 1
+2
+N �FT
+N (which is also the eigenvector of 1
+N �D
+− 1
+2
+N �FT
+N �FN �D
+− 1
+2
+N
+≈ D− 1
+2 �GD− 1
+2
+in the large N limit). Then r(k) = �D
+− 1
+2
+N t(k) ∈ RK can be treated as the combination prefactor of ˆ
+Mk, to obtain the observables
+which correspond to the eigentasks. The merit of SVD analysis of
+1
+√
+N �D
+− 1
+2
+N �FT
+N is that we only need to work with a K-by-N
+matrix of features �FN, which is numerically cheaper than further constructing a Gram matrix 1
+N �FT
+N �FN. We will explore more
+about the usage of our technique in sense of PCA in Appendix H.
+
+21
+FIG. 7. Eigen analysis in a 6-qubit H-ansatz system (with N = 5000 and S = 1000) forming a 1D ring. The Hamiltonian parameters are
+chosen randomly with zero-mean and variance (hx
+rms, hz
+rms, hI
+rms) = (20, 5, 5), and t = 5 (See Appendix B 1 for details). Coupling strength
+is uniformly J ̸= 0 (ES) or J = 0 (PS). (a) All 2L = 64 noisy features ¯
+Xk(u) and (b) noisy eigentasks ¯y(k)(u) = r(k) · ¯
+X(u) for selected k
+from the features in (a), as well as their expected values y(k)(u) = limS→∞ ¯y(k)(u) = r(k) · x(u) (black). (c) NSR spectrum β2
+k and (d) CT
+vs shots S for both ES and PS encodings. (e) CT at S = 105 and (f) ETC, ¯T (ˆρM) in representative random 6-qubit H-ansatz, as a function of
+coupling strength J. The peaks of capacity and correlation coincide, around J ∼ hx
+rms.
+Appendix E: H-ansatz quantum systems: NSR spectra, expressive capacity, and eigentasks
+In this section, we evaluate the EC for quantum systems described by the H-ansatz introduced in Appendix B 1, as an example
+of how EC can be efficiently computed for a variety of general quantum systems, and is not just restricted to parameterized
+quantum circuits. The results of the analysis are compiled in Fig. 7, and discussed below.
+Fig. 7(a) presents the set of features { ¯Xk(u)} for typical L = 6 qubit ES and PS at S = 1000 with randomly chosen
+parameters (referred to as encodings, see caption). The resultant noisy eigentasks {¯y(k)(u)} and NSR spectra {β2
+k} extracted
+via the eigenvalue analysis are shown in Figs. 7(b) and 7(c) respectively. In the side-by-side comparison in Fig. 7(b), we clearly
+see the J = 0 ansatz transitioning to a regime with more noise at much lower k than the J ̸= 0 ansatz. This is reflected in
+Fig. 7(c), the β2
+k spectrum, having a much flatter slope for larger k (note the plot is semilog). Finally, Fig. 7(d) shows the EC of
+both systems as a function of S. EC rapidly rises for small S for both systems, but the rise of the J = 0 system is steeper. After
+a certain threshold in S, however, the ES grows more rapidly, approaching the upper bound 26 = 64 with S ∼ 108; in contrast,
+the PS has a significantly lower CT .
+For J → ∞ we also have ¯T = 0 because ˆρ0 = |0⟩⟨0|⊗L is an eigenstate of the encoding (ˆρ(u) = ˆρ0). This implies there
+must be a peak at some intermediate J, which for both EC and ETC occurs when the coupling is proportional to the transverse
+field J ∼ hx.
+Our results elucidate the same kind of improvement, as can be observed when we consider how the EC C changes with J, and
+compare it to the total correlation ETC ¯T , as shown in Fig. 7(f). For J → 0 we have a PS with ¯T = 0, whereas in the J → ∞
+we also have ¯T = 0 because ˆρ0 = |0⟩⟨0|⊗L is an eigenstate of the encoding (ˆρ(u) = ˆρ0). This implies there must be a peak at
+some intermediate J, which for both EC and ETC occurs when the coupling is proportional to the transverse field J ∼ hx. At
+finite S, increased ETC is directly related to a higher EC.
+Another interesting aspect is the clear trend seen in the maximization of EC around J ∼ hx
+rms for various hx
+rms, possibly
+hinting at the role of increased entanglement around the MBL phase transition in random spin systems [30]. This trend is
+consistent with results in quantum metrology – in general, the SNR obtained from averaging L uncorrelated probes scales as
+1/
+√
+L. This scaling can become favorable in the presence of entanglement and other non-classical correlations, in which case the
+scaling of the SNR can show up to a quadratic improvement 1/L [29]. For even larger J, we find that ˆρ(u) → ˆρ0 = |0⟩⟨0|⊗L,
+which clearly reduces ¯T , but also CT as the quantum system state becomes u-independent.
+
+ES
+PSES
+PS10
+20
+30
+50
+4010
+20
+30
+40
+50W
+>>>>>>>>>>>>>>>
+>>>>>>>>>22
+Appendix F: Scaling with quantum system size
+An important question in quantum machine learning applications is the possible advantage of using larger quantum systems
+for information processing. In this section, we present preliminary results of scaling with quantum system size. The left panel of
+Fig. 8 shows EC vs L at select S values for H-ansatz, while the right panel shows two encodings in the C-ansatz device, as well
+as their noisy simulations. In both plots, the dashed line indicates the S → ∞ result CT = 2L. We see that the EC increases
+when adding more qubits into the Ising chain for the H-ansatz, or when increasing the number of circuit qubits L for the C-
+ansatz. Note, however, that at any finite S the noise-constrained EC falls off the exponential bound for S → ∞. The dropoff
+is particularly severe for the IBMQ device, where we are limited to just S ∼ 104, which significantly suppresses the EC even
+for L = 7 qubits. Note, however, that even if one is well below CT = 2L due to this finite sampling constraint, increasing the
+dimension of the quantum system is always an effective way to increase the EC, particularly when compared to the logarithmic
+growth with S of Fig. 2 of Main Text.
+3
+4
+5
+6
+7
+Qubit numbers L
+0
+32
+64
+96
+128
+EC CT
+S = 101
+S = 102
+S = 103
+S = 104
+S = 105
+S = 106
+S = 107
+S → ∞
+3
+4
+5
+6
+7
+Qubit numbers L
+0
+20
+40
+EC CT
+S =10
+S =27
+S =210
+S =214
+S → ∞
+FIG. 8. (a) H-ansatz and (b) C-ansatz at finite S as a function of qubit number L. Various colours indicate different S values, with the S → ∞
+bound in dashed black. Individual noisy simulations are indicated in small and transparent dots, with their average as a thick line, and the EC
+of the C-ansatz device for encoding 1 and 2 are indicated with ‘×’ and ‘+’ respectively.
+Appendix G: Quantum correlation metrics
+There is no one standard metric to quantify entanglement or correlation in a many-body state. The metric we introduce
+here, the quantum total correlation, is a quantity inspired by the classical total correlation of L random variables (b1, · · · , bL),
+that is �L
+l=1 H(bl) − H(b1, · · · , bL). Using chain rule of Shannon entropy H(b1, b2, · · · , bL) = H(b1) + H(b2|b1) + · · · +
+H(bL|b1, b2, · · · , bL−1)
+L
+�
+l=2
+H(bl) − H(b1, b2, · · · , bL) =
+L
+�
+l=1
+H(bl) −
+L
+�
+l=1
+H(bl|b1, b2, · · · , bl−1) =
+L
+�
+l=2
+I(b1, · · · , bl−1; bl) ∈ [0, L − 1],
+(G1)
+we can see that the classical total correlation tells us how a set of random variables reveals information of each other. Similarly,
+quantum total correlation can be defined as [26, 27]
+T (ˆρ) =
+L
+�
+l=1
+S(ˆρl) − S(ˆρ)
+(G2)
+where S is von Neumann entropy and ˆρl := Tr[L]\{l} {ˆρ} is the subsystem state at qubit l. Due to the subadditivity of von-
+Neumann entropy �L
+l=1 S(ˆρl) ≥ S(ˆρ), we conclude that the quantum total correlation is non-negative, and is zero iff the state
+ˆρ = �L
+l=1 ˆρl is a product state.
+In this paper’s measurement scheme, the specific readout POVMs are the projectors onto the computational states
+{|bk⟩ ⟨bk|}k∈[K]. Thus, we are in particular interested in analyzing the post-measurement state ˆρM(u) = �
+k ρkk(u) |bk⟩ ⟨bk|
+
+23
+whose subsystems are correspondingly in states ˆρM
+l (u) = Tr[L]\{l}
+�
+ˆρM(u)
+�
+. We compute the average quantum total correla-
+tion over the input domain u with respect to the input probability distribution p(u):
+¯T
+�
+ˆρM�
+= Eu
+� L
+�
+l=1
+S(ˆρM
+l (u)) − S(ˆρM(u))
+�
+= Eu
+� L
+�
+l=1
+H(bl(u)) − H(b1(u), · · · , bL(u))
+�
+(G3)
+where the second equality comes from the diagonal nature of post-measurement state which reduces the quantum total correlation
+to a normal classical total correlation.
+The post-measurement quantum total correlation always reaches its maximum L − 1 when the diagonal terms of the state
+is a GHZ-type state. Also as a comparison, for a W-state |W⟩ =
+1
+√
+L (|10 · · · 0⟩ + |01 · · · 0⟩ + · · · + |00 · · · 1⟩), then post-
+measurement quantum total correlation T(|W⟩) is
+L
+�
+−
+� 1
+L
+�
+log2
+� 1
+L
+�
+−
+�L − 1
+L
+�
+log2
+�L − 1
+L
+��
+− L
+�
+−
+� 1
+L
+�
+log2
+� 1
+L
+��
+= (L − 1) log2
+�
+L
+L − 1
+�
+.
+(G4)
+which is upper bounded by limL→∞ T (|W⟩) =
+1
+ln(2) ≈ 1.443.
+Appendix H: Guidance from EC theory: principal component analysis with respect to quantum noise
+Another fundamental use of the capacity spectrum analysis we propose is giving a natural truncation of eigentask. In machine
+learning theory, the technique of projection of a high-dimensional data to a far lower subspace is called principal component
+analysis. Within the computing architecture we are discussing, we are trying to use some K′-dimensional data where K′ ≪ K
+to approximate the original data as much as possible. More specifically, consider a given function f(u), we hope to find K′
+functions {G(k)(u)}k∈[K′] where G(k)(u) = �K−1
+k′=0 g(k)
+k′ xk′(u) lies in the space spanned by measured features G(k)(u) ∈
+Span{x}, such that the relative mean square error
+min
+W
+Eu
+����f − �K′
+k=1 Wk
+��K−1
+k′=0 g(k)
+k′ ¯Xk′
+����
+2�
+Eu[|f|2]
+(H1)
+is much smaller as possible. According to Appendix C, the solution to {g(k)}k∈[K′] is exactly g(k) = r(k). Fig. 9 supplies a
+concrete example of fitting linear function f(u) = u, by setting K′ = 40 in a 6-qubit system (and thus K = 64).
+−1.0
+−0.5
+0.0
+0.5
+1.0
+Input u
+−1.5
+−1.0
+−0.5
+0.0
+0.5
+1.0
+1.5 6-qubit, 40 principal xk(u), with retrain
+Combination of ¯Xk(u)
+Combination of xk(u)
+Target function f(u) = u
+−1.0
+−0.5
+0.0
+0.5
+1.0
+Input u
+−1.5
+−1.0
+−0.5
+0.0
+0.5
+1.0
+1.5 6-qubit, 40 principal y(k)(u), no retrain
+Combination of ¯Xk(u)
+Combination of xk(u)
+Target function f(u) = u
+FIG. 9. Projection onto 40-dimensional space spanned by 40 principal xk(u) vs. spanned by 40 principal y(k), in a 6-qubit H-encoding
+system. The number of shots is fixed as S = 5000.
+Fig. 9(a) shows the projection onto the space spanned by the dominant 40 readout features. Here, by “dominant” we mean
+one can first train by least square regression to get an output weight w ∈ RK, and then select corresponding wk with the leading
+K′ largest w2
+k · Eu[|xk|2]. Then we need to use these K′ features to retrain and obtain a new output weight w′ ∈ RK′. In such
+particular example, g(k) are some one-hot vectors where the index of 1 are chosen by the sorting K′ largest w2
+k · Eu[|xk|2] as we
+
+24
+described before. We can compare the the relative mean square error with the case of g(k) = r(k), the eigentasks. The latter one
+shows an approximation function with conspicuously much smaller relative mean square error.
+One fundamental question is: what will be an appropriate selection of K′ in practice. In Appendix D we claim that those
+β2
+k has stronger noise than signal itself, which should be excluded when taking the linear combination of measured features (or
+equivalently taking the linear combination of eigentasks). Namely we should defined the cut-off Kc(S) such that
+Kc(S) = max
+β2
+k<S k.
+(H2)
+Based on this observation, we can further explore the trend of Kc(S) when qubit number L is scaled. As we showed in main
+text. The eigen-NSR spectra growth much slower when L increases. Then the quantum system is able to provide much more
+eigentasks with more signal than noise. Fig. 10(a) shows spectrum in H-encoding quantum system with size L = 3 ∼ 8 with
+fixed hyperparameters. Notice that shot number S = 5000 here is not a larger number, which means that we cannot sample
+enough shots so that features converges to its mean in 28 = 256 dimensional Hilbert space. But applying eigentasks analysis
+in this example still shows a fast decay of relative error minW Eu[|f − �Kc(S)
+k=0
+Wk¯y(k)|2]/Eu[|f|2] until the fitting accuracy
+saturates at L = 8.
+FIG. 10. PCA for different ES H-encoding system size L = 3, 4, 5, 6, 7, 8 with fixed hyperparameters and S = 5000. (a) Eigen-NSRs
+spectrum of different sized system. (b) Relative error minW Eu[|f − �Kc
+k=1 Wk¯y(k)|2]/Eu[|f|2] for fitting f(u) = u, where Kc can be read
+out from (a). (c) Combination of Kc eigentasks �Kc(S)
+k=0
+wky(k)(u) and noisy eigentasks �Kc(S)
+k=0
+wk¯y(k)(u) in L = 5, 6, 7, 8 qubits system.
+Appendix I: Quantum-noise-PCA in classification problem
+The highly nonlinear readout feature xk(u) should have Taylor expansion xk(u) = �∞
+j (T)kjuj. Such complicated func-
+tions will span a certain functional space. One fundamental question is what the limit of approximation ability based on the
+architecture we proposed. Hereby we first show that this architecture under infinite sampling is capable of approximating any
+continuous function on the domain [−1, 1] to arbitrary precision. Furthermore, the linearity of quantum moment readout and
+complexity of quantum evolution will help us to understand why such a quantum system has capability to approximate a highly
+nonlinear function, under finite and bounded computational resources. Exploring the capacity for function approximation under
+finite measurement resources, as is done in the main text and Appendix C, highlights the fundamental limitations places by
+quantum noise on computation using the QRC.
+
+Ek Wk · g(k)(u)
+Zk Wk : y(k)(u)
+Zk Wk : y(k)(u)
+5000
+S
+f(u) = u
+f(u) =u
+S = 5000, N = 1000
+Zk Wk · g(k)(u)
+Zk Wk · g(k)(u)
+Ek Wk : y(k)(u)
+Ek, Wk y(k)(u)
+f(u) = u
+f() =u25
+−1.0
+−0.5
+0.0
+0.5
+1.0
+Input u
+−1
+0
+1
+Combination of features
+mmax = 1
+mmax = 2
+mmax = 3
+mmax = 4
+mmax = 5
+Sinusoid
+−1.0
+−0.5
+0.0
+0.5
+1.0
+Input u
+−1
+0
+1
+mmax = 1
+mmax = 2
+mmax = 3
+mmax = 4
+mmax = 5
+Steep tanh
+FIG. 11. Function approximation by using y = �K−1
+k=0 wkxk(u) (solid red lines) to approximate sine function and steep tanh function
+(dashed purple lines) in a 5-qubit quantum annealing system, where Keff = �mmax
+m=0
+�L
+m
+�
+depends on different quantum moment thresholds
+mmax = 1, 2, 3, 4, 5. The hyperparameters are (Jmax; ¯hx, hx
+rms; ¯hI, hI
+rms) = (1; 3, 1; 5, 2) in unit 1/t and no hz field. This simulation shows
+that for some simple functions, it is sufficient to merely use lower order moments, e.g., mmax = 2 in sine function and mmax = 3 in steep
+tanh function.
+−1.0
+−0.5
+0.0
+0.5
+1.0
+Input u
+0
+1
+2
+Class C0 distribution
+Class C1 distribution
+−1.0
+−0.5
+0.0
+0.5
+1.0
+Input u
+0
+100
+200
+300
+Class C0 sample histogram
+Class C1 sample histogram
+FIG. 12. (Left) Distribution p0(u) and p1(u) for classes C0 and C1, respectively. (Right) The histogram of C0 and C1. Each class contains
+5000 samples.
+1.
+Function approximation universality
+A very general question is that what type of functions can such a single-step quantum approximate. One conclusion which can
+be drawn is the function approximation universality. That is, give any continuous function from space of continuous functions
+on domain [−1, 1], i.e. φ ∈ C ([−1, 1], R), for any given error ε > 0, there always exists a function ϕ(u) = w · x(u) such that
+|ϕ(u) − φ(u)| ≤ ε
+(I1)
+for any input u ∈ [−1, 1]. The proof is also employing the well-known Stone-Weierstrass theorem. For our particular ar-
+chitecture, D = [−1, 1] is obviously a compact space, while point-separation can also be trivially fulfilled by a single qubit
+system (L = 1). The subalgebra structure of the function family generated by quantum systems is automatically satisfied in
+representation of moment in family of all product systems.
+2.
+1D classification as function approximation for noiseless measured features
+In this section, we will show how the function approximation universality of architecture described in Appendix I 1 enables it
+to perform – among others – paradigmatic machine learning tasks such as classification.
+
+26
+1
+2
+3
+4
+5
+Output feature threshold order mmax
+82
+84
+86
+88
+Testing Accuracy (%)
+Theoretical maximal accuracy
+−1.0
+−0.5
+0.0
+0.5
+1.0
+Input u
+0.00
+0.25
+0.50
+0.75
+1.00
+Probability
+mmax = 1
+mmax = 2
+mmax = 3
+mmax = 4
+Pr[u ∈ C1|u]
+FIG. 13.
+1D classification as function approximation in a 5-qubit quantum system with full connectivity.
+The hyperparameters are
+(Jmax; ¯hx, hx
+rms; ¯hI, hI
+rms) = (1; 3, 1; 8, 5) in unit 1/t and no hz field. (Left) Testing accuracy as a function highest order mmax of mo-
+ment feature. (Right) Conditional distribution Pr[u ∈ C1|u] (purple dashed line) vs. readout features σ(w · x(u)) with mmax = 1, 2, 3, 4
+(red solid line). mmax = 4 saturates the approximation accuracy.
+Suppose two classes C0 and C1 of samples, each of which is generated from distributions p0(u) and p1(u) respectively. The
+probability of occurrence of C0 and C1 are both 50%, and we simply let each class equally contain 5000 samples and thus
+N = 10000 samples in total. Both distribution are artificially defined by summing several Gaussian distributions with different
+amplitudes and widths together. Domain of both distributions are restricted in [−1, 1] and both distributions are also normalized.
+Due to the overlap of two distributions, there is some theoretical maximal classical accuracy to distribution whether a given u
+belongs to either C0 or C1.
+During the training, we feed each sample u(n) (belonging to class Cc(n)) into a 5-qubit quantum system. The quantum system
+will be read out with Keff = �mmax
+m=0
+�L
+m
+�
+different features {xk(u(n))}k∈[Keff]. Then features of N sample forms the regressor
+matrix. According to the standard supervised learning procedure, we simply train based on (x(u(n)), c(n)) by logistics regression
+where one should minimize the cross-entropy loss
+L (W ) =
+1
+N
+N
+�
+n=1
+�
+− c(n)log
+�
+σ(W · x(u(n)))
+�
+−
+�
+1 − c(n)�
+log
+�
+1 − σ(W · x(u(n)))
+� �
+(I2)
+where σ is the sigmoid function σ(y) =
+1
+1+e−y . A small L2 penalty λ∥W ∥2 (where λ = 10−6) is added to Eq. (I2) for
+preventing overfitting. The optimal W is then simply the set of weights that minimizes this cost function,
+w = argminW {L (W )}
+(I3)
+We test the fidelity of learning the classification task by determining the accuracy of classification on a testing set formed
+by drawing N = 10000 new samples (independent of the training set) as a function of the order of output moments extracted,
+mmax = 1, 2, 3, 4, 5, corresponding to reading out Keff = 6, 16, 26, 31, 32 features respectively. The resulting testing accuracy
+is plotted in the left panel of Fig. 13). We see that the testing accuracy converges to the theoretical maximal accuracy (dashed
+green) with increase in readout features.
+Importantly, one can show that this improvement in learning performance coincides with training of optimal weights w such
+that the QRC is able to approximate the conditional distribution Pr[u ∈ C1|u] of the two classes with increasing accuracy (lower
+error). To verify this, we first numerically compute all K = 32 readout feature functions x(u) of the system, by sweeping 500
+equidistant values of u ∈ [−1, 1]. Effectively learning the conditional distribution means that σ(w · x(u)) ≈ Pr[u ∈ C1|u]. It is
+equivalent to use w · x(u) to approximate the following function:
+w · x(u) ≈ σ−1(Pr[u ∈ C1|u]).
+(I4)
+We therefore see that the function approximation universality property of the architecture discussed in Appendix I 1 enables its
+use as a generic classifier.
+
+27
+−1.0
+−0.5
+0.0
+0.5
+1.0
+Input u
+0.00
+0.25
+0.50
+0.75
+1.00
+Probability
+Training
+Testing
+Pr[u ∈ C1|u]
+101
+102
+103
+104
+105
+Shots S
+60
+70
+80
+90
+Accuracy (%)
+Training
+Testing
+Theoretical maximal accuracy
+FIG. 14. (Left) The linear combination with sigmoid activation, that is the stochastic function σ
+��Kc(S)
+k′=1 wk′,Train(˜r(k)
+N · ¯
+XTrain)k′
+�
+(blue
+line) and σ
+��Kc(S)
+k′=1 wk′,Train(˜r(k)
+N · ¯
+XTest)k′
+�
+(red line), compared with the true conditional probability Pr[u ∈ C1|u] (black line). (Right)
+Training accuracy and testing accuracy. They saturate the theoretical maximal accuracy as S reaches 104 ∼ 105. Their agreement shows the
+quantum measurement noise serves well as a regularizer.
+3.
+Solving classification problem by quantum-noise-PCA
+Now we can solve the classification task above by using the quantum-noise princilpal component analysis we learn from
+capacity analysis. Suppose a physical system with L = 5 qubits and ring connectivity, we choose the hyperparameter to be
+J = 2, hx
+rms = hz
+rms = hI
+rms = 5 and t = 3. In this H-encoding scheme, we can obtain K = 32 measured features on each of
+N = 105 samples {u(n)} (5000 in class C0 and 5000 in class C1). We emphasize here that the underlying marginal distribution
+p(u) is no longer uniform here, and it will make both {β2
+k} and {r(k)} very different.
+Given the number of shots S ∈ [101, 105], we can still compute the empirical ˜r(k)
+N and estimating β2
+k by using the correction
+techniques we used in Appendix D. By comparing the estimated (1 − ˜αN,k)/(˜αN,k − 1
+S ) and S, we can figure out the cutoff
+order Kc(S) and combination coefficients ˜r(k)
+N , based on which we can define a set of observables
+ˆOk =
+K−1
+�
+k′=0
+˜r(k)
+N,k′ ˆ
+Mk′
+k = 0, 1, · · · , Kc(S).
+(I5)
+It is equivalent to say, by measuring ˆOk, we can effectively obtain eigentasks ˜r(k)
+N · ¯
+XTrain. Then we can apply standard logistics
+regression on those eigentasks as we did in Eq. I2. The only difference is we no longer need any regularization term as penalty
+like λ∥W ∥2. The training procedure eventual yield wTrain ∈ RKc(S), together with ˜r(k)
+N and Kc(S).
+Now we generate a totally new and independent set of u’s for testing purpose.
+By measuring ˆOk, one get eigentasks
+˜r(k)
+N · ¯
+XTest. By plugging wTrain ∈ RKc(S)+1, together with ˜r(k)
+N
+and Kc(S) in training, we can achieve the testing accu-
+racy. The agreement between training and testing accuracy show that the quantum measurement noise effectively works as a
+regularizer, and do a pretty good job (see Fig. 14).
+Appendix J: Finite sampling bound and uncertainty propagation
+We conclude that the principle advantage brought about by entanglement in this sections. There we observe that for certain
+inputs u (that depend on the input encoding) the measurement of an ES when mapped into the moment space can generate
+distributions that can be highly anisotropic at finite S. While for PS these distributions are generally isotropic unless they are
+close to the boundaries of the output domain (when the encoding produces outputs that are eigenstates of the measurement basis).
+We observe that this trend is also present in the experimental system despite non-idealities. The origin of higher expressive
+capacity at large S provided by ESs can be traced back to this basic feature. To be more specific, let ˆ
+Mk = ˆσz
+l1 ˆσz
+l2 · · · ˆσz
+lm, and
+¯Xk(u) be empirical mean based on S sampling. Notice that the variance of ¯Xk is
+Var[ ¯Xk] = 1
+S
+�
+⟨(ˆσz
+l1 ˆσz
+l2 · · · ˆσz
+lm)2⟩ − ⟨ˆσz
+l1 ˆσz
+l2 · · · ˆσz
+lm⟩2�
+= 1
+S (1 − x2
+k(u)).
+(J1)
+
+28
+1
+2
+3
+4
+5
+6
+7
+8
+9
+10
+Highest order m
+10−1
+100
+101
+1/SNR (Log)
+EC, fit
+PC, fit
+FIG. 15. NSR of ES vs PS in a 10-qubit quantum annealing system with shot number S = 1000 by feeding u = 1/2. The hyperparameters
+are chosen to be (¯hx, hx
+rms; ¯hz, hz
+1,rms) = (8, 2; 3, 2) in unit 1/t. The purple and red colors correspond to coupling being switched on and off,
+respectively; and the coupling hyperparameter in ES is Jmax = 2/t. For each m, the N = 30 dots are relative error x(r)
+k (u)/xk(u) − 1 of
+30 repetitions r = 1, 2, · · · , 30. The standard deviation of those relative errors (namely NSR) are also plotted. The ES NSR (purple stars) is
+well fitted by O(1/
+√
+S) (purple dashed line) while the PS NSR (red stars) scales exponentially as O(2m/
+√
+S) (purple dashed line). We take
+y-axis being log-scale, and one may find in these regime ES 1/SNR grows exponentially faster than PS NSR (red stars) and hence PS readout
+scheme will be less powerful in sense of quantum sampling noise resistant.
+By central limit theorem,
+¯Xk(u) = xk(u) + δk(u) = xk(u) +
+1
+√
+S
+ζk(u),
+(J2)
+where random sampling noise ζk(u) ≈
+�
+1 − x2
+k(u)ϵ and ϵ ∼ N(0, 1) is standard Gaussian. For quantum moment readout, the
+amplitude of relative error is
+����
+δk(u)
+xk(u)
+���� ≈
+�
+1 − x2
+k(u)
+x2
+k(u)
+1
+√
+S
+∝
+1
+√
+S
+.
+(J3)
+For classical polynomial readout the amplitude of relative error is obtained by rule of uncertainty propagation
+����
+(xl1(u) + δl1) · · · (xlm(u) + δlm) − xl1(u) · · · xlm(u)
+xl1(u) · · · xlm(u)
+���� ≈
+����
+δl1
+xl1(u) + · · · +
+δlm
+xlm(u)
+����
+≈
+��
+1 − x2
+l1(u)
+x2
+l1(u)
++ · · · +
+�
+1 − x2
+lm(u)
+x2
+lm(u)
+�
+×
+1
+√
+S
+∝ m ×
+1
+√
+S
+.
+(J4)
+If there is no entanglement in quantum system, then the readout features for both quantum moment readout and classical poly-
+nomial readout are the same ⟨ˆσz
+l1 ˆσz
+l2 · · · ˆσz
+lm⟩ = ⟨ˆσz
+l1⟩⟨ˆσz
+l2⟩ · · · ⟨ˆσz
+lm⟩. However, even if the expectations under infinite sampling
+limit S → ∞ are the same, the measurement noise under finite sampling are still different. For classical polynomial read-
+out, the scaling of still follows the simple additivity relation of uncertainty propagation in Eq. (??). But now the noise of
+xl1(u) · · · xlm(u) in quantum moment readout will be very strong, this is because xl1(u) · · · xlm(u) is now close to zero, thus
+����
+δk
+xk(u)
+���� ≈
+1
+xk(u)
+1
+√
+S
+=
+1
+xl1(u) · · · xlm(u)
+1
+√
+S
+∝ 2m ×
+1
+√
+S
+.
+(J5)
+
diff --git a/5dAyT4oBgHgl3EQfQPaq/content/tmp_files/load_file.txt b/5dAyT4oBgHgl3EQfQPaq/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b700a15c15377858a2273d0e73837b6bf80f6444
--- /dev/null
+++ b/5dAyT4oBgHgl3EQfQPaq/content/tmp_files/load_file.txt
@@ -0,0 +1,1273 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf,len=1272
+page_content='Fundamental Limits to Expressive Capacity of Finitely Sampled Qubit-Based Systems  Fangjun Hu,1, ∗ Gerasimos Angelatos,1, ∗ Saeed A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Khan,1 Marti Vives,1, 2 Esin T¨ureci,3  Leon Bello,1 Graham E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Rowlands,4 Guilhem J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Ribeill,4 and Hakan E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' T¨ureci1  1Department of Electrical and Computer Engineering, Princeton University, Princeton, NJ 08544, USA  2Q-CTRL, Santa Monica, CA 90401, USA  3Department of Computer Science, Princeton University, Princeton, NJ 08544, USA  4Raytheon BBN, Cambridge, MA 02138, USA  (Dated: January 3, 2023)  The expressive capacity for learning with quantum systems is fundamentally limited by the quantum sampling  noise incurred during measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' While studies suggest that noise limits the resolvable capacity of quantum  systems, its precise impact on learning remains an open question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' We develop a framework for quantifying  the expressive capacity of qubit-based systems from finite numbers of projective measurements, and calculate  a tight bound on the expressive capacity and the corresponding accuracy limit that we compare to experiments  on superconducting quantum processors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' We uncover the native function set a finitely-sampled quantum system  can approximate, called eigentasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' We then demonstrate how low-noise eigentasks improve performance for  tasks such as classification in a way that is robust to noise and overfitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' We also present experimental and  numerical analyses suggesting that entanglement enhances learning capacity by reducing noise in eigentasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Our results are broadly relevant to quantum machine learning and sensing applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  INTRODUCTION  Learning with quantum systems is a promising application  of near-term quantum processors, with several recent demon-  strations in both quantum machine learning (QML) [1–5] and  quantum sensing [6–8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' A broad class of such data-driven ap-  plications proceed by embedding data into the evolution of  a quantum system, where the embedding, dynamics, and ex-  tracted outputs via measurement are all governed by a set of  general parameters θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Depending on the learning scheme, dif-  ferent components of this general framework may be trained  for optimal performance of a given task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Irrespective of the  scheme, however, the fundamental role of the quantum sys-  tem is that of a high-dimensional feature generator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Given  inputs u, a set of frequencies for the occurrence of different  measurement outcomes act as a feature vector to learn a func-  tion f(u) that minimizes the chosen loss function (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  The relationship between the physical structure of the model  and the function classes that can be expressed with high accu-  racy, referred to as expressivity, is a fundamental question of  basic importance to the success of quantum models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Recent  results have begun to shed light on this important question  and provide guidance on the choice of parameterized quantum  models [9–16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Yet when it comes to experimental implemen-  tations, the presence of noise is found to substantially curtail  theoretical expectations for performance [1–3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Given an input u to a general dynamical system, we de-  fine its Expressive Capacity (EC) as a measure of the accu-  racy with which K linearly independent functions {f(u)} of  the input can be constructed from K readout features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' This is  a suitable generalization to noisy systems of the Information  ∗ These two authors contributed equally  Processing Capacity introduced in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' A central chal-  lenge in determining the EC for quantum systems is the fun-  damentally stochastic nature of measurement outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Even  when technical noise due to system parameter fluctuations is  minimized as in an error-corrected quantum computer, there  is a fundamental level of noise, the quantum sampling noise  (QSN), which cannot be eliminated in learning with quantum  systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' QSN therefore sets a fundamental limit to the EC  of any physical system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Although QSN is well-understood  theoretically, a formulation of its impact on learning is a chal-  lenging task as it is strongly determined by the quantum state  of the system relative to the measurement basis, and is highly  correlated when entanglement is present.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Consequently, the  impact of QSN is often ignored [18–21] (with a few excep-  tions [14, 22]), even though it can place strong constraints on  practical optimization [23] and performance [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' In this ar-  ticle, we develop a mathematical framework to quantify the  EC that exactly accounts for the structure of QSN, providing  a tight bound for an L-qubit system under S measurements,  and illustrate how a mathematical framework for its quantifi-  cation can guide experimental design for QML applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Our work goes beyond simply defining the EC as a figure of  merit, however.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' In particular, we offer a methodology to iden-  tify the native function set that is most accurately realizable  by a given encoding under finite sampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Equivalently, we  show that this defines a construction of measured features that  is optimally robust to noise in readout, thereby revealing how  such a quantum system can be optimally employed for learn-  ing tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Finally, while the strength of the EC lies in its gener-  ality, we provide numerical examples that suggest that higher  EC is typically indicative of improved performance on spe-  cific QML tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' As such, the EC provides a metric whose op-  timization can be targeted for improved learning performance  in a task-agnostic and parameter-independent manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  This strategy for defining the noise-constrained EC natu-  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='00042v1  [quant-ph]  30 Dec 2022  2  Entangled  system  Increased  sampling  Product  system  Input  dimensional  input domain  Output            under finite sampling  Feature generator  (a)  (b)  Individual function capacity:  Function approximation  features  (Probabilities)  Quantum system  Quantum annealers  Quantum Neural Networks/  Variatonal Quantum Algorithms  Quantum Kernel Methods  Target:  Learned Estimate:  Learned linear weights  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' -Qubit system  Computational basis measurement  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (a) Representation of the learning framework considered in  this work – inputs u are transformed to a set of outputs via a feature  generator, here implemented using a finitely-sampled quantum sys-  tem as shown in (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Inputs are encoded in the state of a quantum  system via a general quantum channel U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Information is extracted  from the quantum system via projective measurements in the com-  putational basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The geometric structure of the quantum sampling  noise in the high-dimensional measured feature space can strongly  depend on the encoding, and the degree of entanglement generated  upon parametric evolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The learning scheme discussed in the  present work optimally leverages the geometric structure of corre-  lated noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  This framework describes a wide range of practical  quantum systems, from quantum circuits used in QML, to quantum  annealers exhibiting continuous evolution, and beyond, all defined by  general parameters θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' As shown in (a), learned estimates for desired  functions are constructed via a trained linear estimator ˜w applied to  K measured observables ¯  X of the quantum system, with a resolu-  tion limited by quantum sampling noise with finite shots S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Capacity  then quantifies the error in the approximation of a target function via  this scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  rally focuses on accessible noisy output features under a spec-  ified measurement scheme, as opposed to unmeasured degrees  of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  This makes the EC an efficiently-computable  quantity in practice, as we demonstrate using both numerical  simulations and experiments on IBM Quantum’s supercon-  ducting multi-qubit processors [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Our work also identifies  enhancement in measurable quantum correlations as a general  principle to increase the EC of quantum systems under finite  sampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  LEARNING WITH QUANTUM SYSTEMS  The most general approach to learning from data using a  generic quantum system is depicted schematically in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  A table with symbols and abbreviations used in the text can  be found in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' For concreteness, we detail a specific  realization for L-qubit systems that are measured projectively,  which will be analyzed in the remainder of this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Any  learning scheme begins with embedding the data u through a  quantum channel parameterized by θ acting on a known initial  state, ˆρ(u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' θ) = U(u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' θ)ˆρ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' For an L-qubit quantum system,  for example, we consider ˆρ0 = |0⟩⟨0|⊗L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Any computation must be performed using outputs ex-  tracted from the quantum system via measurements in a  specified basis parameterized by K operators { ˆ  Mk}, k =  0, · · · , K − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' For a projectively measured L-qubit system,  the measurement basis is defined by the K = 2L projectors  ˆ  Mk = |bk⟩⟨bk| corresponding to measurement of bitstrings  bk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' A single measurement or “shot” yields a discrete out-  come b(s)(u) for each observable: if the outcome of shot s  is state k, then b(s)(u) ← bk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Measured features are then  constructed by ensemble-averaging over S repeated shots:  ¯Xk(u) = 1/S �  s δ(b(s)(u), bk).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Hence ¯Xk(u) in this case  is the measured frequency of occurrence of the bitstring bk in  S repetitions of the experiment with the same input u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' These  measured features are formally random variables that are un-  biased estimators of the expected value of the corresponding  observable as computed from ˆρ(u): explicitly,  limS→∞ ¯Xk(u) ≡ xk(u) = Tr{ ˆ  Mk ˆρ(u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' θ)},  (1)  so that xk is the quantum mechanical probability of occur-  rence of the kth bitstring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  In QML theory, it is standard to consider the limit S → ∞,  and to thus use expected features {xk(u)} for learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' How-  ever, for any practical implementation, measured features  { ¯Xk(u)} must be constructed under finite S, in which case  their fundamentally quantum-stochastic nature can no longer  be ignored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  This quantum sampling noise, like any other  source of noise, can unsurprisingly limit the EC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Completely  unlike classical noise sources however, the statistics of quan-  tum sampling noise are strongly determined by the state of  the quantum system itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' This leads to a rich noise structure  that changes dramatically based on, for example, the entan-  glement of the generated quantum state, as depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  In this work, we exactly account for this structure of quantum  sampling noise to quantify its fundamental impact on EC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' By  further leveraging the complexity and quantum state depen-  dence of sampling noise, we provide a practical, experimen-  tally applicable methodology that maximizes the capacity for  learning functions using finitely-sampled quantum systems,  and also avoids overfitting in ML tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  We begin by observing that ¯  X are samples from a multino-  mial distribution with S trials and K = 2L categories, which  can be decomposed into their expected value and an input-  dependent sampling noise:  ¯  X(u) = x(u) +  1  √  S  ζ(u),  (2)  where ζ(u) is a zero-mean random vector obeying multino-  mial statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  As discussed in Appendix B and C, what  makes quantum systems special is the fundamental relation-  ship between the noise ζ(u) and the ‘signal’ x(u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Pre-  cisely, the covariance Σ(u) of ζ(u) depends on the gen-  erated quantum state:  Σkk′(u)  =  Tr{ ˆ  Mk ˆ  Mk′ ˆρ(u)} −  Tr{ ˆ  Mk ˆρ(u)}Tr{ ˆ  Mk′ ˆρ(u)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' This quantum covariance of the  measured observables therefore comprises non-linear func-  tions of the signal x(u) itself;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' at a given S, we will show  that this allows for more information to be extracted from sys-  tems with more quantum correlations between observables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Note that ζ can be straightforwardly modified to include other  3  noise sources, such as gate or measurement errors (see Ap-  pendix B 2), with 1/  √  S then interpreted as a general noise  strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' However our focus here remains on quantum sam-  pling noise and its fundamental role in learning with quantum  systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  The use of such a quantum system for the learning of func-  tions under finite sampling is then depicted schematically in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' For a target function f(u), an approximation fW (u)  is obtained via a linear (for reasons clarified shortly) esti-  mator applied to readout features under finite S, fW (u) =  W · ¯  X(u), where  ¯  X = ( ¯X0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' , ¯XK−1)T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  To quantify  the fidelity of this approximation, we introduce the capac-  ity [14, 17, 20] to construct the target function as the minimum  achievable (normalized) mean squared error between the tar-  get and its estimate:  C[f] = 1 − min  W ∈RK  Eu[|f(u) − fW (u)|2]  Eu[|f(u)|2]  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (3)  In the above, Eu refers to the expected value with respect to an  input distribution p(u) over a compact input domain, which  can be continuous or discrete: Eu[f] ≡  �  du p(u)f(u) ≃  1  N  �  n f(u(n)) for i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' sampling obeying u(n) ∼ p(u) for  all n ∈ [N].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Minimizing error in the approximation of  f(u) by fW (u) over the input domain to determine capac-  ity thus requires finding ˜w = argminW Eu[|f − fW (u)|2]  (via a resource-efficient pseudoinverse).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' This capacity is con-  structed such that 0 ≤ C[f] ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  The choice of a linear estimator and a mean squared er-  ror loss function may appear restrictive at first glance, but the  generality of our formalism averts such limitations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' For ex-  ample, the use of a linear estimator applied directly to readout  features precludes classical nonlinear post-processing of mea-  surements;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' however, this is simply to ensure the calculated  capacity is a measure of the quantum system itself, and not of  a classical nonlinear layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Importantly, our formalism is gen-  eral enough to incorporate such processing in a calculation  of capacity, via a simple redefinition of readout features ¯  X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Hence the use of a linear estimator does not necessarily lose  generality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Secondly, while higher-order loss functions may  be used, the mean squared loss effectively describes the Tay-  lor expansion of a wide range of loss functions (see Appendix  C 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  To extend the notion of capacity to a task-independent mea-  sure of the expressivity of a physical system, we can eval-  uate the function capacity over a complete orthonormal set  of basis functions {fℓ}ℓ∈N, equipped with the inner product  ⟨fℓ, fℓ′⟩p =  � 1  −1 fℓ(u)fℓ′(u)p(u)du = δℓℓ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The total Ex-  pressive Capacity (EC) is then CT ≡ �∞  ℓ=0 C[fℓ], which ef-  fectively quantifies how many linearly-independent functions  can be expressed from a linear combination of { ¯Xk(u)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Our  main result, which is proven in Appendix C 4, is that the EC  for an L-qubit system whose readout features are stochastic  variables of the form of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (2) is given by  CT (θ) = Tr  ��  G + 1  S V  �−1  G  �  =  K  �  k=1  1  1 + β2  k(θ)/S .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (4)  The first equality is written in terms of the expected feature  Gram and covariance matrices G ≡ Eu[xxT ] and V ≡  Eu[Σ] respectively;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' we later demonstrate that these expected  quantities can be accurately estimated under finite S sam-  pling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  The second equality expresses the total capacity in  a finite-dimensional linear space, in terms of the eigenval-  ues {β2  k}k∈[K] satisfying the generalized eigenvalue prob-  lem Vr(k) = β2  kGr(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Inspecting this expression, we first  note that it is independent of the particular set {fℓ}ℓ∈N cho-  sen, which would have required an evaluation over an infi-  nite set of functions and its numerical evaluation therefore  would be subject to inaccuracies due to truncation [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' In-  stead, CT can be interpreted as the sum of capacities to con-  struct K individual functions living in an otherwise infinite-  dimensional function space;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' the identity of these special func-  tions is closely connected with the generalized eigenvectors  {r(k)}, and will be clarified shortly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Secondly, in the absence  of noise, limS→∞ CT = Rank{G} = K = 2L, provided no  special symmetries exist (see Appendix C 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Such theoreti-  cal exponential growth in expressive capacity with L is often-  cited as a motivator for ML on quantum systems [14, 20, 25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  From the perspective of infinite-shot capacity, this also im-  plies that all L-qubit systems with K measured features are  equivalent, regardless of encoding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Such universality has also  been pointed out for classical dynamical systems subject to  zero input and output noise [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  However, our expression for CT is also valid for any noisy  physical system, corresponding to finite S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  In particular,  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (4) shows that the EC of a qubit-based physical system  satisfies CT ≤ K at finite S, and can be fully characterized in  terms of the spectrum {β2  k}, which is ultimately determined  by parameters θ governing the physical system and embed-  ding via the Gram (G) and covariance (V) matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Related  characterizations of noise-constrained capacity have been at-  tempted for Gaussian quantum systems [22], but to our knowl-  edge no precise formulation exists that also encompasses non-  Gaussian systems such as qubit systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Furthermore, from  the perspective of capacity, what makes one embedding or  physical system different from another is simply its ability to  accurately express functions in the presence of noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Our  expression for CT thus provides a general, comprehensive,  and straightforward metric to assess and compare this capac-  ity across physical systems and their associated embedding  under finite S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Furthermore, via the associated eigenvectors {r(k)}, our  analysis uncovers a finite set of orthogonal functions native  to a particular encoding that is maximally resolvable through  S measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' This set of K orthonormal functions, the  eigentasks y(k)(u) = �  j r(k)  j  xj(u), can be estimated from  measured readout features as described in Appendix D 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The  eigentasks characterize an ordered set of functions that can be  constructed with mean squared error β2  k/S, leading to a natu-  ral interpretation of β2  k as noise-to-signal (NSR) eigenvalues,  determined by fundamental sampling noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' As we will show,  this experimentally extractable information can be utilized for  optimal learning (with minimal degrees of freedom) with a  noisy quantum system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  4  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  EXPERIMENTAL RESULTS  To demonstrate the above results in practice, we now show  how the spectrum {β2  k}, the EC, and eigentasks can all be  computed for real quantum devices in the presence of param-  eter fluctuations and device noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  We emphasize at the outset that our approach for quantify-  ing the EC of a quantum system is very general, and can be  applied to a variety of quantum system models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' For practical  reasons, we perform experiments on IBM Quantum (IBMQ)  processors, whose dynamics is described by a parameterized  quantum circuit containing single and two-qubit gates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' How-  ever, as an example of the general validity of our approach,  in Appendix E we compute the EC for L-qubit quantum an-  nealers via numerical simulations, governed by the markedly  different model of continuous-time Hamiltonian dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  On IBMQ devices, resource limitations restrict our compu-  tation of EC to 1D inputs u that are uniformly distributed,  p(u)  =  Unif[−1, 1], see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 2(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  We emphasize that  this analysis can be straightforwardly extended to multi-  dimensional and arbitrarily-distributed inputs given suitable  hardware resources, without modifying the form of the Gram  and covariance matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  We are only now required to specify the model of the L-  qubit system in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (1), which has been left completely gen-  eral thus far.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The specific ansatz we consider is tailored to  be natively implementable on IBMQ processors;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' more gen-  eral ansatz can also be considered (see Appendix B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' It con-  sists of τ ∈ N repetitions of the same input-dependent circuit  block depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 2(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The block itself is of the form  Rx(θx/2)W(J)Rz(θz + θIu)Rx(θx/2), where Rx/z are  Pauli-rotations applied qubit-wise, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Rz = �  l Rz(θz  l +  θI  l u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  The entangling gate acts between physically con-  nected qubits in the device and can be written as W(J) =  �  ⟨l,l′⟩ exp{−i J  2 ˆσz  l ˆσz  l′}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Note that for this ansatz, the choice J = 0 (mod π) yields  either W = ˆI or ˆσz ⊗ ˆσz, both of which ensure ˆρ(u) is a prod-  uct state and measured features are simply products of uncor-  related individual qubit observables – equivalent to a noisy  classical system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Starting from this product system (PS), tun-  ing the coupling J ̸= 0 (mod π) provides a controllable pa-  rameter to realize an entangled system (ES).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' This control en-  ables us to address a natural question regarding EC of quan-  tum systems under finite S: what is the dependence of EC  and realizable eigentasks on J, and hence on quantum corre-  lations?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  This calculation of EC requires extracting measured fea-  tures from the quantum circuit under input u, one example of  which is shown for the IBMQ ibmq perth device in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 2(a),  for S = 214.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' For comparison, we also show ideal-device  simulations (no device noise), where slight deviations are ob-  served.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The agreement with the experimental feature is im-  proved when the effects of gate and readout errors,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' and qubit  relaxation are included,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' hereafter referred to as “device noise”  simulations,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' highlighting the non-negligible role of device er-  +  +  + C-NOT  +  +  +  +  +  +  +  +  Input  ES  PS  Order  (a)  (b)  (c)  Shots  Coupling  IBM Perth  Output  Experiment  Experiment  Simulations  Simulations  Estimate  Calculate  Device encoding  Device encoding  Device noise  Device noise  Ideal  Ideal  Mean over 8 random  encodings: device noise  Mean over 8 random  encodings: ideal  Ideal sim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Device noise  sim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Experiment  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (a) IBMQ Perth device and quantum circuit schematic for  EC calculation, and classification task in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Here τ = 3 lay-  ers, and random qubit rotation parameters are θx/z  l  ∼ Unif[0, 2π]  and θI  l ∼ Unif[0, 10π].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' On the right, the specific feature plotted is  ¯  X1(u) = P000001(u) for S = 214 shots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (b) Left panel: Device  NSR spectrum β2  k for ES, J = π/2 (blue crosses) and PS, J = 0  (brown diamonds).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Ideal (solid) and device noise (dashed) simula-  tions are also shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Note the agreement between device and simu-  lation, along with distortion from more direct exponential growth in  β2  k with k in the ideal case, due to device errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Right panel: CT  vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' S calculated from the left panel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' At a given S, the CT can be  approximated by performing the indicated sum over all β2  k < S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (c)  EC (top panel) and ETC (lower panel) under S = 214 from the IBM  device, and device noise simulations (dashed peach).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Average met-  rics over 8 random encodings for device noise (solid peach) and ideal  (solid gray) simulations are also shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The S → ∞ EC of these  encodings always attains the max{CT } = 64, indicated in dashed  red.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  rors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  The measured features under finite S are used to estimate  the Gram and covariance matrices (see Appendix D), and to  thus solve the eigenproblem for NSR eigenvalues {β2  k}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Typ-  ical NSR spectra computed for two random encodings on the  device are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 2(b), for J = 0 (PS) and J = π/2  (ES), together with spectra from device noise simulations,  with which they agree well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' We note that at lower k, the device  NSR eigenvalues are larger than those from ideal simulations,  due to device noise contributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' For larger k, device results  deviate from the pure exponential increase (with order) seen in  ideal simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The deviation is captured by device noise  simulations and can therefore be attributed to device errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  The NSR spectra therefore can serve as effective diagnostic  tools for quantum processors and encoding schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' More  examples will be provided later in the discussion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  The NSR spectra can be used to directly compute the EC of  the corresponding quantum device for finite S, via Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' As  a rule of thumb, at a given S only NSR eigenvalues β2  k ≲ S  contribute substantially to the EC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' An NSR spectrum with a  flatter slope therefore has more NSR eigenvalues below S,  0  1  2  3  4  5  65  which gives rise to a higher capacity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 2(b) shows that the  ES generally exhibits an NSR spectrum with a flatter slope  than the PS, yielding a larger capacity for function approxi-  mation across all sampled S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  To more precisely quantify the role of entanglement and  quantum correlations in EC, we introduce the expected total  correlation (ETC) of the measured state over the input domain  of u [26, 27],  ¯T = Eu  � L  �  l=1  S(ˆρM  l (u)) − S(ˆρM(u))  �  ,  (5)  where  ˆρM  is  the  measured  state:  ˆρM(u)  ≡  �  k ˆρkk(u) |bk⟩⟨bk| and S is the von Neumann entropy (see  Appendix G).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' We now compute EC and ETC using S = 214  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 2(c) as a function of J, together with both ideal and  device noise simulations of the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' We note that product  states by definition have ¯T = 0 [28];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' this is seen in ideal  simulations for J = 0 (mod π).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' However, the actual device  retains a small amount of correlation at this operating point,  which is reproduced by device noise simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' This can be  attributed to gate or measurement errors as well as cross-talk,  especially relevant for the transmon-based IBMQ platform  with a parasitic always-on ZZ coupling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  With increasing J, ¯T increases and peaks around J ∼  π/2 (mod π);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' interestingly, CT also peaks for the same cou-  pling range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' From the analogous plot of EC, we clearly see  that at finite S, increased ETC appears directly correlated  with higher EC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' We have observed very similar behaviour us-  ing completely different models of quantum systems (see Ap-  pendix Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 5 [29, 30]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' This indicates the utility of enhancing  quantum correlations as a means of improving the general ex-  pressivity of quantum systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  However, we see that at finite S, even with increased quan-  tum correlations, the maximum EC is still substantially lower  than the upper bound of K = 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Note that this remains true  even for ideal simulations, and over several random encod-  ings, so the underperformance cannot be attributed to device  noise or poor ansatz choice respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' These results clearly  indicate that the resulting sampling noise at finite S is the fun-  damental limitation for QML applications on this particular  IBM device, rather than other types of noise sources and er-  rors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  A ROBUST APPROACH TO LEARNING  While we have demonstrated the EC as an efficiently-  computable metric of general expressivity of a noisy quantum  system, some important practical questions arise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' First, does  the general EC metric have implications for practical perfor-  mance on specific QML tasks?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Secondly, given the limiting –  and unavoidable – nature of correlated sampling noise, does  the EC provide any insights on optimal learning using a par-  ticular noisy quantum system and the associated embedding?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Input  Target  Distinguish inputs from  Class 1 vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Class 2  ES  ES  PS  PS  Input  Eigentasks  ,  (a)  (b)  (c)  Increasing noise  Learning with  eigentasks  Class 1  Training  Testing  Class 2  Equiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' to learning  likelihood function  ,  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (a) Device eigentasks for ES (left) and PS (right), con-  structed from noisy features at S = 210 and S = 214.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (b) Clas-  sification demonstration on IBMQ Perth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Binary distributions to be  classified over the input domain are shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (c) The classification  task can be cast as learning the likelihood function separating the  two distributions;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' this target function is shown in the upper panel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Lower panels show the trained estimate of this target using outputs  from the ES and PS respectively, using KL = 36 eigentasks with  S = 214.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Our formulation addresses both these important questions  naturally, as we now discuss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Beyond being a simple figure of  merit, we show in the Appendix C that the EC is precisely the  sum of capacities to approximate a particular set of orthogonal  functions native to the given noisy quantum system: the eigen-  tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Crucially, these eigentasks ¯y(k)(u) = � r(k)  j  ¯Xj(u) can  be directly estimated from a noisy quantum system via the  generalized eigenvectors {r(k)}, and are ordered by their as-  sociated NSR {β2  k}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' We show a selection of estimated eigen-  tasks from IBMQ, for an ES (J = 5π/3) and PS (J = 0) in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 3(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' For both systems, the increase in noise with eigen-  task order is apparent when comparing two sampling values,  S = 210 and S = 214.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Furthermore, for any order k, eigen-  tasks for the PS are visibly noisier than the ES;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' this is con-  sistent with NSR eigenvalues for PS being larger than those  for ES, as seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 2(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' This ability to more accurately  resolve eigentasks provides a complementary perspective on  the higher expressive capacity of ES in comparison to PS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  The resolvable eigentasks of a finitely-sampled quantum  system are intimately related to its performance at specific  QML applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' To demonstrate this result, we consider  a concrete application: a binary classification task that is  not linearly-separable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Samples u(n), n ∈ [N], obeying the  same distribution p(u) for u ∈ [−1, 1] as considered for the  EC evaluation, are separated into two classes, as depicted in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 3(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' A selection of Ntrain = 150 total samples - with  equal numbers from each class - are input to the IBMQ device,  and readout features ¯  X(u(n)) are extracted using S = 214  shots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  A linear estimator applied to these features is then  trained using logistic regression to learn the class label associ-  ated with each input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Finally, the trained IBMQ device is used  to predict class labels of Ntest = 150 distinct input samples  for testing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  This task can equivalently be cast as one of learning the  likelihood function that discriminates the two input distribu-  6  Classification accuracy  Testing  Classification accuracy  No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' of eigentasks used for learning,  (a)  (b)  ES  PS  Coupling  Experiment  Simulations  Device encoding  Device encoding  Testing  NSR Cutoff  Mean over  8 random encodings  Overfitting  Overfitting  Training  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (a) Training (light) and testing (dark) accuracy for an ES and  PS in blue and brown respectively, as a function of number of eigen-  tasks used in learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The optimal test set performance is found near  the NSR cutoff Kc(S) (dash-dotted lines) informed by the quantum  system’s NSR spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' In all figures, the IBMQ Perth device is sam-  pled with S = 214, and the training and test sets consist of 150 ran-  dom points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (b) Testing set classification accuracy as a function of  J for our optimal learning method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The average of simulated encod-  ings is shown in solid peach, and the horizontal line shows the best  performance of a software neural network with KL = 36 parameters  for comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  tions, shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 3(c), with minimum error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The set of up  to KL eigentasks ¯y(k)(u), where KL ≤ K, serves as the na-  tive basis of readout features used to approximate any target  function using the quantum system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The noisier eigentasks of  the PS therefore limit the accuracy with which it can be used  to learn the target, in comparison to the ES.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' This is clear from  the learned estimates shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 3(c), using an equal num-  ber of KL = 36 eigentasks to ensure a fair comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The  higher approximation capacity translates to improved classi-  fication performance, as we show via the training and testing  classification accuracy in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 4(a) for both ES and PS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' We  plot both as a function of the number of eigentasks KL used  for learning, from which it is clear that the maximum testing  accuracy using the ES exceeds that of the PS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  However, using eigentasks ordered by NSR reveals even  more about learning using noisy quantum systems, and pro-  vides a path towards optimal learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' While intuition sug-  gests that using more eigentasks can only be beneficial,  weights learned when training with noisier eigentasks may  not generalize well to unseen samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' For example, using  all eigentasks (KL = K) yields a test accuracy far lower than  that found in training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The observed deviation is a distinct  signature of overfitting: the optimized estimator learns noise  in the training set, and thus loses generalizability in testing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Crucially, an optimal number of eigentasks clearly emerges,  around KL ≃ Kc(S) = maxk{β2  k < S}, for which the NSR  eigenvalue is closest to S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Eigentasks k > Kc typically con-  tribute more ‘noise’ to the function approximation task than  ‘signal’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Excluding these eigentasks therefore limits overfit-  ting without adversely impacting performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 4(b) also shows the classification accuracy as J is var-  ied, where we highlight the striking similarity with Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 2(c):  encodings with larger quantum correlations and thus higher  expressive capacity will perform generically better on learn-  ing tasks in the presence of noise, because they generate a  larger set of eigentasks that can be resolved at a given sam-  pling S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The NSR spectra and eigentasks therefore provide  a natural truncation scheme to maximise testing accuracy,  avoiding overfitting without any additional regularization (see  also Appendix H and I).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  DISCUSSION  We have developed a straightforward approach to quan-  tify the expressive capacity of any qubit-based system in the  presence of fundamental sampling noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Our analysis is  built upon an underlying framework that determines the native  function set that can be most robustly realized by a finitely-  sampled quantum system: its eigentasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' We use this frame-  work to introduce a methodology for optimal learning using  noisy quantum systems, which centers around identifying the  minimal number of eigentasks required for a given learning  task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The resulting learning methodology is resource-efficient  and robust to overfitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' We demonstrate that eigentasks can  be efficiently estimated from experiments on real devices us-  ing a limited number of training points and finite shots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' We  also demonstrate across two distinct qubit evolution ans¨atze  that the presence of measured quantum correlations enhances  expressive capacity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Our work has direct application to the  design of circuits for learning with qubit-based systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' In  particular, we propose the optimization of expressive capacity  as a meaningful goal for the design of quantum circuits with  finite measurement resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  ACKNOWLEDGEMENT  This research was developed with funding from the  DARPA contract HR00112190072, AFOSR award FA9550-  20-1-0177, and AFOSR MURI award FA9550-22-1-0203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  The views, opinions, and findings expressed are solely the au-  thors and not the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' government.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  [1] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Grant, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Benedetti, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Cao, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Hallam, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Lockhart, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Sto-  jevic, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Green, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Severini, Hierarchical quantum clas-  sifiers, npj Quantum Information 4, 1 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  [2] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Havl´ıˇcek, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' C´orcoles, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Temme, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Harrow, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Kan-  dala, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Chow, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Gambetta, Supervised learning with  quantum-enhanced feature spaces, Nature 567, 209 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  [3] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Tacchino, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Barkoutsos, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Macchiavello, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Tavernelli,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Gerace, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Bajoni, Quantum implementation of an arti-  ficial feed-forward neural network, Quantum Science and Tech-  nology 5, 044010 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  [4] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Chen, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Nurdin, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Yamamoto, Temporal Informa-  tion Processing on Noisy Quantum Computers, Physical Re-  view Applied 14, 024065 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  7  [5] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Suzuki, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Gao, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Pradel, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Yasuoka, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Yamamoto,  Natural quantum reservoir computing for temporal information  processing, Scientific Reports 12, 1353 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  [6] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Meyer, Fisher Information in Noisy Intermediate-Scale  Quantum Applications, Quantum 5, 539 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  [7] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Ma, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Gokhale, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Zheng, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Zhou, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Yu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Jiang,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Maurer, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Chong, Adaptive Circuit Learning for  Quantum Metrology, arXiv:2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='08702 [quant-ph] (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  [8] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Marciniak, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Feldker, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Pogorelov, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Kaubruegger,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Vasilyev, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' van Bijnen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Schindler, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Zoller, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Blatt,  and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Monz, Optimal metrology with programmable quantum  sensors, Nature 603, 604–609 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  [9] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Sim, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Johnson, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Aspuru-Guzik, Expressibility  and Entangling Capability of Parameterized Quantum Circuits  for Hybrid Quantum-Classical Algorithms, Advanced Quantum  Technologies 2, 1900070 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  [10] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' LaRose and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Coyle, Robust data encodings for quantum  classifiers, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' A 102, 032420 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  [11] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Schuld, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Sweke, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Meyer, Effect of data encod-  ing on the expressive power of variational quantum-machine-  learning models, Physical Review A 103, 032430 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  [12] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Abbas, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Sutter, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Zoufal, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Lucchi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Figalli, and  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Woerner, The power of quantum neural networks, Nature  Computational Science 1, 403–409 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  [13] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Wu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Yao, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Zhang, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Zhai, Expressivity of quantum  neural networks, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Research 3, L032049 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  [14] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Wright and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' McMahon, The Capacity of Quantum  Neural Networks, arXiv:1908.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='01364 [quant-ph] (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  [15] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Du, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Hsieh, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Liu, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Tao, Expressive power of  parametrized quantum circuits, Physical Review Research 2,  033125 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  [16] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Holmes, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Sharma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Cerezo, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Coles, Connect-  ing ansatz expressibility to gradient magnitudes and barren  plateaus, PRX Quantum 3, 010313 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  [17] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Dambre, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Verstraeten, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Schrauwen, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Massar, Infor-  mation Processing Capacity of Dynamical Systems, Scientific  Reports 2, 514 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  [18] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Fujii and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Nakajima, Harnessing Disordered-Ensemble  Quantum Dynamics for Machine Learning, Physical Review  Applied 8, 024030 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  [19] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Benedetti, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Lloyd, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Sack, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Fiorentini, Parame-  terized quantum circuits as machine learning models, Quantum  Science and Technology 4, 043001 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  [20] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Mart´ınez-Pe˜na, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Nokkala, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Giorgi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Zambrini, and  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Soriano, Information processing capacity of spin-based  quantum reservoir computing systems, Cognitive Computation  (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  [21] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Schuld and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Petruccione, Machine Learning with Quan-  tum Computers, Quantum Science and Technology (Springer  International Publishing, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  [22] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Garc´ıa-Beni, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Giorgi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Soriano, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Zam-  brini, Scalable photonic platform for real-time quantum reser-  voir computing, arXiv:2207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='14031 [quant-ph] (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  [23] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Arrasmith, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Cerezo, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Czarnik, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Cincio, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Coles,  Effect of barren plateaus on gradient-free optimization, Quan-  tum 5, 558 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  [24] IBM Quantum, https://quantum-computing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='ibm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='com (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  [25] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Kalfus, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Ribeill, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Rowlands, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Krovi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Ohki, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Govia, Hilbert space as a computational  resource in reservoir computing, Physical Review Research 4,  033007 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  [26] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Vedral, The role of relative entropy in quantum information  theory, Reviews of Modern Physics 74, 197 (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  [27] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Modi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Paterek, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Son, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Vedral, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Williamson,  Unified view of quantum and classical correlations, Physical  Review Letters 104, 080501 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  [28] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Nielsen and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Chuang, Quantum computation and quan-  tum information (Cambridge University Press, 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  [29] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Giovannetti, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Lloyd, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Maccone, Quantum metrology,  Physical Review Letters 96, 010401 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  [30] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Mart´ınez-Pe˜na, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Giorgi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Nokkala, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Soriano, and  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Zambrini, Dynamical phase transitions in quantum reservoir  computing, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 127, 100502 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  8  Appendix A: Table of Symbols and Abbreviations  Abbreviations  NISQ  Noisy Intermediate Scale Quantum  (Q)ML  (Quantum) Machine Learning  QSN  Quantum Sampling Noise  VQC  Variational Quantum Circuits  PS  Product System  ES  Entangled System  EC  Total Expressive Capacity,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' CT  ETC  Expected Total Correlation,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' ¯T  Symbols and notation  S  Number of shots  N  Number of inputs  L  Number of qubits  K  ≡ 2L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' number of measured features  u  Input  θ  Quantum system parameters  ˆρ  Generated quantum state  ˆ  Mk  Measured observable  W  Output weights (can be untrained)  ˜w  Optimal learned output weights on S-finite readout data  L  Loss function  bk  Label for eigenstate of ˆ  Mk  b(s)  Measurement outcome for shot s  xk  Expected features Tr{ ˆ  Mk ˆρ}  X(s)  k  Observed bit in shot s  ¯  Xk  Empirical observed feature 1/S �  s δ(b(s),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' bk)  ζk  Noise part in ¯  Xk  G  Gram matrix of expected features {xk}  V  Expected covariance matrix of random variable X(s)  k (u)  R  Noise-to-Signal matrix  β2  k  Eigen-NSR  y(k)  Principal feature  r(k)  Combination coefficients in y(k) = �  k′ r(k)  k′ xk′  ¯y(k)  ≡ �  k′ r(k)  k′ ¯  Xk′,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' noisy eigentask  ξ(k)  ≡ �  k′ r(k)  k′ ζk′,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' noise part in ¯y(k)  ˆOk  ≡ �  k′ r(k)  k′ |bk′⟩⟨bk′|,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' optimal measurement basis  ˆρM  ≡ �  k ˆρkk(u) |bk⟩⟨bk|,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' post-measurement state  Kc(S)  Cutoff index where β2  k reaches S  �  ( · )N  Quantity obtained from finite N sampling data  �  ( · )  Large N limit,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' that is limN→∞ �  ( · )N  TABLE I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Table of notations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Appendix B: Feature maps using quantum systems  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Details of input encodings into quantum systems  In the main text, we introduce the idea of encoding inputs into the state of a quantum system via a parameterized quantum  channel, reproduced below:  ˆρ(u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' θ) = U(u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' θ)ˆρ0  (B1)  Our analysis of EC presented in this work does not depend on the precise details of the quantum channel U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' For practical  calculations, however, we have to consider concrete models, about which we provide more details in this section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  9  To describe these models, we begin by first limiting to 1-D inputs as analyzed in the main text;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' generalizations to multi-  dimensional inputs u are straightforward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Then, we write Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (B1) in the form  ˆρ(u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' θ) = B(u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' θ)ˆρ0B†(u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' θ)  (B2)  In the main text, we have considered a model for dynamics of an L-qubit quantum system that is natively implementable on  modern quantum computing platforms: namely the ansatz of quantum circuits with single and two-qubit gates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' In this case,  which we refer to as the circuit ansatz (or C-ansatz for short), the operator B(u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' θ) takes the precise form  B(u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' θ) =  �  Rx  �θx  2  �  W(J)Rz  �  θz + θIu  �  Rx  �θx  2  ��τ  (C-ansatz)  (B3)  For completeness, we recall that Rx/z are Pauli-rotations applied qubit-wise, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Rz = �  l Rz(θz  l + θI  l u), while the entangling  gate acts between physically connected qubits in the device and can be written as W(J) = �  ⟨l,l′⟩ exp{−i J  2 ˆσz  l ˆσz  l′}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' We empha-  size here again that τ ∈ N+ is an integer, representing the number of repeated blocks in the C-ansatz encoding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' We note that  the actual operations implemented on IBMQ processors also include dynamics due to noise, gate, and measurement errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' As  discussed in the main text, the EC of a quantum system can be computed in the presence of these more general dynamics, and is  sensitive to the limitations introduced by them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  An alternative ansatz which we analyze in this SI, is where the operator B(u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' θ) describes continuous Hamiltonian dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  This ansatz is relevant to computation with general quantum devices, such as quantum annealers and more generally quantum  simulators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' In this case, which we refer to as the Hamiltonian ansatz (or H-ansatz for short),  B(u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' θ) = exp{−i ˆH(u)t}, ˆH(u) = ˆH0 + u · ˆH1  (H-ansatz)  (B4)  Here t is a continuous parameter defining the evolution time;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' and ˆH0 = �L  l,l′ J⟨l,l′⟩ˆσz  l ˆσz  l′ + �L  l=1 hx  l ˆσx  l + �L  l=1 hz  l ˆσz  l and  ˆH1 = �L  l=1 hI  l ˆσz  l .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The transverse x-field strength hx  l = ¯hx + εx  l and longitudinal z-drive strength hz,I  l  = ¯hz,I + εz,I  l  are all  randomly chosen and held fixed for a given realization of the quantum system,  εx,z,I  l  ∼ hx,z,I  rms N(0, 1),  (B5)  where N(0, 1) defines the standard normal distribution with zero mean and unit variance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' We consider nearest-neighbor inter-  actions Jl,l′, which can be constant Jl,l′ ≡ J, or drawn from Jl,l′ ∼ Unif[0, Jmax], where Unif[a, b] is a uniform distribution  with non-zero density within [a, b].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  As an aside, we note that the C-ansatz quantum channel described by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (B3) can be considered a Trotterization-inspired  implementation of the H-ansatz in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (B4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' In particular, if we set θx/z/I = hx/z/I∆ · τ, where t = ∆ · τ, and consider the  limit ∆ → 0 while keeping t fixed, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (B3) corresponds to a Trotterized implementation of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (B4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' This correspondence is  chosen for practical reasons, but is not necessary in our analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  The parameterized quantum channel characterizes how information is injected into the quantum system and processed by it;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  however, to probe information from the quantum system, one must apply an appropriate and feasible quantum measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  For extract information efficiently, we consider a wide family of observable ˆ  Mk: the only restriction of these observables is  that they must be a product of local observables, ˆ  Mk = ˆo1 ⊗ · · · ⊗ ˆoL, which mutually commute with each other (meaning  they are are simultaneously measurable).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' We consider two general schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The first one is the probability representation  ˆol ∈ {|0⟩⟨0| , |1⟩⟨1|}, while the second is the spin moments representation, ˆol ∈ {ˆI, ˆσz};' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' the former representation is used  throughout the main text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' We will show below that these two readout schemes are equivalent up to a unitary transformation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Extracting output features under finite sampling: expressions for features and covariances  Following evolution of the quantum system under the input-dependent Hamiltonian given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (B4), we extract certain  measurable observables that are used as outputs for any learning task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The form of observables is again chosen for compliance  with measurement protocols native to near-term quantum computing implementations: we consider Pauli z basis measurements  only (although this can be generalized easily).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' This means our algorithm has access only to diagonal terms in ˆρ(u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' We abbreviate  vectors ⃗Mk, ⃗ρ(u) ∈ RK such that ( ⃗Mk′)k = ( ˆ  Mk′)kk and (⃗ρ(u))k = ˆρ(u)kk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Then one can check for {+1, −1} readout:  ⃗Mk · ⃗Mk′ = Kδjj′, and the readout features can be expressed into dot product form xk(u) = Tr  �  ˆ  Mk ˆρ(u)  �  = ⃗Mk · ⃗ρ(u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' In  10  QRC, we hope to make full use of all functions in family {(⃗ρ(u))k}k∈[K] as readout features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The collection of all readout  features  x(u) =  �  �  �  �  x0(u)  x1(u)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  xK−1(u)  �  �  �  � =  �  �  �  �  �  ⃗M T  0  ⃗M T  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  ⃗M T  K−1  �  �  �  �  � ⃗ρ(u) =: U⃗ρ(u),  (B6)  The orthonormality of { ⃗Mk}k∈[K] implies that U is unitary up to an overall constant (in fact, U =  �  1  1  1 −1  �⊗L  is the  Hadamard matrix [28]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' This unitarity implies that the above transformation is information-preserving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' In particularly, this  guarantees the ability to reconstruct the diagonal QRC density matrix elements (via tomography), ⃗ρ(u) = U −1x(u), simply  computing the required inverse via the numerically-robust relationship U −1 = 1  K U T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  If each qubit has a readout error ϵ, that is, it will flip |0⟩ ↔ |1⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Then the transition probability of reading out |bk′⟩ from |bk⟩  will be ϵd(bk,bk′)(1 − ϵ)L−d(bk,bk′) where d(bk, bk′) is the Hamming distance between bk and bk′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Thus, readout errors can  furthermore be mathematically modeled by one more transition matrix (more precisely, a stochastic matrix):  x(u) = U  �  1 − ϵ  ϵ  ϵ  1 − ϵ  �⊗L  ⃗ρ(u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (B7)  The covariance of the X(u) ∈ {+1, −1}L (the random features for individual shot S = 1) can also be expressed easily:  V[X(u)] = U  �  diag(⃗ρ(u)) − ⃗ρ(u) · ⃗ρ(u)T �  U T  (B8)  where diag(⃗v) is a diagonal matrix that has the elements of ⃗v as entries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' To prove this expression, it suffices to verify that the  second order moments are entries  V[X(u)]k1k2 ≡ Tr  �  ˆ  Mk1 ˆ  Mk2 ˆρ(u)  �  =  K−1  �  k=0  ( ˆ  Mk1 ˆ  Mk2)kk ˆρkk(u) =  K−1  �  k=0  (U)k1k (U)k2k ˆρkk(u) =  �  Udiag (⃗ρ(u)) U T �  k1k2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (B9)  Appendix C: Information capacity with quantum sampling noise  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Definition of capacity for quantum systems with sampling noise  The function approximation universality (which will be formally stated in Appendix I), as a basic requirement of most neural  network model can be made concrete by defining a metric to quantify how well a given quantum system (generalizable to any  dynamical system) approximates general functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Suppose an arbitrary probability distribution p(u) for a random (scalar)  variable u defined in [−1, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' This naturally defines a function space L2  p([−1, 1]) containing all functions f : [−1, 1] → R with  � 1  −1 f 2(u)p(u)du < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The space is equipped with the inner product structure ⟨f1, f2⟩p =  � 1  −1 f1(u)f2(u)p(u)du.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' A standard  way to check the ability of fitting nonlinear functions by a physical system is the information processing capacity [17],  C[fℓ] = 1 −  min  Wℓ∈RK  � 1  −1  ��K−1  k=0 Wℓkxk(u) − fℓ(u)  �2  p(u)du  � 1  −1 fℓ(u)2p(u)du  ,  (C1)  where functions fℓ(u) are orthogonal target functions ⟨fℓ, fℓ′⟩p =  � 1  −1 fℓ(u)fℓ′(u)p(u)du = 0 for ℓ ̸= ℓ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The total expressive  capacity is computing the limitation CT ≡ �∞  ℓ=0 C[fℓ], capturing the ability of what type of function the linear combination of  physical system readout features can produce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Dambre’s argument claims that the total capacity must be upper bounded by the  number of features CT ≤ K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  While Dambre’s result is quite general [17], it neglects the limitations due to noise in readout features, a fact that is unavoidable  when using quantum systems in the presence of finite computational and measurement resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' In this appendix section, we  will focus on the impact of fundamental quantum readout noise on this upper bound under finite sampling S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Given u and S,  11  the quantum readout features ¯Xk(u) = 1  S  �S  s=1 X(s)  k (u) are stochastic variables (where X(s)  k  ∈ {−1, +1} are binary random  values).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The expectation vector and covariance matrix of ¯  X(u) can be expressed in terms of ⃗ρ(u), the diagonal entries of the  density matrix (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (B8))  E[ ¯  X(u)] ≡ x(u) = U⃗ρ(u),  (C2)  E[ ¯  X(u) ¯  XT (u)] − E[ ¯  X(u)]E[ ¯  X(u)]T ≡ 1  S Σ(u) = 1  S U  �  diag (⃗ρ(u)) − ⃗ρ(u) · ⃗ρ(u)T �  U T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (C3)  The dependence of readout features xk(u) on the input u can always be written in the form of a Taylor expansion,  xk(u) =  ∞  �  j=0  (T)kjuj  (C4)  where we define the transfer matrix T(θ) ≡ T ∈ RK×∞ that depends on the density matrix ˆρ(u), and in particular on  parameters θ characterizing the quantum system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  To determine the optimal capacity to compute an arbitrary normalized function f(u) = �∞  j=0(Y)juj using the noisy readout  features ¯  X(u) extracted from the quantum system,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' we need to find an optimal W such that  C[f] = 1 −  minW  � 1  −1  ��K−1  k=0 Wk ¯Xk(u) − f(u)  �2  p(u)du  � 1  −1 f(u)2p(u)du  (C5)  By expanding the numerator of the right-hand side for a given,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' finite number of shots S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' we find  � 1  −1  f(u)2p(u)du −  � 1  −1  �K−1  �  k=0  Wk ¯Xk(u) − f(u)  �2  p(u)du  = −  K−1  �  k1=0  K−1  �  k2=0  Wk1Wk2  � 1  −1  ¯Xk(u) ¯Xk2(u)p(u)du + 2  K−1  �  k=0  Wk  � 1  −1  ¯Xk(u)f(u)p(u)du  ≈ − 1  N  K−1  �  k1=0  K−1  �  k2=0  Wk1Wk2  N  �  n=1  ¯Xk1(u(n)) ¯Xk2(u(n)) + 2  N  K−1  �  k=0  Wk  N  �  n=1  ¯Xk(u(n))f(u(n)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (C6)  where we have approximated the integral over the input domain by a finite sum in the limit of a large number of inputs N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Next, note that if n ̸= n′, then Xk1(u(n)) and Xk2(u(n′)) are independent random variables (thought not necessarily identically  distributed).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The sums over N on the right hand side are therefore sums of bounded independent random variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' In the  limit of large N ≫ 1, the deviation between stochastic realizations of these sums and their expectation values is exponentially  suppressed, as determined by the Hoeffding inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Then,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' with large probability,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' the sums over N may be replaced by their  expectation values,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='� 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='f(u)2p(u)du −  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='� 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='�K−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='k=0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='Wk ¯Xk(u) − f(u)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='�2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='p(u)du  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='≈ − 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='N  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='K−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='k1=0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='K−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='k2=0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='Wk1Wk2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='N  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='n=1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='E[ ¯Xk1(u(n)) ¯Xk2(u(n))] + 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='N  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='K−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='k=0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='Wk  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='N  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='n=1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='E[ ¯Xk(u(n))f(u(n))]  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='= − 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='N  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='K−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='k1=0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='K−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='k2=0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='Wk1Wk2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='N  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='n=1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='xk1(u(n))xk2(u(n)) + 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='S Σ(u(n))k1k2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='+ 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='N  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='K−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='k=0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='Wk  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='N  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='n=1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='xk(u(n))f(u(n))  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='≈ −  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='K−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='k1=0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='K−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='k2=0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='Wk1Wk2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='� 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='xk1(u)xk2(u) + 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='S Σ(u)k1k2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='p(u)du + 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='K−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='k=0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='Wk  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='� 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='xk(u)f(u)p(u)du.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (C7)  The first approximation above comes from the Hoeffding inequality, where terms that are dropped are proportional to 1/  √  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  In going from the second to the third line, we have used Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (C3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The final expression is obtained by rewriting sums over u as  integrals, with an error proportional to 1/  √  N once more.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Thus we can say the original integral in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (C5) is approximately  equal to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (C7) to O(1/  √  N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  12  The first term in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (C7) does not depend explicitly on the function f(u) being constructed, and introduces quantities that are  determined entirely by the response of the quantum system of interest to inputs over the entire domain of u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' In particular, we  introduce the Gram matrix G ∈ RK×K as  (G)k1k2 =  � 1  −1  xk1(u)xk2(u)p(u)du =  ∞  �  j1=0  ∞  �  j2=0  (T)k1j1  �� 1  −1  uj1+j2p(u)du  �  (T)k2j2 ≡ (TΛTT )k1k2  (C8)  where in the second line we have also introduced the generalized Hilbert matrix Λ ∈ R∞×∞ as  (Λ)j1j2 =  � 1  −1  uj1+j2p(u)du.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (C9)  Secondly, we introduce the noise matrix V ∈ RK×K,  (V)k1k2 =  � 1  −1  Σ(u)k1k2 p(u)du =  � 1  −1  (xk(u) − xk1(u)xk2(u))p(u)du ≡ (D)k1k2 − (G)k1k2  (C10)  for index k satisfying ˆ  Mk = ˆ  Mk1 ˆ  Mk2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Here we have also introduced the second-order-moment matrix D ∈ RK×K such that  (D)k1k2 =  � 1  −1 xk(u)p(u)du.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Then, the noise matrix simply defines the covariance of readout features, and is therefore given  by V = D − G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  The second term in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (C7) depends on f(u) and can be simplified using the Λ matrix as well,  � 1  −1  xk(u)f(u)p(u)du =  ∞  �  j1=0  ∞  �  j2=0  (T)kj1  �� 1  −1  uj1+j2p(u)du  �  (Y)j2 = (TΛY)k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (C11)  With these definitions, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (C5) can be compactly written in matrix form as a Tikhonov regularization problem:  C[f] = max  W  �  −W T �  TΛTT + 1  S V  �  W + 2W T TΛY  YT ΛY  �  = 1 − min  W  �  �  �  ���Λ  1  2 TT W − Λ  1  2 Y  ���  2  + 1  S W T VW  YT ΛY  �  �  � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (C12)  The least-squares form ensures that the optimal value (argmin) �  w of W has closed form  �  w =  �  TΛTT + 1  S V  �−1  TΛY.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (C13)  Substituting w into the expression for C, we obtain the optimal capacity with which a function f can be constructed, which  takes the form of a generalized Rayleigh quotient  C[f] = YT ΛTT �  G + 1  S V  �−1 TΛY  YT ΛY  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (C14)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Eigentasks  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (C14) defines the optimal capacity of approximating an arbitrary function f(u) = �∞  j=0(Y)juj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' We can therefore  naturally ask which functions f maximise this optimal capacity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' To this end, we first note that the denominator of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (C14) is  simply a normalization factor that can be absorbed into the definition of the function f(u) being approximated, without loss of  generality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' More precisely, we consider:  ⟨f, f⟩p = 1 =  �  Λ  1  2 Y  �T �  Λ  1  2 Y  �  = YT ΛY.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (C15)  Then, we can rewrite the optimal capacity from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (C17) as  C[f] = YT Λ  1  2  �  QΛ  1  2 Y  �  (C16)  13  Here we have defined the matrix Q ∈ R∞×∞ as  Q = B  �  I + 1  S R  �−1  BT ,  (C17)  by introducing the matrix square root of G = G  1  2 G  1  2 , where G  1  2 ∈ RK×K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Then, R = G− 1  2 VG− 1  2 becomes the noise-to-  signal matrix, while the matrix B is given by  B = Λ  1  2 TT G− 1  2 ,  (C18)  The decomposition in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (C17) may be verified by direct substitution into Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (C16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The ability to calculate matrix powers and  in particular the inverse of G requires constraints on its rank, which we show are satisfied in Appendix C 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  We now consider the measure-independent part of the eigenvectors of Q, indexed Y(k), satisfying the standard eigenvalue  problem:  Q  �  Λ  1  2 Y(k)�  = CkΛ  1  2 Y(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (C19)  where k = 0, · · · , K − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' From Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (C16), it is clear that these eigenvectors have a particular meaning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Consider the function  y(k)(u) defined by the eigenvector Y(k), namely  y(k)(u) =  ∞  �  j=0  Y(k)  j  uj,  (C20)  which we will refer to from now on as eigentasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Suppose we wish to construct the function y(k)(u) using outputs obtained  from the physical system defined by Q in the S → ∞ limit (namely, with deterministic outputs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' At a first glance, before  we dive into solving the eigenproblem Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (C19), we do not know any relationship between y(k) and x(u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='The rest part of this  subsection is aiming to prove that y(k) must be a specific linear combination of features x(u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Then, the physical system’s  capacity for this construction is simply given by the corresponding eigenvalue Ck, as may be seen by substituting Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (C19)  into Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (C16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Formally, the y(k)(u) serves as the critical point (or stationary point) of the generalized Rayleigh quotient in  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (C14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Consequently, the function that is constructed with largest capacity then corresponds to the nontrivial eigenvector  with largest eigenvalue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  To obtain these eigentasks, we must solve the eigenproblem defined by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (C19).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Here, the representation of Q in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (C17)  becomes useful, as we will see that the eigensystem of Q is related closely to that of the noise-to-signal matrix R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' In particular,  we first define the eigenproblem of R,  R  �  G  1  2 r(k)�  = β2  kG  1  2 r(k)  (C21)  with NSR eigenvalues β2  k and corresponding eigenvectors r(k), which satisfy the orthogonality relation r(k′)T Gr(k) = δk,k′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Here the r(k) is equivalent to be defined as the solution to generalized eigen-problem:  Vr(k) = β2  kGr(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (C22)  This is because Vr(k) = G  1  2 RG  1  2 r(k) = β2  kG  1  2 G  1  2 r(k) = β2  kGr(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The prefactor G  1  2 is introduced for later convenience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (C21) then allows us to define the related eigenproblem  �  I + 1  S R  �−1  G  1  2 r(k) =  �  1 + β2  k  S  �−1  G  1  2 r(k)  (C23)  Next, we note that Q is related to the matrix in brackets above via a generalized similarity transformation defined by B,  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (C17).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' In particular, BT B = G− 1  2 GG− 1  2 = I ∈ RK×K, while we remark that BBT ̸= I since it is in R∞×∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' This  connection allow us to show that  Q  �  BG  1  2 r(k)�  = B  �  I + 1  S R  �−1  BT BG  1  2 r(k) =  1  1 + β2  k/S BG  1  2 r(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (C24)  Comparing with Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (C19), we can now simply read off both the eigenvalues and eigenvectors of Q,  Ck =  1  1+β2  k/S  Λ  1  2 Y(k) = BG  1  2 r(k)  �  =⇒ Y(k) = TT r(k)  (C25)  14  where we have used the definition of B from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (C18).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The functions defined by the eigenvectors Y(k) are automatically  orthonormalized:  �  y(k1), y(k2)�  p =  �  Λ  1  2 Y(k1)�T�  Λ  1  2 Y(k2)�  = r(k1)T G  1  2 BT BG  1  2 r(k2) = r(k1)T Gr(k2) = δk1k2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (C26)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Noisy eigentasks from readout features  We can now also discuss the interpretation of {β2  k} for a physical system - in this case a quantum circuit - for which {r(k)} are  known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Consider a single run of the quantum system under finite shots S, which yields a single instance of the readout features  ¯  X(u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' We can simply read off that an noisy version of the kth eigentask, ¯y(k)(u) can be constructed as  ¯y(k)(u) =  K−1  �  k′=0  r(k)  k′ ¯Xk′(u)  (C27)  which is equivalent to requiring the output weights W = r(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='The corresponding set of noisy function is also orthogonal, this  is because Vr(k) = β2  kGr(k) implies r(k)T Vr(k′) = β2  kδk,k′ and hence  �  ¯y(k1), ¯y(k2)�  p = r(k1)T  �  G + 1  S V  �  r(k2) =  �  1 + β2  k  S  �  δk1k2  (C28)  This equation can be further decomposed into two parts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Let the linear transformation of noise ξ(u) by defining ξ(k)(u) =  �K−1  k=0 r(k)  k′ ζk′(u)  Eu[y(k1)y(k2)] =  �  y(k1), y(k2)�  p = r(k1)T Gr(k2) = δk1k2,  (C29)  Eu[ξ(k1)ξ(k2)] =  �  ξ(k1), ξ(k2)�  p = 1  S r(k1)T Vr(k2) = β2  k1  S δk1k2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (C30)  It means that the combination {r(k) ∈ RK}k∈[K] not only produces orthogonal eigentasks {y(k)(u)} for signal, but also induces  a set of orthogonal noise functions {ξ(k)(u)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  If the quantum circuit can be run multiple times for a given S, multiple instances of ¯  X(u) can be obtained, from each of  which an estimate of the kth eigentask ¯y(k)(u) can be constructed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The expectation value of these estimates then simply yields  E[¯y(k)(u)] =  K−1  �  k′=0  r(k)  k′ E[ ¯Xk′(u)] =  K−1  �  k′=0  r(k)  k′ xk′(u) = y(k)(u)  (C31)  If we have access to only a single instance of ¯  X(u), however, and thus only one estimate ¯y(k)(u) (as y(k)(u) and ¯y(k)(u)  depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 7), it is useful to know the expected error in this estimate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' This error can be extracted from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (C12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' In  particular, requiring Y(k) = TT r(k), we have  ���Λ  1  2 TT r(k) − Λ  1  2 Y(k)���  2  + 1  S r(k)T Vr(k)  Y(k)T ΛY(k)  = 1  S r(k)T Vr(k) = β2  k  S .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (C32)  This mean squared error in using ¯y(k)(u) to estimate y(k)(u) over the domain of u decreases to zero for S → ∞ as expected,  since the noise in ¯  X decreases with S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' However, β2  k defines the S-independent contribution to the error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' In particular, this  indicates that at a given S, certain functions with lowers NSR eigenvalues β2  k may be better approximated using this physical  system than others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' We present in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 7 the measured features ¯  X, the eigentasks y and their S-finite version ¯y in a 6-qubit  Hamiltonian based system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The associated eigen-NSR spectrum, expressive capacity, and total correlations are also depicted for  both ES J ̸= 0 and PS J = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  15  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Expressive capacity  Given an arbitrary set of complete orthonormal basis functions fℓ(u) = �∞  j=0(Yℓ)juj,  ⟨fℓ, fℓ′⟩p =  �  Λ  1  2 Yℓ  �T �  Λ  1  2 Yℓ′  �  = δℓℓ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (C33)  The total capacity is independent of the basis choice  CT (S) =  ∞  �  ℓ=0  C[fℓ] =  ∞  �  ℓ=0  YT  ℓ Λ  1  2  �  Λ  1  2 TT  �  TΛTT + 1  S V  �−1  TΛ  1  2  �  Λ  1  2 Yℓ  = Tr  �  Λ  1  2 TT  �  TΛTT + 1  S V  �−1  TΛ  1  2  �  = Tr  ��  G + 1  S V  �−1  G  �  =  K−1  �  k=0  1  1 + β2  k  S  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (C34)  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Estimation in case of nonlinear functions after linear output layer  Usually, instead of taking the linear transformation W · ¯  X, the training process can involve some complicated nonlinear  activation functions or classical kernel, which may also be fed into a non-quadratic nonlinear loss function afterwards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' These  two processes can be unified to be σNL( ¯  X(u)) with any smooth function σNL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' In this subsection, we show how to translate our  result obtaining from quadratic nonlinear function Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (C5) into a more general loss function with form of  L = Eu[σNL( ¯  X)]  (C35)  Now let us first transform all noisy measured features { ¯Xk} into the naturally orthogonal basis of signal {y(k)} and noise {ξ(k)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  ¯Xk′(u) ≡  K−1  �  k=0  Γk′k(y(k)(u) + ξ(k)(u)),  (C36)  such transformation of Γ ∈ RK×K must uniquely exist, this is because all K of {r(k)} are linearly independent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Recall  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (C30) claims that Eu[ξ(k)] = 0 and Eu[ξ(k)ξ(k′)] = β2  kδkk′/S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' we can deal with the nonlinearity by taking the quadratic  expansion,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' where ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' we get  L = Eu[σNL( ¯  X)] = Eu[σNL(Γ¯y)] = Eu  �  σNL  ��  k  Γ0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='k(y(k) + ξ(k)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' · · · ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  �  k  ΓK−1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='k(y(k) + ξ(k))  ��  ≈ Eu[σNL(Γy)] +  K−1  �  k=0  Eu  �∂σNL  ∂y(k) ξ(k)  �  + 1  2  K−1  �  k1=0  K−1  �  k2=0  Eu  �  ∂2σNL  ∂y(k1)∂y(k2) ξ(k1)ξ(k2)  �  = Eu[σNL(Γy)] + 1  2  K−1  �  k1=0  K−1  �  k2=0  Eu  �  ∂2σNL  ∂y(k1)∂y(k2) ξ(k1)ξ(k2)  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (C37)  where the first order terms vanish due to Hoeffding inequality again.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' We then make a further approximation of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (C37) by  replacing the ξ(k1)ξ(k2) with its u-average Eu[ξ(k1)ξ(k2)] = δk1k2β2  k1/S:  L ≈ Eu[σNL(Γy)] +  K−1  �  k=0  β2  k  S · Eu  � ∂2σNL  (∂y(k))2  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (C38)  In fact, any of the second terms can be further simplified by chain rule: L ≈ Eu[σNL(Γy)] + �  k  β2  k  S · Eu[(ΓT ∇2  xσNLΓ)kk].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  The approximation in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (C38) is rough, but it still gives us a sufficient reason to do the following manipulation: for optimized  L , the dependence on y(k) with β2  k/S > 1 will be strongly suppressed in large-N limit, hence we can pre-exclude the eigentasks  whose β2  k/S > 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Let us use one typical example, the widely used logistic regression in classification, to illustrate our argument here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' As what  we will introduce in Appendix I, the target function is the conditional probability distribution f(u) := Pr[u ∈ C1|u] in such  16  classification model (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (I4)), and then there is one more layer of softmax and cross-entropy function acting on linear  map L = Eu[H(f(u), σ(W · ¯  X(u)))] where σ is sigmoid function (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' softmax function σ(z) = 1/(1 + exp(−z))), and  H(p, q) = −p ln q − (1 − p) ln(1 − q) is the cross-entropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Especially, any linear combination of { ¯Xk} can be translated into  linear combination  W · ¯  X(u) ≡  K−1  �  k=0  Ωk · (y(k)(u) + ξ(k)(u)),  (C39)  Again, such vector Ω = ΓT W must also uniquely exist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  For any σNL = g(W · x), one always have ΓT ∇2  xσNLΓ =  g′′(Ω · y)ΩT Ω:  L ≈ Eu[H(f, σ(Ω · y))] +  �K−1  �  k=0  β2  k  S Ω2  k  �  Eu[σ(Ω · y)(1 − σ(Ω · y))] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (C40)  It helps us read from the prefactor β2  k/S induces a natural regularization on Ωk in loss function, in addition to the S-infinity  term limS→∞ L = Eu[H(f, σ(Ω · y))].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' We will leave the detailed discussion of this important application in Appendix H and  Appendix I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Proof that the Gram matrix G is full rank  Recall that before we analytically find the eigenvectors of Q, we first show that the matrix G is invertible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' It comes from that  all K readout features {xk(u)}k∈[K] being linear independent is entirely equivalent to the full-rankness of the corresponding  Gram matrix Rank(G) = K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Thanks to the linearity of readout, we can show such linear independence by contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Suppose on the contrary there exists coefficients {ck}k∈[K] such that  K−1  �  k=0  ckxk(u) = Tr  ��K−1  �  k=0  ck ˆ  Mk  �  U(u)ˆρ0  �  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (C41)  However, this means that the quantum observable �K−1  k=0 ck ˆ  Mk is a zero-expectation readout-qubit quantity for any state U(u)ˆρ0  under arbitrary input u, which is impossible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' This shows the linear independence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Furthermore, we then argue that it ensures G  has no non-trivial null space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' This is because that any {ck}k∈[K] will satisfy  K  �  k1,k2=1  ck1ck2(G)k1,k2 =  � 1  −1  � K  �  k1=1  ck1xk1(u)  �� K  �  k2=1  ck2xk2(u)  �  p(u)du =  �K−1  �  k=0  ckxk,  K−1  �  k=0  ckxk  �  p  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (C42)  where the RHS is the norm of function �K−1  k=0 ckxk(u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The summation �K  k1,k2=1 ck1ck2(G)k1,k2 = 0 vanishes if and only  if function �K−1  k=0 ckxk(u) is a zero function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' That is why the linear independence of features {ck}k∈[K] is equivalent to that  symmetric matrix G has no zero eigenvalues, namely Rank(G) = K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Numerically speaking, this relation always holds in  general as long as assuming this is for the case where N ≫ K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Simplifying the noise-to-signal matrix and its eigenproblem  We have shown that the problem of obtaining the eigentasks for a generic quantum system, and deducing its expressive  capacity under finite measurement resources, can be reduced simply to solving the eigenproblem of its noise-to-signal matrix  R, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (C21).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Note that constructing R = G− 1  2 VG− 1  2 requires computing the inverse of G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' However, G can have small  (although always nonzero) eigenvalues, especially for larger systems, rendering it ill-conditioned and making the computation  of R numerically unstable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Fortunately, certain simplifications can be made to derive an equivalent eigenproblem that is much  easier to solve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  To begin, we first note that so far, we have placed no requirements on the specific form of measurement operators { ˆ  Mk}, and  thus the readout features xk(u) = Tr{ ˆ  Mk ˆρ(u)} are also unspecified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Our analysis thus far holds for any set of measurement  operators that describe a complete set of commuting observables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' However, specific choices of measurement operators can  17  simplify the form of the matrices G and V involved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' In particular, if one chooses ˆ  Mk to be the projections onto the computational  basis, ˆ  Mk = |bk⟩ ⟨bk|, then according to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (B8), by setting U = I we have x(u) ≡ ⃗ρ(u), which we refer to as the probability  representation of readout features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Practically, the probability representation is native to measurement schemes in contemporary  quantum processors, and therefore minimizes the required post-processing of readout features obtained from a real device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' More  importantly, although it is related to any other readout feature representation via a unitary transformation, the strength of the  probability representation lies in the fact that it renders the second-order moment matrix D diagonal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' In particular,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (D)k1k2 =  � �K−1  k=0 (G)kk1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' if k1 = k2  0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  if k1 ̸= k2  (in probability representation of readout features)  (C43)  Using V = D − G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' we can rewrite the eigenproblem for R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  R  �  G  1  2 r(k)�  = β2  kG  1  2 r(k)  =⇒ G− 1  2 (D − G)G− 1  2  �  G  1  2 r(k)�  = β2  kG  1  2 r(k)  =⇒ G−1Dr(k) = (1 + β2  k)r(k)  (C44)  Finally,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' considering the inverse of the matrix on the left hand side,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' we obtain the simplified eigenproblem for the matrix D−1G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  D−1Gr(k) = (1 + β2  k)−1r(k) ≡ αkr(k),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (C45)  which shares eigenvectors with R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' and whose eigenvalues are a simple transformation of the NSR eigenvalues β2  k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Impor-  tantly, constructing D−1G no longer requires calculating any powers of G, and when further choosing readout features in the  probability representation, it relies only on the inversion of a simple diagonal matrix D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  The matrix D−1G has significance in spectral graph theory, when interpreting the Gram matrix G as the adjacency matrix of  a weighted graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' This connection is elaborated upon in Appendix C 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Connections to spectral graph theory  Let us have a small digression to the graphic theoretic meaning of G and D−1G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Now we consider a weighted graph with  adjacency matrix G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' In spectral graph theory, the matrix D−1G is exactly the random walk matrix associated with graph G, and  then the second order matrix D happens to be the degree matrix of this graph since (D)kk = �K−1  k′=0(G)kk′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Then the eigentask  combination coefficient r(k) is precisely the right eigenvector of random walk matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Another concept associated with a graph  is I − D− 1  2 GD− 1  2 , the normalized Laplacian matrix of G, while the matrix D− 1  2 GD− 1  2 is always referred to be normalized  adjacency matrix in many literatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The eigenproblem of normalized adjacency matrix can also be solved easily, because  D− 1  2 GD− 1  2  �  D  1  2 r(k)�  = D  1  2 D−1Gr(k) = αk  �  D  1  2 r(k)�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (C46)  From perspective of spectral graph theory, roughly speaking, a reservoir with stronger ability to resist noise are those who has  more “bottlenecks” in graph G’s connectivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The extreme case is supposing that αk = 1 (or 1 − αk = 0) for all k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' According  the basic conclusion in spectral graph theory, the normalized Laplacian matrix has K zero eigenvalues iff the graph G is fully  disconnected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' This gives us the condition when noisy information capacity obtain its upper bound K: there exists a partition  {Domk}k∈[K] of domain Dom = [−1, 1] such that ˆρkk(u) = 1 iff u ∈ Domk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Appendix D: Spectral analysis based on finite statistics  While Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (C45) is a numerically simpler eigenproblem to solve than Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (C21), it still requires the approximation of G (recall  that D can be obtained from G) from readout features ¯  X(u) under finite sampling, due to the finiteness of shots S, the number  of input points N, and also the number of realizations of readout features for a given S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' In what follows, we show how an  approximation �GN of G can be constructed from finitely-sampled readout features, as relevant for practical quantum devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Secondly, we also describe an approach to obtain the eigentasks y(k)(u) and corresponding NSR eigenvalues β2  k that avoids  explicit construction of the Gram matrix, and is thus even more numerically robust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  18  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Approximating eigentasks and NSR eigenvalues under finite S and N  For practical computations, readout features ¯  X(u) from the quantum system for finite S can be computed for a discrete set  of u(n) ∈ [−1, 1] for n = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' , N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Labelling the corresponding readout features ¯  X(u(n)), we can define the regression matrix  constructed from these readout features,  �FN ≡ ( ¯  X(u(1)), ¯  X(u(2)), · · · , ¯  X(u(N)))T =  �  �  �  ¯X0(u(1)) · · ·  ¯XK−1(u(1))  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  ¯X0(u(N)) · · ·  ¯XK−1(u(N))  �  �  � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (D1)  Here, �FN ∈ RN×K, with subscript N indicating its construction from a finite set of N inputs, is a random matrix due to the  stochasticity of readout features;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' in particular it can be written as:  �FN = FN +  1  √  S  Z(FN)  (D2)  where (FN)nk = E[ ¯Xk(u(n))] = xk(u(n)), and Z is the centered multinomial stochastic process, so that E[�FN] = FN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Using this regression matrix �FN, we can obtain an estimation of the Gram matrix and second order moment matrix, which  we denote �GN and �DN, and whose matrix elements are defined via  ( �GN)k1k2 ≡ 1  N  N  �  n=1  ¯Xk1(u(n)) ¯Xk2(u(n)) = 1  N (�FT  N �FN)k1k2 ≈  � 1  −1  ¯Xk1(u) ¯Xk2(u)p(u)du,  (D3)  ( �DN)k1k2 ≡ δk1,k2  1  N  N  �  n=1  ¯Xk1(u(n)) ≈ δk1,k2  � 1  −1  ¯Xk1(u)p(u)du.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (D4)  While the quantities �GN and �DN are computed from stochastic readout features, their stochastic contributions are suppressed  in the large N limit by the Hoeffding inequality for sums of bounded stochastic variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' In particular, we can define their  deterministic limit for N → ∞, according to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (C7), as  �G ≡ lim  N→∞  1  N (�FT  N �FN)k1k2 = G + 1  S V = G + 1  S (D − G),  (D5)  �D ≡ lim  N→∞  �DN = D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (D6)  Inverting the above expressions allow us to express the Gram matrix G and second-order moment matrix D in terms of the  estimates �G and �D computed using a finite number of shots S,  G =  S  S − 1  �G −  1  S − 1  �D,  (D7)  D = �D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (D8)  We see that to lowest order in 1  S , G ≈ �G and D ≈ �D, which is what one might expect naively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' However, we clearly see that  the estimation of G can be improved by including a higher-order correction in 1  S .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' This contribution arises due to the highly-  correlated nature of noise and signal for quantum systems: we are able to estimate the noise matrix �G and �D using knowledge  of the readout features, and correct for the contribution to �G and �D that arises from this noise matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' We will see that this  contribution will be important in more accurately approximating quantities of interest derived from G, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  To this end, we recall that our ultimate aim is not just to estimate G and D, but to solve the eigenproblem of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (C45).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Using  the above relation, we can then establish �D−1 �G = S−1  S D−1G + 1  S I, and write Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (C45) in a form entirely in terms of �G and  �D,  D−1Gr(k) = (1 + β2  k)−1r(k),  =⇒ �D−1 �Gr(k) =  �S − 1  S  (1 + β2  k)−1 + 1  S  �  r(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (D9)  19  5  10  15  20  25  30  Order k  100  101  102  103  104  105  Eigen-NSRs β2  k  β2  k, S → ∞  ˜β2  N,k, S = 102  ˜β2  k, S = 102  S· ˜β2  N,k  (S−1)− ˜β2  N,k, S = 102  S = 102  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Eigen-analysis in L = 5 H-ansatz system by taking S = 102 shots on each of N = 104 samples, with true eigen-NSRs β2  k (black),  S-finite sampled ˜β2  N,k (blue) and corrected (S · ˜β2  N,k)/((S − 1) − ˜β2  N,k) (purple).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' ˜β2  k, the large N limit of ˜β2  N,k is also plotted in red for  comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The data correction is necessary since all ˜β2  N,k are below the S = 102, and the corrected data show much better performance  even if β2  k ≫ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The estimated line (in purple) are cutoff at k = 25 since all sampled ˜β2  N,k after that are larger the S − 1 so that they are not  correctable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Note that the final form is conveniently another eigenproblem, now for the finite-S matrix �D−1 �G:  �D−1 �G˜r(k) = (1 + ˜β2  k)−1˜r(k) ≡ ˜αk ˜r(k),  (D10)  whose eigenvalues and eigenvectors can be easily related to the desired eigenvalues β2  k and eigenvectors r(k) of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (C45).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Following some algebra, we find:  β2  k =  S  (S − 1) − ˜β2  k  ˜β2  k = ˜β2  k +  ∞  �  j=1  ˜β2  k  �  1 + ˜β2  k  �j � 1  S  �j  ,  (D11)  r(k) = ˜r(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (D12)  From Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (D11), we see that to lowest order in 1  S , β2  k ≈ ˜β2  k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' However, this expression also supplies corrections to higher orders  in 1  S , which are non-negligible even for β2  k < S, as we see in example of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' In contrast, the estimated eigenvectors ˜r(k) to  any order in 1  S equal the desired eigenvectors r(k) without any corrections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Of course, in practice we do not have access to the matrices �G and �D, as these are only defined precisely in the limit  where N → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' However, for large enough N, we can approximate these matrices to lowest order by their finite N values,  �G = �GN + O  � 1  N  �  and �D = �DN + O  � 1  N  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Then, the eigenproblem in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (D10) can be expressed in the final form,  �D−1  N �GN ˜r(k)  N = (1 + ˜β2  N,k)−1˜r(k)  N ≡ ˜αN,k ˜r(k)  N ,  (D13)  where the eigenvalues ˜β2  N,k, ˜αN,k and eigenvectors ˜r(k)  N in the large N limit must satisfy  lim  N→∞  ˜β2  N,k = ˜β2  k,  lim  N→∞ ˜αN,k = ˜αk,  lim  N→∞ ˜r(k)  N = ˜r(k) ≡ r(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (D14)  Here the invertibility of the empirically-computed matrix �DN required for Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (D13) is numerically checked, based on which  we can establish a better numerical method in Appendix D 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (D13) represents the eigenproblem whose eigenvalues ˜β2  N,k and eigenvectors ˜r(k)  N we actually calculate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' For large enough  N and under finite S, we can use these as valid approximations to the eigenvalues and eigenvectors of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (D10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' This finally  enables us to directly estimate the N, S → ∞ quantities β2  k and r(k) using Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (D11), (D12):  β2  k ≈  S · ˜β2  N,k  (S − 1) − ˜β2  N,k  = 1 − ˜αN,k  ˜αN,k − 1  S  ,  (D15)  r(k) ≈ ˜r(k)  N .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (D16)  20  0  5  10  15  −1  0  1  Coefficient r(k)  r(1): β2  1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0 v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' ˜r(1)  N :  1−˜αN,1  ˜αN,1−1/S = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  Eigenvector of D−1G  Eigenvector of ˜D−1  N ˜GN  0  5  10  15  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='25  r(2): β2  2 = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='656 v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' ˜r(2)  N :  1−˜αN,2  ˜αN,2−1/S = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='663  0  5  10  15  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  r(3): β2  3 = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='898 v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' ˜r(3)  N :  1−˜αN,3  ˜αN,3−1/S = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='03  0  5  10  15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  r(4): β2  4 = 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='661 v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' ˜r(4)  N :  1−˜αN,4  ˜αN,4−1/S = 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='824  0  5  10  15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  Coefficient r(k)  r(5): β2  5 = 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='548 v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' ˜r(5)  N :  1−˜αN,5  ˜αN,5−1/S = 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='571  0  5  10  15  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  r(6): β2  6 = 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='166 v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' ˜r(6)  N :  1−˜αN,6  ˜αN,6−1/S = 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='382  0  5  10  15  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  r(7): β2  7 = 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='809 v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' ˜r(7)  N :  1−˜αN,7  ˜αN,7−1/S = 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='513  0  5  10  15  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  r(8): β2  8 = 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='107 v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' ˜r(8)  N :  1−˜αN,8  ˜αN,8−1/S = 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='635  0  5  10  15  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  Coefficient r(k)  r(9): β2  9 = 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='874 v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' ˜r(9)  N :  1−˜αN,9  ˜αN,9−1/S = 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='21  0  5  10  15  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  r(10): β2  10 = 111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='001 v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' ˜r(10)  N :  1−˜αN,10  ˜αN,10−1/S = 109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='021  0  5  10  15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  r(11): β2  11 = 151.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='254 v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' ˜r(11)  N :  1−˜αN,11  ˜αN,11−1/S = 144.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='208  0  5  10  15  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  r(12): β2  12 = 248.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='423 v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' ˜r(12)  N :  1−˜αN,12  ˜αN,12−1/S = 233.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='445  0  5  10  15  Index k′ of r(k)  k′  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  Coefficient r(k)  r(13): β2  13 = 333.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='471 v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' ˜r(13)  N :  1−˜αN,13  ˜αN,13−1/S = 348.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='828  0  5  10  15  Index k′ of r(k)  k′  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  r(14): β2  14 = 416.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='321 v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' ˜r(14)  N :  1−˜αN,14  ˜αN,14−1/S = 409.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='548  0  5  10  15  Index k′ of r(k)  k′  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  r(15): β2  15 = 655.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='346 v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' ˜r(15)  N :  1−˜αN,15  ˜αN,15−1/S = 743.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='085  0  5  10  15  Index k′ of r(k)  k′  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  r(16): β2  16 = 2191.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='863 v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' ˜r(16)  N :  1−˜αN,16  ˜αN,16−1/S = 1945.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='381  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Estimating NSR eigenvalues and corresponding eigentask coefficients under finite statistics (N = 300, S = 1000) in a 4-qubit  H-encoding system, and comparison with theoretical value for N → ∞, S → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  It is clear that the approximation of β2  k to lowest order will be an underestimate, as the contribution of order 1  S is positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' In  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 6, we plot the estimated eigenvectors ˜r(k)  N computed under finite statistics (N = 300, S = 1000, where these two numbers  are relevant for IBM quantum processors) in H-encoding, together with the N, S → ∞ eigenvectors r(k), and the estimated  eigenvalues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Gram matrix-free construction to approximate eigentasks and NSR eigenvalues  If we consider Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (D13) and multiply through by D  − 1  2  N , the resulting equation can be written as an equivalent eigenproblem,  1  N  �D  − 1  2  N �FT  N �FN �D  − 1  2  N  �  �D  1  2  N ˜r(k)  N  �  = ˜αN,k  �  �D  − 1  2  N ˜r(k)  N  �  (D17)  where we have also written �GN =  1  N �FT  N �FN as in the previous section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Note that as written above, the eigenproblem is  entirely equivalent to obtaining the singular value decomposition of the matrix  1  √  N �D  − 1  2  N �FT  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' This particular normalization factor  1  √  N �D  − 1  2  N  is different from the standard z-score of principal components analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' To obtain the combination coefficients r(k),  let t(k) ∈ RK be the left singular vector of  1  √  N �D  − 1  2  N �FT  N (which is also the eigenvector of 1  N �D  − 1  2  N �FT  N �FN �D  − 1  2  N  ≈ D− 1  2 �GD− 1  2  in the large N limit).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Then r(k) = �D  − 1  2  N t(k) ∈ RK can be treated as the combination prefactor of ˆ  Mk, to obtain the observables  which correspond to the eigentasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The merit of SVD analysis of  1  √  N �D  − 1  2  N �FT  N is that we only need to work with a K-by-N  matrix of features �FN, which is numerically cheaper than further constructing a Gram matrix 1  N �FT  N �FN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' We will explore more  about the usage of our technique in sense of PCA in Appendix H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  21  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Eigen analysis in a 6-qubit H-ansatz system (with N = 5000 and S = 1000) forming a 1D ring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The Hamiltonian parameters are  chosen randomly with zero-mean and variance (hx  rms, hz  rms, hI  rms) = (20, 5, 5), and t = 5 (See Appendix B 1 for details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Coupling strength  is uniformly J ̸= 0 (ES) or J = 0 (PS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (a) All 2L = 64 noisy features ¯  Xk(u) and (b) noisy eigentasks ¯y(k)(u) = r(k) · ¯  X(u) for selected k  from the features in (a), as well as their expected values y(k)(u) = limS→∞ ¯y(k)(u) = r(k) · x(u) (black).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (c) NSR spectrum β2  k and (d) CT  vs shots S for both ES and PS encodings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (e) CT at S = 105 and (f) ETC, ¯T (ˆρM) in representative random 6-qubit H-ansatz, as a function of  coupling strength J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The peaks of capacity and correlation coincide, around J ∼ hx  rms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Appendix E: H-ansatz quantum systems: NSR spectra, expressive capacity, and eigentasks  In this section, we evaluate the EC for quantum systems described by the H-ansatz introduced in Appendix B 1, as an example  of how EC can be efficiently computed for a variety of general quantum systems, and is not just restricted to parameterized  quantum circuits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The results of the analysis are compiled in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 7, and discussed below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 7(a) presents the set of features { ¯Xk(u)} for typical L = 6 qubit ES and PS at S = 1000 with randomly chosen  parameters (referred to as encodings, see caption).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The resultant noisy eigentasks {¯y(k)(u)} and NSR spectra {β2  k} extracted  via the eigenvalue analysis are shown in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 7(b) and 7(c) respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' In the side-by-side comparison in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 7(b), we clearly  see the J = 0 ansatz transitioning to a regime with more noise at much lower k than the J ̸= 0 ansatz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' This is reflected in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 7(c), the β2  k spectrum, having a much flatter slope for larger k (note the plot is semilog).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Finally, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 7(d) shows the EC of  both systems as a function of S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' EC rapidly rises for small S for both systems, but the rise of the J = 0 system is steeper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' After  a certain threshold in S, however, the ES grows more rapidly, approaching the upper bound 26 = 64 with S ∼ 108;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' in contrast,  the PS has a significantly lower CT .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  For J → ∞ we also have ¯T = 0 because ˆρ0 = |0⟩⟨0|⊗L is an eigenstate of the encoding (ˆρ(u) = ˆρ0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' This implies there  must be a peak at some intermediate J, which for both EC and ETC occurs when the coupling is proportional to the transverse  field J ∼ hx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Our results elucidate the same kind of improvement, as can be observed when we consider how the EC C changes with J, and  compare it to the total correlation ETC ¯T , as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 7(f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' For J → 0 we have a PS with ¯T = 0, whereas in the J → ∞  we also have ¯T = 0 because ˆρ0 = |0⟩⟨0|⊗L is an eigenstate of the encoding (ˆρ(u) = ˆρ0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' This implies there must be a peak at  some intermediate J, which for both EC and ETC occurs when the coupling is proportional to the transverse field J ∼ hx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' At  finite S, increased ETC is directly related to a higher EC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Another interesting aspect is the clear trend seen in the maximization of EC around J ∼ hx  rms for various hx  rms, possibly  hinting at the role of increased entanglement around the MBL phase transition in random spin systems [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' This trend is  consistent with results in quantum metrology – in general, the SNR obtained from averaging L uncorrelated probes scales as  1/  √  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' This scaling can become favorable in the presence of entanglement and other non-classical correlations, in which case the  scaling of the SNR can show up to a quadratic improvement 1/L [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' For even larger J, we find that ˆρ(u) → ˆρ0 = |0⟩⟨0|⊗L,  which clearly reduces ¯T , but also CT as the quantum system state becomes u-independent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  ES  PSES  PS10  20  30  50  4010  20  30  40  50W  >>>>>>>>>>>>>>>  >>>>>>>>>22  Appendix F: Scaling with quantum system size  An important question in quantum machine learning applications is the possible advantage of using larger quantum systems  for information processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' In this section, we present preliminary results of scaling with quantum system size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The left panel of  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 8 shows EC vs L at select S values for H-ansatz, while the right panel shows two encodings in the C-ansatz device, as well  as their noisy simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' In both plots, the dashed line indicates the S → ∞ result CT = 2L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' We see that the EC increases  when adding more qubits into the Ising chain for the H-ansatz, or when increasing the number of circuit qubits L for the C-  ansatz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Note, however, that at any finite S the noise-constrained EC falls off the exponential bound for S → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The dropoff  is particularly severe for the IBMQ device, where we are limited to just S ∼ 104, which significantly suppresses the EC even  for L = 7 qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Note, however, that even if one is well below CT = 2L due to this finite sampling constraint, increasing the  dimension of the quantum system is always an effective way to increase the EC, particularly when compared to the logarithmic  growth with S of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 2 of Main Text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  3  4  5  6  7  Qubit numbers L  0  32  64  96  128  EC CT  S = 101  S = 102  S = 103  S = 104  S = 105  S = 106  S = 107  S → ∞  3  4  5  6  7  Qubit numbers L  0  20  40  EC CT  S =10  S =27  S =210  S =214  S → ∞  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (a) H-ansatz and (b) C-ansatz at finite S as a function of qubit number L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Various colours indicate different S values, with the S → ∞  bound in dashed black.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Individual noisy simulations are indicated in small and transparent dots, with their average as a thick line, and the EC  of the C-ansatz device for encoding 1 and 2 are indicated with ‘×’ and ‘+’ respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Appendix G: Quantum correlation metrics  There is no one standard metric to quantify entanglement or correlation in a many-body state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The metric we introduce  here, the quantum total correlation, is a quantity inspired by the classical total correlation of L random variables (b1, · · · , bL),  that is �L  l=1 H(bl) − H(b1, · · · , bL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Using chain rule of Shannon entropy H(b1, b2, · · · , bL) = H(b1) + H(b2|b1) + · · · +  H(bL|b1, b2, · · · , bL−1)  L  �  l=2  H(bl) − H(b1, b2, · · · , bL) =  L  �  l=1  H(bl) −  L  �  l=1  H(bl|b1, b2, · · · , bl−1) =  L  �  l=2  I(b1, · · · , bl−1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' bl) ∈ [0, L − 1],  (G1)  we can see that the classical total correlation tells us how a set of random variables reveals information of each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Similarly,  quantum total correlation can be defined as [26, 27]  T (ˆρ) =  L  �  l=1  S(ˆρl) − S(ˆρ)  (G2)  where S is von Neumann entropy and ˆρl := Tr[L]\\{l} {ˆρ} is the subsystem state at qubit l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Due to the subadditivity of von-  Neumann entropy �L  l=1 S(ˆρl) ≥ S(ˆρ), we conclude that the quantum total correlation is non-negative, and is zero iff the state  ˆρ = �L  l=1 ˆρl is a product state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  In this paper’s measurement scheme, the specific readout POVMs are the projectors onto the computational states  {|bk⟩ ⟨bk|}k∈[K].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Thus, we are in particular interested in analyzing the post-measurement state ˆρM(u) = �  k ρkk(u) |bk⟩ ⟨bk|  23  whose subsystems are correspondingly in states ˆρM  l (u) = Tr[L]\\{l}  �  ˆρM(u)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' We compute the average quantum total correla-  tion over the input domain u with respect to the input probability distribution p(u):  ¯T  �  ˆρM�  = Eu  � L  �  l=1  S(ˆρM  l (u)) − S(ˆρM(u))  �  = Eu  � L  �  l=1  H(bl(u)) − H(b1(u), · · · , bL(u))  �  (G3)  where the second equality comes from the diagonal nature of post-measurement state which reduces the quantum total correlation  to a normal classical total correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  The post-measurement quantum total correlation always reaches its maximum L − 1 when the diagonal terms of the state  is a GHZ-type state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Also as a comparison, for a W-state |W⟩ =  1  √  L (|10 · · · 0⟩ + |01 · · · 0⟩ + · · · + |00 · · · 1⟩), then post-  measurement quantum total correlation T(|W⟩) is  L  �  −  � 1  L  �  log2  � 1  L  �  −  �L − 1  L  �  log2  �L − 1  L  ��  − L  �  −  � 1  L  �  log2  � 1  L  ��  = (L − 1) log2  �  L  L − 1  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (G4)  which is upper bounded by limL→∞ T (|W⟩) =  1  ln(2) ≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='443.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Appendix H: Guidance from EC theory: principal component analysis with respect to quantum noise  Another fundamental use of the capacity spectrum analysis we propose is giving a natural truncation of eigentask.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' In machine  learning theory, the technique of projection of a high-dimensional data to a far lower subspace is called principal component  analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Within the computing architecture we are discussing, we are trying to use some K′-dimensional data where K′ ≪ K  to approximate the original data as much as possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' More specifically, consider a given function f(u), we hope to find K′  functions {G(k)(u)}k∈[K′] where G(k)(u) = �K−1  k′=0 g(k)  k′ xk′(u) lies in the space spanned by measured features G(k)(u) ∈  Span{x}, such that the relative mean square error  min  W  Eu  ����f − �K′  k=1 Wk  ��K−1  k′=0 g(k)  k′ ¯Xk′  ����  2�  Eu[|f|2]  (H1)  is much smaller as possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' According to Appendix C, the solution to {g(k)}k∈[K′] is exactly g(k) = r(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 9 supplies a  concrete example of fitting linear function f(u) = u, by setting K′ = 40 in a 6-qubit system (and thus K = 64).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  Input u  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5 6-qubit, 40 principal xk(u), with retrain  Combination of ¯Xk(u)  Combination of xk(u)  Target function f(u) = u  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  Input u  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5 6-qubit, 40 principal y(k)(u), no retrain  Combination of ¯Xk(u)  Combination of xk(u)  Target function f(u) = u  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Projection onto 40-dimensional space spanned by 40 principal xk(u) vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' spanned by 40 principal y(k), in a 6-qubit H-encoding  system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The number of shots is fixed as S = 5000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 9(a) shows the projection onto the space spanned by the dominant 40 readout features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Here, by “dominant” we mean  one can first train by least square regression to get an output weight w ∈ RK, and then select corresponding wk with the leading  K′ largest w2  k · Eu[|xk|2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Then we need to use these K′ features to retrain and obtain a new output weight w′ ∈ RK′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' In such  particular example, g(k) are some one-hot vectors where the index of 1 are chosen by the sorting K′ largest w2  k · Eu[|xk|2] as we  24  described before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' We can compare the the relative mean square error with the case of g(k) = r(k), the eigentasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The latter one  shows an approximation function with conspicuously much smaller relative mean square error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  One fundamental question is: what will be an appropriate selection of K′ in practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' In Appendix D we claim that those  β2  k has stronger noise than signal itself, which should be excluded when taking the linear combination of measured features (or  equivalently taking the linear combination of eigentasks).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Namely we should defined the cut-off Kc(S) such that  Kc(S) = max  β2  k<S k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (H2)  Based on this observation, we can further explore the trend of Kc(S) when qubit number L is scaled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' As we showed in main  text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The eigen-NSR spectra growth much slower when L increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Then the quantum system is able to provide much more  eigentasks with more signal than noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 10(a) shows spectrum in H-encoding quantum system with size L = 3 ∼ 8 with  fixed hyperparameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Notice that shot number S = 5000 here is not a larger number, which means that we cannot sample  enough shots so that features converges to its mean in 28 = 256 dimensional Hilbert space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' But applying eigentasks analysis  in this example still shows a fast decay of relative error minW Eu[|f − �Kc(S)  k=0  Wk¯y(k)|2]/Eu[|f|2] until the fitting accuracy  saturates at L = 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' PCA for different ES H-encoding system size L = 3, 4, 5, 6, 7, 8 with fixed hyperparameters and S = 5000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (a) Eigen-NSRs  spectrum of different sized system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (b) Relative error minW Eu[|f − �Kc  k=1 Wk¯y(k)|2]/Eu[|f|2] for fitting f(u) = u, where Kc can be read  out from (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (c) Combination of Kc eigentasks �Kc(S)  k=0  wky(k)(u) and noisy eigentasks �Kc(S)  k=0  wk¯y(k)(u) in L = 5, 6, 7, 8 qubits system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Appendix I: Quantum-noise-PCA in classification problem  The highly nonlinear readout feature xk(u) should have Taylor expansion xk(u) = �∞  j (T)kjuj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Such complicated func-  tions will span a certain functional space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' One fundamental question is what the limit of approximation ability based on the  architecture we proposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Hereby we first show that this architecture under infinite sampling is capable of approximating any  continuous function on the domain [−1, 1] to arbitrary precision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Furthermore, the linearity of quantum moment readout and  complexity of quantum evolution will help us to understand why such a quantum system has capability to approximate a highly  nonlinear function, under finite and bounded computational resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Exploring the capacity for function approximation under  finite measurement resources, as is done in the main text and Appendix C, highlights the fundamental limitations places by  quantum noise on computation using the QRC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Ek Wk · g(k)(u)  Zk Wk : y(k)(u)  Zk Wk : y(k)(u)  5000  S  f(u) = u  f(u) =u  S = 5000, N = 1000  Zk Wk · g(k)(u)  Zk Wk · g(k)(u)  Ek Wk : y(k)(u)  Ek, Wk y(k)(u)  f(u) = u  f() =u25  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  Input u  −1  0  1  Combination of features  mmax = 1  mmax = 2  mmax = 3  mmax = 4  mmax = 5  Sinusoid  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  Input u  −1  0  1  mmax = 1  mmax = 2  mmax = 3  mmax = 4  mmax = 5  Steep tanh  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Function approximation by using y = �K−1  k=0 wkxk(u) (solid red lines) to approximate sine function and steep tanh function  (dashed purple lines) in a 5-qubit quantum annealing system, where Keff = �mmax  m=0  �L  m  �  depends on different quantum moment thresholds  mmax = 1, 2, 3, 4, 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The hyperparameters are (Jmax;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' ¯hx, hx  rms;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' ¯hI, hI  rms) = (1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 3, 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 5, 2) in unit 1/t and no hz field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' This simulation shows  that for some simple functions, it is sufficient to merely use lower order moments, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=', mmax = 2 in sine function and mmax = 3 in steep  tanh function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  Input u  0  1  2  Class C0 distribution  Class C1 distribution  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  Input u  0  100  200  300  Class C0 sample histogram  Class C1 sample histogram  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (Left) Distribution p0(u) and p1(u) for classes C0 and C1, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (Right) The histogram of C0 and C1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Each class contains  5000 samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Function approximation universality  A very general question is that what type of functions can such a single-step quantum approximate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' One conclusion which can  be drawn is the function approximation universality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' That is, give any continuous function from space of continuous functions  on domain [−1, 1], i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' φ ∈ C ([−1, 1], R), for any given error ε > 0, there always exists a function ϕ(u) = w · x(u) such that  |ϕ(u) − φ(u)| ≤ ε  (I1)  for any input u ∈ [−1, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The proof is also employing the well-known Stone-Weierstrass theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' For our particular ar-  chitecture, D = [−1, 1] is obviously a compact space, while point-separation can also be trivially fulfilled by a single qubit  system (L = 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The subalgebra structure of the function family generated by quantum systems is automatically satisfied in  representation of moment in family of all product systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  1D classification as function approximation for noiseless measured features  In this section, we will show how the function approximation universality of architecture described in Appendix I 1 enables it  to perform – among others – paradigmatic machine learning tasks such as classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  26  1  2  3  4  5  Output feature threshold order mmax  82  84  86  88  Testing Accuracy (%)  Theoretical maximal accuracy  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  Input u  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='75  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='00  Probability  mmax = 1  mmax = 2  mmax = 3  mmax = 4  Pr[u ∈ C1|u]  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  1D classification as function approximation in a 5-qubit quantum system with full connectivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  The hyperparameters are  (Jmax;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' ¯hx, hx  rms;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' ¯hI, hI  rms) = (1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 3, 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 8, 5) in unit 1/t and no hz field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (Left) Testing accuracy as a function highest order mmax of mo-  ment feature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (Right) Conditional distribution Pr[u ∈ C1|u] (purple dashed line) vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' readout features σ(w · x(u)) with mmax = 1, 2, 3, 4  (red solid line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' mmax = 4 saturates the approximation accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Suppose two classes C0 and C1 of samples, each of which is generated from distributions p0(u) and p1(u) respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The  probability of occurrence of C0 and C1 are both 50%, and we simply let each class equally contain 5000 samples and thus  N = 10000 samples in total.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Both distribution are artificially defined by summing several Gaussian distributions with different  amplitudes and widths together.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Domain of both distributions are restricted in [−1, 1] and both distributions are also normalized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Due to the overlap of two distributions, there is some theoretical maximal classical accuracy to distribution whether a given u  belongs to either C0 or C1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  During the training, we feed each sample u(n) (belonging to class Cc(n)) into a 5-qubit quantum system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The quantum system  will be read out with Keff = �mmax  m=0  �L  m  �  different features {xk(u(n))}k∈[Keff].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Then features of N sample forms the regressor  matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' According to the standard supervised learning procedure, we simply train based on (x(u(n)), c(n)) by logistics regression  where one should minimize the cross-entropy loss  L (W ) =  1  N  N  �  n=1  �  − c(n)log  �  σ(W · x(u(n)))  �  −  �  1 − c(n)�  log  �  1 − σ(W · x(u(n)))  � �  (I2)  where σ is the sigmoid function σ(y) =  1  1+e−y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' A small L2 penalty λ∥W ∥2 (where λ = 10−6) is added to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (I2) for  preventing overfitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The optimal W is then simply the set of weights that minimizes this cost function,  w = argminW {L (W )}  (I3)  We test the fidelity of learning the classification task by determining the accuracy of classification on a testing set formed  by drawing N = 10000 new samples (independent of the training set) as a function of the order of output moments extracted,  mmax = 1, 2, 3, 4, 5, corresponding to reading out Keff = 6, 16, 26, 31, 32 features respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The resulting testing accuracy  is plotted in the left panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' We see that the testing accuracy converges to the theoretical maximal accuracy (dashed  green) with increase in readout features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Importantly, one can show that this improvement in learning performance coincides with training of optimal weights w such  that the QRC is able to approximate the conditional distribution Pr[u ∈ C1|u] of the two classes with increasing accuracy (lower  error).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' To verify this, we first numerically compute all K = 32 readout feature functions x(u) of the system, by sweeping 500  equidistant values of u ∈ [−1, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Effectively learning the conditional distribution means that σ(w · x(u)) ≈ Pr[u ∈ C1|u].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' It is  equivalent to use w · x(u) to approximate the following function:  w · x(u) ≈ σ−1(Pr[u ∈ C1|u]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (I4)  We therefore see that the function approximation universality property of the architecture discussed in Appendix I 1 enables its  use as a generic classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  27  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='0  Input u  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='75  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='00  Probability  Training  Testing  Pr[u ∈ C1|u]  101  102  103  104  105  Shots S  60  70  80  90  Accuracy (%)  Training  Testing  Theoretical maximal accuracy  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (Left) The linear combination with sigmoid activation, that is the stochastic function σ  ��Kc(S)  k′=1 wk′,Train(˜r(k)  N · ¯  XTrain)k′  �  (blue  line) and σ  ��Kc(S)  k′=1 wk′,Train(˜r(k)  N · ¯  XTest)k′  �  (red line), compared with the true conditional probability Pr[u ∈ C1|u] (black line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (Right)  Training accuracy and testing accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' They saturate the theoretical maximal accuracy as S reaches 104 ∼ 105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Their agreement shows the  quantum measurement noise serves well as a regularizer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Solving classification problem by quantum-noise-PCA  Now we can solve the classification task above by using the quantum-noise princilpal component analysis we learn from  capacity analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Suppose a physical system with L = 5 qubits and ring connectivity, we choose the hyperparameter to be  J = 2, hx  rms = hz  rms = hI  rms = 5 and t = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' In this H-encoding scheme, we can obtain K = 32 measured features on each of  N = 105 samples {u(n)} (5000 in class C0 and 5000 in class C1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' We emphasize here that the underlying marginal distribution  p(u) is no longer uniform here, and it will make both {β2  k} and {r(k)} very different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Given the number of shots S ∈ [101, 105], we can still compute the empirical ˜r(k)  N and estimating β2  k by using the correction  techniques we used in Appendix D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' By comparing the estimated (1 − ˜αN,k)/(˜αN,k − 1  S ) and S, we can figure out the cutoff  order Kc(S) and combination coefficients ˜r(k)  N , based on which we can define a set of observables  ˆOk =  K−1  �  k′=0  ˜r(k)  N,k′ ˆ  Mk′  k = 0, 1, · · · , Kc(S).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (I5)  It is equivalent to say, by measuring ˆOk, we can effectively obtain eigentasks ˜r(k)  N · ¯  XTrain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Then we can apply standard logistics  regression on those eigentasks as we did in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' I2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The only difference is we no longer need any regularization term as penalty  like λ∥W ∥2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The training procedure eventual yield wTrain ∈ RKc(S), together with ˜r(k)  N and Kc(S).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Now we generate a totally new and independent set of u’s for testing purpose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  By measuring ˆOk, one get eigentasks  ˜r(k)  N · ¯  XTest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' By plugging wTrain ∈ RKc(S)+1, together with ˜r(k)  N  and Kc(S) in training, we can achieve the testing accu-  racy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The agreement between training and testing accuracy show that the quantum measurement noise effectively works as a  regularizer, and do a pretty good job (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  Appendix J: Finite sampling bound and uncertainty propagation  We conclude that the principle advantage brought about by entanglement in this sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' There we observe that for certain  inputs u (that depend on the input encoding) the measurement of an ES when mapped into the moment space can generate  distributions that can be highly anisotropic at finite S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' While for PS these distributions are generally isotropic unless they are  close to the boundaries of the output domain (when the encoding produces outputs that are eigenstates of the measurement basis).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  We observe that this trend is also present in the experimental system despite non-idealities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The origin of higher expressive  capacity at large S provided by ESs can be traced back to this basic feature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' To be more specific, let ˆ  Mk = ˆσz  l1 ˆσz  l2 · · · ˆσz  lm, and  ¯Xk(u) be empirical mean based on S sampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' Notice that the variance of ¯Xk is  Var[ ¯Xk] = 1  S  �  ⟨(ˆσz  l1 ˆσz  l2 · · · ˆσz  lm)2⟩ − ⟨ˆσz  l1 ˆσz  l2 · · · ˆσz  lm⟩2�  = 1  S (1 − x2  k(u)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (J1)  28  1  2  3  4  5  6  7  8  9  10  Highest order m  10−1  100  101  1/SNR (Log)  EC, fit  PC, fit  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' NSR of ES vs PS in a 10-qubit quantum annealing system with shot number S = 1000 by feeding u = 1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The hyperparameters  are chosen to be (¯hx, hx  rms;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' ¯hz, hz  1,rms) = (8, 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' 3, 2) in unit 1/t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The purple and red colors correspond to coupling being switched on and off,  respectively;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' and the coupling hyperparameter in ES is Jmax = 2/t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' For each m, the N = 30 dots are relative error x(r)  k (u)/xk(u) − 1 of  30 repetitions r = 1, 2, · · · , 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The standard deviation of those relative errors (namely NSR) are also plotted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' The ES NSR (purple stars) is  well fitted by O(1/  √  S) (purple dashed line) while the PS NSR (red stars) scales exponentially as O(2m/  √  S) (purple dashed line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' We take  y-axis being log-scale, and one may find in these regime ES 1/SNR grows exponentially faster than PS NSR (red stars) and hence PS readout  scheme will be less powerful in sense of quantum sampling noise resistant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  By central limit theorem,  ¯Xk(u) = xk(u) + δk(u) = xk(u) +  1  √  S  ζk(u),  (J2)  where random sampling noise ζk(u) ≈  �  1 − x2  k(u)ϵ and ϵ ∼ N(0, 1) is standard Gaussian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' For quantum moment readout, the  amplitude of relative error is  ����  δk(u)  xk(u)  ���� ≈  �  1 − x2  k(u)  x2  k(u)  1  √  S  ∝  1  √  S  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (J3)  For classical polynomial readout the amplitude of relative error is obtained by rule of uncertainty propagation  ����  (xl1(u) + δl1) · · · (xlm(u) + δlm) − xl1(u) · · · xlm(u)  xl1(u) · · · xlm(u)  ���� ≈  ����  δl1  xl1(u) + · · · +  δlm  xlm(u)  ����  ≈  ��  1 − x2  l1(u)  x2  l1(u)  + · · · +  �  1 − x2  lm(u)  x2  lm(u)  �  ×  1  √  S  ∝ m ×  1  √  S  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (J4)  If there is no entanglement in quantum system, then the readout features for both quantum moment readout and classical poly-  nomial readout are the same ⟨ˆσz  l1 ˆσz  l2 · · · ˆσz  lm⟩ = ⟨ˆσz  l1⟩⟨ˆσz  l2⟩ · · · ⟨ˆσz  lm⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' However, even if the expectations under infinite sampling  limit S → ∞ are the same, the measurement noise under finite sampling are still different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' For classical polynomial read-  out, the scaling of still follows the simple additivity relation of uncertainty propagation in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' (?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content=' But now the noise of  xl1(u) · · · xlm(u) in quantum moment readout will be very strong, this is because xl1(u) · · · xlm(u) is now close to zero, thus  ����  δk  xk(u)  ���� ≈  1  xk(u)  1  √  S  =  1  xl1(u) · · · xlm(u)  1  √  S  ∝ 2m ×  1  √  S  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
+page_content='  (J5)' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dAyT4oBgHgl3EQfQPaq/content/2301.00042v1.pdf'}
diff --git a/5dFAT4oBgHgl3EQfmh3P/content/tmp_files/2301.08624v1.pdf.txt b/5dFAT4oBgHgl3EQfmh3P/content/tmp_files/2301.08624v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3a8e228af23e4368ee800b78b017eced9faa9c46
--- /dev/null
+++ b/5dFAT4oBgHgl3EQfmh3P/content/tmp_files/2301.08624v1.pdf.txt
@@ -0,0 +1,1431 @@
+arXiv:2301.08624v1  [math.AP]  20 Jan 2023
+ALMOST MINIMIZERS TO A TRANSMISSION PROBLEM
+FOR (p, q)-LAPLACIAN
+SUNGHAN KIM AND HENRIK SHAHGHOLIAN
+Abstract. This paper concerns almost minimizers of the functional
+J(v, Ω) =
+ˆ
+Ω
+�
+|Dv+|p + |Dv−|q�
+dx,
+where 1 < p ̸= q < ∞ and Ω is a bounded domain of Rn, n ≥ 1. We
+prove the universal H¨older regularity of local (1 + ε)-minimizers, when
+ε is universally small. Moreover, we prove almost Lipschitz regularity
+of the local (1 + ε)-minimizers, when |p − q| ≪ 1 and ε ≪ 1.
+Contents
+1.
+Introduction
+1
+2.
+Technical Tools
+4
+3.
+H¨older regularity
+10
+4.
+Almost Lipschitz regularity
+14
+Declarations
+18
+References
+18
+1. Introduction
+In this paper, we study regularity properties of almost minimizers to the
+functional
+(1.1)
+J(u, Ω) ≡ Jp,q(u, Ω) :=
+ˆ
+Ω
+(|Du+|p + |Du−|q) dx,
+where Ω ⊂ Rn is a bounded domain and 1 < p, q < ∞.
+Our primary
+goal is to prove a universal H¨older estimate for the almost minimizers. We
+shall also study various scenarios, on the relation between p and q, to see
+if the regularity can be improved. In particular, we aim at proving almost
+Lipschitz regularity provided that p and q are close to each other.
+The notion of local K-minimizers is given as follows.
+H. Shahgholian was supported in part by Swedish Research Council. This project
+was finalized during the program Geometric aspects of nonlinear PDE at Institute Mittag
+Leffler, Stockholm.
+1
+
+2
+SUNGHAN KIM AND HENRIK SHAHGHOLIAN
+Definition 1.1 (Local K-minimizers). Let K ≥ 1 be a constant. We shall
+call u ∈ W 1,p∧q
+loc
+(Ω) a local K-minimizer of the functional J, if for any cube
+Q ⊂ Ω, J(u, Q) < ∞, and
+(1.2)
+J(u, Q) ≤ KJ(v, Q),
+for any v ∈ u + W 1,p∧q
+0
+(Q) such that J(v, Q) < ∞.
+In the course of this paper, we shall be interested in the case K = 1 + ε,
+for some small ε > 0. We remark that our analysis does not change, as
+one replaces cubes with balls in the above definition. However, it is worth
+mentioning that the notion with cubes is in general not equivalent to hat
+with balls, unless K = 1, and local K-minimizers with cubes are known to
+be less restrictive; see [Giu03, Example 6.5].
+In the framework of standard functionals (i.e., those without break across
+some level set), the universal H¨older regularity is established for quasi-
+minimzers (those with K > 1 any, and Q in (1.2) replaced with spt(u − v)),
+as the essential arguments for the proof of the H¨older regularity for exact
+minimizers remain unchanged upon the extension; see [Giu03]. In contrast,
+thanks to the particular break across the zero-level set in Jp,q, many impor-
+tant steps in the proof of [CKS21, Theorem 1.2] for the H¨older regularity of
+exact minimizers to our functional Jp,q are destroyed when applied to quasi-
+minimzers. Still, we were able to extend the argument to (1+ε)-minimizers,
+when ε is universally small.
+Theorem 1.2. There are constants ε > 0 and σ ∈ (0, 1), depending only on
+n, p+, and p−, such that if u ∈ W 1,p+∧p−(Q2) is a local (1 + ε)-minimizer
+of Jp+,p−, then u± ∈ C0,σ±
+loc (Q1) with σ+ = σ, σ− = 1 − (1 − σ)p−
+p+ , and
+[u±]C0,σ±(Q1) ≤ c
+�ˆ
+Q2
+((u+)p+ + (u−)p−) dx
+� 1
+p± ,
+where c depends only on n, p+, and p−.
+We remark that the above theorem also shows the exact relation between
+the H¨older exponents for each phase; this was not contained in the authors
+earlier collaboration [CKS21, Theorem 1.2] with M. Colombo. Our proof
+involves a careful extension of the main ingredients for [CKS21, Theorem
+1.2] to local (1 + ε)-minimizers, and a compactness argument.
+A key feature of local (1 + ε)-minimizers, ε ≥ 0, for the functional Jp,q
+is that the positive and negative phase scales differently from each other.
+Namely if u is a local (1+ε)-minimizer in Q2, then one needs ∥u+∥X compa-
+rable with ∥u−∥q/p
+X , with X = Lp(Q1) or L∞(Q1). As for the case of the local
+minimizers, i.e., ε = 0, the comparability was proved by a Harnack inequal-
+ity argument [CKS21, Lemma 3.7, Corollary 3.8], which played an essential
+role in the proof of their universal H¨older regularity [CKS21, Theorem 1.2].
+The main difference, which also amounts to the challenges here, for the
+case of local (1+ε)-minimizers, ε > 0, is the lack of such a Harnack inequality
+
+3
+argument. More fundamentally, local (1 + ε)-minimizers do not possess the
+subsolution properties as opposed to local minimizers (see [CKS21, Lemma
+3.4]). One of the consequences is that the basic estimates for one phase,
+such as the Cacciopoli inequality (Lemma 2.2) and the comparison lemma
+(Lemma 3.1) for local (1+ε)-minimizers, involve an additional ε-factor of the
+other phase. Hence, our main task here is to effectively control the additional
+ε-term, which amounts to some technical difficulties. It is worthwhile to
+mention that the absence of the Harnack inequality argument is overcome
+by a careful compactness argument, by which both phases, although scaled
+differently, survive at the limit. The latter part is new, to the best of the
+authors’ knowledge, and can be applied to a wider range of problems.
+Our second result is about the almost Lipschitz regularity for local (1+ε)-
+minimizers for the functional Jp,q, when |p − q| ≪ 1 and ε ≪ 1.
+Theorem 1.3. Let 1 < p+ < ∞ and σ ∈ (0, 1) be given.
+Then there
+exist ε, δ > 0, depending only on n, p+ and σ, such that for any p− ∈
+(p+−δ, p+ +δ) and any local (1+ε)-minimizer u ∈ W 1,p+∧p−(Q2) of Jp+,p−,
+one has u± ∈ C0,σ±(Q1), with σ+ = σ, σ− = 1 − (1 − σ)p−
+p+ , and
+[u]C0,σ±(Q1) ≤ c
+�ˆ
+Q2
+((u+)p± + (u−)p−) dx
+� 1
+p± ,
+where c depends only on n, p+ and σ.
+A similar statement is proved in [AT15] for uniformly elliptic function-
+als when governing conductivity matrices are close with each other; [AT15]
+however considers local minimizers (i.e., ε = 0) only. Our problem is philo-
+sophically the same, as the limit case is clean, thus possess better regularity.
+On the technical level, our argument is needs slight more care than that
+of [AT15, Theorem 7.1], as the proof for the growth of the functional Jp,q
+changes as (p, q) varies. Moreover, one needs to make sure that the argument
+works well regardless of the relation between p (or q) and the dimension n.
+These are all rigorously treated in Sect. 4.
+Recently, free boundaries for almost minimizers are investigated in various
+settings, see e.g., [DET19], [DS20], and [DJS22] to mention a few. There
+is a possibility of extending the approach with viscosity solutions employed
+in [DS20], but it is beyond the scope of this paper. It would be already
+interesting to extend the result for the clean case, p = q.
+In [CKS21], the authors analyze the free boundary of local minimizers for
+Jp,q, using the measure ∆pu+, which is nonnegative and supported on the
+free boundary, ∂{u > 0}(=∂{u < 0}). This is mainly due to the subsolu-
+tion property of u+, which is no longer valid for almost minimizers. The
+same issue appears in the case of the two-phase Alt-Caffarelli functional
+(see [DET19, Section 4]), which is resolved by the NTA property of the free
+boundary and a clever use of barriers. The NTA property was obtained
+there by the use of the ACF monotonicity formula, which is absent in our
+
+4
+SUNGHAN KIM AND HENRIK SHAHGHOLIAN
+regime. The construction of the barriers and the comparison with the al-
+most minimizers require some regularity of the free boundary, which in the
+case of [DET19] was the NTA property. However, in our problem, none of
+these seems to be analogously carried out. For this reason, we leave out the
+analysis of the free boundary for our almost minimizers to the interested
+reader.
+The paper is organized as follows. In Section 2, we collect some technical
+tools to prepare the proof of Theorem 1.2. In Section 3, we prove Theorem
+1.2. In Section 4, we prove Theorem 1.3.
+We follow the standard notation and terminology. In particular, n denotes
+the dimension of the underlying space, and there is no restriction other than
+n ≥ 1. By Qr(x0), we denote the cube centered at x0 with side-length r,
+i.e., Qr(x0) := {x ∈ Rn : |xi − x0i| < r, 1 ≤ i ≤ n}. For simplicity, we set
+Qr := Qr(0). Given a set A ⊂ Rn, by |A| we denote the Lebesgue measure
+of A. The function spaces C0,σ and W 1,p are standard H¨older and Sobolev
+spaces, and C0,σ
+loc , W 1,p
+loc are their local versions.
+2. Technical Tools
+In this section, we shall present and verify some technical tools, most of
+which generalize those appeared in [CKS21, Sect. 4–5]. The main goal of
+this section is to prove the following proposition, which roughly tells us that
+negative values cannot penetrate the interior if a local (1 + ε)-minimizer
+attains large positive values in most of the domain.
+Let us remark that
+this proposition corresponds to [CKS21, Proposition 5.2] for the case of
+minimizers.
+The main difference here is that (1 + ε)-minimizers do not
+possess in general the subsolution properties. Here we exploit the techniques
+to circumvent this issue. Unless stated otherwise, the constant c throughout
+this section is a positive constant that may differ at each occurrence, and
+will depend at most on n, p, and q. Moreover, the parameter ε will be a
+small constant, whose smallness is determined solely by n, p, and q.
+Proposition 2.1. There exist ε > 0 and µ > 0, depending only on n, p, and
+q, such that if u ∈ W 1,p∧q(Q1) is a local (1 + ε)-minimizer of the functional
+J, satisfyingˆ
+Q1
+((u+)p + (u−)q) dx ≤ 1,
+|{u ≤ 1/2} ∩ Q1| ≤ ε,
+then u > 0 a.e. in Qµ.
+The proof for this proposition will be postponed to the end of this section.
+Let us begin with the Cacciopoli-type inequality.
+Lemma 2.2. Let u ∈ W 1,p∧q(Q2) be a local (1 + ε)-minimizer of the func-
+tional J. There exists ¯ε ∈ (0, 1), depending only on n, p, and q, such that if
+ε ≤ ¯ε, then
+(2.1)
+ˆ
+Q1
+|Du+|p dx ≤ c
+ˆ
+Q2
+((u+)p + ε(u−)q) dx,
+
+5
+where c depends only on n, p, and q.
+Proof. Fix r, R with 1 < r < R < 2, and choose any s, t with r < s < t < R.
+Let η ∈ C1
+c (Qt) be a cutoff function such that η ≡ 1 in Qs, |Dη| ≤
+2c
+t−s in
+Qt, and spt(η) ⊂ Q(t+s)/2. Set w := (1 − η)u+ − u− ∈ W 1,p∧q(Qt). Since
+w+ = (1 − η)u+, w− = u−, and spt(u − w) ⊂ spt(η) ⊂ Q(t+s)/2, we derive
+from the (1 + ε)-minimizerslity of u for Jp,q in Qt that
+ˆ
+Qr
+|Du+|p dx ≤ (1 + ε)
+ˆ
+Qt
+|D((1 − η)u+)|p dx + ε
+ˆ
+Qt
+|Du−|q dx.
+Applying H¨older’s inequality and Young’s inequality, and then using spt(η) ⊂
+Q(t+s)/2 and |Dη| ≤ c/(t − s), we deduce that
+ˆ
+Qs
+|Du+|p dx ≤ c
+ˆ
+Qt
+� (u+)p
+(t − s)p + ε|Du−|q
+�
+dx + cε
+ˆ
+Qt
+|Du+|p dx.
+Since this part is by now standard, we omit the details. Note that the last
+display holds for all s, t, r < s < t < R. Hence, choosing ε small enough such
+that cε < 1
+2, we can employ the standard iteration lemma [Giu03, Lemma
+6.1] to derive that
+(2.2)
+ˆ
+Qr
+|Du+|p dx ≤ c
+ˆ
+QR
+� (u+)p
+(R − r)p + ε|Du−|q
+�
+dx.
+Now replace QR in the right-hand side with Q(R+r)/2, and then apply
+the same argument above to (−u) with Qr replaced with Q(R+r)/2; note
+that (−u) is a local (1 + ε)-minimizer of Jq,p in place of Jp,q. Then we may
+proceed as follows,
+ˆ
+Qr
+|Du+|p dx ≤ c
+ˆ
+Q(R+r)/2
+� (u+)p
+(R − r)p + ε|Du−|q
+�
+dx
+≤ c
+ˆ
+QR
+� (u+)p
+(R − r)p + cε (u−)q
+(R − r)q
+�
+dx + c2ε2
+ˆ
+QR
+|Du+|p dx.
+Recall that r, R were any numbers between 1 and 2. Hence, taking ε smaller
+if necessary such that c2ε2 < 1
+2, we can make use of the iteration lemma
+once again to arrive at (2.1).
+□
+Remark 2.3. In what follows, we shall always assume that ε < ¯ε, with ¯ε
+as in Lemma 2.2.
+Let us remark that the above Cacciopoli inequality is too weak to bring
+forth a local L∞-estimate. Besides, local quasi-minimizers are not neces-
+sarily bounded, even for functionals under standard growth condition (of
+course, only if p ≤ n). Nevertheless, with the aid of the Cacciopoli inequal-
+ity above, we shall observe that the blowup rate of local (1 + ε)-minimizers
+can be made arbitrarily small, for small ε, in case p ≤ n.
+
+6
+SUNGHAN KIM AND HENRIK SHAHGHOLIAN
+Lemma 2.4. Let u ∈ W 1,p∧q(Q1) be a local (1 + ε)-minimizer of the func-
+tional J. Suppose that
+∥u+∥Lp(Q1) ≤ 1,
+sup
+r∈(0,1)
+∥u−∥Lq(Qr)
+r1− p
+q ∥u+∥
+p
+q
+Lp(Qr)
+≤ κ,
+for some constant κ > 0. Then for any δ > 0, there exists a positive constant
+εκ,δ, depending only on n, p, q, κ and δ, such that if ε ≤ εκ,δ, then
+sup
+r∈(0,1)
+1
+rn−δp
+ˆ
+Qr
+(u+)p dx ≤ cκ,δ,
+where cκ,δ depends only on n, p, q, Λ, δ and κ.
+Proof. We remark that the conclusion is trivial for p > n, due to the Sobolev
+embedding theorem. Henceforth, we shall assume that 1 < p ≤ n.
+Let κ and δ be arbitrary positive constants, and suppose the conclusion
+of the lemma is false. Then for each j = 1, 2, · · · , one can find some positive
+constant εj ց 0, and a local (1 + εj)-minimizer uj ∈ W 1,p∧q(Q1) of the
+functional J, such that
+∥u+
+j ∥Lp(Q1) ≤ 1,
+sup
+r∈(0,1)
+∥u−
+j ∥Lq(Qr)
+r1− p
+q ∥u+
+j ∥
+p
+q
+Lp(Qr)
+≤ κ,
+but
+Sj =
+sup
+rj≤r≤1
+1
+rn−δp
+ˆ
+Qr
+(u+
+j )p dx → ∞,
+for some constant rj ∈ (0, 1). In order to have Sj → ∞ to be compatible
+with ∥u+
+j ∥Lp(Q1) = 1, we must have rj → 0.
+Consider an auxiliary function vj : Qr−1
+j
+→ R, defined by
+vj(y) =
+u+
+j (rjy)
+r
+− n
+p
+j
+∥u+
+j ∥Lp(Qrj )
+−
+u−
+j (rjy)
+r
+1− p
+q − n
+q
+j
+∥u+
+j ∥
+p
+q
+Lp(Qrj )
+.
+One easily verifies that vj ∈ W 1,p∧q(Qr−1
+j ) is a local (1 + εj)-minimizer of
+the functional J, and
+(2.3)
+sup
+1≤R≤r−1
+j
+1
+Rn−δp
+ˆ
+QR
+(v+
+j )p dy = 1,
+where the supremum is attained at R = 1, and
+(2.4)
+sup
+1≤R≤r−1
+j
+1
+Rn+q−(1+δ)p
+ˆ
+QR
+(v−
+j )q dy ≤ κq.
+Due to Lemma 2.2, along with (2.3) and (2.4),
+(2.5)
+ˆ
+QR
+(|Dv+
+j |p + |Dv−
+j |q) dx ≤ cRn−(1+δ)p,
+
+7
+where c depends only on n, p and q, whenever 2Rrj ≤ 1. By the Sobolev em-
+bedding theory, there exists a function v ∈ W 1,p∧q
+loc
+(Rn) with v+ ∈ W 1,p
+loc (Rn)
+and v− ∈ W 1,q
+loc (Rn) such that v+
+j → v+ and v−
+j → v−
+j weakly in W 1,p
+loc (Rn)
+and respectively W 1,q
+loc (Rn), after extracting a subsequence if necessary; we
+shall denote this subsequence by vj, for brevity. The weak convergence im-
+plies that v ∈ W 1,p∧q(BR) is a minimizer of the functional J. Since v+
+j → v+
+strongly in Lp(BR) and v−
+j → v− strongly in Lq(BR), letting j → ∞ in (2.3)
+yields that
+(2.6)
+sup
+R≥1
+1
+Rn−δp
+ˆ
+QR
+(v+)p dy = 1.
+However, since v is a minimizer of the functional J, by [CKS21, Lemma
+3.4], v+ is a weak p-subsolution. As a result, the local L∞-estimates [Giu03,
+Theorem 7.3] applies to v+, which along with (2.6) yields
+∥v+∥L∞(QR) ≤ c
+Rδ .
+Hence, letting R → ∞ yields that v+ = 0 a.e. in Rn. This yields a contra-
+diction against (2.6).
+□
+We also have a growth estimate for the p-th Dirichlet energy of the positive
+phase. The idea is the same as in [CKS21, Lemma 4.5], which is based on
+some approximation by positive p-harmonic functions of the positive phase
+of local quasi-minimizers, in terms of the size of the negative phase.
+Lemma 2.5. Let u ∈ W 1,p∧q
+loc
+(Q2) be a local (1 + ε)-minimizer of the func-
+tional J, and v ∈ u+ + W 1,p
+0 (Q1) be the p-harmonic function. Then
+0 ≤
+ˆ
+Q1
+(|Du+|p − |Dv|p) dx ≤ c
+ˆ
+Q2
+((u−)q + ε|Du+|p) dx,
+and
+ˆ
+Qr
+|Du+|p dx ≤ c
+ˆ
+Q1
+((rn + ε)|Du+|p + (u−)q) dx,
+∀r ∈ (0, 1),
+where c depends only on n, p and q.
+Proof. The proof is essentially the same as that of [CKS21, Lemma 4.5].
+The additional term ε
+´
+Q2 |Du+|p dx appears due to the different Cacciopoli
+inequality; more exactly, we use (2.2) with u replaced with −u. We shall
+not repeat this argument here.
+□
+The following lemma corresponds to [CKS21, Lemma 4.8]. The key in-
+gredient of the proof there is the Poincar´e inequality, and Lemma 2.5, which
+corresponds to [CKS21, Lemma 4.5]. As noted above, Lemma 2.5 differs
+from [CKS21, Lemma 4.5] by the additional term, ε
+´
+Q2 |Du+|p dx. How-
+ever, this does not make any difference in the proof of the lemma below.
+Thus, we shall skip the proof.
+
+8
+SUNGHAN KIM AND HENRIK SHAHGHOLIAN
+Lemma 2.6 (Essentially due to [CKS21, Lemma 4.8]). Let u ∈ W 1,p∧q(Q4)
+be a local 2-minimizer for the functional J, satisfying
+ˆ
+Q4
+(u+)p dx = 1,
+ˆ
+Q4
+((u−)q + |Du+|p) dx ≤ ε,
+for some ε > 0. Then
+|{u ≤ 1/2} ∩ Q1| ≤ cε,
+where c depends only on n, p and q.
+Let us prove Proposition 2.1 with additional assumptions that ∥u−∥Lq(Q1)
+and ∥Du+∥Lp(Q!) are sufficiently small. The proof follows the idea of that
+of [CKS21, Lemma 5.5], with some modifications addressing the lack of
+subsolution properties of each phase.
+Lemma 2.7. There exists ε > 0, depending only on n, p and q, such that if
+u ∈ W 1,p∧q(Q4) is a local (1 + ε)-minimizer of the functional J, satisfying
+ˆ
+Q4
+(u+)p dx = 1,
+ˆ
+Q4
+((u−)q + |Du+|p) dx ≤ ε,
+then u > 0 a.e. in Q1.
+Proof. Let us consider the case q < n first. Following the proof of [CKS21,
+Lemma 4.3], we obtain that for σ ∈ (0, 1),
+(2.7)
+ˆ
+Qr
+�(u−)q
+rq
++ |Du+|p
+�
+dx ≤ cεr−(1−σ)p
+ˆ
+Qr
+(u+)p dx,
+∀r ∈ (0, 1),
+where c depends only on n, p, q and σ. The proof is essentially the same,
+as Lemma 2.5 and 2.6 replace [CKS21, Lemma 3.5–3.7], which are the key
+ingredients of the proof there; moreover Lemma 2.2 replaces the usual Cac-
+ciopoli inequality for weak q-subsolutions. These lemmas have additional
+ε-term, which arise from the (1 + ε)-local minimizerslity of u, but this does
+not contribute any major difference from the proof for [CKS21, Lemma 4.3].
+Hence, we shall omit the details.
+We observe that due to (2.7) (as well as the assumption
+´
+Q4(u+)p dx = 1),
+the hypothesis of Lemma 2.4 is satisfied (with κ = 1 > εrσp). Thus, choosing
+ε ≤ εδ with εδ as in Lemma 2.4 with δ < σ, we deduce
+(2.8)
+ˆ
+Qr
+(u+)p dx ≤ cr−δp,
+∀r ∈ (0, 1).
+Inserting (2.8) into (2.7) yields that
+(2.9)
+ˆ
+Qr
+|Du+|p dx ≤ cεr−(1−(σ−δ))p,
+∀r ∈ (0, 1);
+now c depends only on n, p, q, σ and δ. Let us remark that this step does
+not appear for the case of minimizers [CKS21, Lemma 4.3] because for the
+latter case we can use the subsolution property [CKS21, Lemma 3.4] for u+
+to obtain its local boundedness.
+
+9
+The growth estimate in (2.9) is obtained by choosing ε sufficiently small.
+Taking ε even smaller if necessary, we may repeat the above argument
+around any point z ∈ Q1, and obtain
+ˆ
+Qr(z)
+|Du+|p dx ≤ cεr−(1−(σ−δ))p,
+∀r ∈ (0, 1), ∀z ∈ Q1,
+possibly with a larger constant c. Therefore, by Morrey’s lemma, we deduce
+that u+ ∈ C0,σ−δ(Q1) and
+(2.10)
+[u+]C0,σ−δ(Q1) ≤ cε
+1
+p .
+Finally, by Lemma 2.6, |{u ≤ 1
+2} ∩ Q1| ≤ cε. Hence, with cε ≤ 2−2n−1, we
+have |{u > 1
+2} ∩ Q1| > 0, which now implies via (2.10) that
+inf
+Q1 u+ ≥ 1
+2 − cε
+1
+p > 0,
+provided that we choose ε even smaller. Note that the smallness condition
+for ε at this stage can be determined solely by n, p and q, by for instance
+selecting σ = 1
+2 and δ = 1
+4. This finishes the proof for the case q < n.
+The case for q ≥ n can be treated similarly, following the proof of [CKS21,
+Lemma 4.3]; we omit the details.
+□
+We are ready to prove Proposition 2.1.
+Proof of Proposition 2.1. Let ¯ε be as in Lemma 2.7, and suppose that cε ≤ ¯ε.
+Using |{u ≤ 1
+2} ∩ Q1| ≤ ε, we may follow the proof of [CKS21, Proposition
+4.2] to find a constant ρ, depending only on n, p and q, such that
+(2.11)
+ˆ
+Q4ρ
+�(u−)q
+ρq
++ |Du+|p
+�
+dx ≤ cερq−p
+ˆ
+Q4ρ
+(u+)p dx.
+Therefore, defining uρ : Q4 → R by
+uρ(x) =
+u+(ρx)
+(4ρ)− n
+p ∥u+∥Lp(Q4ρ)
+−
+u−(ρx)
+4− n
+q ρ1− p
+q − n
+q ∥u+∥
+p
+q
+Lp(Q4ρ)
+,
+we see that uρ ∈ W 1,p∧q(Q4) is a local (1 + ε)-minimizer of the functional
+J, such that
+ˆ
+Q4
+(u+
+ρ )p dx = 1,
+ˆ
+Q4
+((u−
+ρ )q + |Du+
+ρ |p) dx ≤ cε.
+Since cε ≤ ¯ε, with ¯ε as in Lemma 2.6, we obtain
+uρ > 0
+a.e. in Q1.
+Rescaling back, we obtain that u > 0 a.e. in Q4ρ as desired.
+□
+
+10
+SUNGHAN KIM AND HENRIK SHAHGHOLIAN
+3. H¨older regularity
+In this section, we study the universal H¨older regularity of local (1 + ε)-
+minimizers for the functional Jp,q, and prove our first main result, Theorem
+1.2. Let us begin with a lemma that tells us how each phase of local mini-
+mizers for the functional Jp,q should scale relatively to one another.
+Lemma 3.1. Let u ∈ W 1,p∧q(Q1) be a local minimizer of the functional J,
+such that ∥u+∥Lp(Q1) = 1 and u(0) = 0. If ∥u+∥Lp(Q1/2) ≥ β for some β > 0,
+then ∥u−∥Lq(Q1) ≥ cβ, for some positive constant cβ depending only on n,
+p, q and β.
+Proof. Let β be any constant, with 0 < β < 1. Assume by way of contradic-
+tion that there exists a minimizer uj ∈ W 1,p∧q(Q1) of the functional J, such
+that ∥u+
+j ∥Lp(Q1) = 1, ∥u+
+j ∥Lp(Q1/2) ≥ β, uj(0) = 0 but ∥u−
+j ∥Lq(Q1) ≤ 1
+j . By
+[CKS21, Theorem 1.1], uj ∈ C0,σ(Q1/2) and ∥u+
+j ∥C0,σ(Q1/2) ≤ c∥u+
+j ∥Lp(Q1) ≤
+c, and similarly, ∥u−
+j ∥C0,σ(Q1/2) ≤ c
+j, where both c and σ depend only on n, p
+and q. This together with the Cacciopoli inequality (Lemma 2.2 with ε = 0)
+implies that u+
+j → u0 weakly in W 1,p(Q1/2) and uniformly in Q1/2, while
+u−
+j → 0 weakly in W 1,q(Q1/2) and uniformly in Q1/2, for some nonnegative
+function u0 ∈ W 1,p(Q1/2). The uniform convergence along with uj(0) = 0
+implies that u0(0) = 0. In addition, passing to the limit in ∥u+
+j ∥Lp(Q1/2) ≥ β
+ensures that ∥u0∥Lp(Q1/2) ≥ β. However, the weak convergence of the gradi-
+ent of uj implies that u0 is also a minimizer of the functional J. As u0 ≥ 0
+in Q1/2, u0 is a p-harmonic function, but then it violates the minimizer
+principle, as ∥u0∥Lp(Q1/2) ≥ β > 0.
+□
+Lemma 3.2. Let u ∈ W 1,p∧q(Q1) be a local minimizer of the functional J,
+such that
+∥u+∥Lp(Q1) ≤ 1,
+u(0) = 0,
+sup
+0<r<1
+1
+rn+σ−q
+ˆ
+Qr
+(u−)q dx ≤ c−,
+for some constants c− > 0 and σ− ∈ (0, 1]. Then with σ+ = 1 − (1 − σ−) q
+p,
+sup
+0<r<1
+1
+rn+σ+p
+ˆ
+Qr
+(u+)p dx ≤ c+,
+where c+ depends only on n, p, q, σ− and c−.
+Proof. Let c−, σ− be given, and set σ+ as in the statement. Suppose that
+the conclusion of this lemma is false. Then for each j ∈ N, one can find a
+minimizer uj ∈ W 1,p∧q(Q1) for the functional J, such that
+(3.1)
+ˆ
+Q1
+(u+
+j )p dx ≤ 1,
+uj(0) = 0,
+sup
+0<r<1
+1
+rn+σ−q
+ˆ
+Qr
+(u−
+j )q dx ≤ c−,
+but
+(3.2)
+Sj :=
+sup
+rj
+2 ≤r≤1
+1
+rn+σ+p
+ˆ
+Qr
+(u+
+j )p dx → ∞
+
+11
+where the supremum is achieved at r = 1
+2rj; since ∥u+
+j ∥Lp(Q1) ≤ 1, we must
+have rj → 0. Define
+vj(y) :=
+u+
+j (rjy)
+r
+− n
+p
+j
+∥u+
+j ∥Lp(Qrj )
+−
+u−
+j (rjy)
+r
+1− p
+q − n
+q
+j
+∥u+
+j ∥
+p
+q
+Lp(Qrj )
+.
+Then vj is a local minimizer of the functional J, such that by (3.1) and (3.2),
+∥v+
+j ∥Lp(Q1) = 1, ∥v+
+j ∥Lp(Q1/2) ≥ 2−σ+ and vj(0) = 0. Therefore, Lemma 3.1
+yields that ∥v−
+j ∥Lq(Q1) ≥ cσ+. This implies that
+(3.3)
+1
+rn
+j
+ˆ
+Qrj
+(u−
+j )q dx ≥ cq
+σ+rq−p
+j
+ˆ
+Qrj
+(u+
+j )p dx ≥
+S
+q
+p
+j cq
+σ+
+2σ+q rq−p+σ+p
+j
+.
+Putting (3.1) and (3.3) together, and recalling that σ+ = 1 − (1 − σ−) q
+p,
+cq
+σ− ≥
+S
+q
+p
+j cq
+σ+
+2σ+q ,
+a contradiction to the assumption that Sj → ∞.
+□
+Thanks to the above lemma, we can prove Theorem 1.2 for minimizers of
+the functional J.
+Proof of Theorem 1.2 for minimizers. It suffices to consider the case p > q,
+and
+ˆ
+Q1
+((u+)p + (u+)q) dx = 1.
+By [CKS21, Theorem 1.1], we already know that u ∈ C0,σ(Q1) and that
+[u]C0,σ(Q1) ≤ c, where both c > 0 and σ ∈ (0, 1) depend only on n, p and q.
+Hence, if u(z) = 0 at some z ∈ Q1/2, then
+sup
+0<r< 1
+2
+1
+rn+σq
+ˆ
+Qr(z)
+(u−)q dx ≤ c,
+which along with Lemma 3.2 implies that
+sup
+0<r< 1
+2
+1
+rn+p−q+σq
+ˆ
+Qr(z)
+(u+)p dx ≤ c,
+where the constant c in both displays depends only on n, p and q. Since
+p > q, 1 − (1 − σ) q
+p > σ > 0. Now setting σ− = σ and σ+ = 1 − (1 − σ) q
+p,
+we immediately verify the relation required between σ+ and σ−. Since the
+above growth estimates hold uniformly around all z ∈ {u = 0} ∩ Q1, and
+since ∆pu = 0 in {u > 0}∩Q1 and ∆qu = 0 in {u < 0}∩Q1, one may arrive
+at the conclusion via some standard manipulation. We skip the detail.
+□
+
+12
+SUNGHAN KIM AND HENRIK SHAHGHOLIAN
+Given a measurable function u : Ω → R, define D+(u), D−(u) and Γ(u)
+by the subset of Ω as follows:
+D+(u) = {z ∈ Ω : u > 0 a.e. in some Qr(z) ⊂ Ω},
+D−(u) = D+(−u),
+and
+Γ(u) = Ω \ (D+(u) ∪ D−(u)).
+By definition, both D+(u) and D−(u) are open and hence Γ(u) is closed
+(relative to the topology of Ω). Moreover, z ∈ Γ(u) if and only if |{u ≥
+0} ∩ Qr(z)||{u ≤ 0} ∩ Qr(z)| > 0 for any cube Qr(z) ⊂ Ω.
+With Proposition 2.1 at hand, we shall obtain, as a contraposition along
+with Lemma 3.4 below, that if a local (1 + ε)-minimizer vanishes (in an ap-
+propriate Lebesgue sense) at certain point in the interior, then each phase
+exhibits certain universal H¨older growth. More exactly, we assert the fol-
+lowing.
+Proposition 3.3. There exists a constant ¯σ ∈ (0, 1), depending only on
+n, p, and q, for which the following holds: for each σ ∈ (0, ¯σ), one can
+find a constant εσ ∈ (0, 1), depending only on n, p, q, and σ, such that if
+u ∈ W 1,p∧q(Q1) is a local (1 + εσ)-minimizer of the functional J satisfying
+ˆ
+Q1
+((u+)p + (u−)q) dx ≤ 1,
+0 ∈ Γ(u),
+then with σ+ = σ and σ− = 1 − (1 − σ)p
+q, one has
+sup
+0<r<1
+�
+1
+rσ+p
+ˆ
+Qr
+(u+)p dx +
+1
+rσ−q
+ˆ
+Qr
+(u−)q dx
+�
+≤ cσ,
+where cσ depends only on n, p, q, and σ.
+The following lemma will play a key role (together with Proposition 2.1).
+Lemma 3.4. There exists a constant ¯σ ∈ (0, 1), depending only on n, p,
+and q, for which the following holds: for each σ ∈ (0, ¯σ) and each τ ∈ (0, 1
+2],
+one can find εσ,τ ∈ (0, 1), depending only on n, p, q, σ, and τ, such that if
+u ∈ W 1,p∧q(Q1) is a local (1+εσ+,τ)-minimizer of the functional J satisfying,
+(3.4)
+ˆ
+Q1
+((u+)p + (u−)q) dx = 1,
+|E+(u, Qr)|
+|Qr|
+∧ |E−(u, Qr)|
+|Qr|
+≥ τ,
+for some r ∈ (0, 1), where
+E+(u, Qr) =
+�
+u ≤ 1
+2rΛ(u, Qr)
+1
+p
+�
+,
+E−(u, Qr) =
+�
+u ≥ −1
+2rΛ(u, Qr)
+1
+q
+�
+,
+Λ(u, Qr) =
+ˆ
+Qr
+�(u+)p
+rp
++ (u−)q
+rq
+�
+dx,
+
+13
+then with σ+ = σ and σ− = 1 − (1 − σ)p
+q, one has
+sup
+r≤ρ≤1
+�
+1
+ρσ+p
+ˆ
+Qρ
+(u+)p dx +
+1
+ρσ−q
+ˆ
+Qρ
+(u−)q dx
+�
+≤ cσ,τ,
+where cσ,τ depends on the same parameters that determine εσ,τ.
+Proof. Let ¯σ be determined later, and fix τ ∈ (0, 1
+2], σ ∈ (0, ¯σ), and set σ±
+as in the stastement. Suppose by way of contradiction that for each j ∈ N,
+we can find some positive constant εj → 0, some local (1 + εj)-minimizer
+uj ∈ W 1,p∧q(Q1) of the functional J, and a radius rj ∈ (0, 1) such that
+(3.5)
+ˆ
+Q1
+((u+
+j )p + (u−
+j )q) dx ≤ 1,
+|E+(uj, Qrj)|
+|Qrj|
+∧ |E−(uj, Qrj)|
+|Qrj|
+≥ τ, ,
+but
+(3.6)
+Sj =
+sup
+rj≤r≤1
+�
+1
+rσ+p
+ˆ
+Qr
+(u+
+j )p dx +
+1
+rσ−q
+ˆ
+Qr
+(u−
+j )q dx
+�
+→ ∞,
+with the supremum achieved at level r = rj. In order for (3.6) to be com-
+patible with the first equality in (3.5), we must have rj → 0.
+Define vj : Qr−1
+j
+→ R by
+vj(y) =
+u+
+j (rjy)
+S
+1
+p
+j rσ+
+j
+−
+u−
+j (rjy)
+S
+1
+q
+j rσ−
+j
+.
+By the way that it is rescaled, vj is a local (1+εj)-minimizer of the functional
+J in Q1/rj. Moreover, by (3.5) along with the relation Sjrσ+p
+j
+= Λjrp
+j and
+Sjrσ−q
+j
+= Λjrq
+j, where Λj = Λ(uj, Qrj),
+(3.7)
+����
+�
+|vj| ≤ 1
+2
+�
+∩ Q1
+���� ≥ τ,
+and by (3.6),
+(3.8)
+sup
+1≤R≤r−1
+j
+�
+1
+Rσ+p
+ˆ
+QR
+(v+
+j )p dy +
+1
+Rσ−q
+ˆ
+QR
+(v−
+j )q dy
+�
+= 1,
+where the supremum is achieved at R = 1.
+Thanks to (3.7) and (3.8), one can argue analogously in the proof of
+Lemma 2.4 to obtain a minimizer v ∈ W 1,p∧q
+loc
+(Rn) of the functional J, with
+v+ ∈ W 1,p
+loc (Rn) and v− ∈ W 1,q
+loc (Rn) such that
+(3.9)
+����
+�
+|v| ≤ 1
+2
+�
+∩ Q1
+���� ≥ τ,
+and
+(3.10)
+sup
+R≥1
+�
+1
+Rσ+p
+ˆ
+QR
+(v+)p dy +
+1
+Rσ−q
+ˆ
+QR
+(v−)q dy
+�
+= 1,
+
+14
+SUNGHAN KIM AND HENRIK SHAHGHOLIAN
+where the supremum is achieved at R = 1. In particular, the latter obser-
+vation indicates that v is nontrivial.
+At this point, we choose ¯σ as the positive exponent for Theorem 1.2 for
+minimizers; let us remind the readers that the statement for minimizers is
+proved right after the proof of Lemma 3.2. Set ¯σ+ := ¯σ and ¯σ− := 1 − (1 −
+¯σ) q
+p. As v is a local minimizer of the functional J in Q2R, v+ ∈ C0,¯σ+(QR),
+v− ∈ C0,¯σ−(QR) and then by (3.10), we derive that
+[v+]p
+C0,¯σ+(QR) + [v−]q
+C0,¯σ−(QR) ≤
+c
+R(¯σ+−σ+)p +
+c
+R(¯σ−−σ−)q ,
+for any R > 1. As σ+ = σ < ¯σ+ and σ− = 1 − (1 − σ) q
+p < ¯σ−, sending
+R → ∞ implies that both v+ and v− must be constant. Then by (3.9),
+|v| ≤ 1
+2 everywhere in Q1, whence
+´
+Q1((v+)p + (v+)q) dx ≤ 2−p + 2−q < 1, a
+contradiction to the observation that the supremum in (3.10) is attained at
+R = 1.
+□
+We are ready to prove Proposition 3.3
+Proof of Proposition 3.3. As 0 ∈ Γ(u), there are three cases to consider: (i)
+|{u > 0} ∩ Qρ||{u < 0} ∩ Qρ| > 0 for all ρ ∈ (0, 1), (ii) u ≥ 0 a.e. in Qρ
+for some small ρ > 0, and (iii) u ≤ 0 a.e. in Qρ for some small ρ > 0. The
+last two cases are symmetric, and in those cases u becomes a local (1 + ε)-
+minimizer for the functional Jp,p, or Jq,q depending on its sign. Thus, the
+growth estimate follows easily, once we establish the estimate for the first
+case. We leave out this part as an exercise for the reader.
+Henceforth, let us assume that the first case holds. Let (ε, τ, µ) be the
+triple of constants from Proposition 2.1 that are determined solely by n, p
+and q. Fix any r ∈ (0, 1). Since |{u > 0} ∩ Qµr| · |{u < 0} ∩ Qµr| > 0,
+as a contraposition (applied to both u and −u, after suitable rescaling), we
+obtain that
+(3.11)
+|E+(u, Qr)|
+|Qr|
+∧ |E−(u, Qr)|
+|Qr|
+≥ τ,
+with E+(u, Qr) and E−(u, Qr) defined as in Lemma 3.4. As τ being a con-
+stant depending only on n, p and q, the conclusion of this proposition follows
+immediately from Lemma 3.4; this final step introduces another condition
+on the size of ε, which through the dependence of τ would be determined
+again solely by n, p, q, and σ.
+□
+4. Almost Lipschitz regularity
+Here we prove almost Lipschitz regularity of almost minimizers to J =
+Jp,q, when p and q are close. Our proof is based on the compactness argu-
+ment. The basic ingredient is the universal H¨older estimate for local mini-
+mizers of the functional Jp,q, see [CKS21, Theorem 1.3]. Although it is not
+specified in the statement, one can observe from the higher integrability of
+each phase that the H¨older regularity is uniform when p (or q) is close to n.
+
+15
+We record this fact as a lemma below, as the proof of [CKS21, Theorem 1.3]
+makes use of the local boundedness and the Harnack inequality for weak p-
+harmonic functions, and the constants involved in the latter assertions may
+vary as p → n.
+Lemma 4.1. Let u ∈ W 1,p+∧p−(Q2) be a local minimizer of Jp+,p−. There
+exists ¯δ > 0, depending only on n, such that if |n − p±| ≤ ¯δ, then
+[u±]C0,¯σ(Q1) ≤ ¯c∥u±∥Lp±(Q2),
+where ¯σ ∈ (0, 1) and ¯c > 1 depend only on n.
+Proof. Since u is a local minimizer (instead of (1 + ε)-minimizer) of Jp+,p−,
+u± is a weak p±-subsolution in Q2, according to [CKS21, Lemma 3.4]. Hence,
+by [GG82, Corollary 4.2], there exist constants ¯δ > 0 and ¯γ ∈ (0, 1), both
+depending only on n, such that if |p± − n| < ¯δ, then u± ∈ W 1,p±+¯δ(Q1) ⊂
+W 1,n+¯γ¯δ(Q1). Now setting ¯σ := 1 −
+n
+n+¯γ¯δ, it follows from the Sobolev em-
+bedding, the higher integrability and the Cacciopoli inequality for weak
+p±-subsolutions that
+[u±]C0,¯σ(Q1) ≤ c1(n)
+�ˆ
+Q1
+|Du±|n+¯γ¯δ dx
+�
+1
+n+¯γ¯δ
+≤ c1(n)c2(n, p±)
+�ˆ
+Q3/2
+|Du±|p± dx
+� 1
+p±
+≤ c1(n)c2(n, p±)c3(n, p±)
+�ˆ
+Q2
+(u±)p± dx
+� 1
+p± .
+Note that c2(n, p±), and c3(n, p±) are constants from the higher integrabil-
+ity and respectively the Cacciopoli inequality, and these are all uniformly
+bounded by a constant c(n), as p → p±. Hence, our proof is finished.
+□
+Let us first verify the uniform growth of order σ at free boundary points
+for minimizers. We prove it by compactness.
+Lemma 4.2. Let u ∈ W 1,p∧q(Q1) be a local minimizer of Jp,q such that
+(4.1)
+ˆ
+Q1
+((u+)p + (u−)q) dx ≤ 1,
+u(0) = 0.
+Then for any σ ∈ (0, 1), there exists δ > 0, depending only on n, p, and σ,
+such that if |p − q| < δ, then with σ+ = σ and σ− = 1 − (1 − σ)p
+q,
+1
+rn+σ+p
+ˆ
+Qr
+(u+)p dx +
+1
+rn+σ−q
+ˆ
+Qr
+(u−)q dx ≤ c,
+∀r ∈ (0, 1),
+where c > 1 depends only on n, p, and σ.
+Proof. Let σ > 0 and p ∈ (1, ∞) be given. Suppose that the conclusion of
+this lemma does not hold. Then for each j = 1, 2, · · · , there must exist an
+
+16
+SUNGHAN KIM AND HENRIK SHAHGHOLIAN
+exponent qj > 1 with |qj − p| ց 0, a local minimizer uj ∈ W 1,p∧qj(Q1) of
+the functional Jp,qj, and a scale rj ∈ (0, 1), such that
+(4.2)
+ˆ
+Q1
+((u+
+j )p + (u−
+j )qj) dx ≤ 1,
+uj(0) = 0,
+but with σ+ = σ and σj,− = 1 − (1 − σ) p
+qj → σ,
+(4.3)
+Sj :=
+sup
+rj≤r≤1
+�
+1
+rσ+p
+ˆ
+Qr
+dx +
+1
+rσj,−qj
+ˆ
+Qr
+(u−
+j )qj
+�
+dx ր ∞.
+To have the first inequality in (4.2) and (4.3) to be compatible, we must have
+rj ց 0 up to a subsequence. As in the proof of Lemma 3.4, we consider the
+rescaling
+vj(y) :=
+u+
+j (rjy)
+S
+1
+p
+j rσ+
+j
+−
+u−
+j (rjy)
+S
+1
+qj
+j rσj,−
+j
+.
+Then vj is a minimizer of Jp,qj in Q1/rj and that
+(4.4)
+sup
+1≤R≤ 1
+rj
+�
+1
+Rσ+p
+ˆ
+QR
+(v+
+j )p dx +
+1
+Rσj,−qj
+ˆ
+QR
+(v−
+j )qj dx
+�
+= 1.
+Then by [CKS21, Theorem 1.2], we have
+(4.5)
+sup
+j
+∥vj∥C0,¯σ(QR) < ∞,
+where both c > 1 and ¯σ ∈ (0, 1) depend only on n and p; see Lemma
+4.1 for the stability of ¯σ and c for the case p = n. Moreover, by [CKS21,
+Lemma 3.4], v+
+j (and v−
+j ) is a weak p-(resp. qj-)subsolution, so the higher
+integrability [GG82, Theorem 4.1] applies. Utilizing |qj−p| ց 0, there exists
+η > 0, depending only on n and p, such that
+(4.6)
+sup
+j
+ˆ
+QR
+|Dvj|p+η dx < ∞.
+Also observe from (4.2) that
+(4.7)
+vj(0) = 0.
+By (4.5) and (4.6), we can extract a subsequence of {vj}∞
+j=1 along which
+vj → v weakly in W 1,p+η
+loc
+(Rn) and locally uniformly in Rn, for some v ∈
+W 1,p+η
+loc
+∩ C0,σ
+loc (Rn). Let us continue to denote this subsequence by {vj}∞
+j=1.
+The uniform convergence along with (4.7) implies that
+(4.8)
+v(0) = 0.
+We claim that v is a (weak) p-harmonic function in Rn.
+For any large j, we have qj ∈ (p − η, p + η). By (4.6) and the compact
+embedding, vj → w strongly in W 1,p
+loc (Rn). Now fix R ≥ 1, and let ϕ ∈
+W 1,p+η
+0
+(QR) be arbitrary. Then since |qj − p| ց 0, |Dv−
+j |qj → |Dv−|p and
+
+17
+|D(vj+ϕ)−|qj → |D(v+ϕ)|p a.e. in QR. Then by the dominated convergence
+theorem and the minimizerslity of Jp,qj(vj, QR),
+(4.9)
+ˆ
+QR
+|Dv|p dx = lim
+k→∞
+ˆ
+QR
+(|Dv+
+j |p + |Dv−
+j |qj) dx
+≤ lim
+k→∞
+ˆ
+QR
+(|D(vj + ϕ)+|p + |D(vj + ϕ)−|qj) dx
+=
+ˆ
+QR
+|D(v + ϕ)|p dx.
+Thus, v minimizes Jp,p(·, QR) over all variations v+ϕ with ϕ ∈ W 1,p+η
+0
+(QR).
+This suffices to guarantee v to be (weak) p-harmonic in QR, see [Lin19].
+Since R was any number larger than 1, the claim is now verified.
+Now letting k → ∞ in (4.4) and using qj → p, we obtain
+(4.10)
+sup
+R≥1
+1
+Rσp
+ˆ
+QR
+|v|p dx = 1.
+By the interior Lipschitz estimate for p-harmonic functions,
+(4.11)
+[v]C0,1(QR) ≤
+c
+R1−σ ,
+for some c independent of R. Taking R → ∞ in (4.11), we derive that v is
+constant in Rn, which together with (4.8) implies v ≡ 0. This is yields a
+contradiction against (4.10), and the proof is finished.
+□
+Next we extend the above lemma to local (1 + ε)-minimizers.
+Lemma 4.3. For any σ ∈ (0, 1), there exists ε, δ > 0, depending only on n,
+p, and σ, such that for any q ∈ (1, ∞) with |p − q| < δ, and any local local
+(1 + ε)-minimizer u ∈ W 1,p∧q(Q1) satisfying (4.1), one has, with σ+ = σ
+and σ− = 1 − (1 − σ)p
+q, that
+1
+rn+σ+p
+ˆ
+Qr
+(u+)p dx +
+1
+rn+σ−q
+ˆ
+Qr
+(u−)q dx ≤ c,
+∀r ∈ (0, 1),
+where c > 1 depends only on n, p, and σ.
+Proof. As already observed in the proof of Proposition 3.3, the assumption
+u(0) = 0 implies (3.11) for every r ∈ (0, 1). Hence, the assumption (4.1)
+implies (3.4). The rest of the proof is the same with that of Lemma 3.4. More
+exactly, given σ ∈ (0, 1) and p > 1, we first choose δ > 0 sufficiently small
+such that Lemma 4.2 holds with 1+σ
+2
+in place of σ, for all local minimizers
+for functional Jp,q for any q ∈ (1, ∞) with |p − q| < δ. Then we can take
+ε > 0 small enough such that Lemma 3.4 holds with τ as in (3.11), σ+ = σ
+and σ− = 1 − (1 − σ)p
+q, ¯σ+ = 1+σ
+2
+> σ = σ−, and ¯σ− = 1 − (1−σ
+2 )p
+q >
+1 − (1 − σ)p
+q = σ−. We skip the details.
+□
+We are ready to prove the almost Lipschitz regularity for almost mini-
+mizers, when |p − q| ≪ 1.
+
+18
+SUNGHAN KIM AND HENRIK SHAHGHOLIAN
+Proof of Theorem 1.3. With the same (and simpler) compactness argument,
+we can also prove that local (1 + ε)-minimizers for Jp,p(w) ≡
+´
+|Dw|p dx is
+of class C0,σ, for any σ ∈ (0, 1) and every ε ∈ (0, εσ), since p-harmonic
+functions are of class C1,α ⊂ C0,1. Moreover, we can obtain a uniform C0,σ-
+estimates, with this compactness argument, and the smallness constant εσ
+depends only on n, p, and σ. Thus, the passage from Lemma 4.3 to Theorem
+1.3 is standard. We shall not present the obvious details here.
+□
+Declarations
+Data availability statement: All data needed are contained in the man-
+uscript.
+Funding and/or Conflicts of interests/Competing interests: The
+authors declare that there are no financial, competing or conflict of interests.
+References
+[AT15]
+M. D. Amaral and E. V. Teixeira, Free transmission problems, Comm. Math.
+Phys. 337 (2015), 1465–1489.
+[CKS21] M. Colombo, S. Kim and H. Shahgholian, A transmission problem for (p, q)-
+Laplacian, to appear in Comm. in Partial Differential Equations.
+[DET19] G. David, M. Engelstein, and T. Toro, Free boundary regularity for almost min-
+imizers, Adv. Math. 350 (2019), 1109–1192.
+[DS20]
+D. De Silva and O. Savin, Almost minimizers of the one-phase free boundary
+problem, Comm. Partial Differential Equations 45 (2020), 913–930.
+[DJS22] D. De Silva, S. Jeon and H. Shahgholian, Almost minimizers for a singular system
+with free boundary, J. Differential Equations 336 (2022), 167–203.
+[GG82]
+M. Giaquinta and E. Giusti, On the regularity of the minimizers of variational
+integrals, Acta Math. 148 (1982), 31–46.
+[Giu03]
+E. Giusti, Direct methods in the Calculus of Variations, World Scientific, 2003.
+[Lin19]
+P. Lindqvist, Notes on the Stationary p-Laplace Equation, Springer International
+Publishing, 2019.
+Department of Mathematics, Uppsala University, S-751 06 Uppsala, Sweden
+Email address: sunghan.kim@math.uu.se
+Department of Mathematics, Royal Institute of Technology, 100 44 Stock-
+holm, Sweden
+Email address: henriksh@kth.se
+
diff --git a/5dFAT4oBgHgl3EQfmh3P/content/tmp_files/load_file.txt b/5dFAT4oBgHgl3EQfmh3P/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..af0ee547e514fdff4c72f1db605709dcc6da47d4
--- /dev/null
+++ b/5dFAT4oBgHgl3EQfmh3P/content/tmp_files/load_file.txt
@@ -0,0 +1,570 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf,len=569
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='08624v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='AP]  20 Jan 2023  ALMOST MINIMIZERS TO A TRANSMISSION PROBLEM  FOR (p, q)-LAPLACIAN  SUNGHAN KIM AND HENRIK SHAHGHOLIAN  Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' This paper concerns almost minimizers of the functional  J(v, Ω) =  ˆ  Ω  �  |Dv+|p + |Dv−|q�  dx,  where 1 < p ̸= q < ∞ and Ω is a bounded domain of Rn, n ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' We  prove the universal H¨older regularity of local (1 + ε)-minimizers, when  ε is universally small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Moreover, we prove almost Lipschitz regularity  of the local (1 + ε)-minimizers, when |p − q| ≪ 1 and ε ≪ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Contents  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Introduction  1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Technical Tools  4  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  H¨older regularity  10  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Almost Lipschitz regularity  14  Declarations  18  References  18  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Introduction  In this paper, we study regularity properties of almost minimizers to the  functional  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='1)  J(u, Ω) ≡ Jp,q(u, Ω) :=  ˆ  Ω  (|Du+|p + |Du−|q) dx,  where Ω ⊂ Rn is a bounded domain and 1 < p, q < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Our primary  goal is to prove a universal H¨older estimate for the almost minimizers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' We  shall also study various scenarios, on the relation between p and q, to see  if the regularity can be improved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' In particular, we aim at proving almost  Lipschitz regularity provided that p and q are close to each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  The notion of local K-minimizers is given as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Shahgholian was supported in part by Swedish Research Council.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' This project  was finalized during the program Geometric aspects of nonlinear PDE at Institute Mittag  Leffler, Stockholm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  1  2  SUNGHAN KIM AND HENRIK SHAHGHOLIAN  Definition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='1 (Local K-minimizers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Let K ≥ 1 be a constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' We shall  call u ∈ W 1,p∧q  loc  (Ω) a local K-minimizer of the functional J, if for any cube  Q ⊂ Ω, J(u, Q) < ∞, and  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='2)  J(u, Q) ≤ KJ(v, Q),  for any v ∈ u + W 1,p∧q  0  (Q) such that J(v, Q) < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  In the course of this paper, we shall be interested in the case K = 1 + ε,  for some small ε > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' We remark that our analysis does not change, as  one replaces cubes with balls in the above definition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' However, it is worth  mentioning that the notion with cubes is in general not equivalent to hat  with balls, unless K = 1, and local K-minimizers with cubes are known to  be less restrictive;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' see [Giu03, Example 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  In the framework of standard functionals (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=', those without break across  some level set), the universal H¨older regularity is established for quasi-  minimzers (those with K > 1 any, and Q in (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='2) replaced with spt(u − v)),  as the essential arguments for the proof of the H¨older regularity for exact  minimizers remain unchanged upon the extension;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' see [Giu03].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' In contrast,  thanks to the particular break across the zero-level set in Jp,q, many impor-  tant steps in the proof of [CKS21, Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='2] for the H¨older regularity of  exact minimizers to our functional Jp,q are destroyed when applied to quasi-  minimzers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Still, we were able to extend the argument to (1+ε)-minimizers,  when ε is universally small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' There are constants ε > 0 and σ ∈ (0, 1), depending only on  n, p+, and p−, such that if u ∈ W 1,p+∧p−(Q2) is a local (1 + ε)-minimizer  of Jp+,p−, then u± ∈ C0,σ±  loc (Q1) with σ+ = σ, σ− = 1 − (1 − σ)p−  p+ , and  [u±]C0,σ±(Q1) ≤ c  �ˆ  Q2  ((u+)p+ + (u−)p−) dx  � 1  p± ,  where c depends only on n, p+, and p−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  We remark that the above theorem also shows the exact relation between  the H¨older exponents for each phase;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' this was not contained in the authors  earlier collaboration [CKS21, Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='2] with M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Colombo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Our proof  involves a careful extension of the main ingredients for [CKS21, Theorem  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='2] to local (1 + ε)-minimizers, and a compactness argument.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  A key feature of local (1 + ε)-minimizers, ε ≥ 0, for the functional Jp,q  is that the positive and negative phase scales differently from each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Namely if u is a local (1+ε)-minimizer in Q2, then one needs ∥u+∥X compa-  rable with ∥u−∥q/p  X , with X = Lp(Q1) or L∞(Q1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' As for the case of the local  minimizers, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=', ε = 0, the comparability was proved by a Harnack inequal-  ity argument [CKS21, Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='7, Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='8], which played an essential  role in the proof of their universal H¨older regularity [CKS21, Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  The main difference, which also amounts to the challenges here, for the  case of local (1+ε)-minimizers, ε > 0, is the lack of such a Harnack inequality  3  argument.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' More fundamentally, local (1 + ε)-minimizers do not possess the  subsolution properties as opposed to local minimizers (see [CKS21, Lemma  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='4]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' One of the consequences is that the basic estimates for one phase,  such as the Cacciopoli inequality (Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='2) and the comparison lemma  (Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='1) for local (1+ε)-minimizers, involve an additional ε-factor of the  other phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Hence, our main task here is to effectively control the additional  ε-term, which amounts to some technical difficulties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' It is worthwhile to  mention that the absence of the Harnack inequality argument is overcome  by a careful compactness argument, by which both phases, although scaled  differently, survive at the limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' The latter part is new, to the best of the  authors’ knowledge, and can be applied to a wider range of problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Our second result is about the almost Lipschitz regularity for local (1+ε)-  minimizers for the functional Jp,q, when |p − q| ≪ 1 and ε ≪ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Let 1 < p+ < ∞ and σ ∈ (0, 1) be given.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Then there  exist ε, δ > 0, depending only on n, p+ and σ, such that for any p− ∈  (p+−δ, p+ +δ) and any local (1+ε)-minimizer u ∈ W 1,p+∧p−(Q2) of Jp+,p−,  one has u± ∈ C0,σ±(Q1), with σ+ = σ, σ− = 1 − (1 − σ)p−  p+ , and  [u]C0,σ±(Q1) ≤ c  �ˆ  Q2  ((u+)p± + (u−)p−) dx  � 1  p± ,  where c depends only on n, p+ and σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  A similar statement is proved in [AT15] for uniformly elliptic function-  als when governing conductivity matrices are close with each other;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' [AT15]  however considers local minimizers (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=', ε = 0) only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Our problem is philo-  sophically the same, as the limit case is clean, thus possess better regularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  On the technical level, our argument is needs slight more care than that  of [AT15, Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='1], as the proof for the growth of the functional Jp,q  changes as (p, q) varies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Moreover, one needs to make sure that the argument  works well regardless of the relation between p (or q) and the dimension n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  These are all rigorously treated in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Recently, free boundaries for almost minimizers are investigated in various  settings, see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=', [DET19], [DS20], and [DJS22] to mention a few.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' There  is a possibility of extending the approach with viscosity solutions employed  in [DS20], but it is beyond the scope of this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' It would be already  interesting to extend the result for the clean case, p = q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  In [CKS21], the authors analyze the free boundary of local minimizers for  Jp,q, using the measure ∆pu+, which is nonnegative and supported on the  free boundary, ∂{u > 0}(=∂{u < 0}).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' This is mainly due to the subsolu-  tion property of u+, which is no longer valid for almost minimizers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' The  same issue appears in the case of the two-phase Alt-Caffarelli functional  (see [DET19, Section 4]), which is resolved by the NTA property of the free  boundary and a clever use of barriers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' The NTA property was obtained  there by the use of the ACF monotonicity formula, which is absent in our  4  SUNGHAN KIM AND HENRIK SHAHGHOLIAN  regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' The construction of the barriers and the comparison with the al-  most minimizers require some regularity of the free boundary, which in the  case of [DET19] was the NTA property.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' However, in our problem, none of  these seems to be analogously carried out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' For this reason, we leave out the  analysis of the free boundary for our almost minimizers to the interested  reader.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  The paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' In Section 2, we collect some technical  tools to prepare the proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' In Section 3, we prove Theorem  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' In Section 4, we prove Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  We follow the standard notation and terminology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' In particular, n denotes  the dimension of the underlying space, and there is no restriction other than  n ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' By Qr(x0), we denote the cube centered at x0 with side-length r,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=', Qr(x0) := {x ∈ Rn : |xi − x0i| < r, 1 ≤ i ≤ n}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' For simplicity, we set  Qr := Qr(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Given a set A ⊂ Rn, by |A| we denote the Lebesgue measure  of A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' The function spaces C0,σ and W 1,p are standard H¨older and Sobolev  spaces, and C0,σ  loc , W 1,p  loc are their local versions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Technical Tools  In this section, we shall present and verify some technical tools, most of  which generalize those appeared in [CKS21, Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' 4–5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' The main goal of  this section is to prove the following proposition, which roughly tells us that  negative values cannot penetrate the interior if a local (1 + ε)-minimizer  attains large positive values in most of the domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Let us remark that  this proposition corresponds to [CKS21, Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='2] for the case of  minimizers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  The main difference here is that (1 + ε)-minimizers do not  possess in general the subsolution properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Here we exploit the techniques  to circumvent this issue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Unless stated otherwise, the constant c throughout  this section is a positive constant that may differ at each occurrence, and  will depend at most on n, p, and q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Moreover, the parameter ε will be a  small constant, whose smallness is determined solely by n, p, and q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' There exist ε > 0 and µ > 0, depending only on n, p, and  q, such that if u ∈ W 1,p∧q(Q1) is a local (1 + ε)-minimizer of the functional  J, satisfyingˆ  Q1  ((u+)p + (u−)q) dx ≤ 1,  |{u ≤ 1/2} ∩ Q1| ≤ ε,  then u > 0 a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' in Qµ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  The proof for this proposition will be postponed to the end of this section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Let us begin with the Cacciopoli-type inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Let u ∈ W 1,p∧q(Q2) be a local (1 + ε)-minimizer of the func-  tional J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' There exists ¯ε ∈ (0, 1), depending only on n, p, and q, such that if  ε ≤ ¯ε, then  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='1)  ˆ  Q1  |Du+|p dx ≤ c  ˆ  Q2  ((u+)p + ε(u−)q) dx,  5  where c depends only on n, p, and q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Fix r, R with 1 < r < R < 2, and choose any s, t with r < s < t < R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Let η ∈ C1  c (Qt) be a cutoff function such that η ≡ 1 in Qs, |Dη| ≤  2c  t−s in  Qt, and spt(η) ⊂ Q(t+s)/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Set w := (1 − η)u+ − u− ∈ W 1,p∧q(Qt).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Since  w+ = (1 − η)u+, w− = u−, and spt(u − w) ⊂ spt(η) ⊂ Q(t+s)/2, we derive  from the (1 + ε)-minimizerslity of u for Jp,q in Qt that  ˆ  Qr  |Du+|p dx ≤ (1 + ε)  ˆ  Qt  |D((1 − η)u+)|p dx + ε  ˆ  Qt  |Du−|q dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Applying H¨older’s inequality and Young’s inequality, and then using spt(η) ⊂  Q(t+s)/2 and |Dη| ≤ c/(t − s), we deduce that  ˆ  Qs  |Du+|p dx ≤ c  ˆ  Qt  � (u+)p  (t − s)p + ε|Du−|q  �  dx + cε  ˆ  Qt  |Du+|p dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Since this part is by now standard, we omit the details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Note that the last  display holds for all s, t, r < s < t < R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Hence, choosing ε small enough such  that cε < 1  2, we can employ the standard iteration lemma [Giu03, Lemma  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='1] to derive that  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='2)  ˆ  Qr  |Du+|p dx ≤ c  ˆ  QR  � (u+)p  (R − r)p + ε|Du−|q  �  dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Now replace QR in the right-hand side with Q(R+r)/2, and then apply  the same argument above to (−u) with Qr replaced with Q(R+r)/2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' note  that (−u) is a local (1 + ε)-minimizer of Jq,p in place of Jp,q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Then we may  proceed as follows,  ˆ  Qr  |Du+|p dx ≤ c  ˆ  Q(R+r)/2  � (u+)p  (R − r)p + ε|Du−|q  �  dx  ≤ c  ˆ  QR  � (u+)p  (R − r)p + cε (u−)q  (R − r)q  �  dx + c2ε2  ˆ  QR  |Du+|p dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Recall that r, R were any numbers between 1 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Hence, taking ε smaller  if necessary such that c2ε2 < 1  2, we can make use of the iteration lemma  once again to arrive at (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  □  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' In what follows, we shall always assume that ε < ¯ε, with ¯ε  as in Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Let us remark that the above Cacciopoli inequality is too weak to bring  forth a local L∞-estimate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Besides, local quasi-minimizers are not neces-  sarily bounded, even for functionals under standard growth condition (of  course, only if p ≤ n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Nevertheless, with the aid of the Cacciopoli inequal-  ity above, we shall observe that the blowup rate of local (1 + ε)-minimizers  can be made arbitrarily small, for small ε, in case p ≤ n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  6  SUNGHAN KIM AND HENRIK SHAHGHOLIAN  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Let u ∈ W 1,p∧q(Q1) be a local (1 + ε)-minimizer of the func-  tional J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Suppose that  ∥u+∥Lp(Q1) ≤ 1,  sup  r∈(0,1)  ∥u−∥Lq(Qr)  r1− p  q ∥u+∥  p  q  Lp(Qr)  ≤ κ,  for some constant κ > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Then for any δ > 0, there exists a positive constant  εκ,δ, depending only on n, p, q, κ and δ, such that if ε ≤ εκ,δ, then  sup  r∈(0,1)  1  rn−δp  ˆ  Qr  (u+)p dx ≤ cκ,δ,  where cκ,δ depends only on n, p, q, Λ, δ and κ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' We remark that the conclusion is trivial for p > n, due to the Sobolev  embedding theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Henceforth, we shall assume that 1 < p ≤ n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Let κ and δ be arbitrary positive constants, and suppose the conclusion  of the lemma is false.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Then for each j = 1, 2, · · · , one can find some positive  constant εj ց 0, and a local (1 + εj)-minimizer uj ∈ W 1,p∧q(Q1) of the  functional J, such that  ∥u+  j ∥Lp(Q1) ≤ 1,  sup  r∈(0,1)  ∥u−  j ∥Lq(Qr)  r1− p  q ∥u+  j ∥  p  q  Lp(Qr)  ≤ κ,  but  Sj =  sup  rj≤r≤1  1  rn−δp  ˆ  Qr  (u+  j )p dx → ∞,  for some constant rj ∈ (0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' In order to have Sj → ∞ to be compatible  with ∥u+  j ∥Lp(Q1) = 1, we must have rj → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Consider an auxiliary function vj : Qr−1  j  → R, defined by  vj(y) =  u+  j (rjy)  r  − n  p  j  ∥u+  j ∥Lp(Qrj )  −  u−  j (rjy)  r  1− p  q − n  q  j  ∥u+  j ∥  p  q  Lp(Qrj )  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  One easily verifies that vj ∈ W 1,p∧q(Qr−1  j ) is a local (1 + εj)-minimizer of  the functional J, and  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='3)  sup  1≤R≤r−1  j  1  Rn−δp  ˆ  QR  (v+  j )p dy = 1,  where the supremum is attained at R = 1, and  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='4)  sup  1≤R≤r−1  j  1  Rn+q−(1+δ)p  ˆ  QR  (v−  j )q dy ≤ κq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Due to Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='2, along with (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='3) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='4),  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='5)  ˆ  QR  (|Dv+  j |p + |Dv−  j |q) dx ≤ cRn−(1+δ)p,  7  where c depends only on n, p and q, whenever 2Rrj ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' By the Sobolev em-  bedding theory, there exists a function v ∈ W 1,p∧q  loc  (Rn) with v+ ∈ W 1,p  loc (Rn)  and v− ∈ W 1,q  loc (Rn) such that v+  j → v+ and v−  j → v−  j weakly in W 1,p  loc (Rn)  and respectively W 1,q  loc (Rn), after extracting a subsequence if necessary;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' we  shall denote this subsequence by vj, for brevity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' The weak convergence im-  plies that v ∈ W 1,p∧q(BR) is a minimizer of the functional J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Since v+  j → v+  strongly in Lp(BR) and v−  j → v− strongly in Lq(BR), letting j → ∞ in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='3)  yields that  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='6)  sup  R≥1  1  Rn−δp  ˆ  QR  (v+)p dy = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  However, since v is a minimizer of the functional J, by [CKS21, Lemma  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='4], v+ is a weak p-subsolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' As a result, the local L∞-estimates [Giu03,  Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='3] applies to v+, which along with (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='6) yields  ∥v+∥L∞(QR) ≤ c  Rδ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Hence, letting R → ∞ yields that v+ = 0 a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' in Rn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' This yields a contra-  diction against (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  □  We also have a growth estimate for the p-th Dirichlet energy of the positive  phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' The idea is the same as in [CKS21, Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='5], which is based on  some approximation by positive p-harmonic functions of the positive phase  of local quasi-minimizers, in terms of the size of the negative phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Let u ∈ W 1,p∧q  loc  (Q2) be a local (1 + ε)-minimizer of the func-  tional J, and v ∈ u+ + W 1,p  0 (Q1) be the p-harmonic function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Then  0 ≤  ˆ  Q1  (|Du+|p − |Dv|p) dx ≤ c  ˆ  Q2  ((u−)q + ε|Du+|p) dx,  and  ˆ  Qr  |Du+|p dx ≤ c  ˆ  Q1  ((rn + ε)|Du+|p + (u−)q) dx,  ∀r ∈ (0, 1),  where c depends only on n, p and q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' The proof is essentially the same as that of [CKS21, Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  The additional term ε  ´  Q2 |Du+|p dx appears due to the different Cacciopoli  inequality;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' more exactly, we use (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='2) with u replaced with −u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' We shall  not repeat this argument here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  □  The following lemma corresponds to [CKS21, Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' The key in-  gredient of the proof there is the Poincar´e inequality, and Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='5, which  corresponds to [CKS21, Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' As noted above, Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='5 differs  from [CKS21, Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='5] by the additional term, ε  ´  Q2 |Du+|p dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' How-  ever, this does not make any difference in the proof of the lemma below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Thus, we shall skip the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  8  SUNGHAN KIM AND HENRIK SHAHGHOLIAN  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='6 (Essentially due to [CKS21, Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='8]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Let u ∈ W 1,p∧q(Q4)  be a local 2-minimizer for the functional J, satisfying  ˆ  Q4  (u+)p dx = 1,  ˆ  Q4  ((u−)q + |Du+|p) dx ≤ ε,  for some ε > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Then  |{u ≤ 1/2} ∩ Q1| ≤ cε,  where c depends only on n, p and q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Let us prove Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='1 with additional assumptions that ∥u−∥Lq(Q1)  and ∥Du+∥Lp(Q!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=') are sufficiently small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' The proof follows the idea of that  of [CKS21, Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='5], with some modifications addressing the lack of  subsolution properties of each phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' There exists ε > 0, depending only on n, p and q, such that if  u ∈ W 1,p∧q(Q4) is a local (1 + ε)-minimizer of the functional J, satisfying  ˆ  Q4  (u+)p dx = 1,  ˆ  Q4  ((u−)q + |Du+|p) dx ≤ ε,  then u > 0 a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' in Q1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Let us consider the case q < n first.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Following the proof of [CKS21,  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='3], we obtain that for σ ∈ (0, 1),  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='7)  ˆ  Qr  �(u−)q  rq  + |Du+|p  �  dx ≤ cεr−(1−σ)p  ˆ  Qr  (u+)p dx,  ∀r ∈ (0, 1),  where c depends only on n, p, q and σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' The proof is essentially the same,  as Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='5 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='6 replace [CKS21, Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='5–3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='7], which are the key  ingredients of the proof there;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' moreover Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='2 replaces the usual Cac-  ciopoli inequality for weak q-subsolutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' These lemmas have additional  ε-term, which arise from the (1 + ε)-local minimizerslity of u, but this does  not contribute any major difference from the proof for [CKS21, Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Hence, we shall omit the details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  We observe that due to (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='7) (as well as the assumption  ´  Q4(u+)p dx = 1),  the hypothesis of Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='4 is satisfied (with κ = 1 > εrσp).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Thus, choosing  ε ≤ εδ with εδ as in Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='4 with δ < σ, we deduce  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='8)  ˆ  Qr  (u+)p dx ≤ cr−δp,  ∀r ∈ (0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Inserting (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='8) into (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='7) yields that  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='9)  ˆ  Qr  |Du+|p dx ≤ cεr−(1−(σ−δ))p,  ∀r ∈ (0, 1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  now c depends only on n, p, q, σ and δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Let us remark that this step does  not appear for the case of minimizers [CKS21, Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='3] because for the  latter case we can use the subsolution property [CKS21, Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='4] for u+  to obtain its local boundedness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  9  The growth estimate in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='9) is obtained by choosing ε sufficiently small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Taking ε even smaller if necessary, we may repeat the above argument  around any point z ∈ Q1, and obtain  ˆ  Qr(z)  |Du+|p dx ≤ cεr−(1−(σ−δ))p,  ∀r ∈ (0, 1), ∀z ∈ Q1,  possibly with a larger constant c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Therefore, by Morrey’s lemma, we deduce  that u+ ∈ C0,σ−δ(Q1) and  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='10)  [u+]C0,σ−δ(Q1) ≤ cε  1  p .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Finally, by Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='6, |{u ≤ 1  2} ∩ Q1| ≤ cε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Hence, with cε ≤ 2−2n−1, we  have |{u > 1  2} ∩ Q1| > 0, which now implies via (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='10) that  inf  Q1 u+ ≥ 1  2 − cε  1  p > 0,  provided that we choose ε even smaller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Note that the smallness condition  for ε at this stage can be determined solely by n, p and q, by for instance  selecting σ = 1  2 and δ = 1  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' This finishes the proof for the case q < n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  The case for q ≥ n can be treated similarly, following the proof of [CKS21,  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='3];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' we omit the details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  □  We are ready to prove Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Proof of Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Let ¯ε be as in Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='7, and suppose that cε ≤ ¯ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Using |{u ≤ 1  2} ∩ Q1| ≤ ε, we may follow the proof of [CKS21, Proposition  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='2] to find a constant ρ, depending only on n, p and q, such that  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='11)  ˆ  Q4ρ  �(u−)q  ρq  + |Du+|p  �  dx ≤ cερq−p  ˆ  Q4ρ  (u+)p dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Therefore, defining uρ : Q4 → R by  uρ(x) =  u+(ρx)  (4ρ)− n  p ∥u+∥Lp(Q4ρ)  −  u−(ρx)  4− n  q ρ1− p  q − n  q ∥u+∥  p  q  Lp(Q4ρ)  ,  we see that uρ ∈ W 1,p∧q(Q4) is a local (1 + ε)-minimizer of the functional  J, such that  ˆ  Q4  (u+  ρ )p dx = 1,  ˆ  Q4  ((u−  ρ )q + |Du+  ρ |p) dx ≤ cε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Since cε ≤ ¯ε, with ¯ε as in Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='6, we obtain  uρ > 0  a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' in Q1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Rescaling back, we obtain that u > 0 a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' in Q4ρ as desired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  □  10  SUNGHAN KIM AND HENRIK SHAHGHOLIAN  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' H¨older regularity  In this section, we study the universal H¨older regularity of local (1 + ε)-  minimizers for the functional Jp,q, and prove our first main result, Theorem  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Let us begin with a lemma that tells us how each phase of local mini-  mizers for the functional Jp,q should scale relatively to one another.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Let u ∈ W 1,p∧q(Q1) be a local minimizer of the functional J,  such that ∥u+∥Lp(Q1) = 1 and u(0) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' If ∥u+∥Lp(Q1/2) ≥ β for some β > 0,  then ∥u−∥Lq(Q1) ≥ cβ, for some positive constant cβ depending only on n,  p, q and β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Let β be any constant, with 0 < β < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Assume by way of contradic-  tion that there exists a minimizer uj ∈ W 1,p∧q(Q1) of the functional J, such  that ∥u+  j ∥Lp(Q1) = 1, ∥u+  j ∥Lp(Q1/2) ≥ β, uj(0) = 0 but ∥u−  j ∥Lq(Q1) ≤ 1  j .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' By  [CKS21, Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='1], uj ∈ C0,σ(Q1/2) and ∥u+  j ∥C0,σ(Q1/2) ≤ c∥u+  j ∥Lp(Q1) ≤  c, and similarly, ∥u−  j ∥C0,σ(Q1/2) ≤ c  j, where both c and σ depend only on n, p  and q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' This together with the Cacciopoli inequality (Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='2 with ε = 0)  implies that u+  j → u0 weakly in W 1,p(Q1/2) and uniformly in Q1/2, while  u−  j → 0 weakly in W 1,q(Q1/2) and uniformly in Q1/2, for some nonnegative  function u0 ∈ W 1,p(Q1/2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' The uniform convergence along with uj(0) = 0  implies that u0(0) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' In addition, passing to the limit in ∥u+  j ∥Lp(Q1/2) ≥ β  ensures that ∥u0∥Lp(Q1/2) ≥ β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' However, the weak convergence of the gradi-  ent of uj implies that u0 is also a minimizer of the functional J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' As u0 ≥ 0  in Q1/2, u0 is a p-harmonic function, but then it violates the minimizer  principle, as ∥u0∥Lp(Q1/2) ≥ β > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  □  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Let u ∈ W 1,p∧q(Q1) be a local minimizer of the functional J,  such that  ∥u+∥Lp(Q1) ≤ 1,  u(0) = 0,  sup  0<r<1  1  rn+σ−q  ˆ  Qr  (u−)q dx ≤ c−,  for some constants c− > 0 and σ− ∈ (0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Then with σ+ = 1 − (1 − σ−) q  p,  sup  0<r<1  1  rn+σ+p  ˆ  Qr  (u+)p dx ≤ c+,  where c+ depends only on n, p, q, σ− and c−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Let c−, σ− be given, and set σ+ as in the statement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Suppose that  the conclusion of this lemma is false.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Then for each j ∈ N, one can find a  minimizer uj ∈ W 1,p∧q(Q1) for the functional J, such that  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='1)  ˆ  Q1  (u+  j )p dx ≤ 1,  uj(0) = 0,  sup  0<r<1  1  rn+σ−q  ˆ  Qr  (u−  j )q dx ≤ c−,  but  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='2)  Sj :=  sup  rj  2 ≤r≤1  1  rn+σ+p  ˆ  Qr  (u+  j )p dx → ∞  11  where the supremum is achieved at r = 1  2rj;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' since ∥u+  j ∥Lp(Q1) ≤ 1, we must  have rj → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Define  vj(y) :=  u+  j (rjy)  r  − n  p  j  ∥u+  j ∥Lp(Qrj )  −  u−  j (rjy)  r  1− p  q − n  q  j  ∥u+  j ∥  p  q  Lp(Qrj )  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Then vj is a local minimizer of the functional J, such that by (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='1) and (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='2),  ∥v+  j ∥Lp(Q1) = 1, ∥v+  j ∥Lp(Q1/2) ≥ 2−σ+ and vj(0) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Therefore, Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='1  yields that ∥v−  j ∥Lq(Q1) ≥ cσ+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' This implies that  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='3)  1  rn  j  ˆ  Qrj  (u−  j )q dx ≥ cq  σ+rq−p  j  ˆ  Qrj  (u+  j )p dx ≥  S  q  p  j cq  σ+  2σ+q rq−p+σ+p  j  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Putting (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='1) and (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='3) together, and recalling that σ+ = 1 − (1 − σ−) q  p,  cq  σ− ≥  S  q  p  j cq  σ+  2σ+q ,  a contradiction to the assumption that Sj → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  □  Thanks to the above lemma, we can prove Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='2 for minimizers of  the functional J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='2 for minimizers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' It suffices to consider the case p > q,  and  ˆ  Q1  ((u+)p + (u+)q) dx = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  By [CKS21, Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='1], we already know that u ∈ C0,σ(Q1) and that  [u]C0,σ(Q1) ≤ c, where both c > 0 and σ ∈ (0, 1) depend only on n, p and q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Hence, if u(z) = 0 at some z ∈ Q1/2, then  sup  0<r< 1  2  1  rn+σq  ˆ  Qr(z)  (u−)q dx ≤ c,  which along with Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='2 implies that  sup  0<r< 1  2  1  rn+p−q+σq  ˆ  Qr(z)  (u+)p dx ≤ c,  where the constant c in both displays depends only on n, p and q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Since  p > q, 1 − (1 − σ) q  p > σ > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Now setting σ− = σ and σ+ = 1 − (1 − σ) q  p,  we immediately verify the relation required between σ+ and σ−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Since the  above growth estimates hold uniformly around all z ∈ {u = 0} ∩ Q1, and  since ∆pu = 0 in {u > 0}∩Q1 and ∆qu = 0 in {u < 0}∩Q1, one may arrive  at the conclusion via some standard manipulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' We skip the detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  □  12  SUNGHAN KIM AND HENRIK SHAHGHOLIAN  Given a measurable function u : Ω → R, define D+(u), D−(u) and Γ(u)  by the subset of Ω as follows:  D+(u) = {z ∈ Ω : u > 0 a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' in some Qr(z) ⊂ Ω},  D−(u) = D+(−u),  and  Γ(u) = Ω \\ (D+(u) ∪ D−(u)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  By definition, both D+(u) and D−(u) are open and hence Γ(u) is closed  (relative to the topology of Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Moreover, z ∈ Γ(u) if and only if |{u ≥  0} ∩ Qr(z)||{u ≤ 0} ∩ Qr(z)| > 0 for any cube Qr(z) ⊂ Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  With Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='1 at hand, we shall obtain, as a contraposition along  with Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='4 below, that if a local (1 + ε)-minimizer vanishes (in an ap-  propriate Lebesgue sense) at certain point in the interior, then each phase  exhibits certain universal H¨older growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' More exactly, we assert the fol-  lowing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' There exists a constant ¯σ ∈ (0, 1), depending only on  n, p, and q, for which the following holds: for each σ ∈ (0, ¯σ), one can  find a constant εσ ∈ (0, 1), depending only on n, p, q, and σ, such that if  u ∈ W 1,p∧q(Q1) is a local (1 + εσ)-minimizer of the functional J satisfying  ˆ  Q1  ((u+)p + (u−)q) dx ≤ 1,  0 ∈ Γ(u),  then with σ+ = σ and σ− = 1 − (1 − σ)p  q, one has  sup  0<r<1  �  1  rσ+p  ˆ  Qr  (u+)p dx +  1  rσ−q  ˆ  Qr  (u−)q dx  �  ≤ cσ,  where cσ depends only on n, p, q, and σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  The following lemma will play a key role (together with Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' There exists a constant ¯σ ∈ (0, 1), depending only on n, p,  and q, for which the following holds: for each σ ∈ (0, ¯σ) and each τ ∈ (0, 1  2],  one can find εσ,τ ∈ (0, 1), depending only on n, p, q, σ, and τ, such that if  u ∈ W 1,p∧q(Q1) is a local (1+εσ+,τ)-minimizer of the functional J satisfying,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='4)  ˆ  Q1  ((u+)p + (u−)q) dx = 1,  |E+(u, Qr)|  |Qr|  ∧ |E−(u, Qr)|  |Qr|  ≥ τ,  for some r ∈ (0, 1), where  E+(u, Qr) =  �  u ≤ 1  2rΛ(u, Qr)  1  p  �  ,  E−(u, Qr) =  �  u ≥ −1  2rΛ(u, Qr)  1  q  �  ,  Λ(u, Qr) =  ˆ  Qr  �(u+)p  rp  + (u−)q  rq  �  dx,  13  then with σ+ = σ and σ− = 1 − (1 − σ)p  q, one has  sup  r≤ρ≤1  �  1  ρσ+p  ˆ  Qρ  (u+)p dx +  1  ρσ−q  ˆ  Qρ  (u−)q dx  �  ≤ cσ,τ,  where cσ,τ depends on the same parameters that determine εσ,τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Let ¯σ be determined later, and fix τ ∈ (0, 1  2], σ ∈ (0, ¯σ), and set σ±  as in the stastement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Suppose by way of contradiction that for each j ∈ N,  we can find some positive constant εj → 0, some local (1 + εj)-minimizer  uj ∈ W 1,p∧q(Q1) of the functional J, and a radius rj ∈ (0, 1) such that  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='5)  ˆ  Q1  ((u+  j )p + (u−  j )q) dx ≤ 1,  |E+(uj, Qrj)|  |Qrj|  ∧ |E−(uj, Qrj)|  |Qrj|  ≥ τ, ,  but  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='6)  Sj =  sup  rj≤r≤1  �  1  rσ+p  ˆ  Qr  (u+  j )p dx +  1  rσ−q  ˆ  Qr  (u−  j )q dx  �  → ∞,  with the supremum achieved at level r = rj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' In order for (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='6) to be com-  patible with the first equality in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='5), we must have rj → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Define vj : Qr−1  j  → R by  vj(y) =  u+  j (rjy)  S  1  p  j rσ+  j  −  u−  j (rjy)  S  1  q  j rσ−  j  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  By the way that it is rescaled, vj is a local (1+εj)-minimizer of the functional  J in Q1/rj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Moreover, by (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='5) along with the relation Sjrσ+p  j  = Λjrp  j and  Sjrσ−q  j  = Λjrq  j, where Λj = Λ(uj, Qrj),  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='7)  ����  �  |vj| ≤ 1  2  �  ∩ Q1  ���� ≥ τ,  and by (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='6),  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='8)  sup  1≤R≤r−1  j  �  1  Rσ+p  ˆ  QR  (v+  j )p dy +  1  Rσ−q  ˆ  QR  (v−  j )q dy  �  = 1,  where the supremum is achieved at R = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Thanks to (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='7) and (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='8), one can argue analogously in the proof of  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='4 to obtain a minimizer v ∈ W 1,p∧q  loc  (Rn) of the functional J, with  v+ ∈ W 1,p  loc (Rn) and v− ∈ W 1,q  loc (Rn) such that  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='9)  ����  �  |v| ≤ 1  2  �  ∩ Q1  ���� ≥ τ,  and  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='10)  sup  R≥1  �  1  Rσ+p  ˆ  QR  (v+)p dy +  1  Rσ−q  ˆ  QR  (v−)q dy  �  = 1,  14  SUNGHAN KIM AND HENRIK SHAHGHOLIAN  where the supremum is achieved at R = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' In particular, the latter obser-  vation indicates that v is nontrivial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  At this point, we choose ¯σ as the positive exponent for Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='2 for  minimizers;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' let us remind the readers that the statement for minimizers is  proved right after the proof of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Set ¯σ+ := ¯σ and ¯σ− := 1 − (1 −  ¯σ) q  p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' As v is a local minimizer of the functional J in Q2R, v+ ∈ C0,¯σ+(QR),  v− ∈ C0,¯σ−(QR) and then by (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='10), we derive that  [v+]p  C0,¯σ+(QR) + [v−]q  C0,¯σ−(QR) ≤  c  R(¯σ+−σ+)p +  c  R(¯σ−−σ−)q ,  for any R > 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' As σ+ = σ < ¯σ+ and σ− = 1 − (1 − σ) q  p < ¯σ−, sending  R → ∞ implies that both v+ and v− must be constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Then by (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='9),  |v| ≤ 1  2 everywhere in Q1, whence  ´  Q1((v+)p + (v+)q) dx ≤ 2−p + 2−q < 1, a  contradiction to the observation that the supremum in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='10) is attained at  R = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  □  We are ready to prove Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='3  Proof of Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' As 0 ∈ Γ(u), there are three cases to consider: (i)  |{u > 0} ∩ Qρ||{u < 0} ∩ Qρ| > 0 for all ρ ∈ (0, 1), (ii) u ≥ 0 a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' in Qρ  for some small ρ > 0, and (iii) u ≤ 0 a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' in Qρ for some small ρ > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' The  last two cases are symmetric, and in those cases u becomes a local (1 + ε)-  minimizer for the functional Jp,p, or Jq,q depending on its sign.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Thus, the  growth estimate follows easily, once we establish the estimate for the first  case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' We leave out this part as an exercise for the reader.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Henceforth, let us assume that the first case holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Let (ε, τ, µ) be the  triple of constants from Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='1 that are determined solely by n, p  and q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Fix any r ∈ (0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Since |{u > 0} ∩ Qµr| · |{u < 0} ∩ Qµr| > 0,  as a contraposition (applied to both u and −u, after suitable rescaling), we  obtain that  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='11)  |E+(u, Qr)|  |Qr|  ∧ |E−(u, Qr)|  |Qr|  ≥ τ,  with E+(u, Qr) and E−(u, Qr) defined as in Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' As τ being a con-  stant depending only on n, p and q, the conclusion of this proposition follows  immediately from Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='4;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' this final step introduces another condition  on the size of ε, which through the dependence of τ would be determined  again solely by n, p, q, and σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  □  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Almost Lipschitz regularity  Here we prove almost Lipschitz regularity of almost minimizers to J =  Jp,q, when p and q are close.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Our proof is based on the compactness argu-  ment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' The basic ingredient is the universal H¨older estimate for local mini-  mizers of the functional Jp,q, see [CKS21, Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Although it is not  specified in the statement, one can observe from the higher integrability of  each phase that the H¨older regularity is uniform when p (or q) is close to n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  15  We record this fact as a lemma below, as the proof of [CKS21, Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='3]  makes use of the local boundedness and the Harnack inequality for weak p-  harmonic functions, and the constants involved in the latter assertions may  vary as p → n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Let u ∈ W 1,p+∧p−(Q2) be a local minimizer of Jp+,p−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' There  exists ¯δ > 0, depending only on n, such that if |n − p±| ≤ ¯δ, then  [u±]C0,¯σ(Q1) ≤ ¯c∥u±∥Lp±(Q2),  where ¯σ ∈ (0, 1) and ¯c > 1 depend only on n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Since u is a local minimizer (instead of (1 + ε)-minimizer) of Jp+,p−,  u± is a weak p±-subsolution in Q2, according to [CKS21, Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Hence,  by [GG82, Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='2], there exist constants ¯δ > 0 and ¯γ ∈ (0, 1), both  depending only on n, such that if |p± − n| < ¯δ, then u± ∈ W 1,p±+¯δ(Q1) ⊂  W 1,n+¯γ¯δ(Q1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Now setting ¯σ := 1 −  n  n+¯γ¯δ, it follows from the Sobolev em-  bedding, the higher integrability and the Cacciopoli inequality for weak  p±-subsolutions that  [u±]C0,¯σ(Q1) ≤ c1(n)  �ˆ  Q1  |Du±|n+¯γ¯δ dx  �  1  n+¯γ¯δ  ≤ c1(n)c2(n, p±)  �ˆ  Q3/2  |Du±|p± dx  � 1  p±  ≤ c1(n)c2(n, p±)c3(n, p±)  �ˆ  Q2  (u±)p± dx  � 1  p± .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Note that c2(n, p±), and c3(n, p±) are constants from the higher integrabil-  ity and respectively the Cacciopoli inequality, and these are all uniformly  bounded by a constant c(n), as p → p±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Hence, our proof is finished.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  □  Let us first verify the uniform growth of order σ at free boundary points  for minimizers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' We prove it by compactness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Let u ∈ W 1,p∧q(Q1) be a local minimizer of Jp,q such that  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='1)  ˆ  Q1  ((u+)p + (u−)q) dx ≤ 1,  u(0) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Then for any σ ∈ (0, 1), there exists δ > 0, depending only on n, p, and σ,  such that if |p − q| < δ, then with σ+ = σ and σ− = 1 − (1 − σ)p  q,  1  rn+σ+p  ˆ  Qr  (u+)p dx +  1  rn+σ−q  ˆ  Qr  (u−)q dx ≤ c,  ∀r ∈ (0, 1),  where c > 1 depends only on n, p, and σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Let σ > 0 and p ∈ (1, ∞) be given.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Suppose that the conclusion of  this lemma does not hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Then for each j = 1, 2, · · · , there must exist an  16  SUNGHAN KIM AND HENRIK SHAHGHOLIAN  exponent qj > 1 with |qj − p| ց 0, a local minimizer uj ∈ W 1,p∧qj(Q1) of  the functional Jp,qj, and a scale rj ∈ (0, 1), such that  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='2)  ˆ  Q1  ((u+  j )p + (u−  j )qj) dx ≤ 1,  uj(0) = 0,  but with σ+ = σ and σj,− = 1 − (1 − σ) p  qj → σ,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='3)  Sj :=  sup  rj≤r≤1  �  1  rσ+p  ˆ  Qr  dx +  1  rσj,−qj  ˆ  Qr  (u−  j )qj  �  dx ր ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  To have the first inequality in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='2) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='3) to be compatible, we must have  rj ց 0 up to a subsequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' As in the proof of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='4, we consider the  rescaling  vj(y) :=  u+  j (rjy)  S  1  p  j rσ+  j  −  u−  j (rjy)  S  1  qj  j rσj,−  j  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Then vj is a minimizer of Jp,qj in Q1/rj and that  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='4)  sup  1≤R≤ 1  rj  �  1  Rσ+p  ˆ  QR  (v+  j )p dx +  1  Rσj,−qj  ˆ  QR  (v−  j )qj dx  �  = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Then by [CKS21, Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='2], we have  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='5)  sup  j  ∥vj∥C0,¯σ(QR) < ∞,  where both c > 1 and ¯σ ∈ (0, 1) depend only on n and p;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' see Lemma  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='1 for the stability of ¯σ and c for the case p = n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Moreover, by [CKS21,  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='4], v+  j (and v−  j ) is a weak p-(resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' qj-)subsolution, so the higher  integrability [GG82, Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='1] applies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Utilizing |qj−p| ց 0, there exists  η > 0, depending only on n and p, such that  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='6)  sup  j  ˆ  QR  |Dvj|p+η dx < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Also observe from (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='2) that  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='7)  vj(0) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  By (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='5) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='6), we can extract a subsequence of {vj}∞  j=1 along which  vj → v weakly in W 1,p+η  loc  (Rn) and locally uniformly in Rn, for some v ∈  W 1,p+η  loc  ∩ C0,σ  loc (Rn).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Let us continue to denote this subsequence by {vj}∞  j=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  The uniform convergence along with (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='7) implies that  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='8)  v(0) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  We claim that v is a (weak) p-harmonic function in Rn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  For any large j, we have qj ∈ (p − η, p + η).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' By (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='6) and the compact  embedding, vj → w strongly in W 1,p  loc (Rn).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Now fix R ≥ 1, and let ϕ ∈  W 1,p+η  0  (QR) be arbitrary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Then since |qj − p| ց 0, |Dv−  j |qj → |Dv−|p and  17  |D(vj+ϕ)−|qj → |D(v+ϕ)|p a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' in QR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Then by the dominated convergence  theorem and the minimizerslity of Jp,qj(vj, QR),  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='9)  ˆ  QR  |Dv|p dx = lim  k→∞  ˆ  QR  (|Dv+  j |p + |Dv−  j |qj) dx  ≤ lim  k→∞  ˆ  QR  (|D(vj + ϕ)+|p + |D(vj + ϕ)−|qj) dx  =  ˆ  QR  |D(v + ϕ)|p dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Thus, v minimizes Jp,p(·, QR) over all variations v+ϕ with ϕ ∈ W 1,p+η  0  (QR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  This suffices to guarantee v to be (weak) p-harmonic in QR, see [Lin19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Since R was any number larger than 1, the claim is now verified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Now letting k → ∞ in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='4) and using qj → p, we obtain  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='10)  sup  R≥1  1  Rσp  ˆ  QR  |v|p dx = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  By the interior Lipschitz estimate for p-harmonic functions,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='11)  [v]C0,1(QR) ≤  c  R1−σ ,  for some c independent of R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Taking R → ∞ in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='11), we derive that v is  constant in Rn, which together with (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='8) implies v ≡ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' This is yields a  contradiction against (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='10), and the proof is finished.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  □  Next we extend the above lemma to local (1 + ε)-minimizers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' For any σ ∈ (0, 1), there exists ε, δ > 0, depending only on n,  p, and σ, such that for any q ∈ (1, ∞) with |p − q| < δ, and any local local  (1 + ε)-minimizer u ∈ W 1,p∧q(Q1) satisfying (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='1), one has, with σ+ = σ  and σ− = 1 − (1 − σ)p  q, that  1  rn+σ+p  ˆ  Qr  (u+)p dx +  1  rn+σ−q  ˆ  Qr  (u−)q dx ≤ c,  ∀r ∈ (0, 1),  where c > 1 depends only on n, p, and σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' As already observed in the proof of Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='3, the assumption  u(0) = 0 implies (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='11) for every r ∈ (0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Hence, the assumption (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='1)  implies (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' The rest of the proof is the same with that of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' More  exactly, given σ ∈ (0, 1) and p > 1, we first choose δ > 0 sufficiently small  such that Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='2 holds with 1+σ  2  in place of σ, for all local minimizers  for functional Jp,q for any q ∈ (1, ∞) with |p − q| < δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Then we can take  ε > 0 small enough such that Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='4 holds with τ as in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='11), σ+ = σ  and σ− = 1 − (1 − σ)p  q, ¯σ+ = 1+σ  2  > σ = σ−, and ¯σ− = 1 − (1−σ  2 )p  q >  1 − (1 − σ)p  q = σ−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' We skip the details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  □  We are ready to prove the almost Lipschitz regularity for almost mini-  mizers, when |p − q| ≪ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  18  SUNGHAN KIM AND HENRIK SHAHGHOLIAN  Proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' With the same (and simpler) compactness argument,  we can also prove that local (1 + ε)-minimizers for Jp,p(w) ≡  ´  |Dw|p dx is  of class C0,σ, for any σ ∈ (0, 1) and every ε ∈ (0, εσ), since p-harmonic  functions are of class C1,α ⊂ C0,1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Moreover, we can obtain a uniform C0,σ-  estimates, with this compactness argument, and the smallness constant εσ  depends only on n, p, and σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Thus, the passage from Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='3 to Theorem  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='3 is standard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' We shall not present the obvious details here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  □  Declarations  Data availability statement: All data needed are contained in the man-  uscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Funding and/or Conflicts of interests/Competing interests: The  authors declare that there are no financial, competing or conflict of interests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  References  [AT15]  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Amaral and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Teixeira, Free transmission problems, Comm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' 337 (2015), 1465–1489.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  [CKS21] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Colombo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Kim and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Shahgholian, A transmission problem for (p, q)-  Laplacian, to appear in Comm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' in Partial Differential Equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  [DET19] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' David, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Engelstein, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Toro, Free boundary regularity for almost min-  imizers, Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' 350 (2019), 1109–1192.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  [DS20]  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' De Silva and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Savin, Almost minimizers of the one-phase free boundary  problem, Comm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Partial Differential Equations 45 (2020), 913–930.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  [DJS22] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' De Silva, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Jeon and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Shahgholian, Almost minimizers for a singular system  with free boundary, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Differential Equations 336 (2022), 167–203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  [GG82]  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Giaquinta and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Giusti, On the regularity of the minimizers of variational  integrals, Acta Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' 148 (1982), 31–46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  [Giu03]  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Giusti, Direct methods in the Calculus of Variations, World Scientific, 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  [Lin19]  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content=' Lindqvist, Notes on the Stationary p-Laplace Equation, Springer International  Publishing, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='  Department of Mathematics, Uppsala University, S-751 06 Uppsala, Sweden  Email address: sunghan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='kim@math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='uu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='se  Department of Mathematics, Royal Institute of Technology, 100 44 Stock-  holm, Sweden  Email address: henriksh@kth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
+page_content='se' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dFAT4oBgHgl3EQfmh3P/content/2301.08624v1.pdf'}
diff --git a/5tE2T4oBgHgl3EQfkQe0/vector_store/index.pkl b/5tE2T4oBgHgl3EQfkQe0/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..abc62bdbb6435163dfda9ff431ed4c4d5b95d071
--- /dev/null
+++ b/5tE2T4oBgHgl3EQfkQe0/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:42a4626b4d8333095542c66b1e0e1bbd9cbdc68b8da115cfacfe3728bfe8a23e
+size 125871
diff --git a/7dE2T4oBgHgl3EQfPQbU/content/2301.03758v1.pdf b/7dE2T4oBgHgl3EQfPQbU/content/2301.03758v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..0f921468d7f18b7da32ec0044e8f2a6ef154d3be
--- /dev/null
+++ b/7dE2T4oBgHgl3EQfPQbU/content/2301.03758v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7b9d62c27b115c8bdcd4f61cc184573b0bc7eca30bc814233cf92f90eab0903c
+size 1434593
diff --git a/7dE2T4oBgHgl3EQfPQbU/vector_store/index.pkl b/7dE2T4oBgHgl3EQfPQbU/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..a4e38cb43bfb0b8f691503232f3327e4fd03ed43
--- /dev/null
+++ b/7dE2T4oBgHgl3EQfPQbU/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:65b52441d57070e7e763f73a96251f78087280dba9c3ad7f2d06d98d496f39bd
+size 197780
diff --git a/9tAyT4oBgHgl3EQf3Pnc/content/tmp_files/2301.00767v1.pdf.txt b/9tAyT4oBgHgl3EQf3Pnc/content/tmp_files/2301.00767v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4547a5f91b4d312f974cf47b0caa374bb39a8a86
--- /dev/null
+++ b/9tAyT4oBgHgl3EQf3Pnc/content/tmp_files/2301.00767v1.pdf.txt
@@ -0,0 +1,1836 @@
+IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, VOL. 14, NO. 8, DECEMBER 2022
+1
+A Survey on Federated Recommendation Systems
+Zehua Sun∗, Yonghui Xu∗, Yong Liu, Wei He, Yali Jiang, Fangzhao Wu, Lizhen Cui†
+Abstract—Federated learning has recently been applied to
+recommendation systems to protect user privacy. In federated
+learning settings, recommendation systems can train recom-
+mendation models only collecting the intermediate parameters
+instead of the real user data, which greatly enhances the user
+privacy. Beside, federated recommendation systems enable to
+collaborate with other data platforms to improve recommended
+model performance while meeting the regulation and privacy
+constraints. However, federated recommendation systems faces
+many new challenges such as privacy, security, heterogeneity
+and communication costs. While significant research has been
+conducted in these areas, gaps in the surveying literature still
+exist. In this survey, we—(1) summarize some common privacy
+mechanisms used in federated recommendation systems and
+discuss the advantages and limitations of each mechanism; (2)
+review some robust aggregation strategies and several novel at-
+tacks against security; (3) summarize some approaches to address
+heterogeneity and communication costs problems; (4)introduce
+some open source platforms that can be used to build federated
+recommendation systems; (5) present some prospective research
+directions in the future. This survey can guide researchers and
+practitioners understand the research progress in these areas.
+Index Terms—Recommendation Systems, Federated Learning,
+Privacy, Security, Heterogeneity, Communication costs.
+I. INTRODUCTION
+I
+N recent years, recommendation systems have been widely
+used to model user interests so as to solve information over-
+load problems in many real-world fields, e.g., e-commerce [1]
+[2], news [3] [4] and healthcare [5] [6]. To further improve the
+recommendation performance, such systems usually collect as
+much data as possible, including a lot of private information of
+users, such as user attributes, user behaviors, social relations,
+and context information.
+Although these recommendation systems have achieved
+remarkable results in terms of accuracy, most of them require a
+central server to store collected user data, which exist potential
+privacy leakage risks because user data could be sold to
+a third party without user consent, or stolen by motivated
+attackers. In addition, due to privacy concerns and regulation
+restrictions, it becomes more difficult to integrate data from
+other platforms to improve recommendation performance. For
+example, regulations such as General Data Protection Reg-
+ulation (GDPR) [7] set strict rules on collecting user data
+and sharing data between different platforms, which may lead
+to insufficient data for recommendation systems and further
+affects the recommendation performance.
+Zehua Sun, Yonghui Xu, Wei He, Yali Jiang and Lizhen Cui are with Joint
+SDU-NTU Centre for Artificial Intelligence Research (C-FAIR) & Software
+School, Shandong University.
+Yong Liu are with Alibaba-NTU Singapore Joint Research Institute,
+Nanyang Technological University, Singapore.
+Fangzhao Wu are with Microsoft Research Asia, China.
+∗Zehua Sun and Yonghui Xu are Co-First authors.
+†Corresponding author: clz@sdu.edu.cn.
+Federated learning is a privacy-preserving distributed learn-
+ing scheme proposed by Google [8], which enables par-
+ticipants to collaboratively train a machine learning model
+by sharing intermediate parameters (e.g., model parameters,
+gradients) to the central server instead of their real data.
+Therefore, combining federated learning with recommendation
+systems becomes a promising solution for privacy-preserving
+recommendation systems. In this paper, we term it federated
+recommendation system (FedRS).
+A. Challenges
+While FedRS avoid direct exposure of real user data and
+provides a privacy-aware paradigm for model training, there
+are still some core challenges that need to be addressed.
+Challenge 1: Privacy concerns. Privacy protection is often
+the major goal of FedRS. In FedRS, each participant jointly
+trains a global recommendation model by sharing interme-
+diate parameters instead of their real data, which makes an
+important step towards privacy-preserving recommendation
+systems. However, a curious sever can still infer some sensitive
+information (e.g., user behavior, ratings) from the intermediate
+parameters [9] [10].
+Challenge 2: Security attacks. In FedRS, participants may
+be malicious. They can attack the security of FedRS by
+poisoning the local training samples or the intermediate pa-
+rameters uploaded. As a result, attackers can increase/decrease
+the exposure ratio of specific items [12] or degrade the
+overall performance of the recommendation model [11]. In
+addition, some attackers try to use well-designed constraints to
+approximate the patterns of benign participants, which further
+increases the difficulty of defense and detection [55].
+Challenge 3: Heterogeneity. FedRS also faces the problem
+of system, statistical and privacy heterogeneity. System hetero-
+geneity means that the storage, computing, and communication
+capabilities of clients usually vary greatly, clients with limited
+capability may become stragglers and affect training efficiency.
+Statistical heterogeneity means that data in different clients
+is often not independent and identically distributed (Non-
+IID), which significantly affects global model convergence
+and personalization of recommendation results. Privacy het-
+erogeneity means that users and information usually have
+different privacy constraints, thus using the same privacy
+budgets for them will bring unnecessary loss of accuracy and
+efficiency.
+Challenge 4: Communication costs. To achieve satisfac-
+tory recommendation performance, clients need to commu-
+nicate with the central server for multiple rounds. However,
+the real-world recommendation systems are usually built on
+complex deep learning models and millions of intermediate
+parameters needs to be communicated [13]. Therefore, clients
+arXiv:2301.00767v1  [cs.IR]  27 Dec 2022
+
+IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, VOL. 14, NO. 8, DECEMBER 2022
+2
+Fig. 1: Communication architecture of FedRS.
+may be hard to afford severe communication costs, which lim-
+its the application of FedRS in large-scale industrial scenarios.
+B. Related Surveys
+There are many surveys that have focused on recommenda-
+tion systems or federated learning. For example, Adomavicius
+et al. [14] provide a detailed categorization of recommenda-
+tion methods and introduce various limitations of each method.
+Yang et al. [15] give the definition of federated learning
+and discuss its architectures and applications. And Li et al.
+[16] summarize the unique characteristics and challenges of
+federated learning. However the existing surveys usually treat
+recommendation systems and federated learning separately,
+and few work surveyed specific problems in FedRS [17].
+Yang et al. [17] categorize FedRS from the aspect of the
+federated learning and discuss the algorithm-level and system-
+level challenges for FedRS. However, they do not provide
+comprehensive methods to address privacy, security, hetero-
+geneity, and communication costs challenges.
+C. Our Contribution
+Compared with the previous surveys, this paper makes
+the following contributions: (1) We provide a comprehensive
+overview of FedRS from the perspectives of definition, com-
+munication architectures and categorization. (2) We summarize
+the state-of-the-art studies of FedRS in terms of privacy,
+security, heterogeneity and communication costs areas. (3) We
+introduce some open source platforms for FedRS, which can
+help engineers and researchers develop algorithms and deploy
+applications of FedRS. (4) We discuss the promising future
+directions for FedRS.
+The rest of the paper is organized as follow: Section II
+discusses the overview of FedRS. Section III-Section VI sum-
+marize the state-of-the-art studies of FedRS from the aspects
+of privacy, security, heterogeneity and communication costs.
+Section VII introduces the existing open source platforms.
+Section VIII presents some prospective research directions.
+Finally, Section IX concludes this survey.
+II. OVERVIEW OF FEDERATED RECOMMENDATION
+SYSTEMS
+A. Definition
+FedRS is a technology that provides recommendation ser-
+vices in a privacy preserving way. To protect user privacy, the
+participants in FedRS collaboratively train the recommenda-
+tion model by exchanging intermediate parameters instead of
+sharing their own real data. In ideal case, the performance of
+recommendation model trained in FedRS should be closed to
+the performance of the recommendation model trained in the
+data centralized setting, which can be formalized as:
+|VF ED − VSUM| < δ.
+(1)
+where VF ED is the recommendation model performance in
+FedRS , VSUM is the recommendation model performance
+in traditional recommendation systems for centralized data
+storage, and δ is a small positive numbers.
+B. Communication Architecture
+In FedRS, the data of participants is stored locally, and
+the intermediate parameters are communicated between the
+server and participants. There are two major communication
+architectures used in the study of FedRS, including client-
+server architecture and peer-peer architecture.
+Client-Server Architecture. Client-server architecture is
+the most common communication architecture used in FedRS,
+as shown in Fig. 1(a), which relies on a trusted central server
+to perform initialization and model aggregation tasks. In each
+round, the server distributes the current global recommenda-
+tion model to some selected clients. Then the selected clients
+use the received model and their own data for local training,
+and send the updated intermediate parameters (e.g., model
+parameters, gradients) to the server for global aggregation. The
+
+Server
+① Initialization
+① Initialization
+②
+①
+② Download model
+④
+② Local update
+Participant 1
+③ Local update
+③ Send parameters
+②
+@ Send parameters
+@ Aggregation
+4
+4
+②
+2)
+? Aggregation
+③
+③
+3
+3
+3
+①
+①
+④
+④
+Participant 1
+Participant 2
+Participant N
+Participant 2
+Participant N
+(a) Client-Server ahictecture
+(b) Peer-Peer ahictectureIEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, VOL. 14, NO. 8, DECEMBER 2022
+3
+Fig. 2: Categorization of federated recommendation systems.
+client-server architecture requires a central server to aggregate
+the intermediate parameters uploaded by the clients. Thus,
+once the server has a single point of failure, the entire training
+process will be seriously affected [18]. In addition, the curious
+server may infer the clients’ privacy information through the
+intermediate parameters, leaving potential privacy concerns
+[10].
+Peer-Peer Architecture. Considering the single point of
+failure problem for client-server architecture in FedRS, Hegeds
+et al. [19] design a peer-peer communication architecture
+with no central server involved in the communication process,
+which is shown in Fig. 1(b). During each communication
+round, each participant broadcasts the updated intermediate
+parameters to some random online neighbors in the peer to
+peer network, and aggregates received parameters into its
+own global model. In this architecture, the single point of
+failure and privacy issues associated with a central server
+can be avoided. However, the aggregation process occurs on
+each client, which greatly increases the communication and
+computation overhead for clients [20].
+C. Categorization
+In FedRS, the participants are responsible for the local
+training process as the data owners. They can be different
+mobile devices or data platforms. Considering the unique
+properties for different types of participants, FedRS usually
+have different application scenarios and designs. Besides, there
+are also some differences between different recommendation
+models in the federation process. Thus, we summarize the
+current FedRS and categorize them from the perspectives of
+participant type and recommendation model. Fig. 2 shows the
+summary of the categorization of FedRS.
+1) Participant Type: Based on the type of participants,
+FedRS can be categorized into cross-device FedRS and cross-
+platform FedRS.
+Cross-device FedRS. In cross-device FedRS, different mo-
+bile devices are usually treated as participants [21] [22].
+The typical application of cross-device FedRS is to build a
+personal recommendation model for users without collecting
+their local data. In this way, users can enjoy recommend
+service while protecting their private information. The number
+of participants in cross-device FedRS is relative large and each
+participant keeps a small amount of data. Considering the
+limited computation and communication abilities for mobile
+devices, cross-device FedRS cannot handle very complex
+training tasks. Besides, due to the power and the network
+status, the mobile devices may drop out of the training process.
+Thus, the major challenges for cross-device FedRS are how
+to improve the efficiency and deal with straggler problem of
+devices during training process.
+Cross-platform FedRS. In cross-platform FedRS, different
+data platforms are usually treated as participants who want
+to collaborate to improve recommendation performance while
+meeting regulation and privacy constraints [23] [24] [25].
+For example, In order to improve the recommendation per-
+formance, recommendation systems often integrate data from
+multiple platforms (e.g., e-commercial platforms , social plat-
+forms). However, due to the privacy and regulation concerns,
+the different data platforms are often unable to directly share
+their data with each other. In this scenario, cross-platform
+FedRS can be used to collaboratively train recommendation
+models between different data platforms without directly ex-
+changing their users’ data. Compared to cross-device FedRS,
+the number of participants in cross-platform FedRS is rela-
+tively small, and each participant owns relative large amount of
+data. An important challenge for cross-platform FedRS is how
+to design a fair incentive mechanism to measure contributions
+and benefits of different data platforms. Besides, it is hard
+to find a trusted server to manage training process in cross-
+platform FedRS, so a peer to peer communication architecture
+can be a good choice in this case.
+2) Recommendation Model:
+According to the different
+recommendation models used in FedRS, FedRS can be cat-
+egorized into matrix factorization model based FedRS, deep
+learning model based FedRS and meta learning model FedRS.
+Matrix factorization model based FedRS. Matrix fac-
+torization [26] is the most common model used in FedRS,
+which formulates the user-item interaction or rating matrix
+R ∈ RN×M as a linear combination of user profile matrix
+U ∈ RN×K and item profile matrix V ∈ RM×K:
+R = UV T .
+(2)
+then uses the learned model to recommendation new items to
+the user according to the predicted value. In matrix factoriza-
+tion model based FedRS, the user factor vectors are stored and
+updated locally on the clients, and only the item factor vectors
+[27] or the gradients of item factor vectors [21] [22] [10]
+[28] [29] are uploaded to the server for aggregation. Matrix
+factorization model based FedRS can simply and effectively
+capture user tastes with the interaction and rating information
+between users and items. However it still has many limitations
+such as sparsity (the number of ratings to be predicted is much
+smaller than the known ratings) and cold-start (new users and
+new items lacks ratings information) problems [14].
+Deep learning model based FedRS. To learn more com-
+plex representations of users and items and improve the
+recommendation performance, deep learning technology has
+been widely used in recommendation systems. However, as
+privacy regulations get stricter, it becomes more difficult for
+recommendation systems to collect enough user data to build
+a high performance deep learning model. To make the full
+
+Cross-DeviceFedRS
+Participant Type
+Cross-PlatformFedRS
+Federated
+Recommendation
+System
+Matrix Factorization Mode
+Based FedRS
+Recommendation
+Deep Learning Model
+Model
+Based FedRS
+Meta Learning Model
+Based FedRSIEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, VOL. 14, NO. 8, DECEMBER 2022
+4
+use of user data while meeting privacy regulations, many ef-
+fective deep learning model based FedRS have been proposed
+[30] [31] [32]. Considering different model structures, deep
+learning model based FedRS usually adopt different model
+update and intermediate parameter transmit processes. For
+examples, Perifanis et al. [30] propose a federated neural
+collaborative filtering (FedNCF) framework based on NCF
+[33]. In FedNCF, the clients locally update the network
+weights as well as the user and item profiles, then upload
+the item profile and network weights after masking to the
+server for aggregation. Wu et al. [31] propose a federated
+graph neural network (FedGNN) framework based on GNN.
+In FedGNN, the clients locally train GNN models and update
+the user/item embeddings from their local sub-graph, then send
+the perturbed gradients of GNN model and item embedding to
+the central server for aggregation. Besides, Huang et al. [34]
+propose a federated multi-view recommendation framework
+based on Deep Structured Semantic Model (DSSM [35]). In
+FL-MV-DSSM, each view i locally trains the user and item
+sub-models based on their own user data and local shared item
+data, then send the perturbed gradients of both user and item
+sub-models to server for aggregation. Although deep learning
+model based FedRS achieve outstanding performance in terms
+of accuracy, the massive model parameters of deep learning
+models bring huge computation and communication overhead
+to the clients, which presents a serious challenge for real
+industrial recommendation scenarios.
+Meta learning model based FedRS. The most of existing
+federated recommendation studies are built on the assump-
+tion that data distributed on each client is independent and
+identically (IID). However, learning a unified federated rec-
+ommendation model often performs poorly when handling the
+Non-IID and highly personalized data on clients. Meta learning
+model can quickly adapt to new tasks while maintaining good
+generalization ability [36], which makes it particularly suitable
+for FedRS. In meta learning model based FedRS, the server
+aggregates the intermediate parameters uploaded by clients to
+learn a model parameter initialization, and the clients fine-tune
+the initialed model parameters in local training phase to fit to
+their local data [37] [38]. In this way, meta learning model
+based FedRS can adapt the clients’ local data to provide more
+personalized recommendations. Although the performance of
+meta learning model based FedRS are generally better than
+learning a unified global model, the private information leak-
+age can still occur during the learning process of model
+parameter initialization [37].
+III. PRIVACY OF FEDERATED RECOMMENDATION
+SYSTEMS
+In the model training process of FedRS, the user data is
+stored locally and only the intermediate parameters are up-
+loaded to a server, which can further protect user privacy while
+keeping recommendation performance. Nevertheless, several
+research works show that the central server can still infer
+some sensitive information based on intermediate parameters.
+For examples, a curious server can identify items the user
+has interacted with according to the non-zero gradients sent
+by the client [31]. Besides, the server can also infer the user
+ratings as long as obtaining the user uploaded gradients in two
+consecutive rounds [10]. To further protect privacy of FedRS,
+many studies have incorporated other privacy protection mech-
+anisms into the FedRS, including pseudo items, homomorphic
+encryption, secret sharing and differential privacy. This section
+introduces the application of each privacy mechanism used in
+FedRS, and compare their advantages and limitations.
+A. Pseudo Items
+To prevent the server from inferring the set of items that
+users have interacted with based on non-zero gradients, some
+studies utilize pseudo items to protect user interaction behav-
+iors in FedRS. The key idea of pseudo items is that the clients
+not only upload gradients of items that have been interacted
+with but also upload gradients of some sampled items that
+have not been with.
+For example, Lin et at. [22] propose a federated recom-
+mendation framework for explicit feedback scenario named
+FedRec, in which they design an effective hybrid filling strat-
+egy to generated virtual ratings of unrated items by following
+equation:
+r
+′
+ui =
+�
+�
+�
+�m
+k=1 yukruk
+�m
+k=1 yuk
+, t < Tpredict
+ˆrui, t ≥ Tpredict
+(3)
+where t denotes the number of current training iteration,
+and Tpredict denotes the iteration number when chooses the
+average value or predict value as virtual rating value to a
+sampled item i. However, the hybrid filling strategy in FedRec
+introduces extra noise to the recommendation model, which in-
+evitably affects the model performance. To tackle this problem,
+Feng et at. [39] design a lossless version of FedRec named
+FedRec++. FedRec++ divides clients into ordinary clients and
+denoising clients. The denosing clients collect noisy gradients
+from ordinary clients and send the summation of the noisy
+gradients to server to eliminate the gradient noise.
+Although pseudo items can effectively protect user interac-
+tion behaviors in FedRS, it does not modify the gradients of
+rated items. The curious server can still infer user ratings on
+the gradients uploaded by users [10].
+B. Homomorphic Encryption
+To further protect the user ratings in FedRS, many studies
+attempt to encrypt intermediate parameters before uploading
+them to the server. Homomorphic encryption mechanism al-
+lows mathematical operation on encrypted data [40], so it
+is well suited for the intermediate parameters upload and
+aggregation processes in FedRS.
+For example, Chai et at. [10] propose a secure feder-
+ated matrix factorization framework named FedMF, in which
+clients use Paillier homomorphic encryption mechanism [41]
+to encrypt the gradients of item embedding matrix before
+uploading them to the server, and the server aggregates
+gradients on the cipher-text. Due to the characteristics of
+homomorphic encryption, FedMF can achieve the same rec-
+ommendation accuracy as the traditional matrix factorization.
+
+IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, VOL. 14, NO. 8, DECEMBER 2022
+5
+TABLE I: Comparison between different privacy mechanism.
+Privacy Mechanisms
+Ref
+Main Protect Object
+Accuracy Loss
+Communication/Computation Costs
+Pseudo Items
+[22] [39] [31] [44] [45]
+Interaction Behaviors
+�
+Low Costs
+Homomorphic Encryption
+[10]
+Ratings
+�
+High Computation Costs
+[31]
+High-order Graph
+[42]
+Social Features
+Secret Sharing
+[29] [45]
+Ratings
+�
+High Communication Costs
+Local Differential Privacy
+[27] [31] [44]
+Ratings
+�
+Low Costs
+However, FedMF causes serious computation overheads since
+all computation operations are performed on the ciphertext
+and most of system’s time is spent on server updates. Besides,
+FedMF assumes that all participants are honest and will not
+leak the secret key to the server, which is hard to guarantee
+in reality.
+Besides, many studies also utilize homomorphic encryption
+mechanism to integrate private information from other par-
+ticipants to improve recommendation accuracy [31] [42]. For
+examples, Wu et al. [31] use homomorphic encryption mecha-
+nism to find the anonymous neighbors of users to expanse local
+user-item graph. And Perifanis et al. [42] use Cheon-Kim-
+Kim-Song (CKKS) fully homomorphic encryption mechanism
+[43] to incorporate learned parameters between user’s friends
+after the global model is generated.
+Homomorphic encryption mechanism based FedRS can
+effectively protect user ratings while maintaining recommen-
+dation accuracy. Besides, it can prevent privacy leaks when
+integrating information from other participants. However, ho-
+momorphic encryption brings huge computation costs during
+operation process. And it is also a serious challenge to keep
+the secret key not be obtained by the server or other malicious
+participants.
+C. Secret Sharing
+As another encryption mechanism used in FedRS, secret
+sharing mechanism breaks intermediate parameters up into
+multiple pieces, and distributes the pieces among participants,
+so that only when all pieces are collected can reconstruct the
+intermediate parameters.
+For example, Ying [29] proposes a secret sharing based
+federated matrix factorization framework named ShareMF.
+The participants divide the item matrix gradients gplain into
+several random numbers that meet:
+gplain = gsub1 + gsub2 + ... + gsubt.
+(4)
+Each participant keeps one of the random numbers and send
+the rest to t − 1 sampled participants, then uploads the sum
+of received and kept numbers as hybrid gradients to the
+server for aggregation. ShareMF protects the user ratings and
+interaction behaviors from being inferred by the server, but
+the rated items can still be leaked to other participants who
+received the split numbers. To tackle this problem, Lin et al.
+[45] combine secret sharing and pseudo items mechanisms to
+provide stronger privacy guarantee.
+Secret sharing mechanism based FedRS can protect user
+ratings while maintaining recommendation accuracy, and have
+lower computation costs compared to homomorphic encryp-
+tion based FedRS. But the exchange process of pieces between
+participants greatly increases the communication costs.
+D. Local Differential Privacy
+Considering the huge computation or communication costs
+caused by encryption based mechanisms, many studies try
+to use perturbation based mechanisms to adapt to large-scale
+FedRS for the industrial scenarios. Local differential privacy
+(LDP) mechanism allows to statistical computations while
+guaranteeing each individual participant’s privacynoise [46]
+[47], which can be used to perturb the intermediate parameters
+in FedRS.
+For example, Dolui et al. [27] propose a federated matrix
+factorization framework, which applies differential privacy
+on item embedding matrix before sending it to server for
+weighted average. However, the server can still infer which
+items the user has rated just by comparing the changes in
+item embedding matrix.
+In order to achieve a more comprehensive privacy protection
+during model training process, Wu et al. [31] combines
+pseudo items and LDP mechanisms to protect both user
+interaction behaviors and ratings in FedGNN. Firstly, to protect
+user interaction behaviors in FedGNN, the clients randomly
+sample N items that they have not interacted with, then
+generate the virtual gradients of item embeddings by using
+a same Gaussian distribution as the real embedding gradients.
+Secondly, to protect user ratings in FedGNN, the clients apply
+a LDP module to clip the gradients according to their L2-norm
+with a threshold δ and perturb the gradients by adding zero-
+mean Laplacian noise. The LDP module of FedGNN can be
+formulated as follow:
+gi = clip(gi, δ) + Laplace(0, λ).
+(5)
+where λ is the Laplacian noise strength. However, the gradi-
+ent magnitude of different parameters varies during training
+process, thus it is usually not appropriate to perturb gradients
+at different magnitudes with a constant noise strength. So Liu
+
+IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, VOL. 14, NO. 8, DECEMBER 2022
+6
+et al. [44] propose to add dynamic noise according to the
+gradients, which can be formulated as follow:
+gi = clip(gi, δ) + Laplace(0, λ · mean(gi)).
+(6)
+Local differential privacy mechanism doesn’t bring heavy
+computation and communication overhead to FedRS, but the
+additional noise inevitably affects the performance of the
+recommendation model. Thus, in the actual application sce-
+nario, we must consider the trade-off between the privacy and
+recommendation accuracy.
+E. Comparison
+To protect stronger privacy guarantee, many privacy mech-
+anisms (i.e., pseudo items, homomorphic encryption, differ-
+ential privacy privacy and secret sharing) have been widely
+used in FedRS, and the comparison between these mechanisms
+is shown in Table I. Firstly, the main protect objects of
+these mechanisms are different: pseudo items mechanism is
+to protect user interaction behaviors, and the rest mechanisms
+is to protect user ratings. Besides, homomorphic encryption
+can aslo integrate data from other paritcipants in a privacy-
+preserving way. Secondly, homomorphic encryption and secret
+sharing are both encryption-based mechanisms, and they can
+protect privacy while keeping accuracy. However, the high
+computation cost of homomorphic encryption limits the appli-
+cation in large-scale industrial scenarios. Although the secret
+sharing mechanism reduces the computation costs, the commu-
+nication costs increase greatly. Pseudo items and differential
+privacy mechanisms protect privacy by adding random noise,
+which has low computation costs and don’t bring additional
+communication costs. But the addition of random noise will
+inevitably affect model performance to a certain extent.
+IV. SECURITY OF FEDERATED RECOMMENDATION
+SYSTEMS
+Apart from privacy leakage problems, traditional recom-
+mendation systems for centralized data storage are also vul-
+nerable to poisoning attacks (shilling attacks) [48] [49] [50]
+[51] [52] [53]. Attackers can poison recommendation systems
+and make recommendations as their desires by injecting well-
+crafted data into the training dataset. But most of these
+poisoning attacks assume that the attackers have full prior
+knowledge of entire training datasets. Such assumption may
+be not valid for FedRS since the data in FedRS is distributed
+and stored locally for each participant. Thus, FedRS provides
+a stronger security guarantee than traditional recommendation
+systems. However, the latest studies indicate that attackers can
+still conduct poisoning attacks on FedRS with limited prior
+knowledge [12] [11] [54] [55]. In this section, we summarize
+some novel poisoning attacks against FedRS and provide some
+defense methods.
+A. Poisoning Attacks
+According to the goal of attacks, the poisoning attacks
+against FedRS can be categorized into targeted attacks and
+untargeted attacks as shown in Table II.
+1) Target Poisoning Attacks: The goal of target attacks
+on FedRS is to increase or decrease the exposure chance of
+specific items, which are usually driven by financial profit.
+For example, Zhang et al. [12] propose a poisoning attack
+for item promotion (PipAttack) against FedRS by utilizing
+popularity bias. To boost the rank score of target items,
+PipAttack use popularity bias to align target items with popular
+items in the embedding space. Besides, to avoid damaging
+recommendation accuracy and be detected, PipAttack designs
+a distance constraint to keep modified gradients uploaded by
+malicious clients closed to normal ones.
+In order to further reduce the degradation of recommenda-
+tion accuracy caused by targeted poisoning attacks, and the
+proportion of malicious clients needed to ensure the attack
+effectiveness, Rong [54] propose a model poisoning attack
+against FedRS (FedRecAttack), which makes use of a small
+proportion of public interactions to approximate the user
+feature matrix, then uses it to generate poisoned gradients.
+Both PipAttack and FedRecAttack rely on some prior
+knowledge. For example, PipAttack assumes the attacker is
+available for popularity information, and FedRecAttack as-
+sumes the attacker can get public interactions. So the attack
+effectiveness is greatly reduced in the absence of prior knowl-
+edge, which makes both attacks not generic in all FedRS. To
+make attackers conduct effective poisoning attacks to FedRS
+without the prior knowledge, Rong et al. [55] design two
+methods (i.e., random approximation and hard user mining) for
+malicious clients to generate poisoned gradients. In particular,
+random approximation (A-ra) uses Gaussian distribution to
+approximate normal users’ embedding vectors, and hard user
+mining (A-hum) uses gradient descent to optimize users’
+embedding vectors obtained by A-ra to mine hard users. In this
+way, A-hum can still effectively attack FedRS with extremely
+small proportion of malicious users.
+2) Untarget Poisoning Attacks: The goal of untarget attacks
+on FedRS is to degrade the overall performance of recom-
+mendation model, which are usually conducted by competing
+companies. For example, Wu et al. [11] propose an untargeted
+poisoning attack to FedRS named FedAttack, which uses glob-
+ally hard sampling technique [62] to subvert model training
+process. More specifically, after inferring user’s interest from
+local user profiles, the malicious clients select candidate items
+that best match the user’s interest as negative samples, and
+select candidate items that least match the user’s interest as
+positive samples. FedAttack only modifies training samples,
+and the malicious clients are also similar to normal clients
+with different interests, thus FedAttack can effectively damage
+the performance of FedRS even under defense.
+B. Defense Methods
+To reduce the influence of poisoning attacks on FedRS,
+many defense methods have been proposed in the literature,
+which can be classified into robust aggregation and anomaly
+detection.
+1) Robust Aggregation: The goal of robust aggregation
+is to guarantee global model convergence when up to 50%
+of participants are malicious [63], which selects statistically
+
+IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, VOL. 14, NO. 8, DECEMBER 2022
+7
+TABLE II: Representative works on the security of FedRS. RA refers to robust aggregation and AD refers to anomaly
+detection.
+Works
+Ref
+Attack Type
+Poison Object
+Defense Type
+Goal
+Target
+Untarget
+Model
+Data
+RA
+AD
+PipAttack
+[12]
+�
+�
+Increase/decrease popularity of target items.
+FedRecAttack
+[54]
+�
+�
+Increase/decrease popularity of target items.
+A-ra/A-hum
+[55]
+�
+�
+Increase/decrease popularity of target items.
+FedAttack
+[11]
+�
+�
+Degrade the overall performance of FedRS.
+Median
+[56]
+�
+Guarantee global model convergence.
+Trimmed-Mean
+[56]
+�
+Guarantee global model convergence.
+(Multi-)Krum
+[57]
+�
+Guarantee global model convergence.
+Bulyan
+[58]
+�
+Guarantee global model convergence.
+Norm-Bounding
+[59]
+�
+Guarantee global model convergence.
+A-FRS
+[60]
+�
+Guarantee global model convergence.
+FSAD
+[61]
+�
+Identify and filter poisoned parameters.
+more robust values rather than the mean values of uploaded
+intermediate parameters for aggregation.
+Median [56] selects the median value of each updated
+model parameter independently as aggregated global model
+parameter, which can represent the centre of the distribution
+better. Specifically, the server ranks each i − th parameter of
+n local model update, and uses the median value as i − th
+parameter of global model.
+Trimmed-Mean [56] removes the maximum and minimum
+values of each updated model parameter independently, and
+then takes the mean value as aggregated global model param-
+eter. Specifically, the server ranks each i − th parameter of n
+local model update, remove β smallest and β largest values,
+and uses the mean value of remained n−2β as i−th parameter
+of global model. In this way, Trimmed-Mean can effectively
+reduce the impact of outliers.
+Krum and Multi-Krum [57]. Krum selects a local model
+that is the closest to the others as global model. Multi-Krum
+selects multiple local models by using Krum, then aggregates
+them into a global model. In this way, even if the selected
+parameter vectors are uploaded by malicious clients, their
+impact is still limited because they are similar to other local
+parameters uploaded by normal clients.
+Bulyan [58] is a combination of Krum and Trimmed-Mean,
+which iteratively selects m local model parameter vectors
+through Krum, and then performs Trimmed-Mean on these
+m parameter vectors for aggregation. With high dimensional
+and highly non-convex loss function, Bulyan can still converge
+to effectual models.
+Norm-Bounding [59] clips the received local parameters to
+a fixed threshold, then aggregates them to update the global
+model. Norm-Bounding can limit the contribution of each
+local model updates so as to mitigate the affect of poisoned
+parameters on the aggregated model.
+A-FRS
+[60]
+utilizes
+gradient-based
+Krum
+instead
+of
+model parameter-based Krum to filter malicious clients in
+momentum-based FedRS. A-FRS theoretically guarantees that
+if the selected gradient is closed to the normal gradient, the
+momentum and model parameters will also be close to the
+normal momentum and model parameters.
+Although these robust aggregation strategies provide conver-
+gence guarantees to some extent, most of them (i.e., Bulyan,
+Krum, Median and Trimmed-mean) greatly degrade the per-
+formance of FedRS. Besides, some noval attacks(i.e., PipAt-
+tack, FedAttack) [12] [11] utilize well-designed constraints
+to approximate the patterns of normal users and circumvent
+defenses, which further increases the difficulty of defense.
+2) Anomaly Detection: The purpose of anomaly detection
+strategy is to identify the poisoned model parameters uploaded
+by malicious clients and filter them during the global model
+aggregation process. For example, Jiang et al. [61] propose
+an anomaly detection strategy named federated shilling attack
+detector (FSAD) to detect poisoned gradients in federated
+collaborative filtering scenarios. FSAD extracts 4 novel fea-
+tures according to the gradients uploaded by clients, then uses
+the gradient-based features to train a semi-supervised bayes
+classifier so as to identify and filter the poisoned gradients.
+However, in FedRS, the interests of different users vary widely,
+thus the parameters they uploaded are usually quite different,
+which increases the difficulty of anomaly detection [54].
+V. HETEROGENEITY OF FEDERATED RECOMMENDATION
+SYSTEMS
+Compared with traditional recommendation systems, Fe-
+dRS face more severe challenges in terms of heterogeneity,
+which are mainly reflected in system heterogeneity, statistical
+heterogeneity and model heterogeneity, as shown in Fig. 3.
+
+IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, VOL. 14, NO. 8, DECEMBER 2022
+8
+Fig. 3: Heterogeneity of federated recommendation systems.
+System heterogeneity refers to client devices have signif-
+icantly different storage, computation, and communication
+capabilities. Devices with limited capabilities greatly affects
+training efficiency, and further reduces the accuracy of the
+global recommendation model. [64]; Statistical heterogeneity
+refers to the data collected by different clients is usually
+not independent and identically distributed (non-IID). As a
+result, simply training a single global model is difficult to
+generalize to all clients, which affects the personalization of
+recommendations [65]; Privacy heterogeneity means that the
+privacy constraints of different users and information vary
+greatly, so simply treating them with the same privacy budgets
+will carry unnecessary costs [66]. This section introduces some
+effective approaches to address the heterogeneity of FedRS.
+A. System Heterogeneity
+In FedRS, the hardware configuration, network bandwidth
+and battery capacity of participating clients varies greatly,
+which results in diverse computing capability, communication
+speed, and storage capability [16]. During the training process,
+the clients with limited capacity could become stragglers, and
+even drop out of current training due to network failure, low
+battery and other problems [18]. The system heterogeneity
+significantly delays the training process of FedRS, further
+reducing the recommendation accuracy of the global model. To
+make the training process compatible with different hardware
+structures and tolerate the straggling and exit issues of clients,
+the most common methods are asynchronous communication
+[67] [18] and clients selection [68].
+Asynchronous
+communication.
+Considering
+the
+syn-
+chronous communication based federated learning must wait
+for straggler devices during aggregation process, many asyn-
+chronous communication strategies are presented to improve
+training efficiency. For examples, FedSA [67] proposes a
+semi-asynchronous communication method, where the server
+aggregates the local models based on their arrival order of
+each round. FedAsync [18] uses a weighted average strategy
+to aggregate the local models based on staleness, which assigns
+less weight to delayed feedback in update process.
+Clients selection. Client selection approach selects clients
+for updates based on resource constraints so that the server can
+aggregate as many local updates as possible at the same time.
+For example, in FedCS [68], the server sends a resource re-
+quest to each client so as to get their resource information, then
+estimates the required time of model distribution, updating
+and uploading processes based on the resource information.
+According to the estimated time, the server determine which
+clients can participant in training process.
+B. Statistical Heterogeneity
+Most of the existing federated recommendation studies
+are built on the assumption that data in each participant is
+independent and identically distributed (IID). However, the
+data distribution of each client usually varies greatly, hence
+training a consistent global model is difficult to generalized
+to all clients under non-IID data and inevitably neglects
+the personalization of clients [66]. To address the statistical
+heterogeneity problem of FedRS, many effective strategies
+have been proposed, which are mainly based on meta learning
+[38] [69] and clustering [70] [71].
+Meta learning. As known as “learning to learn”, meta
+learning technology aims to quickly adapt the global model
+learned by other tasks to a new task by using only a few
+number of samples [36]. The rapid adaptation and good
+generalization abilities makes it particularly well-suited for
+building personalized federated recommendation models. For
+examples, FedMeta [38] uses Model-Agnostic Meta-Learning
+(MAML) [73] algorithm to learn a well-initialized model that
+can be quickly adapted to clients, and effectively improve the
+personalization and convergence of FedRS. However, FedMeta
+
+Privacy
+Heterogenity
+8
+Private
+Public
+Private
+Public
+8
+user
+item
+attributes
+Statistical
+Heterogenity
+battery
+Data Distribution
+Data Distribution
+l
+4/5G
+Wi-Fi
+System
+Heterogenity
+Participant 2
+Participant 2IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, VOL. 14, NO. 8, DECEMBER 2022
+9
+needs to compute the second-order gradients, which greatly
+increases computation costs. Besides, the data split process
+also brings a huger challenge for clients with limited samples.
+Based on FedMeta, Wang et al. [69] propose a new meta
+learning algorithm called Reptile which applies the approx-
+imate first-order derivatives for the meta-learning updates,
+which greatly reduces the computation overloads of clients.
+Moreover, Reptile doesn’t need a data split process, which
+makes it also suitable for clients with limited samples.
+Clustering. The core idea of clustering is training person-
+alized models jointly with the same group of homogeneous
+clients. For examples, Jie et al. [70] uses historical parameter
+clustering technology to realize personalized federated recom-
+mendation, in which the server aggregates local parameters to
+generate global model parameters and clusters the local pa-
+rameters to generate clustering parameters for different client
+groups. Then the clients combine the clustering parameters
+with the global parameters to learn personalized models. Luo
+et al. [71] propose a personalized federated recommendation
+framework named PerFedRec, which constructs a collaborative
+graph and integrates attribute information so as to jointly learn
+the user representations by federated GNN. Based on the
+learned user representations, clients are clustered into different
+groups. And each cluster learns a cluster-level recommen-
+dation model. At last, each client can obtain a personalized
+model by merging the global recommendation model, the
+cluster-level recommendation model, and the fine-tuned local
+recommendation model. Although clustering based approaches
+can alleviate statistical heterogeneity, the clustering and com-
+bination process greatly increase the computation costs.
+C. Privacy Heterogeneity
+In reality, the privacy restrictions of different participants
+and information vary greatly, thereby using the same high level
+of privacy budget for all participants and information is unnec-
+essary, which even increases the computation/communication
+costs and degrades the model performance.
+Heterogeneous user privacy. In order to adapt the privacy
+needs for different users, Anelli et al. [72] present a user
+controlled federated recommendation framework named Fed-
+eRank. FedeRank introduces a probability factor π ∈ [0, 1] to
+control the proportion of interacted item updates and masks
+the remain interacted item update by setting them to zero.
+In this way, FedeRank allows users decide the proportion of
+data they want to share by themselves, which addresses the
+heterogeneity of user privacy.
+Heterogeneous information privacy. In order to adapt the
+privacy needs of different information components, HPFL [66]
+designs a differentiated component aggregation strategy. To
+obtain the global public information components, the server
+directly weighted aggregates the local public components with
+same properties. And to obtain the global privacy information
+components, the user and item representations are kept locally,
+and the server only aggregates the local drafts without the need
+to align the presentations. With the differentiated component
+aggregation strategy, HPFL can safely aggregate components
+with heterogeneous privacy constraints in user modeling sce-
+narios.
+VI. COMMUNICATION COSTS OF FEDERATED
+RECOMMENDATION SYSTEMS
+To achieve satisfactory recommendation performance, Fe-
+dRS requires multiple communications between server and
+clients. However, the real-world recommendation systems are
+usually conducted by complexity deep learning models with
+large model size [74], and millions of parameters needs to
+be updated and communicated [13], which brings severe
+communication overload to resource limited clients and further
+affects the application of FedRS in large-scale industrial sce-
+narios. This section summarizes some optimization methods to
+reduce communication costs of FedRS, which can be classified
+into importance-based updating [75] [20] [76] [77], model
+compression [78] [79], active sampling [80] and one shot
+learning [81].
+A. Importance-based Model Updating
+Importance-based model updating selects importance parts
+of the global model instead of the whole model to update and
+communicate, which can effectively reduce the communicated
+parameter size in each round.
+For examples, Qin et al. [75] propose a federated frame-
+work named PPRSF, which uses 4-layers hierarchical structure
+for reducing communication costs, including the recall layer,
+ranking layer, re-ranking layer and service layer. In the recall
+layer, the server roughly sorts the large inventory by using
+public user data, and recalls relatively small number of items
+for each client. In this way, the clients only need to update and
+communicate the candidate item embeddings, which greatly
+reduces the communication costs between server and clients,
+and the computation costs in the local model training and
+inference phases. However, the recall layer of PPRSF need
+to get some public information of users, which raises certain
+difficulty and privacy concerns.
+Yi et al. [20] propose an efficient federated news recom-
+mendation framework called Efficient-FedRec, which breaks
+the news recommendation model into a small user model and
+a big news model. Each client only requests the user model and
+a few news representations involved in their local click history
+for local training, which greatly reduces the communication
+and computation overhead. To further protect specific user
+click history against the server, they transmit the union news
+representations set involved in a group of user click history
+by using a secure aggregation protocol [82].
+Besides, Khan et al. [76] propose a multi-arm bandit
+method (FCF-BTS) to select part of the global model that
+contains a smaller payload to all clients. The rewards of
+selection process is guided by Bayesian Thompson Sampling
+(BTS) [83] approach with Gaussian priors. Experiments show
+that FCF-BTS can reduce 90% model payload for highly
+sparse datasets. Besides, the selection process occurs in the
+server side, thus avoiding additional computation costs on the
+clients. But FCF-BTS causes 4% - 8% loss in recommendation
+accuracy.
+To achieve a better balance between recommendation ac-
+curacy and efficiency, Ai et al. [77] propose an all-MLP
+
+IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, VOL. 14, NO. 8, DECEMBER 2022
+10
+network that uses a Fourier sub-layer to replace the self-
+attention sub-layer in a Transformer encoder so as to filter
+noise data components unrelated to the user’s real interests,
+and adapts an adaptive model pruning technique to discard
+the noise model components that doesn’t contribute to model
+performance. Experiments show that all-MLP network can
+significantly reduce communication and computation costs,
+and accelerates the model convergence.
+Importance-based model updating strategies can greatly
+reduce communication and computation costs at the same time,
+but only selecting the important parts for updating inevitably
+reduces the recommendation performance.
+B. Model Compression
+Model Compression is a well-known technology in dis-
+tributed learning [84], which compresses the communicated
+parameters per round to be more compact.
+For examples, Konen et al. [78] propose two methods
+(i.e., structured updates and sketched updates) to decrease the
+uplink communication costs under federated learning settings.
+Structured updates method directly learns updates from a
+pre-specified structure parameterized using fewer variables.
+Sketched updates method compresses the full local update
+using a lossy compression way before sending it to server.
+These two strategies can reduce the communication costs by
+2 orders of magnitude.
+To reduce the uplink communication costs in deep learning
+based FedRS, JointRec [79] combines low-rank matrix factor-
+ization [85] and 8-bit probabilistic quantization [86] methods
+to compress weight update. Supposing the weight update ma-
+trix of client n is Ha×b
+n
+, a ≤ b, low-rank matrix factorization
+decomposes Ha×b
+n
+into two matrices: Ha×b
+n
+= U a×k
+n
+V k×b
+n
+,
+where k = b/N and N is a positive number that influences the
+compression performance. And 8-bit probabilistic quantization
+method transforms the position of matrix value into 8-bit value
+before send it to server. Experiments demonstrate that JointRec
+can realize 12.83× larger compression ratio while maintaining
+recommendation performance.
+Model compression methods achieve significant results in
+reducing the uplink communication costs. However, the re-
+duction of communication cost sacrifices the computation
+resources of the clients, so it’s necessary to consider the trade-
+off between computation and communication costs when using
+model compression.
+C. Client Sampling
+In traditional federated learning frameworks [8], the server
+randomly selects clients to participate in the training process
+and simply aggregates the local models by average, which
+requires a large number of communications to realize satis-
+factory accuracy. Client sampling utilizes efficient sampling
+strategies so as to improve the training efficiency and reduce
+the communication rounds.
+For example, Muhammad et al. [80] propose an effective
+sampling strategy named FedFast to speed up the training
+efficiency of federated recommendation models while keeping
+more accuracy. FadFast consists of two efficient components:
+ActvSAMP and ActvAGG. ActvSAMP uses K-means algo-
+rithm to cluster users based on their profile, and samples
+clients in equal proportions from each cluster. And ActvAGG
+propagates local updates to the other clients in the same
+cluster. In this way, the learning process for these similar
+users is greatly accelerated and overall efficiency of the FedRS
+is consequently improved. Experiments show that FedFast
+reduces communication rounds by 94% compared to FedAvg
+[8]. However, FedFast is faced with the cold start problem
+because it requires a number of users and items for training.
+Besides, FedFast needs to retrain the model to support new
+users and items.
+D. One Shot Federated Learning
+The goal of one shot federated learning mechanism is to
+reduce communication rounds of FedRS [87] [88], which lim-
+its communication to a single round to aggregate knowledge
+of local models. For example, Eren et al. [81] implement
+an one-shot federated learning framework for cross-platform
+FedRS named FedSPLIT. FedSPLIT aggregates model through
+knowledge distillation [89], which can generate client specific
+recommendation results with just a single pair of communica-
+tion rounds between the server and clients after a small initial
+communication. Experiments show that FedSPLIT realizes
+similar root-mean-square error (RMSE) compared with multi-
+round communication scenarios, but it is not applicable to the
+scenario where the participant is a individual user.
+VII. OPEN SOURCE PLATFORMS
+This section introduces five open source platforms that can
+be used to build FedRS: Federated AI Technology Enabler
+(Fate)1, Tensorflow Federated (TFF)2, Pysyft3, PaddleFL4, and
+FederatedScope5. The comparison among some existing open
+source platforms is shown in Table III.
+A. Federated AI Technology Enabler
+Federated AI Technology Enabler (Fate) [90] is the first
+open source platform for federated learning around the world,
+which aims to enable companies and organizations to collab-
+orate on data while keeping data privacy and security. Fate
+supports various machine learning algorithms under federated
+learning settings, including logistic regression, XGBOOST,
+deep learning and transfer learning. Besides, Fate integrates
+homomorphic encryption, differential privacy and secret shar-
+ing mechanisms to protect privacy against the curious server.
+The structure of FATE consists of seven major modules:
+FederatedML, EggRoll, FATE-FLow, FATE-Board, FATE-
+Serving, KubeFATE and FATE-cloud. FederatedML imple-
+ments privacy-preserving federated machine learning algo-
+rithms; EggRoll manages the distributed computation frame-
+work; FATE-FLow coordinates the execution of the algorithm
+1https://github.com/FederatedAI/FATE
+2https://github.com/tensorflow/federated
+3https://github.com/OpenMined/PySyft
+4https://github.com/PaddlePaddle/PaddleFL
+5https://github.com/alibaba/FederatedScope
+
+IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, VOL. 14, NO. 8, DECEMBER 2022
+11
+components; FATE-Board provides visualization for building
+and evaluating models; FATE-Serving provides online infer-
+ence for the users; KubeFATE helps deploy Fate platform by
+using cloud native technologies; FATE-cloud provide cross-
+cloud deployment and management services.
+Fate provides a federated recommendation module (Federat-
+edRec) to solve the recommendation problems of rate predic-
+tion and item ranking tasks. FederatedRec implements many
+common recommendation algorithms under federated learning
+settings, including factorization machine, matrix factorization,
+SVD, SVD++ and generalized matrix factorization.
+B. Tensorflow Federated
+Tensorflow Federated (TFF) [91] is a lightweight system
+developed by Google, which provides the building blocks to
+enables developers to implement own federated models based
+on TensorFlow. Besides, developers can plug any existing
+Keras model into TFF with just a few lines of code. To
+enhancing privacy guarantees for federated learning, TFF
+integrates differential privacy mechanism.
+The interfaces of TFF are organized in two layers API (i.e.,
+Federated Learning API and Federated Core API). Federated
+Learning API implements high-level interfaces for developers
+to make training and evaluation process of federated learning.
+Federated Core API provides lower-level interfaces to express
+novel federated learning algorithms by using TensorFlow and
+distributed communication operators.
+Based on TFF, Singhal et al. [92] implements a model-
+agnostic framework for fast partial local federated learning,
+which is suitable for large-scale collaborative filtering recom-
+mendation scenarios.
+C. Pysyft
+PySyft [93] is developed by Open-Mined, which also pro-
+vides the building blocks for developers to implement own
+federated recommendation algorithms. Compared with TFF,
+PySyft can work with both Tensorflow and Pytorch. For
+privacy protection, PySyft can flexibly and simply integrate
+homomorphic encryption, differential privacy and secret shar-
+ing mechanisms so as to defend against the honest-but-curious
+server and participants. However, Pysyft doesn’t disclose the
+detailed interface design or system architecture.
+D. PaddleFL
+PaddleFL [94] is an open source federated learning platform
+developed by Baidu, which integrates both differential privacy
+and secret sharing mechanisms to provide privacy guarantees.
+PaddleFL contains two major components: Data Parallel and
+Federated Learning with MPC (PFM). Data Parallel is respon-
+sible for defining, distributing and training a federated learning
+task. PFM implements secure multi-party computation to
+ensure training and inference security.
+PaddleFL provides many federated recommendation algo-
+rithms that can be used directly. For example, PaddleFL
+implements a classical session-based recommendation model
+Gru4rec [95] under the federated learning settings and provide
+simulated experiments on real world dataset. But the simulated
+experiment suppose all datasets in different organizations are
+homogeneous, which is only satisfied under ideal case. In
+addition, PaddleFL also provides a strategy to train a Click-
+Through-Rate(CTR) model by using FedAvg [8] algorithm.
+E. FederatedScope
+FederatedScope [96], developed by Alibaba, is a flexible
+federated learning platform for heterogeneity. FederatedScope
+employs an event-driven architecture to support asynchronous
+training, and coordinate participants with personalized be-
+haviors and multiple goals into federated learning scenarios.
+FederatedScope can easily support different machine learning
+libraries such as Tensorflow and Pytorch. Besides, Federat-
+edScope enables various kinds of plug-in components and
+operations thar can be used for efficient further development.
+For privacy protection plug-ins, FederatedScope integrates ho-
+momorphic encryption, differential privacy and secret sharing
+mechanisms to enhance privacy guarantees. In the federated
+recommendation scenario, FederatedScope has built in matrix
+factorization models, datasets (Netflix and MovieLen) and
+trainer under different federated learning settings.
+VIII. FUTURE DIRECTIONS
+This section presents and discusses many prospective re-
+search directions in the future. Although some directions have
+been covered in above sections, we believe they are necessary
+for FedRS, and need to be further researched.
+Decentralized FedRS. Most of current FedRS are based on
+client-server communication architecture, which faces single-
+point-of-failure and privacy issues caused by the central server
+[97]. While much work has been devoted to decentralized
+federated learning [98] [99], few decentralized FedRS have
+been studied. A feasible solution is to replace client-server
+communication architecture with peer-peer communication
+architecture to achieve fully decentralized federated recom-
+mendation. Hegeds et al. [19] propose a fully decentralized
+matrix factorization framework based on gossip learning [100],
+where each participant sends their copy of the global recom-
+mendation model to random online neighbors in the peer to
+peer network.
+Incentive mechanisms in FedRS. FedRS collaborate with
+multiple participants to train a global recommendation model,
+and the recommendation performance of global model is
+highly dependent on the quantity and quality of data provided
+by the participants. Therefore, it is significant to design an
+appropriate incentive mechanism to inspire participants to
+contribute their own data and participate in collaborative
+training, especially in the cross-organization federated recom-
+mendation scenarios. The incentive mechanisms must be able
+to measure the clients’ contribution to the global model fairly
+and efficiently.
+Privacy of serving phase. Although many studies have
+combined different privacy mechanisms to protect user privacy
+in the training phase of FedRS, the privacy protection for
+the serving phase is still underexplored. To prevent user
+recommendation results from leaking, most of the current
+
+IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, VOL. 14, NO. 8, DECEMBER 2022
+12
+TABLE III: The comparison among some existing open source platforms.
+Platforms
+Fate
+TFF
+Pysyft
+PaddleFL
+FederatedScope
+Publisher
+WeBank
+Google
+OpenMined
+Baidu
+Alibaba
+Audience
+Academia
+�
+�
+�
+�
+�
+Industry
+�
+�
+Models
+Neural Network
+�
+�
+�
+�
+�
+Tree Model
+�
+�
+Linear Model
+�
+�
+�
+�
+�
+Privacy
+Homomorphic encryption
+�
+�
+�
+Differential Privacy
+�
+�
+�
+�
+�
+Secret Sharing
+�
+�
+�
+Libraries
+Tensorflow
+�
+�
+�
+Pytorch
+�
+�
+studies assume local serving, where the server sends the entire
+set of candidate items to clients, and clients generate rec-
+ommendation results locally [10] [21]. However, such design
+brings enormous communication, computation and memory
+costs for clients since there are usually millions of items in
+real-world recommendation systems. Another feasible solution
+is online serving, where clients send encrypted or noised user
+embedding to the server to recall top-N candidate items, then
+clients generate personalized recommendation results based
+one these candidate items [101]. Nevertheless, there is a risk
+of privacy leakage associated with online serving, because
+recalled items are known to the server.
+Cold start problem in FedRS. The cold start problem
+means that recommendation systems cannot generate satisfac-
+tory recommendation results for new users with little history
+interactions. In federated settings, the user data is stored
+locally, so it is more difficult to integrate other auxiliary
+information (e.g., social relationships) to alleviate the cold
+start problem. Therefore, it is a challenging and prospective
+research direction to address the cold start problem while
+ensuring user privacy.
+Secure FedRS. In the real world, the participants in the
+FedRS are likely to be untrustworthy. Therefore, participants
+may upload poisoned intermediate parameters to affect rec-
+ommendation results or destroy recommendation performance.
+Although some robust aggregation strategies [57] and detec-
+tion methods [61] have been proposed to defense poisoning
+attacks in federated learning settings, most of them does not
+work well in FedRS. One one hand, some strategies such
+as Krum, Median and Trimmed-mean degrade the recom-
+mendation performance to a certain extend. One the other
+hand, some novel attacks [11] use well-designed constraints to
+mimic the patterns of normal users, extremely increasing the
+difficulty to be detected and defensed. Currently, there is still
+no effective defense methods against these poisoning attacks
+while maintaining recommendation accuracy.
+IX. CONCLUSION
+A lot of effort has been devoted to federated recommen-
+dation systems. A comprehensive survey is significant and
+meaningful. This survey summarizes the latest studies from
+aspects of the privacy, security, heterogeneity and commu-
+nication costs. Based on these aspects, we also make a
+detailed comparison among the existing designs and solutions.
+Moreover, we present many prospective research directions to
+promote development in this field. FedRS will be a promising
+field with huge potential opportunities, which requires more
+efforts to develop.
+ACKNOWLEDGMENTS
+This research is partially supported by the National Key
+R&D Program of China No.2021YFF0900800, the NSFC
+No.91846205, the Shandong Provincial Key Research and De-
+velopment Program (Major Scientific and Technological Inno-
+vation Project) (No.2021CXGC010108), the Shandong Provin-
+cial Natural Science Foundation (No.ZR202111180007), the
+Fundamental Research Funds of Shandong University, and
+the Special Fund for Science and Technology of Guangdong
+Province under Grant (2021S0053).
+REFERENCES
+[1] B. Sarwar, G. Karypis, J. Konstan, and J. Riedl, “Analysis of recom-
+mendation algorithms for e-commerce,” in Proceedings of the 2nd ACM
+Conference on Electronic Commerce, pp. 158–167, 2000.
+[2] J. B. Schafer, J. A. Konstan, and J. Riedl, “E-commerce recommenda-
+tion applications,” Data mining and knowledge discovery, vol. 5, no. 1,
+pp. 115–153, 2001.
+[3] G. Zheng, F. Zhang, Z. Zheng, Y. Xiang, N. J. Yuan, X. Xie, and
+Z. Li, “Drn: A deep reinforcement learning framework for news rec-
+ommendation,” in Proceedings of the 2018 world wide web conference,
+pp. 167–176, 2018.
+[4] J. Liu, P. Dolan, and E. R. Pedersen, “Personalized news recommenda-
+tion based on click behavior,” in Proceedings of the 15th international
+conference on Intelligent user interfaces, pp. 31–40, 2010.
+[5] W. Yue, Z. Wang, J. Zhang, and X. Liu, “An overview of recom-
+mendation techniques and their applications in healthcare,” IEEE/CAA
+Journal of Automatica Sinica, vol. 8, no. 4, pp. 701–717, 2021.
+
+IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, VOL. 14, NO. 8, DECEMBER 2022
+13
+[6] J. Kim, D. Lee, and K.-Y. Chung, “Item recommendation based on
+context-aware model for personalized u-healthcare service,” Multime-
+dia Tools and Applications, vol. 71, no. 2, pp. 855–872, 2014.
+[7] J. P. Albrecht, “How the gdpr will change the world,” Eur. Data Prot.
+L. Rev., vol. 2, p. 287, 2016.
+[8] B. McMahan, E. Moore, D. Ramage, S. Hampson, and B. A. y Arcas,
+“Communication-efficient learning of deep networks from decentral-
+ized data,” in Artificial intelligence and statistics, pp. 1273–1282,
+PMLR, 2017.
+[9] L. Zhu, Z. Liu, and S. Han, “Deep leakage from gradients,” Advances
+in neural information processing systems, vol. 32, 2019.
+[10] D. Chai, L. Wang, K. Chen, and Q. Yang, “Secure federated matrix
+factorization,” Intelligent Systems, IEEE, vol. PP, no. 99, pp. 1–1, 2020.
+[11] C. Wu, F. Wu, T. Qi, Y. Huang, and X. Xie, “Fedattack: Effective
+and covert poisoning attack on federated recommendation via hard
+sampling,” in Proceedings of the 28th ACM SIGKDD Conference on
+Knowledge Discovery and Data Mining, KDD ’22, (New York, NY,
+USA), p. 4164–4172, Association for Computing Machinery, 2022.
+[12] S. Zhang, H. Yin, T. Chen, Z. Huang, Q. V. H. Nguyen, and L. Cui,
+“Pipattack: Poisoning federated recommender systems for manipulating
+item promotion,” in Proceedings of the Fifteenth ACM International
+Conference on Web Search and Data Mining, pp. 1415–1423, 2022.
+[13] C.-L. Liao and S.-J. Lee, “A clustering based approach to improving
+the efficiency of collaborative filtering recommendation,” Electronic
+Commerce Research and Applications, vol. 18, pp. 1–9, 2016.
+[14] G. Adomavicius and A. Tuzhilin, “Toward the next generation of
+recommender systems: a survey of the state-of-the-art and possible
+extensions,” IEEE Transactions on Knowledge and Data Engineering,
+vol. 17, no. 6, pp. 734–749, 2005.
+[15] Q. Yang, Y. Liu, T. Chen, and Y. Tong, “Federated machine learning:
+Concept and applications,” ACM Transactions on Intelligent Systems
+and Technology, vol. 10, no. 2, pp. 1–19, 2019.
+[16] T. Li, A. K. Sahu, A. Talwalkar, and V. Smith, “Federated learning:
+Challenges, methods, and future directions,” IEEE Signal Processing
+Magazine, vol. 37, no. 3, pp. 50–60, 2020.
+[17] L. Yang, B. Tan, V. W. Zheng, K. Chen, and Q. Yang, “Federated rec-
+ommendation systems,” in Federated Learning, pp. 225–239, Springer,
+2020.
+[18] C. Xie, S. Koyejo, and I. Gupta, “Asynchronous federated optimiza-
+tion,” arXiv preprint arXiv:1903.03934, 2019.
+[19] I. Heged˝us, G. Danner, and M. Jelasity, “Decentralized recommenda-
+tion based on matrix factorization: a comparison of gossip and fed-
+erated learning,” in Joint European Conference on Machine Learning
+and Knowledge Discovery in Databases, pp. 317–332, Springer, 2019.
+[20] J. Yi, F. Wu, C. Wu, R. Liu, G. Sun, and X. Xie, “Efficient-fedrec:
+Efficient federated learning framework for privacy-preserving news
+recommendation,” arXiv preprint arXiv:2109.05446, 2021.
+[21] M. Ammad-Ud-Din, E. Ivannikova, S. A. Khan, W. Oyomno, Q. Fu,
+K. E. Tan, and A. Flanagan, “Federated collaborative filtering
+for privacy-preserving personalized recommendation system,” arXiv
+preprint arXiv:1901.09888, 2019.
+[22] G. Lin, F. Liang, W. Pan, and Z. Ming, “Fedrec: Federated recom-
+mendation with explicit feedback,” Intelligent Systems, IEEE, vol. PP,
+no. 99, pp. 1–1, 2020.
+[23] C. Chen, L. Li, B. Wu, C. Hong, L. Wang, and J. Zhou, “Se-
+cure social recommendation based on secret sharing,” arXiv preprint
+arXiv:2002.02088, 2020.
+[24] WuChuhan, WuFangzhao, LyuLingjuan, HuangYongfeng, and XieX-
+ing, “Fedctr: Federated native ad ctr prediction with cross platform
+user behavior data,” ACM Transactions on Intelligent Systems and
+Technology (TIST), 2021.
+[25] S. Kalloori and S. Klingler, “Horizontal cross-silo federated recom-
+mender systems,” in Fifteenth ACM Conference on Recommender
+Systems, pp. 680–684, 2021.
+[26] Koren, Yehuda, Bell, Robert, Volinsky, and Chris, “Matrix factorization
+techniques for recommender systems.,” Computer, vol. 42, no. 8,
+pp. 30–37, 2009.
+[27] K. Dolui, I. Cuba Gyllensten, D. Lowet, S. Michiels, H. Hallez,
+and D. Hughes, “Towards privacy-preserving mobile applications with
+federated learning: The case of matrix factorization (poster),” in
+Proceedings of the 17th Annual International Conference on Mobile
+Systems, Applications, and Services, pp. 624–625, 2019.
+[28] J. Hua, C. Xia, and S. Zhong, “Differentially private matrix factoriza-
+tion,” in Proceedings of the 24th International Conference on Artificial
+Intelligence, IJCAI’15, p. 1763–1770, AAAI Press, 2015.
+[29] S. Ying, “Shared mf: A privacy-preserving recommendation system,”
+arXiv preprint arXiv:2008.07759, 2020.
+[30] V. Perifanis and P. S. Efraimidis, “Federated neural collaborative
+filtering,” Knowledge-Based Systems, vol. 242, p. 108441, 2022.
+[31] C. Wu, F. Wu, Y. Cao, Y. Huang, and X. Xie, “Fedgnn: Federated
+graph neural network for privacy-preserving recommendation,” arXiv
+preprint arXiv:2102.04925, 2021.
+[32] M. Imran, H. Yin, T. Chen, N. Q. V. Hung, A. Zhou, and K. Zheng,
+“Refrs: Resource-efficient federated recommender system for dynamic
+and diversified user preferences,” ACM Trans. Inf. Syst., aug 2022. Just
+Accepted.
+[33] X. He, L. Liao, H. Zhang, L. Nie, X. Hu, and T.-S. Chua, “Neural
+collaborative filtering,” in Proceedings of the 26th international con-
+ference on world wide web, pp. 173–182, 2017.
+[34] M. Huang, H. Li, B. Bai, C. Wang, K. Bai, and F. Wang, “A
+federated multi-view deep learning framework for privacy-preserving
+recommendations,” arXiv preprint arXiv:2008.10808, 2020.
+[35] P.-S. Huang, X. He, J. Gao, L. Deng, A. Acero, and L. Heck, “Learning
+deep structured semantic models for web search using clickthrough
+data,” in Proceedings of the 22nd ACM international conference on
+Information & Knowledge Management, pp. 2333–2338, 2013.
+[36] W.-Y.
+Chen,
+Y.-C.
+Liu,
+Z.
+Kira,
+Y.-C.
+F.
+Wang,
+and
+J.-B.
+Huang, “A closer look at few-shot classification,” arXiv preprint
+arXiv:1904.04232, 2019.
+[37] A. Nichol, J. Achiam, and J. Schulman, “On first-order meta-learning
+algorithms,” arXiv preprint arXiv:1803.02999, 2018.
+[38] F. Chen, M. Luo, Z. Dong, Z. Li, and X. He, “Federated meta-learning
+with fast convergence and efficient communication,” arXiv preprint
+arXiv:1802.07876, 2018.
+[39] F. Liang, W. Pan, and Z. Ming, “Fedrec++: Lossless federated rec-
+ommendation with explicit feedback,” in Proceedings of the AAAI
+conference on artificial intelligence, vol. 35, pp. 4224–4231, 2021.
+[40] A. Abbas, A. Hidayet, U. A. Selcuk, and C. Mauro, “A survey on
+homomorphic encryption schemes: Theory and implementation,” Acm
+Computing Surveys, vol. 51, no. 4, pp. 1–35, 2017.
+[41] P. Paillier, “Public-key cryptosystems based on composite degree
+residuosity classes,” in International conference on the theory and
+applications of cryptographic techniques, pp. 223–238, Springer, 1999.
+[42] V. Perifanis, G. Drosatos, G. Stamatelatos, and P. S. Efraimidis,
+“Fedpoirec: Privacy preserving federated poi recommendation with
+social influence,” arXiv preprint arXiv:2112.11134, 2021.
+[43] J. H. Cheon, A. Kim, M. Kim, and Y. Song, “Homomorphic encryption
+for arithmetic of approximate numbers,” in International conference
+on the theory and application of cryptology and information security,
+pp. 409–437, Springer, 2017.
+[44] Z. Liu, L. Yang, Z. Fan, H. Peng, and P. S. Yu, “Federated social
+recommendation with graph neural network,” ACM Transactions on
+Intelligent Systems and Technology (TIST), vol. 13, no. 4, pp. 1–24,
+2022.
+[45] Z. Lin, W. Pan, and Z. Ming, “Fr-fmss: federated recommendation
+via fake marks and secret sharing,” in Fifteenth ACM Conference on
+Recommender Systems, pp. 668–673, 2021.
+[46] C. Dwork, “Calibrating noise to sensitivity in private data analysis,”
+Lecture Notes in Computer Science, vol. 3876, no. 8, pp. 265–284,
+2012.
+[47] M. Hardt and K. Talwar, “On the geometry of differential privacy,”
+in Proceedings of the forty-second ACM symposium on Theory of
+computing, pp. 705–714, 2010.
+[48] B. Li, Y. Wang, A. Singh, and Y. Vorobeychik, “Data poisoning
+attacks on factorization-based collaborative filtering,” Advances in
+neural information processing systems, vol. 29, 2016.
+[49] M. Welling and Y. W. Teh, “Bayesian learning via stochastic gradient
+langevin dynamics,” in Proceedings of the 28th international confer-
+ence on machine learning (ICML-11), pp. 681–688, 2011.
+[50] M. Fang, G. Yang, N. Z. Gong, and J. Liu, “Poisoning attacks to
+graph-based recommender systems,” in Proceedings of the 34th annual
+computer security applications conference, pp. 381–392, 2018.
+[51] H. Huang, J. Mu, N. Z. Gong, Q. Li, B. Liu, and M. Xu, “Data
+poisoning attacks to deep learning based recommender systems,” arXiv
+preprint arXiv:2101.02644, 2021.
+[52] H. Zhang, Y. Li, B. Ding, and J. Gao, “Practical data poisoning
+attack against next-item recommendation,” in Proceedings of The Web
+Conference 2020, pp. 2458–2464, 2020.
+[53] V. Mnih, K. Kavukcuoglu, D. Silver, A. Graves, I. Antonoglou,
+D. Wierstra, and M. Riedmiller, “Playing atari with deep reinforcement
+learning,” arXiv preprint arXiv:1312.5602, 2013.
+[54] D. Rong, S. Ye, R. Zhao, H. N. Yuen, J. Chen, and Q. He, “Fedrecat-
+tack: Model poisoning attack to federated recommendation,” arXiv
+preprint arXiv:2204.01499, 2022.
+
+IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, VOL. 14, NO. 8, DECEMBER 2022
+14
+[55] D. Rong, Q. He, and J. Chen, “Poisoning deep learning based
+recommender model in federated learning scenarios,” arXiv preprint
+arXiv:2204.13594, 2022.
+[56] D. Yin, Y. Chen, R. Kannan, and P. Bartlett, “Byzantine-robust dis-
+tributed learning: Towards optimal statistical rates,” in International
+Conference on Machine Learning, pp. 5650–5659, PMLR, 2018.
+[57] P. Blanchard, E. M. El Mhamdi, R. Guerraoui, and J. Stainer, “Ma-
+chine learning with adversaries: Byzantine tolerant gradient descent,”
+Advances in Neural Information Processing Systems, vol. 30, 2017.
+[58] R. Guerraoui, S. Rouault, et al., “The hidden vulnerability of distributed
+learning in byzantium,” in International Conference on Machine Learn-
+ing, pp. 3521–3530, PMLR, 2018.
+[59] Z. Sun, P. Kairouz, A. T. Suresh, and H. B. McMahan, “Can you really
+backdoor federated learning?,” arXiv preprint arXiv:1911.07963, 2019.
+[60] C. Chen, J. Zhang, A. K. Tung, M. Kankanhalli, and G. Chen, “Robust
+federated recommendation system,” arXiv preprint arXiv:2006.08259,
+2020.
+[61] Y. Jiang, Y. Zhou, D. Wu, C. Li, and Y. Wang, “On the detection of
+shilling attacks in federated collaborative filtering,” in 2020 Interna-
+tional Symposium on Reliable Distributed Systems (SRDS), pp. 185–
+194, 2020.
+[62] Y. Kalantidis, M. B. Sariyildiz, N. Pion, P. Weinzaepfel, and D. Larlus,
+“Hard negative mixing for contrastive learning,” Advances in Neural
+Information Processing Systems, vol. 33, pp. 21798–21809, 2020.
+[63] L. Lyu, H. Yu, X. Ma, C. Chen, L. Sun, J. Zhao, Q. Yang, and
+S. Y. Philip, “Privacy and robustness in federated learning: Attacks
+and defenses,” IEEE Transactions on Neural Networks and Learning
+Systems, 2022.
+[64] P. Kairouz, H. B. McMahan, B. Avent, A. Bellet, M. Bennis, A. N.
+Bhagoji, K. Bonawitz, Z. Charles, G. Cormode, R. Cummings, et al.,
+“Advances and open problems in federated learning,” Foundations and
+Trends® in Machine Learning, vol. 14, no. 1–2, pp. 1–210, 2021.
+[65] Z. Jie, S. Chen, J. Lai, M. Arif, and Z. He, “Personalized federated
+recommendation system with historical parameter clustering,” Journal
+of Ambient Intelligence and Humanized Computing, pp. 1–11.
+[66] J. Wu, Q. Liu, Z. Huang, Y. Ning, H. Wang, E. Chen, J. Yi, and
+B. Zhou, “Hierarchical personalized federated learning for user model-
+ing,” in Proceedings of the Web Conference 2021, pp. 957–968, 2021.
+[67] Q. Ma, Y. Xu, H. Xu, Z. Jiang, L. Huang, and H. Huang, “Fedsa:
+A semi-asynchronous federated learning mechanism in heterogeneous
+edge computing,” IEEE Journal on Selected Areas in Communications,
+vol. 39, no. 12, pp. 3654–3672, 2021.
+[68] T. Nishio and R. Yonetani, “Client selection for federated learning
+with heterogeneous resources in mobile edge,” in ICC 2019-2019 IEEE
+international conference on communications (ICC), pp. 1–7, IEEE,
+2019.
+[69] Q. Wang, H. Yin, T. Chen, J. Yu, A. Zhou, and X. Zhang, “Fast-
+adapting and privacy-preserving federated recommender system,” The
+VLDB Journal, vol. 31, no. 5, pp. 877–896, 2022.
+[70] Z. Jie, S. Chen, J. Lai, M. Arif, and Z. He, “Personalized federated
+recommendation system with historical parameter clustering,” Journal
+of Ambient Intelligence and Humanized Computing, pp. 1–11, 2022.
+[71] S. Luo, Y. Xiao, and L. Song, “Personalized federated recommen-
+dation via joint representation learning, user clustering, and model
+adaptation,” in Proceedings of the 31st ACM International Conference
+on Information and Knowledge Management, (New York, NY, USA),
+p. 4289–4293, Association for Computing Machinery, 2022.
+[72] V. W. Anelli, Y. Deldjoo, T. D. Noia, A. Ferrara, and F. Narducci,
+“Federank: User controlled feedback with federated recommender
+systems,” in European Conference on Information Retrieval, pp. 32–47,
+Springer, 2021.
+[73] C. Finn, P. Abbeel, and S. Levine, “Model-agnostic meta-learning
+for fast adaptation of deep networks,” in International conference on
+machine learning, pp. 1126–1135, PMLR, 2017.
+[74] B. Acun, M. Murphy, X. Wang, J. Nie, C.-J. Wu, and K. Hazelwood,
+“Understanding training efficiency of deep learning recommendation
+models at scale,” in 2021 IEEE International Symposium on High-
+Performance Computer Architecture (HPCA), pp. 802–814, IEEE,
+2021.
+[75] J. Qin, B. Liu, and J. Qian, “A novel privacy-preserved recommender
+system framework based on federated learning,” in 2021 The 4th
+International Conference on Software Engineering and Information
+Management, pp. 82–88, 2021.
+[76] F. K. Khan, A. Flanagan, K. E. Tan, Z. Alamgir, and M. Ammad-
+Ud-Din, “A payload optimization method for federated recommender
+systems,” in Fifteenth ACM Conference on Recommender Systems,
+pp. 432–442, 2021.
+[77] Z. Ai, G. Wu, B. Li, Y. Wang, and C. Chen, “Fourier enhanced mlp
+with adaptive model pruning for efficient federated recommendation,”
+in International Conference on Knowledge Science, Engineering and
+Management, pp. 356–368, Springer, 2022.
+[78] J. Koneˇcn`y, H. B. McMahan, F. X. Yu, P. Richt´arik, A. T. Suresh, and
+D. Bacon, “Federated learning: Strategies for improving communica-
+tion efficiency,” arXiv preprint arXiv:1610.05492, 2016.
+[79] Sijing, Duan, Deyu, Zhang, Yanbo, Wang, Lingxiang, Li, Yaoxue, and
+Zhang, “Jointrec: A deep-learning-based joint cloud video recommen-
+dation framework for mobile iot,” IEEE Internet of Things Journal,
+vol. PP, no. 99, pp. 1–1, 2019.
+[80] K. Muhammad, Q. Wang, D. O’Reilly-Morgan, E. Tragos, B. Smyth,
+N. Hurley, J. Geraci, and A. Lawlor, “Fedfast: Going beyond average
+for faster training of federated recommender systems,” in Proceedings
+of the 26th ACM SIGKDD International Conference on Knowledge
+Discovery & Data Mining, pp. 1234–1242, 2020.
+[81] M. E. Eren, L. E. Richards, M. Bhattarai, R. Yus, C. Nicholas,
+and B. S. Alexandrov, “Fedsplit: One-shot federated recommendation
+system based on non-negative joint matrix factorization and knowledge
+distillation,” arXiv preprint arXiv:2205.02359, 2022.
+[82] K. Bonawitz, V. Ivanov, B. Kreuter, A. Marcedone, H. B. McMahan,
+S. Patel, D. Ramage, A. Segal, and K. Seth, “Practical secure aggre-
+gation for privacy-preserving machine learning,” in proceedings of the
+2017 ACM SIGSAC Conference on Computer and Communications
+Security, pp. 1175–1191, 2017.
+[83] W. R. Thompson, “On the likelihood that one unknown probability
+exceeds another in view of the evidence of two samples,” Biometrika,
+vol. 25, no. 3-4, pp. 285–294, 1933.
+[84] H. Wang, S. Sievert, S. Liu, Z. Charles, D. Papailiopoulos, and
+S. Wright, “Atomo: Communication-efficient learning via atomic
+sparsification,” Advances in Neural Information Processing Systems,
+vol. 31, 2018.
+[85] Y. Gong, L. Liu, M. Yang, and L. Bourdev, “Compressing deep
+convolutional networks using vector quantization,” arXiv preprint
+arXiv:1412.6115, 2014.
+[86] Y. Lin, S. Han, H. Mao, Y. Wang, and W. J. Dally, “Deep gradient
+compression: Reducing the communication bandwidth for distributed
+training,” arXiv preprint arXiv:1712.01887, 2017.
+[87] N. Guha, A. Talwalkar, and V. Smith, “One-shot federated learning,”
+arXiv preprint arXiv:1902.11175, 2019.
+[88] A. Kasturi, A. R. Ellore, and C. Hota, “Fusion learning: A one shot
+federated learning,” in International Conference on Computational
+Science, pp. 424–436, Springer, 2020.
+[89] Q. Li, B. He, and D. Song, “Practical one-shot federated learning for
+cross-silo setting,” arXiv preprint arXiv:2010.01017, 2020.
+[90] Y. Liu, T. Fan, T. Chen, Q. Xu, and Q. Yang, “Fate: An industrial grade
+platform for collaborative learning with data protection.,” J. Mach.
+Learn. Res., vol. 22, no. 226, pp. 1–6, 2021.
+[91] K. Bonawitz, H. Eichner, W. Grieskamp, D. Huba, A. Ingerman,
+V. Ivanov, C. Kiddon, J. Koneˇcn`y, S. Mazzocchi, B. McMahan, et al.,
+“Towards federated learning at scale: System design,” Proceedings of
+Machine Learning and Systems, vol. 1, pp. 374–388, 2019.
+[92] K. Singhal, H. Sidahmed, Z. Garrett, S. Wu, J. Rush, and S. Prakash,
+“Federated reconstruction: Partially local federated learning,” Advances
+in Neural Information Processing Systems, vol. 34, pp. 11220–11232,
+2021.
+[93] A. Ziller, A. Trask, A. Lopardo, B. Szymkow, B. Wagner, E. Bluemke,
+J.-M. Nounahon, J. Passerat-Palmbach, K. Prakash, N. Rose, et al.,
+“Pysyft: A library for easy federated learning,” in Federated Learning
+Systems, pp. 111–139, Springer, 2021.
+[94] “Paddlefl.” https://github.com/PaddlePaddle/PaddleFL.
+[95] B. Hidasi, A. Karatzoglou, L. Baltrunas, and D. Tikk, “Session-
+based recommendations with recurrent neural networks,” arXiv preprint
+arXiv:1511.06939, 2015.
+[96] Y. Xie, Z. Wang, D. Chen, D. Gao, L. Yao, W. Kuang, Y. Li,
+B. Ding, and J. Zhou, “Federatedscope: A comprehensive and flexi-
+ble federated learning platform via message passing,” arXiv preprint
+arXiv:2204.05011, 2022.
+[97] L. Lyu, J. Yu, K. Nandakumar, Y. Li, X. Ma, J. Jin, H. Yu, and K. S. Ng,
+“Towards fair and privacy-preserving federated deep models,” IEEE
+Transactions on Parallel and Distributed Systems, vol. 31, no. 11,
+pp. 2524–2541, 2020.
+[98] L. Lyu, Y. Li, K. Nandakumar, J. Yu, and X. Ma, “How to democra-
+tise and protect ai: Fair and differentially private decentralised deep
+learning,” IEEE Transactions on Dependable and Secure Computing,
+2020.
+
+IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, VOL. 14, NO. 8, DECEMBER 2022
+15
+[99] A. G. Roy, S. Siddiqui, S. P¨olsterl, N. Navab, and C. Wachinger,
+“Braintorrent: A peer-to-peer environment for decentralized federated
+learning,” arXiv preprint arXiv:1905.06731, 2019.
+[100] R. Orm´andi, I. Heged˝us, and M. Jelasity, “Gossip learning with linear
+models on fully distributed data,” Concurrency and Computation:
+Practice and Experience, vol. 25, no. 4, pp. 556–571, 2013.
+[101] T. Qi, F. Wu, C. Wu, Y. Huang, and X. Xie, “Uni-FedRec: A
+unified privacy-preserving news recommendation framework for model
+training and online serving,” in Findings of the Association for Compu-
+tational Linguistics: EMNLP 2021, (Punta Cana, Dominican Republic),
+pp. 1438–1448, Association for Computational Linguistics, Nov. 2021.
+Zehua Sun is currently pursuing his master’s degree
+in the School of Software of Shandong University.
+He received his bachelor’s degree in software engi-
+neering from the School of Software of Shandong
+University in 2017. His research interests include
+federated learning, recommendation systems and
+data mining.
+Yonghui Xu is a full professor at Joint SDU-NTU
+Centre for Artificial Intelligence Research (C-FAIR),
+Shandong University. Before that, he was a research
+fellow in the Joint NTU-UBC Research Centre of
+Excellence in Active Living for the Elderly (LILY),
+Nanyang Technological University, Singapore. He
+received his Ph.D. from the School of Computer Sci-
+ence and Engineering at South China University of
+Technology in 2017 and BS from the Department of
+Mathematics and Information Science Engineering
+at Henan University of China in 2011. His research
+areas include various topics in Trustworthy AI, knowledge graphs, expert
+systems and their applications in e-commerce and healthcare. He has been
+invited as reviewer of top journals and leading international conferences, such
+as, TKDE, TNNLS, IEEE Transactions on Cybernetics, Knowledge-Based
+System, TKDD, IJCAI and AAAI.
+Yong Liu is a Senior Research Scientist at Alibaba-
+NTU Singapore Joint Research Institute, Nanyang
+Technological University (NTU). He was a Data
+Scientist at NTUC Enterprise, and a Research Sci-
+entist at Institute for Infocomm Research (I2R),
+A*STAR, Singapore. He received his Ph.D. degree
+in Computer Engineering from NTU in 2016 and
+B.S. degree in Electronic Science and Technology
+from University of Science and Technology of China
+(USTC) in 2008. His research interests include rec-
+ommendation systems, natural language processing,
+and knowledge graph. He has been invited as a PC member of major
+conferences such as KDD, SIGIR, ACL, IJCAI, AAAI, and reviewer for
+IEEE/ACM transactions.
+Wei He is a associate professor at Shandong univer-
+sity. He received bachelor and master degrees from
+computer science department of shandong university
+in 1994 and 1999 respectively, and received Ph.d.
+from engineering of shandong university in 2009.
+He won the progress first prize in science and
+technology of shandong province and the progress
+second prize in science and technology of shandong
+province, and excellent achievement in computer
+application. He has published more than 20 papers
+in the computer journal, journal of software of
+domestic and international journals conference. More papers were recorded
+by SCI, EI.
+Yali Jiang is currently a Lecturer in the School
+of Software, Shandong University. She received her
+B.Sc., M.Sc. and Ph.D. degrees from Shandong
+University in 1999, 2002 and 2011, respectively.
+She is engaged in information security and cryp-
+tography research, her main research areas are pub-
+lic key security authentication system and lattice
+based cryptographic algorithm design and analysis,
+including cloud computing security, big data privacy
+protection, IoT security, etc. She has participated
+in the National 863 Program, Shandong Provincial
+Excellent Young and Middle-aged Research Award Fund, Shandong Provincial
+Natural Science Foundation and joint research projects of enterprises.
+Fangzhao Wu is a Principal Researcher at Microsoft
+Research Asia, President of AAAI2022 and senior
+member of China Computer Society. He received
+the Ph.D. and B.S. degrees both from Electronic
+Engineering Department of Tsinghua University in
+2017 and 2012 respectively. He published more than
+100 academic papers and was cited nearly 3000
+times He has won NLPCC2019 Excellent Paper
+Award, WSDM 2019 Outstanding PC and AAAI
+2021 Best SPC. His research mainly focuses on
+responsible AI, privacy protection, natural language
+processing, and recommender systems. The research results have been applied
+in Microsoft News, Bing Ads and other Microsoft products.
+LiZhen Cui (IET Fellow, IEEE Senior Member)
+is the Dean at School of Software, Shandong Uni-
+versity. He is the Co-Director of Joint SDU-NTU
+Centre for Artificial Intelligence Research (C-FAIR)
+and Research Center of Software & Data Engi-
+neering, Shandong University. He is the Associate
+Director of National Engineering Laboratory for E-
+Commerce Technologies. He is a Professor with
+the School of Software and the Joint SDU-NTU
+Centre for Artificial Intelligence Research (C-FAIR),
+Shandong University, and also a Visiting Professor
+with Nanyang Technological University, Singapore. He was a Visiting Scholar
+with Georgia Tech, Atlanta, GA, USA. He received his bachelor’s, M.Sc.,
+and Ph.D. degrees from Shandong University, Jinan, China, in 1999, 2002
+and 2005, respectively. He has authored or coauthored over 200 articles in
+journals and refereed conference proceedings. His research interests include
+big data management and analysis and AI theory and application.
+
diff --git a/9tAyT4oBgHgl3EQf3Pnc/content/tmp_files/load_file.txt b/9tAyT4oBgHgl3EQf3Pnc/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..19f0bdd0517fe4fc66f3620e0c109066ba6ba52f
--- /dev/null
+++ b/9tAyT4oBgHgl3EQf3Pnc/content/tmp_files/load_file.txt
@@ -0,0 +1,1398 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf,len=1397
+page_content='IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 8, DECEMBER 2022  1  A Survey on Federated Recommendation Systems  Zehua Sun∗, Yonghui Xu∗, Yong Liu, Wei He, Yali Jiang, Fangzhao Wu, Lizhen Cui†  Abstract—Federated learning has recently been applied to  recommendation systems to protect user privacy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' In federated  learning settings, recommendation systems can train recom-  mendation models only collecting the intermediate parameters  instead of the real user data, which greatly enhances the user  privacy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Beside, federated recommendation systems enable to  collaborate with other data platforms to improve recommended  model performance while meeting the regulation and privacy  constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' However, federated recommendation systems faces  many new challenges such as privacy, security, heterogeneity  and communication costs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' While significant research has been  conducted in these areas, gaps in the surveying literature still  exist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' In this survey, we—(1) summarize some common privacy  mechanisms used in federated recommendation systems and  discuss the advantages and limitations of each mechanism;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' (2)  review some robust aggregation strategies and several novel at-  tacks against security;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' (3) summarize some approaches to address  heterogeneity and communication costs problems;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' (4)introduce  some open source platforms that can be used to build federated  recommendation systems;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' (5) present some prospective research  directions in the future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' This survey can guide researchers and  practitioners understand the research progress in these areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Index Terms—Recommendation Systems, Federated Learning,  Privacy, Security, Heterogeneity, Communication costs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' INTRODUCTION  I  N recent years, recommendation systems have been widely  used to model user interests so as to solve information over-  load problems in many real-world fields, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=', e-commerce [1]  [2], news [3] [4] and healthcare [5] [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' To further improve the  recommendation performance, such systems usually collect as  much data as possible, including a lot of private information of  users, such as user attributes, user behaviors, social relations,  and context information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Although these recommendation systems have achieved  remarkable results in terms of accuracy, most of them require a  central server to store collected user data, which exist potential  privacy leakage risks because user data could be sold to  a third party without user consent, or stolen by motivated  attackers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' In addition, due to privacy concerns and regulation  restrictions, it becomes more difficult to integrate data from  other platforms to improve recommendation performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' For  example, regulations such as General Data Protection Reg-  ulation (GDPR) [7] set strict rules on collecting user data  and sharing data between different platforms, which may lead  to insufficient data for recommendation systems and further  affects the recommendation performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Zehua Sun, Yonghui Xu, Wei He, Yali Jiang and Lizhen Cui are with Joint  SDU-NTU Centre for Artificial Intelligence Research (C-FAIR) & Software  School, Shandong University.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Yong Liu are with Alibaba-NTU Singapore Joint Research Institute,  Nanyang Technological University, Singapore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Fangzhao Wu are with Microsoft Research Asia, China.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  ∗Zehua Sun and Yonghui Xu are Co-First authors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  †Corresponding author: clz@sdu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='cn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Federated learning is a privacy-preserving distributed learn-  ing scheme proposed by Google [8], which enables par-  ticipants to collaboratively train a machine learning model  by sharing intermediate parameters (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=', model parameters,  gradients) to the central server instead of their real data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Therefore, combining federated learning with recommendation  systems becomes a promising solution for privacy-preserving  recommendation systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' In this paper, we term it federated  recommendation system (FedRS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Challenges  While FedRS avoid direct exposure of real user data and  provides a privacy-aware paradigm for model training, there  are still some core challenges that need to be addressed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Challenge 1: Privacy concerns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Privacy protection is often  the major goal of FedRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' In FedRS, each participant jointly  trains a global recommendation model by sharing interme-  diate parameters instead of their real data, which makes an  important step towards privacy-preserving recommendation  systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' However, a curious sever can still infer some sensitive  information (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=', user behavior, ratings) from the intermediate  parameters [9] [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Challenge 2: Security attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' In FedRS, participants may  be malicious.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' They can attack the security of FedRS by  poisoning the local training samples or the intermediate pa-  rameters uploaded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' As a result, attackers can increase/decrease  the exposure ratio of specific items [12] or degrade the  overall performance of the recommendation model [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' In  addition, some attackers try to use well-designed constraints to  approximate the patterns of benign participants, which further  increases the difficulty of defense and detection [55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Challenge 3: Heterogeneity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' FedRS also faces the problem  of system, statistical and privacy heterogeneity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' System hetero-  geneity means that the storage, computing, and communication  capabilities of clients usually vary greatly, clients with limited  capability may become stragglers and affect training efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Statistical heterogeneity means that data in different clients  is often not independent and identically distributed (Non-  IID), which significantly affects global model convergence  and personalization of recommendation results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Privacy het-  erogeneity means that users and information usually have  different privacy constraints, thus using the same privacy  budgets for them will bring unnecessary loss of accuracy and  efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Challenge 4: Communication costs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' To achieve satisfac-  tory recommendation performance, clients need to commu-  nicate with the central server for multiple rounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' However,  the real-world recommendation systems are usually built on  complex deep learning models and millions of intermediate  parameters needs to be communicated [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Therefore, clients  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='00767v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='IR]  27 Dec 2022  IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 8, DECEMBER 2022  2  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 1: Communication architecture of FedRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  may be hard to afford severe communication costs, which lim-  its the application of FedRS in large-scale industrial scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Related Surveys  There are many surveys that have focused on recommenda-  tion systems or federated learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' For example, Adomavicius  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' [14] provide a detailed categorization of recommenda-  tion methods and introduce various limitations of each method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' [15] give the definition of federated learning  and discuss its architectures and applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' And Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [16] summarize the unique characteristics and challenges of  federated learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' However the existing surveys usually treat  recommendation systems and federated learning separately,  and few work surveyed specific problems in FedRS [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' [17] categorize FedRS from the aspect of the  federated learning and discuss the algorithm-level and system-  level challenges for FedRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' However, they do not provide  comprehensive methods to address privacy, security, hetero-  geneity, and communication costs challenges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Our Contribution  Compared with the previous surveys, this paper makes  the following contributions: (1) We provide a comprehensive  overview of FedRS from the perspectives of definition, com-  munication architectures and categorization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' (2) We summarize  the state-of-the-art studies of FedRS in terms of privacy,  security, heterogeneity and communication costs areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' (3) We  introduce some open source platforms for FedRS, which can  help engineers and researchers develop algorithms and deploy  applications of FedRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' (4) We discuss the promising future  directions for FedRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  The rest of the paper is organized as follow: Section II  discusses the overview of FedRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Section III-Section VI sum-  marize the state-of-the-art studies of FedRS from the aspects  of privacy, security, heterogeneity and communication costs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Section VII introduces the existing open source platforms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Section VIII presents some prospective research directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Finally, Section IX concludes this survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' OVERVIEW OF FEDERATED RECOMMENDATION  SYSTEMS  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Definition  FedRS is a technology that provides recommendation ser-  vices in a privacy preserving way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' To protect user privacy, the  participants in FedRS collaboratively train the recommenda-  tion model by exchanging intermediate parameters instead of  sharing their own real data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' In ideal case, the performance of  recommendation model trained in FedRS should be closed to  the performance of the recommendation model trained in the  data centralized setting, which can be formalized as:  |VF ED − VSUM| < δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  (1)  where VF ED is the recommendation model performance in  FedRS , VSUM is the recommendation model performance  in traditional recommendation systems for centralized data  storage, and δ is a small positive numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Communication Architecture  In FedRS, the data of participants is stored locally, and  the intermediate parameters are communicated between the  server and participants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' There are two major communication  architectures used in the study of FedRS, including client-  server architecture and peer-peer architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Client-Server Architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Client-server architecture is  the most common communication architecture used in FedRS,  as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 1(a), which relies on a trusted central server  to perform initialization and model aggregation tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' In each  round, the server distributes the current global recommenda-  tion model to some selected clients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Then the selected clients  use the received model and their own data for local training,  and send the updated intermediate parameters (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=', model  parameters, gradients) to the server for global aggregation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' The  Server  ① Initialization  ① Initialization  ②  ①  ② Download model  ④  ② Local update  Participant 1  ③ Local update  ③ Send parameters  ②  @ Send parameters  @ Aggregation  4  4  ②  2)  ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Aggregation  ③  ③  3  3  3  ①  ①  ④  ④  Participant 1  Participant 2  Participant N  Participant 2  Participant N  (a) Client-Server ahictecture  (b) Peer-Peer ahictectureIEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 8, DECEMBER 2022  3  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 2: Categorization of federated recommendation systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  client-server architecture requires a central server to aggregate  the intermediate parameters uploaded by the clients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Thus,  once the server has a single point of failure, the entire training  process will be seriously affected [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' In addition, the curious  server may infer the clients’ privacy information through the  intermediate parameters, leaving potential privacy concerns  [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Peer-Peer Architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Considering the single point of  failure problem for client-server architecture in FedRS, Hegeds  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' [19] design a peer-peer communication architecture  with no central server involved in the communication process,  which is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 1(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' During each communication  round, each participant broadcasts the updated intermediate  parameters to some random online neighbors in the peer to  peer network, and aggregates received parameters into its  own global model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' In this architecture, the single point of  failure and privacy issues associated with a central server  can be avoided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' However, the aggregation process occurs on  each client, which greatly increases the communication and  computation overhead for clients [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Categorization  In FedRS, the participants are responsible for the local  training process as the data owners.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' They can be different  mobile devices or data platforms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Considering the unique  properties for different types of participants, FedRS usually  have different application scenarios and designs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Besides, there  are also some differences between different recommendation  models in the federation process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Thus, we summarize the  current FedRS and categorize them from the perspectives of  participant type and recommendation model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 2 shows the  summary of the categorization of FedRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  1) Participant Type: Based on the type of participants,  FedRS can be categorized into cross-device FedRS and cross-  platform FedRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Cross-device FedRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' In cross-device FedRS, different mo-  bile devices are usually treated as participants [21] [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  The typical application of cross-device FedRS is to build a  personal recommendation model for users without collecting  their local data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' In this way, users can enjoy recommend  service while protecting their private information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' The number  of participants in cross-device FedRS is relative large and each  participant keeps a small amount of data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Considering the  limited computation and communication abilities for mobile  devices, cross-device FedRS cannot handle very complex  training tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Besides, due to the power and the network  status, the mobile devices may drop out of the training process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Thus, the major challenges for cross-device FedRS are how  to improve the efficiency and deal with straggler problem of  devices during training process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Cross-platform FedRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' In cross-platform FedRS, different  data platforms are usually treated as participants who want  to collaborate to improve recommendation performance while  meeting regulation and privacy constraints [23] [24] [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  For example, In order to improve the recommendation per-  formance, recommendation systems often integrate data from  multiple platforms (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=', e-commercial platforms , social plat-  forms).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' However, due to the privacy and regulation concerns,  the different data platforms are often unable to directly share  their data with each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' In this scenario, cross-platform  FedRS can be used to collaboratively train recommendation  models between different data platforms without directly ex-  changing their users’ data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Compared to cross-device FedRS,  the number of participants in cross-platform FedRS is rela-  tively small, and each participant owns relative large amount of  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' An important challenge for cross-platform FedRS is how  to design a fair incentive mechanism to measure contributions  and benefits of different data platforms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Besides, it is hard  to find a trusted server to manage training process in cross-  platform FedRS, so a peer to peer communication architecture  can be a good choice in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  2) Recommendation Model:  According to the different  recommendation models used in FedRS, FedRS can be cat-  egorized into matrix factorization model based FedRS, deep  learning model based FedRS and meta learning model FedRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Matrix factorization model based FedRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Matrix fac-  torization [26] is the most common model used in FedRS,  which formulates the user-item interaction or rating matrix  R ∈ RN×M as a linear combination of user profile matrix  U ∈ RN×K and item profile matrix V ∈ RM×K:  R = UV T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  (2)  then uses the learned model to recommendation new items to  the user according to the predicted value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' In matrix factoriza-  tion model based FedRS, the user factor vectors are stored and  updated locally on the clients, and only the item factor vectors  [27] or the gradients of item factor vectors [21] [22] [10]  [28] [29] are uploaded to the server for aggregation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Matrix  factorization model based FedRS can simply and effectively  capture user tastes with the interaction and rating information  between users and items.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' However it still has many limitations  such as sparsity (the number of ratings to be predicted is much  smaller than the known ratings) and cold-start (new users and  new items lacks ratings information) problems [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Deep learning model based FedRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' To learn more com-  plex representations of users and items and improve the  recommendation performance, deep learning technology has  been widely used in recommendation systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' However, as  privacy regulations get stricter, it becomes more difficult for  recommendation systems to collect enough user data to build  a high performance deep learning model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' To make the full  Cross-DeviceFedRS  Participant Type  Cross-PlatformFedRS  Federated  Recommendation  System  Matrix Factorization Mode  Based FedRS  Recommendation  Deep Learning Model  Model  Based FedRS  Meta Learning Model  Based FedRSIEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 8, DECEMBER 2022  4  use of user data while meeting privacy regulations, many ef-  fective deep learning model based FedRS have been proposed  [30] [31] [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Considering different model structures, deep  learning model based FedRS usually adopt different model  update and intermediate parameter transmit processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' For  examples, Perifanis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' [30] propose a federated neural  collaborative filtering (FedNCF) framework based on NCF  [33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' In FedNCF, the clients locally update the network  weights as well as the user and item profiles, then upload  the item profile and network weights after masking to the  server for aggregation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Wu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' [31] propose a federated  graph neural network (FedGNN) framework based on GNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  In FedGNN, the clients locally train GNN models and update  the user/item embeddings from their local sub-graph, then send  the perturbed gradients of GNN model and item embedding to  the central server for aggregation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Besides, Huang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' [34]  propose a federated multi-view recommendation framework  based on Deep Structured Semantic Model (DSSM [35]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' In  FL-MV-DSSM, each view i locally trains the user and item  sub-models based on their own user data and local shared item  data, then send the perturbed gradients of both user and item  sub-models to server for aggregation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Although deep learning  model based FedRS achieve outstanding performance in terms  of accuracy, the massive model parameters of deep learning  models bring huge computation and communication overhead  to the clients, which presents a serious challenge for real  industrial recommendation scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Meta learning model based FedRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' The most of existing  federated recommendation studies are built on the assump-  tion that data distributed on each client is independent and  identically (IID).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' However, learning a unified federated rec-  ommendation model often performs poorly when handling the  Non-IID and highly personalized data on clients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Meta learning  model can quickly adapt to new tasks while maintaining good  generalization ability [36], which makes it particularly suitable  for FedRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' In meta learning model based FedRS, the server  aggregates the intermediate parameters uploaded by clients to  learn a model parameter initialization, and the clients fine-tune  the initialed model parameters in local training phase to fit to  their local data [37] [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' In this way, meta learning model  based FedRS can adapt the clients’ local data to provide more  personalized recommendations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Although the performance of  meta learning model based FedRS are generally better than  learning a unified global model, the private information leak-  age can still occur during the learning process of model  parameter initialization [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' PRIVACY OF FEDERATED RECOMMENDATION  SYSTEMS  In the model training process of FedRS, the user data is  stored locally and only the intermediate parameters are up-  loaded to a server, which can further protect user privacy while  keeping recommendation performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Nevertheless, several  research works show that the central server can still infer  some sensitive information based on intermediate parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  For examples, a curious server can identify items the user  has interacted with according to the non-zero gradients sent  by the client [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Besides, the server can also infer the user  ratings as long as obtaining the user uploaded gradients in two  consecutive rounds [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' To further protect privacy of FedRS,  many studies have incorporated other privacy protection mech-  anisms into the FedRS, including pseudo items, homomorphic  encryption, secret sharing and differential privacy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' This section  introduces the application of each privacy mechanism used in  FedRS, and compare their advantages and limitations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Pseudo Items  To prevent the server from inferring the set of items that  users have interacted with based on non-zero gradients, some  studies utilize pseudo items to protect user interaction behav-  iors in FedRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' The key idea of pseudo items is that the clients  not only upload gradients of items that have been interacted  with but also upload gradients of some sampled items that  have not been with.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  For example, Lin et at.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' [22] propose a federated recom-  mendation framework for explicit feedback scenario named  FedRec,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' in which they design an effective hybrid filling strat-  egy to generated virtual ratings of unrated items by following  equation:  r  ′  ui =  �  �  �  �m  k=1 yukruk  �m  k=1 yuk  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' t < Tpredict  ˆrui,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' t ≥ Tpredict  (3)  where t denotes the number of current training iteration,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  and Tpredict denotes the iteration number when chooses the  average value or predict value as virtual rating value to a  sampled item i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' However, the hybrid filling strategy in FedRec  introduces extra noise to the recommendation model, which in-  evitably affects the model performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' To tackle this problem,  Feng et at.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' [39] design a lossless version of FedRec named  FedRec++.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' FedRec++ divides clients into ordinary clients and  denoising clients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' The denosing clients collect noisy gradients  from ordinary clients and send the summation of the noisy  gradients to server to eliminate the gradient noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Although pseudo items can effectively protect user interac-  tion behaviors in FedRS, it does not modify the gradients of  rated items.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' The curious server can still infer user ratings on  the gradients uploaded by users [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Homomorphic Encryption  To further protect the user ratings in FedRS, many studies  attempt to encrypt intermediate parameters before uploading  them to the server.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Homomorphic encryption mechanism al-  lows mathematical operation on encrypted data [40], so it  is well suited for the intermediate parameters upload and  aggregation processes in FedRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  For example, Chai et at.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' [10] propose a secure feder-  ated matrix factorization framework named FedMF, in which  clients use Paillier homomorphic encryption mechanism [41]  to encrypt the gradients of item embedding matrix before  uploading them to the server, and the server aggregates  gradients on the cipher-text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Due to the characteristics of  homomorphic encryption, FedMF can achieve the same rec-  ommendation accuracy as the traditional matrix factorization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 8, DECEMBER 2022  5  TABLE I: Comparison between different privacy mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Privacy Mechanisms  Ref  Main Protect Object  Accuracy Loss  Communication/Computation Costs  Pseudo Items  [22] [39] [31] [44] [45]  Interaction Behaviors  �  Low Costs  Homomorphic Encryption  [10]  Ratings  �  High Computation Costs  [31]  High-order Graph  [42]  Social Features  Secret Sharing  [29] [45]  Ratings  �  High Communication Costs  Local Differential Privacy  [27] [31] [44]  Ratings  �  Low Costs  However,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' FedMF causes serious computation overheads since  all computation operations are performed on the ciphertext  and most of system’s time is spent on server updates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Besides,  FedMF assumes that all participants are honest and will not  leak the secret key to the server, which is hard to guarantee  in reality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Besides, many studies also utilize homomorphic encryption  mechanism to integrate private information from other par-  ticipants to improve recommendation accuracy [31] [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' For  examples, Wu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' [31] use homomorphic encryption mecha-  nism to find the anonymous neighbors of users to expanse local  user-item graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' And Perifanis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' [42] use Cheon-Kim-  Kim-Song (CKKS) fully homomorphic encryption mechanism  [43] to incorporate learned parameters between user’s friends  after the global model is generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Homomorphic encryption mechanism based FedRS can  effectively protect user ratings while maintaining recommen-  dation accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Besides, it can prevent privacy leaks when  integrating information from other participants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' However, ho-  momorphic encryption brings huge computation costs during  operation process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' And it is also a serious challenge to keep  the secret key not be obtained by the server or other malicious  participants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Secret Sharing  As another encryption mechanism used in FedRS, secret  sharing mechanism breaks intermediate parameters up into  multiple pieces, and distributes the pieces among participants,  so that only when all pieces are collected can reconstruct the  intermediate parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  For example, Ying [29] proposes a secret sharing based  federated matrix factorization framework named ShareMF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  The participants divide the item matrix gradients gplain into  several random numbers that meet:  gplain = gsub1 + gsub2 + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' + gsubt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  (4)  Each participant keeps one of the random numbers and send  the rest to t − 1 sampled participants, then uploads the sum  of received and kept numbers as hybrid gradients to the  server for aggregation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' ShareMF protects the user ratings and  interaction behaviors from being inferred by the server, but  the rated items can still be leaked to other participants who  received the split numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' To tackle this problem, Lin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [45] combine secret sharing and pseudo items mechanisms to  provide stronger privacy guarantee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Secret sharing mechanism based FedRS can protect user  ratings while maintaining recommendation accuracy, and have  lower computation costs compared to homomorphic encryp-  tion based FedRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' But the exchange process of pieces between  participants greatly increases the communication costs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Local Differential Privacy  Considering the huge computation or communication costs  caused by encryption based mechanisms, many studies try  to use perturbation based mechanisms to adapt to large-scale  FedRS for the industrial scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Local differential privacy  (LDP) mechanism allows to statistical computations while  guaranteeing each individual participant’s privacynoise [46]  [47], which can be used to perturb the intermediate parameters  in FedRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  For example, Dolui et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' [27] propose a federated matrix  factorization framework, which applies differential privacy  on item embedding matrix before sending it to server for  weighted average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' However, the server can still infer which  items the user has rated just by comparing the changes in  item embedding matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  In order to achieve a more comprehensive privacy protection  during model training process, Wu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' [31] combines  pseudo items and LDP mechanisms to protect both user  interaction behaviors and ratings in FedGNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Firstly, to protect  user interaction behaviors in FedGNN, the clients randomly  sample N items that they have not interacted with, then  generate the virtual gradients of item embeddings by using  a same Gaussian distribution as the real embedding gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Secondly, to protect user ratings in FedGNN, the clients apply  a LDP module to clip the gradients according to their L2-norm  with a threshold δ and perturb the gradients by adding zero-  mean Laplacian noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' The LDP module of FedGNN can be  formulated as follow:  gi = clip(gi, δ) + Laplace(0, λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  (5)  where λ is the Laplacian noise strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' However, the gradi-  ent magnitude of different parameters varies during training  process, thus it is usually not appropriate to perturb gradients  at different magnitudes with a constant noise strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' So Liu  IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 8, DECEMBER 2022  6  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' [44] propose to add dynamic noise according to the  gradients, which can be formulated as follow:  gi = clip(gi, δ) + Laplace(0, λ · mean(gi)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  (6)  Local differential privacy mechanism doesn’t bring heavy  computation and communication overhead to FedRS, but the  additional noise inevitably affects the performance of the  recommendation model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Thus, in the actual application sce-  nario, we must consider the trade-off between the privacy and  recommendation accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Comparison  To protect stronger privacy guarantee, many privacy mech-  anisms (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=', pseudo items, homomorphic encryption, differ-  ential privacy privacy and secret sharing) have been widely  used in FedRS, and the comparison between these mechanisms  is shown in Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Firstly, the main protect objects of  these mechanisms are different: pseudo items mechanism is  to protect user interaction behaviors, and the rest mechanisms  is to protect user ratings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Besides, homomorphic encryption  can aslo integrate data from other paritcipants in a privacy-  preserving way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Secondly, homomorphic encryption and secret  sharing are both encryption-based mechanisms, and they can  protect privacy while keeping accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' However, the high  computation cost of homomorphic encryption limits the appli-  cation in large-scale industrial scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Although the secret  sharing mechanism reduces the computation costs, the commu-  nication costs increase greatly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Pseudo items and differential  privacy mechanisms protect privacy by adding random noise,  which has low computation costs and don’t bring additional  communication costs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' But the addition of random noise will  inevitably affect model performance to a certain extent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' SECURITY OF FEDERATED RECOMMENDATION  SYSTEMS  Apart from privacy leakage problems, traditional recom-  mendation systems for centralized data storage are also vul-  nerable to poisoning attacks (shilling attacks) [48] [49] [50]  [51] [52] [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Attackers can poison recommendation systems  and make recommendations as their desires by injecting well-  crafted data into the training dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' But most of these  poisoning attacks assume that the attackers have full prior  knowledge of entire training datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Such assumption may  be not valid for FedRS since the data in FedRS is distributed  and stored locally for each participant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Thus, FedRS provides  a stronger security guarantee than traditional recommendation  systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' However, the latest studies indicate that attackers can  still conduct poisoning attacks on FedRS with limited prior  knowledge [12] [11] [54] [55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' In this section, we summarize  some novel poisoning attacks against FedRS and provide some  defense methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Poisoning Attacks  According to the goal of attacks, the poisoning attacks  against FedRS can be categorized into targeted attacks and  untargeted attacks as shown in Table II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  1) Target Poisoning Attacks: The goal of target attacks  on FedRS is to increase or decrease the exposure chance of  specific items, which are usually driven by financial profit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  For example, Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' [12] propose a poisoning attack  for item promotion (PipAttack) against FedRS by utilizing  popularity bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' To boost the rank score of target items,  PipAttack use popularity bias to align target items with popular  items in the embedding space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Besides, to avoid damaging  recommendation accuracy and be detected, PipAttack designs  a distance constraint to keep modified gradients uploaded by  malicious clients closed to normal ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  In order to further reduce the degradation of recommenda-  tion accuracy caused by targeted poisoning attacks, and the  proportion of malicious clients needed to ensure the attack  effectiveness, Rong [54] propose a model poisoning attack  against FedRS (FedRecAttack), which makes use of a small  proportion of public interactions to approximate the user  feature matrix, then uses it to generate poisoned gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Both PipAttack and FedRecAttack rely on some prior  knowledge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' For example, PipAttack assumes the attacker is  available for popularity information, and FedRecAttack as-  sumes the attacker can get public interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' So the attack  effectiveness is greatly reduced in the absence of prior knowl-  edge, which makes both attacks not generic in all FedRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' To  make attackers conduct effective poisoning attacks to FedRS  without the prior knowledge, Rong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' [55] design two  methods (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=', random approximation and hard user mining) for  malicious clients to generate poisoned gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' In particular,  random approximation (A-ra) uses Gaussian distribution to  approximate normal users’ embedding vectors, and hard user  mining (A-hum) uses gradient descent to optimize users’  embedding vectors obtained by A-ra to mine hard users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' In this  way, A-hum can still effectively attack FedRS with extremely  small proportion of malicious users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  2) Untarget Poisoning Attacks: The goal of untarget attacks  on FedRS is to degrade the overall performance of recom-  mendation model, which are usually conducted by competing  companies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' For example, Wu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' [11] propose an untargeted  poisoning attack to FedRS named FedAttack, which uses glob-  ally hard sampling technique [62] to subvert model training  process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' More specifically, after inferring user’s interest from  local user profiles, the malicious clients select candidate items  that best match the user’s interest as negative samples, and  select candidate items that least match the user’s interest as  positive samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' FedAttack only modifies training samples,  and the malicious clients are also similar to normal clients  with different interests, thus FedAttack can effectively damage  the performance of FedRS even under defense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Defense Methods  To reduce the influence of poisoning attacks on FedRS,  many defense methods have been proposed in the literature,  which can be classified into robust aggregation and anomaly  detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  1) Robust Aggregation: The goal of robust aggregation  is to guarantee global model convergence when up to 50%  of participants are malicious [63], which selects statistically  IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 8, DECEMBER 2022  7  TABLE II: Representative works on the security of FedRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' RA refers to robust aggregation and AD refers to anomaly  detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Works  Ref  Attack Type  Poison Object  Defense Type  Goal  Target  Untarget  Model  Data  RA  AD  PipAttack  [12]  �  �  Increase/decrease popularity of target items.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  FedRecAttack  [54]  �  �  Increase/decrease popularity of target items.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  A-ra/A-hum  [55]  �  �  Increase/decrease popularity of target items.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  FedAttack  [11]  �  �  Degrade the overall performance of FedRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Median  [56]  �  Guarantee global model convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Trimmed-Mean  [56]  �  Guarantee global model convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  (Multi-)Krum  [57]  �  Guarantee global model convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Bulyan  [58]  �  Guarantee global model convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Norm-Bounding  [59]  �  Guarantee global model convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  A-FRS  [60]  �  Guarantee global model convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  FSAD  [61]  �  Identify and filter poisoned parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  more robust values rather than the mean values of uploaded  intermediate parameters for aggregation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Median [56] selects the median value of each updated  model parameter independently as aggregated global model  parameter, which can represent the centre of the distribution  better.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Specifically, the server ranks each i − th parameter of  n local model update, and uses the median value as i − th  parameter of global model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Trimmed-Mean [56] removes the maximum and minimum  values of each updated model parameter independently, and  then takes the mean value as aggregated global model param-  eter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Specifically, the server ranks each i − th parameter of n  local model update, remove β smallest and β largest values,  and uses the mean value of remained n−2β as i−th parameter  of global model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' In this way, Trimmed-Mean can effectively  reduce the impact of outliers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Krum and Multi-Krum [57].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Krum selects a local model  that is the closest to the others as global model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Multi-Krum  selects multiple local models by using Krum, then aggregates  them into a global model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' In this way, even if the selected  parameter vectors are uploaded by malicious clients, their  impact is still limited because they are similar to other local  parameters uploaded by normal clients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Bulyan [58] is a combination of Krum and Trimmed-Mean,  which iteratively selects m local model parameter vectors  through Krum, and then performs Trimmed-Mean on these  m parameter vectors for aggregation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' With high dimensional  and highly non-convex loss function, Bulyan can still converge  to effectual models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Norm-Bounding [59] clips the received local parameters to  a fixed threshold, then aggregates them to update the global  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Norm-Bounding can limit the contribution of each  local model updates so as to mitigate the affect of poisoned  parameters on the aggregated model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  A-FRS  [60]  utilizes  gradient-based  Krum  instead  of  model parameter-based Krum to filter malicious clients in  momentum-based FedRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' A-FRS theoretically guarantees that  if the selected gradient is closed to the normal gradient, the  momentum and model parameters will also be close to the  normal momentum and model parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Although these robust aggregation strategies provide conver-  gence guarantees to some extent, most of them (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=', Bulyan,  Krum, Median and Trimmed-mean) greatly degrade the per-  formance of FedRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Besides, some noval attacks(i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=', PipAt-  tack, FedAttack) [12] [11] utilize well-designed constraints  to approximate the patterns of normal users and circumvent  defenses, which further increases the difficulty of defense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  2) Anomaly Detection: The purpose of anomaly detection  strategy is to identify the poisoned model parameters uploaded  by malicious clients and filter them during the global model  aggregation process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' For example, Jiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' [61] propose  an anomaly detection strategy named federated shilling attack  detector (FSAD) to detect poisoned gradients in federated  collaborative filtering scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' FSAD extracts 4 novel fea-  tures according to the gradients uploaded by clients, then uses  the gradient-based features to train a semi-supervised bayes  classifier so as to identify and filter the poisoned gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  However, in FedRS, the interests of different users vary widely,  thus the parameters they uploaded are usually quite different,  which increases the difficulty of anomaly detection [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' HETEROGENEITY OF FEDERATED RECOMMENDATION  SYSTEMS  Compared with traditional recommendation systems, Fe-  dRS face more severe challenges in terms of heterogeneity,  which are mainly reflected in system heterogeneity, statistical  heterogeneity and model heterogeneity, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 8, DECEMBER 2022  8  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 3: Heterogeneity of federated recommendation systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  System heterogeneity refers to client devices have signif-  icantly different storage, computation, and communication  capabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Devices with limited capabilities greatly affects  training efficiency, and further reduces the accuracy of the  global recommendation model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' [64];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Statistical heterogeneity  refers to the data collected by different clients is usually  not independent and identically distributed (non-IID).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' As a  result, simply training a single global model is difficult to  generalize to all clients, which affects the personalization of  recommendations [65];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Privacy heterogeneity means that the  privacy constraints of different users and information vary  greatly, so simply treating them with the same privacy budgets  will carry unnecessary costs [66].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' This section introduces some  effective approaches to address the heterogeneity of FedRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' System Heterogeneity  In FedRS, the hardware configuration, network bandwidth  and battery capacity of participating clients varies greatly,  which results in diverse computing capability, communication  speed, and storage capability [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' During the training process,  the clients with limited capacity could become stragglers, and  even drop out of current training due to network failure, low  battery and other problems [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' The system heterogeneity  significantly delays the training process of FedRS, further  reducing the recommendation accuracy of the global model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' To  make the training process compatible with different hardware  structures and tolerate the straggling and exit issues of clients,  the most common methods are asynchronous communication  [67] [18] and clients selection [68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Asynchronous  communication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Considering  the  syn-  chronous communication based federated learning must wait  for straggler devices during aggregation process, many asyn-  chronous communication strategies are presented to improve  training efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' For examples, FedSA [67] proposes a  semi-asynchronous communication method, where the server  aggregates the local models based on their arrival order of  each round.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' FedAsync [18] uses a weighted average strategy  to aggregate the local models based on staleness, which assigns  less weight to delayed feedback in update process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Clients selection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Client selection approach selects clients  for updates based on resource constraints so that the server can  aggregate as many local updates as possible at the same time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  For example, in FedCS [68], the server sends a resource re-  quest to each client so as to get their resource information, then  estimates the required time of model distribution, updating  and uploading processes based on the resource information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  According to the estimated time, the server determine which  clients can participant in training process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Statistical Heterogeneity  Most of the existing federated recommendation studies  are built on the assumption that data in each participant is  independent and identically distributed (IID).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' However, the  data distribution of each client usually varies greatly, hence  training a consistent global model is difficult to generalized  to all clients under non-IID data and inevitably neglects  the personalization of clients [66].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' To address the statistical  heterogeneity problem of FedRS, many effective strategies  have been proposed, which are mainly based on meta learning  [38] [69] and clustering [70] [71].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Meta learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' As known as “learning to learn”, meta  learning technology aims to quickly adapt the global model  learned by other tasks to a new task by using only a few  number of samples [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' The rapid adaptation and good  generalization abilities makes it particularly well-suited for  building personalized federated recommendation models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' For  examples, FedMeta [38] uses Model-Agnostic Meta-Learning  (MAML) [73] algorithm to learn a well-initialized model that  can be quickly adapted to clients, and effectively improve the  personalization and convergence of FedRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' However, FedMeta  Privacy  Heterogenity  8  Private  Public  Private  Public  8  user  item  attributes  Statistical  Heterogenity  battery  Data Distribution  Data Distribution  l  4/5G  Wi-Fi  System  Heterogenity  Participant 2  Participant 2IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 8, DECEMBER 2022  9  needs to compute the second-order gradients, which greatly  increases computation costs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Besides, the data split process  also brings a huger challenge for clients with limited samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Based on FedMeta, Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' [69] propose a new meta  learning algorithm called Reptile which applies the approx-  imate first-order derivatives for the meta-learning updates,  which greatly reduces the computation overloads of clients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Moreover, Reptile doesn’t need a data split process, which  makes it also suitable for clients with limited samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' The core idea of clustering is training person-  alized models jointly with the same group of homogeneous  clients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' For examples, Jie et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' [70] uses historical parameter  clustering technology to realize personalized federated recom-  mendation, in which the server aggregates local parameters to  generate global model parameters and clusters the local pa-  rameters to generate clustering parameters for different client  groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Then the clients combine the clustering parameters  with the global parameters to learn personalized models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Luo  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' [71] propose a personalized federated recommendation  framework named PerFedRec, which constructs a collaborative  graph and integrates attribute information so as to jointly learn  the user representations by federated GNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Based on the  learned user representations, clients are clustered into different  groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' And each cluster learns a cluster-level recommen-  dation model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' At last, each client can obtain a personalized  model by merging the global recommendation model, the  cluster-level recommendation model, and the fine-tuned local  recommendation model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Although clustering based approaches  can alleviate statistical heterogeneity, the clustering and com-  bination process greatly increase the computation costs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Privacy Heterogeneity  In reality, the privacy restrictions of different participants  and information vary greatly, thereby using the same high level  of privacy budget for all participants and information is unnec-  essary, which even increases the computation/communication  costs and degrades the model performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Heterogeneous user privacy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' In order to adapt the privacy  needs for different users, Anelli et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' [72] present a user  controlled federated recommendation framework named Fed-  eRank.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' FedeRank introduces a probability factor π ∈ [0, 1] to  control the proportion of interacted item updates and masks  the remain interacted item update by setting them to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  In this way, FedeRank allows users decide the proportion of  data they want to share by themselves, which addresses the  heterogeneity of user privacy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Heterogeneous information privacy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' In order to adapt the  privacy needs of different information components, HPFL [66]  designs a differentiated component aggregation strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' To  obtain the global public information components, the server  directly weighted aggregates the local public components with  same properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' And to obtain the global privacy information  components, the user and item representations are kept locally,  and the server only aggregates the local drafts without the need  to align the presentations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' With the differentiated component  aggregation strategy, HPFL can safely aggregate components  with heterogeneous privacy constraints in user modeling sce-  narios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' COMMUNICATION COSTS OF FEDERATED  RECOMMENDATION SYSTEMS  To achieve satisfactory recommendation performance, Fe-  dRS requires multiple communications between server and  clients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' However, the real-world recommendation systems are  usually conducted by complexity deep learning models with  large model size [74], and millions of parameters needs to  be updated and communicated [13], which brings severe  communication overload to resource limited clients and further  affects the application of FedRS in large-scale industrial sce-  narios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' This section summarizes some optimization methods to  reduce communication costs of FedRS, which can be classified  into importance-based updating [75] [20] [76] [77], model  compression [78] [79], active sampling [80] and one shot  learning [81].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Importance-based Model Updating  Importance-based model updating selects importance parts  of the global model instead of the whole model to update and  communicate, which can effectively reduce the communicated  parameter size in each round.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  For examples, Qin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' [75] propose a federated frame-  work named PPRSF, which uses 4-layers hierarchical structure  for reducing communication costs, including the recall layer,  ranking layer, re-ranking layer and service layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' In the recall  layer, the server roughly sorts the large inventory by using  public user data, and recalls relatively small number of items  for each client.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' In this way, the clients only need to update and  communicate the candidate item embeddings, which greatly  reduces the communication costs between server and clients,  and the computation costs in the local model training and  inference phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' However, the recall layer of PPRSF need  to get some public information of users, which raises certain  difficulty and privacy concerns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Yi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' [20] propose an efficient federated news recom-  mendation framework called Efficient-FedRec, which breaks  the news recommendation model into a small user model and  a big news model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Each client only requests the user model and  a few news representations involved in their local click history  for local training, which greatly reduces the communication  and computation overhead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' To further protect specific user  click history against the server, they transmit the union news  representations set involved in a group of user click history  by using a secure aggregation protocol [82].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Besides, Khan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' [76] propose a multi-arm bandit  method (FCF-BTS) to select part of the global model that  contains a smaller payload to all clients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' The rewards of  selection process is guided by Bayesian Thompson Sampling  (BTS) [83] approach with Gaussian priors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Experiments show  that FCF-BTS can reduce 90% model payload for highly  sparse datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Besides, the selection process occurs in the  server side, thus avoiding additional computation costs on the  clients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' But FCF-BTS causes 4% - 8% loss in recommendation  accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  To achieve a better balance between recommendation ac-  curacy and efficiency, Ai et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' [77] propose an all-MLP  IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 8, DECEMBER 2022  10  network that uses a Fourier sub-layer to replace the self-  attention sub-layer in a Transformer encoder so as to filter  noise data components unrelated to the user’s real interests,  and adapts an adaptive model pruning technique to discard  the noise model components that doesn’t contribute to model  performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Experiments show that all-MLP network can  significantly reduce communication and computation costs,  and accelerates the model convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Importance-based model updating strategies can greatly  reduce communication and computation costs at the same time,  but only selecting the important parts for updating inevitably  reduces the recommendation performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Model Compression  Model Compression is a well-known technology in dis-  tributed learning [84], which compresses the communicated  parameters per round to be more compact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  For examples, Konen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' [78] propose two methods  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=', structured updates and sketched updates) to decrease the  uplink communication costs under federated learning settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Structured updates method directly learns updates from a  pre-specified structure parameterized using fewer variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Sketched updates method compresses the full local update  using a lossy compression way before sending it to server.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  These two strategies can reduce the communication costs by  2 orders of magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  To reduce the uplink communication costs in deep learning  based FedRS, JointRec [79] combines low-rank matrix factor-  ization [85] and 8-bit probabilistic quantization [86] methods  to compress weight update.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Supposing the weight update ma-  trix of client n is Ha×b  n  , a ≤ b, low-rank matrix factorization  decomposes Ha×b  n  into two matrices: Ha×b  n  = U a×k  n  V k×b  n  ,  where k = b/N and N is a positive number that influences the  compression performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' And 8-bit probabilistic quantization  method transforms the position of matrix value into 8-bit value  before send it to server.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Experiments demonstrate that JointRec  can realize 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='83× larger compression ratio while maintaining  recommendation performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Model compression methods achieve significant results in  reducing the uplink communication costs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' However, the re-  duction of communication cost sacrifices the computation  resources of the clients, so it’s necessary to consider the trade-  off between computation and communication costs when using  model compression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Client Sampling  In traditional federated learning frameworks [8], the server  randomly selects clients to participate in the training process  and simply aggregates the local models by average, which  requires a large number of communications to realize satis-  factory accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Client sampling utilizes efficient sampling  strategies so as to improve the training efficiency and reduce  the communication rounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  For example, Muhammad et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' [80] propose an effective  sampling strategy named FedFast to speed up the training  efficiency of federated recommendation models while keeping  more accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' FadFast consists of two efficient components:  ActvSAMP and ActvAGG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' ActvSAMP uses K-means algo-  rithm to cluster users based on their profile, and samples  clients in equal proportions from each cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' And ActvAGG  propagates local updates to the other clients in the same  cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' In this way, the learning process for these similar  users is greatly accelerated and overall efficiency of the FedRS  is consequently improved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Experiments show that FedFast  reduces communication rounds by 94% compared to FedAvg  [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' However, FedFast is faced with the cold start problem  because it requires a number of users and items for training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Besides, FedFast needs to retrain the model to support new  users and items.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' One Shot Federated Learning  The goal of one shot federated learning mechanism is to  reduce communication rounds of FedRS [87] [88], which lim-  its communication to a single round to aggregate knowledge  of local models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' For example, Eren et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' [81] implement  an one-shot federated learning framework for cross-platform  FedRS named FedSPLIT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' FedSPLIT aggregates model through  knowledge distillation [89], which can generate client specific  recommendation results with just a single pair of communica-  tion rounds between the server and clients after a small initial  communication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Experiments show that FedSPLIT realizes  similar root-mean-square error (RMSE) compared with multi-  round communication scenarios, but it is not applicable to the  scenario where the participant is a individual user.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' OPEN SOURCE PLATFORMS  This section introduces five open source platforms that can  be used to build FedRS: Federated AI Technology Enabler  (Fate)1, Tensorflow Federated (TFF)2, Pysyft3, PaddleFL4, and  FederatedScope5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' The comparison among some existing open  source platforms is shown in Table III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Federated AI Technology Enabler  Federated AI Technology Enabler (Fate) [90] is the first  open source platform for federated learning around the world,  which aims to enable companies and organizations to collab-  orate on data while keeping data privacy and security.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Fate  supports various machine learning algorithms under federated  learning settings, including logistic regression, XGBOOST,  deep learning and transfer learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Besides, Fate integrates  homomorphic encryption, differential privacy and secret shar-  ing mechanisms to protect privacy against the curious server.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  The structure of FATE consists of seven major modules:  FederatedML, EggRoll, FATE-FLow, FATE-Board, FATE-  Serving, KubeFATE and FATE-cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' FederatedML imple-  ments privacy-preserving federated machine learning algo-  rithms;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' EggRoll manages the distributed computation frame-  work;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' FATE-FLow coordinates the execution of the algorithm  1https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='com/FederatedAI/FATE  2https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='com/tensorflow/federated  3https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='com/OpenMined/PySyft  4https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='com/PaddlePaddle/PaddleFL  5https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='com/alibaba/FederatedScope  IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 8, DECEMBER 2022  11  components;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' FATE-Board provides visualization for building  and evaluating models;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' FATE-Serving provides online infer-  ence for the users;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' KubeFATE helps deploy Fate platform by  using cloud native technologies;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' FATE-cloud provide cross-  cloud deployment and management services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Fate provides a federated recommendation module (Federat-  edRec) to solve the recommendation problems of rate predic-  tion and item ranking tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' FederatedRec implements many  common recommendation algorithms under federated learning  settings, including factorization machine, matrix factorization,  SVD, SVD++ and generalized matrix factorization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Tensorflow Federated  Tensorflow Federated (TFF) [91] is a lightweight system  developed by Google, which provides the building blocks to  enables developers to implement own federated models based  on TensorFlow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Besides, developers can plug any existing  Keras model into TFF with just a few lines of code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' To  enhancing privacy guarantees for federated learning, TFF  integrates differential privacy mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  The interfaces of TFF are organized in two layers API (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=',  Federated Learning API and Federated Core API).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Federated  Learning API implements high-level interfaces for developers  to make training and evaluation process of federated learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Federated Core API provides lower-level interfaces to express  novel federated learning algorithms by using TensorFlow and  distributed communication operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Based on TFF, Singhal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' [92] implements a model-  agnostic framework for fast partial local federated learning,  which is suitable for large-scale collaborative filtering recom-  mendation scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Pysyft  PySyft [93] is developed by Open-Mined, which also pro-  vides the building blocks for developers to implement own  federated recommendation algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Compared with TFF,  PySyft can work with both Tensorflow and Pytorch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' For  privacy protection, PySyft can flexibly and simply integrate  homomorphic encryption, differential privacy and secret shar-  ing mechanisms so as to defend against the honest-but-curious  server and participants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' However, Pysyft doesn’t disclose the  detailed interface design or system architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' PaddleFL  PaddleFL [94] is an open source federated learning platform  developed by Baidu, which integrates both differential privacy  and secret sharing mechanisms to provide privacy guarantees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  PaddleFL contains two major components: Data Parallel and  Federated Learning with MPC (PFM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Data Parallel is respon-  sible for defining, distributing and training a federated learning  task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' PFM implements secure multi-party computation to  ensure training and inference security.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  PaddleFL provides many federated recommendation algo-  rithms that can be used directly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' For example, PaddleFL  implements a classical session-based recommendation model  Gru4rec [95] under the federated learning settings and provide  simulated experiments on real world dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' But the simulated  experiment suppose all datasets in different organizations are  homogeneous, which is only satisfied under ideal case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' In  addition, PaddleFL also provides a strategy to train a Click-  Through-Rate(CTR) model by using FedAvg [8] algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' FederatedScope  FederatedScope [96], developed by Alibaba, is a flexible  federated learning platform for heterogeneity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' FederatedScope  employs an event-driven architecture to support asynchronous  training, and coordinate participants with personalized be-  haviors and multiple goals into federated learning scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  FederatedScope can easily support different machine learning  libraries such as Tensorflow and Pytorch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Besides, Federat-  edScope enables various kinds of plug-in components and  operations thar can be used for efficient further development.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  For privacy protection plug-ins, FederatedScope integrates ho-  momorphic encryption, differential privacy and secret sharing  mechanisms to enhance privacy guarantees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' In the federated  recommendation scenario, FederatedScope has built in matrix  factorization models, datasets (Netflix and MovieLen) and  trainer under different federated learning settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  VIII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' FUTURE DIRECTIONS  This section presents and discusses many prospective re-  search directions in the future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Although some directions have  been covered in above sections, we believe they are necessary  for FedRS, and need to be further researched.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Decentralized FedRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Most of current FedRS are based on  client-server communication architecture, which faces single-  point-of-failure and privacy issues caused by the central server  [97].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' While much work has been devoted to decentralized  federated learning [98] [99], few decentralized FedRS have  been studied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' A feasible solution is to replace client-server  communication architecture with peer-peer communication  architecture to achieve fully decentralized federated recom-  mendation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Hegeds et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' [19] propose a fully decentralized  matrix factorization framework based on gossip learning [100],  where each participant sends their copy of the global recom-  mendation model to random online neighbors in the peer to  peer network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Incentive mechanisms in FedRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' FedRS collaborate with  multiple participants to train a global recommendation model,  and the recommendation performance of global model is  highly dependent on the quantity and quality of data provided  by the participants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Therefore, it is significant to design an  appropriate incentive mechanism to inspire participants to  contribute their own data and participate in collaborative  training, especially in the cross-organization federated recom-  mendation scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' The incentive mechanisms must be able  to measure the clients’ contribution to the global model fairly  and efficiently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Privacy of serving phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Although many studies have  combined different privacy mechanisms to protect user privacy  in the training phase of FedRS, the privacy protection for  the serving phase is still underexplored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' To prevent user  recommendation results from leaking, most of the current  IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 8, DECEMBER 2022  12  TABLE III: The comparison among some existing open source platforms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Platforms  Fate  TFF  Pysyft  PaddleFL  FederatedScope  Publisher  WeBank  Google  OpenMined  Baidu  Alibaba  Audience  Academia  �  �  �  �  �  Industry  �  �  Models  Neural Network  �  �  �  �  �  Tree Model  �  �  Linear Model  �  �  �  �  �  Privacy  Homomorphic encryption  �  �  �  Differential Privacy  �  �  �  �  �  Secret Sharing  �  �  �  Libraries  Tensorflow  �  �  �  Pytorch  �  �  studies assume local serving,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' where the server sends the entire  set of candidate items to clients,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' and clients generate rec-  ommendation results locally [10] [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' However, such design  brings enormous communication, computation and memory  costs for clients since there are usually millions of items in  real-world recommendation systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Another feasible solution  is online serving, where clients send encrypted or noised user  embedding to the server to recall top-N candidate items, then  clients generate personalized recommendation results based  one these candidate items [101].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Nevertheless, there is a risk  of privacy leakage associated with online serving, because  recalled items are known to the server.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Cold start problem in FedRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' The cold start problem  means that recommendation systems cannot generate satisfac-  tory recommendation results for new users with little history  interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' In federated settings, the user data is stored  locally, so it is more difficult to integrate other auxiliary  information (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=', social relationships) to alleviate the cold  start problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Therefore, it is a challenging and prospective  research direction to address the cold start problem while  ensuring user privacy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Secure FedRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' In the real world, the participants in the  FedRS are likely to be untrustworthy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Therefore, participants  may upload poisoned intermediate parameters to affect rec-  ommendation results or destroy recommendation performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Although some robust aggregation strategies [57] and detec-  tion methods [61] have been proposed to defense poisoning  attacks in federated learning settings, most of them does not  work well in FedRS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' One one hand, some strategies such  as Krum, Median and Trimmed-mean degrade the recom-  mendation performance to a certain extend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' One the other  hand, some novel attacks [11] use well-designed constraints to  mimic the patterns of normal users, extremely increasing the  difficulty to be detected and defensed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Currently, there is still  no effective defense methods against these poisoning attacks  while maintaining recommendation accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  IX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' CONCLUSION  A lot of effort has been devoted to federated recommen-  dation systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' A comprehensive survey is significant and  meaningful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' This survey summarizes the latest studies from  aspects of the privacy, security, heterogeneity and commu-  nication costs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Based on these aspects, we also make a  detailed comparison among the existing designs and solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Moreover, we present many prospective research directions to  promote development in this field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' FedRS will be a promising  field with huge potential opportunities, which requires more  efforts to develop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  ACKNOWLEDGMENTS  This research is partially supported by the National Key  R&D Program of China No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='2021YFF0900800, the NSFC  No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='91846205, the Shandong Provincial Key Research and De-  velopment Program (Major Scientific and Technological Inno-  vation Project) (No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='2021CXGC010108), the Shandong Provin-  cial Natural Science Foundation (No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='ZR202111180007), the  Fundamental Research Funds of Shandong University, and  the Special Fund for Science and Technology of Guangdong  Province under Grant (2021S0053).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  REFERENCES  [1] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Sarwar, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Karypis, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Konstan, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Riedl, “Analysis of recom-  mendation algorithms for e-commerce,” in Proceedings of the 2nd ACM  Conference on Electronic Commerce, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 158–167, 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [2] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Schafer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Konstan, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Riedl, “E-commerce recommenda-  tion applications,” Data mining and knowledge discovery, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 5, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 1,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 115–153, 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [3] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Zheng, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Zhang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Zheng, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Xiang, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Yuan, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Xie, and  Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Li, “Drn: A deep reinforcement learning framework for news rec-  ommendation,” in Proceedings of the 2018 world wide web conference,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 167–176, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [4] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Liu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Dolan, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Pedersen, “Personalized news recommenda-  tion based on click behavior,” in Proceedings of the 15th international  conference on Intelligent user interfaces, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 31–40, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [5] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Yue, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Zhang, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Liu, “An overview of recom-  mendation techniques and their applications in healthcare,” IEEE/CAA  Journal of Automatica Sinica, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 8, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 701–717, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 8, DECEMBER 2022  13  [6] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Kim, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Lee, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Chung, “Item recommendation based on  context-aware model for personalized u-healthcare service,” Multime-  dia Tools and Applications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 71, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 855–872, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [7] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Albrecht, “How the gdpr will change the world,” Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Data Prot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 2, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 287, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [8] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' McMahan, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Moore, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Ramage, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Hampson, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' y Arcas,  “Communication-efficient learning of deep networks from decentral-  ized data,” in Artificial intelligence and statistics, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 1273–1282,  PMLR, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [9] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Zhu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Liu, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Han, “Deep leakage from gradients,” Advances  in neural information processing systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 32, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [10] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Chai, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Wang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Chen, and Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Yang, “Secure federated matrix  factorization,” Intelligent Systems, IEEE, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' PP, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 99, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 1–1, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [11] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Wu, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Wu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Qi, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Huang, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Xie, “Fedattack: Effective  and covert poisoning attack on federated recommendation via hard  sampling,” in Proceedings of the 28th ACM SIGKDD Conference on  Knowledge Discovery and Data Mining, KDD ’22, (New York, NY,  USA), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 4164–4172, Association for Computing Machinery, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [12] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Zhang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Yin, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Chen, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Huang, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Nguyen, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Cui,  “Pipattack: Poisoning federated recommender systems for manipulating  item promotion,” in Proceedings of the Fifteenth ACM International  Conference on Web Search and Data Mining, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 1415–1423, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [13] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Liao and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Lee, “A clustering based approach to improving  the efficiency of collaborative filtering recommendation,” Electronic  Commerce Research and Applications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 18, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 1–9, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [14] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Adomavicius and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Tuzhilin, “Toward the next generation of  recommender systems: a survey of the state-of-the-art and possible  extensions,” IEEE Transactions on Knowledge and Data Engineering,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 17, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 734–749, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [15] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Yang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Liu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Chen, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Tong, “Federated machine learning:  Concept and applications,” ACM Transactions on Intelligent Systems  and Technology, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 10, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 1–19, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [16] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Li, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Sahu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Talwalkar, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Smith, “Federated learning:  Challenges, methods, and future directions,” IEEE Signal Processing  Magazine, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 37, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 50–60, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [17] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Yang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Tan, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Zheng, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Chen, and Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Yang, “Federated rec-  ommendation systems,” in Federated Learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 225–239, Springer,  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [18] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Xie, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Koyejo, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Gupta, “Asynchronous federated optimiza-  tion,” arXiv preprint arXiv:1903.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='03934, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [19] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Heged˝us, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Danner, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Jelasity, “Decentralized recommenda-  tion based on matrix factorization: a comparison of gossip and fed-  erated learning,” in Joint European Conference on Machine Learning  and Knowledge Discovery in Databases, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 317–332, Springer, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [20] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Yi, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Wu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Wu, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Liu, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Sun, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Xie, “Efficient-fedrec:  Efficient federated learning framework for privacy-preserving news  recommendation,” arXiv preprint arXiv:2109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='05446, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [21] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Ammad-Ud-Din, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Ivannikova, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Khan, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Oyomno, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Fu,  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Tan, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Flanagan, “Federated collaborative filtering  for privacy-preserving personalized recommendation system,” arXiv  preprint arXiv:1901.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='09888, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [22] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Lin, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Liang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Pan, and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Ming, “Fedrec: Federated recom-  mendation with explicit feedback,” Intelligent Systems, IEEE, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' PP,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 99, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 1–1, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [23] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Chen, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Li, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Wu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Hong, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Wang, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Zhou, “Se-  cure social recommendation based on secret sharing,” arXiv preprint  arXiv:2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='02088, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [24] WuChuhan, WuFangzhao, LyuLingjuan, HuangYongfeng, and XieX-  ing, “Fedctr: Federated native ad ctr prediction with cross platform  user behavior data,” ACM Transactions on Intelligent Systems and  Technology (TIST), 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [25] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Kalloori and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Klingler, “Horizontal cross-silo federated recom-  mender systems,” in Fifteenth ACM Conference on Recommender  Systems, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 680–684, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [26] Koren, Yehuda, Bell, Robert, Volinsky, and Chris, “Matrix factorization  techniques for recommender systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=',” Computer, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 42, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 8,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 30–37, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [27] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Dolui, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Cuba Gyllensten, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Lowet, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Michiels, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Hallez,  and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Hughes, “Towards privacy-preserving mobile applications with  federated learning: The case of matrix factorization (poster),” in  Proceedings of the 17th Annual International Conference on Mobile  Systems, Applications, and Services, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 624–625, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [28] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Hua, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Xia, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Zhong, “Differentially private matrix factoriza-  tion,” in Proceedings of the 24th International Conference on Artificial  Intelligence, IJCAI’15, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 1763–1770, AAAI Press, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [29] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Ying, “Shared mf: A privacy-preserving recommendation system,”  arXiv preprint arXiv:2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='07759, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [30] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Perifanis and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Efraimidis, “Federated neural collaborative  filtering,” Knowledge-Based Systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 242, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 108441, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [31] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Wu, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Wu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Cao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Huang, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Xie, “Fedgnn: Federated  graph neural network for privacy-preserving recommendation,” arXiv  preprint arXiv:2102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='04925, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [32] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Imran, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Yin, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Chen, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Hung, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Zhou, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Zheng,  “Refrs: Resource-efficient federated recommender system for dynamic  and diversified user preferences,” ACM Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=', aug 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Just  Accepted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [33] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' He, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Liao, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Zhang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Nie, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Hu, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Chua, “Neural  collaborative filtering,” in Proceedings of the 26th international con-  ference on world wide web, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 173–182, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [34] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Huang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Li, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Bai, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Wang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Bai, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Wang, “A  federated multi-view deep learning framework for privacy-preserving  recommendations,” arXiv preprint arXiv:2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='10808, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [35] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Huang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' He, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Gao, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Deng, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Acero, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Heck, “Learning  deep structured semantic models for web search using clickthrough  data,” in Proceedings of the 22nd ACM international conference on  Information & Knowledge Management, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 2333–2338, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [36] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Chen,  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Liu,  Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Kira,  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Wang,  and  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Huang, “A closer look at few-shot classification,” arXiv preprint  arXiv:1904.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='04232, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [37] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Nichol, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Achiam, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Schulman, “On first-order meta-learning  algorithms,” arXiv preprint arXiv:1803.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='02999, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [38] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Chen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Luo, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Dong, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Li, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' He, “Federated meta-learning  with fast convergence and efficient communication,” arXiv preprint  arXiv:1802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='07876, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [39] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Liang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Pan, and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Ming, “Fedrec++: Lossless federated rec-  ommendation with explicit feedback,” in Proceedings of the AAAI  conference on artificial intelligence, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 35, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 4224–4231, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [40] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Abbas, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Hidayet, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Selcuk, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Mauro, “A survey on  homomorphic encryption schemes: Theory and implementation,” Acm  Computing Surveys, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 51, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 1–35, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [41] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Paillier, “Public-key cryptosystems based on composite degree  residuosity classes,” in International conference on the theory and  applications of cryptographic techniques, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 223–238, Springer, 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [42] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Perifanis, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Drosatos, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Stamatelatos, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Efraimidis,  “Fedpoirec: Privacy preserving federated poi recommendation with  social influence,” arXiv preprint arXiv:2112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='11134, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [43] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Cheon, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Kim, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Kim, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Song, “Homomorphic encryption  for arithmetic of approximate numbers,” in International conference  on the theory and application of cryptology and information security,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 409–437, Springer, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [44] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Liu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Yang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Fan, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Peng, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Yu, “Federated social  recommendation with graph neural network,” ACM Transactions on  Intelligent Systems and Technology (TIST), vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 13, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 1–24,  2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [45] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Lin, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Pan, and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Ming, “Fr-fmss: federated recommendation  via fake marks and secret sharing,” in Fifteenth ACM Conference on  Recommender Systems, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 668–673, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [46] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Dwork, “Calibrating noise to sensitivity in private data analysis,”  Lecture Notes in Computer Science, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 3876, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 8, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 265–284,  2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [47] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Hardt and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Talwar, “On the geometry of differential privacy,”  in Proceedings of the forty-second ACM symposium on Theory of  computing, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 705–714, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [48] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Wang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Singh, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Vorobeychik, “Data poisoning  attacks on factorization-based collaborative filtering,” Advances in  neural information processing systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 29, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [49] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Welling and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Teh, “Bayesian learning via stochastic gradient  langevin dynamics,” in Proceedings of the 28th international confer-  ence on machine learning (ICML-11), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 681–688, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [50] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Fang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Yang, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Gong, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Liu, “Poisoning attacks to  graph-based recommender systems,” in Proceedings of the 34th annual  computer security applications conference, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 381–392, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [51] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Huang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Mu, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Gong, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Li, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Liu, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Xu, “Data  poisoning attacks to deep learning based recommender systems,” arXiv  preprint arXiv:2101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='02644, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [52] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Li, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Ding, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Gao, “Practical data poisoning  attack against next-item recommendation,” in Proceedings of The Web  Conference 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 2458–2464, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [53] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Mnih, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Kavukcuoglu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Silver, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Graves, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Antonoglou,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Wierstra, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Riedmiller, “Playing atari with deep reinforcement  learning,” arXiv preprint arXiv:1312.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='5602, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [54] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Rong, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Ye, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Zhao, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Yuen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Chen, and Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' He, “Fedrecat-  tack: Model poisoning attack to federated recommendation,” arXiv  preprint arXiv:2204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='01499, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 8, DECEMBER 2022  14  [55] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Rong, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' He, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Chen, “Poisoning deep learning based  recommender model in federated learning scenarios,” arXiv preprint  arXiv:2204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='13594, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [56] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Yin, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Chen, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Kannan, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Bartlett, “Byzantine-robust dis-  tributed learning: Towards optimal statistical rates,” in International  Conference on Machine Learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 5650–5659, PMLR, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [57] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Blanchard, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' El Mhamdi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Guerraoui, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Stainer, “Ma-  chine learning with adversaries: Byzantine tolerant gradient descent,”  Advances in Neural Information Processing Systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 30, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [58] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Guerraoui, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Rouault, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=', “The hidden vulnerability of distributed  learning in byzantium,” in International Conference on Machine Learn-  ing, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 3521–3530, PMLR, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [59] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Sun, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Kairouz, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Suresh, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' McMahan, “Can you really  backdoor federated learning?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=',” arXiv preprint arXiv:1911.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='07963, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [60] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Zhang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Tung, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Kankanhalli, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Chen, “Robust  federated recommendation system,” arXiv preprint arXiv:2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='08259,  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [61] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Jiang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Zhou, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Wu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Li, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Wang, “On the detection of  shilling attacks in federated collaborative filtering,” in 2020 Interna-  tional Symposium on Reliable Distributed Systems (SRDS), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 185–  194, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [62] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Kalantidis, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Sariyildiz, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Pion, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Weinzaepfel, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Larlus,  “Hard negative mixing for contrastive learning,” Advances in Neural  Information Processing Systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 33, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 21798–21809, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [63] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Lyu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Yu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Ma, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Chen, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Sun, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Zhao, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Yang, and  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Philip, “Privacy and robustness in federated learning: Attacks  and defenses,” IEEE Transactions on Neural Networks and Learning  Systems, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [64] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Kairouz, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' McMahan, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Avent, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Bellet, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Bennis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Bhagoji, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Bonawitz, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Charles, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Cormode, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Cummings, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=',  “Advances and open problems in federated learning,” Foundations and  Trends® in Machine Learning, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 14, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 1–2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 1–210, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [65] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Jie, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Lai, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Arif, and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' He, “Personalized federated  recommendation system with historical parameter clustering,” Journal  of Ambient Intelligence and Humanized Computing, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 1–11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [66] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Wu, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Liu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Huang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Ning, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Wang, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Yi, and  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Zhou, “Hierarchical personalized federated learning for user model-  ing,” in Proceedings of the Web Conference 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 957–968, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [67] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Ma, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Xu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Xu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Jiang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Huang, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Huang, “Fedsa:  A semi-asynchronous federated learning mechanism in heterogeneous  edge computing,” IEEE Journal on Selected Areas in Communications,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 39, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 12, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 3654–3672, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [68] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Nishio and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Yonetani, “Client selection for federated learning  with heterogeneous resources in mobile edge,” in ICC 2019-2019 IEEE  international conference on communications (ICC), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 1–7, IEEE,  2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [69] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Yin, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Yu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Zhou, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Zhang, “Fast-  adapting and privacy-preserving federated recommender system,” The  VLDB Journal, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 31, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 877–896, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [70] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Jie, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Lai, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Arif, and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' He, “Personalized federated  recommendation system with historical parameter clustering,” Journal  of Ambient Intelligence and Humanized Computing, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 1–11, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [71] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Luo, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Xiao, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Song, “Personalized federated recommen-  dation via joint representation learning, user clustering, and model  adaptation,” in Proceedings of the 31st ACM International Conference  on Information and Knowledge Management, (New York, NY, USA),  p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 4289–4293, Association for Computing Machinery, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [72] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Anelli, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Deldjoo, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Noia, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Ferrara, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Narducci,  “Federank: User controlled feedback with federated recommender  systems,” in European Conference on Information Retrieval, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 32–47,  Springer, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [73] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Finn, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Abbeel, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Levine, “Model-agnostic meta-learning  for fast adaptation of deep networks,” in International conference on  machine learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 1126–1135, PMLR, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [74] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Acun, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Murphy, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Nie, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Wu, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Hazelwood,  “Understanding training efficiency of deep learning recommendation  models at scale,” in 2021 IEEE International Symposium on High-  Performance Computer Architecture (HPCA), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 802–814, IEEE,  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [75] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Qin, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Liu, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Qian, “A novel privacy-preserved recommender  system framework based on federated learning,” in 2021 The 4th  International Conference on Software Engineering and Information  Management, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 82–88, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [76] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Khan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Flanagan, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Tan, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Alamgir, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Ammad-  Ud-Din, “A payload optimization method for federated recommender  systems,” in Fifteenth ACM Conference on Recommender Systems,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 432–442, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [77] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Ai, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Wu, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Wang, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Chen, “Fourier enhanced mlp  with adaptive model pruning for efficient federated recommendation,”  in International Conference on Knowledge Science, Engineering and  Management, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 356–368, Springer, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [78] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Koneˇcn`y, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' McMahan, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Yu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Richt´arik, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Suresh, and  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Bacon, “Federated learning: Strategies for improving communica-  tion efficiency,” arXiv preprint arXiv:1610.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='05492, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [79] Sijing, Duan, Deyu, Zhang, Yanbo, Wang, Lingxiang, Li, Yaoxue, and  Zhang, “Jointrec: A deep-learning-based joint cloud video recommen-  dation framework for mobile iot,” IEEE Internet of Things Journal,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' PP, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 99, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 1–1, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [80] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Muhammad, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Wang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' O’Reilly-Morgan, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Tragos, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Smyth,  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Hurley, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Geraci, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Lawlor, “Fedfast: Going beyond average  for faster training of federated recommender systems,” in Proceedings  of the 26th ACM SIGKDD International Conference on Knowledge  Discovery & Data Mining, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 1234–1242, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [81] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Eren, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Richards, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Bhattarai, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Yus, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Nicholas,  and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Alexandrov, “Fedsplit: One-shot federated recommendation  system based on non-negative joint matrix factorization and knowledge  distillation,” arXiv preprint arXiv:2205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='02359, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [82] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Bonawitz, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Ivanov, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Kreuter, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Marcedone, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' McMahan,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Patel, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Ramage, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Segal, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Seth, “Practical secure aggre-  gation for privacy-preserving machine learning,” in proceedings of the  2017 ACM SIGSAC Conference on Computer and Communications  Security, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 1175–1191, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [83] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Thompson, “On the likelihood that one unknown probability  exceeds another in view of the evidence of two samples,” Biometrika,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 25, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 3-4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 285–294, 1933.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [84] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Wang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Sievert, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Liu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Charles, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Papailiopoulos, and  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Wright, “Atomo: Communication-efficient learning via atomic  sparsification,” Advances in Neural Information Processing Systems,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 31, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [85] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Gong, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Liu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Yang, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Bourdev, “Compressing deep  convolutional networks using vector quantization,” arXiv preprint  arXiv:1412.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='6115, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [86] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Lin, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Han, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Mao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Wang, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Dally, “Deep gradient  compression: Reducing the communication bandwidth for distributed  training,” arXiv preprint arXiv:1712.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='01887, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [87] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Guha, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Talwalkar, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Smith, “One-shot federated learning,”  arXiv preprint arXiv:1902.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='11175, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [88] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Kasturi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Ellore, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Hota, “Fusion learning: A one shot  federated learning,” in International Conference on Computational  Science, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 424–436, Springer, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [89] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Li, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' He, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Song, “Practical one-shot federated learning for  cross-silo setting,” arXiv preprint arXiv:2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='01017, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [90] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Liu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Fan, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Chen, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Xu, and Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Yang, “Fate: An industrial grade  platform for collaborative learning with data protection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=',” J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Mach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Learn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 22, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 226, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 1–6, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [91] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Bonawitz, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Eichner, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Grieskamp, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Huba, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Ingerman,  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Ivanov, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Kiddon, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Koneˇcn`y, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Mazzocchi, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' McMahan, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=',  “Towards federated learning at scale: System design,” Proceedings of  Machine Learning and Systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 374–388, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [92] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Singhal, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Sidahmed, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Garrett, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Wu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Rush, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Prakash,  “Federated reconstruction: Partially local federated learning,” Advances  in Neural Information Processing Systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 34, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 11220–11232,  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [93] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Ziller, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Trask, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Lopardo, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Szymkow, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Wagner, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Bluemke,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Nounahon, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Passerat-Palmbach, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Prakash, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Rose, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=',  “Pysyft: A library for easy federated learning,” in Federated Learning  Systems, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 111–139, Springer, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [94] “Paddlefl.” https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='com/PaddlePaddle/PaddleFL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [95] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Hidasi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Karatzoglou, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Baltrunas, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Tikk, “Session-  based recommendations with recurrent neural networks,” arXiv preprint  arXiv:1511.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='06939, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [96] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Xie, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Wang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Chen, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Gao, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Yao, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Kuang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Li,  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Ding, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Zhou, “Federatedscope: A comprehensive and flexi-  ble federated learning platform via message passing,” arXiv preprint  arXiv:2204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='05011, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [97] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Lyu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Yu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Nandakumar, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Ma, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Jin, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Yu, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Ng,  “Towards fair and privacy-preserving federated deep models,” IEEE  Transactions on Parallel and Distributed Systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 31, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 11,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 2524–2541, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [98] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Lyu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Li, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Nandakumar, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Yu, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Ma, “How to democra-  tise and protect ai: Fair and differentially private decentralised deep  learning,” IEEE Transactions on Dependable and Secure Computing,  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 8, DECEMBER 2022  15  [99] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Roy, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Siddiqui, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' P¨olsterl, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Navab, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Wachinger,  “Braintorrent: A peer-to-peer environment for decentralized federated  learning,” arXiv preprint arXiv:1905.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='06731, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [100] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Orm´andi, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Heged˝us, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Jelasity, “Gossip learning with linear  models on fully distributed data,” Concurrency and Computation:  Practice and Experience, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 25, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 556–571, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  [101] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Qi, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Wu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Wu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Huang, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Xie, “Uni-FedRec: A  unified privacy-preserving news recommendation framework for model  training and online serving,” in Findings of the Association for Compu-  tational Linguistics: EMNLP 2021, (Punta Cana, Dominican Republic),  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 1438–1448, Association for Computational Linguistics, Nov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Zehua Sun is currently pursuing his master’s degree  in the School of Software of Shandong University.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  He received his bachelor’s degree in software engi-  neering from the School of Software of Shandong  University in 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' His research interests include  federated learning, recommendation systems and  data mining.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Yonghui Xu is a full professor at Joint SDU-NTU  Centre for Artificial Intelligence Research (C-FAIR),  Shandong University.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' Before that, he was a research  fellow in the Joint NTU-UBC Research Centre of  Excellence in Active Living for the Elderly (LILY),  Nanyang Technological University, Singapore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' He  received his Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' from the School of Computer Sci-  ence and Engineering at South China University of  Technology in 2017 and BS from the Department of  Mathematics and Information Science Engineering  at Henan University of China in 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' His research  areas include various topics in Trustworthy AI, knowledge graphs, expert  systems and their applications in e-commerce and healthcare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' He has been  invited as reviewer of top journals and leading international conferences, such  as, TKDE, TNNLS, IEEE Transactions on Cybernetics, Knowledge-Based  System, TKDD, IJCAI and AAAI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Yong Liu is a Senior Research Scientist at Alibaba-  NTU Singapore Joint Research Institute, Nanyang  Technological University (NTU).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' He was a Data  Scientist at NTUC Enterprise, and a Research Sci-  entist at Institute for Infocomm Research (I2R),  A*STAR, Singapore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' He received his Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' degree  in Computer Engineering from NTU in 2016 and  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' degree in Electronic Science and Technology  from University of Science and Technology of China  (USTC) in 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' His research interests include rec-  ommendation systems, natural language processing,  and knowledge graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' He has been invited as a PC member of major  conferences such as KDD, SIGIR, ACL, IJCAI, AAAI, and reviewer for  IEEE/ACM transactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Wei He is a associate professor at Shandong univer-  sity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' He received bachelor and master degrees from  computer science department of shandong university  in 1994 and 1999 respectively, and received Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  from engineering of shandong university in 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  He won the progress first prize in science and  technology of shandong province and the progress  second prize in science and technology of shandong  province, and excellent achievement in computer  application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' He has published more than 20 papers  in the computer journal, journal of software of  domestic and international journals conference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' More papers were recorded  by SCI, EI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Yali Jiang is currently a Lecturer in the School  of Software, Shandong University.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' She received her  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='Sc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=', M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='Sc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' and Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' degrees from Shandong  University in 1999, 2002 and 2011, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  She is engaged in information security and cryp-  tography research, her main research areas are pub-  lic key security authentication system and lattice  based cryptographic algorithm design and analysis,  including cloud computing security, big data privacy  protection, IoT security, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' She has participated  in the National 863 Program, Shandong Provincial  Excellent Young and Middle-aged Research Award Fund, Shandong Provincial  Natural Science Foundation and joint research projects of enterprises.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  Fangzhao Wu is a Principal Researcher at Microsoft  Research Asia, President of AAAI2022 and senior  member of China Computer Society.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' He received  the Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' degrees both from Electronic  Engineering Department of Tsinghua University in  2017 and 2012 respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' He published more than  100 academic papers and was cited nearly 3000  times He has won NLPCC2019 Excellent Paper  Award, WSDM 2019 Outstanding PC and AAAI  2021 Best SPC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' His research mainly focuses on  responsible AI, privacy protection, natural language  processing, and recommender systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' The research results have been applied  in Microsoft News, Bing Ads and other Microsoft products.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='  LiZhen Cui (IET Fellow, IEEE Senior Member)  is the Dean at School of Software, Shandong Uni-  versity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' He is the Co-Director of Joint SDU-NTU  Centre for Artificial Intelligence Research (C-FAIR)  and Research Center of Software & Data Engi-  neering, Shandong University.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' He is the Associate  Director of National Engineering Laboratory for E-  Commerce Technologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' He is a Professor with  the School of Software and the Joint SDU-NTU  Centre for Artificial Intelligence Research (C-FAIR),  Shandong University, and also a Visiting Professor  with Nanyang Technological University, Singapore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' He was a Visiting Scholar  with Georgia Tech, Atlanta, GA, USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' He received his bachelor’s, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='Sc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=',  and Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' degrees from Shandong University, Jinan, China, in 1999, 2002  and 2005, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' He has authored or coauthored over 200 articles in  journals and refereed conference proceedings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
+page_content=' His research interests include  big data management and analysis and AI theory and application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tAyT4oBgHgl3EQf3Pnc/content/2301.00767v1.pdf'}
diff --git a/A9E4T4oBgHgl3EQf5A6T/content/2301.05319v1.pdf b/A9E4T4oBgHgl3EQf5A6T/content/2301.05319v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..dc958659e539a690fe015336a7209e0289344c3e
--- /dev/null
+++ b/A9E4T4oBgHgl3EQf5A6T/content/2301.05319v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8f085db6a6fdb04425956d4a65bb469a5008b897614b24dda717ec7490aef79c
+size 3061011
diff --git a/A9E4T4oBgHgl3EQf5A6T/vector_store/index.faiss b/A9E4T4oBgHgl3EQf5A6T/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..156535538599ce5d9d56923d2334448211e7a948
--- /dev/null
+++ b/A9E4T4oBgHgl3EQf5A6T/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6fc529eb096f60b87e64f3c56109d00e43957803232a1bbb33fabbaa75099bbd
+size 7667757
diff --git a/A9E4T4oBgHgl3EQf5A6T/vector_store/index.pkl b/A9E4T4oBgHgl3EQf5A6T/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..5978b31e540d6cd01a932428775f502db5c5d106
--- /dev/null
+++ b/A9E4T4oBgHgl3EQf5A6T/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8980010c87d88f987f5e355cc0f76ad294953134f9ac08122c65076db351f311
+size 264462
diff --git a/BdAzT4oBgHgl3EQf___2/content/2301.01958v1.pdf b/BdAzT4oBgHgl3EQf___2/content/2301.01958v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..d86b7d5873536735ccf4b1ffda3e3219a9b71aec
--- /dev/null
+++ b/BdAzT4oBgHgl3EQf___2/content/2301.01958v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c113ca248d6a3af1e9d36ff6e3601102d3525a54893e182ca588a12e309d7e99
+size 246572
diff --git a/BdAzT4oBgHgl3EQf___2/vector_store/index.faiss b/BdAzT4oBgHgl3EQf___2/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..957281b4236efdcecfe8c3c5be078941dc44ec7f
--- /dev/null
+++ b/BdAzT4oBgHgl3EQf___2/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b3facbee4b19396f7927c8c2bca84a6e1dc663817f49c6487596898f71bb6871
+size 3342381
diff --git a/BdAzT4oBgHgl3EQf___2/vector_store/index.pkl b/BdAzT4oBgHgl3EQf___2/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..cda2ace5d06b9096a45f575b8227bf8b5182276f
--- /dev/null
+++ b/BdAzT4oBgHgl3EQf___2/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ab59193166bf6b1b48aa57efaf42fe2d9b784b5edfddf0ffc848a96d8f1b42d7
+size 133895
diff --git a/CNE2T4oBgHgl3EQfRwe0/content/2301.03785v1.pdf b/CNE2T4oBgHgl3EQfRwe0/content/2301.03785v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..1b97322917a3fb5e48f1bb92450b8b5c46884bc0
--- /dev/null
+++ b/CNE2T4oBgHgl3EQfRwe0/content/2301.03785v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:be1b9aecc0aa2e4c282f4fe3bd9069ecb4d444374dda1a58c6d1d971967ebba9
+size 1083406
diff --git a/CNE2T4oBgHgl3EQfRwe0/vector_store/index.pkl b/CNE2T4oBgHgl3EQfRwe0/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..762bf5c90af20aaf33c5fba93529f8b82e2c7ed6
--- /dev/null
+++ b/CNE2T4oBgHgl3EQfRwe0/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1391b0fd478e7cb77f3b8509dada2ad233a37bff93dcabc49d4942d299741619
+size 170031
diff --git a/CdE2T4oBgHgl3EQf9AmF/vector_store/index.faiss b/CdE2T4oBgHgl3EQf9AmF/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..f4cd4246d24f9dfe447428c83e48fdbffb68d0a5
--- /dev/null
+++ b/CdE2T4oBgHgl3EQf9AmF/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:87b0c3ccf1119773e0b093c101b48dfb087a656a5f4a56633db56ff9cee55827
+size 6225965
diff --git a/DtE1T4oBgHgl3EQfWQTV/content/tmp_files/2301.03113v1.pdf.txt b/DtE1T4oBgHgl3EQfWQTV/content/tmp_files/2301.03113v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..852ec69c983b7ad5d17d8d220efc568eb64aa38e
--- /dev/null
+++ b/DtE1T4oBgHgl3EQfWQTV/content/tmp_files/2301.03113v1.pdf.txt
@@ -0,0 +1,2486 @@
+arXiv:2301.03113v1  [math.OC]  8 Jan 2023
+Accelerated Randomized Block-Coordinate Algorithms for
+Co-coercive Equations and Applications
+Quoc Tran-Dinh
+Department of Statistics and Operations Research
+The University of North Carolina at Chapel Hill
+318 Hanes Hall, UNC-Chapel Hill, NC 27599-3260.
+Email: quoctd@email.unc.edu.
+July 2022
+Abstract
+In this paper, we develop an accelerated randomized block-coordinate algorithm to
+approximate a solution of a co-coercive equation. Such an equation plays a central role
+in optimization and related fields and covers many mathematical models as special cases,
+including convex optimization, convex-concave minimax, and variational inequality prob-
+lems. Our algorithm relies on a recent Nesterov’s accelerated interpretation of the Halpern
+fixed-point iteration in [48].
+We establish that the new algorithm achieves O
+�
+1/k2�
+-
+convergence rate on E
+�
+∥Gxk∥2�
+through the last-iterate, where G is the underlying co-
+coercive operator, E [·] is the expectation, and k is the iteration counter. This rate is signif-
+icantly faster than O (1/k) rates in standard forward or gradient-based methods from the
+literature. We also prove o
+�
+1/k2�
+rates on both E
+�
+∥Gxk∥2�
+and E
+�
+∥xk+1 − xk∥2�
+. Next,
+we apply our method to derive two accelerated randomized block coordinate variants
+of the forward-backward splitting and Douglas-Rachford splitting schemes, respectively
+for solving a monotone inclusion involving the sum of two operators. As a byproduct,
+these variants also have faster convergence rates than their non-accelerated counterparts.
+Finally, we apply our scheme to a finite-sum monotone inclusion that has various appli-
+cations in machine learning and statistical learning, including federated learning. As a
+result, we obtain a novel federated learning-type algorithm with fast and provable con-
+vergence rates.
+1
+Introduction
+Monotone inclusion provides a powerful tool to model several problems in optimization,
+nonlinear analysis, mechanics, and machine learning, among many other areas, see, e.g.,
+[5, 9, 17, 41, 44, 45, 46]. Though it is a classical mathematical tool [5, 28, 45, 46], there
+has been a notable research surge of this topic in the last few years due to new applications
+in modern machine learning and data science. Methods for solving monotone inclusions often
+generalize existing optimization algorithms, and exploit structures of the underlying operators
+1
+
+such as splitting property. Classical methods include gradient or forward, extragradient, past-
+extragradient, proximal-point, forward-backward splitting, forward-backward-forward split-
+ting, Douglas-Rachford splitting, projective splitting methods, and their variants, see, e.g.,
+[5, 12, 14, 28, 17, 31, 42, 52]. However, developing accelerated [block-]coordinate methods
+with fast convergence rates for lare-scale monotone inclusions is still a challenging task.
+In this paper, we focus on a very basic model of monotone inclusions, which is called a
+co-coercive equation of the form:
+Find x⋆ ∈ Rp such that:
+Gx⋆ = 0,
+(CE)
+where G : Rp → Rp is a co-coercive operator (see Section 2 for definition). For our convenience,
+we assume that the solution set zer(G) := G−1(0) = {x⋆ ∈ Rp : Gx⋆ = 0} of (CE) is nonempty.
+The co-coercive equation (CE) though looks simple, it is equivalent to the problem of
+finding a fixed-point x⋆ of a nonexpansive operator T := I − G, i.e. x⋆ = Tx⋆, where I is the
+identity operator (see [5]). Therefore, it covers many fundamental problems in different fields
+by appropriately reformulating them into special cases of (CE), or equivalently, fixed-point
+problems (see, e.g., [13, 40] and also Sections 4 and 5 below).
+Motivation and related work. We are interested in the case that G in (CE) lives in a
+high-dimensional space Rp such that operating on full-dimensional vectors x of Rp is expensive
+or even prohibited. Such models are ubiquitous in large-scale modern machine learning and
+data science applications [8, 23, 47]. One common approach to tackle these models is block-
+coordinate methods, which iteratively update one or a small number of blocks of the model
+parameters instead of the full parameter vector. Such an approach is though very classical
+[4, 38], it has attracted a huge attention in recent years in optimization, monotone inclusions,
+and fixed-point problems, see, e.g., [6, 11, 24, 36, 37, 40, 43, 53]. However, developing efficient
+variants of the block-coordinate method to solve co-coercive equation (CE) remains largely
+elusive. Most existing works focus on special cases of (CE) such as optimization, convex-
+concave minimax, and supervised learning models, see e.g., [6, 24, 37, 36, 43, 53].
+Our goal in this paper is to advance a recent development of accelerated methods and
+apply it to randomized [block-]coordinate schemes. Unlike non-accelerated algorithms, it has
+been recognized that [2, 54] generalizing accelerated methods from convex minimization to
+monotone inclusions is not straightforward. Recent attempt on designing accelerated methods
+for monotone inclusions and variational inequality (VIPs) has been made, see, e.g., in [2, 10,
+20, 30, 50].
+These algorithms often achieve a faster convergence rate than their classical
+counterparts on the gradient norm or some appropriate operator residual norms. Typical
+rates on the square of a residual norm are usually O
+�
+1/k2�
+(or faster, o
+�
+1/k2�
+) compared
+to O (1/k) (or o (1/k)) in non-accelerated methods, where k is the iteration counter. The
+O
+�
+1/k2�
+rate matches the convergence rate lower bound in different settings, see [21, 35, 39]
+for some concrete examples.
+As mentioned earlier, since the problem of approximating a
+solution of (CE) can be reformulated equivalently to a fixed-point problem of a non-expansive
+operator [5], theory and solution methods from one field can be applied to another and vice
+versa. Due to its generality, (CE) can cover many common applications in scientific computing
+as discussed, e.g., in [40, 46]. For instance, it can be customized to handle linear systems,
+[composite] smooth and nonsmooth convex optimization, feasibility problems, decentralized
+2
+
+optimization, federated learning, among others. To avoid repetition, we do not present these
+applications in this paper, but refer to [40, 46] for more details on how to reformulate them
+into a fixed-point problem, or equivalently, a co-coercive equation of the form (CE).
+Motivated by applications in high-dimensional spaces, we aim at developing an accelerated
+randomized block-coordinate method to solve (CE).
+Our basic mathematical tool is the
+Halpern fixed-point iteration from [19] for solving (CE) and its recent development in, e.g., [16,
+25, 27, 54]. Our central idea is to represent the accelerated Halpern fixed-point method into
+a two-step iterative scheme (in Nesterov’s accelerated sense) using two consecutive iterates as
+discussed in [48]. Then, we combine this resulting scheme and a randomized block-coordinate
+strategy to derive a novel randomized block-coordinate algorithm for solving (CE).
+Contribution. Our concrete contribution can be summarized as follows. Firstly, we pro-
+pose a new accelerated randomized block-coordinate algorithm to solve (CE) which achieves a
+O
+�
+1/k2�
+last-iterate convergence rate, or even a o
+�
+1/k2�
+-rate on E
+�
+∥Gxk∥2�
+. Our algorithm
+is very simple to implement and significantly different from existing methods. To the best
+of our knowledge, this is the first randomized block-coordinate algorithm for (CE) achieving
+o
+�
+1/k2�
+-fast convergence rates. Next, we utilize a change of variable to develop a practical
+variant of our method, which can avoid full-dimensional operations on the iterates. Alter-
+natively, we apply our algorithm to the forward-backward splitting and Douglas-Rachford
+splitting methods to obtain new accelerated randomized block-coordinate variants for solving
+monotone inclusions involving the sum of two maximally monotone operators. As a byprod-
+uct of our convergence analysis, these variants also achieve faster convergence rates than their
+classical counterparts. Finally, we apply our method to tackle a class of finite-sum mono-
+tone inclusions which forms the basis of many supervised machine learning tasks, including
+federated learning [22, 26, 32, 33]. It leads to a new federated learning-type algorithm with
+O
+�
+1/k2�
+and o
+�
+1/k2�
+- convergence rates for a general class of finite-sum monotone inclusions.
+Let us highlight the following points of our contribution and discuss its limitation. Firstly,
+one of the most related works to our method is [40], which extends the asynchronous ran-
+domized block-coordinate method to (CE). Though their method is asynchronous, it is non-
+accelerated, and therefore, in our context, achieves O (1/k) and at most o (1/k) convergence
+rates on the squared norm of the residual mapping. Note that the form of our algorithm is also
+different from [40], while achieving O
+�
+1/k2�
+and o
+�
+1/k2�
+faster rates. Unfortunately, asyn-
+chronous variants of our method remain open. Secondly, unlike methods for convex problems,
+convergence analysis of algorithms for monotone inclusions, including (CE) is fundamentally
+different, including the construction of a potential or Lyapunov function. Moreover, it remains
+unclear if some recent techniques, e.g., in [16, 25, 27, 54] can be extended to [randomized
+block-] coordinate variants. In this paper, we follow a different approach compared to those,
+including convergence analysis technique. Thirdly, our randomized block-coordinate variants
+for splitting schemes in Section 4 are also very different from the ones in [11] since their
+methods rely on standard splitting methods. However, as a limitation of our new forward-
+backward splitting method, it still requires a co-coercive assumption of one operator. Finally,
+our application to a finite-sum monotone inclusion in Section 5 is new compared to [13] since
+our problem setting is more general than that of [13], and our scheme relies on an accelerated
+Douglas-Rachford splitting scheme instead of a forward-type method as in [13].
+3
+
+Paper organization. The rest of this paper is organized as follows. In Section 2 we
+briefly review some background related to (CE) and recall some preliminary results used in
+this paper. Our main result is in Section 3, where we develop a new algorithm and establish its
+convergence rate guarantees. We also show how to apply our method to fixed-point problems
+and derive its practical variant. Section 4 presents two applications of our method to the
+forward-backward and Douglas-Rachford splitting schemes for solving monotone inclusions.
+Section 5 is an application of our method to a general finite-sum monotone inclusion which
+potentially has many applications in machine learning and networks. We close this paper
+with some concluding remarks.
+2
+Background and Preliminary Results
+We first review some background on monotone operators and related concepts. Then, we
+recall the Halpern fixed-point iteration from [19] and its relation to Nesterov’s accelerated
+methods.
+2.1
+Monotone operators and related concepts
+We work with a finite dimensional space Rp equipped with the standard inner product ⟨·, ·⟩ and
+Euclidean norm ∥ · ∥. For a set-valued mapping G : Rp ⇒ 2Rp, dom(G) = {x ∈ Rp : Gx ̸= ∅}
+denotes its domain, graph(G) = {(x, y) ∈ Rp × Rp : y ∈ Gx} denotes its graph, where 2Rp is
+the set of all subsets of Rp. The inverse of G is defined by G−1y := {x ∈ Rp : y ∈ Gx}. For
+x = [x1, · · · , xn] ∈ Rp, we define a weighted norm ∥x∥w :=
+��n
+i=1 wi∥xi∥2�1/2, where xi is
+the i-the block of x and wi > 0 is a given weight (i = 1, · · · , n).
+Monotonicity. For a set-valued mapping G : Rp ⇒ 2Rp, we say that G is monotone if
+⟨u − v, x − y⟩ ≥ 0 for all x, y ∈ dom(G), u ∈ Gx, and v ∈ Gy. G is said to be µG-strongly
+monotone (or sometimes called coercive) if ⟨u − v, x − y⟩ ≥ µG∥x − y∥2 for all x, y ∈ dom(G),
+u ∈ Gx, and v ∈ Gy, where µG > 0 is called a strong monotonicity parameter. If G is single-
+valued, then these conditions reduce to ⟨Gx−Gy, x−y⟩ ≥ 0 and ⟨Gx−Gy, x−y⟩ ≥ µG∥x−y∥2
+for all x, y ∈ dom(G), respectively. We say that G is maximally monotone if graph(G) is not
+properly contained in the graph of any other monotone operator. Note that G is maximally
+monotone, then αG is also maximally monotone for any α > 0, and if G and H are maximally
+monotone, and dom(F) ∩ int (dom(H)) ̸= ∅, then G + H is maximally monotone.
+Lipschitz continuity and co-coerciveness. A single-valued operator G is said to be
+L-Lipschitz continuous if ∥Gx − Gy∥ ≤ L∥x − y∥ for all x, y ∈ dom(G), where L ≥ 0 is a
+Lipschitz constant. If L = 1, then we say that G is nonexpansive, while if L ∈ [0, 1), then we
+say that G is L-contractive, and L is its contraction factor. We say that G is 1
+L-co-coercive if
+⟨Gx−Gy, x−y⟩ ≥ 1
+L∥Gx−Gy∥2 for all x, y ∈ dom(G). If L = 1, then we say that G is firmly
+nonexpansive. If G is 1
+L-cocoercive, then it is also monotone and L-Lipschitz continuous (by
+using the Cauchy-Schwarz inequality), but the reverse statement is not true in general.
+Resolvent operator. The operator JGx := {y ∈ Rp : x ∈ y + Gy} is called the resolvent
+of G, often denoted by JGx = (I+G)−1x, where I is the identity mapping. Clearly, evaluating
+JG requires solving a strongly monotone inclusion 0 ∈ y−x+Gy. If G is monotone, then JG is
+singled-valued, and if G is maximally monotone then JG is singled-valued and dom(JG) = Rp.
+If G is monotone, then JG is firmly nonexpansive [5, Proposition 23.10].
+4
+
+2.2
+The Halpern fixed-point iteration and its variants
+Let us recall the following Halpern fixed-point iteration from [19] for approximating a fixed-
+point x⋆ of a non-expansive operator T : Rp → Rp (i.e. x⋆ = Tx⋆):
+xk+1 := βkx0 + (1 − βk)Txk,
+where
+βk :=
+1
+k+2.
+(1)
+As proven in [27], this scheme achieves ∥xk−Txk∥2 = O
+� 1
+k2
+�
+rate guarantee, which is optimal.
+Now, for a given operator G : Rp → Rp, G is 1
+L-co-coercive if and only if T := I − 2
+LG is
+nonexpansive [5, Proposition 4.11]. Therefore, the Halpern fixed-point method (1) applying
+to approximate a solution x⋆ of the co-coercive equation Gx⋆ = 0 can be written as
+xk+1 := βkx0 + (1 − βk)
+�
+xk − 2
+LGxk�
+= βkx0 + (1 − βk)xk − ηkGxk,
+(2)
+where ηk := 2(1−βk)
+L
+. As shown in [16], this scheme also achieves an optimal convergence rate,
+i.e. ∥Gxk∥2 = O
+�
+1/k2�
+. Clearly, (1) and (2) are equivalent.
+Next, it has been shown in [48] that if we eliminate x0 in (2) using two consecutive updates
+xk and xk+1, then we obtain the following scheme:
+xk+1 := xk + θk(xk − xk−1) −
+�
+ηkGxk − γkGxk−1�
+,
+(3)
+where θk := βk(1−βk)
+βk−1
+and γk := βkηk−1
+βk−1 .
+Finally, if we additionally introduce yk+1 := xk − αkGxk, then we can equivalently trans-
+form (3) into the following form (see [48] for details):
+�
+yk+1 := xk − αkGxk,
+xk+1 := yk+1 + θk(yk+1 − yk) + νk(xk − yk+1),
+(4)
+where αk :=
+ηk
+1−βk and νk :=
+βk
+βk−1.
+The scheme (4) shows a connection between the Halpern-type method [19] and Nesterov’s
+accelerated algorithms [2, 29, 34, 35]. Compared to Nesterov’s accelerated methods for solving
+smooth convex optimization problems, (4) has an additional correction term νk(xk −yk+1). It
+is also related to Ravine’s method as shown in [3]. Note that, both (3) and (4) can be applied
+to proximal-point, forward-backward splitting, Douglas-Rachford splitting, and three-operator
+splitting schemes for solving monotone inclusions, variational inequality, and convex-concave
+saddle-point problems, see, e.g., [2, 7, 20, 30, 48] for more details.
+3
+Accelerated Randomized Block-Coordinate Algorithms
+In this section, we develop a new randomized block-coordinate variant of (3) to solve (CE).
+We assume that the variable x of (CE) is decomposed into n-blocks as x = [x1, x2, · · · , xn]
+(1 ≤ n ≤ p), where xi ∈ Rpi for i ∈ [n] := {1, 2, · · · , n}. For the operator G, we denote
+[Gx]i as the i-the block coordinate of Gx such that Gx = [[Gx]1, · · · , [Gx]n]. We also denote
+G[i]x = [0, · · · , 0, [Gx]i, 0, · · · , 0] so that only the i-th block is computed, while others are
+zero.
+Throughout this paper, we assume that G in (CE) satisfies the following assumption.
+5
+
+Assumption 3.1. The operator G in (CE) is L−1-block-coordinate-wise co-coercive, i.e. for
+any x, y ∈ dom(G), there exist Li ∈ [0, +∞) (∀i ∈ [n]) such that
+⟨Gx − Gy, x − y⟩ ≥
+n
+�
+i=1
+1
+Li ∥[Gx]i − [Gy]i∥2 ≡ ∥Gx − Gy∥2
+L−1,
+(CP)
+where L−1 := ( 1
+L1 , · · · , 1
+Ln ). Moreover, dom(G) = Rp and zer(G) := {x⋆ ∈ Rp : Gx⋆ = 0} ̸= ∅.
+Clearly, Assumption 3.1 extends the standard co-coerciveness [5] of a monotone operator
+to block-coordinate-wise settings, and therefore, it is still very common. Moreover, due to
+the equivalence between the co-coercive equation (CE) and the fixed-point problem as we
+mentioned earlier, our setting appears to be sufficiently general to cover many applications.
+Since we will develop randomized methods operating on blocks xi of x for some i ∈ [n],
+we introduce the following probability model for selecting block coordinates of x. Let ik be a
+random variable on [n] := {1, 2, · · · , n} that satisfies the following probability distribution:
+Prob (ik = i) = pi,
+for all i ∈ [n],
+(5)
+where pi > 0 for all i ∈ [n] and �n
+i=1 pi = 1. We also denote pmin := mini∈[n] pi > 0. If
+pi =
+1
+n, then ik is a uniformly random variable. Otherwise, we also cover non-uniformly
+randomized block-coordinate methods.
+To define convergence guarantees of our methods, we denote Fk to be the smallest σ-
+algebra generated by the random set {x0, x1, · · · , xk} collecting all iterate vectors up to the
+k-the iteration of our algorithm. We also use Ek [X] := Eik [X | Fk] to denote the conditional
+expectation of X taken overall the randomness generated by the random variable ik ∈ [n]
+(and therefore xk) conditioned on Fk, and E [·] for the total expectation.
+3.1
+Accelerated RBC Method and Convergence Analysis: Main Result
+Inspired by our expression (3), we propose the following Accelerated Randomized Block-
+Coordinate (ARBC) scheme for solving (CE).
+Starting from x0 ∈ Rp, we set x−1 := x0,
+and at each iteration k ≥ 0, randomly generate ik ∈ [n] following the probability law (5) and
+update:
+xk+1 := xk + θk(xk − xk−1) −
+ψ
+pik
+�
+ηkG[ik]xk − γkG[ik]xk−1�
+,
+(ARBC)
+where θk > 0, ψ > 0, ηk > 0, and γk ≥ 0 are given parameters, which will be determined later,
+and G[i]xk = [0, · · · , 0, [Gxk]i, 0, · · · , 0] such that [Gxk]i is the i-the block of Gxk (i ∈ [n]).
+The scheme (ARBC) requires two block-coordinate evaluations [Gxk]ik and [Gxk−1]ik of
+G at the two consecutive iterates xk and xk−1, respectively. Clearly, it is different from ex-
+isting randomized [block]-coordinate methods in the literature, including methods for convex
+optimization [6, 18, 24, 36, 37, 43, 53]. However, due to the extrapolation term θk(xk −xk−1),
+(ARBC) still requires full vector update at each iteration. This is unavoidable in accelerated
+methods as in [18, 36, 37]. We will further discuss this point in Subsection 3.2.
+To establish the convergence of (ARBC), we introduce the following potential function:
+Vk := 2ψtkηk−1
+�
+⟨Gxk−1, xk−1 − x⋆⟩ − �n
+i=1
+1
+Li ∥[Gxk−1]i∥2�
++ ∥xk−1 − x⋆ + tk(xk − xk−1)∥2 + µk∥xk−1 − x⋆∥2,
+(6)
+6
+
+where x⋆ ∈ zer(G), and tk > 0 and µk ≥ 0 are given parameters, which will be determined
+later. It is obvious that under Assumption 3.1, {xk} is well-defined, and we have Vk ≥ 0 for
+all k ≥ 0 regardless the choice of xk−1 and xk. We first prove the following key result.
+Lemma 3.1. Suppose that Assumption 3.1 holds for (CE). Let {xk} be generated by (ARBC)
+and Vk be defined by (6). Suppose further that the parameters in (ARBC) and (6) satisfy
+
+
+
+
+
+
+
+
+
+tkηk−1 ≥
+�
+1 −
+1
+tk−µk
+�
+tk+1ηk,
+θk
+:= tk−µk−1
+tk+1
+,
+γk
+:=
+tk+1θk
+tk+1θk+1 · ηk.
+(7)
+Then, the following inequality holds:
+Vk − Ek
+�
+Vk+1�
+≥ µk(2tk − µk − 1)∥xk − xk−1∥2 − (µk+1 − µk)∥xk − x⋆∥2
++ �n
+i=1
+ψtk+1[2pi(tk+1θk+1)−ψLitk+1ηk]
+ηkLipi
+��ηk[Gxk]i − γk[Gxk−1]i
+��2.
+(8)
+Proof. First of all, let us introduce dk := ηkGxk − γkGxk−1. Then, from (ARBC), we have
+xk+1 − xk = θk(xk − xk−1) −
+ψ
+pik dk
+[ik]. Hence we can expand the second term of (6) as
+T[1]
+:=
+∥xk + tk+1(xk+1 − xk) − x⋆∥2
+(ARBC)
+=
+∥xk − x⋆ + tk+1θk(xk − xk−1) − ψtk+1p−1
+ik dk
+[ik]∥2
+=
+∥xk − x⋆∥2 + t2
+k+1θ2
+k∥xk − xk−1∥2 + ψ2t2
+k+1∥p−1
+ik dk
+[ik]∥2 − 2ψtk+1⟨p−1
+ik dk
+[ik], xk − x⋆⟩
++ 2tk+1θk⟨xk − xk−1, xk − x⋆⟩ − 2ψt2
+k+1θk⟨p−1
+ik dk
+[ik], xk − xk−1⟩.
+Alternatively, we can also expand
+∥xk−1 + tk(xk − xk−1) − x⋆∥2 = ∥xk − x⋆ + (tk − 1)(xk − xk−1)∥2
+= ∥xk − x⋆∥2 + 2(tk − 1)⟨xk − xk−1, xk − x⋆⟩
++ (tk − 1)2∥xk − xk−1∥2.
+Moreover, we also have the following elementary expression
+µk∥xk−1 − x⋆∥2 − µk+1∥xk − x⋆∥2 = µk∥xk − xk−1∥2 − 2µk⟨xk − xk−1, xk − x⋆⟩
+− (µk+1 − µk)∥xk − x⋆∥2.
+Now, let us consider the following function:
+Qk := ∥xk−1 + tk(xk − xk−1) − x⋆∥2 + µk∥xk−1 − x⋆∥2.
+(9)
+Then, combining the last three expressions, and using the definition (9) of Qk, we have
+Qk − Qk+1 =
+�
+(tk − 1)2 − θ2
+kt2
+k+1 + µk
+�
+∥xk − xk−1∥2 − ψ2t2
+k+1∥p−1
+ik dk
+[ik]∥2
++ 2 (tk − 1 − θktk+1 − µk) ⟨xk − x⋆, xk − xk−1⟩ − (µk+1 − µk)∥xk − x⋆∥2
++ 2ψtk+1⟨p−1
+ik dk
+[ik], xk − x⋆⟩ + 2ψt2
+k+1θk⟨p−1
+ik dk
+[ik], xk − xk−1⟩.
+(10)
+7
+
+Next, using the fact that dk
+[ik] = [0, · · · , 0, dk
+ik, 0, · · · , 0] and (5), we can easily show that
+Ek
+�
+∥p−1
+ik dk
+[ik]∥2�
+= �n
+i=1 p−1
+i ∥dk
+i ∥2,
+Ek
+�
+⟨p−1
+ik dk
+[ik], xk − x⋆⟩
+�
+= �n
+i=1⟨dk
+i , xk
+i − x⋆
+i ⟩,
+Ek
+�
+⟨p−1
+ik dk
+[ik], xk − xk−1⟩
+�
+= �n
+i=1⟨dk
+i , xk
+i − xk−1
+i
+⟩.
+(11)
+Taking conditional expectation Ek [·] both sides of (10) and then using (11) and dk = ηkGxk −
+γkGxk−1 into the resulting expression, and rearranging it, we can derive
+Qk − Ek
+�
+Qk+1�
+=
+�
+(tk − 1)2 − θ2
+kt2
+k+1 + µk
+�
+∥xk − xk−1∥2 − (µk+1 − µk)∥xk − x⋆∥2
++ 2 (tk − 1 − θktk+1 − µk) ⟨xk − x⋆, xk − xk−1⟩
++ 2ψtk+1ηk
+�n
+i=1⟨[Gxk]i, xk
+i − x⋆
+i ⟩ − 2ψtk+1γk
+�n
+i=1⟨[Gxk−1]i, xk−1
+i
+− x⋆
+i ⟩
+− ψ2t2
+k+1
+�n
+i=1
+1
+pi ∥ηk[Gxk]i − γk[Gxk−1]i∥2
++ 2ψt2
+k+1θkηk
+�n
+i=1⟨[Gxk]i − [Gxk−1]i, xk
+i − xk−1
+i
+⟩
++ 2ψtk+1 [tk+1θk(ηk − γk) − γk] �n
+i=1⟨[Gxk−1]i, xk
+i − xk−1
+i
+⟩.
+Utilizing the condition (CP) of G as
+�n
+i=1⟨[Gxk]i − [Gxk−1]i, xk
+i − xk−1
+i
+⟩ ≥ �n
+i=1
+1
+Li ∥[Gxk]i − [Gxk−1]i∥2,
+into the last expression, we arrive at
+Qk − Ek
+�
+Qk+1�
+≥
+�
+(tk − 1)2 − θ2
+kt2
+k+1 + µk
+�
+∥xk − xk−1∥2 − (µk+1 − µk)∥xk − x⋆∥2
++ 2
+�
+tk − 1 − θktk+1 − µk
+�
+⟨xk − x⋆, xk − xk−1⟩ + 2ψtk+1ηk⟨Gxk, xk − x⋆⟩
+− 2ψtk+1γk⟨Gxk−1, xk−1 − x⋆⟩ − ψ2t2
+k+1
+�n
+i=1
+1
+pi ∥ηk[Gxk]i − γk[Gxk−1]i∥2
++ 2ψt2
+k+1θkηk
+�n
+i=1
+1
+Li ∥[Gxk]i − [Gxk−1]i∥2
++ 2ψtk+1
+�
+tk+1θk(ηk − γk) − γk
+�
+⟨Gxk−1, xk − xk−1⟩.
+Rearranging this inequality, we get
+Qk − Ek
+�
+Qk+1�
+≥
+�
+(tk − 1)2 − θ2
+kt2
+k+1 + µk
+�
+∥xk − xk−1∥2 − (µk+1 − µk)∥xk − x⋆∥2
++ 2
+�
+tk − 1 − θktk+1 − µk
+�
+⟨xk − x⋆, xk − xk−1⟩
++ ψtk+1
+�n
+i=1
+�
+2(tk+1θkηk−γk)
+Li
+− ψtk+1γ2
+k
+pi
+�
+∥[Gxk−1]i∥2
+− 2ψt2
+k+1ηk
+�n
+i=1
+�
+2θk
+Li − ψγk
+pi
+�
+⟨[Gxk]i, [Gxk−1]i⟩
++ ψtk+1ηk
+�n
+i=1
+�
+2(tk+1θk+1)
+Li
+− ψtk+1ηk
+pi
+�
+∥[Gxk]i∥2
++ 2ψtk+1ηk
+�
+⟨Gxk, xk − x⋆⟩ − �n
+i=1
+1
+Li ∥[Gxk]i∥2�
+− 2ψtk+1γk
+�
+⟨Gxk−1, xk−1 − x⋆⟩ − �n
+i=1
+1
+Li ∥[Gxk−1]i∥2�
++ 2ψtk+1
+�
+tk+1θk(ηk − γk) − γk
+�
+⟨Gxk−1, xk − xk−1⟩.
+(12)
+8
+
+Let us first impose the following condition as in the third line of (7):
+tk+1θk(ηk − γk) − γk = 0
+⇔
+γk :=
+tk+1θk
+tk+1θk+1 · ηk.
+(13)
+This condition leads to
+
+
+
+
+
+
+
+
+
+
+
+Ak
+i := ψtk+1
+�
+2(tk+1θkηk−γk)
+Li
+− ψtk+1γ2
+k
+pi
+�
+= ψtk+1ηk[2pi(tk+1θk+1)−ψLitk+1ηk]
+Lipi
+·
+t2
+k+1θ2
+k
+(tk+1θk+1)2 ,
+Bk
+i := ψt2
+k+1ηk
+�
+2θk
+Li − ψγk
+pi
+�
+= ψtk+1ηk[2pi(tk+1θk+1)−ψLitk+1ηk]
+Lipi(tk+1θk+1)
+·
+tk+1θk
+(tk+1θk+1),
+Ck
+i := ψtk+1ηk
+�
+2(tk+1θk+1)
+Li
+− ψtk+1ηk
+pi
+�
+= ψtk+1ηk[2pi(tk+1θk+1)−ψLitk+1ηk]
+Lipi
+.
+Therefore, using these three coefficients Ak
+i , Bk
+i , and Ck
+i , we can show that
+T [i]
+[2] := ψtk+1
+�
+2(tk+1θkηk−γk)
+Li
+− ψtk+1γ2
+k
+pi
+�
+∥[Gxk−1]i∥2
+− 2ψt2
+k+1ηk
+�
+2θk
+Li − ψγk
+pi
+�
+⟨[Gxk]i, [Gxk−1]i⟩
++ ψtk+1ηk
+�
+2(tk+1θk+1)
+Li
+− ψtk+1ηk
+pi
+�
+∥[Gxk]i∥2
+=
+ψtk+1ηk
+�
+2pi(tk+1θk+1)−ψLitk+1ηk
+�
+Lipi
+��[Gxk]i −
+tk+1θk
+tk+1θk+1[Gxk−1]i
+��2.
+In this case, we can simplify (12) as
+Qk − Ek
+�
+Qk+1�
+≥
+�
+(tk − 1)2 − θ2
+kt2
+k+1 + µk
+�
+∥xk − xk−1∥2 − (µk+1 − µk)∥xk − x⋆∥2
++ 2
+�
+tk − 1 − θktk+1 − µk
+�
+⟨xk − x⋆, xk − xk−1⟩
++ 2ψtk+1ηk
+�
+⟨Gxk, xk − x⋆⟩ − �n
+i=1
+1
+Li ∥[Gxk]i∥2�
+− 2ψtk+1γk
+�
+⟨Gxk−1, xk−1 − x⋆⟩ − �n
+i=1
+1
+Li ∥[Gxk−1]i∥2�
++ �n
+i=1
+ψtk+1ηk[2pi(tk+1θk+1)−ψLitk+1ηk]
+Lipi
+��[Gxk]i −
+tk+1θk
+tk+1θk+1[Gxk−1]i
+��2.
+(14)
+Let us impose the following two conditions:
+tk − µk − 1 = θktk+1
+and
+tkηk−1 ≥ tk+1γk.
+(15)
+The first equality leads to the choice of θk as in (7), i.e. θk := tk−µk−1
+tk+1
+.
+Next, let us check the second condition of (15). Using (13) and tk+1θk = tk − µk − 1 from
+(15), the second condition of (15) is equivalent to
+tkηk−1 ≥ tk+1ηk
+�
+1 −
+1
+tk−µk
+�
+,
+which is the first line of (7). Hence, the second condition of (15) holds.
+Finally, by (15), we can easily show that
+T[3] := µk + (tk − 1)2 − θ2
+kt2
+k+1 = (tk − 1)tk − (tk − µk)tk+1θk = µk(2tk − µk − 1).
+Using this expression, (CP), the conditions in (15),
+tk+1θk
+tk+1θk+1 = γk
+ηk from (13), and ηk − γk =
+ηk
+tk+1θk+1 into (14), and then using the definition of Vk from (6) for the resulting inequality,
+we obtain (8).
+9
+
+Now, we are ready to prove the convergence of (ARBC) in the following theorem.
+Theorem 3.1. Suppose that Assumption 3.1 holds for (CE).
+Let {xk} be generated by
+(ARBC) and Vk be defined by (6). For given ω > 3 and 0 < ψ < min
+�
+2pi
+Li : i ∈ [n]
+�
+, we
+update
+µk := 1,
+tk := k+2ω+1
+ω
+,
+θk := tk−2
+tk+1 ,
+ηk := tk−1
+tk+1 ,
+and
+γk := tk−2
+tk+1 = θk.
+(16)
+Then, we obtain the following bounds:
+�+∞
+k=0(k + 2ω + 2)2E
+�
+∥ηkGxk − γkGxk−1∥2�
+≤
+ω2
+ψC V0,
+�+∞
+k=0(k + ω + 1)E
+�
+∥xk − xk−1∥2�
+≤ 2
+ωV0,
+�+∞
+k=0(k + ω)E
+�
+∥Gxk−1∥2�
+≤
+16
+ψ2ωV0 +
+8C0
+ψ2(ω−3),
+�+∞
+k=1(k + 1)2E
+�
+∥Gxk − Gxk−1∥2�
+≤ C0,
+(17)
+where C := min
+i∈[n]
+�
+2
+Li − ψ
+pi
+�
+> 0 and C0 :=
+ψ2ω2(ω−1)2
+(ω+1)2
+∥Gx0∥2 +
+�
+8(ω−1)
+ω
++ ψω2(1−pmin)
+pminC
+�
+V0.
+Moreover, the following statements also hold:
+�
+E
+�
+∥xk+1 − xk∥2�
+= O
+� 1
+k2
+�
+and
+E
+�
+∥xk+1 − xk∥2�
+= o
+� 1
+k2
+�
+,
+E
+�
+∥Gxk∥2�
+= O
+� 1
+k2
+�
+and
+E
+�
+∥Gxk∥2�
+= o
+� 1
+k2
+�
+.
+(18)
+Theorem 3.1 establishes convergence rates of (ARBC) on two main criteria E
+�
+∥Gxk∥2�
+and E
+�
+∥xk+1 − xk∥2�
+, among other side results as stated in (17). However, the statement (18)
+does not show the independence of the rates on the number of blocks n. As we can observe
+from our proof below that these convergence rates depend on
+1
+ψ2 , where ψ is a given stepsize in
+Theorem 3.1. If we choose pi = 1
+n, i.e. uniformly random, and assume that Li = L for i ∈ [n],
+then ψ is proportional to 1
+n, leading to E
+�
+∥xk+1 − xk∥2�
+= O
+�
+n2
+k2
+�
+and E
+�
+∥Gxk∥2�
+= O
+�
+n2
+k2
+�
+.
+The dependence of the convergence rates on n2 has been observed in Nesterov’s accelerated
+methods for convex optimization, see, e.g. [1, 18, 36]. In (18), we state both Big-O and
+small-o convergence rates where Big-O rates are often proved when k ≤ O (n), while small-o
+rates are achieved when k is sufficiently large.
+The proof of Theorem 3.1. Firstly, we fix µk := 1 for all k ≥ 0 and since θk is updated by
+θk := tk−µk−1
+tk+1
+= tk−2
+tk+1 as in (7), if we choose ηk := tk−µk
+tk+1
+= tk−1
+tk+1 , then the first condition
+of (7) reduces to 1 ≤ tk−1−1
+tk−2 , which holds if tk−1 − tk + 1 ≥ 0. Let us choose tk := k+2ω+1
+ω
+for some ω > 3.
+Clearly, we have tk−1 − tk + 1 =
+ω−1
+ω
+> 0.
+Moreover, we also have
+γk = tk+1θkηk
+tk+1θk+1 = tk−2
+tk+1 = θk as shown in (16).
+Next, under the choice of parameters as above, (8) reduces to
+Vk − Ek
+�
+Vk+1�
+≥ �n
+i=1
+ψt2
+k+1
+Lipi (2pi − ψLi) ∥ηk[Gxk]i − γk[Gxk−1]i∥2
++ 2(tk − 1)∥xk − xk−1∥2.
+10
+
+Taking full expectation this inequality and using tk = k+2ω+1
+ω
+and tk−2
+tk−1 ≥
+1
+ω+1, we obtain
+E
+�
+Vk�
+− E
+�
+Vk+1�
+≥ �n
+i=1
+ψ(k+2ω+2)2
+Lipiω2
+(2pi − ψLi) E
+�
+∥ηk[Gxk]i − γk[Gxk−1]i∥2�
++ 2(k+ω+1)
+ω
+E
+�
+∥xk − xk−1∥2�
+.
+(19)
+Since E
+�
+Vk�
+≥ 0, summing up (20) from k := 0 to k := K ≥ 0, we obtain
+�K−1
+k=0
+ψ(k+2ω+2)2
+ω2
+�n
+i=1
+�
+2
+Li − ψ
+pi
+�
+E
+�
+∥ηk[Gxk]i − γk[Gxk−1]i∥2�
+≤ E
+�
+V0�
+,
+�K−1
+k=0 (k + ω + 1)E
+�
+∥xk − xk−1∥2�
+≤ 2
+ωE
+�
+V0�
+.
+(20)
+This implies the first two lines of (17) after taking the limit as K → +∞ and noting that
+E [V0] = V0 due to the certainty of x0 and x−1.
+Next, let us define the following full vector ¯xk+1 as
+¯xk+1 := xk + θk(xk − xk−1) − ψ
+�
+ηkGxk − γkGxk−1�
+= zk − ψdk,
+(21)
+where zk := xk +θk(xk −xk−1) and dk := ηkGxk −γkGxk−1 ≡ ηkGxk −θkGxk−1. Then, from
+(ARBC), we have xk+1 = zk −
+ψ
+pik dk
+[ik]. Therefore, for any uk independent of ik, we have
+Ek
+�
+∥xk+1 − uk∥2�
+= ∥zk − uk∥2 − 2ψEk
+�
+⟨p−1
+ik dk
+[ik], zk − uk⟩
+�
++ ψ2Ek
+�
+∥p−1
+ik dk
+[ik]∥2�
+= ∥zk − uk∥2 − 2ψ⟨dk, zk − uk⟩ + ψ2 �n
+i=1
+1
+pi ∥dk
+i ∥2
+= ∥zk − ψdk − uk∥2 + ψ2 �n
+i=1
+�
+1
+pi − 1
+�
+∥dk
+i ∥2
+= ∥¯xk+1 − uk∥2 + ψ2 �n
+i=1
+�
+1
+pi − 1
+�
+∥dk
+i ∥2.
+(22)
+Now, from (21), we have
+¯xk+1 − xk + ψηkGxk =
+θk
+ηk−1 (xk − xk−1 + ψηk−1Gxk−1) +
+�
+1 −
+θk
+ηk−1
+�
+· θk(1−ηk−1)
+ηk−1−θk (xk−1 − xk).
+Note also that since ω > 1, we have 0 <
+θk
+ηk−1 =
+tk−2
+tk−1−1 =
+k+1
+k+ω ≤ 1. Moreover, using the
+update rule (16), we can easily show that θk(1−ηk−1)
+ηk−1−θk
+= (ω+1)(k+1)
+ωk+2ω2−1 ≤ ω+1
+ω
+≤ 2 for all k ≥ 0.
+Hence, by convexity of ∥ · ∥2, we have
+∥¯xk+1 − xk + ψηkGxk∥2 ≤
+θk
+ηk−1∥xk − xk−1 + ψηk−1Gxk−1∥2 + 4(ω−1)
+k+ω ∥xk − xk−1∥2.
+Substituting uk := xk − ψηkGxk into (22) and combining the result with the last inequality
+and using max{ 1
+pi − 1 : i ∈ [n]} = 1−pmin
+pmin , we can show that
+Ek
+�
+∥xk+1 − xk + ψηkGxk∥2�
+≤
+θk
+ηk−1 ∥xk − xk−1 + ψηk−1Gxk−1∥2 + 4(ω−1)
+k+ω ∥xk − xk−1∥2
++ ψ2(1−pmin)
+pmin
+∥ηkGxk − θkGxk−1∥2.
+Taking full expectation of both sides of this inequality, we arrive at
+E
+�
+∥xk+1 − xk + ψηkGxk∥2�
+≤
+θk
+ηk−1 E
+�
+∥xk − xk−1 + ψηk−1Gxk−1∥2�
++ 4(ω−1)
+k+ω E
+�
+∥xk − xk−1∥2�
++ ψ2(1−pmin)
+pmin
+E
+�
+∥ηkGxk − θkGxk−1∥2�
+.
+11
+
+Multiplying this inequality by (k + ω)2 and rearranging the result, we obtain
+(k + ω)2E
+�
+∥xk+1 − xk + ψηkGxk∥2�
+≤ (k + ω − 1)2E
+�
+∥xk − xk−1 + ψηk−1Gxk−1∥2�
+− [(ω − 3)(k + ω) + 1] E
+�
+∥xk − xk−1 + ψηk−1Gxk−1∥2�
++ 4(ω − 1)(k + ω)E
+�
+∥xk − xk−1∥2�
++ ψ2(1−pmin)
+pmin
+(k + ω)2E
+�
+∥ηkGxk − θkGxk−1∥2�
+.
+This inequality also implies that limk→∞(k+ω)2E
+�
+∥xk+1 − xk + ψηkGxk∥2�
+exists. Summing
+up this inequality from k := 0 to k := K − 1, then using the first and second lines of (17) and
+x−1 := x0, we get
+(K + ω − 1)2E
+�
+∥xK − xK−1 + ψηK−1GxK−1∥2�
+≤ ψ2η2
+−1(ω − 1)2E
+�
+∥Gx0∥2�
++
+�
+8(ω−1)
+ω
++ ψω2(1−pmin)
+pminC
+�
+E
+�
+V0�
+.
+(23)
+Alternatively, we also have
+�K−1
+k=0 (k + ω)E
+�
+∥xk − xk−1 + ψηk−1Gxk−1∥2�
+≤ E[C0]
+ω−3 ,
+where C0 := ψ2η2
+−1(ω − 1)2E
+�
+∥Gx0∥2�
++
+�
+8(ω−1)
+ω
++ ψω2(1−pmin)
+pminC
+�
+E
+�
+V0�
+. Since E
+�
+V0�
+= V0,
+E
+�
+∥Gx0∥2�
+= ∥Gx0∥2, and η−1 = η0 =
+ω
+ω+1, we obtain C0 as in Theorem 3.1. The last
+inequality and the existence of limk→∞(k + ω + 1)2E
+�
+∥xk+1 − xk + ψηkGxk∥2�
+imply
+limk→∞(k + ω + 1)2E
+�
+∥xk+1 − xk + ψηkGxk∥2�
+= 0.
+(24)
+Next, noting that ηk ≥
+k+ω+1
+k+2ω+2 ≥ 1
+2, we can show that
+ψ2
+4 ∥Gxk−1∥2 ≤ ψ2η2
+k−1∥Gxk−1∥2 ≤ 2∥xk − xk−1∥2 + 2∥xk − xk−1 + ψηk−1Gxk−1∥2.
+(25)
+Therefore, we can easily obtain
+�K−1
+k=0 (k + ω)E
+�
+∥Gxk−1∥2�
+≤
+16
+ψ2ωE
+�
+V0�
++
+8E[C0]
+ψ2(ω−3).
+(26)
+This proves the third line of (17).
+Now, from xk+1 := xk + θk(xk − xk−1) − ψp−1
+ik dk
+[ik] of (ARBC), we have
+∥xk+1 − xk∥2 = θ2
+k∥xk − xk−1∥2 − 2ψθk⟨p−1
+ik dk
+[ik], xk − xk−1⟩ + ψ2∥p−1
+ik dk
+[ik]∥2.
+Taking conditional expectation Ek [·] of this expression and using (11) and θk = γk, we have
+Ek
+�
+∥xk+1 − xk∥2�
+= θ2
+k∥xk − xk−1∥2 − 2ψθk⟨dk, xk − xk−1⟩ + ψ2 �n
+i=1
+1
+pi ∥dk
+i ∥2
+= θ2
+k∥xk − xk−1∥2 + ψ2 �n
+i=1
+1
+pi ∥ηk[Gxk]i − θk[Gxk−1]i∥2
+− 2ψθ2
+k⟨Gxk − Gxk−1, xk − xk−1⟩ − 2ψθk(ηk − θk)⟨Gxk, xk − xk−1⟩.
+12
+
+Utilizing (CP) and the Young inequality into the last expression, we can show that
+Ek
+�
+∥xk+1 − xk∥2�
+≤
+�
+θ2
+k + 2θk(ηk − θk)
+�
+∥xk − xk−1∥2 + ψ2θk(ηk−θk)
+2
+∥Gxk∥2
+− 2ψθ2
+k
+�n
+i=1
+1
+Li ∥[Gxk]i − [Gxk−1]i∥2
++ ψ2 �n
+i=1
+1
+pi ∥ηk[Gxk]i − θk[Gxk−1]i∥2.
+Multiplying this inequality by ω2t2
+k+1 = (k + 2ω + 2)2 and noting that ω2t2
+k+1[θ2
+k + 2θk(ηk −
+θk)] = ω2t2
+k−2ω(k+2ω+1) and ω2t2
+k+1θk(ηk−θk) = ω(k+1), and then taking full expectation
+of the resulting inequality, we obtain
+ω2t2
+k+1E
+�
+∥xk+1 − xk∥2�
+≤ ω2t2
+kE
+�
+∥xk − xk−1∥2�
+− 2ω(k + 2ω + 1)E
+�
+∥xk − xk−1∥2�
++
+ψ2ω2t2
+k+1
+pmin
+E
+�
+∥ηkGxk − θkGxk−1∥2�
++ ψ2ω(k+1)
+2
+E
+�
+∥Gxk∥2�
+− 2ψ(k+1)2
+Lmax
+E
+�
+∥Gxk − Gxk−1∥2�
+,
+where Lmax := max{Li : i ∈ [n]}. This inequality leads to
+T[3] := (k + 2ω + 2)2E
+�
+∥xk+1 − xk∥2�
++ 2ω(k + 2ω + 1)E
+�
+∥xk − xk−1∥2�
++ 2ψ(k+1)2
+Lmax
+E
+�
+∥Gxk − Gxk−1∥2�
+≤ (k + 2ω + 1)2E
+�
+∥xk − xk−1∥2�
++
+ψ2
+pmin(k + 2ω + 2)2E
+�
+∥ηkGxk − θkGxk−1∥2�
++ ψ2ω(k+1)
+2
+∥Gxk∥2.
+Utilizing this inequality, (26), and the second line of (17), we can conclude that limk→∞(k +
+2ω + 2)2E
+�
+∥xk+1 − xk∥2�
+exists. Summing up the inequality T[3] from k := 0 to k := K − 1
+and noting that 4ω2 ≥ (4ω − 1)ω and x0 = x−1, we obtain
+(K + 2ω + 1)2 E
+�
+∥xK − xK−1∥2�
++ 2ω �K−1
+k=0 (k + 2ω + 1)E
+�
+∥xk − xk−1∥2�
++
+2ψ
+Lmax
+�K−1
+k=0 (k + 1)2E
+�
+∥Gxk − Gxk−1∥2�
+≤
+ψ2
+pmin
+�K−1
+k=0 (k + 2ω + 2)2∥ηkGxk − θkGxk−1∥2
++ ψ2ω
+2
+�K−1
+k=0 (k + 1)E
+�
+∥Gxk∥2�
+(17),(26)
+≤
+�
+ψω2
+pminC + 8
+�
+E
+�
+V0�
++ 4ωE[C0]
+(ω−3) .
+(27)
+This inequality shows that E
+�
+∥xk+1 − xk∥2�
+= O
+�
+1/k2�
+as in (18). Combining the existence
+of limk→∞(k + 2ω + 2)2E
+�
+∥xk+1 − xk∥2�
+and �k
+k=0(k + ω + 1)E
+�
+∥xk − xk−1∥2�
+< +∞, we
+obtain limk→∞(k + 2ω + 2)2E
+�
+∥xk+1 − xk∥
+�2 = 0, which proves the o-rate in (18).
+Finally, from (23), (25), and (27), we have
+(k + ω)2E
+�
+∥Gxk∥2�
+(25)
+≤
+8(k+ω)2
+ψ2
+E
+�
+∥xk+1 − xk∥2�
++ 8(k+ω)2
+ψ2
+E
+�
+∥xk+1 − xk + ψηkGxk∥2�
+(23),(27)
+≤
+8
+ψ2
+�
+ψω2
+pminC + 8(ω−1)
+ω
++ ψω2(1−pmin)
+pminC
++ 8
+�
+E
+�
+V0�
++ 32ωE[C0]
+ψ2(ω−3) .
+This inequality shows that E
+�
+∥Gxk∥2�
+= O
+�
+1/k2�
+. The o-rate E
+�
+∥Gxk∥2�
+= o
+� 1
+k2
+�
+immedi-
+ately follows from the first line of this inequality, the first line of (18), and (24).
+13
+
+Application to fixed-point problems.
+Let us apply (ARBC) to approximate a fixed-
+point x⋆ of a nonexpansive operator T : Rp → Rp, i.e. x⋆ = Tx⋆. As mentioned earlier, if we
+define G := I − T, then G is firmly nonexpansive, or equivalently, 1-co-coercive. Moreover,
+x⋆ is a fixed-point of T iff Gx⋆ = 0.
+Therefore, we can apply (ARBC) to solve Gx⋆ =
+0. For simplicity of presentation, we assume that ik is generated uniformly randomly, i.e.
+Prob (ik = i) = 1
+n for all i ∈ [n]. In this case, (ARBC) reduces to
+xk+1
+i
+:=
+�
+xk
+i + ˆηkxk
+i − ˆγkxk−1
+i
++ ˆψ
+�
+ηk[Txk]ik) − γk[Txk−1]ik
+�
+, if i = ik,
+xk
+i + θk(xk
+i − xk−1
+i
+),
+otherwise,
+(28)
+where ˆψ := nψ, ˆηk := θk − ˆψηk, and ˆγk := θk − ˆψγk. Clearly, our new scheme (28) is different
+from existing methods for approximating a fixed-point x⋆ of a non-expansive operator T. The
+convergence rates of the residual E
+�
+∥xk − Txk∥2�
+and E
+�
+∥xk+1 − xk∥2�
+of (28) are guaranteed
+by Theorem 3.1. However, we omit them here to avoid repetition.
+3.2
+Practical variant of ARBC
+Let us derive an alternative form of (ARBC) so that it is easier to implement in practice. First,
+from (ARBC), we have xk+1 − xk = θk(xk − xk−1) −
+ψ
+pik dk
+[ik], where dk := ηkGxk − γkGxk−1.
+Let us assume that θk =
+τk+1
+τk
+for a given positive sequence {τk}.
+This relation leads to
+τk+1 = τkθk. Moreover, we can write (ARBC) as
+1
+τk+1(xk+1 − xk) = 1
+τk (xk − xk−1) −
+ψ
+pik τk+1dk
+[ik].
+Now, if we introduce wk := 1
+τk (xk − xk−1), then (ARBC) can be rewritten as
+xk := xk−1 + τkwk
+and
+wk+1 := wk −
+ψ
+pik τk+1dk
+[ik].
+By induction, we can show that xk = x0 + �k
+i=1 τiwi. Let us express this representation as
+xk = x0 − τ1(w2 − w1) − (τ1 + τ2)(w3 − w2) − (τ1 + τ2 + τ3)(w4 − w3)
+− · · · − (τ1 + · · · + τk−1)(wk − wk−1) + (τ1 + · · · + τk−1 + τk)wk.
+Therefore, if we define ck := �k
+i=1 τi with a convention that c0 := 0, and ∆wk := wk+1 − wk,
+then we can write xk as
+xk = x0 − �k−1
+i=1 ci∆wi + ckwk.
+If we introduce zk := x0 − �k−1
+i=1 ci∆wi, then we get zk = zk−1 − ck−1∆wk−1 with z0 := x0,
+and hence xk = zk + ckwk. Therefore, we can summarize our derivation above as
+
+
+
+
+
+
+
+
+
+wk+1 := wk −
+ψ
+pikτk+1 dk
+ik,
+zk+1
+:= zk − ck∆wk = zk +
+ckψ
+pikτk+1 dk
+ik
+xk+1
+= zk+1 + ck+1wk+1.
+14
+
+Eliminating xk and xk−1 from the last scheme, we can write (ARBC) equivalently to
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+dk
+i
+:= ηk[G(zk + ckwk)]i − γk[G(zk−1 + ck−1wk−1)]i,
+if i = ik,
+wk+1
+i
+:=
+� wk
+i −
+ψ
+piτk+1dk
+i , if i = ik,
+wk
+i ,
+otherwise,
+zk+1
+i
+:=
+� zk
+i +
+ψck
+piτk+1 dk
+i , if i = ik,
+zk
+i ,
+otherwise.
+(29)
+Here, x0 ∈ Rp is given, z0 = z−1 := x0, and w0 = w−1 := 0. Moreover, the parameters τk
+and ck are respectively updated as
+τk+1 := τkθk
+and
+ck := ck−1 + τk,
+(30)
+where c0 = c−1 := 0 and τ0 := 1.
+The scheme (29) is though different from accelerated randomized block-coordinate meth-
+ods for convex optimization such as [1, 18, 36, 49], it has some common features as those
+methods such as the block-coordinate evaluations of G at zk + ckwk and zk−1 + ck−1wk−1,
+respectively. One notable property of (29) is that it does not require full dimensional updates
+of wk and zk. Note that one can also extend our method (ARBC) (or equivalently, (29)) to up-
+date multiple blocks by randomly choosing a subset Sk ⊂ [n] such that Prob (i ∈ Sk) = pi > 0
+for i ∈ [n].
+4
+Applications to Monotone Inclusions
+In this section, we derive two variants of (ARBC) to approximate a solution of the following
+monotone inclusion involving the sum of two monotone operators:
+Find x⋆ ∈ Rp such that:
+0 ∈ Ax⋆ + Bx⋆,
+(MI)
+where A, B : Rp ⇒ Rp are maximally monotone operators. Moreover, we assume that Ax =
+[A1x1, A2x2, · · · , Anxn] is a separable operator compounded by n independent blocks.
+We apply (ARBC) to two common methods for solving (MI): the forward-backward split-
+ting (FBS) and the Douglas-Rachford (splitting (DRS) schemes.
+4.1
+ARBC Forward-Backward Splitting Method
+Let us first reformulate (MI) equivalently to (CE) by using the following forward-backward
+(FB) residual mapping:
+Gβx := β−1(x − JβA(x − βBx)),
+(31)
+where β > 0 is given and JβA := (I + βA)−1 is the resolvent of βA. As shown in [48], if B
+is 1
+L-co-coercive and 0 < β < 4
+L, then Gβ(·) defined by (31) is β(4−βL)
+4
+-co-coercive. Moreover,
+x⋆ ∈ zer(A + B) is a solution of (MI) iff Gβx⋆ = 0. The latter is exactly a special case of
+(CE). If dom(B) = Rp, then Gβ satisfies Assumption 3.1 with Li = β(4−βL)
+4
+for i ∈ [n]. Note
+that we can extend our results to the case B is L−1-block coordinate-wise co-coercive as in
+(CP). However, we omit this extension here.
+15
+
+Our goal is to specify (ARBC) to solve Gβx⋆ = 0. In this case, we obtain the following
+variant of (ARBC):
+xk+1 := xk + θk(xk − xk−1) −
+ψ
+pik
+�
+ηkGβ
+[ik]xk − γkGβ
+[ik]xk−1�
+,
+where θk, ψ, ηk, and γk are updated as in (ARBC). Clearly, by taking into account the
+separable structure of A and using (31), we can explicitly write the block-coordinate of Gβx
+as
+[Gβx]i = 1
+β(xi − JβAi(xi − β[Bx]i)).
+Combining the last two expressions, we can write the new variant of (ARBC) as follows:
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ˆdk−1
+i
+:= xk−1
+i
+− JβAi(xk−1
+i
+− β[Bxk−1]i),
+if i = ik,
+dk
+i
+:= xk
+i − JβAi(xk
+i − β[Bxk]i),
+if i = ik,
+xk+1
+i
+:=
+
+
+
+xk
+i + θk(xk
+i − xk−1
+i
+) −
+ψ
+βpi
+�
+ηkdk
+i − γk ˆdk−1
+i
+�
+, if i = ik,
+xk
+i + θk(xk
+i − xk−1
+i
+),
+otherwise,
+(32)
+where x0 ∈ Rp is a given initial point, x−1 := x0, and ik ∈ [n] is randomly generated based
+on the probability law (5), i.e. Prob (i = ik) = pi for i ∈ [n].
+The scheme (32) requires two block-coordinate evaluations [Bxk−1]i and [Bxk]i of B and
+two evaluations of JβAi at each iteration k. Therefore, it essentially costs as twice as existing
+standard block-coordinate FBS methods. However, its convergence rate is significantly faster
+than those standard block-coordinate FBS methods, typically O
+�
+1/k2�
+compared to O (1/k).
+Finally, we specify Theorem 3.1 (without proof) to obtain convergence results of (32).
+Corollary 4.1. Let B be 1
+L-co-coercive on Rp, A be maximally monotone, and zer(A+B) ̸= ∅
+in (MI). Let {xk} be generated by (32) using pi :=
+1
+n (∀i ∈ [n]). For given ω > 3 and
+0 < β < 4
+L, we choose 0 < ψ <
+8
+nβ(4−βL) and update θk, ηk, and γk as in (16). Then, both
+quantities E
+�
+∥Gβxk∥2�
+and E
+�
+∥xk+1 − xk∥2�
+simultaneously achieve O
+�
+1/k2�
+and o
+�
+1/k2�
+convergence rates.
+In fact, if {xk} is generated by (32), then the bounds in (17) of Theorem 3.1 still hold for
+{xk} and Gβxk defined by (31). However, we only state the convergence rates in Corollary
+4.1.
+4.2
+ARBC Douglas-Rachford Splitting Method
+We consider the case B in (MI) is just maximally monotone. In this case, we consider the DR
+residual mapping of (MI) defined as follows (see also [48]):
+Eβu := 1
+β (JβBu − JβA(2JβBu − u)) ,
+(33)
+where β > 0 is given, and JβA and JβB are the resolvents of βA and βB, respectively. As
+shown in [48], Eβ(·) is β-co-coercive and dom(Eβ) = Rp. Moreover, x⋆ ∈ zer(A + B) is a
+solution of (MI) if and only if there exists u⋆ ∈ Rp such that Eβu⋆ = 0 and x⋆ = JβBu⋆.
+16
+
+Now, if we directly apply (ARBC) to solve Eβu⋆ = 0, then by exploiting the separable
+structure of A, we obtain the following scheme for solving (MI):
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ˆvk−1
+i
+:= [JβBuk−1]i,
+if i = ik,
+vk
+i
+:= [JβBuk]i,
+if i = ik,
+ˆdk−1
+i
+:= ˆvk−1
+i
+− JβAi(2ˆvk−1
+i
+− uk−1
+i
+),
+if i = ik,
+dk
+i
+:= vk
+i − JβAi(2vk
+i − uk
+i ),
+if i = ik,
+uk+1
+i
+:=
+
+
+
+uk
+i + θk(uk
+i − uk−1
+i
+) − ψ
+pi
+�
+ηkdk
+i − γk ˆdk−1
+i
+�
+, if i = ik,
+uk
+i + θk(uk
+i − uk−1
+i
+),
+otherwise,
+(34)
+where u0 ∈ Rp is given, u−1 := u0, and ik ∈ [n] is randomly generated based on (5).
+Unlike (32), which operates directly on the sequence
+�
+xk�
+, (34) generates an intermediate
+sequence {uk}. To recover an approximate solution xk of (MI), we can compute xk := JβBuk
+at the end of the algorithm. Again, our new scheme (34) is very different from existing ones
+in the literature, including [11]. Note that (34) requires two block-coordinate evaluations
+[JβBxk]i and [JβBxk−1]i of JβB, and two evaluations of JβAi at each iteration k. Hence, its
+per-iteration complexity costs as twice as the method in [11]. However, we believe that the
+convergence rate of (34) is significantly faster than the one in [11].
+Finally, similar to Corollary 4.1, we specify Theorem 3.1 to obtain convergence of (34).
+Corollary 4.2. Assume that zer(A + B) ̸= ∅ and both A and B in (MI) are maximally
+monotone. Let {uk} be generated by (34) using pi := 1
+n for all i ∈ [n]. For given ω > 3,
+β > 0, and 0 < ψ < 2β
+n , we update θk, ηk, and γk as in (16). Then, both E
+�
+∥Eβuk∥2�
+and E
+�
+∥uk+1 − uk∥2�
+simultaneously achieve O
+�
+1/k2�
+and o
+�
+1/k2�
+convergence rates. If, in
+addition, B is single-valued and xk := JβBuk, then both E
+�
+∥Gβxk∥2�
+and E
+�
+∥xk+1 − xk∥2�
+simultaneously achieve O
+�
+1/k2�
+and o
+�
+1/k2�
+convergence rates, where Gβxk is given by (31).
+This corollary is a direct consequence of Theorem 3.1, and we omit its proof. The last
+conclusion of Corollary 4.2 can easily be obtained by using the relation between Eβu and Gβu
+as stated in [48, Lemma 2].
+5
+Application to Finite-Sum Monotone Inclusions
+Many machine learning applications and optimization models over networks, including fed-
+erated learning, can be formulated into the following finite-sum monotone inclusion [13, 40]:
+Find x⋆ ∈ dom(A) ∩ dom(B) such that
+0 ∈ 1
+n
+n
+�
+i=1
+Aix⋆ + Bx⋆ ≡ Ax⋆ + Bx⋆,
+(35)
+where Ai : Rp ⇒ Rp (∀i ∈ [n]) are maximally monotone and B : Rp ⇒ Rp is also maximally
+monotone. Here, we also assume that zer(A + B) ̸= ∅. Note that A := 1
+n
+�n
+i=1 Ai in (35) is
+the average of a finite-sum operator, and it is different from the block separable operator in
+(MI). Therefore, we cannot directly apply the methods in Section 4 to solve (35).
+17
+
+One important special case of (35) is the optimality condition of the following finite-sum
+convex minimization problem which is ubiquitous in machine learning and statistical learning:
+min
+x∈Rp
+�
+F(x) := 1
+n
+n
+�
+i=1
+fi(x) + g(x)
+�
+,
+(36)
+where fi : Rp → R ∪ {+∞} and g : Rp → R ∪ {+∞} are proper, closed, and convex. The
+optimality condition of (36) can be written as 0 ∈ 1
+n
+�n
+i=1 ∂fi(x⋆) + ∂g(x⋆), which is covered
+by (35) by setting Ai := ∂fi and B := ∂g.
+To develop a new variant of (ARBC) for solving (35), we first reformulate (35) into (MI)
+by duplicating the variable x as x := [x1, x2, · · · , xn], where xi ∈ Rp for all i ∈ [n]. Then, we
+can reformulate (35) into the following monotone inclusion:
+0 ∈ Ax⋆ + Bx⋆ + ∂δL(x⋆), where Ax := [A1x1, · · · , Anxn],
+Bx := [nBx1, 0, · · · , 0], (37)
+and ∂δL is the subdifferential of the indicator of the linear subspace L := {x = [x1, · · · , xn] ∈
+Rnp : xi = x1, ∀i ∈ [n]}. It is obvious to show that x⋆ is a solution of (35) if and only if
+x⋆ = [x⋆, · · · , x⋆] solves (37), see, e.g., [51]. Moreover, A and B in (37) are separable.
+Let us apply the ARBC DR splitting scheme (34) to solve (37). Then we use the interpre-
+tation in Subsection 3.2 to obtain a practical variant. Here, we view A as A and B + ∂δL as
+B in (MI). Let us first compute the resolvent of β(B + ∂δL) at uk. This requires solving
+�
+0 ∈ nβBu1 + βs1 + u1 − uk
+1,
+0 = βsi + ui − uk
+i ,
+i = 2, · · · , n,
+(38)
+where s := [s1, · · · , sn] ∈ ∂δL(u) ≡ L⊥ := {s := [s1, · · · , sn] : �n
+i=1 si = 0}. The last line of
+(38) leads to ui = uk
+i − βzi if ui = u1 for i = 2, · · · , n. Therefore, we obtain
+(n − 1)u1 =
+n
+�
+i=2
+uk
+i − β
+n
+�
+i=2
+si =
+n
+�
+i=2
+uk
+i − β
+n
+�
+i=1
+si + βs1 =
+n
+�
+i=2
+uk
+i + βs1,
+due to the fact that �n
+i=1 si = 0. This equation implies that u1 + βs1 = nu1 − �n
+i=2 uk
+i . Sub-
+stituting this expression into the first line of (38), we get 0 ∈ nβBu1+nu1−�n
+i=1 uk
+i , or equiv-
+alently, 0 ∈ βBu1 + u1 − 1
+n
+�n
+i=1 uk
+i . Solving this inclusion, we obtain u1 = JβB
+� 1
+n
+�n
+i=1 uk
+i
+�
+.
+Let us defined ˆuk := JβB
+� 1
+n
+�n
+i=1 uk
+i
+�
+. Then, we have Jβ(B+∂δL)uk = [ˆuk, · · · , ˆuk]. Conse-
+quently, for any i ∈ [n], we obtain [Jβ(B+∂δL)uk]i = ˆuk.
+Next, we use the trick in Subsection 3.2 to eliminate uk
+i in (34). Since uk
+i = zk
+i + ckwk
+i ,
+we have ¯uk := 1
+n
+�n
+i=1 uk
+i = 1
+n
+�n
+i=1(zk
+i + ckwk
+i ) = ¯zk + ck ¯wk, where ¯zk := 1
+n
+�n
+i=1 zk
+i and
+¯wk := 1
+n
+�n
+i=1 wk
+i . However, at each iteration k, only wk
+ik and zk
+ik are updated, we have
+�
+¯zk+1 := 1
+n
+�n
+i=1 zk+1
+i
+= 1
+n
+�n
+i=1 zk
+i + 1
+n(zk+1
+ik
+− zk
+ik) = ¯zk + 1
+n∆zk+1
+ik
+,
+¯wk+1 := 1
+n
+�n
+i=1 wk+1
+i
+= 1
+n
+�n
+i=1 wk
+i + 1
+n(wk+1
+ik
+− wk
+ik) = ¯wk + 1
+n∆wk+1
+ik
+,
+where ∆zk+1
+ik
+:= zk+1
+ik
+− zk
+ik and ∆wk+1
+ik
+:= wk+1
+ik
+− wk
+ik.
+Now, we are ready to specify (34) to solve (37) as in Algorithm 1.
+18
+
+Algorithm 1 (Accelerated Federated Douglas-Rachford Algorithm (AccFedDR))
+1: Initialization: Input an initial point u0 ∈ Rp and set c0 := c−1 := 0 and τ0 := 1.
+2:
+Initialize each user i with z0
+i = z−1
+i
+:= u0 and w0
+i = w−1
+i
+= 0 for i ∈ [n].
+3:
+Initialize sever with ˆu0 = ˆu−1 := u0, ¯z0 := 0, and ¯w0 := 0.
+4: For k := 0, · · · , kmax do
+5:
+Sample an active user ik ∈ [n] following the probability law (5).
+6:
+[Communication] Server sends ˆuk and ˆuk−1 to user ik.
+7:
+[Local update] User ik updates its iterates wk+1
+ik
+and zk+1
+ik
+as
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ˆdk−1
+ik
+:= ˆuk−1 − JβAik (2ˆuk−1 − zk−1
+ik
+− ck−1wk−1
+ik
+),
+dk
+ik
+:= ˆuk − JβAik (2ˆuk − zk
+ik − ckwk
+ik),
+wk+1
+ik
+:= wk
+ik −
+ψ
+pik τk+1 (ηkdk
+ik − γk ˆdk−1
+ik
+),
+zk+1
+ik
+:= zk
+ik +
+ψck
+pikτk+1 (ηkdk
+ik − γk ˆdk−1
+ik
+).
+(39)
+8:
+[Communication] User ik sends ∆wk+1
+ik
+:= wk+1
+ik
+−wk
+ik and ∆zk+1
+ik
+:= zk+1
+ik
+−zk
+ik to server.
+9:
+[Server update] Server updates
+¯wk+1 := ¯wk + 1
+n∆wk+1
+ik
+,
+¯zk+1 := ¯zk + 1
+n∆zk+1
+ik
+, and ˆuk+1 := JβB(¯zk+1 + ck+1 ¯wk+1).
+10: End For
+Let us abbreviate Algorithm 1 by AccFedDR. Note that the parameters are updated as in
+(16) and (30). Clearly, AccFedDR is still synchronous, but it only requires the participation
+of one user ik at each communication round k. This scheme is also similar to SAGA [15] and
+a SAGA variant for co-coercive equations in [13]. However, our AccFedDR can solve a more
+general class of problems described by (35), where A is not necessarily co-coercive as in [13].
+This algorithm can also be applied to federated learning, see, e.g., [22, 26, 32, 33].
+To prove convergence of Algorithm 1, let us define the following residual operator:
+�
+ˆu
+:= JβB
+� 1
+n
+�n
+i=1 ui
+�
+,
+Eβu := 1
+β[ˆu − JβA1(2ˆu − u1), · · · , ˆu − JβAn(2ˆu − un)].
+(40)
+One can easily show that if Eβu⋆ = 0, then ˆu⋆ = JβB
+� 1
+n
+�n
+i=1 u⋆
+i
+�
+solves (35). Now, we can
+specify the convergence of AccFedDR as a consequence of Theorem 3.1.
+Corollary 5.1. Let Ai (i ∈ [n]) and B in (35) be maximally monotone and zer(A + B) ̸= ∅.
+Let {wk
+i } and {zk
+i } be generated by AccFedDR. Let uk := [uk
+1, · · · , uk
+n] with uk
+i := zk
+i + ckwk
+i
+for all i ∈ [n] and Eβu be defined by (40). For given ω > 3, β > 0, and 0 < ψ < 2βpmin, we
+update θk, ηk, and γk as in (16). Then, we obtain the following bounds:
+�+∞
+k=0(k + ω + 1)E
+�
+∥Eβuk−1∥2�
+< +∞,
+�+∞
+k=0(k + ω)E
+�
+∥uk − uk−1∥2�
+< +∞,
+�+∞
+k=0(k + 1)2E
+�
+∥Eβuk − Eβuk−1∥2�
+< +∞.
+(41)
+19
+
+Moreover, the following statements also hold:
+�
+E
+�
+∥uk+1 − uk∥2�
+= O
+� 1
+k2
+�
+and
+E
+�
+∥uk+1 − uk∥2�
+= o
+� 1
+k2
+�
+,
+E
+�
+∥Eβuk∥2�
+= O
+� 1
+k2
+�
+and
+E
+�
+∥Eβuk∥2�
+= o
+� 1
+k2
+�
+.
+(42)
+Note that Corollary 5.1 only shows convergence on {uk}. To form an approximate solution
+¯xk of (35), we simply compute ¯xk := JβB
+� 1
+n
+�n
+i=1 uk
+i
+�
+. Clearly, we can also easily show that
+E
+�
+∥¯xk − ¯xk−1∥2�
+= O
+� 1
+k2
+�
+and E
+�
+∥¯xk − ¯xk−1∥2�
+= o
+� 1
+k2
+�
+by the nonexpansiveness of JβB.
+Remark 5.1. Since our model (35) is more general than that of [13], our AccFedDR al-
+gorithm developed in this section can be applied to solve special cases as discussed in [13].
+However, we omit the details of these applications here to avoid repetition.
+6
+Concluding Remarks
+We have developed a novel accelerated randomized block-coordinate method for solving a co-
+coercive equation of the form (CE). The new algorithm achieves O
+�
+1/k2�
+and even o
+�
+1/k2�
+convergence rates on the squared norm of the underlying operator G and some other quantities
+in expectation. We have also derived a practical variant and investigated three applications
+of our method for more general problems to cope with broader classes of applications. Several
+research questions remain open to us. Firstly, how to develop an accelerated randomized block-
+coordinate method for (CE) under weaker assumptions: monotone and Lipschitz continuous?
+For example, how to extend our method to extra-anchored gradient schemes [54] or their
+variants [25, 50]? Secondly, how to extend such a type of methods to (MI) without the co-
+coerciveness of B? Thirdly, how to develop asynchronous variants of our method, including
+the variant of Algorithm 1. In addition, several practical and implementation aspects of our
+methods as well as numerical verification are still left out in this paper.
+We leave these
+research questions for our future research.
+References
+[1] A. Alacaoglu, Q. Tran-Dinh, O. Fercoq, and V. Cevher.
+Smooth Primal-Dual Coor-
+dinate Descent Algorithms for Nonsmooth Convex Optimization. Advances in Neural
+Information Processing Systems (NIPS), pages 1–9, 2017.
+[2] H. Attouch and A. Cabot.
+Convergence of a relaxed inertial proximal algorithm for
+maximally monotone operators. Math. Program., 184(1):243–287, 2020.
+[3] H. Attouch and J. Fadili. From the Ravine method to the Nesterov method and vice
+versa: a dynamical system perspective. arXiv preprint arXiv:2201.11643, 2022.
+[4] A Auslender. Méthodes numériques pour la décomposition et la minimisation de fonctions
+non différentiables. Numerische Mathematik, 18(3):213–223, 1971.
+[5] H. H. Bauschke and P. Combettes. Convex analysis and monotone operators theory in
+Hilbert spaces. Springer-Verlag, 2nd edition, 2017.
+20
+
+[6] Amir Beck, Edouard Pauwels, and Shoham Sabach. The cyclic block conditional gradient
+method for convex optimization problems. SIAM Journal on Optimization, 25(4):2024–
+2049, 2015.
+[7] R. I. Bot, E. R. Csetnek, and D. K. Nguyen. Fast OGDA in continuous and discrete
+time. arXiv preprint arXiv:2203.10947, 2022.
+[8] L. Bottou, F. E. Curtis, and J. Nocedal. Optimization Methods for Large-Scale Machine
+Learning. SIAM Rev., 60(2):223–311, 2018.
+[9] R. S. Burachik and A. Iusem.
+Set-Valued Mappings and Enlargements of Monotone
+Operators. New York: Springer, 2008.
+[10] Y. Chen, G. Lan, and Y. Ouyang. Accelerated schemes for a class of variational inequal-
+ities. Math. Program., 165(1):113–149, 2017.
+[11] P. L. Combettes and J.-C. Pesquet. Stochastic quasi-Fejér block-coordinate fixed point
+iterations with random sweeping. SIAM J. Optim., 25(2):1221–1248, 2015.
+[12] P. L. Combettes and V. R. Wajs. Signal recovery by proximal forward-backward splitting.
+Multiscale Model. Simul., 4:1168–1200, 2005.
+[13] D. Davis. Variance reduction for root-finding problems. Math. Program., pages 1–36,
+2022.
+[14] D. Davis and W. Yin. A three-operator splitting scheme and its optimization applications.
+Set-valued and Variational Analysis, 25(4):829–858, 2017.
+[15] A. Defazio, F. Bach, and S. Lacoste-Julien. SAGA: A fast incremental gradient method
+with support for non-strongly convex composite objectives. In Advances in Neural Infor-
+mation Processing Systems (NIPS), pages 1646–1654, 2014.
+[16] J. Diakonikolas. Halpern iteration for near-optimal and parameter-free monotone inclu-
+sion and strong solutions to variational inequalities. In Conference on Learning Theory,
+pages 1428–1451. PMLR, 2020.
+[17] F. Facchinei and J.-S. Pang. Finite-dimensional variational inequalities and complemen-
+tarity problems, volume 1-2. Springer-Verlag, 2003.
+[18] Olivier Fercoq and Peter Richtárik. Accelerated, parallel, and proximal coordinate de-
+scent. SIAM J. Optim., 25(4):1997–2023, 2015.
+[19] B. Halpern. Fixed points of nonexpanding maps. Bull. Am. Math. Soc., 73(6):957–961,
+1967.
+[20] D. Kim. Accelerated proximal point method for maximally monotone operators. Math.
+Program., pages 1–31, 2021.
+[21] D. Kim and J. A. Fessler. Optimized first-order methods for smooth convex minimization.
+Math. Program., 159(1-2):81–107, 2016.
+21
+
+[22] J. Konečn`y, H. B. McMahan, D. Ramage, and P. Richtárik. Federated optimization:
+Distributed machine learning for on-device intelligence. arXiv preprint arXiv:1610.02527,
+2016.
+[23] G. Lan. First-order and Stochastic Optimization Methods for Machine Learning. Springer,
+2020.
+[24] P. Latafat, A. Themelis, and P. Patrinos. Block-coordinate and incremental aggregated
+proximal gradient methods for nonsmooth nonconvex problems. Math. Program., pages
+1–30, 2019.
+[25] S. Lee and D. Kim.
+Fast extra gradient methods for smooth structured nonconvex-
+nonconcave minimax problems. Thirty-fifth Conference on Neural Information Processing
+Systems (NeurIPs2021), 2021.
+[26] T. Li, A. K. Sahu, A. Talwalkar, and V. Smith. Federated learning: Challenges, methods,
+and future directions. IEEE Signal Processing Magazine, 37(3):50–60, 2020.
+[27] F. Lieder.
+On the convergence rate of the halpern-iteration.
+Optimization Letters,
+15(2):405–418, 2021.
+[28] P. L. Lions and B. Mercier. Splitting algorithms for the sum of two nonlinear operators.
+SIAM J. Num. Anal., 16:964–979, 1979.
+[29] P.-E. Maingé.
+Accelerated proximal algorithms with a correction term for monotone
+inclusions. Applied Mathematics & Optimization, 84(2):2027–2061, 2021.
+[30] P. E. Maingé. Fast convergence of generalized forward-backward algorithms for structured
+monotone inclusions. arXiv preprint arXiv:2107.10107, 2021.
+[31] Y. Malitsky. Projected reflected gradient methods for monotone variational inequalities.
+SIAM J. Optim., 25(1):502–520, 2015.
+[32] B. McMahan and D. Ramage. Federated learning: Collaborative machine learning with-
+out centralized training data, Jul 2017.
+[33] H Brendan McMahan et al. Advances and open problems in federated learning. Founda-
+tions and Trends® in Machine Learning, 14(1), 2021.
+[34] Y. Nesterov. A method for unconstrained convex minimization problem with the rate of
+convergence O(1/k2). Doklady AN SSSR, 269:543–547, 1983. Translated as Soviet Math.
+Dokl.
+[35] Y. Nesterov. Introductory lectures on convex optimization: A basic course, volume 87 of
+Applied Optimization. Kluwer Academic Publishers, 2004.
+[36] Y. Nesterov. Efficiency of coordinate descent methods on huge-scale optimization prob-
+lems. SIAM J. Optim., 22(2):341–362, 2012.
+22
+
+[37] Y. Nesterov and S. U. Stich. Efficiency of the accelerated coordinate descent method on
+structured optimization problems. SIAM J. Optim., 27(1):110–123, 2017.
+[38] James M. Ortega and Werner C. Rheinboldt. Iterative solution of nonlinear equations
+in several variables. Society for Industrial and Applied Mathematics, Philadelphia, PA,
+USA, 2000.
+[39] Y. Ouyang and Y. Xu.
+Lower complexity bounds of first-order methods for convex-
+concave bilinear saddle-point problems. Math. Program., online first:1–35, 2019.
+[40] Z. Peng, Y. Xu, M. Yan, and W. Yin. ARock: an algorithmic framework for asynchronous
+parallel coordinate updates. SIAM J. Scientific Comput., 38(5):2851–2879, 2016.
+[41] R. R. Phelps. Convex functions, monotone operators and differentiability, volume 1364.
+Springer, 2009.
+[42] L. D. Popov. A modification of the Arrow-Hurwicz method for search of saddle points.
+Math. notes of the Academy of Sciences of the USSR, 28(5):845–848, 1980.
+[43] P. Richtárik and M. Takáč. Parallel coordinate descent methods for big data optimization.
+Math. Program., 156(1-2):433–484, 2016.
+[44] R. Rockafellar and R. Wets. Variational Analysis, volume 317. Springer, 2004.
+[45] R.T. Rockafellar. Monotone operators and the proximal point algorithm. SIAM J. Con-
+trol Optim., 14:877–898, 1976.
+[46] E. K. Ryu and S. Boyd. Primer on monotone operator methods. Appl. Comput. Math,
+15(1):3–43, 2016.
+[47] S. Sra, S. Nowozin, and S. J. Wright. Optimization for Machine Learning. MIT Press,
+2012.
+[48] Q. Tran-Dinh.
+The connection between Nesterov’s accelerated methods and Halpern
+fixed-point iterations. arXiv preprint arXiv:2203.04869, 2022.
+[49] Q. Tran-Dinh and D. Liu. A new randomized primal-dual algorithm for convex opti-
+mization with optimal last iterate rates. Optimization Methods & Software), pages 1–34
+(online first), 2022.
+[50] Q. Tran-Dinh and Y. Luo. Halpern-type accelerated and splitting algorithms for mono-
+tone inclusions. arXiv preprint arXiv:2110.08150, 2021.
+[51] Q. Tran-Dinh, N. H. Pham, D. T. Phan, and L. M. Nguyen. FedDR–Randomized Douglas-
+Rachford splitting algorithms for nonconvex federated composite optimization. NeurIPs
+2021, pages 1–39, 2021.
+[52] P. Tseng. A modified forward-backward splitting method for maximal monotone map-
+pings. SIAM J. Control and Optim., 38(2):431–446, 2000.
+23
+
+[53] Stephen J Wright. Coordinate descent algorithms. Math. Program., 151(1):3–34, 2015.
+[54] T. Yoon and E. K. Ryu. Accelerated algorithms for smooth convex-concave minimax
+problems with O(1/k2) rate on squared gradient norm. In International Conference on
+Machine Learning, pages 12098–12109. PMLR, 2021.
+24
+
diff --git a/DtE1T4oBgHgl3EQfWQTV/content/tmp_files/load_file.txt b/DtE1T4oBgHgl3EQfWQTV/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2d6f93724011b76d552786201f336f9d13eb9c35
--- /dev/null
+++ b/DtE1T4oBgHgl3EQfWQTV/content/tmp_files/load_file.txt
@@ -0,0 +1,830 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf,len=829
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='03113v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='OC]  8 Jan 2023  Accelerated Randomized Block-Coordinate Algorithms for  Co-coercive Equations and Applications  Quoc Tran-Dinh  Department of Statistics and Operations Research  The University of North Carolina at Chapel Hill  318 Hanes Hall, UNC-Chapel Hill, NC 27599-3260.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Email: quoctd@email.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='unc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  July 2022  Abstract  In this paper, we develop an accelerated randomized block-coordinate algorithm to  approximate a solution of a co-coercive equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Such an equation plays a central role  in optimization and related fields and covers many mathematical models as special cases,  including convex optimization, convex-concave minimax, and variational inequality prob-  lems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Our algorithm relies on a recent Nesterov’s accelerated interpretation of the Halpern  fixed-point iteration in [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  We establish that the new algorithm achieves O  �  1/k2� convergence rate on E  �  ∥Gxk∥2�  through the last-iterate, where G is the underlying co-  coercive operator, E [·] is the expectation, and k is the iteration counter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' This rate is signif-  icantly faster than O (1/k) rates in standard forward or gradient-based methods from the  literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' We also prove o  �  1/k2�  rates on both E  �  ∥Gxk∥2�  and E  �  ∥xk+1 − xk∥2�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Next,  we apply our method to derive two accelerated randomized block coordinate variants  of the forward-backward splitting and Douglas-Rachford splitting schemes, respectively  for solving a monotone inclusion involving the sum of two operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' As a byproduct,  these variants also have faster convergence rates than their non-accelerated counterparts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Finally, we apply our scheme to a finite-sum monotone inclusion that has various appli-  cations in machine learning and statistical learning, including federated learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' As a  result, we obtain a novel federated learning-type algorithm with fast and provable con-  vergence rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  1  Introduction  Monotone inclusion provides a powerful tool to model several problems in optimization,  nonlinear analysis, mechanics, and machine learning, among many other areas, see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=',  [5, 9, 17, 41, 44, 45, 46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Though it is a classical mathematical tool [5, 28, 45, 46], there  has been a notable research surge of this topic in the last few years due to new applications  in modern machine learning and data science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Methods for solving monotone inclusions often  generalize existing optimization algorithms, and exploit structures of the underlying operators  1  such as splitting property.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Classical methods include gradient or forward, extragradient, past-  extragradient, proximal-point, forward-backward splitting, forward-backward-forward split-  ting, Douglas-Rachford splitting, projective splitting methods, and their variants, see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=',  [5, 12, 14, 28, 17, 31, 42, 52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' However, developing accelerated [block-]coordinate methods  with fast convergence rates for lare-scale monotone inclusions is still a challenging task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  In this paper, we focus on a very basic model of monotone inclusions, which is called a  co-coercive equation of the form:  Find x⋆ ∈ Rp such that:  Gx⋆ = 0,  (CE)  where G : Rp → Rp is a co-coercive operator (see Section 2 for definition).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' For our convenience,  we assume that the solution set zer(G) := G−1(0) = {x⋆ ∈ Rp : Gx⋆ = 0} of (CE) is nonempty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  The co-coercive equation (CE) though looks simple, it is equivalent to the problem of  finding a fixed-point x⋆ of a nonexpansive operator T := I − G, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' x⋆ = Tx⋆, where I is the  identity operator (see [5]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Therefore, it covers many fundamental problems in different fields  by appropriately reformulating them into special cases of (CE), or equivalently, fixed-point  problems (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=', [13, 40] and also Sections 4 and 5 below).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Motivation and related work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' We are interested in the case that G in (CE) lives in a  high-dimensional space Rp such that operating on full-dimensional vectors x of Rp is expensive  or even prohibited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Such models are ubiquitous in large-scale modern machine learning and  data science applications [8, 23, 47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' One common approach to tackle these models is block-  coordinate methods, which iteratively update one or a small number of blocks of the model  parameters instead of the full parameter vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Such an approach is though very classical  [4, 38], it has attracted a huge attention in recent years in optimization, monotone inclusions,  and fixed-point problems, see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=', [6, 11, 24, 36, 37, 40, 43, 53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' However, developing efficient  variants of the block-coordinate method to solve co-coercive equation (CE) remains largely  elusive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Most existing works focus on special cases of (CE) such as optimization, convex-  concave minimax, and supervised learning models, see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=', [6, 24, 37, 36, 43, 53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Our goal in this paper is to advance a recent development of accelerated methods and  apply it to randomized [block-]coordinate schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Unlike non-accelerated algorithms, it has  been recognized that [2, 54] generalizing accelerated methods from convex minimization to  monotone inclusions is not straightforward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Recent attempt on designing accelerated methods  for monotone inclusions and variational inequality (VIPs) has been made, see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=', in [2, 10,  20, 30, 50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  These algorithms often achieve a faster convergence rate than their classical  counterparts on the gradient norm or some appropriate operator residual norms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Typical  rates on the square of a residual norm are usually O  �  1/k2�  (or faster, o  �  1/k2�  ) compared  to O (1/k) (or o (1/k)) in non-accelerated methods, where k is the iteration counter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' The  O  �  1/k2�  rate matches the convergence rate lower bound in different settings, see [21, 35, 39]  for some concrete examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  As mentioned earlier, since the problem of approximating a  solution of (CE) can be reformulated equivalently to a fixed-point problem of a non-expansive  operator [5], theory and solution methods from one field can be applied to another and vice  versa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Due to its generality, (CE) can cover many common applications in scientific computing  as discussed, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=', in [40, 46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' For instance, it can be customized to handle linear systems,  [composite] smooth and nonsmooth convex optimization, feasibility problems, decentralized  2  optimization, federated learning, among others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' To avoid repetition, we do not present these  applications in this paper, but refer to [40, 46] for more details on how to reformulate them  into a fixed-point problem, or equivalently, a co-coercive equation of the form (CE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Motivated by applications in high-dimensional spaces, we aim at developing an accelerated  randomized block-coordinate method to solve (CE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Our basic mathematical tool is the  Halpern fixed-point iteration from [19] for solving (CE) and its recent development in, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=', [16,  25, 27, 54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Our central idea is to represent the accelerated Halpern fixed-point method into  a two-step iterative scheme (in Nesterov’s accelerated sense) using two consecutive iterates as  discussed in [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Then, we combine this resulting scheme and a randomized block-coordinate  strategy to derive a novel randomized block-coordinate algorithm for solving (CE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Contribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Our concrete contribution can be summarized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Firstly, we pro-  pose a new accelerated randomized block-coordinate algorithm to solve (CE) which achieves a  O  �  1/k2�  last-iterate convergence rate, or even a o  �  1/k2�  rate on E  �  ∥Gxk∥2�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Our algorithm  is very simple to implement and significantly different from existing methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' To the best  of our knowledge, this is the first randomized block-coordinate algorithm for (CE) achieving  o  �  1/k2�  fast convergence rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Next, we utilize a change of variable to develop a practical  variant of our method, which can avoid full-dimensional operations on the iterates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Alter-  natively, we apply our algorithm to the forward-backward splitting and Douglas-Rachford  splitting methods to obtain new accelerated randomized block-coordinate variants for solving  monotone inclusions involving the sum of two maximally monotone operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' As a byprod-  uct of our convergence analysis, these variants also achieve faster convergence rates than their  classical counterparts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Finally, we apply our method to tackle a class of finite-sum mono-  tone inclusions which forms the basis of many supervised machine learning tasks, including  federated learning [22, 26, 32, 33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' It leads to a new federated learning-type algorithm with  O  �  1/k2�  and o  �  1/k2�  convergence rates for a general class of finite-sum monotone inclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Let us highlight the following points of our contribution and discuss its limitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Firstly,  one of the most related works to our method is [40], which extends the asynchronous ran-  domized block-coordinate method to (CE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Though their method is asynchronous, it is non-  accelerated, and therefore, in our context, achieves O (1/k) and at most o (1/k) convergence  rates on the squared norm of the residual mapping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Note that the form of our algorithm is also  different from [40], while achieving O  �  1/k2�  and o  �  1/k2�  faster rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Unfortunately, asyn-  chronous variants of our method remain open.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Secondly, unlike methods for convex problems,  convergence analysis of algorithms for monotone inclusions, including (CE) is fundamentally  different, including the construction of a potential or Lyapunov function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Moreover, it remains  unclear if some recent techniques, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=', in [16, 25, 27, 54] can be extended to [randomized  block-] coordinate variants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' In this paper, we follow a different approach compared to those,  including convergence analysis technique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Thirdly, our randomized block-coordinate variants  for splitting schemes in Section 4 are also very different from the ones in [11] since their  methods rely on standard splitting methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' However, as a limitation of our new forward-  backward splitting method, it still requires a co-coercive assumption of one operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Finally,  our application to a finite-sum monotone inclusion in Section 5 is new compared to [13] since  our problem setting is more general than that of [13], and our scheme relies on an accelerated  Douglas-Rachford splitting scheme instead of a forward-type method as in [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  3  Paper organization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' The rest of this paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' In Section 2 we  briefly review some background related to (CE) and recall some preliminary results used in  this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Our main result is in Section 3, where we develop a new algorithm and establish its  convergence rate guarantees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' We also show how to apply our method to fixed-point problems  and derive its practical variant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Section 4 presents two applications of our method to the  forward-backward and Douglas-Rachford splitting schemes for solving monotone inclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Section 5 is an application of our method to a general finite-sum monotone inclusion which  potentially has many applications in machine learning and networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' We close this paper  with some concluding remarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  2  Background and Preliminary Results  We first review some background on monotone operators and related concepts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Then, we  recall the Halpern fixed-point iteration from [19] and its relation to Nesterov’s accelerated  methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='1  Monotone operators and related concepts  We work with a finite dimensional space Rp equipped with the standard inner product ⟨·, ·⟩ and  Euclidean norm ∥ · ∥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' For a set-valued mapping G : Rp ⇒ 2Rp, dom(G) = {x ∈ Rp : Gx ̸= ∅}  denotes its domain, graph(G) = {(x, y) ∈ Rp × Rp : y ∈ Gx} denotes its graph, where 2Rp is  the set of all subsets of Rp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' The inverse of G is defined by G−1y := {x ∈ Rp : y ∈ Gx}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' For  x = [x1, · · · , xn] ∈ Rp, we define a weighted norm ∥x∥w :=  ��n  i=1 wi∥xi∥2�1/2, where xi is  the i-the block of x and wi > 0 is a given weight (i = 1, · · · , n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Monotonicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' For a set-valued mapping G : Rp ⇒ 2Rp, we say that G is monotone if  ⟨u − v, x − y⟩ ≥ 0 for all x, y ∈ dom(G), u ∈ Gx, and v ∈ Gy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' G is said to be µG-strongly  monotone (or sometimes called coercive) if ⟨u − v, x − y⟩ ≥ µG∥x − y∥2 for all x, y ∈ dom(G),  u ∈ Gx, and v ∈ Gy, where µG > 0 is called a strong monotonicity parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' If G is single-  valued, then these conditions reduce to ⟨Gx−Gy, x−y⟩ ≥ 0 and ⟨Gx−Gy, x−y⟩ ≥ µG∥x−y∥2  for all x, y ∈ dom(G), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' We say that G is maximally monotone if graph(G) is not  properly contained in the graph of any other monotone operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Note that G is maximally  monotone, then αG is also maximally monotone for any α > 0, and if G and H are maximally  monotone, and dom(F) ∩ int (dom(H)) ̸= ∅, then G + H is maximally monotone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Lipschitz continuity and co-coerciveness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' A single-valued operator G is said to be  L-Lipschitz continuous if ∥Gx − Gy∥ ≤ L∥x − y∥ for all x, y ∈ dom(G), where L ≥ 0 is a  Lipschitz constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' If L = 1, then we say that G is nonexpansive, while if L ∈ [0, 1), then we  say that G is L-contractive, and L is its contraction factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' We say that G is 1  L-co-coercive if  ⟨Gx−Gy, x−y⟩ ≥ 1  L∥Gx−Gy∥2 for all x, y ∈ dom(G).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' If L = 1, then we say that G is firmly  nonexpansive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' If G is 1  L-cocoercive, then it is also monotone and L-Lipschitz continuous (by  using the Cauchy-Schwarz inequality), but the reverse statement is not true in general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Resolvent operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' The operator JGx := {y ∈ Rp : x ∈ y + Gy} is called the resolvent  of G, often denoted by JGx = (I+G)−1x, where I is the identity mapping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Clearly, evaluating  JG requires solving a strongly monotone inclusion 0 ∈ y−x+Gy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' If G is monotone, then JG is  singled-valued, and if G is maximally monotone then JG is singled-valued and dom(JG) = Rp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  If G is monotone, then JG is firmly nonexpansive [5, Proposition 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='2  The Halpern fixed-point iteration and its variants  Let us recall the following Halpern fixed-point iteration from [19] for approximating a fixed-  point x⋆ of a non-expansive operator T : Rp → Rp (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' x⋆ = Tx⋆):  xk+1 := βkx0 + (1 − βk)Txk,  where  βk :=  1  k+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  (1)  As proven in [27], this scheme achieves ∥xk−Txk∥2 = O  � 1  k2  �  rate guarantee, which is optimal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Now, for a given operator G : Rp → Rp, G is 1  L-co-coercive if and only if T := I − 2  LG is  nonexpansive [5, Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Therefore, the Halpern fixed-point method (1) applying  to approximate a solution x⋆ of the co-coercive equation Gx⋆ = 0 can be written as  xk+1 := βkx0 + (1 − βk)  �  xk − 2  LGxk�  = βkx0 + (1 − βk)xk − ηkGxk,  (2)  where ηk := 2(1−βk)  L  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' As shown in [16], this scheme also achieves an optimal convergence rate,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' ∥Gxk∥2 = O  �  1/k2�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Clearly, (1) and (2) are equivalent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Next, it has been shown in [48] that if we eliminate x0 in (2) using two consecutive updates  xk and xk+1, then we obtain the following scheme:  xk+1 := xk + θk(xk − xk−1) −  �  ηkGxk − γkGxk−1�  ,  (3)  where θk := βk(1−βk)  βk−1  and γk := βkηk−1  βk−1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Finally, if we additionally introduce yk+1 := xk − αkGxk, then we can equivalently trans-  form (3) into the following form (see [48] for details):  �  yk+1 := xk − αkGxk,  xk+1 := yk+1 + θk(yk+1 − yk) + νk(xk − yk+1),  (4)  where αk :=  ηk  1−βk and νk :=  βk  βk−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  The scheme (4) shows a connection between the Halpern-type method [19] and Nesterov’s  accelerated algorithms [2, 29, 34, 35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Compared to Nesterov’s accelerated methods for solving  smooth convex optimization problems, (4) has an additional correction term νk(xk −yk+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' It  is also related to Ravine’s method as shown in [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Note that, both (3) and (4) can be applied  to proximal-point, forward-backward splitting, Douglas-Rachford splitting, and three-operator  splitting schemes for solving monotone inclusions, variational inequality, and convex-concave  saddle-point problems, see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=', [2, 7, 20, 30, 48] for more details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  3  Accelerated Randomized Block-Coordinate Algorithms  In this section, we develop a new randomized block-coordinate variant of (3) to solve (CE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  We assume that the variable x of (CE) is decomposed into n-blocks as x = [x1, x2, · · · , xn]  (1 ≤ n ≤ p), where xi ∈ Rpi for i ∈ [n] := {1, 2, · · · , n}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' For the operator G, we denote  [Gx]i as the i-the block coordinate of Gx such that Gx = [[Gx]1, · · · , [Gx]n].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' We also denote  G[i]x = [0, · · · , 0, [Gx]i, 0, · · · , 0] so that only the i-th block is computed, while others are  zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Throughout this paper, we assume that G in (CE) satisfies the following assumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  5  Assumption 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' The operator G in (CE) is L−1-block-coordinate-wise co-coercive, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' for  any x, y ∈ dom(G), there exist Li ∈ [0, +∞) (∀i ∈ [n]) such that  ⟨Gx − Gy, x − y⟩ ≥  n  �  i=1  1  Li ∥[Gx]i − [Gy]i∥2 ≡ ∥Gx − Gy∥2  L−1,  (CP)  where L−1 := ( 1  L1 , · · · , 1  Ln ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Moreover, dom(G) = Rp and zer(G) := {x⋆ ∈ Rp : Gx⋆ = 0} ̸= ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Clearly, Assumption 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='1 extends the standard co-coerciveness [5] of a monotone operator  to block-coordinate-wise settings, and therefore, it is still very common.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Moreover, due to  the equivalence between the co-coercive equation (CE) and the fixed-point problem as we  mentioned earlier, our setting appears to be sufficiently general to cover many applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Since we will develop randomized methods operating on blocks xi of x for some i ∈ [n],  we introduce the following probability model for selecting block coordinates of x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Let ik be a  random variable on [n] := {1, 2, · · · , n} that satisfies the following probability distribution:  Prob (ik = i) = pi,  for all i ∈ [n],  (5)  where pi > 0 for all i ∈ [n] and �n  i=1 pi = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' We also denote pmin := mini∈[n] pi > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' If  pi =  1  n, then ik is a uniformly random variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Otherwise, we also cover non-uniformly  randomized block-coordinate methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  To define convergence guarantees of our methods, we denote Fk to be the smallest σ-  algebra generated by the random set {x0, x1, · · · , xk} collecting all iterate vectors up to the  k-the iteration of our algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' We also use Ek [X] := Eik [X | Fk] to denote the conditional  expectation of X taken overall the randomness generated by the random variable ik ∈ [n]  (and therefore xk) conditioned on Fk, and E [·] for the total expectation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='1  Accelerated RBC Method and Convergence Analysis: Main Result  Inspired by our expression (3), we propose the following Accelerated Randomized Block-  Coordinate (ARBC) scheme for solving (CE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Starting from x0 ∈ Rp, we set x−1 := x0,  and at each iteration k ≥ 0, randomly generate ik ∈ [n] following the probability law (5) and  update:  xk+1 := xk + θk(xk − xk−1) −  ψ  pik  �  ηkG[ik]xk − γkG[ik]xk−1�  ,  (ARBC)  where θk > 0, ψ > 0, ηk > 0, and γk ≥ 0 are given parameters, which will be determined later,  and G[i]xk = [0, · · · , 0, [Gxk]i, 0, · · · , 0] such that [Gxk]i is the i-the block of Gxk (i ∈ [n]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  The scheme (ARBC) requires two block-coordinate evaluations [Gxk]ik and [Gxk−1]ik of  G at the two consecutive iterates xk and xk−1, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Clearly, it is different from ex-  isting randomized [block]-coordinate methods in the literature, including methods for convex  optimization [6, 18, 24, 36, 37, 43, 53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' However, due to the extrapolation term θk(xk −xk−1),  (ARBC) still requires full vector update at each iteration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' This is unavoidable in accelerated  methods as in [18, 36, 37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' We will further discuss this point in Subsection 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  To establish the convergence of (ARBC), we introduce the following potential function:  Vk := 2ψtkηk−1  �  ⟨Gxk−1, xk−1 − x⋆⟩ − �n  i=1  1  Li ∥[Gxk−1]i∥2�  + ∥xk−1 − x⋆ + tk(xk − xk−1)∥2 + µk∥xk−1 − x⋆∥2,  (6)  6  where x⋆ ∈ zer(G), and tk > 0 and µk ≥ 0 are given parameters, which will be determined  later.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' It is obvious that under Assumption 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='1, {xk} is well-defined, and we have Vk ≥ 0 for  all k ≥ 0 regardless the choice of xk−1 and xk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' We first prove the following key result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Suppose that Assumption 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='1 holds for (CE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Let {xk} be generated by (ARBC)  and Vk be defined by (6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Suppose further that the parameters in (ARBC) and (6) satisfy  \uf8f1  \uf8f4  \uf8f4  \uf8f4  \uf8f2  \uf8f4  \uf8f4  \uf8f4  \uf8f3  tkηk−1 ≥  �  1 −  1  tk−µk  �  tk+1ηk,  θk  := tk−µk−1  tk+1  ,  γk  :=  tk+1θk  tk+1θk+1 · ηk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  (7)  Then, the following inequality holds:  Vk − Ek  �  Vk+1�  ≥ µk(2tk − µk − 1)∥xk − xk−1∥2 − (µk+1 − µk)∥xk − x⋆∥2  + �n  i=1  ψtk+1[2pi(tk+1θk+1)−ψLitk+1ηk]  ηkLipi  ��ηk[Gxk]i − γk[Gxk−1]i  ��2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  (8)  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' First of all, let us introduce dk := ηkGxk − γkGxk−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Then, from (ARBC), we have  xk+1 − xk = θk(xk − xk−1) −  ψ  pik dk  [ik].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Hence we can expand the second term of (6) as  T[1]  :=  ∥xk + tk+1(xk+1 − xk) − x⋆∥2  (ARBC)  =  ∥xk − x⋆ + tk+1θk(xk − xk−1) − ψtk+1p−1  ik dk  [ik]∥2  =  ∥xk − x⋆∥2 + t2  k+1θ2  k∥xk − xk−1∥2 + ψ2t2  k+1∥p−1  ik dk  [ik]∥2 − 2ψtk+1⟨p−1  ik dk  [ik], xk − x⋆⟩  + 2tk+1θk⟨xk − xk−1, xk − x⋆⟩ − 2ψt2  k+1θk⟨p−1  ik dk  [ik], xk − xk−1⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Alternatively, we can also expand  ∥xk−1 + tk(xk − xk−1) − x⋆∥2 = ∥xk − x⋆ + (tk − 1)(xk − xk−1)∥2  = ∥xk − x⋆∥2 + 2(tk − 1)⟨xk − xk−1, xk − x⋆⟩  + (tk − 1)2∥xk − xk−1∥2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Moreover, we also have the following elementary expression  µk∥xk−1 − x⋆∥2 − µk+1∥xk − x⋆∥2 = µk∥xk − xk−1∥2 − 2µk⟨xk − xk−1, xk − x⋆⟩  − (µk+1 − µk)∥xk − x⋆∥2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Now, let us consider the following function:  Qk := ∥xk−1 + tk(xk − xk−1) − x⋆∥2 + µk∥xk−1 − x⋆∥2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  (9)  Then, combining the last three expressions, and using the definition (9) of Qk, we have  Qk − Qk+1 =  �  (tk − 1)2 − θ2  kt2  k+1 + µk  �  ∥xk − xk−1∥2 − ψ2t2  k+1∥p−1  ik dk  [ik]∥2  + 2 (tk − 1 − θktk+1 − µk) ⟨xk − x⋆, xk − xk−1⟩ − (µk+1 − µk)∥xk − x⋆∥2  + 2ψtk+1⟨p−1  ik dk  [ik], xk − x⋆⟩ + 2ψt2  k+1θk⟨p−1  ik dk  [ik], xk − xk−1⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  (10)  7  Next, using the fact that dk  [ik] = [0, · · · , 0, dk  ik, 0, · · · , 0] and (5), we can easily show that  Ek  �  ∥p−1  ik dk  [ik]∥2�  = �n  i=1 p−1  i ∥dk  i ∥2,  Ek  �  ⟨p−1  ik dk  [ik], xk − x⋆⟩  �  = �n  i=1⟨dk  i , xk  i − x⋆  i ⟩,  Ek  �  ⟨p−1  ik dk  [ik], xk − xk−1⟩  �  = �n  i=1⟨dk  i , xk  i − xk−1  i  ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  (11)  Taking conditional expectation Ek [·] both sides of (10) and then using (11) and dk = ηkGxk −  γkGxk−1 into the resulting expression,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' and rearranging it,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' we can derive  Qk − Ek  �  Qk+1�  =  �  (tk − 1)2 − θ2  kt2  k+1 + µk  �  ∥xk − xk−1∥2 − (µk+1 − µk)∥xk − x⋆∥2  + 2 (tk − 1 − θktk+1 − µk) ⟨xk − x⋆,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' xk − xk−1⟩  + 2ψtk+1ηk  �n  i=1⟨[Gxk]i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' xk  i − x⋆  i ⟩ − 2ψtk+1γk  �n  i=1⟨[Gxk−1]i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' xk−1  i  − x⋆  i ⟩  − ψ2t2  k+1  �n  i=1  1  pi ∥ηk[Gxk]i − γk[Gxk−1]i∥2  + 2ψt2  k+1θkηk  �n  i=1⟨[Gxk]i − [Gxk−1]i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' xk  i − xk−1  i  ⟩  + 2ψtk+1 [tk+1θk(ηk − γk) − γk] �n  i=1⟨[Gxk−1]i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' xk  i − xk−1  i  ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Utilizing the condition (CP) of G as  �n  i=1⟨[Gxk]i − [Gxk−1]i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' xk  i − xk−1  i  ⟩ ≥ �n  i=1  1  Li ∥[Gxk]i − [Gxk−1]i∥2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  into the last expression,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' we arrive at  Qk − Ek  �  Qk+1�  ≥  �  (tk − 1)2 − θ2  kt2  k+1 + µk  �  ∥xk − xk−1∥2 − (µk+1 − µk)∥xk − x⋆∥2  + 2  �  tk − 1 − θktk+1 − µk  �  ⟨xk − x⋆,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' xk − xk−1⟩ + 2ψtk+1ηk⟨Gxk,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' xk − x⋆⟩  − 2ψtk+1γk⟨Gxk−1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' xk−1 − x⋆⟩ − ψ2t2  k+1  �n  i=1  1  pi ∥ηk[Gxk]i − γk[Gxk−1]i∥2  + 2ψt2  k+1θkηk  �n  i=1  1  Li ∥[Gxk]i − [Gxk−1]i∥2  + 2ψtk+1  �  tk+1θk(ηk − γk) − γk  �  ⟨Gxk−1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' xk − xk−1⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Rearranging this inequality,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' we get  Qk − Ek  �  Qk+1�  ≥  �  (tk − 1)2 − θ2  kt2  k+1 + µk  �  ∥xk − xk−1∥2 − (µk+1 − µk)∥xk − x⋆∥2  + 2  �  tk − 1 − θktk+1 − µk  �  ⟨xk − x⋆,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' xk − xk−1⟩  + ψtk+1  �n  i=1  �  2(tk+1θkηk−γk)  Li  − ψtk+1γ2  k  pi  �  ∥[Gxk−1]i∥2  − 2ψt2  k+1ηk  �n  i=1  �  2θk  Li − ψγk  pi  �  ⟨[Gxk]i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' [Gxk−1]i⟩  + ψtk+1ηk  �n  i=1  �  2(tk+1θk+1)  Li  − ψtk+1ηk  pi  �  ∥[Gxk]i∥2  + 2ψtk+1ηk  �  ⟨Gxk,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' xk − x⋆⟩ − �n  i=1  1  Li ∥[Gxk]i∥2�  − 2ψtk+1γk  �  ⟨Gxk−1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' xk−1 − x⋆⟩ − �n  i=1  1  Li ∥[Gxk−1]i∥2�  + 2ψtk+1  �  tk+1θk(ηk − γk) − γk  �  ⟨Gxk−1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' xk − xk−1⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  (12)  8  Let us first impose the following condition as in the third line of (7):  tk+1θk(ηk − γk) − γk = 0  ⇔  γk :=  tk+1θk  tk+1θk+1 · ηk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  (13)  This condition leads to  \uf8f1  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f2  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f3  Ak  i := ψtk+1  �  2(tk+1θkηk−γk)  Li  − ψtk+1γ2  k  pi  �  = ψtk+1ηk[2pi(tk+1θk+1)−ψLitk+1ηk]  Lipi t2  k+1θ2  k  (tk+1θk+1)2 ,  Bk  i := ψt2  k+1ηk  �  2θk  Li − ψγk  pi  �  = ψtk+1ηk[2pi(tk+1θk+1)−ψLitk+1ηk]  Lipi(tk+1θk+1) tk+1θk  (tk+1θk+1),  Ck  i := ψtk+1ηk  �  2(tk+1θk+1)  Li  − ψtk+1ηk  pi  �  = ψtk+1ηk[2pi(tk+1θk+1)−ψLitk+1ηk]  Lipi  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Therefore, using these three coefficients Ak  i , Bk  i , and Ck  i , we can show that  T [i]  [2] := ψtk+1  �  2(tk+1θkηk−γk)  Li  − ψtk+1γ2  k  pi  �  ∥[Gxk−1]i∥2  − 2ψt2  k+1ηk  �  2θk  Li − ψγk  pi  �  ⟨[Gxk]i, [Gxk−1]i⟩  + ψtk+1ηk  �  2(tk+1θk+1)  Li  − ψtk+1ηk  pi  �  ∥[Gxk]i∥2  =  ψtk+1ηk  �  2pi(tk+1θk+1)−ψLitk+1ηk  �  Lipi  ��[Gxk]i −  tk+1θk  tk+1θk+1[Gxk−1]i  ��2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  In this case, we can simplify (12) as  Qk − Ek  �  Qk+1�  ≥  �  (tk − 1)2 − θ2  kt2  k+1 + µk  �  ∥xk − xk−1∥2 − (µk+1 − µk)∥xk − x⋆∥2  + 2  �  tk − 1 − θktk+1 − µk  �  ⟨xk − x⋆, xk − xk−1⟩  + 2ψtk+1ηk  �  ⟨Gxk, xk − x⋆⟩ − �n  i=1  1  Li ∥[Gxk]i∥2�  − 2ψtk+1γk  �  ⟨Gxk−1, xk−1 − x⋆⟩ − �n  i=1  1  Li ∥[Gxk−1]i∥2�  + �n  i=1  ψtk+1ηk[2pi(tk+1θk+1)−ψLitk+1ηk]  Lipi  ��[Gxk]i −  tk+1θk  tk+1θk+1[Gxk−1]i  ��2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  (14)  Let us impose the following two conditions:  tk − µk − 1 = θktk+1  and  tkηk−1 ≥ tk+1γk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  (15)  The first equality leads to the choice of θk as in (7), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' θk := tk−µk−1  tk+1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Next, let us check the second condition of (15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Using (13) and tk+1θk = tk − µk − 1 from  (15), the second condition of (15) is equivalent to  tkηk−1 ≥ tk+1ηk  �  1 −  1  tk−µk  �  ,  which is the first line of (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Hence, the second condition of (15) holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Finally, by (15), we can easily show that  T[3] := µk + (tk − 1)2 − θ2  kt2  k+1 = (tk − 1)tk − (tk − µk)tk+1θk = µk(2tk − µk − 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Using this expression, (CP), the conditions in (15),  tk+1θk  tk+1θk+1 = γk  ηk from (13), and ηk − γk =  ηk  tk+1θk+1 into (14), and then using the definition of Vk from (6) for the resulting inequality,  we obtain (8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  9  Now, we are ready to prove the convergence of (ARBC) in the following theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Suppose that Assumption 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='1 holds for (CE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Let {xk} be generated by  (ARBC) and Vk be defined by (6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' For given ω > 3 and 0 < ψ < min  �  2pi  Li : i ∈ [n]  �  , we  update  µk := 1,  tk := k+2ω+1  ω  ,  θk := tk−2  tk+1 ,  ηk := tk−1  tk+1 ,  and  γk := tk−2  tk+1 = θk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  (16)  Then, we obtain the following bounds:  �+∞  k=0(k + 2ω + 2)2E  �  ∥ηkGxk − γkGxk−1∥2�  ≤  ω2  ψC V0,  �+∞  k=0(k + ω + 1)E  �  ∥xk − xk−1∥2�  ≤ 2  ωV0,  �+∞  k=0(k + ω)E  �  ∥Gxk−1∥2�  ≤  16  ψ2ωV0 +  8C0  ψ2(ω−3),  �+∞  k=1(k + 1)2E  �  ∥Gxk − Gxk−1∥2�  ≤ C0,  (17)  where C := min  i∈[n]  �  2  Li − ψ  pi  �  > 0 and C0 :=  ψ2ω2(ω−1)2  (ω+1)2  ∥Gx0∥2 +  �  8(ω−1)  ω  + ψω2(1−pmin)  pminC  �  V0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Moreover, the following statements also hold:  �  E  �  ∥xk+1 − xk∥2�  = O  � 1  k2  �  and  E  �  ∥xk+1 − xk∥2�  = o  � 1  k2  �  ,  E  �  ∥Gxk∥2�  = O  � 1  k2  �  and  E  �  ∥Gxk∥2�  = o  � 1  k2  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  (18)  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='1 establishes convergence rates of (ARBC) on two main criteria E  �  ∥Gxk∥2�  and E  �  ∥xk+1 − xk∥2�  , among other side results as stated in (17).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' However, the statement (18)  does not show the independence of the rates on the number of blocks n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' As we can observe  from our proof below that these convergence rates depend on  1  ψ2 , where ψ is a given stepsize in  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' If we choose pi = 1  n, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' uniformly random, and assume that Li = L for i ∈ [n],  then ψ is proportional to 1  n, leading to E  �  ∥xk+1 − xk∥2�  = O  �  n2  k2  �  and E  �  ∥Gxk∥2�  = O  �  n2  k2  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  The dependence of the convergence rates on n2 has been observed in Nesterov’s accelerated  methods for convex optimization, see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' [1, 18, 36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' In (18), we state both Big-O and  small-o convergence rates where Big-O rates are often proved when k ≤ O (n), while small-o  rates are achieved when k is sufficiently large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  The proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Firstly, we fix µk := 1 for all k ≥ 0 and since θk is updated by  θk := tk−µk−1  tk+1  = tk−2  tk+1 as in (7), if we choose ηk := tk−µk  tk+1  = tk−1  tk+1 , then the first condition  of (7) reduces to 1 ≤ tk−1−1  tk−2 , which holds if tk−1 − tk + 1 ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Let us choose tk := k+2ω+1  ω  for some ω > 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Clearly, we have tk−1 − tk + 1 =  ω−1  ω  > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Moreover, we also have  γk = tk+1θkηk  tk+1θk+1 = tk−2  tk+1 = θk as shown in (16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Next, under the choice of parameters as above, (8) reduces to  Vk − Ek  �  Vk+1�  ≥ �n  i=1  ψt2  k+1  Lipi (2pi − ψLi) ∥ηk[Gxk]i − γk[Gxk−1]i∥2  + 2(tk − 1)∥xk − xk−1∥2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  10  Taking full expectation this inequality and using tk = k+2ω+1  ω  and tk−2  tk−1 ≥  1  ω+1, we obtain  E  �  Vk�  − E  �  Vk+1�  ≥ �n  i=1  ψ(k+2ω+2)2  Lipiω2  (2pi − ψLi) E  �  ∥ηk[Gxk]i − γk[Gxk−1]i∥2�  + 2(k+ω+1)  ω  E  �  ∥xk − xk−1∥2�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  (19)  Since E  �  Vk�  ≥ 0, summing up (20) from k := 0 to k := K ≥ 0, we obtain  �K−1  k=0  ψ(k+2ω+2)2  ω2  �n  i=1  �  2  Li − ψ  pi  �  E  �  ∥ηk[Gxk]i − γk[Gxk−1]i∥2�  ≤ E  �  V0�  ,  �K−1  k=0 (k + ω + 1)E  �  ∥xk − xk−1∥2�  ≤ 2  ωE  �  V0�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  (20)  This implies the first two lines of (17) after taking the limit as K → +∞ and noting that  E [V0] = V0 due to the certainty of x0 and x−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Next, let us define the following full vector ¯xk+1 as  ¯xk+1 := xk + θk(xk − xk−1) − ψ  �  ηkGxk − γkGxk−1�  = zk − ψdk,  (21)  where zk := xk +θk(xk −xk−1) and dk := ηkGxk −γkGxk−1 ≡ ηkGxk −θkGxk−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Then, from  (ARBC), we have xk+1 = zk −  ψ  pik dk  [ik].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Therefore, for any uk independent of ik, we have  Ek  �  ∥xk+1 − uk∥2�  = ∥zk − uk∥2 − 2ψEk  �  ⟨p−1  ik dk  [ik], zk − uk⟩  �  + ψ2Ek  �  ∥p−1  ik dk  [ik]∥2�  = ∥zk − uk∥2 − 2ψ⟨dk, zk − uk⟩ + ψ2 �n  i=1  1  pi ∥dk  i ∥2  = ∥zk − ψdk − uk∥2 + ψ2 �n  i=1  �  1  pi − 1  �  ∥dk  i ∥2  = ∥¯xk+1 − uk∥2 + ψ2 �n  i=1  �  1  pi − 1  �  ∥dk  i ∥2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  (22)  Now, from (21), we have  ¯xk+1 − xk + ψηkGxk =  θk  ηk−1 (xk − xk−1 + ψηk−1Gxk−1) +  �  1 −  θk  ηk−1  �  θk(1−ηk−1)  ηk−1−θk (xk−1 − xk).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Note also that since ω > 1, we have 0 <  θk  ηk−1 =  tk−2  tk−1−1 =  k+1  k+ω ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Moreover, using the  update rule (16), we can easily show that θk(1−ηk−1)  ηk−1−θk  = (ω+1)(k+1)  ωk+2ω2−1 ≤ ω+1  ω  ≤ 2 for all k ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Hence, by convexity of ∥ · ∥2, we have  ∥¯xk+1 − xk + ψηkGxk∥2 ≤  θk  ηk−1∥xk − xk−1 + ψηk−1Gxk−1∥2 + 4(ω−1)  k+ω ∥xk − xk−1∥2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Substituting uk := xk − ψηkGxk into (22) and combining the result with the last inequality  and using max{ 1  pi − 1 : i ∈ [n]} = 1−pmin  pmin , we can show that  Ek  �  ∥xk+1 − xk + ψηkGxk∥2�  ≤  θk  ηk−1 ∥xk − xk−1 + ψηk−1Gxk−1∥2 + 4(ω−1)  k+ω ∥xk − xk−1∥2  + ψ2(1−pmin)  pmin  ∥ηkGxk − θkGxk−1∥2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Taking full expectation of both sides of this inequality, we arrive at  E  �  ∥xk+1 − xk + ψηkGxk∥2�  ≤  θk  ηk−1 E  �  ∥xk − xk−1 + ψηk−1Gxk−1∥2�  + 4(ω−1)  k+ω E  �  ∥xk − xk−1∥2�  + ψ2(1−pmin)  pmin  E  �  ∥ηkGxk − θkGxk−1∥2�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  11  Multiplying this inequality by (k + ω)2 and rearranging the result, we obtain  (k + ω)2E  �  ∥xk+1 − xk + ψηkGxk∥2�  ≤ (k + ω − 1)2E  �  ∥xk − xk−1 + ψηk−1Gxk−1∥2�  − [(ω − 3)(k + ω) + 1] E  �  ∥xk − xk−1 + ψηk−1Gxk−1∥2�  + 4(ω − 1)(k + ω)E  �  ∥xk − xk−1∥2�  + ψ2(1−pmin)  pmin  (k + ω)2E  �  ∥ηkGxk − θkGxk−1∥2�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  This inequality also implies that limk→∞(k+ω)2E  �  ∥xk+1 − xk + ψηkGxk∥2�  exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Summing  up this inequality from k := 0 to k := K − 1, then using the first and second lines of (17) and  x−1 := x0, we get  (K + ω − 1)2E  �  ∥xK − xK−1 + ψηK−1GxK−1∥2�  ≤ ψ2η2  −1(ω − 1)2E  �  ∥Gx0∥2�  +  �  8(ω−1)  ω  + ψω2(1−pmin)  pminC  �  E  �  V0�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  (23)  Alternatively, we also have  �K−1  k=0 (k + ω)E  �  ∥xk − xk−1 + ψηk−1Gxk−1∥2�  ≤ E[C0]  ω−3 ,  where C0 := ψ2η2  −1(ω − 1)2E  �  ∥Gx0∥2�  +  �  8(ω−1)  ω  + ψω2(1−pmin)  pminC  �  E  �  V0�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Since E  �  V0�  = V0,  E  �  ∥Gx0∥2�  = ∥Gx0∥2, and η−1 = η0 =  ω  ω+1, we obtain C0 as in Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' The last  inequality and the existence of limk→∞(k + ω + 1)2E  �  ∥xk+1 − xk + ψηkGxk∥2�  imply  limk→∞(k + ω + 1)2E  �  ∥xk+1 − xk + ψηkGxk∥2�  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  (24)  Next, noting that ηk ≥  k+ω+1  k+2ω+2 ≥ 1  2, we can show that  ψ2  4 ∥Gxk−1∥2 ≤ ψ2η2  k−1∥Gxk−1∥2 ≤ 2∥xk − xk−1∥2 + 2∥xk − xk−1 + ψηk−1Gxk−1∥2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  (25)  Therefore, we can easily obtain  �K−1  k=0 (k + ω)E  �  ∥Gxk−1∥2�  ≤  16  ψ2ωE  �  V0�  +  8E[C0]  ψ2(ω−3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  (26)  This proves the third line of (17).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Now, from xk+1 := xk + θk(xk − xk−1) − ψp−1  ik dk  [ik] of (ARBC), we have  ∥xk+1 − xk∥2 = θ2  k∥xk − xk−1∥2 − 2ψθk⟨p−1  ik dk  [ik], xk − xk−1⟩ + ψ2∥p−1  ik dk  [ik]∥2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Taking conditional expectation Ek [·] of this expression and using (11) and θk = γk, we have  Ek  �  ∥xk+1 − xk∥2�  = θ2  k∥xk − xk−1∥2 − 2ψθk⟨dk, xk − xk−1⟩ + ψ2 �n  i=1  1  pi ∥dk  i ∥2  = θ2  k∥xk − xk−1∥2 + ψ2 �n  i=1  1  pi ∥ηk[Gxk]i − θk[Gxk−1]i∥2  − 2ψθ2  k⟨Gxk − Gxk−1, xk − xk−1⟩ − 2ψθk(ηk − θk)⟨Gxk, xk − xk−1⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  12  Utilizing (CP) and the Young inequality into the last expression, we can show that  Ek  �  ∥xk+1 − xk∥2�  ≤  �  θ2  k + 2θk(ηk − θk)  �  ∥xk − xk−1∥2 + ψ2θk(ηk−θk)  2  ∥Gxk∥2  − 2ψθ2  k  �n  i=1  1  Li ∥[Gxk]i − [Gxk−1]i∥2  + ψ2 �n  i=1  1  pi ∥ηk[Gxk]i − θk[Gxk−1]i∥2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Multiplying this inequality by ω2t2  k+1 = (k + 2ω + 2)2 and noting that ω2t2  k+1[θ2  k + 2θk(ηk −  θk)] = ω2t2  k−2ω(k+2ω+1) and ω2t2  k+1θk(ηk−θk) = ω(k+1), and then taking full expectation  of the resulting inequality, we obtain  ω2t2  k+1E  �  ∥xk+1 − xk∥2�  ≤ ω2t2  kE  �  ∥xk − xk−1∥2�  − 2ω(k + 2ω + 1)E  �  ∥xk − xk−1∥2�  +  ψ2ω2t2  k+1  pmin  E  �  ∥ηkGxk − θkGxk−1∥2�  + ψ2ω(k+1)  2  E  �  ∥Gxk∥2�  − 2ψ(k+1)2  Lmax  E  �  ∥Gxk − Gxk−1∥2�  ,  where Lmax := max{Li : i ∈ [n]}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' This inequality leads to  T[3] := (k + 2ω + 2)2E  �  ∥xk+1 − xk∥2�  + 2ω(k + 2ω + 1)E  �  ∥xk − xk−1∥2�  + 2ψ(k+1)2  Lmax  E  �  ∥Gxk − Gxk−1∥2�  ≤ (k + 2ω + 1)2E  �  ∥xk − xk−1∥2�  +  ψ2  pmin(k + 2ω + 2)2E  �  ∥ηkGxk − θkGxk−1∥2�  + ψ2ω(k+1)  2  ∥Gxk∥2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Utilizing this inequality, (26), and the second line of (17), we can conclude that limk→∞(k +  2ω + 2)2E  �  ∥xk+1 − xk∥2�  exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Summing up the inequality T[3] from k := 0 to k := K − 1  and noting that 4ω2 ≥ (4ω − 1)ω and x0 = x−1, we obtain  (K + 2ω + 1)2 E  �  ∥xK − xK−1∥2�  + 2ω �K−1  k=0 (k + 2ω + 1)E  �  ∥xk − xk−1∥2�  +  2ψ  Lmax  �K−1  k=0 (k + 1)2E  �  ∥Gxk − Gxk−1∥2�  ≤  ψ2  pmin  �K−1  k=0 (k + 2ω + 2)2∥ηkGxk − θkGxk−1∥2  + ψ2ω  2  �K−1  k=0 (k + 1)E  �  ∥Gxk∥2�  (17),(26)  ≤  �  ψω2  pminC + 8  �  E  �  V0�  + 4ωE[C0]  (ω−3) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  (27)  This inequality shows that E  �  ∥xk+1 − xk∥2�  = O  �  1/k2�  as in (18).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Combining the existence  of limk→∞(k + 2ω + 2)2E  �  ∥xk+1 − xk∥2�  and �k  k=0(k + ω + 1)E  �  ∥xk − xk−1∥2�  < +∞, we  obtain limk→∞(k + 2ω + 2)2E  �  ∥xk+1 − xk∥  �2 = 0, which proves the o-rate in (18).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Finally, from (23), (25), and (27), we have  (k + ω)2E  �  ∥Gxk∥2�  (25)  ≤  8(k+ω)2  ψ2  E  �  ∥xk+1 − xk∥2�  + 8(k+ω)2  ψ2  E  �  ∥xk+1 − xk + ψηkGxk∥2�  (23),(27)  ≤  8  ψ2  �  ψω2  pminC + 8(ω−1)  ω  + ψω2(1−pmin)  pminC  + 8  �  E  �  V0�  + 32ωE[C0]  ψ2(ω−3) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  This inequality shows that E  �  ∥Gxk∥2�  = O  �  1/k2�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' The o-rate E  �  ∥Gxk∥2�  = o  � 1  k2  �  immedi-  ately follows from the first line of this inequality, the first line of (18), and (24).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  13  Application to fixed-point problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Let us apply (ARBC) to approximate a fixed-  point x⋆ of a nonexpansive operator T : Rp → Rp, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' x⋆ = Tx⋆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' As mentioned earlier, if we  define G := I − T, then G is firmly nonexpansive, or equivalently, 1-co-coercive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Moreover,  x⋆ is a fixed-point of T iff Gx⋆ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Therefore, we can apply (ARBC) to solve Gx⋆ =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' For simplicity of presentation, we assume that ik is generated uniformly randomly, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Prob (ik = i) = 1  n for all i ∈ [n].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' In this case, (ARBC) reduces to  xk+1  i  :=  �  xk  i + ˆηkxk  i − ˆγkxk−1  i  + ˆψ  �  ηk[Txk]ik) − γk[Txk−1]ik  �  , if i = ik,  xk  i + θk(xk  i − xk−1  i  ),  otherwise,  (28)  where ˆψ := nψ, ˆηk := θk − ˆψηk, and ˆγk := θk − ˆψγk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Clearly, our new scheme (28) is different  from existing methods for approximating a fixed-point x⋆ of a non-expansive operator T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' The  convergence rates of the residual E  �  ∥xk − Txk∥2�  and E  �  ∥xk+1 − xk∥2�  of (28) are guaranteed  by Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' However, we omit them here to avoid repetition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='2  Practical variant of ARBC  Let us derive an alternative form of (ARBC) so that it is easier to implement in practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' First,  from (ARBC), we have xk+1 − xk = θk(xk − xk−1) −  ψ  pik dk  [ik], where dk := ηkGxk − γkGxk−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Let us assume that θk =  τk+1  τk  for a given positive sequence {τk}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  This relation leads to  τk+1 = τkθk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Moreover, we can write (ARBC) as  1  τk+1(xk+1 − xk) = 1  τk (xk − xk−1) −  ψ  pik τk+1dk  [ik].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Now, if we introduce wk := 1  τk (xk − xk−1), then (ARBC) can be rewritten as  xk := xk−1 + τkwk  and  wk+1 := wk −  ψ  pik τk+1dk  [ik].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  By induction, we can show that xk = x0 + �k  i=1 τiwi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Let us express this representation as  xk = x0 − τ1(w2 − w1) − (τ1 + τ2)(w3 − w2) − (τ1 + τ2 + τ3)(w4 − w3)  − · · · − (τ1 + · · · + τk−1)(wk − wk−1) + (τ1 + · · · + τk−1 + τk)wk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Therefore, if we define ck := �k  i=1 τi with a convention that c0 := 0, and ∆wk := wk+1 − wk,  then we can write xk as  xk = x0 − �k−1  i=1 ci∆wi + ckwk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  If we introduce zk := x0 − �k−1  i=1 ci∆wi, then we get zk = zk−1 − ck−1∆wk−1 with z0 := x0,  and hence xk = zk + ckwk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Therefore, we can summarize our derivation above as  \uf8f1  \uf8f4  \uf8f4  \uf8f4  \uf8f2  \uf8f4  \uf8f4  \uf8f4  \uf8f3  wk+1 := wk −  ψ  pikτk+1 dk  ik,  zk+1  := zk − ck∆wk = zk +  ckψ  pikτk+1 dk  ik  xk+1  = zk+1 + ck+1wk+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  14  Eliminating xk and xk−1 from the last scheme, we can write (ARBC) equivalently to  \uf8f1  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f2  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f3  dk  i  := ηk[G(zk + ckwk)]i − γk[G(zk−1 + ck−1wk−1)]i,  if i = ik,  wk+1  i  :=  � wk  i −  ψ  piτk+1dk  i , if i = ik,  wk  i ,  otherwise,  zk+1  i  :=  � zk  i +  ψck  piτk+1 dk  i , if i = ik,  zk  i ,  otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  (29)  Here, x0 ∈ Rp is given, z0 = z−1 := x0, and w0 = w−1 := 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Moreover, the parameters τk  and ck are respectively updated as  τk+1 := τkθk  and  ck := ck−1 + τk,  (30)  where c0 = c−1 := 0 and τ0 := 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  The scheme (29) is though different from accelerated randomized block-coordinate meth-  ods for convex optimization such as [1, 18, 36, 49], it has some common features as those  methods such as the block-coordinate evaluations of G at zk + ckwk and zk−1 + ck−1wk−1,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' One notable property of (29) is that it does not require full dimensional updates  of wk and zk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Note that one can also extend our method (ARBC) (or equivalently, (29)) to up-  date multiple blocks by randomly choosing a subset Sk ⊂ [n] such that Prob (i ∈ Sk) = pi > 0  for i ∈ [n].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  4  Applications to Monotone Inclusions  In this section, we derive two variants of (ARBC) to approximate a solution of the following  monotone inclusion involving the sum of two monotone operators:  Find x⋆ ∈ Rp such that:  0 ∈ Ax⋆ + Bx⋆,  (MI)  where A, B : Rp ⇒ Rp are maximally monotone operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Moreover, we assume that Ax =  [A1x1, A2x2, · · · , Anxn] is a separable operator compounded by n independent blocks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  We apply (ARBC) to two common methods for solving (MI): the forward-backward split-  ting (FBS) and the Douglas-Rachford (splitting (DRS) schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='1  ARBC Forward-Backward Splitting Method  Let us first reformulate (MI) equivalently to (CE) by using the following forward-backward  (FB) residual mapping:  Gβx := β−1(x − JβA(x − βBx)),  (31)  where β > 0 is given and JβA := (I + βA)−1 is the resolvent of βA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' As shown in [48], if B  is 1  L-co-coercive and 0 < β < 4  L, then Gβ(·) defined by (31) is β(4−βL)  4  co-coercive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Moreover,  x⋆ ∈ zer(A + B) is a solution of (MI) iff Gβx⋆ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' The latter is exactly a special case of  (CE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' If dom(B) = Rp, then Gβ satisfies Assumption 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='1 with Li = β(4−βL)  4  for i ∈ [n].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Note  that we can extend our results to the case B is L−1-block coordinate-wise co-coercive as in  (CP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' However, we omit this extension here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  15  Our goal is to specify (ARBC) to solve Gβx⋆ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' In this case, we obtain the following  variant of (ARBC):  xk+1 := xk + θk(xk − xk−1) −  ψ  pik  �  ηkGβ  [ik]xk − γkGβ  [ik]xk−1�  ,  where θk, ψ, ηk, and γk are updated as in (ARBC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Clearly, by taking into account the  separable structure of A and using (31), we can explicitly write the block-coordinate of Gβx  as  [Gβx]i = 1  β(xi − JβAi(xi − β[Bx]i)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Combining the last two expressions,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' we can write the new variant of (ARBC) as follows:  \uf8f1  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f2  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f3  ˆdk−1  i  := xk−1  i  − JβAi(xk−1  i  − β[Bxk−1]i),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  if i = ik,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  dk  i  := xk  i − JβAi(xk  i − β[Bxk]i),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  if i = ik,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  xk+1  i  :=  \uf8f1  \uf8f2  \uf8f3  xk  i + θk(xk  i − xk−1  i  ) −  ψ  βpi  �  ηkdk  i − γk ˆdk−1  i  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' if i = ik,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  xk  i + θk(xk  i − xk−1  i  ),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  otherwise,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  (32)  where x0 ∈ Rp is a given initial point,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' x−1 := x0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' and ik ∈ [n] is randomly generated based  on the probability law (5),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Prob (i = ik) = pi for i ∈ [n].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  The scheme (32) requires two block-coordinate evaluations [Bxk−1]i and [Bxk]i of B and  two evaluations of JβAi at each iteration k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Therefore, it essentially costs as twice as existing  standard block-coordinate FBS methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' However, its convergence rate is significantly faster  than those standard block-coordinate FBS methods, typically O  �  1/k2�  compared to O (1/k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Finally, we specify Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='1 (without proof) to obtain convergence results of (32).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Let B be 1  L-co-coercive on Rp, A be maximally monotone, and zer(A+B) ̸= ∅  in (MI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Let {xk} be generated by (32) using pi :=  1  n (∀i ∈ [n]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' For given ω > 3 and  0 < β < 4  L, we choose 0 < ψ <  8  nβ(4−βL) and update θk, ηk, and γk as in (16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Then, both  quantities E  �  ∥Gβxk∥2�  and E  �  ∥xk+1 − xk∥2�  simultaneously achieve O  �  1/k2�  and o  �  1/k2�  convergence rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  In fact, if {xk} is generated by (32), then the bounds in (17) of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='1 still hold for  {xk} and Gβxk defined by (31).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' However, we only state the convergence rates in Corollary  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='2  ARBC Douglas-Rachford Splitting Method  We consider the case B in (MI) is just maximally monotone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' In this case, we consider the DR  residual mapping of (MI) defined as follows (see also [48]):  Eβu := 1  β (JβBu − JβA(2JβBu − u)) ,  (33)  where β > 0 is given, and JβA and JβB are the resolvents of βA and βB, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' As  shown in [48], Eβ(·) is β-co-coercive and dom(Eβ) = Rp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Moreover, x⋆ ∈ zer(A + B) is a  solution of (MI) if and only if there exists u⋆ ∈ Rp such that Eβu⋆ = 0 and x⋆ = JβBu⋆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  16  Now,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' if we directly apply (ARBC) to solve Eβu⋆ = 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' then by exploiting the separable  structure of A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' we obtain the following scheme for solving (MI):  \uf8f1  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f2  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f3  ˆvk−1  i  := [JβBuk−1]i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  if i = ik,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  vk  i  := [JβBuk]i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  if i = ik,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  ˆdk−1  i  := ˆvk−1  i  − JβAi(2ˆvk−1  i  − uk−1  i  ),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  if i = ik,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  dk  i  := vk  i − JβAi(2vk  i − uk  i ),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  if i = ik,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  uk+1  i  :=  \uf8f1  \uf8f2  \uf8f3  uk  i + θk(uk  i − uk−1  i  ) − ψ  pi  �  ηkdk  i − γk ˆdk−1  i  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' if i = ik,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  uk  i + θk(uk  i − uk−1  i  ),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  otherwise,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  (34)  where u0 ∈ Rp is given,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' u−1 := u0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' and ik ∈ [n] is randomly generated based on (5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Unlike (32), which operates directly on the sequence  �  xk�  , (34) generates an intermediate  sequence {uk}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' To recover an approximate solution xk of (MI), we can compute xk := JβBuk  at the end of the algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Again, our new scheme (34) is very different from existing ones  in the literature, including [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Note that (34) requires two block-coordinate evaluations  [JβBxk]i and [JβBxk−1]i of JβB, and two evaluations of JβAi at each iteration k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Hence, its  per-iteration complexity costs as twice as the method in [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' However, we believe that the  convergence rate of (34) is significantly faster than the one in [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Finally, similar to Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='1, we specify Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='1 to obtain convergence of (34).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Assume that zer(A + B) ̸= ∅ and both A and B in (MI) are maximally  monotone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Let {uk} be generated by (34) using pi := 1  n for all i ∈ [n].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' For given ω > 3,  β > 0, and 0 < ψ < 2β  n , we update θk, ηk, and γk as in (16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Then, both E  �  ∥Eβuk∥2�  and E  �  ∥uk+1 − uk∥2�  simultaneously achieve O  �  1/k2�  and o  �  1/k2�  convergence rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' If, in  addition, B is single-valued and xk := JβBuk, then both E  �  ∥Gβxk∥2�  and E  �  ∥xk+1 − xk∥2�  simultaneously achieve O  �  1/k2�  and o  �  1/k2�  convergence rates, where Gβxk is given by (31).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  This corollary is a direct consequence of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='1, and we omit its proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' The last  conclusion of Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='2 can easily be obtained by using the relation between Eβu and Gβu  as stated in [48, Lemma 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  5  Application to Finite-Sum Monotone Inclusions  Many machine learning applications and optimization models over networks, including fed-  erated learning, can be formulated into the following finite-sum monotone inclusion [13, 40]:  Find x⋆ ∈ dom(A) ∩ dom(B) such that  0 ∈ 1  n  n  �  i=1  Aix⋆ + Bx⋆ ≡ Ax⋆ + Bx⋆,  (35)  where Ai : Rp ⇒ Rp (∀i ∈ [n]) are maximally monotone and B : Rp ⇒ Rp is also maximally  monotone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Here, we also assume that zer(A + B) ̸= ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Note that A := 1  n  �n  i=1 Ai in (35) is  the average of a finite-sum operator, and it is different from the block separable operator in  (MI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Therefore, we cannot directly apply the methods in Section 4 to solve (35).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  17  One important special case of (35) is the optimality condition of the following finite-sum  convex minimization problem which is ubiquitous in machine learning and statistical learning:  min  x∈Rp  �  F(x) := 1  n  n  �  i=1  fi(x) + g(x)  �  ,  (36)  where fi : Rp → R ∪ {+∞} and g : Rp → R ∪ {+∞} are proper, closed, and convex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' The  optimality condition of (36) can be written as 0 ∈ 1  n  �n  i=1 ∂fi(x⋆) + ∂g(x⋆), which is covered  by (35) by setting Ai := ∂fi and B := ∂g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  To develop a new variant of (ARBC) for solving (35), we first reformulate (35) into (MI)  by duplicating the variable x as x := [x1, x2, · · · , xn], where xi ∈ Rp for all i ∈ [n].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Then, we  can reformulate (35) into the following monotone inclusion:  0 ∈ Ax⋆ + Bx⋆ + ∂δL(x⋆), where Ax := [A1x1, · · · , Anxn],  Bx := [nBx1, 0, · · · , 0], (37)  and ∂δL is the subdifferential of the indicator of the linear subspace L := {x = [x1, · · · , xn] ∈  Rnp : xi = x1, ∀i ∈ [n]}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' It is obvious to show that x⋆ is a solution of (35) if and only if  x⋆ = [x⋆, · · · , x⋆] solves (37), see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=', [51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Moreover, A and B in (37) are separable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Let us apply the ARBC DR splitting scheme (34) to solve (37).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Then we use the interpre-  tation in Subsection 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='2 to obtain a practical variant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Here, we view A as A and B + ∂δL as  B in (MI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Let us first compute the resolvent of β(B + ∂δL) at uk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' This requires solving  �  0 ∈ nβBu1 + βs1 + u1 − uk  1,  0 = βsi + ui − uk  i ,  i = 2, · · · , n,  (38)  where s := [s1, · · · , sn] ∈ ∂δL(u) ≡ L⊥ := {s := [s1, · · · , sn] : �n  i=1 si = 0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' The last line of  (38) leads to ui = uk  i − βzi if ui = u1 for i = 2, · · · , n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Therefore, we obtain  (n − 1)u1 =  n  �  i=2  uk  i − β  n  �  i=2  si =  n  �  i=2  uk  i − β  n  �  i=1  si + βs1 =  n  �  i=2  uk  i + βs1,  due to the fact that �n  i=1 si = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' This equation implies that u1 + βs1 = nu1 − �n  i=2 uk  i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Sub-  stituting this expression into the first line of (38), we get 0 ∈ nβBu1+nu1−�n  i=1 uk  i , or equiv-  alently, 0 ∈ βBu1 + u1 − 1  n  �n  i=1 uk  i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Solving this inclusion, we obtain u1 = JβB  � 1  n  �n  i=1 uk  i  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Let us defined ˆuk := JβB  � 1  n  �n  i=1 uk  i  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Then, we have Jβ(B+∂δL)uk = [ˆuk, · · · , ˆuk].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Conse-  quently, for any i ∈ [n], we obtain [Jβ(B+∂δL)uk]i = ˆuk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Next, we use the trick in Subsection 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='2 to eliminate uk  i in (34).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Since uk  i = zk  i + ckwk  i ,  we have ¯uk := 1  n  �n  i=1 uk  i = 1  n  �n  i=1(zk  i + ckwk  i ) = ¯zk + ck ¯wk, where ¯zk := 1  n  �n  i=1 zk  i and  ¯wk := 1  n  �n  i=1 wk  i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' However, at each iteration k, only wk  ik and zk  ik are updated, we have  �  ¯zk+1 := 1  n  �n  i=1 zk+1  i  = 1  n  �n  i=1 zk  i + 1  n(zk+1  ik  − zk  ik) = ¯zk + 1  n∆zk+1  ik  ,  ¯wk+1 := 1  n  �n  i=1 wk+1  i  = 1  n  �n  i=1 wk  i + 1  n(wk+1  ik  − wk  ik) = ¯wk + 1  n∆wk+1  ik  ,  where ∆zk+1  ik  := zk+1  ik  − zk  ik and ∆wk+1  ik  := wk+1  ik  − wk  ik.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Now, we are ready to specify (34) to solve (37) as in Algorithm 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  18  Algorithm 1 (Accelerated Federated Douglas-Rachford Algorithm (AccFedDR))  1: Initialization: Input an initial point u0 ∈ Rp and set c0 := c−1 := 0 and τ0 := 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  2:  Initialize each user i with z0  i = z−1  i  := u0 and w0  i = w−1  i  = 0 for i ∈ [n].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  3:  Initialize sever with ˆu0 = ˆu−1 := u0, ¯z0 := 0, and ¯w0 := 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  4: For k := 0, · · · , kmax do  5:  Sample an active user ik ∈ [n] following the probability law (5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  6:  [Communication] Server sends ˆuk and ˆuk−1 to user ik.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  7:  [Local update] User ik updates its iterates wk+1  ik  and zk+1  ik  as  \uf8f1  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f2  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f3  ˆdk−1  ik  := ˆuk−1 − JβAik (2ˆuk−1 − zk−1  ik  − ck−1wk−1  ik  ),  dk  ik  := ˆuk − JβAik (2ˆuk − zk  ik − ckwk  ik),  wk+1  ik  := wk  ik −  ψ  pik τk+1 (ηkdk  ik − γk ˆdk−1  ik  ),  zk+1  ik  := zk  ik +  ψck  pikτk+1 (ηkdk  ik − γk ˆdk−1  ik  ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  (39)  8:  [Communication] User ik sends ∆wk+1  ik  := wk+1  ik  −wk  ik and ∆zk+1  ik  := zk+1  ik  −zk  ik to server.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  9:  [Server update] Server updates  ¯wk+1 := ¯wk + 1  n∆wk+1  ik  ,  ¯zk+1 := ¯zk + 1  n∆zk+1  ik  , and ˆuk+1 := JβB(¯zk+1 + ck+1 ¯wk+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  10: End For  Let us abbreviate Algorithm 1 by AccFedDR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Note that the parameters are updated as in  (16) and (30).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Clearly, AccFedDR is still synchronous, but it only requires the participation  of one user ik at each communication round k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' This scheme is also similar to SAGA [15] and  a SAGA variant for co-coercive equations in [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' However, our AccFedDR can solve a more  general class of problems described by (35), where A is not necessarily co-coercive as in [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  This algorithm can also be applied to federated learning, see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=', [22, 26, 32, 33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  To prove convergence of Algorithm 1, let us define the following residual operator:  �  ˆu  := JβB  � 1  n  �n  i=1 ui  �  ,  Eβu := 1  β[ˆu − JβA1(2ˆu − u1), · · · , ˆu − JβAn(2ˆu − un)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  (40)  One can easily show that if Eβu⋆ = 0, then ˆu⋆ = JβB  � 1  n  �n  i=1 u⋆  i  �  solves (35).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Now, we can  specify the convergence of AccFedDR as a consequence of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Corollary 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Let Ai (i ∈ [n]) and B in (35) be maximally monotone and zer(A + B) ̸= ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Let {wk  i } and {zk  i } be generated by AccFedDR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Let uk := [uk  1, · · · , uk  n] with uk  i := zk  i + ckwk  i  for all i ∈ [n] and Eβu be defined by (40).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' For given ω > 3, β > 0, and 0 < ψ < 2βpmin, we  update θk, ηk, and γk as in (16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Then, we obtain the following bounds:  �+∞  k=0(k + ω + 1)E  �  ∥Eβuk−1∥2�  < +∞,  �+∞  k=0(k + ω)E  �  ∥uk − uk−1∥2�  < +∞,  �+∞  k=0(k + 1)2E  �  ∥Eβuk − Eβuk−1∥2�  < +∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  (41)  19  Moreover, the following statements also hold:  �  E  �  ∥uk+1 − uk∥2�  = O  � 1  k2  �  and  E  �  ∥uk+1 − uk∥2�  = o  � 1  k2  �  ,  E  �  ∥Eβuk∥2�  = O  � 1  k2  �  and  E  �  ∥Eβuk∥2�  = o  � 1  k2  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  (42)  Note that Corollary 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='1 only shows convergence on {uk}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' To form an approximate solution  ¯xk of (35), we simply compute ¯xk := JβB  � 1  n  �n  i=1 uk  i  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Clearly, we can also easily show that  E  �  ∥¯xk − ¯xk−1∥2�  = O  � 1  k2  �  and E  �  ∥¯xk − ¯xk−1∥2�  = o  � 1  k2  �  by the nonexpansiveness of JβB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Remark 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Since our model (35) is more general than that of [13], our AccFedDR al-  gorithm developed in this section can be applied to solve special cases as discussed in [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  However, we omit the details of these applications here to avoid repetition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  6  Concluding Remarks  We have developed a novel accelerated randomized block-coordinate method for solving a co-  coercive equation of the form (CE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' The new algorithm achieves O  �  1/k2�  and even o  �  1/k2�  convergence rates on the squared norm of the underlying operator G and some other quantities  in expectation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' We have also derived a practical variant and investigated three applications  of our method for more general problems to cope with broader classes of applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Several  research questions remain open to us.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Firstly, how to develop an accelerated randomized block-  coordinate method for (CE) under weaker assumptions: monotone and Lipschitz continuous?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  For example, how to extend our method to extra-anchored gradient schemes [54] or their  variants [25, 50]?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Secondly, how to extend such a type of methods to (MI) without the co-  coerciveness of B?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Thirdly, how to develop asynchronous variants of our method, including  the variant of Algorithm 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' In addition, several practical and implementation aspects of our  methods as well as numerical verification are still left out in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  We leave these  research questions for our future research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  References  [1] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Alacaoglu, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Tran-Dinh, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Fercoq, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Cevher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Smooth Primal-Dual Coor-  dinate Descent Algorithms for Nonsmooth Convex Optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Advances in Neural  Information Processing Systems (NIPS), pages 1–9, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [2] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Attouch and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Cabot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Convergence of a relaxed inertial proximal algorithm for  maximally monotone operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Program.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=', 184(1):243–287, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [3] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Attouch and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Fadili.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' From the Ravine method to the Nesterov method and vice  versa: a dynamical system perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' arXiv preprint arXiv:2201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='11643, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [4] A Auslender.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Méthodes numériques pour la décomposition et la minimisation de fonctions  non différentiables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Numerische Mathematik, 18(3):213–223, 1971.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [5] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Bauschke and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Combettes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Convex analysis and monotone operators theory in  Hilbert spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Springer-Verlag, 2nd edition, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  20  [6] Amir Beck, Edouard Pauwels, and Shoham Sabach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' The cyclic block conditional gradient  method for convex optimization problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' SIAM Journal on Optimization, 25(4):2024–  2049, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [7] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Bot, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Csetnek, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Nguyen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Fast OGDA in continuous and discrete  time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' arXiv preprint arXiv:2203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='10947, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [8] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Bottou, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Curtis, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Nocedal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Optimization Methods for Large-Scale Machine  Learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' SIAM Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=', 60(2):223–311, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [9] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Burachik and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Iusem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Set-Valued Mappings and Enlargements of Monotone  Operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' New York: Springer, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [10] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Chen, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Lan, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Ouyang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Accelerated schemes for a class of variational inequal-  ities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Program.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=', 165(1):113–149, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [11] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Combettes and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Pesquet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Stochastic quasi-Fejér block-coordinate fixed point  iterations with random sweeping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' SIAM J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Optim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=', 25(2):1221–1248, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [12] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Combettes and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Wajs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Signal recovery by proximal forward-backward splitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Multiscale Model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Simul.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=', 4:1168–1200, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [13] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Davis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Variance reduction for root-finding problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Program.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=', pages 1–36,  2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [14] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Davis and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Yin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' A three-operator splitting scheme and its optimization applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Set-valued and Variational Analysis, 25(4):829–858, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [15] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Defazio, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Bach, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Lacoste-Julien.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' SAGA: A fast incremental gradient method  with support for non-strongly convex composite objectives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' In Advances in Neural Infor-  mation Processing Systems (NIPS), pages 1646–1654, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [16] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Diakonikolas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Halpern iteration for near-optimal and parameter-free monotone inclu-  sion and strong solutions to variational inequalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' In Conference on Learning Theory,  pages 1428–1451.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' PMLR, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [17] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Facchinei and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Pang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Finite-dimensional variational inequalities and complemen-  tarity problems, volume 1-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Springer-Verlag, 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [18] Olivier Fercoq and Peter Richtárik.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Accelerated, parallel, and proximal coordinate de-  scent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' SIAM J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Optim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=', 25(4):1997–2023, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [19] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Halpern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Fixed points of nonexpanding maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Bull.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Am.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=', 73(6):957–961,  1967.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [20] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Kim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Accelerated proximal point method for maximally monotone operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Program.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=', pages 1–31, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [21] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Kim and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Fessler.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Optimized first-order methods for smooth convex minimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Program.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=', 159(1-2):81–107, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  21  [22] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Konečn`y, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' McMahan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Ramage, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Richtárik.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Federated optimization:  Distributed machine learning for on-device intelligence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' arXiv preprint arXiv:1610.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='02527,  2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [23] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Lan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' First-order and Stochastic Optimization Methods for Machine Learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Springer,  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [24] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Latafat, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Themelis, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Patrinos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Block-coordinate and incremental aggregated  proximal gradient methods for nonsmooth nonconvex problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Program.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=', pages  1–30, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [25] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Lee and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Kim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Fast extra gradient methods for smooth structured nonconvex-  nonconcave minimax problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Thirty-fifth Conference on Neural Information Processing  Systems (NeurIPs2021), 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [26] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Li, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Sahu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Talwalkar, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Smith.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Federated learning: Challenges, methods,  and future directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' IEEE Signal Processing Magazine, 37(3):50–60, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [27] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Lieder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  On the convergence rate of the halpern-iteration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Optimization Letters,  15(2):405–418, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [28] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Lions and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Mercier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Splitting algorithms for the sum of two nonlinear operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  SIAM J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Num.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=', 16:964–979, 1979.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [29] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='-E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Maingé.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Accelerated proximal algorithms with a correction term for monotone  inclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Applied Mathematics & Optimization, 84(2):2027–2061, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [30] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Maingé.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Fast convergence of generalized forward-backward algorithms for structured  monotone inclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' arXiv preprint arXiv:2107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='10107, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [31] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Malitsky.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Projected reflected gradient methods for monotone variational inequalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  SIAM J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Optim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=', 25(1):502–520, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [32] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' McMahan and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Ramage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Federated learning: Collaborative machine learning with-  out centralized training data, Jul 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [33] H Brendan McMahan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Advances and open problems in federated learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Founda-  tions and Trends® in Machine Learning, 14(1), 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [34] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Nesterov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' A method for unconstrained convex minimization problem with the rate of  convergence O(1/k2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Doklady AN SSSR, 269:543–547, 1983.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Translated as Soviet Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Dokl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [35] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Nesterov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Introductory lectures on convex optimization: A basic course, volume 87 of  Applied Optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Kluwer Academic Publishers, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [36] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Nesterov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Efficiency of coordinate descent methods on huge-scale optimization prob-  lems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' SIAM J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Optim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=', 22(2):341–362, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  22  [37] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Nesterov and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Stich.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Efficiency of the accelerated coordinate descent method on  structured optimization problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' SIAM J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Optim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=', 27(1):110–123, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [38] James M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Ortega and Werner C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Rheinboldt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Iterative solution of nonlinear equations  in several variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Society for Industrial and Applied Mathematics, Philadelphia, PA,  USA, 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [39] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Ouyang and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Xu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Lower complexity bounds of first-order methods for convex-  concave bilinear saddle-point problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Program.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=', online first:1–35, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [40] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Peng, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Xu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Yan, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Yin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' ARock: an algorithmic framework for asynchronous  parallel coordinate updates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' SIAM J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Scientific Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=', 38(5):2851–2879, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [41] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Phelps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Convex functions, monotone operators and differentiability, volume 1364.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Springer, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [42] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Popov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' A modification of the Arrow-Hurwicz method for search of saddle points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' notes of the Academy of Sciences of the USSR, 28(5):845–848, 1980.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [43] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Richtárik and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Takáč.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Parallel coordinate descent methods for big data optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Program.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=', 156(1-2):433–484, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [44] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Rockafellar and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Wets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Variational Analysis, volume 317.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Springer, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [45] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Rockafellar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Monotone operators and the proximal point algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' SIAM J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Con-  trol Optim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=', 14:877–898, 1976.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [46] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Ryu and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Boyd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Primer on monotone operator methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Math,  15(1):3–43, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [47] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Sra, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Nowozin, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Wright.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Optimization for Machine Learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' MIT Press,  2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [48] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Tran-Dinh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  The connection between Nesterov’s accelerated methods and Halpern  fixed-point iterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' arXiv preprint arXiv:2203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='04869, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [49] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Tran-Dinh and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Liu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' A new randomized primal-dual algorithm for convex opti-  mization with optimal last iterate rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Optimization Methods & Software), pages 1–34  (online first), 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [50] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Tran-Dinh and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Luo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Halpern-type accelerated and splitting algorithms for mono-  tone inclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' arXiv preprint arXiv:2110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='08150, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [51] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Tran-Dinh, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Pham, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Phan, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Nguyen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' FedDR–Randomized Douglas-  Rachford splitting algorithms for nonconvex federated composite optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' NeurIPs  2021, pages 1–39, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [52] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Tseng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' A modified forward-backward splitting method for maximal monotone map-  pings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' SIAM J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Control and Optim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=', 38(2):431–446, 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  23  [53] Stephen J Wright.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Coordinate descent algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Program.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=', 151(1):3–34, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  [54] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Yoon and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Ryu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' Accelerated algorithms for smooth convex-concave minimax  problems with O(1/k2) rate on squared gradient norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' In International Conference on  Machine Learning, pages 12098–12109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content=' PMLR, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
+page_content='  24' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE1T4oBgHgl3EQfWQTV/content/2301.03113v1.pdf'}
diff --git a/F9E0T4oBgHgl3EQfRAC9/content/2301.02202v1.pdf b/F9E0T4oBgHgl3EQfRAC9/content/2301.02202v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..de417d371fffe5c85befec38cd9f74c3bccaa49d
--- /dev/null
+++ b/F9E0T4oBgHgl3EQfRAC9/content/2301.02202v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:bdd9441cf249974b9220d4dda39fe253b35cf9c03b1dee8c366096df18e9ce20
+size 332266
diff --git a/F9E0T4oBgHgl3EQfRAC9/vector_store/index.faiss b/F9E0T4oBgHgl3EQfRAC9/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..8daff5412d7e83c9133714dd9f3f61b9080ab7ab
--- /dev/null
+++ b/F9E0T4oBgHgl3EQfRAC9/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7da9a43235801a91bd657c3cb1b407d1c102eff096c221c5eae438bed127da56
+size 6094893
diff --git a/FtAyT4oBgHgl3EQf5Poe/content/2301.00799v1.pdf b/FtAyT4oBgHgl3EQf5Poe/content/2301.00799v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..17ebd94ca0d8d3c450c341583b6dafc0b4977c04
--- /dev/null
+++ b/FtAyT4oBgHgl3EQf5Poe/content/2301.00799v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:84b57f93518ac1f71e3c0703d901f6e5ffd40dc31c9685786803b660a24dfe70
+size 19787039
diff --git a/FtE4T4oBgHgl3EQfHAzF/content/2301.04900v1.pdf b/FtE4T4oBgHgl3EQfHAzF/content/2301.04900v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..634dae455e57a7b205f5b6fdd271027091714fc0
--- /dev/null
+++ b/FtE4T4oBgHgl3EQfHAzF/content/2301.04900v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f5f14bc182a4cbdc8757e2615277d4c2e36f1f90884419022895ab9812986477
+size 612773
diff --git a/FtE4T4oBgHgl3EQfHAzF/vector_store/index.faiss b/FtE4T4oBgHgl3EQfHAzF/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..f81b5602281c3bd603c1217ec321cc05c723e743
--- /dev/null
+++ b/FtE4T4oBgHgl3EQfHAzF/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:27cee23da7a79174d6a40286a3867b8e4871027a9e94a124f4572bee00baa2b0
+size 1900589
diff --git a/FtE4T4oBgHgl3EQfHAzF/vector_store/index.pkl b/FtE4T4oBgHgl3EQfHAzF/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..a179aee1e1e6910326395aad737dc384df35c599
--- /dev/null
+++ b/FtE4T4oBgHgl3EQfHAzF/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:856b674a68de0c40fb8cfc98322173cc2ee614aeba0dd8c1fcde2316a906dd7c
+size 70418
diff --git a/HNAyT4oBgHgl3EQfS_eb/content/2301.00097v1.pdf b/HNAyT4oBgHgl3EQfS_eb/content/2301.00097v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..2983d60a91dc26c157b14e7989baa8cc59c98123
--- /dev/null
+++ b/HNAyT4oBgHgl3EQfS_eb/content/2301.00097v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:62e98c92ffff72f951a1cf3996d31dce900acf5ed455cc0d1e71f57600fff39b
+size 225234
diff --git a/HNAyT4oBgHgl3EQfS_eb/vector_store/index.faiss b/HNAyT4oBgHgl3EQfS_eb/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..d053899979b765209a9e23c96c91299949099d93
--- /dev/null
+++ b/HNAyT4oBgHgl3EQfS_eb/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:367629a771feb0d14f6657af48dbc1ed8e59503264f627f0bc13a11ee1098af0
+size 3342381
diff --git a/HNAyT4oBgHgl3EQfS_eb/vector_store/index.pkl b/HNAyT4oBgHgl3EQfS_eb/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..4a5b01e351cc0cc7a0ebf92a402ccec568841d72
--- /dev/null
+++ b/HNAyT4oBgHgl3EQfS_eb/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d598f9afe6cb2ece2fa94bf8c081db1c37a3ed1e30aea87eefc95d60221ee398
+size 131391
diff --git a/HdAyT4oBgHgl3EQfffgY/content/tmp_files/2301.00339v1.pdf.txt b/HdAyT4oBgHgl3EQfffgY/content/tmp_files/2301.00339v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f62db24bacf46f8b255ce7c39d845c00672d24f9
--- /dev/null
+++ b/HdAyT4oBgHgl3EQfffgY/content/tmp_files/2301.00339v1.pdf.txt
@@ -0,0 +1,922 @@
+arXiv:2301.00339v1  [cond-mat.mtrl-sci]  1 Jan 2023
+The Origin of Two-dimensional Electron Gas in Zn1−xMgxO/ZnO Heterostructures
+Xiang-Hong Chen,1 Dong-Yu Hou,1 Zhi-Xin Hu,2 Kuang-Hong Gao,1, ∗ and Zhi-Qing Li1, †
+1Tianjin Key Laboratory of Low Dimensional Materials Physics and Preparing Technology,
+Department of Physics, Tianjin University, Tianjin 300354, China
+2Center for Joint Quantum Studies and Department of Physics, Tianjin University, Tianjin 300354, China
+(Dated: January 3, 2023)
+Although the two-dimensional electron gas (2DEG) in (001) Zn1−xMgxO/ZnO heterostructures
+has been discovered for about twenty years, the origin of the 2DEG is still inconclusive. In the
+present letter, the formation mechanisms of 2DEG near the interfaces of (001) Zn1−xMgxO/ZnO
+heterostructures were investigated via the first-principles calculations method. It is found that the
+polarity discontinuity near the interface can neither lead to the formation of 2DEG in devices with
+thick Zn1−xMgxO layers nor in devices with thin Zn1−xMgxO layers. For the heterostructure with
+thick Zn1−xMgxO layers, the oxygen vacancies near the interface introduce a defect band in the
+band gap, and the top of the defect band overlaps with the bottom of the conduction band, leading
+to the formation of the 2DEG near the interface of the device. For the heterostructure with thin
+Zn1−xMgxO layers, the absorption of hydrogen atoms, oxygen atoms, or OH groups on the surface
+of Zn1−xMgxO film plays a key role for the formation of 2DEG in the device. Our results manifest
+the sources of 2DEGs in Zn1−xMgxO/ZnO heterostructures on the electronic structure level.
+Since
+the
+discovery
+of
+two-dimensional
+electron
+gas (2DEG) at the interface of LaAlO3/SrTiO3 het-
+erojunction [1],
+2DEG has been found at various
+oxide heterostructures, such as Zn1−xMgxO/ZnO [2–
+4],
+Al2O3/SrTiO3
+[5,
+6],
+EuO/KTaO3
+[7],
+(AlxGa1−x)2O3/Ga2O3
+[8]
+and
+LaAlO3/KTaO3
+[9].
+The 2DEG at oxide heterostructures not only provides
+a platform for fundamental research, but also promotes
+the development of novel all-oxide electronic devices.
+Among these oxide heterostructures, Zn1−xMgxO/ZnO
+heterostructures
+are
+particularly
+attractive
+due
+to
+their ultra-high Hall mobility (up to 106 cm2V−1s−1
+at low temperature [10]).
+However, the origin of the
+2DEG at the Zn1−xMgxO/ZnO interface is still unclear.
+Researchers only empirically attribute it to the polar
+discontinuity [11–14]: since Zn1−xMgxO (0 < x < 0.6)
+and ZnO have different spontaneous polarization, the
+polarization at the
+interface is
+discontinuous after
+they form heterojunctions.
+This discontinuity causes
+a large number of bound charges to be generated at
+the heterointerface, creating a built-in electric field
+throughout the
+heterostructure.
+This field drives
+electrons toward the interface to form 2DEG. In con-
+trast, some researchers believe that the 2DEG at the
+Zn1−xMgxO/ZnO interface originates from the donor on
+the Zn1−xMgxO surface [15, 16]. Experimentally, 2DEG
+can also be formed when the thickness of Zn1−xMgxO
+layer
+is
+greater
+than
+300 nm
+in
+Zn1−xMgxO/ZnO
+heterostructures [17–20].
+There would be no internal
+potential gradient in the aforementioned heterostructure
+with thick Zn1−xMgxO layer, and the contribution of
+surface donors to 2DEG could also be negligible [21, 22].
+Thus the formation of 2DEG in this case cannot be
+explained by the mechanisms mentioned above.
+On
+∗ Corresponding author, e-mail: khgao@tju.edu.cn
+† Corresponding author, e-mail: zhiqingli@tju.edu.cn
+the whole, the origin of 2DEG at Zn1−xMgxO/ZnO
+heterointerface needs to be further studied. In this letter,
+the origin of 2DEG at Zn1−xMgxO/ZnO heterointerface
+is studied from the perspective of microscopic electronic
+structures by first-principles calculations. Interestingly,
+it is found that the polar discontinuity mechanism is
+not responsible for the formation of the 2DEG. For the
+heterostructures with thick Zn1−xMgxO layers, 2DEG
+mainly arises from oxygen vacancies, while the 2DEG
+originates from surface adsorption for heterostructures
+with thin Zn1−xMgxO layers.
+Considering
+that
+the
+2DEG
+can
+be
+formed
+in
+Zn1−xMgxO/ZnO
+heterostructures
+with
+both
+thick
+(∼100 to 500 nm) [23–27] and thin Zn1−xMgxO layers
+(∼10 to 30 nm) [14–16] experimentally, we construct the
+configurations as follows.
+For Zn1−xMgxO/ZnO het-
+erostructures with thick Zn1−xMgxO layers, we passi-
+vated the oxygen terminal of ZnO slab and the Zn-Mg
+terminal of Zn1−xMgxO slab by pseudo-H atoms with
+fractional charges. ZnO slab with passivated oxygen ter-
+minal can be used to simulate ZnO substrate, and the
+charge of H is taken as 0.48e with e being the elementary
+charge [21]. The charge of the pseudo-H atoms in the
+passivated Zn-Mg terminal is taken as 1.52e [21]. After
+passivation, the pseudo-H atoms not only saturate the
+surface dangling bonds but also make the passivated sur-
+face and the adjacent atomic layers exhibit bulk prop-
+erties [21, 23]. In this case, the Zn1−xMgxO and ZnO
+slabs can be treated as semi-infinite thick films.
+Con-
+sidering the Mg content x can be as high as 0.60 in
+Zn1−xMgxO/ZnO heterostructures experimentally [24],
+we set the Mg content x as 0.25 and 0.50, respectively.
+For each doping level, the Mg ions are uniformly doped
+into the ZnO film, which together with the ZnO sub-
+strate forms a heterostructure with a clear interface.
+For the Zn1−xMgxO/ZnO heterostructures with thin
+Zn1−xMgxO layers, the difference in the configuration is
+that there is no pseudo-H atom at the Zn-Mg terminal.
+
+2
+Generally, the unpassivated Zn1−xMgxO (001) surface
+is unstable and the surface adsorption or reconstruction
+is inevitable [25–31]. Thus, the surface adsorption and
+defects are considered to simulate the Zn1−xMgxO/ZnO
+heterostructures with thin Zn1−xMgxO layers [26]. As
+an example, in Fig. 1(a) we give the structure diagram
+of a Zn1−xMgxO/ZnO heterostructure with two surfaces
+passivated by pseudo-H atoms. The heterostructure con-
+tains a 2×2 in-plane (001) Zn0.75Mg0.25O/ZnO supercell
+and 18 Zn-Mg-O layers and 18 Zn-O layers. A 15-˚A-thick
+vacuum layer is added along the [001] direction to prevent
+any unintentional interactions between the slabs. From
+the interface to surface, the atomic layers on the ZnO side
+are labeled as L¯1, L¯2, · · · , L ¯17, and L ¯18, while the atomic
+layers on the Zn0.75Mg0.25O side are labeled as L1, L2,
+· · · , L17, and L18, respectively. The top view of Fig. 1(a)
+along the [001] direction is shown in Fig. 1(b).
+Three
+adsorption sites named On-top, Fcc-hollow, and Hcp-
+hollow, are indicated by the arrows. The positions of zinc
+atoms in each layer are numbered as 1, 2, 3, and 4, respec-
+tively. For the Mg doping level x = 0.25 case, the zinc
+atoms at position 1 are substituted by magnesium atoms
+in the odd layers, while the zinc atoms at position 3 are
+replaced in the even layers. For the x = 0.50 situation,
+the zinc atoms at positions 2 and 4 are replaced by mag-
+nesium atoms in each layer. All calculations are carried
+out in framework of density functional theory using the
+Viennaab initio Simulation Package (VASP) [32]. The
+in-plane lattice constants of Zn1−xMgxO/ZnO (x = 0.25
+and 0.50) heterostructures are fixed to those of ZnO dur-
+ing the calculations.
+FIG.
+1.
+(a)
+Schematic
+geometrical
+structure
+of
+Zn1−xMgxO/ZnO
+(x=0.25
+and
+0.50)
+heterostructure
+with two pseudo-H-passivated surfaces.
+(b) The top view
+of the heterostructure along the [001] direction.
+Here the
+“On-top, Fcc-hollow, and Hcp-hollow” are the adsorption
+sites for exotic atoms or groups.
+Figure
+2(a)
+shows
+the
+band
+structure
+of
+Zn0.75Mg0.25O/ZnO heterostructure shown in Fig. 1(a)
+(i.e., the heterostructure has 18 Zn-O and 18 Zn-Mg-O
+-1
+0
+1
+2
+3
+4
+0
+20
+40
+60
+80
+100
+-6
+-4
+-2
+0
+2
+4
+6
+ 
+ 
+Energy (eV)
+M
+K
+(a)
+(b)
+L18
+ Planar average
+ Macroscopic average
+L2
+ 
+ 
+Electrostatic potential (eV)
+Distance along the [001] (�
+)
+L18
+L4
+Interface
+ZnO
+Zn
+0. 75
+Mg
+0. 25
+O
+FIG.
+2.
+(a)
+The
+energy
+band
+structure
+of
+the
+Zn0.75Mg0.25O/ZnO heterostructure without oxygen vacan-
+cies and with two pseudo-H-atoms-passivated surfaces.
+(b)
+The plane average (solid curve) and macroscopic average
+(dash-dot curve) electrostatic potential (seen by electron)
+across the Zn0.75Mg0.25O/ZnO heterostructure along the [001]
+direction.
+layers and two pseudo-H-atoms-passivated surfaces).
+Clearly, the valence band maximum (VBM) and the con-
+duction band minimum (CBM) are both located at the Γ
+point, and the Fermi level lies in the band gap. Thus the
+energy band of the Zn0.75Mg0.25O/ZnO heterostructure
+exhibits direct-gap semiconductor characteristics (the
+calculated band gap is 1.45 eV) and no 2DEG is formed
+at the interface. For the x = 0.50 case, the band struc-
+ture is similar to that of the x = 0.25 and the calculated
+bad gap is 1.56 eV. Therefore, 2DEG cannot appear near
+the interfaces of the perfect Zn1−xMgxO/ZnO (x = 0.25
+and 0.50) heterostructures (without defects) with thick
+Zn1−xMgxO layers. We also calculated the electrostatic
+potential distribution for the above heterostructures,
+and Fig. 2(b) presents the results for the x = 0.25 case
+as an example.
+There is a conspicuous bulge in the
+macroscopic average potential curve near the interface
+(from the L¯4 Zn-O layer to the L2 Zn-Mg-O layer). In
+the atomic layers away from the interface, e.g., the Zn-O
+layers from L¯4 to L ¯18 or Zn-Mg-O layers from L2 to
+L18, the average potential almost retains a constant.
+Thus, a potential barrier rather than a quantum well
+is formed near the interface of the Zn0.75Mg0.25O/ZnO
+heterostructure.
+Similar phenomena are also observed
+in the macroscopic average potential curve of the
+Zn0.5Mg0.5O/ZnO
+heterostructure.
+This
+potential
+barrier should be caused by the polar discontinuity at
+the interface, which could induce a localized polarization
+field near the interface.
+The polarization field cannot
+cause the bottom of the conduction band to overlap
+with the top of the valence band as in the case of
+LaAlO3/SrTiO3 heterostructures [33]. Thus, the polar
+discontinuity alone cannot explain the observed 2DEG
+near the interface of Zn1−xMgxO/ZnO heterostructure
+with thick Zn1−xMgxO layers.
+Then,
+why
+the
+2DEGs
+can
+be
+formed
+in
+Zn1−xMgxO/ZnO
+heterostructures
+with
+thick
+
+wollod-qoH
+ECC-JOJJOM
+OU-tob
+(p) Lob AIGM sJoua e [ool]q!lGcrIo
+U
+M
+·H
+T18
+r18
+SUO
+(B)3
+-0.5
+-0.4
+-0.3
+-0.2
+-0.1
+-0.4
+-0.2
+0.0
+0.2
+0.4
+ 
+ 
+Formation energy (eV)
+Zn O
+Zn
+0.75
+Mg
+0.25
+O
+In t erface
+(a)
+L1
+L6
+L12
+L12
+L6
+L1
+L1
+L6
+L12
+L12
+L6
+L1
+Formation energy (eV)
+ 
+In t erface
+Zn O
+Zn
+0.5
+Mg
+0.5
+O
+(b)
+FIG. 3. Formation energies of oxygen vacancies at different
+atomic layers in Zn1−xMgxO/ZnO heterostructures with two
+pseudo-H-passivated surfaces. (a) For the x = 0.25, and (b)
+for the x = 0.50 heterostructures.
+Zn1−xMgxO layers?
+It should be noticed that as
+intrinsic defects in ZnO and Zn1−xMgxO films, oxygen
+vacancies are inevitable during device fabrication and
+could play crucial roles for the formation of 2DEG in
+Zn1−xMgxO/ZnO heterostructures [34–37]. Next, we in-
+vestigate the effect of oxygen vacancies on the electronic
+structures of Zn1−xMgxO/ZnO (x = 0.25 and 0.50)
+heterostructures with thick Zn1−xMgxO layers.
+First,
+we calculate the formation energy of oxygen vacancies
+(Ef) in each atomic layer of the above heterostructures.
+In the oxygen-rich limit, Ef can be written as [38]
+Ef = E(VO) − (E0 − 0.5EO2),
+(1)
+where E(VO) and E0 are the calculated total energies of
+the Zn1−xMgxO/ZnO (x = 0.25 and 0.50) heterostruc-
+tures with and without oxygen vacancies, and EO2 is the
+calculated total energy of the single O2 molecule. For
+the configuration in Fig. 1, each in-plane supercell con-
+tains four oxygen atoms, whose positions are labeled as
+a, b, c, and d, respectively. The oxygen atoms at d po-
+sition are removed in a certain fixed layer to create oxy-
+gen vacancies in the calculations.
+Figure 3 shows the
+formation energies of the oxygen vacancies in each layer
+of the Zn0.75Mg0.25O/ZnO and Zn0.5Mg0.5O/ZnO het-
+erostructures with 18 Zn-O and 18 Zn-Mg-O layers, and
+two pseudo-H-passivated surfaces. Inspection of Fig. 3
+indicates that the overall variation trends of the Ef vs
+layer number curves for the two heterostructures are sim-
+ilar.
+Thus we only discuss the variation of Ef in the
+Zn0.75Mg0.25O/ZnO heterostructure. On the ZnO side,
+the value Ef keeps as a constant in the first two layers,
+and then sharply increases with increasing layer number,
+reaches its maximum at L¯4, then decreases with further
+increasing layer number, and tends to be saturated as the
+layer number is greater than 9. On the Zn0.75Mg0.25O
+side, the values of Ef near the interface (L1 to L6 Zn-
+Mg-O layers) vary between −0.3 eV and −0.1 eV, while
+those for the layers with layer number being greater than
+6 are almost fixed at −0.1 eV. Obviously, the oxygen va-
+cancies can be easily formed on the ZnO side, especially
+in the first two Zn-O layers near the interface.
+Considering the variation trends in electronic struc-
+tures with VO position for the x = 0.25 and 0.50 het-
+erostructures with two pseudo-H passivated surfaces are
+also similar, we only present and discuss the results ob-
+tained from the x = 0.25 ones.
+We first discuss the
+case that oxygen vacancies are located at the most eas-
+ily formed position (L¯1 layer). Figure 4(a) presents the
+band structure of this configuration. From this figure,
+one can see that the oxygen vacancies in the L¯1 Zn-O
+layer introduce a defect band in the band gap and the
+top of the defect band is higher than the Fermi level.
+At the same time, the Fermi level enters into the bot-
+tom of the conduction band, i.e., the conduction band
+overlaps with the defect band. Thus, part of the elec-
+trons in the defect band would be transferred into the
+conduction band and become conduction electrons. Fig-
+ure 4(b) shows the partial density of states (DOS) pro-
+jected onto atomic planes for the x = 0.25 heterostruc-
+ture with oxygen vacancies in the L¯1 Zn-O layer and two
+pseudo-H passivated surfaces. Clearly, only in L¯2 , L¯1,
+and L1 layers the DOS near the Fermi level is nonzero,
+i.e., the conduction electrons are concentrated in the two
+Zn-O layers and one Zn-Mg-O layer near the interface.
+These three layers occupy a space with thickness ∼8.4 ˚A,
+which indicates that the 2DEG is formed near the in-
+terface of the heterostructure. From the orbital DOS of
+L¯2 to L1 layers, it is found that these conduction elec-
+trons are mainly composed of Zn-4s and O-2p orbitals
+(not shown). In addition, it is found that when the oxy-
+gen vacancies are located in the L¯2 and L¯3 Zn-O lay-
+ers and the L1 to L6 Zn-Mg-O layers, their band struc-
+FIG. 4. (a) The band structure of Zn0.75Mg0.25O/ZnO het-
+erostructure with oxygen vacancies in the L¯1 Zn-O layer.
+(b) The partial DOS projected onto atomic planes for
+the Zn0.75Mg0.25O/ZnO heterostructure with oxygen vacan-
+cies in the L¯1 Zn-O layer.
+(c) The band structure of
+Zn0.75Mg0.25O/ZnO heterostructure with oxygen vacancies in
+the L ¯15 Zn-O layer.
+(d) The partial DOS projected onto
+atomic planes for the Zn0.75Mg0.25O/ZnO heterostructure
+with oxygen vacancies in the L ¯15 Zn-O layer.
+
+　K
+I
+M
+D02 (e)G)
+0
+0
+(C)
+S
+(b)
+L
+M
+L
+-3
+3
+5
+EUGL& (GA)
+EUGLS (GA)
+0
+0
+(g)
+(d)
+r18
+II
+I184
+tures are similar to that in Fig. 4(a). However, the band
+structures of the heterostructures would reveal semicon-
+ductor characteristics when the oxygen vacancies are far
+from the interface (i.e., behind the L¯3 Zn-O layer and
+L6 Zn-Mg-O layer).
+We take the Zn0.75Mg0.25O/ZnO
+heterostructure with oxygen vacancies in the L ¯15 Zn-O
+layer as an example. Figure 4(c) shows the band struc-
+ture of this configuration. The oxygen vacancies in the
+L ¯15 Zn-O layer also introduce a defect band in the gap,
+while the top of the defect band is located at 0.11 eV be-
+low the bottom of the conduction band. The Fermi level
+lies between the conduction band and the defect band.
+Therefore, the introduction of oxygen vacancies in the
+L ¯15 Zn-O layer cannot induce 2DEG at the interface of
+the heterostructure. Figure 4(d) shows the partial DOS
+projected onto atomic planes for the Zn0.75Mg0.25O/ZnO
+heterostructure with oxygen vacancies in the L ¯15 Zn-O
+layer. From this figure, one can see that the defect band
+of the oxygen vacancies is in fact composed of a large
+number of deep energy levels as far as the energy band
+of the inner atomic layer is concerned. These deep lev-
+els cannot overlap with the conduction band even if the
+bottom conduction band of the Zn-O layer near the in-
+terface is lower than that of the inner Zn-O layer. On
+the contrary, the defect levels of the oxygen vacancies
+near the interface layers are so shallow that the bottom
+of the conduction band overlaps with the top of the de-
+fect band [see Fig. 4(b)]. This is why 2DEG exists only
+when the oxygen vacancies are located near the interface
+of the heterostructure. On the other hand, the defect
+band formed by oxygen vacancies of inner Zn-O layers
+could enhance the conductivity of the heterostructure:
+the device will exhibit a thermal-activated form conduc-
+tance with activation energy Ea, where Ea is about half
+of the energy difference between the bottom of conduc-
+tion band and the top of the defect band. Summarizing
+the results mentioned above, one can readily conclude
+that the oxygen vacancies near the interface are the ori-
+gin of the 2DEGs in Zn1−xMgxO/ZnO (x = 0.25 and
+0.50) heterostructures with thick Zn1−xMgxO layers.
+Now,
+we
+study
+the
+origin
+of
+2DEGs
+in
+Zn1−xMgxO/ZnO (x
+=
+0.25 and 0.50) heterostruc-
+tures when the Zn1−xMgxO films are very thin. In this
+situation, we calculate the electronic structures of the
+heterostructures with 42 Zn-O and 18 Zn-Mg-O layers,
+in which the surface of the Zn1−xMgxO film is no longer
+passivated.
+The reason for choosing 42 Zn-O layers
+(instead of 18 layers) is to obtain the distribution range
+of 2DEG on the ZnO side.
+Since the results obtained
+from the x = 0.25 and 0.50 heterostructures are also
+similar, we only present and discuss the results for the
+x = 0.25 heterostructure. Figure 5(a) shows the electro-
+static potential of Zn0.75Mg0.25O/ZnO heterostructure
+(with 42 Zn-O and 18 Zn-Mg-O layers) in which only
+the surface of ZnO film is passivated by pseudo-H
+atoms.
+Obviously, the macroscopic average potential
+on the ZnO side is insensitive to the position, while it
+decreases with increasing distance to the interface on
+0
+40
+80
+120
+160
+-10
+-5
+0
+5
+10
+0
+40
+80
+120
+160
+-10
+-5
+0
+5
+10
+Interface
+ 
+ 
+Electrostatic potential (eV)
+Distance along the [001] direction (�)
+ZnO
+Zn
+0 .7 5
+Mg
+0 .2 5
+O
+(a)
+ Macroscopic-Average
+ Planar-Average
+Electrostatic potential (eV)
+ 
+Interface
+ZnO
+Zn
+0 .7 5
+Mg
+0 .2 5
+O
+L10
+L18
+(b)
+FIG. 5. (a) The plane average (solid curve) and macroscopic
+average (dash-dot curve) electrostatic potential (seen by elec-
+tron) along [001] direction for the Zn0.75Mg0.25O/ZnO het-
+erostructure, in which only the surface of ZnO film is pas-
+sivated by pseudo-H atoms.
+(b) The plane average (solid
+curve) and macroscopic average (dash-dot curve) electro-
+static potential (seen by electron) along [001] direction of the
+Zn0.75Mg0.25O/ZnO heterostructure with a Zn0.75Mg0.25O
+surface of H-atom adsorption.
+the Zn0.75Mg0.25O side.
+A macroscopic field perpen-
+dicular to the surface with the magnitude of 0.06 V/˚A
+is obtained by linear fitting the macroscopic average
+electrostatic potential.
+This kind of field or potential
+would lead to an instability of the (001) polar (so-called
+Tasker type III) surface [29, 39]. In the light of recent
+experimental and theoretical results, the polar oxide
+surfaces can be stabilized via charge transfer between the
+upper and lower surfaces [25, 26], adsorption of external
+atoms [25–29], and stoichiometry variations [25–28].
+For Zn1−xMgxO/ZnO heterostructures, we consider the
+effects of adsorption (hydrogen atoms, OH groups, and
+oxygen atoms) and stoichiometry variations (defects) on
+the electronic structures of Zn1−xMgxO/ZnO (x = 0.25
+and 0.50) heterostructures.
+Through structural relax-
+ations, it is found that the hydrogen atoms prefer to
+be adsorbed atop the zinc atom (On-top site), while
+the preferred adsorption sites for the OH groups and
+oxygen atoms are the Fcc-hollow sites [see Fig. 1(b)].
+Our results are consistent with those in Refs. [25–27].
+For the 2 × 2 in-plane (001) Zn1−xMgxO supercell, the
+numbers of the On-top and Fcc-hollow sites are both 4.
+In our calculations, the coverages of hydrogen atoms,
+OH groups, and oxygen atoms adsorbed on the surface
+of Zn1−xMgxO are 50%, 50%, and, 25%, respectively,
+while the concentration of vacancies on the Zn or Mg
+sites is 25% [25–27].
+Specifically, for the x = 0.25
+heterostructure, the absorption sites of the hydrogen
+atoms are set on the top of the zinc atoms at positions
+1 and 4 [see Fig. 1(b)]; the adsorption sites for the OH
+groups are set at Fcc-hollow positions located at the
+top of the arrow and the position of the black dot; the
+Fcc-hollow position at the top of the arrow is also set
+as the adsorption site of oxygen atoms; the Zn vacancies
+are obtained via removing the zinc atoms located at
+
+5
+H
+ads
+L42
+ZnO
+Zn
+0. 75
+Mg
+0. 25
+O
+L10
+L12
+ 
+ 
+Energy (eV)
+(a)
+(b)
+ZnO
+Zn
+0. 75
+Mg
+0. 25
+O
+L1
+L42
+H
+pass
+L10
+L15
+L1
+ 
+DOS (states/eV)
+ 
+Energy (eV)
+FIG. 6. The partial DOS projected onto the atomic layers for
+the Zn0.75Mg0.25O/ZnO heterostructures with surfaces of (a)
+H-atom absorption, and (b) O-atom absorption.
+position 1.
+Figure
+5(b)
+shows
+the
+electrostatic
+potential
+of
+Zn0.75Mg0.25O/ZnO
+heterostructures
+with
+hydrogen
+atoms adsorbed on the Zn0.75Mg0.25O surface (and with
+42 Zn-O and 18 Zn-Mg-O layers). The results for the
+Zn0.75Mg0.25O surface with oxygen atoms adsorption,
+OH groups adsorption, and Zn or Mg vacancies are simi-
+lar to that shown in Fig. 5(b). The macroscopic average
+potential on the ZnO side remains nearly a constant af-
+ter adsorption of hydrogen atoms. On the Zn0.75Mg0.25O
+side, the macroscopic average potential is almost insensi-
+tive to the position from L1 to L9 layers, and then slightly
+increases with increasing distance to the interface. An
+electrostatic field (with magnitude of ∼0.038 V/˚A) being
+opposite to that shown in Fig 5(b) exists between L10
+and L18 layers.
+Thus surface adsorption or metal ion
+vacancies could really stabilize the polar surfaces of the
+Zn1−xMgxO/ZnO (x = 0.25 and 0.50) heterostructures.
+The electronic structures of the Zn1−xMgxO/ZnO
+(x = 0.25 and 0.50) heterostructures with exotic-atoms-
+adsorbed surfaces or with surfaces having metal ion va-
+cancies, have been also calculated.
+It is found that
+the electronic structures of the heterostructures reveal
+semiconductor characteristics when the surface contains
+metal ion vacancies, while the electronic structure ex-
+hibits metallic characteristics as the hydrogen, oxygen
+atoms, and OH groups are adsorbed on the surface, re-
+spectively.
+Figure 6(a) show the partial DOS decom-
+posed to the atomic layers for the Zn0.75Mg0.25O/ZnO
+heterostructures (42 Zn-O and 18 Zn-Mg-O layers) with
+hydrogen atoms adsorption.
+For the oxygen-atom- or
+OH-groups-adsorption case, the partial DOS plot is sim-
+ilar to that in Fig. 6(a). Clearly, the adsorption of hy-
+drogen atoms on the surface introduces defect states in
+the gap. Although polarization field distributed in the
+L10 to L18 Zn-Mg-O layers has significantly lifted up
+the top of the valence band, the valence band is still far
+from overlapping with the conduction band. However,
+the defect states introduced by hydrogen atoms are lo-
+cated near the Fermi level, and partially higher than the
+Fermi level. As a result, the defect band overlaps with
+the conduction band, which renders the heterostructure
+to exhibit metallic characteristics in electronic structures.
+Inspection of Fig. 6(a) also indicates that the conduction
+electrons are distributed from L ¯12 to L10 layers, i.e., in
+the range of ∼5.53 nm near the interface. Thus, the het-
+erostructure would reveal 2D or quasi-2D behaviors in
+transport properties. We also calculated the electronic
+structures of the Zn1−xMgxO/ZnO (x = 0.25 and 0.50)
+heterostructures with oxygen vacancies and surfaces ad-
+sorbed with exotic atoms. It is found that the introduc-
+tion of an oxygen vacancy in a certain atomic layer of the
+2×2 in-plane supercell would also produce a defect band
+in the gap. However, the defect band does not overlap
+with the conduction band, i.e., the introduction of oxygen
+vacancies does not change the ultimate properties of the
+heterostructures. As an example, in Fig. 6(b) we give the
+partial DOS projected onto the atomic layers for the H-
+adsorbed Zn0.75Mg0.25O/ZnO heterostructure (with 42
+Zn-O and 18 Zn-Mg-O layers) with oxygen vacancies in
+L¯1. Comparing the partial DOS of the heterostructure
+without oxygen vacancies [Fig. 6(a)], one can see that
+oxygen vacancies in L¯1 introduce an extra defect band,
+whose maximum is located at 0.15 eV below the bottom
+of the conduction band.
+In this situation, the 2DEG
+distributes from L ¯15 to L10 layers (∼6.53 nm) and still
+originates from the adsorption of hydrogen atoms. The
+electronic structure of the heterostructures with oxygen-
+atoms-adsorbed or OH-groups-adsorbed surface is simi-
+lar to that for the H-adsorbed heterostructure. In ad-
+dition, the introduction of oxygen vacancies in Zn-O
+layer near the interface does not change the semicon-
+ductor characteristic of the electronic structure for the
+heterostructure with metal ion vacancies in the surface
+of Zn1−xMgxO film. Thus, for Zn0.75Mg0.25O/ZnO het-
+erostructure with thin Zn1−xMgxO film, the adsorption
+of hydrogen atoms, oxygen atoms, or OH groups on the
+surface of Zn1−xMgxO layer is responsible for the forma-
+tion of 2DEG near the interface.
+In summary, to explore the origin of 2DEGs in
+Zn1−xMgxO/ZnO heterostructures, we constructed the
+Zn1−xMgxO/ZnO (x
+=
+0.25 and 0.50) heterostruc-
+tures with different surfaces and investigated their elec-
+tronic structures by first-principles calculations.
+It is
+found that the polarity discontinuity near the interface
+can neither lead to the formation of 2DEGs in devices
+with thick Zn1−xMgxO layers nor in devices with thin
+Zn1−xMgxO layers. For the heterostructures with thick
+Zn1−xMgxO layers, the oxygen vacancies near the inter-
+face are the source of the 2DEGs. For the heterostruc-
+tures with thin Zn1−xMgxO layers, adsorption of hydro-
+gen atoms, oxygen atoms, or OH groups on the surface
+of Zn1−xMgxO films can not only stabilize the polar sur-
+face of Zn1−xMgxO layer, but also cause the formation
+
+-J
+-1
+03
+-56
+of 2DEGs near the interfaces of the devices.
+The calculation was conducted on the CJQS-HPC plat-
+form at Tianjin University. This work is supported by the
+National Natural Science Foundation of China through
+Grants No. 12174282.
+[1] A. Ohtomo and H. Y. Hwang, Nature 427, 423 (2004).
+[2] K. Koike, K. Hama, I. Nakashima, G. Takada, M. Ozaki,
+K. Ogata, S. Sasa, M. Inoue, and M. Yano, Jpn. J. Appl.
+Phys 43 L1372 (2004)
+[3] A. Tsukazaki, A. Ohtomo, T. Kita, Y. Ohno, H. Ohno,
+and M. Kawasaki, Science 315, 1388 (2007).
+[4] A. Tsukazaki, S. Akasaka, K. Nakahara, Y. Ohno, H.
+Ohno, D. Maryenko, A. Ohtomo, and M. Kawasaki, Nat.
+Mater. 9, 889 (2010).
+[5] S. W. Lee, J. Heo, and R. G. Gordon, Nanoscale 5, 8940
+(2013).
+[6] P. Sch¨utz, F. Pfaff, P. Scheiderer, Y. Z. Chen, N. Pryds,
+M. Gorgoi, M. Sing and R. Claessen, Phys. Rev. B 91,
+165118 (2015).
+[7] H. Zhang, Y. Yun, X. Zhang, H. Zhang, Y. Ma, X. Yan,
+F. Wang, G. Li, R. Li, T. Khan, Y. Chen, W. Liu, F. Hu,
+B. Liu, B. Shen, W. Han, and J. Sun, Phys. Rev. Lett.
+121, 116803 (2018).
+[8] Y. Zhang, A. Neal, Z. Xia, C. Joishi, J. M. Johnson, Y.
+Zheng, S. Bajaj, M. Brenner, D. Dorsey, K. Chabak, G.
+Jessen, J. Hwang, S. Mou, J. P. Heremans, and S. Rajan,
+Appl. Phys. Lett. 112, 173502 (2018).
+[9] Z. Chen, Y. Liu, H. Zhang, Z. Liu, H. Tian, Y. Sun, M.
+Zhang, Y. Zhou, J. Sun, and Y. Xie, Science 372, 721
+(2021).
+[10] J. Falson, Y. Kozuka, M. Uchida, J. H. Smet, T. Arima,
+A. Tsukazaki, and M. Kawasaki, Sci. Rep. 6, 26598
+(2016).
+[11] H. A. Chin, I. C. Cheng, C. I. Huang, Y. R. Wu, W. S.
+Lu, W. L. Lee, J. Z. Chen, K. C. Chiu, and T. S. Lin, J.
+Appl. Phys. 108, 054503 (2010).
+[12] J. Ye, S. Ter Lim, M. Bosman, S. Gu, Y. Zheng, H. H.
+Tan, C. Jagadish, X. Sun, and K. L. Teo, Sci. Rep 2, 533
+(2012).
+[13] T. Makino, Y. Segawa, A. Tsukazaki, H. Saito, S.
+Takeyama, S. Akasaka, K. Nakahara, and M. Kawasaki,
+Phys. Rev. B 87, 085312 (2013).
+[14] H. Tampo, H. Shibata, K. Maejima, A. Yamada, K. Mat-
+subara, P. Fons, S. Kashiwaya, S. Niki, Y. Chiba, T.
+Wakamatsu, and H. Kanie, Appl. Phys. Lett. 93, 202104
+(2008).
+[15] H. Tampo, H. Shibata, K. Maejima, T. W. Chiu, H. Itoh,
+A. Yamada, K. Matsubara, P. Fons, Y. Chiba, T. Waka-
+matsu, Y. Takeshita, H. Kanie, and S. Niki, Appl. Phys.
+Lett. 94, 242107 (2009).
+[16] J. D. Ye, S. Pannirselvam, S. T. Lim, J. F. Bi, X. W. Sun,
+G. Q. Lo, and K. L. Teo, Appl. Phys. Lett. 97, 111908
+(2010).
+[17] J. Falson, D. Maryenko, Y. Kozuka, A. Tsukazaki, and
+M. Kawasaki, Appl. Phys. Express 4, 091101 (2011).
+[18] J. D. Hwang, C. C. Yang, and C. M. Chu, ACS Appl.
+Mater. Interfaces 9, 23904 (2017).
+[19] K. Imasaka, J. Falson, Y. Kozuka, A. Tsukazaki, and M.
+Kawasaki, Appl. Phys. Lett. 104, 242112 (2014).
+[20] S. Akasaka, A. Tsukazaki, K. Nakahara, A. Ohtomo, and
+M. Kawasaki, Jpn. J. Appl. Phys. 50, 080215 (2011).
+[21] S. H. Yoo, M. Todorova, D. Wickramaratne, L. Weston,
+C. G. V. de Walle, and J. Neugebauer, Npj Comput.
+Mater. 7, 58, (2021).
+[22] K. A. Brown, S. He, D. J. Eichelsdoerfer, M. Huang, I.
+Levy, H. lee, S. Ryu, P. Irvin, J. Mendez-Arroyo, C. A.
+Mirkin, and J. Levy, Nat. Commun. 5, 5019 (2014).
+[23] X. Huang, E. Lindgren, and J. R. Chelikowsky, Phys.
+Rev. B 71, 165328 (2005).
+[24] H. Tampo, H. Shibata, K. Maejima, A. Yamada, K. Mat-
+subara, P. Fons, S. Niki, T. Tainaka, Y. Chiba, and H.
+Kanie, Appl. Phys. Lett. 91, 261907 (2007).
+[25] G. Kresse, O. Dulub, and U. Diebold, Phys. Rev. Lett.
+68, 245409 (2003).
+[26] O. Dulub, U. Diebold and G. Kresse, Phys. Rev. Lett.
+90, 016102 (2003).
+[27] M. Valtiner, M. Todorova, G. Grundmeier, and J. Neuge-
+bauer, Phys. Rev. Lett. 103, 065502 (2009).
+[28] J. Goniakowski, F. Finocchi, and C. Noguera, Rep. Prog.
+Phys. 71, 016501 (2008).
+[29] J. V. Lauritsen, S. Porsgaard, M. K. Rasmussen, M. C.
+R. Jensen, R. Bechstein, K. Meinander, B. S. Clausen,
+S. Helveg, R. Wahl, G. Kresse, and F. Besenbacher, ACS
+Nano 5, 5987 (2011).
+[30] B. Meyer, Phys. Rev. B 69, 045416 (2004).
+[31] A. Calzolari, M. Bazzani, and A. Catellani, Surf. Sci.
+607, 181 (2013).
+[32] In the calculations, the generalized gradient approxi-
+mation (GGA) parametrized by Perdew-Burk-Ernzerhof
+plus the on-site coulomb interaction approach (GGA+U)
+was used for the exchange-correlation functional. The
+Hubbard interaction parameter U is taken as 8.5 eV
+(7.4 eV) for Zn 3d (O 2p) orbitals. For the bulk ZnO,
+the band gaps calculated by GGA+U and GGA methods
+are 2.48 eV and 0.72 eV, respectively. The former is more
+close to the experimental value (3.37 eV). The plane-wave
+cutoff energy was set as 500 eV and a Brillouin zone with
+4×4×1 Monkhorst-Pack k-point grids was employed. The
+structure relation was finished until the residual force was
+smaller than 0.03 eV/˚A. To remove the undesired elec-
+trostatic interaction between periodic cells along the z
+direction, the dipole correction is applied.
+[33] J. Lee and A. A. Demkov, Phys. Rev. B 78, 193104 (2008)
+[34] L. Liu, Z. Mei, A. Tang, A. Azarov, A. Kuznetsov, Q. K.
+Xue, and X. Du, Phys. Rev. B 93, 235305 (2016).
+[35] F. Oba, A. Togo, I. Tanaka, J. Paier, and G. Kresse,
+Phys. Rev. B 77, 245202 (2008).
+[36] S. J. Clark, J. Robertson, S. Lany, and A. Zunger, Phys.
+Rev. B 81, 115311 (2010).
+[37] A. Alkauskas and A. Pasquarello, Phys. Rev. B 84,
+125206 (2011).
+[38] Y. Li, S. N. Phattalung, S. Limpijumnong, J. Kim, and
+J. Yu, Phys. Rev. B 84, 245307 (2011).
+[39] P. W. Tasker, J. Phys. C: Solid State Phys. 12, 4977
+(1979).
+
diff --git a/HdAyT4oBgHgl3EQfffgY/content/tmp_files/load_file.txt b/HdAyT4oBgHgl3EQfffgY/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..911ad31d295d77375af6afd2b552aee249e7dc53
--- /dev/null
+++ b/HdAyT4oBgHgl3EQfffgY/content/tmp_files/load_file.txt
@@ -0,0 +1,786 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf,len=785
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='00339v1  [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='mtrl-sci]  1 Jan 2023  The Origin of Two-dimensional Electron Gas in Zn1−xMgxO/ZnO Heterostructures  Xiang-Hong Chen,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='1 Dong-Yu Hou,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='1 Zhi-Xin Hu,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='2 Kuang-Hong Gao,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' ∗ and Zhi-Qing Li1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' †  1Tianjin Key Laboratory of Low Dimensional Materials Physics and Preparing Technology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Department of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Tianjin University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Tianjin 300354,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' China  2Center for Joint Quantum Studies and Department of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Tianjin University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Tianjin 300354,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' China  (Dated: January 3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 2023)  Although the two-dimensional electron gas (2DEG) in (001) Zn1−xMgxO/ZnO heterostructures  has been discovered for about twenty years,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' the origin of the 2DEG is still inconclusive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' In the  present letter, the formation mechanisms of 2DEG near the interfaces of (001) Zn1−xMgxO/ZnO  heterostructures were investigated via the first-principles calculations method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' It is found that the  polarity discontinuity near the interface can neither lead to the formation of 2DEG in devices with  thick Zn1−xMgxO layers nor in devices with thin Zn1−xMgxO layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' For the heterostructure with  thick Zn1−xMgxO layers, the oxygen vacancies near the interface introduce a defect band in the  band gap, and the top of the defect band overlaps with the bottom of the conduction band, leading  to the formation of the 2DEG near the interface of the device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' For the heterostructure with thin  Zn1−xMgxO layers, the absorption of hydrogen atoms, oxygen atoms, or OH groups on the surface  of Zn1−xMgxO film plays a key role for the formation of 2DEG in the device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Our results manifest  the sources of 2DEGs in Zn1−xMgxO/ZnO heterostructures on the electronic structure level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Since  the  discovery  of  two-dimensional  electron  gas (2DEG) at the interface of LaAlO3/SrTiO3 het-  erojunction [1],  2DEG has been found at various  oxide heterostructures, such as Zn1−xMgxO/ZnO [2–  4],  Al2O3/SrTiO3  [5,  6],  EuO/KTaO3  [7],  (AlxGa1−x)2O3/Ga2O3  [8]  and  LaAlO3/KTaO3  [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  The 2DEG at oxide heterostructures not only provides  a platform for fundamental research, but also promotes  the development of novel all-oxide electronic devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Among these oxide heterostructures, Zn1−xMgxO/ZnO  heterostructures  are  particularly  attractive  due  to  their ultra-high Hall mobility (up to 106 cm2V−1s−1  at low temperature [10]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  However, the origin of the  2DEG at the Zn1−xMgxO/ZnO interface is still unclear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Researchers only empirically attribute it to the polar  discontinuity [11–14]: since Zn1−xMgxO (0 < x < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='6)  and ZnO have different spontaneous polarization, the  polarization at the  interface is  discontinuous after  they form heterojunctions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  This discontinuity causes  a large number of bound charges to be generated at  the heterointerface, creating a built-in electric field  throughout the  heterostructure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  This field drives  electrons toward the interface to form 2DEG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' In con-  trast, some researchers believe that the 2DEG at the  Zn1−xMgxO/ZnO interface originates from the donor on  the Zn1−xMgxO surface [15, 16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Experimentally, 2DEG  can also be formed when the thickness of Zn1−xMgxO  layer  is  greater  than  300 nm  in  Zn1−xMgxO/ZnO  heterostructures [17–20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  There would be no internal  potential gradient in the aforementioned heterostructure  with thick Zn1−xMgxO layer, and the contribution of  surface donors to 2DEG could also be negligible [21, 22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Thus the formation of 2DEG in this case cannot be  explained by the mechanisms mentioned above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  On  ∗ Corresponding author, e-mail: khgao@tju.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='cn  † Corresponding author, e-mail: zhiqingli@tju.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='cn  the whole, the origin of 2DEG at Zn1−xMgxO/ZnO  heterointerface needs to be further studied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' In this letter,  the origin of 2DEG at Zn1−xMgxO/ZnO heterointerface  is studied from the perspective of microscopic electronic  structures by first-principles calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Interestingly,  it is found that the polar discontinuity mechanism is  not responsible for the formation of the 2DEG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' For the  heterostructures with thick Zn1−xMgxO layers, 2DEG  mainly arises from oxygen vacancies, while the 2DEG  originates from surface adsorption for heterostructures  with thin Zn1−xMgxO layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Considering  that  the  2DEG  can  be  formed  in  Zn1−xMgxO/ZnO  heterostructures  with  both  thick  (∼100 to 500 nm) [23–27] and thin Zn1−xMgxO layers  (∼10 to 30 nm) [14–16] experimentally, we construct the  configurations as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  For Zn1−xMgxO/ZnO het-  erostructures with thick Zn1−xMgxO layers, we passi-  vated the oxygen terminal of ZnO slab and the Zn-Mg  terminal of Zn1−xMgxO slab by pseudo-H atoms with  fractional charges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' ZnO slab with passivated oxygen ter-  minal can be used to simulate ZnO substrate, and the  charge of H is taken as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='48e with e being the elementary  charge [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' The charge of the pseudo-H atoms in the  passivated Zn-Mg terminal is taken as 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='52e [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' After  passivation, the pseudo-H atoms not only saturate the  surface dangling bonds but also make the passivated sur-  face and the adjacent atomic layers exhibit bulk prop-  erties [21, 23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' In this case, the Zn1−xMgxO and ZnO  slabs can be treated as semi-infinite thick films.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Con-  sidering the Mg content x can be as high as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='60 in  Zn1−xMgxO/ZnO heterostructures experimentally [24],  we set the Mg content x as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='50, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  For each doping level, the Mg ions are uniformly doped  into the ZnO film, which together with the ZnO sub-  strate forms a heterostructure with a clear interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  For the Zn1−xMgxO/ZnO heterostructures with thin  Zn1−xMgxO layers, the difference in the configuration is  that there is no pseudo-H atom at the Zn-Mg terminal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  2  Generally, the unpassivated Zn1−xMgxO (001) surface  is unstable and the surface adsorption or reconstruction  is inevitable [25–31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Thus, the surface adsorption and  defects are considered to simulate the Zn1−xMgxO/ZnO  heterostructures with thin Zn1−xMgxO layers [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' As  an example, in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 1(a) we give the structure diagram  of a Zn1−xMgxO/ZnO heterostructure with two surfaces  passivated by pseudo-H atoms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' The heterostructure con-  tains a 2×2 in-plane (001) Zn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='75Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25O/ZnO supercell  and 18 Zn-Mg-O layers and 18 Zn-O layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' A 15-˚A-thick  vacuum layer is added along the [001] direction to prevent  any unintentional interactions between the slabs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' From  the interface to surface, the atomic layers on the ZnO side  are labeled as L¯1, L¯2, · · · , L ¯17, and L ¯18, while the atomic  layers on the Zn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='75Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25O side are labeled as L1, L2,  · · , L17, and L18, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' The top view of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 1(a)  along the [001] direction is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 1(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Three  adsorption sites named On-top, Fcc-hollow, and Hcp-  hollow, are indicated by the arrows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' The positions of zinc  atoms in each layer are numbered as 1, 2, 3, and 4, respec-  tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' For the Mg doping level x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25 case, the zinc  atoms at position 1 are substituted by magnesium atoms  in the odd layers, while the zinc atoms at position 3 are  replaced in the even layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' For the x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='50 situation,  the zinc atoms at positions 2 and 4 are replaced by mag-  nesium atoms in each layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' All calculations are carried  out in framework of density functional theory using the  Viennaab initio Simulation Package (VASP) [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' The  in-plane lattice constants of Zn1−xMgxO/ZnO (x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25  and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='50) heterostructures are fixed to those of ZnO dur-  ing the calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  (a)  Schematic  geometrical  structure  of  Zn1−xMgxO/ZnO  (x=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25  and  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='50)  heterostructure  with two pseudo-H-passivated surfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  (b) The top view  of the heterostructure along the [001] direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Here the  “On-top, Fcc-hollow, and Hcp-hollow” are the adsorption  sites for exotic atoms or groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Figure  2(a)  shows  the  band  structure  of  Zn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='75Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25O/ZnO heterostructure shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 1(a)  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=', the heterostructure has 18 Zn-O and 18 Zn-Mg-O  1  0  1  2  3  4  0  20  40  60  80  100  6  4  2  0  2  4  6  Energy (eV)  M  K  (a)  (b)  L18  Planar average  Macroscopic average  L2  Electrostatic potential (eV)  Distance along the [001] (�  )  L18  L4  Interface  ZnO  Zn  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 75  Mg  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 25  O  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  (a)  The  energy  band  structure  of  the  Zn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='75Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25O/ZnO heterostructure without oxygen vacan-  cies and with two pseudo-H-atoms-passivated surfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  (b)  The plane average (solid curve) and macroscopic average  (dash-dot curve) electrostatic potential (seen by electron)  across the Zn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='75Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25O/ZnO heterostructure along the [001]  direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  layers and two pseudo-H-atoms-passivated surfaces).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Clearly, the valence band maximum (VBM) and the con-  duction band minimum (CBM) are both located at the Γ  point, and the Fermi level lies in the band gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Thus the  energy band of the Zn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='75Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25O/ZnO heterostructure  exhibits direct-gap semiconductor characteristics (the  calculated band gap is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='45 eV) and no 2DEG is formed  at the interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' For the x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='50 case, the band struc-  ture is similar to that of the x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25 and the calculated  bad gap is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='56 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Therefore, 2DEG cannot appear near  the interfaces of the perfect Zn1−xMgxO/ZnO (x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25  and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='50) heterostructures (without defects) with thick  Zn1−xMgxO layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' We also calculated the electrostatic  potential distribution for the above heterostructures,  and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 2(b) presents the results for the x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25 case  as an example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  There is a conspicuous bulge in the  macroscopic average potential curve near the interface  (from the L¯4 Zn-O layer to the L2 Zn-Mg-O layer).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' In  the atomic layers away from the interface, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=', the Zn-O  layers from L¯4 to L ¯18 or Zn-Mg-O layers from L2 to  L18, the average potential almost retains a constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Thus, a potential barrier rather than a quantum well  is formed near the interface of the Zn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='75Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25O/ZnO  heterostructure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Similar phenomena are also observed  in the macroscopic average potential curve of the  Zn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='5Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='5O/ZnO  heterostructure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  This  potential  barrier should be caused by the polar discontinuity at  the interface, which could induce a localized polarization  field near the interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  The polarization field cannot  cause the bottom of the conduction band to overlap  with the top of the valence band as in the case of  LaAlO3/SrTiO3 heterostructures [33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Thus, the polar  discontinuity alone cannot explain the observed 2DEG  near the interface of Zn1−xMgxO/ZnO heterostructure  with thick Zn1−xMgxO layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Then,  why  the  2DEGs  can  be  formed  in  Zn1−xMgxO/ZnO  heterostructures  with  thick  wollod-qoH  ECC-JOJJOM  OU-tob  (p) Lob AIGM sJoua e [ool]q!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='lGcrIo  U  M  H  T18  r18  SUO  (B)3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='4  Formation energy (eV)  Zn O  Zn  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='75  Mg  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25  O  In t erface  (a)  L1  L6  L12  L12  L6  L1  L1  L6  L12  L12  L6  L1  Formation energy (eV)  In t erface  Zn O  Zn  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='5  Mg  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='5  O  (b)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Formation energies of oxygen vacancies at different  atomic layers in Zn1−xMgxO/ZnO heterostructures with two  pseudo-H-passivated surfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' (a) For the x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25, and (b)  for the x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='50 heterostructures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Zn1−xMgxO layers?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  It should be noticed that as  intrinsic defects in ZnO and Zn1−xMgxO films, oxygen  vacancies are inevitable during device fabrication and  could play crucial roles for the formation of 2DEG in  Zn1−xMgxO/ZnO heterostructures [34–37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Next, we in-  vestigate the effect of oxygen vacancies on the electronic  structures of Zn1−xMgxO/ZnO (x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='50)  heterostructures with thick Zn1−xMgxO layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  First,  we calculate the formation energy of oxygen vacancies  (Ef) in each atomic layer of the above heterostructures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  In the oxygen-rich limit, Ef can be written as [38]  Ef = E(VO) − (E0 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='5EO2),  (1)  where E(VO) and E0 are the calculated total energies of  the Zn1−xMgxO/ZnO (x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='50) heterostruc-  tures with and without oxygen vacancies, and EO2 is the  calculated total energy of the single O2 molecule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' For  the configuration in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 1, each in-plane supercell con-  tains four oxygen atoms, whose positions are labeled as  a, b, c, and d, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' The oxygen atoms at d po-  sition are removed in a certain fixed layer to create oxy-  gen vacancies in the calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Figure 3 shows the  formation energies of the oxygen vacancies in each layer  of the Zn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='75Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25O/ZnO and Zn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='5Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='5O/ZnO het-  erostructures with 18 Zn-O and 18 Zn-Mg-O layers, and  two pseudo-H-passivated surfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Inspection of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 3  indicates that the overall variation trends of the Ef vs  layer number curves for the two heterostructures are sim-  ilar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Thus we only discuss the variation of Ef in the  Zn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='75Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25O/ZnO heterostructure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' On the ZnO side,  the value Ef keeps as a constant in the first two layers,  and then sharply increases with increasing layer number,  reaches its maximum at L¯4, then decreases with further  increasing layer number, and tends to be saturated as the  layer number is greater than 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' On the Zn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='75Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25O  side, the values of Ef near the interface (L1 to L6 Zn-  Mg-O layers) vary between −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='3 eV and −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='1 eV, while  those for the layers with layer number being greater than  6 are almost fixed at −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='1 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Obviously, the oxygen va-  cancies can be easily formed on the ZnO side, especially  in the first two Zn-O layers near the interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Considering the variation trends in electronic struc-  tures with VO position for the x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='50 het-  erostructures with two pseudo-H passivated surfaces are  also similar, we only present and discuss the results ob-  tained from the x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25 ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  We first discuss the  case that oxygen vacancies are located at the most eas-  ily formed position (L¯1 layer).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Figure 4(a) presents the  band structure of this configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' From this figure,  one can see that the oxygen vacancies in the L¯1 Zn-O  layer introduce a defect band in the band gap and the  top of the defect band is higher than the Fermi level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  At the same time, the Fermi level enters into the bot-  tom of the conduction band, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=', the conduction band  overlaps with the defect band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Thus, part of the elec-  trons in the defect band would be transferred into the  conduction band and become conduction electrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Fig-  ure 4(b) shows the partial density of states (DOS) pro-  jected onto atomic planes for the x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25 heterostruc-  ture with oxygen vacancies in the L¯1 Zn-O layer and two  pseudo-H passivated surfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Clearly, only in L¯2 , L¯1,  and L1 layers the DOS near the Fermi level is nonzero,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=', the conduction electrons are concentrated in the two  Zn-O layers and one Zn-Mg-O layer near the interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  These three layers occupy a space with thickness ∼8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='4 ˚A,  which indicates that the 2DEG is formed near the in-  terface of the heterostructure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' From the orbital DOS of  L¯2 to L1 layers, it is found that these conduction elec-  trons are mainly composed of Zn-4s and O-2p orbitals  (not shown).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' In addition, it is found that when the oxy-  gen vacancies are located in the L¯2 and L¯3 Zn-O lay-  ers and the L1 to L6 Zn-Mg-O layers, their band struc-  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' (a) The band structure of Zn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='75Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25O/ZnO het-  erostructure with oxygen vacancies in the L¯1 Zn-O layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  (b) The partial DOS projected onto atomic planes for  the Zn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='75Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25O/ZnO heterostructure with oxygen vacan-  cies in the L¯1 Zn-O layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  (c) The band structure of  Zn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='75Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25O/ZnO heterostructure with oxygen vacancies in  the L ¯15 Zn-O layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  (d) The partial DOS projected onto  atomic planes for the Zn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='75Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25O/ZnO heterostructure  with oxygen vacancies in the L ¯15 Zn-O layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  K  I  M  D02 (e)G)  0  0  (C)  S  (b)  L  M  L  3  3  5  EUGL& (GA)  EUGLS (GA)  0  0  (g)  (d)  r18  II  I184  tures are similar to that in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 4(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' However, the band  structures of the heterostructures would reveal semicon-  ductor characteristics when the oxygen vacancies are far  from the interface (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=', behind the L¯3 Zn-O layer and  L6 Zn-Mg-O layer).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  We take the Zn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='75Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25O/ZnO  heterostructure with oxygen vacancies in the L ¯15 Zn-O  layer as an example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Figure 4(c) shows the band struc-  ture of this configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' The oxygen vacancies in the  L ¯15 Zn-O layer also introduce a defect band in the gap,  while the top of the defect band is located at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='11 eV be-  low the bottom of the conduction band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' The Fermi level  lies between the conduction band and the defect band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Therefore, the introduction of oxygen vacancies in the  L ¯15 Zn-O layer cannot induce 2DEG at the interface of  the heterostructure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Figure 4(d) shows the partial DOS  projected onto atomic planes for the Zn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='75Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25O/ZnO  heterostructure with oxygen vacancies in the L ¯15 Zn-O  layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' From this figure, one can see that the defect band  of the oxygen vacancies is in fact composed of a large  number of deep energy levels as far as the energy band  of the inner atomic layer is concerned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' These deep lev-  els cannot overlap with the conduction band even if the  bottom conduction band of the Zn-O layer near the in-  terface is lower than that of the inner Zn-O layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' On  the contrary, the defect levels of the oxygen vacancies  near the interface layers are so shallow that the bottom  of the conduction band overlaps with the top of the de-  fect band [see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 4(b)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' This is why 2DEG exists only  when the oxygen vacancies are located near the interface  of the heterostructure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' On the other hand, the defect  band formed by oxygen vacancies of inner Zn-O layers  could enhance the conductivity of the heterostructure:  the device will exhibit a thermal-activated form conduc-  tance with activation energy Ea, where Ea is about half  of the energy difference between the bottom of conduc-  tion band and the top of the defect band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Summarizing  the results mentioned above, one can readily conclude  that the oxygen vacancies near the interface are the ori-  gin of the 2DEGs in Zn1−xMgxO/ZnO (x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25 and  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='50) heterostructures with thick Zn1−xMgxO layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Now,  we  study  the  origin  of  2DEGs  in  Zn1−xMgxO/ZnO (x  =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='50) heterostruc-  tures when the Zn1−xMgxO films are very thin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' In this  situation, we calculate the electronic structures of the  heterostructures with 42 Zn-O and 18 Zn-Mg-O layers,  in which the surface of the Zn1−xMgxO film is no longer  passivated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  The reason for choosing 42 Zn-O layers  (instead of 18 layers) is to obtain the distribution range  of 2DEG on the ZnO side.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Since the results obtained  from the x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='50 heterostructures are also  similar, we only present and discuss the results for the  x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25 heterostructure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Figure 5(a) shows the electro-  static potential of Zn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='75Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25O/ZnO heterostructure  (with 42 Zn-O and 18 Zn-Mg-O layers) in which only  the surface of ZnO film is passivated by pseudo-H  atoms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Obviously, the macroscopic average potential  on the ZnO side is insensitive to the position, while it  decreases with increasing distance to the interface on  0  40  80  120  160  10  5  0  5  10  0  40  80  120  160  10  5  0  5  10  Interface  Electrostatic potential (eV)  Distance along the [001] direction (�)  ZnO  Zn  0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='7 5  Mg  0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='2 5  O  (a)  Macroscopic-Average  Planar-Average  Electrostatic potential (eV)  Interface  ZnO  Zn  0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='7 5  Mg  0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='2 5  O  L10  L18  (b)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' (a) The plane average (solid curve) and macroscopic  average (dash-dot curve) electrostatic potential (seen by elec-  tron) along [001] direction for the Zn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='75Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25O/ZnO het-  erostructure, in which only the surface of ZnO film is pas-  sivated by pseudo-H atoms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  (b) The plane average (solid  curve) and macroscopic average (dash-dot curve) electro-  static potential (seen by electron) along [001] direction of the  Zn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='75Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25O/ZnO heterostructure with a Zn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='75Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25O  surface of H-atom adsorption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  the Zn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='75Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25O side.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  A macroscopic field perpen-  dicular to the surface with the magnitude of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='06 V/˚A  is obtained by linear fitting the macroscopic average  electrostatic potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  This kind of field or potential  would lead to an instability of the (001) polar (so-called  Tasker type III) surface [29, 39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' In the light of recent  experimental and theoretical results, the polar oxide  surfaces can be stabilized via charge transfer between the  upper and lower surfaces [25, 26], adsorption of external  atoms [25–29], and stoichiometry variations [25–28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  For Zn1−xMgxO/ZnO heterostructures, we consider the  effects of adsorption (hydrogen atoms, OH groups, and  oxygen atoms) and stoichiometry variations (defects) on  the electronic structures of Zn1−xMgxO/ZnO (x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25  and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='50) heterostructures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Through structural relax-  ations, it is found that the hydrogen atoms prefer to  be adsorbed atop the zinc atom (On-top site), while  the preferred adsorption sites for the OH groups and  oxygen atoms are the Fcc-hollow sites [see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 1(b)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Our results are consistent with those in Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' [25–27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  For the 2 × 2 in-plane (001) Zn1−xMgxO supercell, the  numbers of the On-top and Fcc-hollow sites are both 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  In our calculations, the coverages of hydrogen atoms,  OH groups, and oxygen atoms adsorbed on the surface  of Zn1−xMgxO are 50%, 50%, and, 25%, respectively,  while the concentration of vacancies on the Zn or Mg  sites is 25% [25–27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Specifically, for the x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25  heterostructure, the absorption sites of the hydrogen  atoms are set on the top of the zinc atoms at positions  1 and 4 [see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 1(b)];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' the adsorption sites for the OH  groups are set at Fcc-hollow positions located at the  top of the arrow and the position of the black dot;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' the  Fcc-hollow position at the top of the arrow is also set  as the adsorption site of oxygen atoms;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' the Zn vacancies  are obtained via removing the zinc atoms located at  5  H  ads  L42  ZnO  Zn  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 75  Mg  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 25  O  L10  L12  Energy (eV)  (a)  (b)  ZnO  Zn  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 75  Mg  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 25  O  L1  L42  H  pass  L10  L15  L1  DOS (states/eV)  Energy (eV)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' The partial DOS projected onto the atomic layers for  the Zn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='75Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25O/ZnO heterostructures with surfaces of (a)  H-atom absorption, and (b) O-atom absorption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  position 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Figure  5(b)  shows  the  electrostatic  potential  of  Zn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='75Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25O/ZnO  heterostructures  with  hydrogen  atoms adsorbed on the Zn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='75Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25O surface (and with  42 Zn-O and 18 Zn-Mg-O layers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' The results for the  Zn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='75Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25O surface with oxygen atoms adsorption,  OH groups adsorption, and Zn or Mg vacancies are simi-  lar to that shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 5(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' The macroscopic average  potential on the ZnO side remains nearly a constant af-  ter adsorption of hydrogen atoms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' On the Zn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='75Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25O  side, the macroscopic average potential is almost insensi-  tive to the position from L1 to L9 layers, and then slightly  increases with increasing distance to the interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' An  electrostatic field (with magnitude of ∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='038 V/˚A) being  opposite to that shown in Fig 5(b) exists between L10  and L18 layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Thus surface adsorption or metal ion  vacancies could really stabilize the polar surfaces of the  Zn1−xMgxO/ZnO (x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='50) heterostructures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  The electronic structures of the Zn1−xMgxO/ZnO  (x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='50) heterostructures with exotic-atoms-  adsorbed surfaces or with surfaces having metal ion va-  cancies, have been also calculated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  It is found that  the electronic structures of the heterostructures reveal  semiconductor characteristics when the surface contains  metal ion vacancies, while the electronic structure ex-  hibits metallic characteristics as the hydrogen, oxygen  atoms, and OH groups are adsorbed on the surface, re-  spectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Figure 6(a) show the partial DOS decom-  posed to the atomic layers for the Zn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='75Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25O/ZnO  heterostructures (42 Zn-O and 18 Zn-Mg-O layers) with  hydrogen atoms adsorption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  For the oxygen-atom- or  OH-groups-adsorption case, the partial DOS plot is sim-  ilar to that in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 6(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Clearly, the adsorption of hy-  drogen atoms on the surface introduces defect states in  the gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Although polarization field distributed in the  L10 to L18 Zn-Mg-O layers has significantly lifted up  the top of the valence band, the valence band is still far  from overlapping with the conduction band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' However,  the defect states introduced by hydrogen atoms are lo-  cated near the Fermi level, and partially higher than the  Fermi level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' As a result, the defect band overlaps with  the conduction band, which renders the heterostructure  to exhibit metallic characteristics in electronic structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Inspection of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 6(a) also indicates that the conduction  electrons are distributed from L ¯12 to L10 layers, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=', in  the range of ∼5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='53 nm near the interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Thus, the het-  erostructure would reveal 2D or quasi-2D behaviors in  transport properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' We also calculated the electronic  structures of the Zn1−xMgxO/ZnO (x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='50)  heterostructures with oxygen vacancies and surfaces ad-  sorbed with exotic atoms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' It is found that the introduc-  tion of an oxygen vacancy in a certain atomic layer of the  2×2 in-plane supercell would also produce a defect band  in the gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' However, the defect band does not overlap  with the conduction band, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=', the introduction of oxygen  vacancies does not change the ultimate properties of the  heterostructures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' As an example, in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 6(b) we give the  partial DOS projected onto the atomic layers for the H-  adsorbed Zn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='75Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25O/ZnO heterostructure (with 42  Zn-O and 18 Zn-Mg-O layers) with oxygen vacancies in  L¯1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Comparing the partial DOS of the heterostructure  without oxygen vacancies [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 6(a)], one can see that  oxygen vacancies in L¯1 introduce an extra defect band,  whose maximum is located at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='15 eV below the bottom  of the conduction band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  In this situation, the 2DEG  distributes from L ¯15 to L10 layers (∼6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='53 nm) and still  originates from the adsorption of hydrogen atoms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' The  electronic structure of the heterostructures with oxygen-  atoms-adsorbed or OH-groups-adsorbed surface is simi-  lar to that for the H-adsorbed heterostructure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' In ad-  dition, the introduction of oxygen vacancies in Zn-O  layer near the interface does not change the semicon-  ductor characteristic of the electronic structure for the  heterostructure with metal ion vacancies in the surface  of Zn1−xMgxO film.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Thus, for Zn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='75Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25O/ZnO het-  erostructure with thin Zn1−xMgxO film, the adsorption  of hydrogen atoms, oxygen atoms, or OH groups on the  surface of Zn1−xMgxO layer is responsible for the forma-  tion of 2DEG near the interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  In summary, to explore the origin of 2DEGs in  Zn1−xMgxO/ZnO heterostructures, we constructed the  Zn1−xMgxO/ZnO (x  =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='25 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='50) heterostruc-  tures with different surfaces and investigated their elec-  tronic structures by first-principles calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  It is  found that the polarity discontinuity near the interface  can neither lead to the formation of 2DEGs in devices  with thick Zn1−xMgxO layers nor in devices with thin  Zn1−xMgxO layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' For the heterostructures with thick  Zn1−xMgxO layers, the oxygen vacancies near the inter-  face are the source of the 2DEGs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' For the heterostruc-  tures with thin Zn1−xMgxO layers, adsorption of hydro-  gen atoms, oxygen atoms, or OH groups on the surface  of Zn1−xMgxO films can not only stabilize the polar sur-  face of Zn1−xMgxO layer, but also cause the formation  J  1  03  56  of 2DEGs near the interfaces of the devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  The calculation was conducted on the CJQS-HPC plat-  form at Tianjin University.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' This work is supported by the  National Natural Science Foundation of China through  Grants No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 12174282.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  [1] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Ohtomo and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Hwang, Nature 427, 423 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  [2] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Koike, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Hama, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Nakashima, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Takada, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Ozaki,  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Ogata, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Sasa, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Inoue, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Yano, Jpn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Phys 43 L1372 (2004)  [3] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Tsukazaki, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Ohtomo, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Kita, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Ohno, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Ohno,  and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Kawasaki, Science 315, 1388 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  [4] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Tsukazaki, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Akasaka, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Nakahara, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Ohno, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Ohno, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Maryenko, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Ohtomo, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Kawasaki, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 9, 889 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  [5] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Heo, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Gordon, Nanoscale 5, 8940  (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  [6] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Sch¨utz, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Pfaff, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Scheiderer, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Chen, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Pryds,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Gorgoi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Sing and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Claessen, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' B 91,  165118 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  [7] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Yun, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Zhang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Ma, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Yan,  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Wang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Li, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Li, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Khan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Chen, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Liu, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Hu,  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Liu, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Shen, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Han, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Sun, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  121, 116803 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  [8] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Zhang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Neal, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Xia, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Joishi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Johnson, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Zheng, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Bajaj, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Brenner, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Dorsey, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Chabak, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Jessen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Hwang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Mou, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Heremans, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Rajan,  Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 112, 173502 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  [9] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Chen, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Liu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Zhang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Liu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Tian, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Sun, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Zhou, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Sun, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Xie, Science 372, 721  (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  [10] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Falson, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Kozuka, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Uchida, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Smet, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Arima,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Tsukazaki, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Kawasaki, Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 6, 26598  (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  [11] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Chin, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Cheng, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Huang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Wu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Lu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Chen, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Chiu, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Lin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 108, 054503 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  [12] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Ye, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Ter Lim, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Bosman, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Gu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Zheng, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Tan, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Jagadish, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Sun, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Teo, Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Rep 2, 533  (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  [13] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Makino, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Segawa, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Tsukazaki, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Saito, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Takeyama, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Akasaka, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Nakahara, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Kawasaki,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' B 87, 085312 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  [14] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Tampo, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Shibata, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Maejima, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Yamada, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Mat-  subara, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Fons, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Kashiwaya, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Niki, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Chiba, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Wakamatsu, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Kanie, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 93, 202104  (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  [15] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Tampo, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Shibata, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Maejima, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Chiu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Itoh,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Yamada, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Matsubara, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Fons, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Chiba, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Waka-  matsu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Takeshita, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Kanie, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Niki, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 94, 242107 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  [16] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Ye, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Pannirselvam, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Lim, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Bi, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Sun,  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Lo, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Teo, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 97, 111908  (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  [17] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Falson, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Maryenko, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Kozuka, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Tsukazaki, and  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Kawasaki, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Express 4, 091101 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  [18] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Hwang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Yang, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Chu, ACS Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Interfaces 9, 23904 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  [19] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Imasaka, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Falson, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Kozuka, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Tsukazaki, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Kawasaki, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 104, 242112 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  [20] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Akasaka, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Tsukazaki, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Nakahara, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Ohtomo, and  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Kawasaki, Jpn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 50, 080215 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  [21] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Yoo, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Todorova, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Wickramaratne, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Weston,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' de Walle, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Neugebauer, Npj Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 7, 58, (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  [22] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Brown, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' He, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Eichelsdoerfer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Huang, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Levy, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' lee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Ryu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Irvin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Mendez-Arroyo, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Mirkin, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Levy, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 5, 5019 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  [23] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Huang, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Lindgren, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Chelikowsky, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' B 71, 165328 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  [24] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Tampo, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Shibata, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Maejima, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Yamada, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Mat-  subara, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Fons, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Niki, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Tainaka, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Chiba, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Kanie, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 91, 261907 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  [25] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Kresse, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Dulub, and U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Diebold, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  68, 245409 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  [26] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Dulub, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Diebold and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Kresse, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  90, 016102 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  [27] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Valtiner, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Todorova, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Grundmeier, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Neuge-  bauer, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 103, 065502 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  [28] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Goniakowski, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Finocchi, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Noguera, Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 71, 016501 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  [29] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Lauritsen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Porsgaard, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Rasmussen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Jensen, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Bechstein, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Meinander, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Clausen,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Helveg, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Wahl, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Kresse, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Besenbacher, ACS  Nano 5, 5987 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  [30] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Meyer, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' B 69, 045416 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  [31] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Calzolari, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Bazzani, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Catellani, Surf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  607, 181 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  [32] In the calculations, the generalized gradient approxi-  mation (GGA) parametrized by Perdew-Burk-Ernzerhof  plus the on-site coulomb interaction approach (GGA+U)  was used for the exchange-correlation functional.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' The  Hubbard interaction parameter U is taken as 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='5 eV  (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='4 eV) for Zn 3d (O 2p) orbitals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' For the bulk ZnO,  the band gaps calculated by GGA+U and GGA methods  are 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='48 eV and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='72 eV, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' The former is more  close to the experimental value (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='37 eV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' The plane-wave  cutoff energy was set as 500 eV and a Brillouin zone with  4×4×1 Monkhorst-Pack k-point grids was employed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' The  structure relation was finished until the residual force was  smaller than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='03 eV/˚A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' To remove the undesired elec-  trostatic interaction between periodic cells along the z  direction, the dipole correction is applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  [33] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Lee and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Demkov, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' B 78, 193104 (2008)  [34] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Liu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Mei, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Tang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Azarov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Kuznetsov, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Xue, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Du, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' B 93, 235305 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  [35] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Oba, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Togo, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Tanaka, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Paier, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Kresse,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' B 77, 245202 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  [36] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Clark, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Robertson, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Lany, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Zunger, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' B 81, 115311 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  [37] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Alkauskas and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Pasquarello, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' B 84,  125206 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  [38] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Li, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Phattalung, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Limpijumnong, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Kim, and  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Yu, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' B 84, 245307 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content='  [39] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Tasker, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' C: Solid State Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
+page_content=' 12, 4977  (1979).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAyT4oBgHgl3EQfffgY/content/2301.00339v1.pdf'}
diff --git a/IdE1T4oBgHgl3EQf_waP/content/tmp_files/2301.03584v1.pdf.txt b/IdE1T4oBgHgl3EQf_waP/content/tmp_files/2301.03584v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..eeaa05c3d164662842ec9b6747f2f3faea505435
--- /dev/null
+++ b/IdE1T4oBgHgl3EQf_waP/content/tmp_files/2301.03584v1.pdf.txt
@@ -0,0 +1,1213 @@
+Network Message Field Type Clustering for
+Reverse Engineering of Unknown Binary Protocols
+Stephan Kleber and Frank Kargl
+Institute of Distributed Systems,
+Ulm University, Germany
+{stephan.kleber,frank.kargl}@uni-ulm.de
+Milan Stute and Matthias Hollick
+Secure Mobile Networking Lab,
+Technical University of Darmstadt, Germany
+{mstute,mhollick}@seemoo.de
+Abstract—Reverse engineering of unknown network protocols
+based on recorded traffic traces enables security analyses and
+debugging of undocumented network services. One important
+step in protocol reverse engineering is to determine data types
+of message fields. Existing approaches for binary protocols (1)
+lack comprehensive methods to interpret message content and
+determine the data types of discovered segments in a message
+and (2) assume the availability of context, which prevents the
+analysis of complex and lower-layer protocols. Overcoming these
+limitations, we propose the first generic method to analyze mes-
+sage field data types in unknown binary protocols by clustering
+of segments with the same data type. Our extensive evaluation
+shows that our method in most cases provides clustering of up to
+100 % precision at reasonable recall. Particularly relevant for use
+in fuzzing and misbehavior detection, we increase the coverage
+of message bytes over the state-of-the-art to 87 % by almost a
+factor of 30. We provide an open-source implementation to allow
+follow-up works.
+Index Terms—field data type clustering, protocol reverse en-
+gineering, vulnerability research, network security
+I. INTRODUCTION
+Protocol reverse engineering (PRE) based on traffic traces
+aims to infer the specification of unknown network protocols
+by analyzing traces of network messages typically gained
+from observing communication of devices implementing this
+protocol. PRE is often applied to understand malware commu-
+nication and uncover data exfiltration [4], to configure smart
+fuzzers [8], or to validate the correct and secure design and
+implementation of undocumented network services [23]. As
+a recent example, PRE was necessary to discover a severe
+vulnerability in the proprietary Apple Wireless Direct Link
+(AWDL) protocol stack [20], enabling a zero-click exploit [1]
+affecting all of Apple’s iOS-based product lines. Thus, PRE
+helps in identifying security implications that result from the
+intended or unintended use of a specific unknown protocol.
+PRE based on traffic traces encompasses the uncovering of
+message types, message formats, semantics, and behavior of
+the protocol. During this kind of analysis, semantic deduction
+is one of the most tedious and scarcely automated tasks [13,
+20]. One step in semantic analysis is inferring the data type or
+value domain of fields which can help, for example, to more
+efficiently configure smart fuzzers or to identify exfiltration [2,
+4, 24]. While some methods are available that recognize
+single field data types and correlations of values, no approach
+determines relations between fields by their value similarity
+that can be used to interpret the message contents.
+Contribution. This paper proposes a novel method to
+automatically cluster field data types. We base this inference
+on the analysis of segments, i. e., subsequences of network
+messages. We propose to distinguish segments into clusters
+of the same field data type according to their similarity to
+each other without actually identifying the data type. The
+resulting knowledge of segments with identical type simplifies
+follow-up analyses as value domains can be inferred and
+spoofing or fuzzing require this knowledge. As opposed to
+previous approaches [2, 3, 5] and particularly important for
+security assessments of custom and proprietary protocols, we
+make very few assumptions about the format and sequence of
+messages. We summarize our main contributions as follows:
+• We design the first method to cluster field types of
+network messages and do so without a limiting set of
+individual rules per type, making our approach applicable
+to a wide range of protocols with diverse and unantici-
+pated data representations.
+• Based on empirical observations of typical network pro-
+tocols, we devise a fully-automated parameter selection
+method that is use-case-specific to the clustering of field
+values.
+• We implement our method as well as FieldHunter [2] and
+CSP [9] and make all three publicly available.1
+• Through extensive evaluation of both well-known and
+proprietary protocols, we show that our method on aver-
+age achieves an F-score of 0.92 for field type clustering.
+At the same time, coverage of 87 % message bytes
+exceeds the state-of-the-art by almost a factor of 30.
+II. RELATED WORK
+Surveys have proposed to structure the overall PRE process
+into multiple phases [6, 12]. Typical phases are data collection
+into traces, feature extraction, message type identification,
+message format inference, semantic deduction, and behavior
+model reconstruction. Existing PRE approaches differ substan-
+tially for textual and binary protocols, where analysis of textual
+protocols is often considered the easier task [2, 5, 6, 12]. Thus,
+1https://github.com/vs-uulm/nemesys, fieldhunter, and goo-csp
+©2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including
+reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or
+reuse of any copyrighted component of this work in other works.
+IEEE DSN Workshop on Data-Centric Dependability and Security 2022. DOI: 10.1109/DSN-W54100.2022.00023
+
+Preprocess
+trace
+Section III-A
+Heuristic
+segments
+Section III-B
+Calculate
+dissimilarity
+Section III-C
+Clustering parameter
+auto-configuration
+Section III-D
+Cluster segments
+on dissimilarities
+Section III-E
+Refine
+clusters
+Section III-F
+Netzob | CSP
+| NEMESYS
+Canberra
+min_samples and ε
+DBSCAN
+Fig. 1. Clustering of common kinds of message content data.
+we focus on providing a solution for binary network protocols.
+Previous work, like Discoverer [5], PRISMA [14], Netzob [3],
+Goo et al. [9], NEMETYL [10], and many others, focused
+either on the message type and format or on the behavior
+model of unknown protocols. While most phases are well
+covered in literature, approaches specifically addressing the
+interpretation of the message contents, i. e., semantic deduction
+of fields, are rare. All existing methods are rule-based [2, 3,
+5, 9], i. e., they consist of a finite set of individual heuristic
+rules that explicitly deduce the semantics of a predefined small
+number of single specific field types, like number, identifier,
+or network address. We consider FieldHunter [2] the state-
+of-the-art approach as it has also been re-applied in recent
+work [9]. If either, the protocol uses a representation of data
+types that was not anticipated in any of the heuristic rules, or
+the encapsulation is unknown so that context like addresses is
+not available, FieldHunter fails to work. As there is no public
+implementation, we re-implemented FieldHunter and evaluate
+its results in comparison to our approach in this paper.
+As opposed to FieldHunter and all previous rudimentary
+field type inference approaches mentioned in this section, we
+aim for a more generic goal than using only a limited number
+of individual heuristics for field types: Our work is the first to
+propose clustering of arbitrary data types of message fields. We
+stress that we do not attempt to identify particular field types
+so that we are not limited to a predefined set of data types.
+In this work, we do not consider clustering whole messages
+into different message types since previous work like , e. g.,
+Discoverer [5], PRISMA [14], Netzob [3], or NEMETYL [10],
+already achieve this goal.
+Our approach relies on message segmentation and dif-
+ferent methods might achieve different quality. To consider
+segmentation accuracy in our evaluation, we compare three
+existing segmenters that work with variable-length fields:
+Netzob [3] is based on sequence alignment, CSP [9] applies
+frequency analysis of byte-strings, and NEMESYS [11] uses
+statistical properties of the message contents to discern one
+approximated field candidate from the other, forming heuristic
+segmentations of unknown binary messages. Furthermore,
+to compare segments to each other, we use the Canberra
+dissimilarity [10], which we originally proposed for message
+type identification. We now apply it directly for clustering of
+segments while, in contrast, its original usage was to be input
+for sequence alignment of messages.
+III. CLUSTERING DATA TYPES
+Our approach provides the means to cluster independent
+message segments into what we call pseudo data types without
+any further knowledge about the protocol. Individual steps
+of this process are outlined in Figure 1. It is a heuristical
+method to cluster the same types of data into groups of similar
+field contents. Having such clusters of segments throughout
+different messages of a trace reveals relationships of values
+between messages regardless of the byte positions of the
+segments within each message. We call the resulting clusters
+pseudo data types because, at this point, we do not know which
+data type or field semantic the cluster represents. An analyst
+can still use this knowledge as basis to analyze the properties
+of the clustered segments and infer their semantic meaning.
+We now discuss the individual steps.
+A. Preprocessing
+We first preprocess each raw trace. This step includes
+filtering for the desired protocol and de-duplicating payloads.
+Our analysis method exploits variances in the contents of
+messages, so duplicates carry no additional information.
+B. Segmentation
+We define a field in a binary protocol specification as a
+sequence of bytes at a specific position in a message, with
+a specific data type such as an integer, a sequence of chars,
+or a timestamp, and a value domain. In contrast, we define a
+segment to be a field candidate determined from the inference
+that—in an optimal case—matches the true field from the
+unknown protocol specification. Segmentation is an important
+prerequisite for characterizing the contents of messages, which
+is needed to determine the segments’ data types, infer their
+semantics, and ultimately deduce an accurate field definition.
+To obtain segments from the messages in the traces, we split
+individual messages into subsequences. Messages of known
+protocols can be segmented by using dissectors, like those
+provided by Wireshark.2 While dissectors are unavailable
+for unknown protocols to reliably determine message fields,
+heuristic approximations can be used to find probable field
+boundaries and obtain segments that are field candidates.
+Thus, we require a segmenter that can identify segments in
+unknown protocols. Available solutions include Netzob [3],
+Goo et al. [9], and NEMESYS [11]. We evaluate these three
+2https://www.wireshark.org
+2
+
+segmenters that have the advantage that they work equally well
+for protocols of fixed structure and such with dynamic field
+lengths differing between messages. The idenfified segments
+are now treated as candidates for protocols fields.
+C. Dissimilarity
+To calculate a similarity measure for segments, we interpret
+each of these as a vector of byte values. We then calculate
+a normalized dissimilarity value for each pair of segments
+using the so-called Canberra dissimilarity [10], which extends
+the better-known Canberra distance [15] to vectors of different
+dimensions. We store the pairwise dissimilarities between all
+segments in a dissimilarity matrix D.
+We exclude segments from the analysis that are only
+one byte long as coincidental similarity of arbitrary single
+bytes throughout messages prevents meaningful analysis of
+such short segments. Using alternative analysis methods,
+like frequency analysis, these one-byte segments can later
+be reincorporated in the analysis. Furthermore, we consider
+duplicate segment values only once since they increase the
+computational load without adding new information for the
+subsequent clustering.
+The dissimilarity values for each pair of remaining unique
+segments serve as affinity values to guide clustering by
+Density-Based Spatial Clustering of Applications with Noise
+(DBSCAN) [7] in the next steps.
+D. Auto-Configuration
+Before clustering, we need to configure two parameters of
+DBSCAN: the minimum number of elements to form a density
+core min_samples and a measure ε of the least density to
+be considered part of a cluster. Normally, these parameters
+need to be configured and tuned manually. For unsupervised
+and fully automated, configuration-less clustering, we present
+a new method to automatically determine the parameters for
+DBSCAN from the properties of the segments identified in the
+previous step.
+The ε auto-configuration searches for the knee point in the
+empirical cumulative distribution function (ECDF) [22] �Ek(d)
+of the dissimilarities between the k-nearest-neighbors (k-NN)
+of unique segments. For each trace, a set of functions �Ek
+exists, one ECDF for each k. An ECDF is an evenly-spaced
+step function, jumping by 1
+n for each of the n samples with a
+measured value d. In our case, the samples are the segments si
+and sj in a trace, and their measured value is the dissimilarity
+d(si, sj). Applied to the k-NN function, the ECDF’s value
+thereby is the fraction of all segments in a trace that have
+a Canberra dissimilarity less or equal to their respective kth
+nearest-neighbor. The ECDF plots the changes in distances
+between neighbors. A clear drop dκ, located at the knee point
+�Ek(κ), is then considered a suitable choice for ε that allows
+DBSCAN to reliably detect cluster boundaries.
+Of all possible �Ek, we want to dynamically select k in
+such a way that its ECDF has the most distinct drop in the
+density of the segment similarity. The function that contains
+the most distinct change in distances between neighbors has
+the sharpest knee point. Consequently, we search for the �Ek
+with the sharpest knee, with sharpness measured as the value
+of the δd at the maximum of δ �Ek. Algorithm 1 describes the
+process to select the desired k. We iterate k only between 2 and
+round(ln n) to limit the number of unnecessary calculations.
+This is sufficient since the sharpest relevant knees always are
+in the distance distributions of neighboring segments.
+To determine the rightmost knee point in �Ek with the
+selected k, we apply the Kneedle algorithm [19]. Kneedle
+requires smoothing of the ECDF, for which we use a spline,
+to remove local statistical fluctuations before accepting it as
+input. Figure 2 illustrates the ECDF, the max(δ �Ek), the effect
+of smoothing, and the detected knee, used as ε with segments
+generated from a trace of 1,000 NTP messages. For the 2nd
+parameter min_samples, we note that DBSCAN is not very
+sensitive and setting it to ln n simply prevents scattering large
+traces into too many small clusters.
+E. Clustering
+Next, we cluster segments with DBSCAN using the de-
+termined parameters ε and min_samples. DBSCAN is
+a popular and efficient clustering algorithm that makes no
+assumptions about the shape of clusters, does not require
+the target number of clusters as input, and treats outliers
+as noise. These properties set it apart from traditional clus-
+tering methods, e. g., k-means or spectral clustering, which
+are unsuitable for our purpose since we do not know the
+shape and number of clusters. For other clustering methods,
+like agglomerative clustering, affinity propagation, or support
+vector machines, automating the tuning of the parameters
+for previously unseen traces is challenging. In comparison,
+DBSCAN’s main advantage is that we can design a method
+to directly derive its parameters from the dissimilarity distri-
+bution of a trace, as described in the previous section. Thus,
+Algorithm 1: ε auto-configuration
+input : Set of dissimilarities D;
+Sensitivity parameter of Kneedle S;
+Smoothness parameter of B-Spline interpolation s;
+output: ε
+function kNN(D, k)
+Determine the k-NN of all segments represented in
+D;
+return Dissimilarities of all segments’ kth-NN;
+end
+foreach 2 ≤ k ≤ round(ln n) do
+�Ek ← ecdf(kNN(D, k));
+�Bk ← bSpline( �Ek, s);
+end
+k′ ← argmax
+k
+δ �Bk ; /* Value of the maximum
+increase in distance */
+dκ ← Kneedle( �Bk′, s);
+ε ← dκ;
+3
+
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+dissimilarity
+fraction of neighboring segments
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+maximum difference max(δ �
+E2)
+adjusted ε shifted from knee
+smoothed ECDF �
+E2
+raw ECDF �
+E2
+differences of ECDF �
+E2
+knee = 0.167
+Fig. 2.
+ECDF �
+E2 and its knee, detected by Kneedle, at a dissimilarity of
+0.167 used as ε.
+the proposed configuration procedure is completely automated
+and requires no re-training or iterative tuning for new traces
+as may be the case for other clusterers.
+The algorithm identifies high-density cores within noisy
+data and determines them to be clusters of similar segments.
+The segment density is high in areas where segments have
+a low dissimilarity to each other. Each cluster groups similar
+segments and thus comprises fields of a common data type.
+We validate the underlying assumption that clusters regularly
+coincide with data types in the first part of our evaluation
+(Section IV-B).
+In rare cases where the dissimilarity distribution leads to
+multiple knees in the ECDF, the so-determined ε does not
+denote suitable densities to cluster field data types and is too
+large. In this situation, a single large cluster contains more
+than 60 % of the segments that are not considered noise. To
+prevent this and instead select the next smaller knee for an ε,
+we consider only a subset of the original �Ek. More specifically,
+we repeat the whole ε auto-configuration process for a �E′
+k that
+is trimmed to the last detected knee κ, which becomes the
+rightmost value. Thus, �E′
+k = �Ek({d < dκ : d ∈ D}). We then
+cluster with the new ε value.
+F. Cluster Refinement
+In situations where the variability of the field values in the
+input trace is not uniformly distributed, multiple clusters may
+result for the same data type. This overclassification is not
+only a limitation of DBSCAN and we noticed that similar
+alternatives, e. g., HDBSCAN and OPTICS, suffer from the
+same effect. We favor DBSCAN since it provides more pos-
+sibilities to fine-tune the cluster boundaries for our use case.
+During pilot analyses of known protocols, we observed that
+overclassified clusters are often linked via sparsely populated
+but detectable areas. To mitigate the overclassification, we
+introduce an additional step: cluster refinement.
+In cluster refinement, we aim to automate the detection and
+merging of clusters that are nearby and have a similar density.
+For any two clusters ci and cj, we define the link segment
+slink
+i,j
+as the segment in ci that is closest to cj, i. e.,
+slink
+i,j = argmin
+si∈ci
+d(si, sj),
+∀sj ∈ cj
+dlink
+i,j
+is the distance between the link segments slink
+i,j
+and slink
+j,i .
+Using this definition, we propose two heuristic cluster merge
+conditions: (1) The clusters are very close-by, and the densities
+within an ε around the link segments are similar. (2) The
+clusters are somewhat close-by, and the whole clusters have
+similar densities. We quantify closeness and density differently
+in both conditions since we intend to capture different notions
+of closeness and density, i.e., local ε-density at elements
+linking clusters and density of clusters as a whole.
+In Condition 1, clusters are very close by if the link-
+dissimilarity is less than the mean D(ci)arithm of the set of
+pairwise dissimilarities in ci or respectively cj:
+dlink
+i,j < max(D(ci)arithm, D(cj)arithm)
+Further, we use a density definition for an ε-neighborhood
+around the nearest points between similar clusters. W. l. o. g.,
+we define sl = slink
+i,j . The density ρ within an ε around the
+link segment in ci with the set of dissimilarities D(ci),
+D(ε, sl) = {d(sl, sc) : d(sl, sc) ≤ ε, sl ̸= sc, sc ∈ ci},
+with D(ε, sl)
+⊆
+D(ci), is thus defined by ρε(sl)
+=
+D(ε, sl)median. We observed that a suitable ε is half of the
+maximum extent dmax of the cluster with the fewer segments:
+ε = dmax
+2 . The density around the link segment in cj is defined
+accordingly. Finally, ε-densities around link segments are
+considered similar if their difference is less than ερThreshold:
+��ρε(slink
+i,j ) − ρε(slink
+j,i )
+�� < ερThreshold
+Condition 2 allows a larger cluster distance but has a
+stronger density requirement. Close-by here means closer
+than the mean between both cluster’s “neighbor densities”
+normalized to the extent of the cluster. To formalize this,
+we need minmed(i), the median values for the 1st-nearest
+neighbors that are the minimum distances for each segment to
+any other in ci, respectively cj:
+minmed(i) = {min
+sb∈ci({d(sa, sb) : sa ̸= sb}) : sa ∈ ci}
+median
+In terms of Condition 2, clusters are somewhat-close-by if
+dlink
+i,j <
+minmed(i)
+D(ci)arithm
++ minmed(j)
+D(cj)arithm
+2
+As expression of the overall density in the cluster, we use
+minmed. In contrast to the ε density defined above, whole
+clusters have similar density if
+|minmed(i) − minmed(j)| < neighborDensityThreshold.
+4
+
+The selection of the values ερThreshold
+=
+0.01 and
+neighborDensityThreshold = 0.002 results from empirical
+observation of real-world protocols.
+Unlike
+overclassification,
+occasional
+underclassification
+combines different field data types in one cluster. This may be
+the case if a single value is similar to a group of others but has
+a distinct function, like an enumeration value. To compensate
+for this, we split clusters if they have extremely polarized value
+occurrences, e. g., they exhibit many unique values, together
+with very few, very high occurring ones. For this purpose,
+occurrences are defined as the count |b| of segments s ∈ c
+with a value b. We count all different values bi and calculate
+the standard deviation σ({|bi| : 0 ≤ i < |c′|}) for this cluster
+c′, with bi being the value of one or multiple segments s. To
+interpret the counts of values of one cluster, we use the percent
+rank PR [18] as a combined measure of the value occurrence
+frequency and value diversity. A PR(c′, F) = 95 means that
+95 % of the value counts in cluster c′ are below the given
+occurrence frequency of interest F. We select F depending on
+the cluster size to be ln |c′|. Thus, the same value is the pivot to
+split the cluster into two subclusters containing all segments
+with value count |bi| ≤ F and another for |bi| > F for i
+enumerating all distinct values of segments in the cluster. Con-
+sequently, if PR(c′, F) > 95 ∧ σ({|bi| : 0 ≤ i < |c′|}) > F,
+we split c′ at the pivot F = ln |c′|.
+G. Summary
+After completing this fully automated procedure, we now
+have generated vectors for each segment, calculated their
+pairwise Canberra dissimilarity, determined a suitable ε value,
+clustered the segments using DBSCAN, and refined the clus-
+ters. This completes the clustering of segments into pseudo
+data types. Next, our evaluation will show how accurately this
+can be done.
+IV. EVALUATION
+Using our proof-of-concept implementation, we evaluate
+two different aspects of our approach. First, we validate that
+data types can be clustered accurately by segment similarity.
+Second, we evaluate the accuracy achievable by using heuristic
+segmentation in the absence of ground truth. We illustrate the
+validity of these two aspects by clustering statistics.
+A. Metrics and Setup
+For a quantitative representation of the clustering quality, we
+calculate precision P and recall R of the clusters compared
+to the true data types by the number of true positives (TP),
+false positives (FP), and false negatives (FN) as:
+P =
+TP
+TP + FP
+and
+R =
+TP
+TP + FN
+For clustering into more than two clusters, TP, FP, true
+negatives (TN), and FN are defined combinatorically via the
+correct and incorrect pairwise assignments of unique segments,
+as described by Manning et al. [16]. Hence, the number of
+positives and negatives for m clusters ci are given as:
+TP+FP =
+�
+i
+�|ci|
+2
+�
+and
+TN+FN =
+�
+i,j
+(|ci| · |cj|) ,
+where j = {0 . . . (m − 1)} \ i. The true positives are:
+TP =
+�
+i
+�
+l
+�|ti,l|
+2
+�
+,
+where ti,l denotes the segments of data type l in cluster i.
+The false negatives are defined through the missed true pairs
+by false assignments to different clusters and to the noise.
+Thus, the count of false negatives is given by the sum of both
+kinds of false negatives through:
+FN =
+�
+i
+�
+l
+(|tl| − |ti,l|) · |ti,l|
+2
++
+�
+l
+�|tn,l|
+2
+�
++
+�
+l
+(|tl| − |tn,l|) · |tn,l|
+2
+,
+where tn,l are the segments of data type l assigned to the
+noise.
+To compare the quality between different protocols and
+input segments, we require an overall quality measure. There-
+fore, we calculate the F 1
+4 score from precision and recall. The
+Fβ score is a common measure for the clustering accuracy and
+defined by the harmonic mean of precision and recall [17].
+Parameter β adjusts the weight of precision and recall in
+the mean. With β = 1
+4, we place four times more emphasis
+on precision than recall. We decided on this weighting since
+precise clusters are crucial for a meaningful data type analysis
+in protocols. At the same time, low recall diminishes the
+coverage but does not reduce the validity of the overall analysis
+result. As coverage we define the ratio between the number of
+inferred bytes and all bytes of all messages in a trace. Since
+coverage refers to the number of bytes and precision and recall
+to segment pairs the result statistics are not directly correlated.
+The messages we use for developing our approach are
+collected from traces of the binary network protocols DHCP,
+DNS, NBNS, NTP, and SMB.3 All traces are publicly avail-
+able.4 In addition, we also use traces of two proprietary pro-
+tocols, namely Apple Wireless Direct Link (AWDL) and Auto
+Unlock (AU). AWDL is a Wi-Fi-based link-layer protocol
+for peer-to-peer communication. AU is a proprietary distance
+bounding protocol.5 Both protocols were not publicly docu-
+mented until they recently were reverse engineered manually.
+The reverse-engineered specification of AWDL, including a
+dissector, is publicly available [20], and we had access to a
+private Wireshark dissector of the AU protocol. Thus, both
+3Dynamic Host Configuration Protocol (RFC 2131), Domain Name System
+(RFC 1035), NetBIOS Name Service (RFC 1002), Network Time Protocol
+(RFC 958), and Server Message Block
+4DHCP, NBNS, NTP, and SMB extracted from http://download.netresec.
+com/pcap/smia-2011/; DNS extracted from https://ictf.cs.ucsb.edu/archive/
+2010/dumps/ictf2010pcap.tar.gz
+5https://support.apple.com/en-us/HT206995
+5
+
+TABLE I
+CLUSTERING STATISTICS FOR DATA TYPE
+CLUSTERING FROM GROUND TRUTH.
+proto.
+msg.s
+fields
+ε
+P
+R
+F 1
+4
+DHCP
+1000
+1017
+0.172
+0.96
+0.93
+0.95
+DNS
+1000
+839
+0.063
+1.00
+0.95
+1.00
+NBNS
+1000
+734
+0.049
+1.00
+0.91
+0.99
+NTP
+1000
+3822
+0.121
+1.00
+0.96
+1.00
+SMB
+1000
+1175
+0.218
+0.59
+0.70
+0.60
+AWDL
+768
+2190
+0.096
+1.00
+0.77
+0.98
+DHCP
+100
+229
+0.212
+0.76
+0.66
+0.75
+DNS
+100
+114
+0.143
+1.00
+0.89
+0.99
+NBNS
+100
+131
+0.121
+1.00
+0.56
+0.96
+NTP
+100
+470
+0.198
+1.00
+1.00
+1.00
+SMB
+100
+171
+0.169
+0.92
+0.48
+0.87
+AWDL
+100
+396
+0.101
+0.99
+0.59
+0.95
+AU
+123
+316
+0.366
+1.00
+0.44
+0.93
+Worst cases are printed in bold.
+TABLE II
+COMBINATORIAL CLUSTERING STATISTICS AND COVERAGE (COV.)
+FOR PSEUDO DATA TYPES OF HEURISTIC SEGMENTS.
+Netzob
+NEMESYS
+CSP
+P
+R
+F 1
+4
+cov.
+P
+R
+F 1
+4
+cov.
+P
+R
+F 1
+4
+cov.
+fails
+0.88
+0.33
+0.80
+99 %
+0.85
+0.35
+0.79
+99 %
+0.99
+0.96
+0.99
+100 %
+1.00
+0.85
+0.99
+99 %
+0.95
+0.76
+0.93
+99 %
+0.99
+0.74
+0.97
+100 %
+1.00
+0.95
+1.00
+100 %
+0.90
+0.30
+0.80
+99 %
+0.94
+0.90
+0.94
+88 %
+0.65
+0.61
+0.64
+95 %
+0.68
+0.53
+0.67
+73 %
+fails
+0.57
+0.02
+0.24
+81 %
+0.38
+0.01
+0.11
+79 %
+1.00
+0.93
+0.99
+99 %
+0.80
+0.16
+0.64
+98 %
+fails
+0.44
+0.11
+0.38
+83 %
+0.83
+0.52
+0.80
+87 %
+0.24
+0.07
+0.21
+87 %
+0.98
+0.86
+0.97
+100 %
+0.98
+0.75
+0.96
+95 %
+0.46
+0.13
+0.40
+87 %
+0.91
+0.85
+0.91
+93 %
+0.98
+0.56
+0.94
+99 %
+0.93
+0.32
+0.84
+82 %
+0.98
+0.23
+0.82
+65 %
+0.87
+0.01
+0.19
+39 %
+0.71
+0.00
+0.05
+65 %
+0.59
+0.20
+0.53
+81 %
+0.84
+0.12
+0.63
+67 %
+0.42
+0.11
+0.36
+74 %
+0.99
+0.51
+0.94
+90 %
+0.59
+0.05
+0.35
+92 %
+0.99
+0.43
+0.92
+92 %
+fails
+1.00
+0.05
+0.49
+84 %
+1.00
+0.14
+0.74
+81 %
+Best (green) and worst (red) cases are printed in bold and colored.
+protocols constitute realistic use cases where ground truth is
+available to verify our results. We use only protocols with
+ground truth to compare our results to, which is not available
+for truly unknown protocols. Otherwise, statistical analysis of
+the quality of our approach would not be possible.
+As the source of the ground truth, we parse the Wireshark
+dissectors’ output for each message. All evaluated protocols
+are binary, while DNS, DHCP, SMB, and AWDL also contain
+embedded char sequences. The binary fields of DNS, NBNS,
+and NTP have fixed length, while DHCP, SMB, AWDL, and
+AU use a mix of fixed and variable-length fields. DHCP,
+DNS, NBNS, SMB, AWDL, and AU support varying num-
+bers of fields in different messages while NTP has a fixed
+structure. Thus, our set of traces represents a wide variety of
+different protocol properties. For the evaluation of clustering
+and recognition, we truncate the traces to achieve comparable
+results. We truncate to 100 and 1 000 messages per protocol
+to show the impact of the trace size on the inference quality.
+Fewer messages were available for AWDL and AU, which we
+consider in the discussion of the results.
+B. Pseudo Data Type Clustering Validation
+First, we validate our base assumption that data types of
+segments can be clustered using the Canberra dissimilarity.
+Section III describes the process to cluster for pseudo data
+types. For validation, we compare the clustering results to
+the true field data types from the Wireshark dissectors. This
+provides a baseline to validate that different data types can
+correctly be distinguished by our dissimilarity measure.
+Cluster statistics quantify the accuracy of the match between
+data types and clusters. As overall quality metrics, we provide
+P, R, and F-score for our test protocols in Table I. For
+reference, we include the number of messages in the trace, the
+number of unique fields in the trace, and the auto-configured
+ε. The amount of noise identified by DBSCAN is always zero.
+The F-score values in Table I are near the optimum of 1
+which shows that data types can be clustered with high utility.
+However, the SMB trace with 1 000 messages stays behind
+the other results due to its low precision. Inspection of the
+individual clusters shows that timestamps and signatures have
+erroneously been placed together in one cluster. Ignoring this
+single cluster for the sake of the argument, we gain a precision
+of 0.96 while the recall drops to 0.37. This is the only instance
+in all our test runs where a parameter selection fails with
+such a significant impact, hinting towards great robustness
+of the method. Protocols with complex message formats,
+like DHCP and SMB, require a large amount of variability
+in the trace to allow for a decent analysis result. Table I
+shows this by the lower F-scores and specifically the lower
+recall for these complex protocols with smaller traces of 100
+messages compared to the results for 1 000 messages of the
+same protocols. This is due to multiple clusters representing
+a disjointed group of similar segments, reducing the recall.
+Based on the high precision of almost all clustering results,
+we conclude that most field types can accurately be clustered
+by means of dissimilarity. Overall, this aspect of our evaluation
+shows that clusters match with true field types and thus
+validate our approach of data type clustering.
+C. Clustering with Imperfect Segmentation
+Next, we present our evaluation of clustering similar seg-
+ments of real-world protocols without relying on perfect
+segmentation from Wireshark dissectors. Instead, we use the
+existing heuristic segmenters Netzob [3], NEMESYS [11],
+and CSP [9] on our set of known test protocols. This way,
+we emulate the lack of ground truth during clustering while
+retaining the possibility to measure the inference quality.
+We compare three existing heuristics segmenters that are
+available for unknown binary protocols as a basis for our
+field data type clustering. According to our results, no single
+segmenter is clearly superior to the others and each has its
+strengths and weaknesses with regard to the kind of analyzed
+protocol. Table II contains the clustering statistics P, R, and
+the F-score per test protocol. We mark the best-performing
+segmenter for each protocol trace by bold printed values in
+the table. Four analysis runs fail due to exceeding runtime or
+memory constraints.
+A significant number of segments cannot be clustered cor-
+rectly and concisely as their boundaries are shifted relative to
+the true position they should optimally mark. These fragments
+6
+
+d23d1903b3fcdab1
+d23d197a01581062
+d23d191cd025d074
+NTP timestamp A
+NTP timestamp B
+NTP timestamp C
+Fig. 3.
+Typical errors in heuristically inferred segment boundaries (vertical
+lines) that should approximate timestamps. The shaded area marks static bytes.
+blur some segment clusters to the extent that we cannot clearly
+separate the affected data types. Figure 3 illustrates how this
+affects the dissimilarity measure and, thus, the clustering result
+with an example of three timestamps that have incorrect addi-
+tional boundaries splitting the true field. These least significant
+bytes of the timestamps, regarded by themselves, seem random
+and thus cannot be clustered based on their value. This error is
+not an effect of the dissimilarities used as segment features or
+the clustering algorithm, but stems from incorrect partitioning
+of the message by the segmenters.
+This error in the approximated boundaries of high-entropy
+fields is the reason for SMB’s low recall as it contains a
+signature that is randomly split by all of the segmenters,
+since its contents look random across different messages. AU’s
+segments suffer from a slightly different but related issue:
+long sequences of 32-bit integers, representing measurement
+results, look static in some instances and random in others
+so that the dissimilarity is not successfully exploitable for
+clustering. Since for AU we only have 123 messages available
+to evaluate, we hypothesize that the variance incurred by larger
+traces would have a positive impact if available. For the other
+traces of different sizes of all protocols, the precision stays
+high compared to the true-fields baseline (Section IV-B).
+Considering the best case per protocol, only the larger trace
+of SMB exhibits an unsatisfactory precision of of 0.57, which
+is still remarkable, since knowing the true segments leads
+to only a very small improvement (R = 0.59). The smaller
+SMB trace and the AU trace are unsatisfying due to their low
+recall while precision in both cases remains high. We marked
+the three unsatisfying cases by red-colored F-scores and in
+contrast colored all F-scores of at least 0.8 green, which we
+consider successful analyzes. Most of the results even score
+above 0.9 with a precision of also better than 0.9. In the face
+of the identified problems that are realistic for working with
+unknown protocols, we argue that our method can cope with
+the inaccurate segmentation to a large degree.
+The remaining challenge is to select the most suited seg-
+menter for a protocol trace. We see that Netzob is most
+suited for protocols with distinct patterns of repeating value
+sequences, e. g., NTP having fixed structure and AWDL with
+a type-length-value (TLV) record structure. Large messages
+cause Netzob to fail due to the exponential increase in runtime,
+which is the case for larger traces of DHCP and SMB, and for
+the AU trace. NEMESYS deals well with large and complex
+messages, especially since they contain a mixture of number
+values and chars, which fits the heuristic of NEMESYS
+best. CSP performs minimally worse for larger traces than
+NEMEYS, but it lags behind for smaller traces. As CSP is
+more dependent an the variance in the trace, it is best applied
+to large traces where it poses an alternative to NEMESYS.
+D. Evaluation Summary
+This evaluation provides two insights about our approach:
+(1) field data type clustering works as intended with very little
+requirements towards and assumptions about the protocols, but
+(2) field data type clustering highly depends on the segmenta-
+tion result, where we rely on existing approaches that provide
+results of only limited quality. The higher the correctness of
+the heuristic segmentation, the better the message field type
+clustering can perform.
+In comparison, FieldHunter is able to discern the concrete
+data type of typically one or two fields per message, leading
+to a coverage of 3 % on average across all protocols. While,
+in contrast, our clustering method per se cannot determine
+the field type, it achieves an average coverage of 87 % (see
+Table II), which means that we can provide information about
+the structure of messages in terms of field similarity and field’s
+value domains for almost the complete content of all messages.
+V. CONCLUSION
+In this paper, we propose a novel method to cluster field data
+types in messages of unknown binary protocols. It requires
+recorded network traces and leverages the similarity of seg-
+ments to group them into clusters representing a common data
+type. Our efficient clustering of message segments facilitates
+subsequent analyses to identify their likely semantic function.
+We envision that identified data types and visual analytics will
+improve the analysis efficiency of unknown network messages
+by providing the means to determine the most security relevant
+message parts to investigate further in a given trace.
+In PRE, a typical high-effort task is to understand the large-
+scale structure of messages. Knowing such structure is often
+the basis to analyze, e. g., data exfiltration by malware, privacy
+violations, targets for spoofing and fuzzing for vulnerability
+testing as we illustrated, e. g., in Kröll et al. [13] and Stute
+et al. [21]. Automating this process saves effort and time and
+our work contributes to such automation. Opposed to previous
+work that uses a set of heuristics to recognize a fixed number
+of field types, clustering of segments is also applicable if
+the protocol contains unanticipated data representations, e. g.,
+encodings, since it only relies on the segments’ similarity and
+occurrence. Thus, we can cover large parts of the messages in
+the trace, while previous work—with a coverage of only 3 %
+on average—leaves most of the message content completely
+unintelligible. While clustering per se does not reveal data
+types, it simplifies an analyst’s interpretation of the message
+content. Our method increases the coverage of the interpretable
+message content to 87 % on average, outperforming the state-
+of-the-art by almost factor 30 and enabling comprehension of
+the large-scale message structure.
+We first evaluated our approach for both publicly docu-
+mented as well as undocumented protocols relying on ground
+truth message fields derived from Wireshark dissectors. We
+find that most field data types can be clustered with high
+7
+
+precision when knowing correct field boundaries. In realistic
+situations, where field boundaries are not known and heuristic
+segmenters like Netzob, NEMESYS, or CSP are applied, the
+recall is lower, but data types can still be distinguished with a
+precision close to 100 % in most cases. Our approach works
+also for protocols without IP encapsulation, like AWDL and
+AU, where previous work could not be applied due to the field
+type heuristics’ reliance on context information.
+We see two main areas for future work. Firstly, we propose
+to combine our data type clustering with the deduction of intra-
+and inter-message semantics similar to FieldHunter [2]. This
+would enable the interpretation of, e. g., length fields and mes-
+sage counter fields. Moreover, we intend to automatically learn
+value generation rules from the cluster contents using LSTM
+or similar machine learning methods to predict probable field
+values for fuzzing and misbehavior detection.
+ACKNOWLEDGMENT
+We would like to thank Steffen Klee for providing us with a
+Wireshark dissector and traces for Apple’s Auto Unlock (AU)
+protocol.
+REFERENCES
+[1]
+I. Beer. Google Project Zero: An iOS Zero-Click Ra-
+dio Proximity Exploit Odyssey. 2020. URL: https : / /
+googleprojectzero.blogspot.com/2020/12/an-ios-zero-
+click-radio-proximity.html.
+[2]
+I. Bermudez, A. Tongaonkar, M. Iliofotou, M. Mellia,
+and M. M. Munafò. “Towards Automatic Protocol Field
+Inference”. In: Computer Communications 84 (June
+2016). Elsevier.
+[3]
+G. Bossert, F. Guihéry, and G. Hiet. “Towards Auto-
+mated Protocol Reverse Engineering Using Semantic
+Information”. In: AsiaCCS. 2014.
+[4]
+C. Y. Cho, D. Babi´c, E. C. R. Shin, and D. Song.
+“Inference and Analysis of Formal Models of Botnet
+Command and Control Protocols”. In: CCS. 2010.
+[5]
+W. Cui, J. Kannan, and H. J. Wang. “Discoverer:
+Automatic Protocol Reverse Engineering from Network
+Traces”. In: USENIX Security. 2007.
+[6]
+J. Duchêne, C. L. Guernic, E. Alata, V. Nicomette, and
+M. Kaâniche. “State of the Art of Network Protocol
+Reverse Engineering Tools”. In: Journal of Computer
+Virology and Hacking Techniques 14.1 (Feb. 2018).
+Springer.
+[7]
+M. Ester, H.-P. Kriegel, J. Sander, and X. Xu. “A
+Density-Based Algorithm for Discovering Clusters in
+Large Spatial Databases with Noise”. In: KDD. 1996.
+[8]
+H. Gascon, C. Wressnegger, F. Yamaguchi, D. Arp,
+and K. Rieck. “PULSAR: Stateful Black-Box Fuzzing
+of Proprietary Network Protocols”. In: SecureComm.
+2015.
+[9]
+Y.-H. Goo, K.-S. Shim, M.-S. Lee, and M.-S. Kim.
+“Protocol Specification Extraction Based on Contigu-
+ous Sequential Pattern Algorithm”. In: IEEE Access 7
+(2019).
+[10]
+S. Kleber, R. W. v. d. Heijden, and F. Kargl. “Message
+Type Identification of Binary Network Protocols using
+Continuous Segment Similarity”. In: INFOCOM. 2020.
+[11]
+S. Kleber, H. Kopp, and F. Kargl. “NEMESYS: Net-
+work Message Syntax Reverse Engineering by Analysis
+of the Intrinsic Structure of Individual Messages”. In:
+WOOT. 2018.
+[12]
+S. Kleber, L. Maile, and F. Kargl. “Survey of Pro-
+tocol Reverse Engineering Algorithms: Decomposition
+of Tools for Static Traffic Analysis”. In: IEEE Com-
+munications Surveys and Tutorials 21.1 (Feb. 2019).
+Firstquarter.
+[13]
+T. Kröll, S. Kleber, F. Kargl, M. Hollick, and J. Classen.
+“ARIstoteles - Dissecting Apple’s Baseband Interface”.
+In: ESORICS. 2021.
+[14]
+T. Krueger, H. Gascon, N. Krämer, and K. Rieck.
+“Learning Stateful Models for Network Honeypots”. In:
+AISec. 2012.
+[15]
+G. N. Lance and W. T. Williams. “Computer Programs
+for Hierarchical Polythetic Classification (“Similarity
+Analyses”)”. In: The Computer Journal 9.1 (May 1966).
+[16]
+C. D. Manning, P. Raghavan, and H. Schütze. Intro-
+duction to Information Retrieval. Online edition. Cam-
+bridge, England: Cambridge University Press, 2009.
+[17]
+C. J. van Rijsbergen. Information Retrieval. 2nd Revised
+edition. London, Boston: Butterworth-Heinemann Ltd,
+Mar. 1979.
+[18]
+J. T. Roscoe. Fundamental Research Statistics for the
+Behavioral Sciences. 2nd edition. International Series
+in Decision Processes. New York: Holt, Rinehart and
+Winston, 1975.
+[19]
+V. Satopaa, J. Albrecht, D. Irwin, and B. Raghavan.
+“Finding a "Kneedle" in a Haystack: Detecting Knee
+Points in System Behavior”. In: ICDCSW. 2011.
+[20]
+M. Stute, D. Kreitschmann, and M. Hollick. “One
+Billion Apples’ Secret Sauce: Recipe for the Apple
+Wireless Direct Link Ad hoc Protocol”. In: MobiCom.
+2018.
+[21]
+M. Stute, S. Narain, A. Mariotto, A. Heinrich, D.
+Kreitschmann, G. Noubir, and M. Hollick. “A Billion
+Open Interfaces for Eve and Mallory: MitM, DoS, and
+Tracking Attacks on iOS and macOS Through Apple
+Wireless Direct Link”. In: USENIX Security. 2019.
+[22]
+A. W. van der Vaart. “Empirical Processes”. In: Asymp-
+totic Statistics. Cambridge, England: Cambridge Uni-
+versity Press, 1998.
+[23]
+S. Wen, Q. Meng, C. Feng, and C. Tang. “Protocol Vul-
+nerability Detection Based on Network Traffic Analysis
+and Binary Reverse Engineering”. In: PLOS ONE 12.10
+(Oct. 2017). Public Library of Science.
+[24]
+C. Wressnegger, A. Kellner, and K. Rieck. “ZOE:
+Content-based Anomaly Detection for Industrial Con-
+trol Systems”. In: DSN. 2018.
+8
+
diff --git a/IdE1T4oBgHgl3EQf_waP/content/tmp_files/load_file.txt b/IdE1T4oBgHgl3EQf_waP/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c9697dbf70bae66fc9ac41d69fa2ac6d879e03c3
--- /dev/null
+++ b/IdE1T4oBgHgl3EQf_waP/content/tmp_files/load_file.txt
@@ -0,0 +1,765 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf,len=764
+page_content='Network Message Field Type Clustering for  Reverse Engineering of Unknown Binary Protocols  Stephan Kleber and Frank Kargl  Institute of Distributed Systems,  Ulm University, Germany  {stephan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='kleber,frank.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='kargl}@uni-ulm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='de  Milan Stute and Matthias Hollick  Secure Mobile Networking Lab,  Technical University of Darmstadt, Germany  {mstute,mhollick}@seemoo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='de  Abstract—Reverse engineering of unknown network protocols  based on recorded traffic traces enables security analyses and  debugging of undocumented network services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' One important  step in protocol reverse engineering is to determine data types  of message fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Existing approaches for binary protocols (1)  lack comprehensive methods to interpret message content and  determine the data types of discovered segments in a message  and (2) assume the availability of context, which prevents the  analysis of complex and lower-layer protocols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Overcoming these  limitations, we propose the first generic method to analyze mes-  sage field data types in unknown binary protocols by clustering  of segments with the same data type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Our extensive evaluation  shows that our method in most cases provides clustering of up to  100 % precision at reasonable recall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Particularly relevant for use  in fuzzing and misbehavior detection, we increase the coverage  of message bytes over the state-of-the-art to 87 % by almost a  factor of 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' We provide an open-source implementation to allow  follow-up works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  Index Terms—field data type clustering, protocol reverse en-  gineering, vulnerability research, network security  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' INTRODUCTION  Protocol reverse engineering (PRE) based on traffic traces  aims to infer the specification of unknown network protocols  by analyzing traces of network messages typically gained  from observing communication of devices implementing this  protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' PRE is often applied to understand malware commu-  nication and uncover data exfiltration [4], to configure smart  fuzzers [8], or to validate the correct and secure design and  implementation of undocumented network services [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' As  a recent example, PRE was necessary to discover a severe  vulnerability in the proprietary Apple Wireless Direct Link  (AWDL) protocol stack [20], enabling a zero-click exploit [1]  affecting all of Apple’s iOS-based product lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Thus, PRE  helps in identifying security implications that result from the  intended or unintended use of a specific unknown protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  PRE based on traffic traces encompasses the uncovering of  message types, message formats, semantics, and behavior of  the protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' During this kind of analysis, semantic deduction  is one of the most tedious and scarcely automated tasks [13,  20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' One step in semantic analysis is inferring the data type or  value domain of fields which can help, for example, to more  efficiently configure smart fuzzers or to identify exfiltration [2,  4, 24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' While some methods are available that recognize  single field data types and correlations of values, no approach  determines relations between fields by their value similarity  that can be used to interpret the message contents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  Contribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' This paper proposes a novel method to  automatically cluster field data types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' We base this inference  on the analysis of segments, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=', subsequences of network  messages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' We propose to distinguish segments into clusters  of the same field data type according to their similarity to  each other without actually identifying the data type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' The  resulting knowledge of segments with identical type simplifies  follow-up analyses as value domains can be inferred and  spoofing or fuzzing require this knowledge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' As opposed to  previous approaches [2, 3, 5] and particularly important for  security assessments of custom and proprietary protocols, we  make very few assumptions about the format and sequence of  messages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' We summarize our main contributions as follows:  We design the first method to cluster field types of  network messages and do so without a limiting set of  individual rules per type, making our approach applicable  to a wide range of protocols with diverse and unantici-  pated data representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  Based on empirical observations of typical network pro-  tocols, we devise a fully-automated parameter selection  method that is use-case-specific to the clustering of field  values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  We implement our method as well as FieldHunter [2] and  CSP [9] and make all three publicly available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='1  Through extensive evaluation of both well-known and  proprietary protocols, we show that our method on aver-  age achieves an F-score of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='92 for field type clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  At the same time, coverage of 87 % message bytes  exceeds the state-of-the-art by almost a factor of 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' RELATED WORK  Surveys have proposed to structure the overall PRE process  into multiple phases [6, 12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Typical phases are data collection  into traces, feature extraction, message type identification,  message format inference, semantic deduction, and behavior  model reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Existing PRE approaches differ substan-  tially for textual and binary protocols, where analysis of textual  protocols is often considered the easier task [2, 5, 6, 12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Thus,  1https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='com/vs-uulm/nemesys, fieldhunter, and goo-csp  ©2020 IEEE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Personal use of this material is permitted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Permission from IEEE must be obtained for all other uses, in any current or future media, including  reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or  reuse of any copyrighted component of this work in other works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  IEEE DSN Workshop on Data-Centric Dependability and Security 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='1109/DSN-W54100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='00023  Preprocess  trace  Section III-A  Heuristic  segments  Section III-B  Calculate  dissimilarity  Section III-C  Clustering parameter  auto-configuration  Section III-D  Cluster segments  on dissimilarities  Section III-E  Refine  clusters  Section III-F  Netzob | CSP  | NEMESYS  Canberra  min_samples and ε  DBSCAN  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Clustering of common kinds of message content data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  we focus on providing a solution for binary network protocols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  Previous work, like Discoverer [5], PRISMA [14], Netzob [3],  Goo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' [9], NEMETYL [10], and many others, focused  either on the message type and format or on the behavior  model of unknown protocols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' While most phases are well  covered in literature, approaches specifically addressing the  interpretation of the message contents, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=', semantic deduction  of fields, are rare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' All existing methods are rule-based [2, 3,  5, 9], i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=', they consist of a finite set of individual heuristic  rules that explicitly deduce the semantics of a predefined small  number of single specific field types, like number, identifier,  or network address.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' We consider FieldHunter [2] the state-  of-the-art approach as it has also been re-applied in recent  work [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' If either, the protocol uses a representation of data  types that was not anticipated in any of the heuristic rules, or  the encapsulation is unknown so that context like addresses is  not available, FieldHunter fails to work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' As there is no public  implementation, we re-implemented FieldHunter and evaluate  its results in comparison to our approach in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  As opposed to FieldHunter and all previous rudimentary  field type inference approaches mentioned in this section, we  aim for a more generic goal than using only a limited number  of individual heuristics for field types: Our work is the first to  propose clustering of arbitrary data types of message fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' We  stress that we do not attempt to identify particular field types  so that we are not limited to a predefined set of data types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  In this work, we do not consider clustering whole messages  into different message types since previous work like , e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=',  Discoverer [5], PRISMA [14], Netzob [3], or NEMETYL [10],  already achieve this goal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  Our approach relies on message segmentation and dif-  ferent methods might achieve different quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' To consider  segmentation accuracy in our evaluation, we compare three  existing segmenters that work with variable-length fields:  Netzob [3] is based on sequence alignment, CSP [9] applies  frequency analysis of byte-strings, and NEMESYS [11] uses  statistical properties of the message contents to discern one  approximated field candidate from the other, forming heuristic  segmentations of unknown binary messages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Furthermore,  to compare segments to each other, we use the Canberra  dissimilarity [10], which we originally proposed for message  type identification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' We now apply it directly for clustering of  segments while, in contrast, its original usage was to be input  for sequence alignment of messages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' CLUSTERING DATA TYPES  Our approach provides the means to cluster independent  message segments into what we call pseudo data types without  any further knowledge about the protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Individual steps  of this process are outlined in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' It is a heuristical  method to cluster the same types of data into groups of similar  field contents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Having such clusters of segments throughout  different messages of a trace reveals relationships of values  between messages regardless of the byte positions of the  segments within each message.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' We call the resulting clusters  pseudo data types because, at this point, we do not know which  data type or field semantic the cluster represents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' An analyst  can still use this knowledge as basis to analyze the properties  of the clustered segments and infer their semantic meaning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  We now discuss the individual steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Preprocessing  We first preprocess each raw trace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' This step includes  filtering for the desired protocol and de-duplicating payloads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  Our analysis method exploits variances in the contents of  messages, so duplicates carry no additional information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Segmentation  We define a field in a binary protocol specification as a  sequence of bytes at a specific position in a message, with  a specific data type such as an integer, a sequence of chars,  or a timestamp, and a value domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' In contrast, we define a  segment to be a field candidate determined from the inference  that—in an optimal case—matches the true field from the  unknown protocol specification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Segmentation is an important  prerequisite for characterizing the contents of messages, which  is needed to determine the segments’ data types, infer their  semantics, and ultimately deduce an accurate field definition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  To obtain segments from the messages in the traces, we split  individual messages into subsequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Messages of known  protocols can be segmented by using dissectors, like those  provided by Wireshark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='2 While dissectors are unavailable  for unknown protocols to reliably determine message fields,  heuristic approximations can be used to find probable field  boundaries and obtain segments that are field candidates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  Thus, we require a segmenter that can identify segments in  unknown protocols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Available solutions include Netzob [3],  Goo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' [9], and NEMESYS [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' We evaluate these three  2https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='wireshark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='org  2  segmenters that have the advantage that they work equally well  for protocols of fixed structure and such with dynamic field  lengths differing between messages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' The idenfified segments  are now treated as candidates for protocols fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Dissimilarity  To calculate a similarity measure for segments, we interpret  each of these as a vector of byte values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' We then calculate  a normalized dissimilarity value for each pair of segments  using the so-called Canberra dissimilarity [10], which extends  the better-known Canberra distance [15] to vectors of different  dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' We store the pairwise dissimilarities between all  segments in a dissimilarity matrix D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  We exclude segments from the analysis that are only  one byte long as coincidental similarity of arbitrary single  bytes throughout messages prevents meaningful analysis of  such short segments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Using alternative analysis methods,  like frequency analysis, these one-byte segments can later  be reincorporated in the analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Furthermore, we consider  duplicate segment values only once since they increase the  computational load without adding new information for the  subsequent clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  The dissimilarity values for each pair of remaining unique  segments serve as affinity values to guide clustering by  Density-Based Spatial Clustering of Applications with Noise  (DBSCAN) [7] in the next steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Auto-Configuration  Before clustering, we need to configure two parameters of  DBSCAN: the minimum number of elements to form a density  core min_samples and a measure ε of the least density to  be considered part of a cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Normally, these parameters  need to be configured and tuned manually.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' For unsupervised  and fully automated, configuration-less clustering, we present  a new method to automatically determine the parameters for  DBSCAN from the properties of the segments identified in the  previous step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  The ε auto-configuration searches for the knee point in the  empirical cumulative distribution function (ECDF) [22] �Ek(d)  of the dissimilarities between the k-nearest-neighbors (k-NN)  of unique segments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' For each trace, a set of functions �Ek  exists, one ECDF for each k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' An ECDF is an evenly-spaced  step function, jumping by 1  n for each of the n samples with a  measured value d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' In our case, the samples are the segments si  and sj in a trace, and their measured value is the dissimilarity  d(si, sj).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Applied to the k-NN function, the ECDF’s value  thereby is the fraction of all segments in a trace that have  a Canberra dissimilarity less or equal to their respective kth  nearest-neighbor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' The ECDF plots the changes in distances  between neighbors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' A clear drop dκ, located at the knee point  �Ek(κ), is then considered a suitable choice for ε that allows  DBSCAN to reliably detect cluster boundaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  Of all possible �Ek, we want to dynamically select k in  such a way that its ECDF has the most distinct drop in the  density of the segment similarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' The function that contains  the most distinct change in distances between neighbors has  the sharpest knee point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Consequently, we search for the �Ek  with the sharpest knee, with sharpness measured as the value  of the δd at the maximum of δ �Ek.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Algorithm 1 describes the  process to select the desired k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' We iterate k only between 2 and  round(ln n) to limit the number of unnecessary calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  This is sufficient since the sharpest relevant knees always are  in the distance distributions of neighboring segments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  To determine the rightmost knee point in �Ek with the  selected k, we apply the Kneedle algorithm [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Kneedle  requires smoothing of the ECDF, for which we use a spline,  to remove local statistical fluctuations before accepting it as  input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Figure 2 illustrates the ECDF, the max(δ �Ek), the effect  of smoothing, and the detected knee, used as ε with segments  generated from a trace of 1,000 NTP messages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' For the 2nd  parameter min_samples, we note that DBSCAN is not very  sensitive and setting it to ln n simply prevents scattering large  traces into too many small clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Clustering  Next, we cluster segments with DBSCAN using the de-  termined parameters ε and min_samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' DBSCAN is  a popular and efficient clustering algorithm that makes no  assumptions about the shape of clusters, does not require  the target number of clusters as input, and treats outliers  as noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' These properties set it apart from traditional clus-  tering methods, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=', k-means or spectral clustering, which  are unsuitable for our purpose since we do not know the  shape and number of clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' For other clustering methods,  like agglomerative clustering, affinity propagation, or support  vector machines, automating the tuning of the parameters  for previously unseen traces is challenging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' In comparison,  DBSCAN’s main advantage is that we can design a method  to directly derive its parameters from the dissimilarity distri-  bution of a trace, as described in the previous section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Thus,  Algorithm 1: ε auto-configuration  input : Set of dissimilarities D;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  Sensitivity parameter of Kneedle S;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  Smoothness parameter of B-Spline interpolation s;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  output: ε  function kNN(D, k)  Determine the k-NN of all segments represented in  D;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  return Dissimilarities of all segments’ kth-NN;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  end  foreach 2 ≤ k ≤ round(ln n) do  �Ek ← ecdf(kNN(D, k));' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  �Bk ← bSpline( �Ek, s);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  end  k′ ← argmax  k  δ �Bk ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' /* Value of the maximum  increase in distance */  dκ ← Kneedle( �Bk′, s);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  ε ← dκ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='0  dissimilarity  fraction of neighboring segments  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='0  maximum difference max(δ �  E2)  adjusted ε shifted from knee  smoothed ECDF �  E2  raw ECDF �  E2  differences of ECDF �  E2  knee = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='167  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  ECDF �  E2 and its knee, detected by Kneedle, at a dissimilarity of  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='167 used as ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  the proposed configuration procedure is completely automated  and requires no re-training or iterative tuning for new traces  as may be the case for other clusterers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  The algorithm identifies high-density cores within noisy  data and determines them to be clusters of similar segments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  The segment density is high in areas where segments have  a low dissimilarity to each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Each cluster groups similar  segments and thus comprises fields of a common data type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  We validate the underlying assumption that clusters regularly  coincide with data types in the first part of our evaluation  (Section IV-B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  In rare cases where the dissimilarity distribution leads to  multiple knees in the ECDF, the so-determined ε does not  denote suitable densities to cluster field data types and is too  large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' In this situation, a single large cluster contains more  than 60 % of the segments that are not considered noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' To  prevent this and instead select the next smaller knee for an ε,  we consider only a subset of the original �Ek.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' More specifically,  we repeat the whole ε auto-configuration process for a �E′  k that  is trimmed to the last detected knee κ, which becomes the  rightmost value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Thus, �E′  k = �Ek({d < dκ : d ∈ D}).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' We then  cluster with the new ε value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Cluster Refinement  In situations where the variability of the field values in the  input trace is not uniformly distributed, multiple clusters may  result for the same data type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' This overclassification is not  only a limitation of DBSCAN and we noticed that similar  alternatives, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=', HDBSCAN and OPTICS, suffer from the  same effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' We favor DBSCAN since it provides more pos-  sibilities to fine-tune the cluster boundaries for our use case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  During pilot analyses of known protocols, we observed that  overclassified clusters are often linked via sparsely populated  but detectable areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' To mitigate the overclassification, we  introduce an additional step: cluster refinement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  In cluster refinement, we aim to automate the detection and  merging of clusters that are nearby and have a similar density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  For any two clusters ci and cj, we define the link segment  slink  i,j  as the segment in ci that is closest to cj, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=',  slink  i,j = argmin  si∈ci  d(si, sj),  ∀sj ∈ cj  dlink  i,j  is the distance between the link segments slink  i,j  and slink  j,i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  Using this definition, we propose two heuristic cluster merge  conditions: (1) The clusters are very close-by, and the densities  within an ε around the link segments are similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' (2) The  clusters are somewhat close-by, and the whole clusters have  similar densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' We quantify closeness and density differently  in both conditions since we intend to capture different notions  of closeness and density, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=', local ε-density at elements  linking clusters and density of clusters as a whole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  In Condition 1, clusters are very close by if the link-  dissimilarity is less than the mean D(ci)arithm of the set of  pairwise dissimilarities in ci or respectively cj:  dlink  i,j < max(D(ci)arithm, D(cj)arithm)  Further, we use a density definition for an ε-neighborhood  around the nearest points between similar clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=',  we define sl = slink  i,j .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' The density ρ within an ε around the  link segment in ci with the set of dissimilarities D(ci),  D(ε, sl) = {d(sl, sc) : d(sl, sc) ≤ ε, sl ̸= sc, sc ∈ ci},  with D(ε, sl)  ⊆  D(ci), is thus defined by ρε(sl)  =  D(ε, sl)median.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' We observed that a suitable ε is half of the  maximum extent dmax of the cluster with the fewer segments:  ε = dmax  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' The density around the link segment in cj is defined  accordingly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Finally, ε-densities around link segments are  considered similar if their difference is less than ερThreshold:  ��ρε(slink  i,j ) − ρε(slink  j,i )  �� < ερThreshold  Condition 2 allows a larger cluster distance but has a  stronger density requirement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Close-by here means closer  than the mean between both cluster’s “neighbor densities”  normalized to the extent of the cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' To formalize this,  we need minmed(i), the median values for the 1st-nearest  neighbors that are the minimum distances for each segment to  any other in ci, respectively cj:  minmed(i) = {min  sb∈ci({d(sa, sb) : sa ̸= sb}) : sa ∈ ci}  median  In terms of Condition 2, clusters are somewhat-close-by if  dlink  i,j <  minmed(i)  D(ci)arithm  + minmed(j)  D(cj)arithm  2  As expression of the overall density in the cluster, we use  minmed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' In contrast to the ε density defined above, whole  clusters have similar density if  |minmed(i) − minmed(j)| < neighborDensityThreshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  4  The selection of the values ερThreshold  =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='01 and  neighborDensityThreshold = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='002 results from empirical  observation of real-world protocols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  Unlike  overclassification,  occasional  underclassification  combines different field data types in one cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' This may be  the case if a single value is similar to a group of others but has  a distinct function, like an enumeration value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' To compensate  for this, we split clusters if they have extremely polarized value  occurrences, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=', they exhibit many unique values, together  with very few, very high occurring ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' For this purpose,  occurrences are defined as the count |b| of segments s ∈ c  with a value b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' We count all different values bi and calculate  the standard deviation σ({|bi| : 0 ≤ i < |c′|}) for this cluster  c′, with bi being the value of one or multiple segments s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' To  interpret the counts of values of one cluster, we use the percent  rank PR [18] as a combined measure of the value occurrence  frequency and value diversity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' A PR(c′, F) = 95 means that  95 % of the value counts in cluster c′ are below the given  occurrence frequency of interest F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' We select F depending on  the cluster size to be ln |c′|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Thus, the same value is the pivot to  split the cluster into two subclusters containing all segments  with value count |bi| ≤ F and another for |bi| > F for i  enumerating all distinct values of segments in the cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Con-  sequently, if PR(c′, F) > 95 ∧ σ({|bi| : 0 ≤ i < |c′|}) > F,  we split c′ at the pivot F = ln |c′|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Summary  After completing this fully automated procedure, we now  have generated vectors for each segment, calculated their  pairwise Canberra dissimilarity, determined a suitable ε value,  clustered the segments using DBSCAN, and refined the clus-  ters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' This completes the clustering of segments into pseudo  data types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Next, our evaluation will show how accurately this  can be done.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' EVALUATION  Using our proof-of-concept implementation, we evaluate  two different aspects of our approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' First, we validate that  data types can be clustered accurately by segment similarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  Second, we evaluate the accuracy achievable by using heuristic  segmentation in the absence of ground truth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' We illustrate the  validity of these two aspects by clustering statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Metrics and Setup  For a quantitative representation of the clustering quality,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' we  calculate precision P and recall R of the clusters compared  to the true data types by the number of true positives (TP),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  false positives (FP),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' and false negatives (FN) as:  P =  TP  TP + FP  and  R =  TP  TP + FN  For clustering into more than two clusters,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' TP,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' FP,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' true  negatives (TN),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' and FN are defined combinatorically via the  correct and incorrect pairwise assignments of unique segments,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  as described by Manning et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Hence, the number of  positives and negatives for m clusters ci are given as:  TP+FP =  �  i  �|ci|  2  �  and  TN+FN =  �  i,j  (|ci| · |cj|) ,  where j = {0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' (m − 1)} \\ i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' The true positives are:  TP =  �  i  �  l  �|ti,l|  2  �  ,  where ti,l denotes the segments of data type l in cluster i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  The false negatives are defined through the missed true pairs  by false assignments to different clusters and to the noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  Thus, the count of false negatives is given by the sum of both  kinds of false negatives through:  FN =  �  i  �  l  (|tl| − |ti,l|) · |ti,l|  2  +  �  l  �|tn,l|  2  �  +  �  l  (|tl| − |tn,l|) · |tn,l|  2  ,  where tn,l are the segments of data type l assigned to the  noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  To compare the quality between different protocols and  input segments, we require an overall quality measure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' There-  fore, we calculate the F 1  4 score from precision and recall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' The  Fβ score is a common measure for the clustering accuracy and  defined by the harmonic mean of precision and recall [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  Parameter β adjusts the weight of precision and recall in  the mean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' With β = 1  4, we place four times more emphasis  on precision than recall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' We decided on this weighting since  precise clusters are crucial for a meaningful data type analysis  in protocols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' At the same time, low recall diminishes the  coverage but does not reduce the validity of the overall analysis  result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' As coverage we define the ratio between the number of  inferred bytes and all bytes of all messages in a trace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Since  coverage refers to the number of bytes and precision and recall  to segment pairs the result statistics are not directly correlated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  The messages we use for developing our approach are  collected from traces of the binary network protocols DHCP,  DNS, NBNS, NTP, and SMB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='3 All traces are publicly avail-  able.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='4 In addition, we also use traces of two proprietary pro-  tocols, namely Apple Wireless Direct Link (AWDL) and Auto  Unlock (AU).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' AWDL is a Wi-Fi-based link-layer protocol  for peer-to-peer communication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' AU is a proprietary distance  bounding protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='5 Both protocols were not publicly docu-  mented until they recently were reverse engineered manually.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  The reverse-engineered specification of AWDL, including a  dissector, is publicly available [20], and we had access to a  private Wireshark dissector of the AU protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Thus, both  3Dynamic Host Configuration Protocol (RFC 2131), Domain Name System  (RFC 1035), NetBIOS Name Service (RFC 1002), Network Time Protocol  (RFC 958), and Server Message Block  4DHCP, NBNS, NTP, and SMB extracted from http://download.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='netresec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  com/pcap/smia-2011/;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' DNS extracted from https://ictf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='ucsb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='edu/archive/  2010/dumps/ictf2010pcap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='tar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='gz  5https://support.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='apple.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='com/en-us/HT206995  5  TABLE I  CLUSTERING STATISTICS FOR DATA TYPE  CLUSTERING FROM GROUND TRUTH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  proto.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  msg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='s  fields  ε  P  R  F 1  4  DHCP  1000  1017  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='172  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='96  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='93  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='95  DNS  1000  839  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='063  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='95  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='00  NBNS  1000  734  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='049  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='91  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='99  NTP  1000  3822  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='121  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='96  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='00  SMB  1000  1175  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='218  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='59  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='70  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='60  AWDL  768  2190  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='096  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='77  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='98  DHCP  100  229  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='212  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='76  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='66  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='75  DNS  100  114  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='143  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='89  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='99  NBNS  100  131  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='121  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='56  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='96  NTP  100  470  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='198  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='00  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='00  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='00  SMB  100  171  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='169  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='92  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='48  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='87  AWDL  100  396  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='101  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='99  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='59  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='95  AU  123  316  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='366  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='44  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='93  Worst cases are printed in bold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  TABLE II  COMBINATORIAL CLUSTERING STATISTICS AND COVERAGE (COV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=')  FOR PSEUDO DATA TYPES OF HEURISTIC SEGMENTS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  Netzob  NEMESYS  CSP  P  R  F 1  4  cov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  P  R  F 1  4  cov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  P  R  F 1  4  cov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  fails  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='88  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='33  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='80  99 %  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='85  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='35  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='79  99 %  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='99  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='96  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='99  100 %  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='85  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='99  99 %  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='95  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='76  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='93  99 %  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='99  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='74  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='97  100 %  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='95  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='00  100 %  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='90  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='80  99 %  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='94  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='90  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='94  88 %  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='65  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='61  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='64  95 %  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='68  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='53  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='67  73 %  fails  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='57  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='24  81 %  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='38  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='11  79 %  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='93  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='99  99 %  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='16  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='64  98 %  fails  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='44  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='11  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='38  83 %  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='83  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='52  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='80  87 %  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='24  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='07  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='21  87 %  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='98  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='86  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='97  100 %  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='98  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='96  95 %  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='46  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='13  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='40  87 %  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='91  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='85  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='91  93 %  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='98  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='56  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='94  99 %  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='93  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='32  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='84  82 %  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='98  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='23  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='82  65 %  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='87  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='19  39 %  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='71  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='05  65 %  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='59  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='53  81 %  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='84  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='12  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='63  67 %  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='42  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='11  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='36  74 %  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='99  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='51  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='94  90 %  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='59  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='35  92 %  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='99  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='43  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='92  92 %  fails  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='49  84 %  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='14  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='74  81 %  Best (green) and worst (red) cases are printed in bold and colored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  protocols constitute realistic use cases where ground truth is  available to verify our results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' We use only protocols with  ground truth to compare our results to, which is not available  for truly unknown protocols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Otherwise, statistical analysis of  the quality of our approach would not be possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  As the source of the ground truth, we parse the Wireshark  dissectors’ output for each message.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' All evaluated protocols  are binary, while DNS, DHCP, SMB, and AWDL also contain  embedded char sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' The binary fields of DNS, NBNS,  and NTP have fixed length, while DHCP, SMB, AWDL, and  AU use a mix of fixed and variable-length fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' DHCP,  DNS, NBNS, SMB, AWDL, and AU support varying num-  bers of fields in different messages while NTP has a fixed  structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Thus, our set of traces represents a wide variety of  different protocol properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' For the evaluation of clustering  and recognition, we truncate the traces to achieve comparable  results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' We truncate to 100 and 1 000 messages per protocol  to show the impact of the trace size on the inference quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  Fewer messages were available for AWDL and AU, which we  consider in the discussion of the results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Pseudo Data Type Clustering Validation  First, we validate our base assumption that data types of  segments can be clustered using the Canberra dissimilarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  Section III describes the process to cluster for pseudo data  types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' For validation, we compare the clustering results to  the true field data types from the Wireshark dissectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' This  provides a baseline to validate that different data types can  correctly be distinguished by our dissimilarity measure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  Cluster statistics quantify the accuracy of the match between  data types and clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' As overall quality metrics, we provide  P, R, and F-score for our test protocols in Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' For  reference, we include the number of messages in the trace, the  number of unique fields in the trace, and the auto-configured  ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' The amount of noise identified by DBSCAN is always zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  The F-score values in Table I are near the optimum of 1  which shows that data types can be clustered with high utility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  However, the SMB trace with 1 000 messages stays behind  the other results due to its low precision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Inspection of the  individual clusters shows that timestamps and signatures have  erroneously been placed together in one cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Ignoring this  single cluster for the sake of the argument, we gain a precision  of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='96 while the recall drops to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' This is the only instance  in all our test runs where a parameter selection fails with  such a significant impact, hinting towards great robustness  of the method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Protocols with complex message formats,  like DHCP and SMB, require a large amount of variability  in the trace to allow for a decent analysis result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Table I  shows this by the lower F-scores and specifically the lower  recall for these complex protocols with smaller traces of 100  messages compared to the results for 1 000 messages of the  same protocols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' This is due to multiple clusters representing  a disjointed group of similar segments, reducing the recall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  Based on the high precision of almost all clustering results,  we conclude that most field types can accurately be clustered  by means of dissimilarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Overall, this aspect of our evaluation  shows that clusters match with true field types and thus  validate our approach of data type clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Clustering with Imperfect Segmentation  Next, we present our evaluation of clustering similar seg-  ments of real-world protocols without relying on perfect  segmentation from Wireshark dissectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Instead, we use the  existing heuristic segmenters Netzob [3], NEMESYS [11],  and CSP [9] on our set of known test protocols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' This way,  we emulate the lack of ground truth during clustering while  retaining the possibility to measure the inference quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  We compare three existing heuristics segmenters that are  available for unknown binary protocols as a basis for our  field data type clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' According to our results, no single  segmenter is clearly superior to the others and each has its  strengths and weaknesses with regard to the kind of analyzed  protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Table II contains the clustering statistics P, R, and  the F-score per test protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' We mark the best-performing  segmenter for each protocol trace by bold printed values in  the table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Four analysis runs fail due to exceeding runtime or  memory constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  A significant number of segments cannot be clustered cor-  rectly and concisely as their boundaries are shifted relative to  the true position they should optimally mark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' These fragments  6  d23d1903b3fcdab1  d23d197a01581062  d23d191cd025d074  NTP timestamp A  NTP timestamp B  NTP timestamp C  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  Typical errors in heuristically inferred segment boundaries (vertical  lines) that should approximate timestamps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' The shaded area marks static bytes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  blur some segment clusters to the extent that we cannot clearly  separate the affected data types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Figure 3 illustrates how this  affects the dissimilarity measure and, thus, the clustering result  with an example of three timestamps that have incorrect addi-  tional boundaries splitting the true field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' These least significant  bytes of the timestamps, regarded by themselves, seem random  and thus cannot be clustered based on their value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' This error is  not an effect of the dissimilarities used as segment features or  the clustering algorithm, but stems from incorrect partitioning  of the message by the segmenters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  This error in the approximated boundaries of high-entropy  fields is the reason for SMB’s low recall as it contains a  signature that is randomly split by all of the segmenters,  since its contents look random across different messages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' AU’s  segments suffer from a slightly different but related issue:  long sequences of 32-bit integers, representing measurement  results, look static in some instances and random in others  so that the dissimilarity is not successfully exploitable for  clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Since for AU we only have 123 messages available  to evaluate, we hypothesize that the variance incurred by larger  traces would have a positive impact if available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' For the other  traces of different sizes of all protocols, the precision stays  high compared to the true-fields baseline (Section IV-B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  Considering the best case per protocol, only the larger trace  of SMB exhibits an unsatisfactory precision of of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='57, which  is still remarkable, since knowing the true segments leads  to only a very small improvement (R = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='59).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' The smaller  SMB trace and the AU trace are unsatisfying due to their low  recall while precision in both cases remains high.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' We marked  the three unsatisfying cases by red-colored F-scores and in  contrast colored all F-scores of at least 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='8 green, which we  consider successful analyzes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Most of the results even score  above 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='9 with a precision of also better than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' In the face  of the identified problems that are realistic for working with  unknown protocols, we argue that our method can cope with  the inaccurate segmentation to a large degree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  The remaining challenge is to select the most suited seg-  menter for a protocol trace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' We see that Netzob is most  suited for protocols with distinct patterns of repeating value  sequences, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=', NTP having fixed structure and AWDL with  a type-length-value (TLV) record structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Large messages  cause Netzob to fail due to the exponential increase in runtime,  which is the case for larger traces of DHCP and SMB, and for  the AU trace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' NEMESYS deals well with large and complex  messages, especially since they contain a mixture of number  values and chars, which fits the heuristic of NEMESYS  best.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' CSP performs minimally worse for larger traces than  NEMEYS, but it lags behind for smaller traces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' As CSP is  more dependent an the variance in the trace, it is best applied  to large traces where it poses an alternative to NEMESYS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Evaluation Summary  This evaluation provides two insights about our approach:  (1) field data type clustering works as intended with very little  requirements towards and assumptions about the protocols, but  (2) field data type clustering highly depends on the segmenta-  tion result, where we rely on existing approaches that provide  results of only limited quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' The higher the correctness of  the heuristic segmentation, the better the message field type  clustering can perform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  In comparison, FieldHunter is able to discern the concrete  data type of typically one or two fields per message, leading  to a coverage of 3 % on average across all protocols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' While,  in contrast, our clustering method per se cannot determine  the field type, it achieves an average coverage of 87 % (see  Table II), which means that we can provide information about  the structure of messages in terms of field similarity and field’s  value domains for almost the complete content of all messages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' CONCLUSION  In this paper, we propose a novel method to cluster field data  types in messages of unknown binary protocols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' It requires  recorded network traces and leverages the similarity of seg-  ments to group them into clusters representing a common data  type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Our efficient clustering of message segments facilitates  subsequent analyses to identify their likely semantic function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  We envision that identified data types and visual analytics will  improve the analysis efficiency of unknown network messages  by providing the means to determine the most security relevant  message parts to investigate further in a given trace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  In PRE, a typical high-effort task is to understand the large-  scale structure of messages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Knowing such structure is often  the basis to analyze, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=', data exfiltration by malware, privacy  violations, targets for spoofing and fuzzing for vulnerability  testing as we illustrated, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=', in Kröll et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' [13] and Stute  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Automating this process saves effort and time and  our work contributes to such automation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Opposed to previous  work that uses a set of heuristics to recognize a fixed number  of field types, clustering of segments is also applicable if  the protocol contains unanticipated data representations, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=',  encodings, since it only relies on the segments’ similarity and  occurrence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Thus, we can cover large parts of the messages in  the trace, while previous work—with a coverage of only 3 %  on average—leaves most of the message content completely  unintelligible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' While clustering per se does not reveal data  types, it simplifies an analyst’s interpretation of the message  content.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Our method increases the coverage of the interpretable  message content to 87 % on average, outperforming the state-  of-the-art by almost factor 30 and enabling comprehension of  the large-scale message structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  We first evaluated our approach for both publicly docu-  mented as well as undocumented protocols relying on ground  truth message fields derived from Wireshark dissectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' We  find that most field data types can be clustered with high  7  precision when knowing correct field boundaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' In realistic  situations, where field boundaries are not known and heuristic  segmenters like Netzob, NEMESYS, or CSP are applied, the  recall is lower, but data types can still be distinguished with a  precision close to 100 % in most cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Our approach works  also for protocols without IP encapsulation, like AWDL and  AU, where previous work could not be applied due to the field  type heuristics’ reliance on context information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  We see two main areas for future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Firstly, we propose  to combine our data type clustering with the deduction of intra-  and inter-message semantics similar to FieldHunter [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' This  would enable the interpretation of, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=', length fields and mes-  sage counter fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Moreover, we intend to automatically learn  value generation rules from the cluster contents using LSTM  or similar machine learning methods to predict probable field  values for fuzzing and misbehavior detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  ACKNOWLEDGMENT  We would like to thank Steffen Klee for providing us with a  Wireshark dissector and traces for Apple’s Auto Unlock (AU)  protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  REFERENCES  [1]  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Beer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Google Project Zero: An iOS Zero-Click Ra-  dio Proximity Exploit Odyssey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' URL: https : / /  googleprojectzero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='blogspot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='com/2020/12/an-ios-zero-  click-radio-proximity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='html.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  [2]  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Bermudez, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Tongaonkar, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Iliofotou, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Mellia,  and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Munafò.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' “Towards Automatic Protocol Field  Inference”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' In: Computer Communications 84 (June  2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  [3]  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Bossert, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Guihéry, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Hiet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' “Towards Auto-  mated Protocol Reverse Engineering Using Semantic  Information”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' In: AsiaCCS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  [4]  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Cho, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Babi´c, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Shin, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Song.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  “Inference and Analysis of Formal Models of Botnet  Command and Control Protocols”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' In: CCS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  [5]  W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Cui, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Kannan, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' “Discoverer:  Automatic Protocol Reverse Engineering from Network  Traces”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' In: USENIX Security.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  [6]  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Duchêne, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Guernic, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Alata, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Nicomette, and  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Kaâniche.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' “State of the Art of Network Protocol  Reverse Engineering Tools”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' In: Journal of Computer  Virology and Hacking Techniques 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='1 (Feb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  Springer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  [7]  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Ester, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Kriegel, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Sander, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Xu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' “A  Density-Based Algorithm for Discovering Clusters in  Large Spatial Databases with Noise”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' In: KDD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  [8]  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Gascon, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Wressnegger, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Yamaguchi, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Arp,  and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Rieck.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' “PULSAR: Stateful Black-Box Fuzzing  of Proprietary Network Protocols”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' In: SecureComm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  [9]  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Goo, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Shim, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Lee, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Kim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  “Protocol Specification Extraction Based on Contigu-  ous Sequential Pattern Algorithm”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' In: IEEE Access 7  (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  [10]  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Kleber, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Heijden, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Kargl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' “Message  Type Identification of Binary Network Protocols using  Continuous Segment Similarity”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' In: INFOCOM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  [11]  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Kleber, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Kopp, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Kargl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' “NEMESYS: Net-  work Message Syntax Reverse Engineering by Analysis  of the Intrinsic Structure of Individual Messages”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' In:  WOOT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  [12]  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Kleber, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Maile, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Kargl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' “Survey of Pro-  tocol Reverse Engineering Algorithms: Decomposition  of Tools for Static Traffic Analysis”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' In: IEEE Com-  munications Surveys and Tutorials 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='1 (Feb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  Firstquarter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  [13]  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Kröll, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Kleber, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Kargl, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Hollick, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Classen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  “ARIstoteles - Dissecting Apple’s Baseband Interface”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  In: ESORICS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  [14]  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Krueger, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Gascon, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Krämer, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Rieck.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  “Learning Stateful Models for Network Honeypots”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' In:  AISec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  [15]  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Lance and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Williams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' “Computer Programs  for Hierarchical Polythetic Classification (“Similarity  Analyses”)”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' In: The Computer Journal 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='1 (May 1966).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  [16]  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Manning, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Raghavan, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Schütze.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Intro-  duction to Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Online edition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Cam-  bridge, England: Cambridge University Press, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  [17]  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' van Rijsbergen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' 2nd Revised  edition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' London, Boston: Butterworth-Heinemann Ltd,  Mar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' 1979.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  [18]  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Roscoe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Fundamental Research Statistics for the  Behavioral Sciences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' 2nd edition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' International Series  in Decision Processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' New York: Holt, Rinehart and  Winston, 1975.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  [19]  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Satopaa, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Albrecht, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Irwin, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Raghavan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  “Finding a "Kneedle" in a Haystack: Detecting Knee  Points in System Behavior”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' In: ICDCSW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  [20]  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Stute, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Kreitschmann, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Hollick.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' “One  Billion Apples’ Secret Sauce: Recipe for the Apple  Wireless Direct Link Ad hoc Protocol”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' In: MobiCom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  [21]  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Stute, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Narain, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Mariotto, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Heinrich, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  Kreitschmann, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Noubir, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Hollick.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' “A Billion  Open Interfaces for Eve and Mallory: MitM, DoS, and  Tracking Attacks on iOS and macOS Through Apple  Wireless Direct Link”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' In: USENIX Security.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  [22]  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' van der Vaart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' “Empirical Processes”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' In: Asymp-  totic Statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Cambridge, England: Cambridge Uni-  versity Press, 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  [23]  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Wen, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Meng, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Feng, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Tang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' “Protocol Vul-  nerability Detection Based on Network Traffic Analysis  and Binary Reverse Engineering”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' In: PLOS ONE 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='10  (Oct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Public Library of Science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  [24]  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Wressnegger, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Kellner, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' Rieck.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' “ZOE:  Content-based Anomaly Detection for Industrial Con-  trol Systems”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' In: DSN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
+page_content='  8' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdE1T4oBgHgl3EQf_waP/content/2301.03584v1.pdf'}
diff --git a/JdE4T4oBgHgl3EQfIwx_/content/tmp_files/2301.04915v1.pdf.txt b/JdE4T4oBgHgl3EQfIwx_/content/tmp_files/2301.04915v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..66eb8bfd96655047ee63e499999c7d8bd914ab83
--- /dev/null
+++ b/JdE4T4oBgHgl3EQfIwx_/content/tmp_files/2301.04915v1.pdf.txt
@@ -0,0 +1,718 @@
+Rydberg level shift due to the electric field generated by Rydberg atom collision
+induced ionization in cesium atomic ensemble
+Xin Wang1, Xiaokai Hou1, Feifei Lu1, Rui Chang1, Lili Hao1,
+Wenjing Su1, Jiandong Bai12, Jun He13, and Junmin Wang13∗
+1State Key Laboratory of Quantum Optics and Quantum Optics Decices,
+Shanxi University, Institute of Opto-Electronics,Taiyuan 030006,China
+2Department of Physics,North University of China,Taiyuan 030051,China
+3Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006,China
+We experimentally investigate trap-loss spectra of the cesium 6S1/2(F = 4) → 71P3/2 Ry-
+dberg state by combining the cesium atomic magneto-optical trap with the narrow-linewidth,
+continuously-tunable 318.6 nm ultraviolet laser. That is, the atoms in the magneto-optical trap
+are excited to the Rydberg state due to the ultraviolet laser single-step Rydberg excitation, which
+leads to the reduction of atomic fluorescence. Based on the trap-loss spectroscopy technology, the
+Autler-Townes splitting due to strong cooling laser is observed, and the parameter dependence
+of the AT splitting interval of trap-loss spectroscopy is investigated.
+Furthermore, the effective
+temperature of cold atoms is measured by means of simplified time-of-flight fluorescence imaging.
+In addition, closed-loop positive feedback power stabilization of 318.6 nm ultraviolet laser is carried
+out. This lays the foundation for further experimental research related to Rydberg atoms using
+ultraviolet lasers, which is of great significance for the development of quantum computing and
+quantum information fields.
+Keywords: magneto-optical trap; single-step Rydberg excitation; trap-loss spectroscopy; power
+stabilization;
+I.
+INTRODUCTION
+The stronger long-range dipole-dipole interactions be-
+tween highly excited Rydberg atoms resulting in Ry-
+dberg blockade.
+It is very promising for applications
+in multi-body physics1, quantum computing2, quantum
+information3, nonlinear optics4−5, and imaging6−7. For
+the detection of Rydberg atoms, optical detection8 and
+field ionization detection9 are generally adopted.
+For
+the applications of quantum information, non-destructive
+detection is necessary.
+Therefore, the method of all-
+optical detection using the step-type electromagneti-
+cally induced transparency (EIT) spectra of Rydberg
+atoms10−11 is widely used.
+Experimentally, highly ex-
+cited Rydberg atoms are usually prepared by cascaded
+two-photon or three-photon excitation.
+The single-
+photon excitation can avoid atomic decoherence from
+population in the intermediate state, the photon scatter-
+ing, the AC-Stark shift during multi-photon excitation.
+Therefore, the single-photon excitation scheme has obvi-
+ous advantages for the preparation of Rydberg atoms for
+quantum computing and quantum information.
+The use of single-step excitation to prepare Rydberg
+state atoms has a low probability of direct excitation,
+and the transition wavelength is generally in the violet
+or ultraviolet (UV) band, which is not easy to achieve, so
+there are fewer experiments using single-photon excita-
+tion to prepare Rydberg state atoms. In 2004, Tong et al.
+obtained a 297 nm UV pulsed laser by doubling the fre-
+quency of a 594 nm dye laser and achieved single-photon
+∗ wwjjmm@sxu.edu.cn
+Rydberg excitation of 85Rb atoms 5S1/2 → nP3/2(n =
+30-80) in rubidium cold atomic magneto-optical trap12.
+In 2009, Becker’s group used a similar device to obtain
+a 297 nm UV continuum laser to achieve single-photon
+Rydberg excitation of the 85Rb atom 5S1/2 → 63P3/2 in
+a room atomic vapor cell13. In 2019, Whitlock’s group
+used a 572 nm dye laser to doubling the frequency to
+produce a 286 nm laser for the experimental study of
+the 39K cold-atom Rydberg-dressed-ground-state Ram-
+sey interferometer14.
+In recent years, with the development of nonlinear op-
+tical frequency conversion technology and quasi-phase
+matching technology, as well as the maturity of crystal
+materials and crystal coating technology, the implemen-
+tation of continuously tunable UV laser has been gradu-
+ally developed. In 2014, the Biedermann’s group used the
+sum frequency of 1071 nm and 1574 nm to generate a 638
+nm laser, after which a 300 mW 319 nm continuous UV
+laser was obtained by frequency doubling and used for
+single-photon Rydberg excitation of cesium atoms. The
+Rydberg blocking effect was observed in two single-atom
+optical dipole traps at a distance of 6.6 µm 15. In 2019,
+Li Xiaolin’s group obtained a 297 nm ultraviolet laser
+of about 200 mW by quadrupling the frequency of 1188
+nm infrared laser, which was used for the experimental
+study of single-step Rydberg excitation in the rubidium
+hot atomic vapor cell16−17. In 2020, our experimental
+group explored the DC electric field sensing of cesium
+cold atomic systems using a 319 nm UV laser18.
+In the paper, single-step Rydberg excitation in cesium
+cold atomic ensemble is achieved by using a narrow-
+linewidth single-frequency 318.6 nm ultraviolet laser and
+all-optical detection scheme.
+In the experiment, 637.2
+arXiv:2301.04915v1  [physics.atom-ph]  12 Jan 2023
+
+2
+nm red light is generated by the sum frequency of 1560.5
+nm and 1076.9 nm, and then 318.6 nm UV laser of
+2W is generated by the double frequency of red light.
+Then a cesium magneto-optical trap is constructed to
+measure the effective temperature, size and atomic den-
+sity of cold atoms by means of simplified time-of-flight
+fluorescence imaging.
+Finally, the trap-loss spectra of
+6S1/2(F = 4) → 71P3/2 Rydberg state is studied by 318.6
+nm UV laser combined with cesium magneto-optical
+trap.
+Based on the trap-loss spectroscopy technology,
+the Autler-Townes (AT) splitting due to strong cooling
+laser is observed, and the parameter dependence of the
+AT splitting interval with trap-loss spectroscopy is inves-
+tigated. The single-photon Rydberg excitation in this pa-
+per has positive implications for the further development
+of quantum optics and quantum information processing
+using cold atomic samples.
+II.
+THE VAPOR-CELL MAGNETO-OPTICAL
+TRAP OF CESIUM ATOMS
+The specific Cs atomic MOT schematic is shown in Fig.
+1(a), where the MOT is loaded in a vacuum glass cell with
+size of 30 mm × 30 mm× 120 mm, with wall thickness
+of 5 mm and vacuum degree maintained at ∼ 10−10 torr.
+In figure, the quadrupole magnetic field gradient required
+for the MOT is provided by a pair of inverted helmholtz
+coils, as shown in the gray coil, which are fixed in front (-
+z) and behind (z) of the glass cell, producing a magnetic
+field gradient of 32.0 Gauss/cm when the current is 1.6
+A.
+The 852-nm cooling laser is provided by a grating
+feedback external cavity diode laser (ECDL) of Wavi-
+cle with output power of ∼ 90 mW, and then through
+the laser amplifier of Toptia can produce 852 nm laser
+of ∼ 200 mW, and beam diameter of ∼ 10 mm.
+The
+cooling laser is detuned by ∆12=-12.4 MHz from the
+Cs 6S1/2(F = 4) → 6P3/2(F ′ = 5) transition.
+The
+852-nm repumping laser is provided by a distributed-
+Bragg-reflector (DBR) diode Laser with output power
+of ∼ 80 mW. The repumping laser resonance at the Cs
+6S1/2(F = 3) → 6P3/2(F ′ = 4)transition.
+and beam
+diameter of ∼ 11.5 mm. The Angle of cooling laser and
+repumping laser in the XY plane is 30◦. As shown in Fig.
+1(a), the six cooling laser and repumping laser overlap in
+the cesium atomic vacuum glass cell, and the intersec-
+tion point coincides with the zero point of the magnetic
+field of anti-helmholtz coil. The effective temperature,
+cold atomic size and atomic number density of cesium
+magneto-optical trap are measured by simplified time-
+of-flight fluorescence imaging. The relevant energy levels
+are shown in Fig.1(b).
+For the temperature measurement of cold atomic sam-
+ples, we use a simplified time-of-flight fluorescence imag-
+ing method, specifically, the cooling laser for laser cool-
+ing and trapping atom instead of additional probe laser
+of standard time-of-flight fluorescence imaging, which
+FIG. 1.
+Relevant hyperfine levels for Cs atomic MOT. (a)
+Schematic diagram of cesium atomic magneto-optical trap;
+(b) Energy level diagram, the cooling beams have Rabi fre-
+quency Ω12. ∆12 is the detuning of cooling laser, the 852-nm
+cooling laser is detuned by ∆12 from the Cs 6S1/2(F = 4) →
+6P3/2(F ′ = 5) transition, the 852-nm repumping laser reso-
+nance at the Cs 6S1/2(F = 3) → 6P3/2(F ′ = 4) transition.
+makes the experimental operation simpler and also al-
+lows for accurate measurement of the effective tempera-
+ture of cold atomic samples. Experimentally, the atoms
+are loaded in the MOT for 6 s, then the magnetic field
+is quickly turned off, and the repumping laser is always
+on, in order to make the atoms in the 6S1/2(F = 4) →
+6P3/2(F ′ = 5) cycle transition, and the CCD is turned on
+at different time intervals to collect the atomic fluores-
+cence pictures. In the whole process, the cooling laser is
+normally open, which aims to replace the probe laser re-
+quired in the time-of-flight fluorescence imaging method.
+The inset shown in Fig. 2 can be obtained as a grayscale
+of the fluorescence image with time intervals of 2.1, 4.0,
+6.0, 8.0, and 10.0 ms, respectively. The atomic Gaussian
+radii are obtained by processing different atomic fluores-
+cence images as a function of diffusion time.
+Using the relationship between the rate of diffusive ex-
+pansion of the atomic cloud and the temperature:σ2
+t =
+σ2
+0+ kBT
+m t2 , the initial temperature of the atom and the
+initial size of the atomic cloud can be obtained after the
+fit, where m is the atomic mass (for 133 Cs atoms m =
+
+Auti-Helmholtz coils
+CCD
+30°
+X
+Cs MOT
+Cooling and
+repumping laser
+212
+Repumping laser@852 nm
+Cooling laser@852 nm3
+FIG. 2.
+Fitting of effective temperature data for cold
+atoms, green is the atomic Gaussian radius measured in the
+Z-direction with time of flight, and the fitted effective tem-
+perature is 15.4 ± 2.7 µK, pink is the atomic Gaussian radius
+measured in the Y-direction with time of flight, and the fitted
+effective temperature is 22.3 ± 2.2 µK; The inset is a grayscale
+of the cold atomic fluorescence with time intervals of 2.1, 4.0,
+6.0, 8.0, and 10.0 ms, respectively.
+2.2× 10−25 Kg), kB = 1.38× 10−23 J/K is the Boltzmann
+constant, T is the effective temperature of the cold atom,
+σt is the Gaussian radius of the atomic cloud at time t,
+and σ0 is the initial radius of the cold atomic cloud.
+As shown in Fig.2, where pink represents the Z direc-
+tion, squares are measured data, and dashed lines are fit
+lines, green represents the Y direction, circles are mea-
+sured data, and solid lines are fit lines.
+Along the Z-
+direction, the atomic diameter is 365.4 ± 3.2 µm and the
+effective temperature is 15.4 ± 2.7 µK, while along the
+Y-direction the atomic diameter is 436.3 ± 4.5 µm and
+the effective temperature is 22.3 ± 2.2 µK. Note that
+when measuring the cold atomic effective temperature
+with standard time-of-flight fluorescence imaging meth-
+ods, the additional probe laser introduced is a square-
+wave pulse, and the duration of the pulse, which is the
+typical exposure time for imaging.
+The typical expo-
+sure time of this method depends on the time to trigger
+the CCD into a frame of the image. In the experiment,
+the timing sequence is used to control the trigger of the
+CCD, and the typical exposure time is 2 ms, which will
+bring errors. In addition, the cooling laser is always on,
+which causes the atoms to cool further during the mea-
+surement process, thus leading to biased measurement
+results.
+However, The simplified time-of-flight fluores-
+cence imaging scheme proposed in this paper is easier to
+execution and promotion in experiments. It has positive
+significance and good promotion value for the application
+of cold atom microwave atomic clock 19, cold atom op-
+tical frequency atomic clock 20, cold atom gravimeter 21
+and other quantum precision measurement fields, as well
+as the further development of quantum optics and quan-
+tum information processing by using cold atom sample.
+Based on the fluorescence image obtained at the initial
+moment, the average number of cold atoms can be esti-
+mated by substituting it into the cold atom number cal-
+culation equation N= S
+Gη
+1
+hν
+4π
+Ω
+2
+Γ
+1+I/Isat+(2∆12/Γ)2
+I/Isat
+, then
+the average density of cold atoms can be estimated to
+be ∼2.2×1010 cm−3. Where S is the calibration voltage
+signal, G is the detector gain, η is the detector response
+rate, h is Planck’s constant 6.626×10−34 J·s, ν is the flu-
+orescence frequency, Ω is the solid angle of CCD, Γ is
+the spontaneous radiation decay rate of the excited state
+of the atom (for the 6P3/2 (F’=5) state of the cesium
+atom is Γ=2π×5.2 MHz ), ∆12 is the detuning of the
+light field relative to the atomic transition frequency, I is
+average intensity of the light field, and Isat is the satura-
+tion intensity (Isat 22 for circularly polarized light is 1.12
+mW/cm2).
+III.
+ULTRAVIOLET LASER SYSTEM AND
+POWER STABILITY
+The experimental setup is shown in Fig.3, with refer-
+ences to the literature 23−25 for details. The 1560.5 nm
+MOPA system consists of a 1560.5 nm distributed feed-
+back erbium-doped fiber laser (DFB-ErDFL) with out-
+put power of ∼ 200 mW and linewidth of ∼ 160 Hz. It
+is used as a seed laser injected an erbium-doped ampli-
+fier (ErDFA) with wavelength of 1540 ∼ 1565 nm. The
+beam is ∼ 1.4 mm in diameter and can produce a nomi-
+nal 1560.5 nm laser of ∼ 15W. A waveguide-type electro-
+optic phase modulator (EOPM) is inserted between the
+1560.5 nm laser and the amplifier for phase modulation.
+The 1076.9 nm MOPA system consists of a 1076.9 nm
+distributed feedback ytterbium-doped fiber laser (DFB-
+YbDFL) with output power of ∼ 80 mW and linewidth of
+∼ 2 kHz. It is used as a seed laser injected an ytterbium-
+doped amplifier (YbDFA) with wavelength of 1060 ∼
+1090 nm. The beam is ∼ 1.7 mm in diameter and can
+produce a nominal 1076.9 nm laser of ∼ 10 W. As can be
+seen from the figure, the 1560.5 nm laser and 1076.9 nm
+laser pass through the periodically polarized PPMgO:LN
+(PPLN)crystal, and the sum frequency to produce 637.2
+nm red light, after which the 637.2 nm laser is injected
+into the four-mirror ring doubling cavity to produce ∼
+2 W of narrow-linewidth, continuously-tunable 318.6 nm
+UV laser, and the doubling crystal is BBO crystal.
+The 1560.5 nm laser frequency is locked by inject-
+ing the 1560.5 nm infrared laser into a ultralow expan-
+sion (ULE) cavity (cavity length is 47.6 mm, free spec-
+tral range is 3.145 GHz, fineness is 34000@1560.5 nm,
+30000@637.2 nm), and the laser frequency is locked by
+using the PDH sideband modulation technology. Here, a
+waveguide-type EOPM is added between the 1560.5 nm
+laser seed source and the amplifier for phase modulation
+of the laser, mainly because the EOPM cannot operate
+above the watt power due to its low damage threshold.
+On the other hand, the modulation frequency added to
+the 1560.5 nm laser can be transferred to the generated
+637.2 nm red light through the sum-frequency process,
+
+10.0 ms
+Tv=22.3 ± 2.2 uK
+8.0 ms
+6.0 ms
+4.0 ms
+2.1 ms
+Tz=15.4 ± 2.7 uK4
+FIG. 3. Diagram of the experimental setup, where the 1560.5 nm MOPA system consists of a distributed feedback erbium-
+doped fiber laser (DFB-ErDFL) with a narrow linewidth (160 Hz) of 1560.5 nm and an erbium-doped amplifier (ErDFA),
+between which a waveguide-type electro-optical phase modulator (EOPM) with an input-output polarization-preserving pigtail
+is inserted; 1076.9 nm MOPA system consists of a distributed feedback ytterbium-doped fiber laser (DFB-YbDFL) with a
+narrow linewidth (2 kHz) of 1076.9 nm and an ytterbium-doped amplifier (YbDFA); AOM closed-loop positive feedback power
+stabilization device; Cesium atomic magneto-optical trap including auti-helmholtz coil, vacuum glass cell.
+which in turn enables the frequency-doubling cavity lock-
+ing.
+The frequency stabilization of 1076.9 nm laser is per-
+formed with the aid of 637.2 nm laser, using the electronic
+sideband (ESB) frequency stabilization technology26,
+which is different from the PDH frequency stabilization
+by phase modulation of the modulation sideband carried
+by the 637.2 nm laser. Finally, the feedback signal is fed
+back to the PZT port of the 1076.9 nm fiber laser to re-
+alize the frequency stabilization of 1076.9 nm laser. This
+results in frequency stabilization of the entire 318.6 nm
+UV laser system, which has the advantage of continuous
+tuning (range ¿6 GHz) while locking the laser.
+The experimentally generated 318.6 nm laser is power
+stabilized by acousto-optic modulator(AOM), as shown
+in Fig.3, experimentally the 318.6 nm laser pass through
+the AOM and the 0-level light is blocked out and the -1-
+level diffracted light is taken, followed by a small angle
+sampling with BS, and the sampled laser pass through
+the servo control system after the detector and finally
+is used to control the AOM. The other laser beam after
+beam splitting is sampled by BS small-angle, one way
+for subsequent laser use, and one way through the detec-
+tor divided into two parts for monitoring, using a digital
+multimeter to monitor the intensity fluctuations in the
+time domain, as well as the SR785 fast Fourier trans-
+form spectrometer to monitor the intensity fluctuations
+in the frequency domain. The laser intensity fluctuation
+in the time domain is suppressed from ± 12.50 % to ±
+0.08 %, the pink and green are the intensity fluctuation
+under the feedback open loop and closed loop, respec-
+tively, and the response bandwidth of the feedback loop
+in the frequency domain is about ∼ 13.0 kHz, as shown
+in Fig.4, after which the trap-loss spectrum is studied by
+combining the UV laser with a cesium magneto-optical
+trap.
+
+Servo
+Servo
+SFG
+1560.5 nm
+MOPA
+PPMgO:LN
+Crystal
+ULE Cavity @1560.5 nm
+1076.9 nm
+and 637.2 nm
+MOPA
+SHG
+Cavity
+Cs MOT
+AOM5
+FIG. 4.
+When the feedback loop is open or closed, (a)
+the peak-peak value of power fluctuation in the time domain
+decreases from ± 12.50 % to ± 0.08 %; (b) the effective band-
+width in the frequency domain is ∼ 13.0 kHz.
+IV.
+FLUORESCENCE TRAP-LOSS SPECTRA
+OF CESIUM COLD ATOM SAMPLES IN
+MAGNETO-OPTICAL TRAP
+The single-step Rydberg excitation of cold cesium
+atoms is studied, experimentally, we adopt high-precision
+trap-loss spectroscopy to determine the Rydberg excita-
+tion, because Rydberg atoms cannot be trapped by MOT
+27−28. In MOT, Rydberg excitation results in a reduction
+of the atom number in the 6S1/2(F = 4) ground state, as
+atoms are excited to the Rydberg state. The cold atom
+fluorescence loss rate of atoms in MOT is proportional
+to the number of atoms excited to Rydberg state. The
+number of atoms excited to the Rydberg state can be es-
+timated by measuring the cold atom fluorescence before
+and after the Rydberg excitation, to obtain the fluores-
+cence loss rate. Specifically, we use a digital CCD camera
+(Thorlabs, 1500M-GE) to take spatially-resolved images
+of MOT and monitor the atom number of the ground
+state [6S1/2(F = 4)]. MOT is continuously loaded, and
+the MOT fluorescence is recorded on the CCD with and
+without UV beam for 10 s each.
+FIG. 5.
+(a) Trap-loss spectrum of 6S1/2(F = 4) → 71P3/2
+Rydberg state, error bars are standard deviations obtained by
+means of multiple measurements; (b) Energy level of dressed
+states.When the strong coupling laser interacts with a two-
+level system, the atomic energy level is split into two which
+is induced by dressing splitting.
+Therefore, 6S1/2(F = 4)
+state forms two dressed-ground-states, | 1D′⟩ and | 1D′′⟩, re-
+spectively. Ω1r is the Rabi frequency of 318.6-nm UV laser,
+∆12 is the detuning of 318.6-nm UV laser, excitation of Ryd-
+berg states is accomplished by a single-step direct excitation
+scheme from 6S1/2(F = 4) → 71P3/2 state with a 318.6-nm
+UV laser.
+In the experiment, we use standing laser field excita-
+tion to reduce the radiation pressure of the laser, which
+can push cold atoms out of the magneto-optical trap.
+Since the UV laser is weak, the photoionization of ce-
+sium atoms due to UV laser should be relatively small.
+Therefore, the reduction of cold atoms in the magneto-
+optical trap is mainly due to the interaction of UV laser
+with cold atoms, which excites them from the ground
+state to the Rydberg state.
+In the cold atom system, since MOT cannot capture
+Rydberg atoms, when 318.6 nm ultraviolet laser is ap-
+plied to the cold cesium atoms in MOT, the atoms will
+be lost from the trap. Therefore, the excitation of Ry-
+dberg atoms is judged experimentally by trap-loss spec-
+troscopy. That is, the fluorescence change of cold atom
+cloud caused by UV laser resonance with atoms is di-
+rectly measured. The loss rate of cold atom fluorescence
+of atoms in MOT is proportional to the number of atoms
+
+urh
+feedback open loop
+feedback closed loop
+feedback closed loop
+feedback open loop71P3/2 Rydberg state
+Rydberg
+21r
+excitation
+laser(a319 nm
+2126
+FIG. 6. Trap-loss loss spectra are obtained by changing Rabi frequency of cooling laser; (a) The trap-loss spectra are observed
+when the Rabi frequencies of the cooling laser are 19.9, 24.9 and 27.2 MHz respectively. The solid lines are the results of
+theoretical calculations, and AT splitting intervals are 23.9, 27.4 and 30.0 MHz respectively. (b) The AT split interval varies
+with the Rabi frequency of the cooling laser. The red solid line is the fitting result of the dressed state theory, containing the
+three data sets of (a) plot. (c) shows the linewidths of the AT splitting double pits as a function of the cooling laser Rabi
+frequency, respectively.
+excited to Rydberg state.
+The typical trap-loss spec-
+trum is observed experimentally, corresponding to the
+6S1/2(F = 4) → 71P3/2 Rydberg state.
+As shown in
+Fig.5(a), Ω12 = 22.8 MHz, Ω1r = 156.0 kHz, the dou-
+ble pits in the spectrum are due to AT splitting caused
+by cooling laser strong coupling. When the strong cou-
+pling light interacts with a two-level system (transition),
+the atomic energy level will dressed splitting, that is, the
+strong cooling laser interacts with the cold atom leads to
+the splitting of atomic energy levels, and the UV laser
+acting on the atomic level leads to new resonance. As
+shown in Fig. 5(b), the 6S1/2(F = 4) state forms two
+dressed ground states(| 1D′⟩ and | 1D′′⟩), so that when
+the 318.6 nm UV laser acts on the atoms, two absorption
+pits are formed at the two dressed state positions.
+Based on a frequency-stabilized tunable UV laser sys-
+tem, we measure the fluorescence trap-loss spectra of
+the 71P3/2 Rydberg state at different Rabi frequencies
+of cooling laser.
+As shown in Fig.
+6(a), here the UV
+power is fixed at ∼ 2 mW and the Rabi frequency of the
+cooling laser is varied, and the trap-loss spectrum is mea-
+sured when the weak 318.6 nm UV laser is scanned near
+the 6S1/2(F = 4) → 71P3/2 transition. Among them,
+Rabi frequencies of cooling laser corresponding to black,
+blue and green squares of data are 19.9, 24.9 and 27.2
+MHz respectively, and the measured AT split intervals
+are 23.9, 27.4 and 30.0 MHz respectively, which are ex-
+perimental measurement results. The solid line is based
+on the theoretical calculation of AT splitting spectra in a
+V-type three-level system. It can be seen from the figure
+
+212 = 27.2 MHz , Ω = 30.0 MHz
+工
+Q12 = 24.9 MHz , 2 = 27.4 MHz
+212 = 19.9 MHz , Q = 23.9 MHz7
+FIG. 7. Trap-loss spectra are obtained by changing the power of the ultraviolet laser; (a) The trap- loss spectra are observed
+when the UV power are 8.0, 20.0 and 30.0 mW respectively. The solid lines are the results of theoretical calculations, and AT
+splitting intervals are 25.8, 25.9 and 25.6 MHz respectively. (b) The AT split interval varies with the power of the ultraviolet
+laser. The red solid line is the fitting result of the dressed state theory, containing the three data sets of (a) plot. (c) shows
+the linewidths of AT split pits as a function of UV power.
+that there are two pits in the spectrum, namely AT split-
+ting. The AT splitting is caused by the strong coupling
+of the cooling laser. To further prove our inference, we
+also measure the variation of the AT interval with the
+Rabi frequency of cooling laser. As shown in Fig. 6(b),
+the black data are the experimentally measured extrac-
+tion values, which are the AT splitting intervals extracted
+from the trap-loss spectra measured by changing Rabi
+frequencies of different cooling laser. It can be seen from
+the figure that the AT splitting intervals in the trap-loss
+spectra increase as the cooling light Rabi frequency in-
+creases, and the red solid line is the calculation result of
+the dressed state theory 29.
+According to the theory of dressed states, the in-
+terval of the AT double pits can be expressed as ˜Ω
+=
+�
+Ω2
+12 + ∆2
+12, where Ω12 is the total Rabi frequency of
+the cooling laser and ∆12 = -12.4 MHz is the detuning
+of the cooling laser with respect to the 6S1/2(F = 4) →
+6P3/2(F ′ = 5) hyperfine transition. The asymmetry of
+the AT double is due to the non-zero detuning of the
+cooling beam with respect to the hyperfine transition.
+We can see that the theoretical calculations are in gen-
+eral agreement with the experimental data, which further
+proves that the double pits are caused by the strong cool-
+ing laser leading to the dressed splitting of the cesium
+atom ground state.
+Fig.6(c) shows the linewidths of the AT splitting dou-
+ble pits as a function of the cooling laser Rabi fre-
+quency, respectively.
+According to reference
+22, the
+linewidth of AT split double pits can be expressed as:
+Γ±= Γ+D
+2
+(1∓
+∆12
+√
+∆2
+12+4Ω2
+12 )+W, where Γ± is linewidth of
+two states, D is the Doppler broadening, W is the other
+broadening mechanism, and Γ is the decay rate from the
+
+8
+excited state to the ground state. The spectral linewidth
+is mainly affected by Doppler broadening, power broad-
+ening, interatomic collision broadening, and transition
+broadening, etc. The squares are the experimental data
+and the solid lines are the fitting results.
+The fluorescence trap-loss spectra of the 6S1/2(F =
+4) → 71P3/2 Rydberg state under varying UV power con-
+ditions are measured in Fig. 7(a). The black, blue, and
+green squares of the data correspond to the UV power of
+8.0, 20.0, and 30.0 mW, respectively, and the measured
+AT splitting intervals are 25.8, 25.9, and 25.6 MHz, which
+are the experimental measurement results. The solid line
+is based on the theoretical calculation of AT splitting
+spectra in a V-type three-level system. Here, the Rabi
+frequency Ω12 of the cooling laser is 22.8 MHz, and the
+frequency detuning ∆12 is -12.4 MHz.
+It can be seen
+from the figure that the AT splitting interval changes lit-
+tle with the change of UV power. This is because the
+Rabi frequency of the UV laser is much smaller than the
+Rabi frequency of the cooling laser, so the AT splitting in-
+terval basically does not vary with the power of weak UV
+laser, as shown in Fig. 7(b), we measure the AT splitting
+interval for six groups of UV laser power varying from
+5-40 mW, respectively, and it can be seen from the fig-
+ure that the AT splitting interval is about 25.8(2) MHz,
+which is basically consistent with the theoretical calcula-
+tion value of 25.9 MHz. Fig. 7(c) shows the linewidths of
+AT split pits as a function of UV power, from the figure,
+it can be seen that the linewidth basically does not vary
+with the UV power.
+V.
+CONCLUSION
+In the paper, a single-step Rydberg excitation experi-
+ment of the cesium cold atomic system is carried out by
+a power-stabilized 318.6 nm laser system. Based on the
+trap-loss spectroscopy technology, we realize the nonde-
+structive detection of the Rydberg state and observe the
+Autler-Townes splitting in the cold atom ensemble due
+to the strong cooling laser, and investigate the parameter
+dependence of the AT splitting interval in the trap-loss
+spectroscopy, which satisfy the theory of dressed states.
+Furthermore, the relevant parameters of cold atom sam-
+ples are measured in the cesium magneto-optical trap, in-
+cluding the size, effective temperature, and atomic num-
+ber density of the cold atoms.
+It has positive signifi-
+cance for further development of quantum information
+processing and quantum computing by using single-step
+Rydberg excitation in cold atom system.
+ACKNOWLEDGMENTS
+This research is partially funded by the National Key
+R&D Program of China (2021YFA1402002), the National
+Natural Science Foundation of China ( 61875111 and
+12104417), and the Fundamental Research Program of
+Shanxi Province (20210302124161).
+[1] A. Browaeys, T. Lahaye. Many-body physics with indi-
+vidually controlled Rydberg atoms[J]. Nature Phys., 16,
+132-142, (2020).
+[2] C. S. Adams, J. D. Pritchard, J. P. Shaffer, Rydberg
+atom quantum technologies[J], J. Phys. B: At. Mol. Opt.
+Phys.,53, 012002, (2020).
+[3] M. Saffman, T. G. Walker, K. Mølmer. Quantum infor-
+mation with Rydberg atoms[J]. Rev. Mod. Phys., 82,
+2313-2363, (2010).
+[4] A. V. Zasedatelev, A. V. Baranikov, D. Sannikov, D. Ur-
+bonas, F. Scafirimuto, V. Yu. Shishkov, E. S. Andrianov,
+Y. E. Lozovik, U. Scherf, T. St¨oferle, R. F. Mahrt, and P.
+G. Lagoudakis, Single-photon nonlinearity at room tem-
+perature[J], Nature, 597, 493-497, (2021).
+[5] M. Moreno-Cardoner, D. Goncalves, D. E. Chang, Quan-
+tum nonlinear optics based on two-dimensional Rydberg
+atom arrays[J]. Phys. Rev. Lett., 127, 263602, (2021).
+[6] M. Ferreira-Cao, V. Gavryusev, T. Franz, R. F. Alves, A.
+Signoles, G. Z¨urn and M. Weidem¨uller, Depletion imag-
+ing of Rydberg atoms in cold atomic gases[J]. J. Phys. B:
+At. Mol. Opt. Phys., 53, 084004, (2020).
+[7] C. Gross, T. Vogt, W. Li, Ion imaging via long-range in-
+teraction with Rydberg atoms[J]. Phys. Rev. Lett., 124,
+053401, (2020).
+[8] B. S. Silpa, A. B. Shovan, C. Saptarishi, and R. Sanjukta,
+Transition frequency measurement of highly excited Ryd-
+berg states of 87Rb for a wide range of principal quantum
+numbers[J]. Optics Continuum, 1, 1176-1192, (2022).
+[9] J. M. Zhao, H. Zhang, Z. G. Feng, X. B. Zhu, L. J. Zhang,
+C. Y. Li, and S. T. Jia, Measurement of polarizability of
+cesium nD state in magneto-optical trap[J]. J. Phys. Soc.
+Japan, 80, 034303, (2011).
+[10] W. C. Xu, A. V. Venkatramani, S. H. Cant´u, T. ˇSumarac,
+V. Kl¨usener, M. D. Lukin, and V. Vuleti´c, Fast prepa-
+ration and detection of a Rydberg qubit using atomic
+ensembles[J], Phys. Rev. Lett., 127, 050501, (2021).
+[11] T. Firdoshi, S. Garain, V. Gupta, D. Kara, and A. K.
+Mohapatra, Electromagnetically induced transparency in
+the strong blockade regime using the four-photon excita-
+tion process in thermal rubidium vapor[J], Phys. Rev. A,
+104, 013711, (2021).
+[12] D. Tong, S. M. Farooqi, J. Stanojevic, S. Krishnan, Y.
+P. Zhang, R. Cˆot´e, E. E. Eyler, and P. L. Gould, Local
+blockade of Rydberg excitation in an ultracold gas[J].
+Phys. Rev. Lett., 93, 063001, (2004).
+[13] P. Thoumany, T. H¨ansch, G. Stania, L. Urbonas, and Th.
+Becker, Optical spectroscopy of rubidium Rydberg atoms
+with a 297 nm frequency-doubled dye laser[J]. Opt. Lett.,
+34, 1621-1623, (2009).
+[14] A. Arias, G. Lochead, T. M. Wintermantel, S. Helmrich,
+and S. Whitlock, Realization of a Rydberg-dressed ram-
+sey interferometer and electrometer[J], Phys. Rev. Lett.,
+
+9
+122 053601, (2019).
+[15] A. M. Hankin, Y. Y. Jau, L. P. Parazzoli, C. W. Chou,
+D. J. Armstrong, A. J. Landahl, and G. W. Biedermann,
+Two-atom Rydberg blockade using direct 6S to nP exci-
+tation[J]. Phys. Rev. A, 89, 033416, (2014).
+[16] M. Li, B. Li, X. Jiang, J. Qian, X. Li, and L. Liu,
+Measurement of
+85Rb nP-state transition frequencies
+via single-photon Rydberg excitation spectroscopy[J]. J.
+Opt. Soc. Am. B, 36, 1850-1857, (2019).
+[17] B. Li, M. Li, X. Jiang, J. Qian, X. Li, L. Liu, and Y.
+Wang, Optical spectroscopy of nP Rydberg states of 87Rb
+atoms with a 297-nm ultraviolet laser[J]. Phys. Rev. A,
+99, 042502, (2019).
+[18] J. D. Bai, S. Liu, J. Y. Wang, J. He, and J. M. Wang,
+Single-photon Rydberg excitation and trap-loss spec-
+troscopy of cold cesium atoms in a magneto-optical trap
+by using of a 319-nm ultraviolet laser system[J], IEEE J.
+Sel. Top. Quant. Electr., 26, 1600106, (2020).
+[19] C. Liu, S. Wang, Z. Chen, Y. Wang, and S. Hou, Optical
+detection in magnetic state-selection Cs beam tubes for
+transportable Cs beam clocks[J]. Meas. Sci. Technol., 30,
+075004, (2019).
+[20] Y. Zhang, C. X. Shan, K. Mølmer. Active Frequency
+Measurement on Superradiant Strontium Clock Transi-
+tions[J]. Phys. Rev. Lett., 128, 013604, (2022)
+[21] P. W. Huang, B. Tang, X. Chen, J. Q. Zhong, Z. Y.
+Xiong, L. Zhou, J. Wang, and M. S. Zhan, Accuracy and
+stability evaluation of the 85Rb atom gravimeter WAG-
+H5-1 at the 2017 international comparison of absolute
+gravimeters[J]. Metrologia, 56, 045012, (2019).
+[22] A. D. Steck, Cesium D line data, 23 January 1998, http:
+//george. ph. utexas. edu/ dsteck/ alkalidata/.
+[23] J. Y. Wang, J. D. Bai, J. He, and J. M. Wang, Real-
+ization and characterization of single-frequency tunable
+637.2nm high-power laser[J], Opt. Commun., 370, 150-
+155, (2016).
+[24] J. M. Wang, J. D. Bai, J. Y, Wang, and J. He, Realization
+of a watt-level 319-nm single-frequency CW ultraviolet
+laser and its application in single-photon Rydberg exci-
+tation of cesium atoms[J], Chinese Optics, 12, 701-718,
+(2019). (in Chinese)
+[25] J. Y. Wang, J. D. Bai, J. He, and J. M. Wang, Develop-
+ment and characterization of a 2.2 W narrow-linewidth
+318.6 nm ultraviolet laser[J], J. Opt. Soc. Am. B, 33,
+2020-2025, (2016).
+[26] J. D. Bai, J. Y. Wang, J. He, and J. M. Wang, Electronic
+sideband locking of a broadly tunable 318.6 nm ultravio-
+let laser to an ultra-stable optical cavity[J]. J. Opt., 19,
+045501, (2017).
+[27] A. G. Boetes, R. V. Skannrup, J. B. Naber, S. J. J. M. F.
+Kokkelmans, and R. J. C. Spreeuw, Trapping of Rydberg
+atoms in tight magnetic microtraps[J]. Phys. Rev. A, 97,
+013430, (2018).
+[28] Y. F. Cao, W. G. Yang, H. Zhang, M. Y. Jing, W. B.
+Li, L. J. Zhang, L. T. Xiao, and S. T. Jia, Dephasing
+effect of Rydberg states on trap loss spectroscopy of cold
+atoms[J], J. Opt. Soc. Am. B, 39, 2032-2036, (2022).
+[29] S. Menon, and G. S. Agarwal. Gain components in the
+Autler-Townes doublet from quantum interferences in de-
+cay channels[J]. Phys. Rev. A, 61, 013807, (1999).
+
diff --git a/JdE4T4oBgHgl3EQfIwx_/content/tmp_files/load_file.txt b/JdE4T4oBgHgl3EQfIwx_/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..82e9543afeb9016d8333ba775842693471c09544
--- /dev/null
+++ b/JdE4T4oBgHgl3EQfIwx_/content/tmp_files/load_file.txt
@@ -0,0 +1,703 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf,len=702
+page_content='Rydberg level shift due to the electric field generated by Rydberg atom collision  induced ionization in cesium atomic ensemble  Xin Wang1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Xiaokai Hou1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Feifei Lu1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Rui Chang1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Lili Hao1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  Wenjing Su1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Jiandong Bai12,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Jun He13,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' and Junmin Wang13∗  1State Key Laboratory of Quantum Optics and Quantum Optics Decices,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  Shanxi University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Institute of Opto-Electronics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='Taiyuan 030006,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='China  2Department of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='North University of China,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='Taiyuan 030051,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='China  3Collaborative Innovation Center of Extreme Optics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Shanxi University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Taiyuan 030006,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='China  We experimentally investigate trap-loss spectra of the cesium 6S1/2(F = 4) → 71P3/2 Ry-  dberg state by combining the cesium atomic magneto-optical trap with the narrow-linewidth,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  continuously-tunable 318.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='6 nm ultraviolet laser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' That is, the atoms in the magneto-optical trap  are excited to the Rydberg state due to the ultraviolet laser single-step Rydberg excitation, which  leads to the reduction of atomic fluorescence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Based on the trap-loss spectroscopy technology, the  Autler-Townes splitting due to strong cooling laser is observed, and the parameter dependence  of the AT splitting interval of trap-loss spectroscopy is investigated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  Furthermore, the effective  temperature of cold atoms is measured by means of simplified time-of-flight fluorescence imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  In addition, closed-loop positive feedback power stabilization of 318.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='6 nm ultraviolet laser is carried  out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' This lays the foundation for further experimental research related to Rydberg atoms using  ultraviolet lasers, which is of great significance for the development of quantum computing and  quantum information fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  Keywords: magneto-optical trap;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' single-step Rydberg excitation;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' trap-loss spectroscopy;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' power  stabilization;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  INTRODUCTION  The stronger long-range dipole-dipole interactions be-  tween highly excited Rydberg atoms resulting in Ry-  dberg blockade.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  It is very promising for applications  in multi-body physics1, quantum computing2, quantum  information3, nonlinear optics4−5, and imaging6−7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' For  the detection of Rydberg atoms, optical detection8 and  field ionization detection9 are generally adopted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  For  the applications of quantum information, non-destructive  detection is necessary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  Therefore, the method of all-  optical detection using the step-type electromagneti-  cally induced transparency (EIT) spectra of Rydberg  atoms10−11 is widely used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  Experimentally, highly ex-  cited Rydberg atoms are usually prepared by cascaded  two-photon or three-photon excitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  The single-  photon excitation can avoid atomic decoherence from  population in the intermediate state, the photon scatter-  ing, the AC-Stark shift during multi-photon excitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  Therefore, the single-photon excitation scheme has obvi-  ous advantages for the preparation of Rydberg atoms for  quantum computing and quantum information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  The use of single-step excitation to prepare Rydberg  state atoms has a low probability of direct excitation,  and the transition wavelength is generally in the violet  or ultraviolet (UV) band, which is not easy to achieve, so  there are fewer experiments using single-photon excita-  tion to prepare Rydberg state atoms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' In 2004, Tong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  obtained a 297 nm UV pulsed laser by doubling the fre-  quency of a 594 nm dye laser and achieved single-photon  ∗ wwjjmm@sxu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='cn  Rydberg excitation of 85Rb atoms 5S1/2 → nP3/2(n =  30-80) in rubidium cold atomic magneto-optical trap12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  In 2009, Becker’s group used a similar device to obtain  a 297 nm UV continuum laser to achieve single-photon  Rydberg excitation of the 85Rb atom 5S1/2 → 63P3/2 in  a room atomic vapor cell13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' In 2019, Whitlock’s group  used a 572 nm dye laser to doubling the frequency to  produce a 286 nm laser for the experimental study of  the 39K cold-atom Rydberg-dressed-ground-state Ram-  sey interferometer14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  In recent years, with the development of nonlinear op-  tical frequency conversion technology and quasi-phase  matching technology, as well as the maturity of crystal  materials and crystal coating technology, the implemen-  tation of continuously tunable UV laser has been gradu-  ally developed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' In 2014, the Biedermann’s group used the  sum frequency of 1071 nm and 1574 nm to generate a 638  nm laser, after which a 300 mW 319 nm continuous UV  laser was obtained by frequency doubling and used for  single-photon Rydberg excitation of cesium atoms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' The  Rydberg blocking effect was observed in two single-atom  optical dipole traps at a distance of 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='6 µm 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' In 2019,  Li Xiaolin’s group obtained a 297 nm ultraviolet laser  of about 200 mW by quadrupling the frequency of 1188  nm infrared laser, which was used for the experimental  study of single-step Rydberg excitation in the rubidium  hot atomic vapor cell16−17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' In 2020, our experimental  group explored the DC electric field sensing of cesium  cold atomic systems using a 319 nm UV laser18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  In the paper, single-step Rydberg excitation in cesium  cold atomic ensemble is achieved by using a narrow-  linewidth single-frequency 318.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='6 nm ultraviolet laser and  all-optical detection scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  In the experiment, 637.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='2  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='04915v1  [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='atom-ph]  12 Jan 2023  2  nm red light is generated by the sum frequency of 1560.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='5  nm and 1076.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='9 nm, and then 318.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='6 nm UV laser of  2W is generated by the double frequency of red light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  Then a cesium magneto-optical trap is constructed to  measure the effective temperature, size and atomic den-  sity of cold atoms by means of simplified time-of-flight  fluorescence imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  Finally, the trap-loss spectra of  6S1/2(F = 4) → 71P3/2 Rydberg state is studied by 318.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='6  nm UV laser combined with cesium magneto-optical  trap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  Based on the trap-loss spectroscopy technology,  the Autler-Townes (AT) splitting due to strong cooling  laser is observed, and the parameter dependence of the  AT splitting interval with trap-loss spectroscopy is inves-  tigated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' The single-photon Rydberg excitation in this pa-  per has positive implications for the further development  of quantum optics and quantum information processing  using cold atomic samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  THE VAPOR-CELL MAGNETO-OPTICAL  TRAP OF CESIUM ATOMS  The specific Cs atomic MOT schematic is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  1(a), where the MOT is loaded in a vacuum glass cell with  size of 30 mm × 30 mm× 120 mm, with wall thickness  of 5 mm and vacuum degree maintained at ∼ 10−10 torr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  In figure, the quadrupole magnetic field gradient required  for the MOT is provided by a pair of inverted helmholtz  coils, as shown in the gray coil, which are fixed in front (-  z) and behind (z) of the glass cell, producing a magnetic  field gradient of 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='0 Gauss/cm when the current is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='6  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  The 852-nm cooling laser is provided by a grating  feedback external cavity diode laser (ECDL) of Wavi-  cle with output power of ∼ 90 mW, and then through  the laser amplifier of Toptia can produce 852 nm laser  of ∼ 200 mW, and beam diameter of ∼ 10 mm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  The  cooling laser is detuned by ∆12=-12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='4 MHz from the  Cs 6S1/2(F = 4) → 6P3/2(F ′ = 5) transition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  The  852-nm repumping laser is provided by a distributed-  Bragg-reflector (DBR) diode Laser with output power  of ∼ 80 mW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' The repumping laser resonance at the Cs  6S1/2(F = 3) → 6P3/2(F ′ = 4)transition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  and beam  diameter of ∼ 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='5 mm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' The Angle of cooling laser and  repumping laser in the XY plane is 30◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  1(a), the six cooling laser and repumping laser overlap in  the cesium atomic vacuum glass cell, and the intersec-  tion point coincides with the zero point of the magnetic  field of anti-helmholtz coil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' The effective temperature,  cold atomic size and atomic number density of cesium  magneto-optical trap are measured by simplified time-  of-flight fluorescence imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' The relevant energy levels  are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='1(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  For the temperature measurement of cold atomic sam-  ples, we use a simplified time-of-flight fluorescence imag-  ing method, specifically, the cooling laser for laser cool-  ing and trapping atom instead of additional probe laser  of standard time-of-flight fluorescence imaging, which  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  Relevant hyperfine levels for Cs atomic MOT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' (a)  Schematic diagram of cesium atomic magneto-optical trap;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  (b) Energy level diagram, the cooling beams have Rabi fre-  quency Ω12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' ∆12 is the detuning of cooling laser, the 852-nm  cooling laser is detuned by ∆12 from the Cs 6S1/2(F = 4) →  6P3/2(F ′ = 5) transition, the 852-nm repumping laser reso-  nance at the Cs 6S1/2(F = 3) → 6P3/2(F ′ = 4) transition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  makes the experimental operation simpler and also al-  lows for accurate measurement of the effective tempera-  ture of cold atomic samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Experimentally, the atoms  are loaded in the MOT for 6 s, then the magnetic field  is quickly turned off, and the repumping laser is always  on, in order to make the atoms in the 6S1/2(F = 4) →  6P3/2(F ′ = 5) cycle transition, and the CCD is turned on  at different time intervals to collect the atomic fluores-  cence pictures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' In the whole process, the cooling laser is  normally open, which aims to replace the probe laser re-  quired in the time-of-flight fluorescence imaging method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  The inset shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' 2 can be obtained as a grayscale  of the fluorescence image with time intervals of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='1, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='0,  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='0, 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='0, and 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='0 ms, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' The atomic Gaussian  radii are obtained by processing different atomic fluores-  cence images as a function of diffusion time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  Using the relationship between the rate of diffusive ex-  pansion of the atomic cloud and the temperature:σ2  t =  σ2  0+ kBT  m t2 , the initial temperature of the atom and the  initial size of the atomic cloud can be obtained after the  fit, where m is the atomic mass (for 133 Cs atoms m =  Auti-Helmholtz coils  CCD  30°  X  Cs MOT  Cooling and  repumping laser  212  Repumping laser@852 nm  Cooling laser@852 nm3  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  Fitting of effective temperature data for cold  atoms, green is the atomic Gaussian radius measured in the  Z-direction with time of flight, and the fitted effective tem-  perature is 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='4 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='7 µK, pink is the atomic Gaussian radius  measured in the Y-direction with time of flight, and the fitted  effective temperature is 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='3 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='2 µK;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' The inset is a grayscale  of the cold atomic fluorescence with time intervals of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='1, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='0,  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='0, 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='0, and 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='0 ms, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='2× 10−25 Kg), kB = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='38× 10−23 J/K is the Boltzmann  constant, T is the effective temperature of the cold atom,  σt is the Gaussian radius of the atomic cloud at time t,  and σ0 is the initial radius of the cold atomic cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='2, where pink represents the Z direc-  tion, squares are measured data, and dashed lines are fit  lines, green represents the Y direction, circles are mea-  sured data, and solid lines are fit lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  Along the Z-  direction, the atomic diameter is 365.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='4 ± 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='2 µm and the  effective temperature is 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='4 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='7 µK, while along the  Y-direction the atomic diameter is 436.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='3 ± 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='5 µm and  the effective temperature is 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='3 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='2 µK.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Note that  when measuring the cold atomic effective temperature  with standard time-of-flight fluorescence imaging meth-  ods, the additional probe laser introduced is a square-  wave pulse, and the duration of the pulse, which is the  typical exposure time for imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  The typical expo-  sure time of this method depends on the time to trigger  the CCD into a frame of the image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' In the experiment,  the timing sequence is used to control the trigger of the  CCD, and the typical exposure time is 2 ms, which will  bring errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' In addition, the cooling laser is always on,  which causes the atoms to cool further during the mea-  surement process, thus leading to biased measurement  results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  However, The simplified time-of-flight fluores-  cence imaging scheme proposed in this paper is easier to  execution and promotion in experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' It has positive  significance and good promotion value for the application  of cold atom microwave atomic clock 19, cold atom op-  tical frequency atomic clock 20, cold atom gravimeter 21  and other quantum precision measurement fields, as well  as the further development of quantum optics and quan-  tum information processing by using cold atom sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  Based on the fluorescence image obtained at the initial  moment, the average number of cold atoms can be esti-  mated by substituting it into the cold atom number cal-  culation equation N= S  Gη  1  hν  4π  Ω  2  Γ  1+I/Isat+(2∆12/Γ)2  I/Isat  , then  the average density of cold atoms can be estimated to  be ∼2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='2×1010 cm−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Where S is the calibration voltage  signal, G is the detector gain, η is the detector response  rate, h is Planck’s constant 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='626×10−34 J·s, ν is the flu-  orescence frequency, Ω is the solid angle of CCD, Γ is  the spontaneous radiation decay rate of the excited state  of the atom (for the 6P3/2 (F’=5) state of the cesium  atom is Γ=2π×5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='2 MHz ), ∆12 is the detuning of the  light field relative to the atomic transition frequency, I is  average intensity of the light field, and Isat is the satura-  tion intensity (Isat 22 for circularly polarized light is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='12  mW/cm2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  ULTRAVIOLET LASER SYSTEM AND  POWER STABILITY  The experimental setup is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='3, with refer-  ences to the literature 23−25 for details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' The 1560.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='5 nm  MOPA system consists of a 1560.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='5 nm distributed feed-  back erbium-doped fiber laser (DFB-ErDFL) with out-  put power of ∼ 200 mW and linewidth of ∼ 160 Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' It  is used as a seed laser injected an erbium-doped ampli-  fier (ErDFA) with wavelength of 1540 ∼ 1565 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' The  beam is ∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='4 mm in diameter and can produce a nomi-  nal 1560.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='5 nm laser of ∼ 15W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' A waveguide-type electro-  optic phase modulator (EOPM) is inserted between the  1560.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='5 nm laser and the amplifier for phase modulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  The 1076.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='9 nm MOPA system consists of a 1076.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='9 nm  distributed feedback ytterbium-doped fiber laser (DFB-  YbDFL) with output power of ∼ 80 mW and linewidth of  ∼ 2 kHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' It is used as a seed laser injected an ytterbium-  doped amplifier (YbDFA) with wavelength of 1060 ∼  1090 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' The beam is ∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='7 mm in diameter and can  produce a nominal 1076.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='9 nm laser of ∼ 10 W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' As can be  seen from the figure, the 1560.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='5 nm laser and 1076.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='9 nm  laser pass through the periodically polarized PPMgO:LN  (PPLN)crystal, and the sum frequency to produce 637.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='2  nm red light, after which the 637.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='2 nm laser is injected  into the four-mirror ring doubling cavity to produce ∼  2 W of narrow-linewidth, continuously-tunable 318.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='6 nm  UV laser, and the doubling crystal is BBO crystal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  The 1560.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='5 nm laser frequency is locked by inject-  ing the 1560.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='5 nm infrared laser into a ultralow expan-  sion (ULE) cavity (cavity length is 47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='6 mm, free spec-  tral range is 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='145 GHz, fineness is 34000@1560.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='5 nm,  30000@637.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='2 nm), and the laser frequency is locked by  using the PDH sideband modulation technology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Here, a  waveguide-type EOPM is added between the 1560.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='5 nm  laser seed source and the amplifier for phase modulation  of the laser, mainly because the EOPM cannot operate  above the watt power due to its low damage threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  On the other hand, the modulation frequency added to  the 1560.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='5 nm laser can be transferred to the generated  637.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='2 nm red light through the sum-frequency process,  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='0 ms  Tv=22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='3 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='2 uK  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='0 ms  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='0 ms  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='0 ms  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='1 ms  Tz=15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='4 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='7 uK4  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Diagram of the experimental setup, where the 1560.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='5 nm MOPA system consists of a distributed feedback erbium-  doped fiber laser (DFB-ErDFL) with a narrow linewidth (160 Hz) of 1560.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='5 nm and an erbium-doped amplifier (ErDFA),  between which a waveguide-type electro-optical phase modulator (EOPM) with an input-output polarization-preserving pigtail  is inserted;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' 1076.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='9 nm MOPA system consists of a distributed feedback ytterbium-doped fiber laser (DFB-YbDFL) with a  narrow linewidth (2 kHz) of 1076.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='9 nm and an ytterbium-doped amplifier (YbDFA);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' AOM closed-loop positive feedback power  stabilization device;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Cesium atomic magneto-optical trap including auti-helmholtz coil, vacuum glass cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  which in turn enables the frequency-doubling cavity lock-  ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  The frequency stabilization of 1076.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='9 nm laser is per-  formed with the aid of 637.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='2 nm laser, using the electronic  sideband (ESB) frequency stabilization technology26,  which is different from the PDH frequency stabilization  by phase modulation of the modulation sideband carried  by the 637.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='2 nm laser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Finally, the feedback signal is fed  back to the PZT port of the 1076.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='9 nm fiber laser to re-  alize the frequency stabilization of 1076.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='9 nm laser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' This  results in frequency stabilization of the entire 318.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='6 nm  UV laser system, which has the advantage of continuous  tuning (range ¿6 GHz) while locking the laser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  The experimentally generated 318.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='6 nm laser is power  stabilized by acousto-optic modulator(AOM), as shown  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='3, experimentally the 318.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='6 nm laser pass through  the AOM and the 0-level light is blocked out and the -1-  level diffracted light is taken, followed by a small angle  sampling with BS, and the sampled laser pass through  the servo control system after the detector and finally  is used to control the AOM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' The other laser beam after  beam splitting is sampled by BS small-angle, one way  for subsequent laser use, and one way through the detec-  tor divided into two parts for monitoring, using a digital  multimeter to monitor the intensity fluctuations in the  time domain, as well as the SR785 fast Fourier trans-  form spectrometer to monitor the intensity fluctuations  in the frequency domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' The laser intensity fluctuation  in the time domain is suppressed from ± 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='50 % to ±  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='08 %, the pink and green are the intensity fluctuation  under the feedback open loop and closed loop, respec-  tively, and the response bandwidth of the feedback loop  in the frequency domain is about ∼ 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='0 kHz, as shown  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='4, after which the trap-loss spectrum is studied by  combining the UV laser with a cesium magneto-optical  trap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  Servo  Servo  SFG  1560.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='5 nm  MOPA  PPMgO:LN  Crystal  ULE Cavity @1560.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='5 nm  1076.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='9 nm  and 637.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='2 nm  MOPA  SHG  Cavity  Cs MOT  AOM5  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  When the feedback loop is open or closed, (a)  the peak-peak value of power fluctuation in the time domain  decreases from ± 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='50 % to ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='08 %;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' (b) the effective band-  width in the frequency domain is ∼ 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='0 kHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  FLUORESCENCE TRAP-LOSS SPECTRA  OF CESIUM COLD ATOM SAMPLES IN  MAGNETO-OPTICAL TRAP  The single-step Rydberg excitation of cold cesium  atoms is studied, experimentally, we adopt high-precision  trap-loss spectroscopy to determine the Rydberg excita-  tion, because Rydberg atoms cannot be trapped by MOT  27−28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' In MOT, Rydberg excitation results in a reduction  of the atom number in the 6S1/2(F = 4) ground state, as  atoms are excited to the Rydberg state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' The cold atom  fluorescence loss rate of atoms in MOT is proportional  to the number of atoms excited to Rydberg state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' The  number of atoms excited to the Rydberg state can be es-  timated by measuring the cold atom fluorescence before  and after the Rydberg excitation, to obtain the fluores-  cence loss rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Specifically, we use a digital CCD camera  (Thorlabs, 1500M-GE) to take spatially-resolved images  of MOT and monitor the atom number of the ground  state [6S1/2(F = 4)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' MOT is continuously loaded, and  the MOT fluorescence is recorded on the CCD with and  without UV beam for 10 s each.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  (a) Trap-loss spectrum of 6S1/2(F = 4) → 71P3/2  Rydberg state, error bars are standard deviations obtained by  means of multiple measurements;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' (b) Energy level of dressed  states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='When the strong coupling laser interacts with a two-  level system, the atomic energy level is split into two which  is induced by dressing splitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  Therefore, 6S1/2(F = 4)  state forms two dressed-ground-states, | 1D′⟩ and | 1D′′⟩, re-  spectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Ω1r is the Rabi frequency of 318.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='6-nm UV laser,  ∆12 is the detuning of 318.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='6-nm UV laser, excitation of Ryd-  berg states is accomplished by a single-step direct excitation  scheme from 6S1/2(F = 4) → 71P3/2 state with a 318.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='6-nm  UV laser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  In the experiment, we use standing laser field excita-  tion to reduce the radiation pressure of the laser, which  can push cold atoms out of the magneto-optical trap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  Since the UV laser is weak, the photoionization of ce-  sium atoms due to UV laser should be relatively small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  Therefore, the reduction of cold atoms in the magneto-  optical trap is mainly due to the interaction of UV laser  with cold atoms, which excites them from the ground  state to the Rydberg state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  In the cold atom system, since MOT cannot capture  Rydberg atoms, when 318.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='6 nm ultraviolet laser is ap-  plied to the cold cesium atoms in MOT, the atoms will  be lost from the trap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Therefore, the excitation of Ry-  dberg atoms is judged experimentally by trap-loss spec-  troscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' That is, the fluorescence change of cold atom  cloud caused by UV laser resonance with atoms is di-  rectly measured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' The loss rate of cold atom fluorescence  of atoms in MOT is proportional to the number of atoms  urh  feedback open loop  feedback closed loop  feedback closed loop  feedback open loop71P3/2 Rydberg state  Rydberg  21r  excitation  laser(a319 nm  2126  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Trap-loss loss spectra are obtained by changing Rabi frequency of cooling laser;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' (a) The trap-loss spectra are observed  when the Rabi frequencies of the cooling laser are 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='9, 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='9 and 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='2 MHz respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' The solid lines are the results of  theoretical calculations, and AT splitting intervals are 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='9, 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='4 and 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='0 MHz respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' (b) The AT split interval varies  with the Rabi frequency of the cooling laser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' The red solid line is the fitting result of the dressed state theory, containing the  three data sets of (a) plot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' (c) shows the linewidths of the AT splitting double pits as a function of the cooling laser Rabi  frequency, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  excited to Rydberg state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  The typical trap-loss spec-  trum is observed experimentally, corresponding to the  6S1/2(F = 4) → 71P3/2 Rydberg state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  As shown in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='5(a), Ω12 = 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='8 MHz, Ω1r = 156.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='0 kHz, the dou-  ble pits in the spectrum are due to AT splitting caused  by cooling laser strong coupling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' When the strong cou-  pling light interacts with a two-level system (transition),  the atomic energy level will dressed splitting, that is, the  strong cooling laser interacts with the cold atom leads to  the splitting of atomic energy levels, and the UV laser  acting on the atomic level leads to new resonance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' As  shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' 5(b), the 6S1/2(F = 4) state forms two  dressed ground states(| 1D′⟩ and | 1D′′⟩), so that when  the 318.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='6 nm UV laser acts on the atoms, two absorption  pits are formed at the two dressed state positions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  Based on a frequency-stabilized tunable UV laser sys-  tem, we measure the fluorescence trap-loss spectra of  the 71P3/2 Rydberg state at different Rabi frequencies  of cooling laser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  6(a), here the UV  power is fixed at ∼ 2 mW and the Rabi frequency of the  cooling laser is varied, and the trap-loss spectrum is mea-  sured when the weak 318.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='6 nm UV laser is scanned near  the 6S1/2(F = 4) → 71P3/2 transition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Among them,  Rabi frequencies of cooling laser corresponding to black,  blue and green squares of data are 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='9, 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='9 and 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='2  MHz respectively, and the measured AT split intervals  are 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='9, 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='4 and 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='0 MHz respectively, which are ex-  perimental measurement results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' The solid line is based  on the theoretical calculation of AT splitting spectra in a  V-type three-level system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' It can be seen from the figure  212 = 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='2 MHz , Ω = 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='0 MHz  工  Q12 = 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='9 MHz , 2 = 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='4 MHz  212 = 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='9 MHz , Q = 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='9 MHz7  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Trap-loss spectra are obtained by changing the power of the ultraviolet laser;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' (a) The trap- loss spectra are observed  when the UV power are 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='0, 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='0 and 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='0 mW respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' The solid lines are the results of theoretical calculations, and AT  splitting intervals are 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='8, 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='9 and 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='6 MHz respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' (b) The AT split interval varies with the power of the ultraviolet  laser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' The red solid line is the fitting result of the dressed state theory, containing the three data sets of (a) plot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' (c) shows  the linewidths of AT split pits as a function of UV power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  that there are two pits in the spectrum, namely AT split-  ting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' The AT splitting is caused by the strong coupling  of the cooling laser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' To further prove our inference, we  also measure the variation of the AT interval with the  Rabi frequency of cooling laser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' 6(b),  the black data are the experimentally measured extrac-  tion values, which are the AT splitting intervals extracted  from the trap-loss spectra measured by changing Rabi  frequencies of different cooling laser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' It can be seen from  the figure that the AT splitting intervals in the trap-loss  spectra increase as the cooling light Rabi frequency in-  creases, and the red solid line is the calculation result of  the dressed state theory 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  According to the theory of dressed states, the in-  terval of the AT double pits can be expressed as ˜Ω  =  �  Ω2  12 + ∆2  12, where Ω12 is the total Rabi frequency of  the cooling laser and ∆12 = -12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='4 MHz is the detuning  of the cooling laser with respect to the 6S1/2(F = 4) →  6P3/2(F ′ = 5) hyperfine transition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' The asymmetry of  the AT double is due to the non-zero detuning of the  cooling beam with respect to the hyperfine transition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  We can see that the theoretical calculations are in gen-  eral agreement with the experimental data, which further  proves that the double pits are caused by the strong cool-  ing laser leading to the dressed splitting of the cesium  atom ground state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='6(c) shows the linewidths of the AT splitting dou-  ble pits as a function of the cooling laser Rabi fre-  quency, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  According to reference  22, the  linewidth of AT split double pits can be expressed as:  Γ±= Γ+D  2  (1∓  ∆12  √  ∆2  12+4Ω2  12 )+W, where Γ± is linewidth of  two states, D is the Doppler broadening, W is the other  broadening mechanism, and Γ is the decay rate from the  8  excited state to the ground state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' The spectral linewidth  is mainly affected by Doppler broadening, power broad-  ening, interatomic collision broadening, and transition  broadening, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' The squares are the experimental data  and the solid lines are the fitting results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  The fluorescence trap-loss spectra of the 6S1/2(F =  4) → 71P3/2 Rydberg state under varying UV power con-  ditions are measured in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' 7(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' The black, blue, and  green squares of the data correspond to the UV power of  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='0, 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='0, and 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='0 mW, respectively, and the measured  AT splitting intervals are 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='8, 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='9, and 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='6 MHz, which  are the experimental measurement results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' The solid line  is based on the theoretical calculation of AT splitting  spectra in a V-type three-level system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Here, the Rabi  frequency Ω12 of the cooling laser is 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='8 MHz, and the  frequency detuning ∆12 is -12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='4 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  It can be seen  from the figure that the AT splitting interval changes lit-  tle with the change of UV power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' This is because the  Rabi frequency of the UV laser is much smaller than the  Rabi frequency of the cooling laser, so the AT splitting in-  terval basically does not vary with the power of weak UV  laser, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' 7(b), we measure the AT splitting  interval for six groups of UV laser power varying from  5-40 mW, respectively, and it can be seen from the fig-  ure that the AT splitting interval is about 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='8(2) MHz,  which is basically consistent with the theoretical calcula-  tion value of 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='9 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' 7(c) shows the linewidths of  AT split pits as a function of UV power, from the figure,  it can be seen that the linewidth basically does not vary  with the UV power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  CONCLUSION  In the paper, a single-step Rydberg excitation experi-  ment of the cesium cold atomic system is carried out by  a power-stabilized 318.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='6 nm laser system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Based on the  trap-loss spectroscopy technology, we realize the nonde-  structive detection of the Rydberg state and observe the  Autler-Townes splitting in the cold atom ensemble due  to the strong cooling laser, and investigate the parameter  dependence of the AT splitting interval in the trap-loss  spectroscopy, which satisfy the theory of dressed states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  Furthermore, the relevant parameters of cold atom sam-  ples are measured in the cesium magneto-optical trap, in-  cluding the size, effective temperature, and atomic num-  ber density of the cold atoms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  It has positive signifi-  cance for further development of quantum information  processing and quantum computing by using single-step  Rydberg excitation in cold atom system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  ACKNOWLEDGMENTS  This research is partially funded by the National Key  R&D Program of China (2021YFA1402002), the National  Natural Science Foundation of China ( 61875111 and  12104417), and the Fundamental Research Program of  Shanxi Province (20210302124161).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  [1] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Browaeys, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Lahaye.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Many-body physics with indi-  vidually controlled Rydberg atoms[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Nature Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=', 16,  132-142, (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  [2] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Adams, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Pritchard, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Shaffer, Rydberg  atom quantum technologies[J], J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' B: At.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=',53, 012002, (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  [3] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Saffman, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Walker, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Mølmer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Quantum infor-  mation with Rydberg atoms[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=', 82,  2313-2363, (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  [4] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Zasedatelev, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Baranikov, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Sannikov, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Ur-  bonas, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Scafirimuto, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Yu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Shishkov, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Andrianov,  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Lozovik, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Scherf, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' St¨oferle, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Mahrt, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Lagoudakis, Single-photon nonlinearity at room tem-  perature[J], Nature, 597, 493-497, (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  [5] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Moreno-Cardoner, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Goncalves, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Chang, Quan-  tum nonlinear optics based on two-dimensional Rydberg  atom arrays[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=', 127, 263602, (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  [6] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Ferreira-Cao, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Gavryusev, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Franz, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Alves, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  Signoles, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Z¨urn and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Weidem¨uller, Depletion imag-  ing of Rydberg atoms in cold atomic gases[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' B:  At.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=', 53, 084004, (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  [7] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Gross, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Vogt, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Li, Ion imaging via long-range in-  teraction with Rydberg atoms[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=', 124,  053401, (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  [8] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Silpa, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Shovan, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Saptarishi, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Sanjukta,  Transition frequency measurement of highly excited Ryd-  berg states of 87Rb for a wide range of principal quantum  numbers[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Optics Continuum, 1, 1176-1192, (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  [9] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Zhao, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Zhang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Feng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Zhu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Zhang,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Li, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Jia, Measurement of polarizability of  cesium nD state in magneto-optical trap[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  Japan, 80, 034303, (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  [10] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Xu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Venkatramani, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Cant´u, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' ˇSumarac,  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Kl¨usener, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Lukin, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Vuleti´c, Fast prepa-  ration and detection of a Rydberg qubit using atomic  ensembles[J], Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=', 127, 050501, (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  [11] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Firdoshi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Garain, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Gupta, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Kara, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  Mohapatra, Electromagnetically induced transparency in  the strong blockade regime using the four-photon excita-  tion process in thermal rubidium vapor[J], Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' A,  104, 013711, (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  [12] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Tong, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Farooqi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Stanojevic, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Krishnan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Zhang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Cˆot´e, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Eyler, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Gould, Local  blockade of Rydberg excitation in an ultracold gas[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=', 93, 063001, (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  [13] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Thoumany, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' H¨ansch, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Stania, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Urbonas, and Th.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  Becker, Optical spectroscopy of rubidium Rydberg atoms  with a 297 nm frequency-doubled dye laser[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=',  34, 1621-1623, (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  [14] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Arias, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Lochead, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Wintermantel, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Helmrich,  and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Whitlock, Realization of a Rydberg-dressed ram-  sey interferometer and electrometer[J], Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=',  9  122 053601, (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  [15] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Hankin, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Jau, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Parazzoli, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Chou,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Armstrong, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Landahl, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Biedermann,  Two-atom Rydberg blockade using direct 6S to nP exci-  tation[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' A, 89, 033416, (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  [16] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Li, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Jiang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Qian, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Li, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Liu,  Measurement of  85Rb nP-state transition frequencies  via single-photon Rydberg excitation spectroscopy[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Am.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' B, 36, 1850-1857, (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  [17] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Li, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Jiang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Qian, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Li, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Liu, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  Wang, Optical spectroscopy of nP Rydberg states of 87Rb  atoms with a 297-nm ultraviolet laser[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' A,  99, 042502, (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  [18] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Bai, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Liu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' He, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Wang,  Single-photon Rydberg excitation and trap-loss spec-  troscopy of cold cesium atoms in a magneto-optical trap  by using of a 319-nm ultraviolet laser system[J], IEEE J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  Sel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Top.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Electr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=', 26, 1600106, (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  [19] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Liu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Wang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Chen, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Wang, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Hou, Optical  detection in magnetic state-selection Cs beam tubes for  transportable Cs beam clocks[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Meas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Technol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=', 30,  075004, (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  [20] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Zhang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Shan, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Mølmer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Active Frequency  Measurement on Superradiant Strontium Clock Transi-  tions[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=', 128, 013604, (2022)  [21] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Huang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Tang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Zhong, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  Xiong, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Zhou, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Wang, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Zhan, Accuracy and  stability evaluation of the 85Rb atom gravimeter WAG-  H5-1 at the 2017 international comparison of absolute  gravimeters[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Metrologia, 56, 045012, (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  [22] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Steck, Cesium D line data, 23 January 1998, http:  //george.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' utexas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' edu/ dsteck/ alkalidata/.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  [23] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Bai, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' He, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Wang, Real-  ization and characterization of single-frequency tunable  637.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='2nm high-power laser[J], Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=', 370, 150-  155, (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  [24] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Bai, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Y, Wang, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' He, Realization  of a watt-level 319-nm single-frequency CW ultraviolet  laser and its application in single-photon Rydberg exci-  tation of cesium atoms[J], Chinese Optics, 12, 701-718,  (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' (in Chinese)  [25] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Bai, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' He, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Wang, Develop-  ment and characterization of a 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='2 W narrow-linewidth  318.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='6 nm ultraviolet laser[J], J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Am.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' B, 33,  2020-2025, (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  [26] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Bai, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' He, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Wang, Electronic  sideband locking of a broadly tunable 318.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='6 nm ultravio-  let laser to an ultra-stable optical cavity[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=', 19,  045501, (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  [27] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Boetes, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Skannrup, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Naber, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  Kokkelmans, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Spreeuw, Trapping of Rydberg  atoms in tight magnetic microtraps[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' A, 97,  013430, (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  [28] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Cao, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Yang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Zhang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Jing, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  Li, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Zhang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Xiao, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Jia, Dephasing  effect of Rydberg states on trap loss spectroscopy of cold  atoms[J], J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Am.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' B, 39, 2032-2036, (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content='  [29] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Menon, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Agarwal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Gain components in the  Autler-Townes doublet from quantum interferences in de-  cay channels[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
+page_content=' A, 61, 013807, (1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE4T4oBgHgl3EQfIwx_/content/2301.04915v1.pdf'}
diff --git a/KdFAT4oBgHgl3EQfvx7k/content/tmp_files/2301.08678v1.pdf.txt b/KdFAT4oBgHgl3EQfvx7k/content/tmp_files/2301.08678v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..276cec97882b4e2161046a954fed2d2b53e19ac0
--- /dev/null
+++ b/KdFAT4oBgHgl3EQfvx7k/content/tmp_files/2301.08678v1.pdf.txt
@@ -0,0 +1,2148 @@
+arXiv:2301.08678v1  [math-ph]  20 Jan 2023
+Symmetries in non-relativistic quantum
+electrodynamics
+David Hasler1∗and Markus Lange2†
+1. Department of Mathematics, Friedrich Schiller University Jena
+Jena, Germany
+2. German Aerospace Center (DLR), Institute for AI-Safety and Security
+Sankt Augustin & Ulm, Germany
+January 23, 2023
+Abstract
+We define symmetries in non-relativistic quantum electrodynamics, which have
+the physical interpretation of rotation, parity and time reversal symmetry. We collect
+transformation properties related to these symmetries in Fock space representation
+as well as in the Schr¨odinger representation. As an application, we generalize and
+improve theorems about Kramer’s degeneracy in non-relativistic quantum electrody-
+namics.
+1
+Introduction
+Symmetries are often used to analyze various properties of physical systems. In particular
+in quantum mechanics symmetries are used to determine spectral properties of the Hamil-
+tonian. In this paper we study symmetries of non-relativistic quantum electrodynamics
+(qed), which have the physical interpretation of rotation, parity and time reversal symme-
+try. We give explicit formulas for these symmetries both in Fock space representation as
+well as in the so called Schr¨odinger representation and apply these symmetries to prove
+multiplicities of eigenvalues.
+The transformation properties described in the present paper are of general interest in
+non-relativistic qed. In particular, in the Fock representation these symmetries are helpful
+for operator theoretic renormalization analysis of non-relativistic qed. On the one hand,
+∗E-mail: david.hasler@uni-jena.de
+†E-mail: markus.lange@dlr.de
+1
+
+symmetries can be used to control marginal terms [12,13,14,25]. On the other hand sym-
+metries allow the treatment of degenerate eigenvalues in the frame work of renormalization,
+provided the symmetries act irreducibly on the eigenspace [15]. In fact, the latter is the
+main interest, which we had in mind, for collecting the transformation properties of the
+aforementioned symmetries.
+In physics literature continuous symmetries are often described by means of their in-
+finitesimal generator. That is, as a representation of the Lie-algebra. For non-relativistic
+qed the generators of the Lie-algebra of SU(2) are readily available in textbooks about
+non-relativistic aspects of quantum electrodynamics [4, 27]. In this paper we express the
+SU(2)-symmetry directly as a representation of the Lie-group.
+As already mentioned, symmetries are helpful in the spectral analysis of Hamiltonian
+operators of quantum mechanics. For example the classical Kramers degeneracy theorem
+states, that the eigenvalues of a time-reversal symmetric Hamiltonian describing an odd
+number of spin 1/2-particles have even multiplicity. Using a theorem of this type it was
+shown in [20, 21] that Hamiltonians of non-relativistic qed, which describe odd number
+of spin 1/2-particles have a doubly degenerate ground state, provided the external poten-
+tial is symmetric with respect to parity. In this paper we improve that result and show
+that parity symmetry is not necessary. This is of physical relevance, since potentials de-
+scribing molecules with static nuclei, are not necessarily symmetric with respect to parity.
+Furthermore, we include external magnetic fields in the mathematical model. Finally, we
+consider translation invariant systems and generalize degeneracy results for a single spin
+1/2-particle [16,17] to atoms and molecules.
+Let us give a short outline of the paper. In the next section we review the notion of
+a symmetry in quantum mechanics and state an abstract version of Kramers degeneracy
+theorem. In Section 3 we introduce non-relativistic qed. In Section 4 we define rotation,
+parity, and time-reversal symmetry. Moreover we collect various transformation properties.
+In Section 5 we study symmetry properties of Hamiltonians of non-relativistic qed. In par-
+ticular we show the aforementioned degeneracy theorems. In Section 6 we study symmetry
+properties of fibers of translationally invariant Hamiltonians of non-relativistic qed. In Sec-
+tion 7 we define rotation, parity, and time-reversal symmetry in the so called Schr¨odinger
+representation.
+We show that the definitions in Schr¨odinger representation agree with
+the definitions in Fock space representation. To show this, we use the canonical unitary
+transformation mapping the Fock space representation to the Schr¨odinger representation.
+2
+Symmetries in Quantum Mechanical Systems
+In this section we collect some well-known definitions and properties.
+Definition 2.1. Let V be a complex vector space. A mapping A : V → V is called anti-
+linear (or conjugate linear) if
+(i) A(x + y) = Ax + Ay for all x, y ∈ V .
+2
+
+(ii) A(αx) = αAx, for all x ∈ V and α ∈ C.
+If H is a complex Hilbert space and T : H → H anti-linear, then the adjoint T ∗ : H → H
+is defined by
+⟨T ∗x, y⟩ = ⟨Ty, x⟩
+,
+∀x, y ∈ H.
+If H is a complex Hilbert space and S : H → H anti-linear, then S is called anti-unitary
+if it is surjective and satisfies
+⟨Sx, Sy⟩ = ⟨y, x⟩
+,
+∀x, y ∈ H.
+The assertions of the following Lemma are straightforward to verify.
+Lemma 2.2. The following holds.
+(a) Let Ci be anti-linear (anti-unitary) transformations on complex vector spaces Vi (Hilbert
+spaces), i = 1, 2. Then C1 ⊗ C2 : V1 ⊗ V2 → V1 ⊗ V2 is also anti-linear (anti-unitary).
+(b) If T : H → H is an anti-linear mapping on a Hilbert space H, then also T ∗ is
+anti-linear.
+(c) If S is anti-unitary, then S is bijective and S∗S = 1 and SS∗ = 1.
+Definition 2.3. Let S be a unitary or anti-unitary operator. Let H be a densely defined
+operator in H. We call S a symmetry of H, if
+SH = HS
+when S is unitary, and
+SH = H∗S
+when S is anti-unitary.
+The following theorem, whose formulation is from [20], can be viewed as an abstract
+version of Kramer’s degeneracy theorem, [18,29].
+Theorem 2.4 (Abstract Kramers Degeneracy). Let θ be a an anti-unitary symmetry of
+a self-adjoint operator H and θ2 = −1.
+Then each eigenvalue of H is at least doubly
+degenerate. Any eigenvalue of H with finite multiplicity has even multiplicity.
+The proof follows from the following lemma.
+Lemma 2.5. Let J be an anti-unitary operator on a complex Hilbert space V with J2 = −1.
+Then the following holds.
+(a) For any nonzero v ∈ V , also Jv is nonzero and v ⊥ Jv.
+(b) The Hilbert space V cannot have finite odd dimension.
+3
+
+Proof. (a) Since J(Jv) = J2v = −v, the vector Jv is nonzero. Since J is anti-unitary
+⟨v, Jv⟩ = ⟨JJv, Jv⟩ = −⟨v, Jv⟩.
+So ⟨v, Jv⟩ = 0.
+(b) We show by induction that V cannot have dimension 2n − 1 for n ∈ N. Clearly, the
+induction hypothesis holds true for n = 1 by (a). Suppose the induction hypothesis holds
+for n, and suppose V has dimension 2n + 1. Pick a nonzero v ∈ V . Then Jv ∈ V and
+Jv ⊥ v by (a). Thus W := {v, Jv}⊥ is a complex vector space, which has dimension 2n−1.
+Since J2 = −1, it follows that J leaves the complex linear span linC{v, Jv} invariant. Since
+J is anti-unitary, it leaves also W invariant. But the complex vector space W together
+with J|W contradict the induction hypothesis.
+Proof of Theorem 2.4. Let E be an eigenvalue of H. Since H is self-adjoint E is real. So θ
+leaves the space V = ker(H − E) invariant, since (H − E)θψ = θ(H − E)ψ. Thus the first
+and second statement follow from (b) of Lemma 2.5 with J = θ.
+3
+Non-relativistic qed
+For a complex Hilbert space H we denote the n-fold tensor product by
+H⊗n :=
+n
+�
+j=1
+H
+and we set H⊗0 := C. Let S{1,...,n} be the permutation group of the set {1, ..., n}. For each
+σ ∈ S{1,...,n} we define an operator U(σ) on H⊗n by
+U(σ)(ϕ1 ⊗ ϕ2 ⊗ · · · ⊗ ϕn) = ϕσ(1) ⊗ ϕσ(2) ⊗ · · · ⊗ ϕσ(n)
+(3.1)
+for any ϕj ∈ H, j = 1, ..., n, and extending it linearly. This yields a bounded operator (of
+norm one) on H⊗n so we can define Sn =
+1
+n!
+�
+σ∈S{1,...,n} U(σ). We define the symmetric
+n-fold tensor product of H by
+H⊗sn := Sn
+�
+H⊗n�
+.
+Let Ds denote the representation space of SU(2) with dimension 2s + 1. In this paper
+we shall only consider the case s = 0, describing spinless particles, and the case s = 1
+2,
+describing particles with spin 1/2.
+The model consists of N particles with spins sj ∈ {0, 1/2}, masses mj > 0, charges
+qj ∈ R, values of the spin magnetic moments µj ∈ R, j = 1, ..., N. By xj ∈ R3 we shall
+denote the position of the j-the particle. The Hilbert space describing the non-relativistic
+quantum mechanical matter is
+Hmat =
+N
+�
+j=1
+L2(R3; Dsj).
+4
+
+We note that the description of physical systems usually requires the restriction to a sub-
+space determined by the particle statistics of identical particles. This will be considered
+below.
+If s = 0, let ˆsl = 0 for l = 1, 2, 3, and if s = 1/2, let ˆsl = 1
+2σl for l = 1, 2, 3, where σl
+denotes the l-th Pauli-matrix.
+Remark 3.1. Note that ˆs1, ˆs2 and ˆs3 are representations of the generators of su(2) in the
+representation Ds = C2s+1, s ∈ {0, 1/2}. They are linear maps in Ds satisfying
+[ˆsj, ˆsk] =
+3
+�
+l=1
+iǫj,k,lˆsl,
+ˆs∗
+l = ˆsl, l = 1, 2, 3,
+ˆs1 = ˆs1,
+ˆs2 = −ˆs2,
+ˆs3 = ˆs3,
+(3.2)
+where ǫj,k,l denotes the totally antisymmetric tensor in three dimensions.
+For j = 1, ..., N and l = 1, 2, 3 we define
+(�Sj)l =
+� j−1
+�
+k=1
+1IDsk
+�
+⊗ ˆsl ⊗
+�
+N
+�
+k=j+1
+1IDsk
+�
+.
+For a Hilbert space h define the symmetric Fock space over h by
+Fs(h) :=
+∞
+�
+n=0
+h⊗sn.
+Thus we can identify ψ ∈ Fs(h) with a sequence of functions ψ = (ψ(0), ψ(1), ψ(2), ....) such
+that ψ(n) ∈ h⊗sn. We introduce the set F0(h) := {ψ ∈ Fs(h) : ∃N, ∀n ≥ N, ψ(n) = 0} of
+finite particle vectors. For f ∈ h let a∗(f) denote the usual creation operator, which is a
+densely defined closed linear operator which satisfies for η ∈ h⊗sn
+a∗(f)η =
+√
+n + 1Sn+1(f ⊗ η).
+(3.3)
+Let a(f) denote the adjoint of the creation operator. If T be a symmetry in h, then Γ(T)
+denotes the unique operator on F(h) such that on h⊗sn
+Γ(T)|h⊗sn =
+n
+�
+j=1
+T.
+It is straight forward to see that also Γ(T) is a symmetry.
+Let A be any self-adjoint
+operator on H with domain of essential self-adjointness D. Let DA = {ψ ∈ F0(h) : ψ(n) ∈
+⊗n
+k=1D for each n} and define dΓ(A) on DA ∩ h⊗sn as
+A ⊗ 1 ⊗ · · · ⊗ 1 + 1 ⊗ A ⊗ · · · ⊗ 1 + · · · + 1 ⊗ · · · ⊗ 1 ⊗ A.
+5
+
+In [24, Section VIII.10] it is shown that dΓ(A) is essentially self-adjoint on DA, and we
+shall denote this self-adjoint extension again by dΓ(A). It follows from the definitions that
+for a symmetry T on h and f ∈ h
+Γ(T)a#(f)Γ(T)∗ = a#(Tf),
+(3.4)
+Γ(T)dΓ(A)Γ(T)∗ = dΓ(TAT ∗),
+(3.5)
+where a# stands for a or a∗. Let us now define operators acting on the composite Hilbert
+space
+H ⊗ Fs(h),
+where H denotes a Hilbert space, which is used to describe the matter. For a bounded
+linear operator G ∈ L(H, H ⊗ h) we define for ϕ ∈ H and η ∈ h⊗sn
+a∗(G)(ϕ ⊗ η) =
+√
+n + 1(1 ⊗ Sn+1)((Gϕ) ⊗ η).
+(3.6)
+This extends by linearity to a closable operator in H ⊗ Fs(h), which we shall again denote
+by a∗(G). We define a(G) = [a∗(G)]∗.
+In non-relativistic qed one consider the Fock space over g := L2(R3 × Z2). In that case
+we can identify ψ ∈ Fs(g) with a sequence of functions ψ = (ψ(0), ψ(1), ψ(2), . . .) such that
+ψ(n) ∈ L2
+s((R3×Z2)n), where the subscript s stands for wave functions which are symmetric
+with respect to interchange of components of the n-fold Cartesian product. Let Mf denote
+the operator of multiplication by the function f. We define
+Hf = dΓ(Mω),
+where the so-called dispersion relation ω : R3 → [0, ∞) is defined such that ω(k) = ω(k′)
+whenever |k′| = |k|. Moreover define
+Pf = dΓ(Mπj),
+where πj : R3 → R with πj(k) = kj. Next we introduce creation and annihilation operators
+in terms of operator valued distributions. We define
+DS := {ψ ∈ F0(g) : ψ(n) ∈ S((R3 × Z2)n)}.
+where S((R3 × Z2)n) denotes the space of smooth rapidly decaying functions. For each
+(k, λ) ∈ R3 × Z2 we define an operator a(k, λ) on Fs(g) with domain DS by
+(a(k, λ)ψ)n(k1, λ1, ..., kn, λn) =
+√
+n + 1ψn+1(k, λ, k1, λ1, ..., kn, λn).
+We define a∗(k, λ) in the sense of quadratic forms on DS × DS by
+⟨ψ1, a∗(k, λ)ψ2⟩ = ⟨a(k, λ)ψ1, ψ2⟩.
+6
+
+Then it is straight forward to see that
+a∗(f) =
+�
+λ=1,2
+�
+R3 f(k, λ)a∗(k, λ)dk,
+a(f) =
+�
+λ=1,2
+�
+R3 f(k, λ)a(k, λ)dk,
+where the equalities are understood in the sense of quadratic forms and the integrals are
+understood as weak integrals. Let us now relate the definition given in (3.6) to integrals of
+operator valued distributions. To this end we use the natural embedding
+I : L2(R3 × Z2; L(Hmat)) → L(Hmat; L2(R3 × Z2; Hmat)) ∼= L(Hmat; Hmat ⊗ g)
+g �→ (ϕ �→ [(k, λ) �→ g(k, λ)ϕ]) ,
+which is a bounded injection, cf. [24, Theorem II.10]. Then for g ∈ L2(R3 × Z2; L(Hmat))
+it is straight forward to show that
+a∗(I(g)) =
+�
+λ=1,2
+�
+R3 g(k) ⊗ a∗(k, λ)dk,
+a(I(g)) =
+�
+λ=1,2
+�
+R3 g(k)∗ ⊗ a(k, λ)dk
+(3.7)
+in the sense of quadratic forms on Hmat ⊗DS, where the integral is a weak integral. Hence-
+forth we shall drop the tensor sign in (3.7) if it is clear on which factor the operator
+acts. The definition of the vector potential involves the so called polarization vectors. For
+λ = 1, 2 we choose a measurable function
+ε(·, λ) : S2 → R3
+(3.8)
+on the 3-dimensional sphere S2 with the following properties. For each k ∈ S2 the vectors
+(ε(k, 1), ε(k, 2), k) form an orthonormal basis of R3. We extend ε(·, λ) to R3\{0} by setting
+ε(k, λ) := ε(k/|k|, λ) for all nonzero k. We assume that we are given a measurable coupling
+function κ : R3 → C. We note that the Fourier transform of κ is real, if and only if
+κ(k) = κ(−k).
+(3.9)
+We define the coupling functions for l = 1, 2, 3 and x ∈ R3
+g(ε)
+x,l(k, λ) = εl(k, λ)
+�
+2ω(k)
+κ(k)e−ik·x.
+We can now define the field operators. If ω−1/2κ ∈ L2(R3), we define the magnetic vector
+potential
+Al(x) :=a(g(ε)
+x,l) + a∗(g(ε)
+x,l)
+=
+�
+λ=1,2
+�
+R3
+εl(k, λ)
+�
+2ω(k)
+�
+κ(k)eik·xa(k, λ) + κ(k)e−ik·xa∗(k, λ)
+�
+dk,
+l = 1, 2, 3,
+7
+
+where in the second line we made use of (3.7).
+If | · |ω−1/2κ ∈ L2(R3), we define the
+quantized magnetic field
+Bl(x) :=[∇ × A(x)]l
+=
+�
+λ=1,2
+�
+R3
+i[k × ε(k, λ)]l
+�
+2ω(k)
+�
+κ(k)eik·xa(k, λ) − κ(k)e−ik·xa∗(k, λ)
+�
+dk,
+l = 1, 2, 3.
+If ω1/2κ ∈ L2(R3), we define the quantized electric field
+E⊥
+l (x) :=a(−iωg(ε)
+x,j) + a∗(−iωg(ε)
+x,j)
+=
+�
+λ=1,2
+�
+R3 iεl(k, λ)
+�
+ω(k)
+2
+�
+κ(k)eik·xa(k, λ) − κ(k)e−ik·xa∗(k, λ)
+�
+dk,
+l = 1, 2, 3.
+The Hamiltonian acting in the Hilbert space
+Hmat ⊗ Fs(g)
+is given by
+H =
+N
+�
+j=1
+�
+(pj ⊗ 1 + qj(A(ˆxj) + Aext(ˆxj)))2 + µj �Sj · (B(ˆxj) + Bext(ˆxj))
+�
++ 1 ⊗ Hf + V (ˆx1, ..., ˆxN) ⊗ 1,
+(3.10)
+where ˆxj denotes the operator of multiplication with xj, the coordinates of the j-th particle,
+and pj = −i∇xj. We assume that V : R3N → R is a function and that Bext : R3 → R3 is a
+function. Furthermore, we defined
+Aext(x) := −
+� (x − y) × Bext(y)
+4π|x − y|3
+dy,
+(3.11)
+cf. Remark 3.2.
+Remark 3.2. Provided Bext is sufficiently regular and has sufficient decay, we can write
+Aext(x) := −
+� (x − y) × Bext(y)
+4π|x − y|3
+dy = ∇x ×
+�
+Bext(y)
+4π|x − y|dy =
+� ∇y × Bext(y)
+4π|x − y|
+dy, (3.12)
+by calculating the derivative and using integration by parts, respectively. In particular, if
+∇ · Bext = 0, it follows that ∇ × Aext = Bext.
+Physically, V is called the external potential, Bext the external magnetic field, Aext the
+external magnetic vector potential. We assume that Bext is such that Aext in (3.11) is well
+defined for almost all x ∈ R3. Moreover, we assume that κ and ω are such that the fields
+occurring in the Hamiltonian exist. Furthermore, we assume that κ, ω, V , and Bext are
+such that the Hamiltonian is essentially self-adjoint on
+��N
+j=1 C∞
+c (R3; Dsj)
+�
+⊗ F0(g), for
+details we refer the reader to [23, Theorem X.35, Theorem X.34] and [11].
+8
+
+4
+Symmetries
+In this subsection we define symmetries associated to rotations, space inversion and time
+inversion. To define these symmetries on Fock space it is convenient to identity h with the
+space of so called divergence free vector fields. In this section we shall denote by F the
+Fourier transform and by F −1 its inverse, i.e. for f ∈ L1(R3)
+(Ff)(k) = (2π)−3/2
+�
+R3 e−ik·xf(x)dx,
+(F −1f)(x) = (2π)−3/2
+�
+R3 eik·xf(k)dk,
+where both transformations are canonically extended to L2(R3) by Plancherel’s theorem.
+4.1
+Space of divergent free vector fields
+We introduce the space of divergence free vector fields
+v := {v ∈ L2(R3; C3) :
+3
+�
+j=1
+kj�vj(k) = 0 , a.e. k ∈ R3}.
+Given a specific measurable choice for the polarization vectors (3.8) we obtain a canonical
+identification with the one photon Hilbert space g = L2(R3 × Z2). This is the content of
+the following lemma.
+Lemma 4.1. For the polarization vector ε : S2 × Z2 → R3, as in (3.8), the map
+τε : g → v,
+h �→
+�
+F −1 �
+λ=1,2
+εj(·, λ)h(·, λ)
+�
+j=1,2,3
+,
+is unitary and its inverse acting on v ∈ v is determined by (τ −1
+ε v)(k, λ) = ε(k, λ) · (Fv)(k)
+for almost all (k, λ) ∈ R3 × {1, 2}.
+For the proof we first note the following. For k ∈ R3 \ {0} define
+P(k)a,b := δab − kakb
+|k|2 ,
+a, b = 1, 2, 3,
+k ̸= 0
+(4.1)
+From the definition it follows that P(k)a,b = P(k)b,a, and that P(k) is equal to the projection
+operator in C3 onto the subspace in C3, which is perpendicular to k.
+Thus from the
+definition of the polarization vectors, (3.8), we infer that for k ∈ R3 \ {0}
+P(k)a,b =
+�
+λ=1,2
+εa(k, λ)εb(k, λ).
+(4.2)
+9
+
+Proof of Lemma 4.1. The lemma follows from a straight forward calculation using the
+properties of the polarization vectors.
+Let h ∈ g.
+Clearly, τε is well defined, since
+k · F(τε(h))(k) = k · �
+λ=1,2 ε(k, λ)h(k, λ) = 0. The map is an isometry, since
+∥τεh∥2 =
+�
+R3
+3
+�
+j=1
+�
+λ,λ′=1,2
+εj(k, λ)h(k, λ)εj(k, λ′)h(k, λ′)d3k
+=
+�
+R3
+�
+λ,λ′=1,2
+δλ,λ′h(k, λ)h(k, λ′)d3k = ∥h∥2.
+Furthermore for v ∈ v let (βǫv)(k, λ) = ε(k, λ) · (Fv)(k). Then
+F(τε(βεv)j)(k) =
+�
+λ=1,2
+εj(k, λ)(βεv)(k, λ)
+=
+�
+λ=1,2
+εj(k, λ)
+3
+�
+l=1
+εl(k, λ) · (Fvl)(k)
+= Fvj(k),
+where we used that (4.2) and that v is divergence free. This shows the surjectivity of τε
+and that its inverse is given by βε.
+Define for x ∈ R3 and a = 1, 2, 3 the function vx,a : R3 → C3 by
+[vx,b(y)]a :=
+1
+(2π)3/2
+�
+R3 e−ik·(x−y)
+κ(k)
+�
+2ω(k)
+P(k)a,b dk,
+y ∈ R3.
+(4.3)
+The properties collected in the following lemma are straight forward to verify using the
+definitions.
+Lemma 4.2. We have the following properties for x ∈ R3 and b = 1, 2, 3
+(a) vx,b ∈ v,
+(b) vx,b = τεg(ε)
+x,b,
+τ −1
+ε vx,b = g(ε)
+x,b.
+The next lemma will be needed to determine transformation properties of the field
+energy and field momentum with respect to rotations, parity transformations, and time
+reversal symmetry.
+Lemma 4.3. Let f : R3 → C be a measurable function.
+Then we have the following
+properties.
+(a) τεMfτ −1
+ε
+= F −1MfF.
+(b) For ϕ ∈ L2(R3) and S ∈ O(3) we define the transformation TSϕ = ϕ ◦ S−1. Then
+TSF = FTS,
+TSF −1 = F −1TS.
+(4.4)
+10
+
+(c) Let TS be defined as in (b). Then T −1
+S
+= TS−1 and
+TSMfT −1
+S
+= Mf◦S−1.
+(4.5)
+Proof. Part (a) follows from
+(τεMfτ −1
+ε v)j = F −1 �
+λ=1,2
+εj(·, λ)Mf(τ −1
+ε v)(·, λ)
+= F −1 �
+λ=1,2
+εj(·, λ)f(·)ε(·, λ) · (Fv)(·)
+= F −1(MfFvj)
+(4.6)
+(b) If ϕ ∈ S(R3), we find by the transformation formula for integrals for arbitrary S ∈ O(3)
+(TSFϕ)(k) = (2π)−3/2
+�
+R3 e−i(S−1k)·xϕ(x)dx = (2π)−3/2
+�
+R3 e−ik·xϕ(S−1x)dx = (FTSϕ)(k).
+(4.7)
+So (b) follows by density and continuity. Part (c) is straight forward to verify.
+The following lemma will be needed to determine transformation properties of the
+interaction with respect to rotations and parity transformations.
+Lemma 4.4. Let S ∈ O(3). Then the following holds.
+(a) For all k ∈ R3 we have P(Sk) = SP(k)ST.
+(b) For all x ∈ R3 and b = 1, 2, 3
+3
+�
+c′=1
+Sc,c′
+�
+R3 e−ik·(x−S−1y)
+κ(k)
+�
+2ω(k)
+Pb,c′(k)dk
+(4.8)
+=
+3
+�
+b′=1
+Sb′,b
+�
+R3 e−ik·(Sx−y)κ(S−1k)
+�
+2ω(k)
+Pb′,c(k)dk.
+(4.9)
+(c) lf κ(S·) = κ(·), then for all x ∈ R3 and b = 1, 2, 3
+Svx,b(S−1y) =
+3
+�
+b′=1
+Sb′,bvSx,b′(y).
+(4.10)
+Proof. Part (a) is straight forward to verify using the definition (4.1). For x ∈ C3 and
+k ∈ R3 \ {0} we find for �k = k/|k|
+P(Sk)x = x − S�k(S�k · x) = SSTx − S�k(�k · STx) = SP(k)STx.
+11
+
+(b) follows from a change of variables and (a)
+(4.8) =
+3
+�
+c′=1
+�
+e−i(Sk)·(Sx−y)
+κ(k)
+�
+2ω(k)
+Pb,c′(k)Sc,c′dk
+=
+3
+�
+c′=1
+�
+e−ik·(Sx−y)κ(S−1k)
+�
+2ω(k)
+Pb,c′(S−1k)Sc,c′dk = (4.9).
+(c) Now (4.10) follows from (4.9) and the definition (4.3).
+4.2
+Rotation Invariance
+We introduce the so called canonical double covering homomorphism
+π : SU(2) → SO(3),
+U �→ π(U),
+where π(U) is the unique element of SO(3) such that
+UσmU∗ =
+3
+�
+l=1
+π(U)l,mσl,
+m = 1, 2, 3,
+with σ1, σ2, σ3 denoting the Pauli matrices. On the one electron Hilbert space L2(R3; Ds)
+we define
+(Up,s(U)ψ)(x) = Ds(U)ψ(π(U)−1x),
+where Ds denotes the representation of SU(2) with spin s. Similarly we define for v ∈ v
+the transformation for R ∈ SO(3)
+(Uv(R)v)(x) = Rv(R−1x).
+Moreover, we define
+Ug(R) = τ −1
+ǫ Uv(R)τǫ,
+which depends on the choice of the polarization vectors. For R ∈ SO(3) we define the
+unitary mapping
+Uf(R) = Γ(Ug(R)),
+and for U ∈ SU(2) we define the unitary mappings
+Umat(U) =
+N
+�
+j=1
+Up,sj(U)
+U(U) = Umat(U) ⊗ Uf(π(U))
+on the Hilbert spaces Hmat and Hmat ⊗Fs(g), respectively. This defines a representation of
+SU(2) on these Hilbert spaces. The next proposition collects elementary properties, which
+follow directly from the definitions.
+12
+
+Proposition 4.5. The map Uf is a unitary representation of R ∈ SO(3), and the maps
+Umat, and U are unitary representations of SU(2).
+Remark 4.6. By abuse of notation we denote the unitary representation Uf ◦ π on SU(2)
+also by Uf.
+Lemma 4.7. Let R ∈ SO(3) and κ(R·) = κ(·). Then
+(a)
+Uf(R)A(x)U∗
+f (R) = R−1A(Rx),
+(b)
+Uf(R)B(x)U∗
+f (R) = R−1B(Rx),
+(c)
+Uf(R)E⊥(x)U∗
+f (R) = R−1E⊥(Rx).
+Proof. We observe that for R ∈ SO(3) we find
+(Uv(R)vx,b)(y) = Rvx,b(R−1y) =
+3
+�
+b′=1
+Rb′,bvRx,b′(y),
+(4.11)
+where we used Lemma 4.4 (c). Using Eqs. (3.4) and (4.11) as well as Lemma 4.2 we obtain
+Uf(R)a#(g(ε)
+x,b)U∗
+f (R) = a#(Ug(R)g(ε)
+x,b) = a#(τ −1
+ε Uv(R)τεg(ε)
+x,b)
+= a#(τ −1
+ε Uv(R)vx,b) =
+3
+�
+b′=1
+Rb′,ba#(τ −1
+ε vRx,b′)
+=
+3
+�
+b′=1
+Rb′,ba#(g(ε)
+Rx,b′)
+This implies
+Uf(R)Ab(x)U∗
+f (R) =
+3
+�
+b′=1
+Rb′,bAb′(Rx).
+Thus (a) follows. Now (b) follows from (a) and by calculating the rotation. (c) Follows
+similarly as (a) observing that ω is invariant under rotations.
+Proposition 4.8. Let U ∈ SU(2) and R = π(U). Then the following holds
+(a)
+U(U)ˆxjU(U)∗ = R−1ˆxj,
+(b)
+U(U)pjU(U)∗ = R−1pj,
+(c)
+U(U)�SjU(U)∗ = R−1 �Sj,
+(d)
+U(U)A(ˆxj)U(U)∗ = R−1A(ˆxj),
+if κ(R·) = κ(·),
+(e)
+U(U)B(ˆxj)U(U)∗ = R−1B(ˆxj),
+if κ(R·) = κ(·),
+(f)
+U(U)E⊥(ˆxj)U(U)∗ = R−1E⊥(ˆxj),
+if κ(R·) = κ(·),
+(g)
+U(U)HfU(U)∗ = Hf,
+(h)
+U(U)PfU(U)∗ = R−1Pf.
+13
+
+Proof. Parts (a), (b), and (c) are straight forward to verify. Parts (d)-(f) follow from (a)
+and Lemma 4.7. Next we show (g) and (h). Using Lemma 4.3 and the identity (3.5) we
+find for any measurable f : R3 → R and U ∈ SU(2) with R = π(U)
+U(U)dΓ(Mf)U(U)∗ = dΓ(τ −1
+ε Uv(π(U))τεMfτ −1
+ε U∗
+v (π(U))τε)
+= dΓ(τ −1
+ε Uv(R)F −1MfFU∗
+v (R)τε)
+= dΓ(τ −1
+ε F −1Mf◦R−1Fτε)
+= dΓ(Mf◦R−1)
+Now choosing f = ω or f : k �→ kj Parts (g) and (h) follow.
+In the following proposition we give a formula for the action of the rotation transfor-
+mation in g.
+Proposition 4.9. For R ∈ SO(3) define
+DU
+λ,λ′(R; k) := (R−1ε(k, λ)) · ε(R−1k, λ′).
+Then for R ∈ SO(3)
+DU
+λ,λ′(R−1; k) = DU
+λ′,λ(R; Rk)
+(4.12)
+and the following holds.
+(a) For any h ∈ g
+(Ug(R)h)(k, λ) =
+�
+λ′=1,2
+DU
+λ,λ′(R; k)h(R−1k, λ′).
+(4.13)
+(b) In the sense of operator valued distributions for all (k, λ) ∈ R3 × Z2
+Uf(R)a#(k, λ)Uf(R)∗ =
+�
+λ′=1,2
+DU
+λ,λ′(R−1; k)a#(Rk, λ′)
+Proof. Equation (4.12) follows from a straight forward calculation using that the elements
+of SO(3) preserve the inner product. Now we prove (a). Using the property (4.4) of the
+Fourier transform, we find
+(Ug(R)h)(k, λ) = ε(k, λ) · F
+�
+F −1 �
+λ′=1,2
+Rε(·, λ′)h(·, λ′)
+�
+(R−1k)
+=
+�
+λ′=1,2
+ε(k, λ) · Rε(R−1k, λ′)h(R−1k, λ′).
+14
+
+(b) We have by linearity and (a)
+�
+λ=1,2
+�
+R3 h(k, λ)Uf(R)a∗(k, λ)U∗
+f (R)dk = Uf(R)a∗(h)U∗
+f (R) = a∗(Ug(R)h)
+=
+�
+λ=1,2
+�
+R3(Ug(R)h)(k, λ)a∗(k, λ)dk
+=
+�
+λ,λ′=1,2
+�
+R3 DU
+λ,λ′(R; k)h(R−1k, λ′)a∗(k, λ)dk
+=
+�
+λ,λ′=1,2
+�
+R3 DU
+λ′,λ(R; Rk)h(k, λ)a∗(Rk, λ′)dk.
+Since h ∈ g is arbitrary the claim follows for a∗(k, λ) in view of (4.12). Taking adjoints
+the claim then follows also for a(k, λ).
+4.3
+Parity Symmetry
+Parity is the operation x �→ −x. On the particle space we define
+Pp,s : L2(R3; Ds) → L2(R3; Ds),
+ψ �→ (x �→ ψ(−x))
+for s = 0, 1/2. On the photon space we define
+Pv : v → v,
+v �→ (x �→ −v(−x)),
+and
+Pg = τ −1
+ε Pvτε.
+We define
+Pmat =
+N
+�
+j=1
+Pp,sj,
+Pf = Γ(Pg),
+P = Pmat ⊗ Pf.
+Proposition 4.10. The maps Pmat, Pf and P are unitary and commute with the repre-
+sentations Umat, Uf and U, respectively.
+Proof. The unitarity property is straight forward to verify. The commutativity follows from
+the commutativity of Pp with Up and Pv with Uv, which are straight forward to verify.
+Lemma 4.11. Suppose κ(−·) = κ(·). Then
+(a)
+PfA(x)P∗
+f = −A(−x),
+(b)
+PfB(x)P∗
+f = B(−x),
+(c)
+PfE⊥(x)P∗
+f = −E(−x).
+15
+
+Proof. We observe that for S = −1I3×3 we find from (4.10)
+(Pvvx,b)(y) = −vx,b(−y) = −v−x,b(y).
+(4.14)
+Now we find similar as in the proof of Lemma 4.7 using Lemma 4.2 and (4.14)
+Pfa#(g(ε)
+x,b))P∗
+f = a#(Pgg(ε)
+x,b) = a#(τ −1
+ε Pvτεg(ε)
+x,b)
+= a#(τ −1
+ε Pvvx,b) = a#(−τ −1
+ε v−x,b)
+= −a#(g(ε)
+−x,b).
+This implies
+PfAb(x)P∗
+f = −Ab(−x).
+Thus (a) follows. Now (b) follows from (a) and by calculating the rotation. (c) Follows
+similarly as in (a) observing that ω(−·) = ω.
+In view of the following proposition we see that P has the physical interpretation of
+parity inversion.
+Proposition 4.12. P has satisfies the following properties.
+(a)
+PˆxjP = −ˆxj,
+(b)
+PpjP∗ = −pj,
+(c)
+P �SjP∗ = �Sj,
+(d)
+PA(ˆxj)P∗ = −A(ˆxj),
+if κ(−·) = κ(·),
+(e)
+PB(ˆxj)P∗ = B(ˆxj),
+if κ(−·) = κ(·),
+(f)
+PE⊥(ˆxj)P∗ = −E⊥(ˆxj),
+if κ(−·) = κ(·),
+(g)
+PHfP∗ = Hf,
+(h)
+PPfP∗ = −Pf.
+Proof. The proof is analogous to that of Proposition 4.8.
+In the following proposition we give a formula for the action of the parity in g.
+Proposition 4.13. The map Pg has the following properties. Define
+DP
+λ,λ′(k) := −ε(k, λ) · ε(−k, λ′).
+Then DP
+λ,λ′(k) = DP
+λ′,λ(−k).
+(a) For any h ∈ g we have for almost all (k, λ) ∈ R3 × {1, 2}
+(Pgh)(k, λ) =
+�
+λ′=1,2
+DP
+λ,λ′(k)h(−k, λ′).
+16
+
+(b) We have in the sense of operator valued distributions for all (k, λ) ∈ R3 × Z2
+Pfa#(k, λ)P∗
+f =
+�
+λ′=1,2
+DP
+λ,λ′(k)a#(−k, λ′)
+Proof. The first statement follows from the symmetry of the scalar product. (a) Using
+(4.4), we find
+(Pgh)(k, λ) = ε(k, λ) · F
+�
+F −1 �
+λ′=1,2
+(−ε(·, λ′))h(·, λ′)
+�
+(−k)
+=
+�
+λ′=1,2
+(−ε(k, λ)) · ε(−k, λ′)h(−k, λ′).
+(b) We have by linearity and (a)
+�
+λ=1,2
+�
+h(k, λ)Pfa∗(k, λ)P∗
+f dk = Pfa∗(h)P∗
+f = a∗(Pgh)
+=
+�
+λ=1,2
+�
+R3(Pgh)(λ, k)a∗(k, λ)dk
+=
+�
+λ,λ′=1,2
+�
+R3 DP
+λ,λ′(k)a∗(k, λ)h(−k, λ′)dk
+=
+�
+λ,λ′=1,2
+�
+R3 DP
+λ′,λ(−k)a∗(−k, λ′)h(k, λ′)dk
+Since h ∈ g is arbitrary the claim follows for a∗(k, λ). Taking adjoints the claim then
+follows also for a(k, λ).
+4.4
+Time reversal symmetry
+We define time reversal symmetry.
+Let K denote complex conjugation on L2(R3; Ds).
+Define the operators
+Tp,s :=
+� K
+,
+if
+s = 0,
+(Kσ2)
+,
+if
+s = 1/2
+and
+Tmat :=
+N
+�
+j=1
+Tp,sj.
+Let Kv denote complex conjugation in v, and let
+Kg = τ −1
+ε Kvτε
+(4.15)
+17
+
+denote its action on g. Next we define operator of time reversal on the quantum field
+Tf := Γ(−Kg).
+(4.16)
+We define the operator of time reversal in the full Hilbert space by
+T = Tmat ⊗ Tf.
+(4.17)
+Proposition 4.14. The maps Tmat, Tf, and T are anti-unitary operators, which commute
+with the representations Umat, Uf, and U and the operators Pmat, Pf, and P, respectively.
+We have T 2
+f = 1, and
+T 2
+mat = (−1)
+�N
+j=1 2sj,
+T 2 = (−1)
+�N
+j=1 2sj.
+Proof. The anti-unitarity is straight forward to verify on the one particle spaces. On the
+tensor product it then follows by Lemma 2.2. The commutativity can be seen by verifying
+it on the one particle spaces. The last statement follows from
+T 2
+mat =
+N
+�
+j=1
+(Tmat,sj)2
+with (Tmat,0)2 = 1 and (Tmat,1/2)2 = (Kσ2)(Kσ2) = K2σ2(−σ2) = −1,
+Lemma 4.15. Suppose κ(·) = κ(−·). Then the following holds
+(d)
+TfA(x)T ∗
+f = −A(x),
+(e)
+TfB(x)T ∗
+f = −B(x),
+(e)
+TfE⊥(x)T ∗
+f = E⊥(x).
+Proof. It follows directly from the definition, a trivial change of variables, and the assump-
+tion about κ that
+(Kvvx,b)(y) = vx,b(y) .
+(4.18)
+Now we find using Lemma 4.2
+Γ(−Kg)a∗(g(ε)
+x,b)Γ(−Kg)∗ = a∗(−Kgg(ε)
+x,b) = −a∗(τ −1
+ε Kvτεg(ε)
+x,b)
+= −a∗(τ −1
+ε Kvvx,b) = −a∗(τ −1
+ε vx,b)
+= −a∗(g(ε)
+x,b)
+This implies Tfa∗(g(ε)
+x,b)T ∗
+f = −a∗(g(ε)
+x,b) and by taking adjoints Tfa(g(ε)
+x,b)T ∗
+f = −a(g(ε)
+x,b). Hence
+TfAb(x)T ∗
+f = −Ab(x).
+This shows (a). Now (b) follows from (a) and by calculating the rotation. (c) Follows
+similarly as in (a) observing that iω changes sign when complex conjugating.
+18
+
+In view of the following proposition we see that T has the physical interpretation of
+time reversal.
+Proposition 4.16. Suppose κ(·) = κ(−·). Then T is anti-unitary and satisfies the follow-
+ing properties
+(a)
+T ˆxjT ∗ = ˆxj,
+(b)
+T pjT ∗ = −pj,
+(c)
+T �SjT ∗ = −�Sj,
+(d)
+T A(ˆxj)T ∗ = −A(ˆxj),
+if κ(−·) = κ(·),
+(e)
+T B(ˆxj)T ∗ = −B(ˆxj),
+if κ(−·) = κ(·),
+(f)
+T E⊥(ˆxj)T ∗ = E⊥(ˆxj),
+if κ(−·) = κ(·),
+(g)
+T HfT ∗ = Hf,
+(h)
+T PfT ∗ = −Pf.
+Proof. Parts (a), (b), and (c) are straight forward to verify. Parts (d), (e), and (f) follow
+from Lemma 4.15. Using Lemma 4.3 we find for any measurable f : R3 → R
+TfdΓ(Mf)T ∗
+f = dΓ(τ −1
+ε KvτεMfτ −1
+ε K∗
+vτε)
+= dΓ(τ −1
+ε KvF −1MfFK∗
+vτε)
+= dΓ(τ −1
+ε F −1Mf(−·)Fτε)
+= dΓ(Mf(−·)),
+where in the third equality we used that the Fourier transform satisfies the following prop-
+erties Fϕ = Fϕ(−·) and F −1ϕ = F −1ϕ(−·) for ϕ ∈ L2(R3). Now choosing f = ω or
+f : k �→ kj Parts (g) and (h) follow.
+In the following proposition we give a formula for the action of the time reversal sym-
+metry in g.
+Proposition 4.17. For h ∈ g we have for almost all (k, λ) ∈ R3 × {1, 2}
+(Kgh)(k, λ) =
+�
+λ′=1,2
+DT
+λ,λ′(k)h(−k, λ′),
+where DT
+λ,λ′(k) := ε(k, λ)·ε(−k, λ′). Then DT
+λ,λ′(k) = DT
+λ′,λ(−k) and in the sense of operator
+valued distributions for all (k, λ) ∈ R3 × Z2
+Tfa#(k, λ)T ∗
+f = −
+�
+λ′=1,2
+DT
+λ,λ′(k)a#(−k, λ′).
+19
+
+Proof. Using for ϕ ∈ L2(R3) the following property of the Fourier transform F(F −1ϕ)(k) =
+ϕ(−k), we find
+(Kgh)(k, λ) = ǫ(k, λ) · F
+�
+F −1 �
+λ′=1,2
+ε(·, λ′)h(·, λ′)
+�
+(k)
+=
+�
+λ′=1,2
+ε(k, λ) · ε(−k, λ′)h(−k, λ′).
+This shows the first identity. Using this, we find by anti-linearity
+�
+λ=1,2
+�
+h(k, λ)Tfa∗(k, λ)T ∗
+f dk = Tfa∗(h)T ∗
+f = a∗(−Kgh)
+= −
+�
+λ=1,2
+�
+R3(Kgh)(λ, k)a∗(k, λ)dk
+= −
+�
+λ,λ′=1,2
+�
+R3 h(−k, λ′)DT
+λ,λ′(k)a∗(k, λ)dk
+= −
+�
+λ,λ′=1,2
+�
+R3 h(k, λ)DT
+λ′,λ(−k)a∗(−k, λ′)dk.
+Since h ∈ g is arbitrary the second identity follows for a∗(k, λ). Taking adjoints the claim
+then follows also for a(k, λ).
+5
+Hamiltonians with Symmetries
+In this section we consider Hamiltonians of non-relativistic qed, and discuss their symmetry
+properties.
+Theorem 5.1. Suppose U ∈ SU(2), R = π(U), V (x1, ..., xN) = V (Rx1, ..., RxN) for all
+x1, ..., xN ∈ R3, Bext(x) = RBext(R−1x) for all x ∈ R3, and κ(R·) = κ(·). Then
+U(U)HU(U)∗ = H.
+Proof. Using (3.11), properties of the cross product, a change of variables, and the sym-
+metry properties of Bext we find
+RAext(R−1x) = −
+� (x − Ry) × RBext(y)
+4π|x − Ry|3
+dy = Aext(x).
+Thus using Proposition 4.8
+U(U)HU(U)∗
+=
+N
+�
+j=1
+� 1
+2mj
+�
+R−1pj + qj(R−1A(ˆxj) + Aext(R−1ˆxj))
+�2 + µjR−1 �Sj · (R−1B(ˆxj) + Bext(R−1ˆxj))
+�
++ Hf + V (R−1ˆx1, ..., R−1ˆxN)
+= H,
+20
+
+where in the last line we used the assumed properties of Bext and V .
+Theorem 5.2. Suppose V (x1, ..., xN) = V (−x1, ..., −xN) for all x1, ..., xN ∈ R3, Bext(·) =
+Bext(−·), and κ(−·) = κ(·). Then
+PHP∗ = H.
+Proof. Using (3.11), the properties of the cross product, a change of variables, and the
+symmetry properties of Bext we find
+Aext(−x) = −
+� (−(x − y)) × Bext(−y)
+4π|x − y|3
+dy = −Aext(x).
+Thus we find from Proposition 4.12
+PHP∗
+=
+N
+�
+j=1
+� 1
+2mj
+(−pj − qjA(ˆxj) + qjAext(−ˆxj)))2 + µj �Sj · (B(ˆxj) + Bext(−ˆxj))
+�
++ Hf + V (−ˆx1, ..., −ˆxN)
+= H,
+where in the last line we used the assumed properties of Bext and V .
+Theorem 5.3. Suppose Bext = 0 and κ(·) = κ(−·). Then
+T HT ∗ = H.
+Proof. We find from Proposition 4.16
+T HT ∗ =
+N
+�
+j=1
+� 1
+2mj
+(−pj − qjA(ˆxj))2 + µj �Sj · B(ˆxj)
+�
++ Hf + V (ˆx1, ..., ˆxN) = H.
+Theorem 5.4. If V (x1, ..., xN) = V (−x1, ..., −xN) for all x1, ..., xN ∈ R3, Bext(·) =
+−Bext(−·), and κ(·) = κ(−·) = κ(·). Then
+T PH(T P)∗ = H.
+Proof. Using (3.11), the properties of the cross product, a change of variables, and the
+symmetry properties of Bext we find
+Aext(−x) = −
+� (−(x − y)) × Bext(−y)
+4π|x − y|3
+dy = Aext(x).
+21
+
+Thus we find from Propositions 4.12 and 4.16
+T PHP∗ T ∗
+= T
+�
+N
+�
+j=1
+� 1
+2mj
+(−pj − qjA(ˆxj) + qjAext(−ˆxj))2 + µj �Sj · (B(ˆxj) + Bext(−ˆxj))
+�
++ Hf + V (−ˆx1, ..., −ˆxN)
+�
+T ∗
+=
+N
+�
+j=1
+� 1
+2mj
+(pj + qjA(ˆxj) + qjAext(ˆxj)))2 + µj �Sj(B(ˆxj) − Bext(−ˆxj))
+�
++ Hf + V (−ˆx1, ..., −ˆxN)
+= H,
+where we used the assumed properties of Bext and V .
+As an application of the abstract Kramer theorem, we now show the following degen-
+eracy result.
+Theorem 5.5. Suppose �N
+j=1 2sj is odd, and that at least one of the following two assump-
+tions hold.
+(i) Bext = 0 and κ(·) = κ(−·)
+(ii) V (−x1, ..., −xN) = V (x1, ..., xN) and Bext(−x) = −Bext(x), and κ(·) = κ(−·) = κ(·).
+Then, any eigenvalue of H is at least two fold degenerate. If the multiplicity of an eigenvalue
+is finite, it is even.
+Proof. In case (i) the assertion follows from Kramers degeneracy theorem 2.4 for θ =
+T , Proposition 4.14, and Theorem 5.3. In case (ii) the assertion follows from Kramers
+degeneracy theorem 2.4 for θ = T P, Proposition 4.14, and Theorem 5.4.
+Remark 5.6.
+(a) We note that Theorem 5.5 for the case N = 1, s1 = 1/2, and (i) with the additional
+assumption V (−x) = V (x) was shown in [20, 21]. Thus Theorem 5.5 relaxes the
+unnecessary parity-symmetry assumption for the external potential V . In fact, the
+proof given in [20] uses the symmetry PT , while the proof in [21] uses the symmetry
+T in the so called Schr¨odinger representation, cf. Section 7 of this paper.
+(b) Since the classical Kramer theorem uses time inversion symmetry it cannot be applied
+to situations with external magnetic fields. However if one considers the anti-linear
+symmetry PT one can include external magnetic fields, which satisfy a symmetry
+condition. We note that the result (ii) also holds for an ordinary Schr¨odinger oper-
+ator without any quantized electromagnetic field, as the proof also applies to such a
+situation with a straight forward (trivial) modification of the proof.
+22
+
+Next we consider the restriction to symmetric subspaces. To this end we introduce
+notation satisfying the following hypothesis.
+Hypothesis A. The set P = {p1, ...., pL}, L ∈ N ∩ {1, ..., N}, is a partition of {1, ...., N}
+such that on each element p ∈ P of the partition the numbers mj, sj, qj, and µj are equal
+(cf. (3.10)). The function τ maps P to {0, 1}. The potential V is symmetric with respect
+to interchange of particle coordinates of particles which belong to the same element p ∈ P.
+Remark 5.7. The function τ in Hypothesis A is used to specify the statistics of identical
+particles.
+The value 0 will be used to describe bosons while the value 1 will be used
+describe fermions. By physical laws, spin zero particles are bosons while spin 1/2 particles
+are fermions.
+For a finite set S we shall denote by SS the set of all permutations of the set S. For
+a subset S ⊂ {1, ..., N} and σ ∈ SS we denote by σ its extension to {1, ..., N} by setting
+it equal to the identity on {1, ...., N} \ S. Suppose the partition P satisfies Hypothesis A.
+Then for any p ∈ P and σ ∈ Sp it follows that U(σ), defined in (3.1), leaves Hmat invariant,
+and we can define the subspace
+Hmat,P,τ = {ψ ∈ Hmat : ∀p ∈ P, ∀σ ∈ Sp, U(σ)ψ = sgn(σ)τ(p)ψ},
+(5.1)
+where sgn(σ) defines the signum of the permutation σ. Furthermore, it follows from the
+definitions that U(σ) commutes with the symmetries Umat, Pmat, Tmat as well as the Hamil-
+tonian H. In particular, Hmat,P,τ ⊗ Fs(g) is an invariant subspace of H.
+Theorem 5.8. Suppose that the partition P, the function τ and the potential V , satisfy
+Hypothesis A. Suppose �N
+j=1 2sj is odd, and (i) or (ii) of Theorem 5.5 holds. Then, any
+eigenvalue of H|Hmat,P,τ ⊗Fs(g) has even or infinite multiplicity.
+Proof. Follows from the same proof as Theorem 5.5, by observing in addition that T and
+P commute with U(σ) for any σ ∈ Sp and p ∈ P, and thus leave Hmat,P,τ invariant.
+Remark 5.9. We note that Theorem 5.8 for the special case P = {p} with p = {1, ...., N},
+sj = 1/2 for all j ∈ p, and τ(p) = 1, and with the additional assumption that V is given
+by the Coulomb potential of N electrons in the presence of the electric field of a nucleus
+was shown in [20].
+6
+Translationally invariant Hamiltonians
+We write the Hamiltonian (3.10) acting in the Hilbert space Hmat ⊗ Fs(g) in the following
+notation
+H =
+N
+�
+j=1
+Tj + Hf + V (�x1, ..., �xN),
+Tj :=
+1
+2mj
+(pj + qjA(�xj))2 + µj �Sj · B(�xj),
+23
+
+and we assume that there is no external magnetic field. Furthermore, we assume that the
+potential V in the definition of the Hamiltonian (3.10) is translationally invariant, i.e., that
+for all a ∈ R3
+V (x1 + a, ..., xN + a) = V (x1, ..., xN).
+(6.1)
+Using the unitary transformation
+U = exp(ixN · (Pf +
+N−1
+�
+j=1
+pj))
+and a Fourier transform in the variable xN we can write
+H =
+� ⊕
+R3 H(ξ)dξ,
+where
+H(ξ) :=
+1
+2mN
+(ξ −
+N−1
+�
+j=1
+pj − Pf + qNA(0))2 + µN �SN · B(0) +
+N−1
+�
+j=1
+Tj + Hf + V (�x1, ..., �xN−1, 0)
+acts in
+H′
+mat ⊗ DsN ⊗ Fs(g),
+(6.2)
+where
+H′
+mat :=
+N−1
+�
+j=1
+L2(R3; Dsj),
+cf. [10,19]. We define U′
+mat, P′
+mat, and T ′
+mat on H′
+mat as in Section 4. On (6.2) we define the
+symmetries
+U′(U) := U′
+mat(U) ⊗ DsN(U) ⊗ Uf(π(U)),
+U ∈ SU(2)
+P′ := P′
+mat ⊗ 1IDsN ⊗ Pf
+T ′ := T ′
+mat ⊗ T ′
+p,s ⊗ Tf,
+where we defined
+T ′
+p,s :=
+� Ks
+,
+if
+s = 0,
+(Ksσ2)
+,
+if
+s = 1/2
+where Ks denotes complex conjugation on Ds = C2s+1.
+Lemma 6.1. Suppose V is translationally invariant, cf. (6.1).
+(a) Let U ∈ SU(2), R = π(U), V (Rx1, ..., RxN, 0) = V (x1, ..., xN, 0) for all xj ∈ R3, and
+κ(·) = κ(R·). Then for all ξ ∈ R3
+U′(U)H(ξ)U′(U)∗ = H(Rξ).
+24
+
+(b) Let V (x1, ..., xN−1, 0) = V (−x1, ..., −xN−1, 0) for all xj ∈ R3 and κ(·) = κ(−·). Then
+for all ξ ∈ R3
+P′H(ξ)P′∗ = H(−ξ).
+(c) If κ(·) = κ(−·), then for all ξ ∈ R3
+T ′H(ξ)T ′∗ = H(−ξ).
+Proof. The Lemma follows as a consequence of Lemmas 4.7, 4.11, and 4.15 and Proposi-
+tions 4.8, 4.12, and 4.16, respectively, and their trivial adaption to (6.2).
+Theorem 6.2. Suppose V is translationally invariant and �N
+j=1 2sj is odd. If κ(·) = κ(−·)
+each eigenvalue of H(0) has even or infinite multiplicity. If in addition V (x1, ..., xN−1, 0) =
+V (−x1, ..., −xN−1, 0) for all xj ∈ R3 and κ(−·) = κ(·), then for all ξ ∈ R3 each eigenvalue
+of H(ξ) has even or infinite multiplicity.
+Proof. The theorem follows as a consequence of Parts (c) and (b) of Lemma 6.1, The-
+orem 2.4.
+The first statement follows using the anti-linear symmetry T ′.
+The second
+statement follows using the anti-linear symmetry P′T ′ and their commutativity property,
+cf. Proposition 4.14 and its trivial adaption to (6.2).
+Next we consider quantum systems with identical particles. For notational simplicity,
+we shall assume that there is a single particle which is distinguishable from the rest. This is
+satisfied for atoms, ions and many molecules. Otherwise, a further restriction to subspaces
+would be necessary.
+Theorem 6.3. Suppose V is translationally invariant and �N
+j=1 2sj is odd. Suppose that
+the partition P, the function τ and the potential V , satisfy Hypothesis A. Furthermore,
+assume {N} ∈ P and let P′ = P \ {{N}} and τ ′ = τ|P′. If κ(·) = κ(−·) each eigenvalue
+of H(0) when restricted to H′
+mat,P′,τ ′ ⊗ DsN ⊗ Fs(g) has even or infinite multiplicity. If in
+addition V (x1, ..., xN−1, 0) = V (−x1, ..., −xN−1, 0) for all xj ∈ R3 and κ(−·) = κ(·), then
+each eigenvalue of H(ξ) when restricted to H′
+mat,P′,τ ′ ⊗ DsN ⊗ Fs(g) has even or infinite
+multiplicity.
+Proof. Follows from the same proof as Theorem 6.2, by observing in addition that T ′ and
+P′ commute with U(σ) for any σ ∈ Sp and p ∈ P′.
+Remark 6.4. We note that the statement of Theorem 6.2 was proven for the special case
+where N = 1 and V = 0 for small coupling in [16] and for general coupling in [17]. Clearly,
+Theorem 6.3 covers the special case of N −1 electrons with spin 1/2 and a spinless nucleus
+with pairwise Coulomb interactions (P = {{1, ...., N − 1}, {N}}), cf. Remark 5.2 in [20].
+We note that whereas ground states of fiber Hamiltonians describing electrons do not exist
+for nonzero momentum [10], they are shown to exist for atoms and small absolute values
+of the momentum [19].
+25
+
+7
+Schr¨odinger Representation
+In this section we define rotation, parity and time reversal symmetry in the so called
+Schr¨odinger representation of non-relativistic qed.
+To this end, we recall the Schwartz
+space of smooth functions of rapid decrease S(Rd; F), with F = R or F = C, which is the
+set of infinitely differentiable F-valued functions f(x) on Rd for which
+∥f∥α,β = sup
+x∈Rd |xα∂βf(x)| < ∞
+(7.1)
+for all α, β ∈ Nd
+0. Let S = S(R3; R)3 equipped with the product topology. The topological
+dual space S′ can be identified with the set of all T ∈ S′(R3; R)3, with T(f) = T1(f1) +
+T2(f2) + T3(f3).
+On S we define the symmetric positive semi-definite form
+B(v, w) =
+�
+i,j
+�
+1
+|k|ˆvi(k)Pi,j(k) ˆwj(k)d3k,
+(7.2)
+where we recall
+P(k)a,b := δab − kakb
+|k|2 ,
+a, b = 1, 2, 3,
+k ̸= 0.
+(7.3)
+Let
+c(f) = e− 1
+4 B(f,f)
+for f ∈ S.
+By definition a cylinder set in S′ is a set
+{T ∈ S′ : (T(f1), ...., T(fn)) ∈ Ω},
+where f1, ..., fn are n fixed elements in S and Ω is a fixed Borel set in Rn. A cylinder
+set measure on S′ is a measure, µ, on the σ-algebra, generated by the cylinder sets, with
+µ(S′) = 1. By construction, each f ∈ S defines a measurable function ϕ(f) on S′ by
+ϕ(f)(T) = T(f).
+(7.4)
+In particular it follows that for all α, β ∈ R and f, g ∈ S
+ϕ(αf + βg) = αϕ(f) + βϕ(g).
+(7.5)
+We shall use the following theorem, see [5,6,7,8,9].
+Theorem 7.1. There exists a unique cylinder set measure ν on S′ such that for all f ∈ S
+exp(−1
+4B(f, f)) =
+�
+exp(iϕ(f))dν
+(7.6)
+Furthermore, ν has the following properties.
+26
+
+(a) For each f ∈ S the function ϕ(f) is a Gaussian random variable with mean zero and
+variance 1
+2B(f, f).
+(b) For f1, ...fn ∈ S the random variables ϕ(f1), ..., ϕ(fn) are jointly Gaussian random
+variables.
+(c) Let U = {F(ϕ(f1), ..., ϕ(fn)) : F ∈ S(Rn; C), f1, ..., fn ∈ S}. Then U is dense in
+L2(S′, dν).
+(d) If f ∈ S and P �f = 0, then ϕ(f) = 0 almost surely, cf. (7.3). In particular, for
+almost all T = (T1, T2, T3) ∈ S′ we have ∇ · T = 0.
+A proof of Theorem 7.1 will be given in Appendix B. Henceforth, we shall denote by ν
+the unique measure on S′ satisfying (7.6).
+Remark 7.2. We note that part (d) of Theorem 7.1 will not be needed. Nevertheless it is
+interesting in its own.
+To formulate the next theorem we define
+S0 := {g ∈ S : ∇ · g = 0}.
+By ( · )
+cl we shall denote the operator closure.
+Theorem 7.3. There exists a unique unitary transformation Vv : Fs(v) → L2(S′, dν) with
+the following properties
+(i) VvΩ = 1,
+(ii) Vv(a∗(iωf) + a(iωf))
+clV −1
+v
+= ϕ(f), for all f ∈ S0,
+where iωf = (ω−1/2 ˆf)∨ and ϕ(f) is understood as a multiplication operator. Moreover, we
+have VvΓ(Kv) = JVv, where J denotes complex conjugation in L2(S′, dν).
+The proof of Theorem 7.3 will be given in Appendix B. Using Lemma 4.1 we obtain
+immediately the following corollary.
+Corollary 7.4. Let the notation be as in in Theorem 7.3. There exists a unique unitary
+transformation Vg : Fs(g) → L2(S′, dν) with the following properties
+(i) VgΩ = 1,
+(ii) Vg(a∗(τ −1
+ǫ iωf) + a(τ −1
+ǫ iωf))
+clV −1
+g
+= ϕ(f), for all f ∈ S0.
+Moreover, we have VgΓ(Kg) = JVg, where J denotes complex conjugation in L2(S′, dν).
+27
+
+Next we define symmetries in Schr¨odinger representation. We will show in Theorem 7.6,
+below, that they agree by the unitary transformations of Theorem 7.3 and Corollary 7.4
+with the definitions in Fock space representation.
+We define for U ∈ SU(2) on S the
+representation
+(US(U)f)(x) = Rf(R−1x),
+f ∈ S, x ∈ R3,
+where R = π(U). We define for f ∈ S
+(PSf)(x) = −f(−x).
+As a consequence of the definition P−1
+S
+= PS. Then this defines by duality a transformation
+on S′ by
+(US′(U)T)(f) = T(US(U)−1f)
+and
+(PS′T)(f) = T(P−1
+S f),
+for all T ∈ S′ and f ∈ S. On L2(S′, dν) we define for any F ∈ L2(S′, dν)
+(USch(U)F)(T) = F(US′(U)−1T),
+U ∈ SU(2),
+(PSchF)(T) = F(P−1
+S′ T),
+(KSchF)(T) = F(T)
+(ΘSchF)(T) = F(−T)
+for all T ∈ S′.
+Lemma 7.5. Let U ∈ SU(2). The measure ν is invariant with respect to US′(U) and
+PS′. The transformations USch(U), PSch are unitary transformations on L2(S′, dν). The
+transformation KSch is an anti-unitary transformation on L2(S′, dν), which squares to one.
+The measure ν is invariant with respect to −1S′, and ΘSch is a unitary transformation on
+L2(S′, dν), which squares to one.
+Proof. Let G stand for US′(U) and PS′ and g for US(U) and PS, respectively. Then G
+leaves the set of cylinder sets invariant, and hence the σ-algebra generated by the cylinder
+sets. Since the form B is invariant with respect to G, so is the measure ν. To see this
+define νG(A) = ν(G(A)) for any measurable set A. Then for any f ∈ S we find from the
+definition of the integral
+exp(−1
+4B(f, f)) = exp(−1
+4B(gf, gf)) =
+�
+exp(iϕ(gf))dν =
+�
+exp(i(G−1T)(f))dν(T)
+=
+�
+exp(iT(f))dνG(T) =
+�
+exp(iϕ(f))dνG.
+Thus it follows ν = νG from the uniqueness property in Theorem 7.1. Thus the unitarity
+properties of USch(U) and PSch on L2(S′, dν) now follow by the definition of the integral as
+a limit of simple functions. The anti-unitarity of KSch is obvious. The last statement about
+ΘSch follows analogously as above with G = −1S′ and g = −1S.
+28
+
+The following theorem relates the symmetries in the Fock representation to the sym-
+metries in the Schr¨odinger representation.
+Theorem 7.6. Let Vv and Vg be the unique unitary transformations satisfying (i) and (ii)
+of Theorem 7.3 and Corollary 7.4, respectively. Then the following identities hold.
+(a) VgUf(U)V −1
+g
+= USch(U) and VvΓ(Uv(π(U))V −1
+v
+= USch(U), for U ∈ SU(2),
+(b) VgPfV −1
+g
+= PSch and VvΓ(Pv)V −1
+v
+= PSch,
+(c) VgΓ(Kg)V −1
+g
+= KSch and VvΓ(Kv)V −1
+v
+= KSch.
+(d) VgΓ(−1g)V −1
+g
+= ΘSch and VvΓ(−1v)V −1
+v
+= ΘSch.
+(e) VgTfV −1
+g
+= ΘSchKSch.
+Proof. We only discuss the case for v, the case for g then follows using Lemma 4.1.
+(a) Let W = USch(U)VvΓ(Uv(π(U))−1). Then it follows from the definitions that WΩ = 1.
+Furthermore, it follows for all f ∈ S0 using (3.4), the invariance of ω and Theorem 7.3 (ii)
+W(a∗(iωf) + a(iωf))clW −1 = USch(U)Vv(a∗(iωUv(U)−1f) + a(iωUv(U)−1f))clV −1
+v
+USch(U)−1
+= USch(U)ϕ(Uv(U)−1f)USch(U)−1 = ϕ(f),
+(7.7)
+where the last equality can be seen as follows.
+For any F ∈ L2(S′, dν) we find with
+F ′ := USch(U)−1F using Uv(U)f = US(U)f and inserting into the definitions, e.g. (7.4),
+that
+(USch(U)(ϕ(Uv(U)−1f)F ′))(T) = (ϕ(US(U)−1f)F ′)(US′(U)−1T)
+= (US′(U)−1T)(US(U)−1f)F ′(US′(U)−1T)
+= T(f)F ′(US′(U)−1T) = ϕ(f)F(T).
+This show the last equality in (7.7).
+It now follows from (7.7) that W = Vv by the
+uniqueness statement of Theorem 7.3. This shows (a). Now (b) is shown similarly as (a).
+(c) Let W = KSchVvΓ(Kv). Then it follows from the definitions that WΩ = 1. Furthermore,
+it follows for all f ∈ S0 using (3.4), the reality and symmetry assumptions of ω, and
+Theorem 7.3 (ii) that
+W(a∗(iωf) + a(iωf))clW −1 = KSchVv(a∗(Kviωf) + a(Kviωf))clV −1
+v
+K−1
+Sch
+= KSchVv(a∗(iωKvf) + a(iωKvf))clV −1
+v
+K−1
+Sch
+= KSchϕ(Kvf)K−1
+Sch = ϕ(f).
+As in (a) it now follows that W = Vv by the uniqueness statement of Theorem 7.3. This
+shows (c), since K−1
+v
+= Kv.
+Now (d) follows analogously to (c) by considering W =
+29
+
+ΘSchVvΓ(−1v) and observing that
+W(a∗(iωf) + a(iωf))clW −1 = ΘSchVv(a∗(−iωf) + a(−iωf))clV −1
+v
+Θ−1
+Sch
+= ΘSchVv(a∗(iω(−f)) + a(iω(−f))clV −1
+v
+Θ−1
+Sch
+= ΘSchϕ(−f)Θ−1
+Sch = ϕ(f).
+Again by uniqueness W = Vv. This shows (d). Finally, (e) follows from (c) and (d).
+Remark 7.7. We see from Subsection 4.4 and Theorem 7.6 that USch, PSch and TSch :=
+ΘSchKSch correspond to the rotation, parity and time reversal symmetries in the Schr¨odinger
+representation. Alternatively, one could redefine the field operators in the Hamiltonian so
+that KSch has the property of a time reversal symmetry, cf. [21].
+Acknowledgements
+Both authors acknowledge financial support by the Research Training Group (1523/2)
+“Quantum and Gravitational Fields” when this project was initiated. D. Hasler wants
+to thank I. Herbst for valuable discussions on the subject. M. Lange also acknowledges
+financial support from the European Research Council (ERC) under the European Union’s
+Horizon 2020 research and innovation programme (ERC StG MaMBoQ, grant agreement
+n.802901).
+A
+Gaussian Random Processes
+In this appendix we review notations and results about so called Gaussian random pro-
+cesses. We follow [26]. The main result is Theorem A.6, which will be used in the proof of
+Theorem 7.3 in Appendix B. First we introduce the following definitions.
+Definition A.1. Let (M, µ) be a probability measure space. Let V be a real vector space.
+A random process indexed by V is a map φ from V to the random variables on M, so
+that almost everywhere
+φ(v + w) = φ(v) + φ(w)
+∀v, w ∈ V
+φ(αv) = αφ(v)
+∀α ∈ R, ∀v ∈ V.
+For a random variable Y on probability measure space (M, µ) we will use the notation
+⟨Y ⟩ :=
+�
+Y dµ.
+Definition A.2. Let r be a real Hilbert space with inner product ⟨·, ·⟩r.
+A Gaussian
+random process indexed by r is a random process φ indexed by r so that the following
+holds.
+30
+
+(a) The set {F(φ(v1), ..., φ(vn)) : v1, ..., vn ∈ r, F ∈ S(Rn)} is dense in L2(M, dµ), where
+(M, µ) is the probability measure space of the random process φ.
+(b) Each φ(v) is a Gaussian random variable.
+(c) ⟨φ(v)φ(w)⟩ = 1
+2⟨v, w⟩r.
+Remark A.3.
+(a) We note that in (a) of Definition A.2, we use a different assumption than in the
+definition of a Gaussian random process indexed by a Hilbert space in [26]. However,
+in view of [26, Lemma I.5] this is equivalent.
+(b) One can show that two Gaussian random processes indexed by the same real Hilbert
+space are unique up to isomorphisms of probability measure spaces, see for example
+[26, Theorem I.6].
+(c) For any real Hilbert space r, a Gaussian process indexed by r exists. For a proof see
+Theorem I.9 in [26].
+Let r be the complexification of r, i.e., rC = r ⊕r as a real Hilbert space with a complex
+structure given by i(u, v) = (−v, u). We define
+J : rC → rC,
+J(u, v) = (u, −v).
+(A.1)
+Then J is anti-linear and satisfies J2 = 1. Without mention we shall imbed r in rC by
+the map ι : u �→ (u, 0). For the operator introduced in (3.3) we shall write for notational
+convenience a#(f) = a#(ιf) for f ∈ r.
+Next we introduce the notion of Wick powers and Wick product of random variables.
+To this end we introduce the following multi-index notation. For k ∈ N, n ∈ Nk
+0 and
+α, β ∈ Ck we define
+αn =
+k
+�
+j=1
+αnj,
+αβ =
+k
+�
+j=1
+αjβj,
+|n| =
+k
+�
+j=1
+nj,
+n! =
+k
+�
+j=1
+nj!
+.
+Given a formal power series in random variables f1, ..., fk with finite moments on a measure
+space (M, µ), which we denote by �
+n∈Nk
+0 anf n, where an ∈ C and
+f n :=
+k
+�
+j=1
+f
+nj
+j ,
+we define the formal derivative
+∂
+∂fi
+�
+n∈Nk
+0
+anf n =
+�
+n∈Nk
+0
+annif n−ei.
+where ei ∈ Nk is defined such that all components vanish except the i-th, which equals 1.
+31
+
+Remark A.4. As in [26] we don’t identify two series which are identical by virtue of
+substituting in specific arguments (e.g. f and f 2 are distinct as formal power series even if
+f = 1).
+Definition A.5. Let f1, ..., fk be random variables with finite moments on a measure space
+(M, µ). The Wick product : f n : is defined inductively in n = |n| by
+(i) : f 0 : = 1, where 0 = (0, ...., 0),
+(ii) ⟨: f n :⟩ = 0 if n ̸= 0,
+(iii)
+∂
+∂fi : f n : = ni : f n−ei :
+.
+The following theorem is the main theorem of this section.
+Theorem A.6. Let φ be a Gaussian random process indexed by a separable real Hilbert
+space r on the probability measure space (M, µ), and let D be a dense subset of r. Then
+there exists a unique unitary transformation V : Fs(rC) → L2(M, dµ) satisfying
+(i) V Ω = 1
+(ii) V (a∗(f) + a(f))clV −1 = φ(f) for all f ∈ D.
+Moreover, the following holds. We have
+(a) V (a∗(f) + a(f))clV −1 = φ(f) holds for all f ∈ r.
+(b) J V = V Γ(J), where J is defined in (A.1) and J denotes ordinary complex conjuga-
+tion in L2(M, dµ).
+(c) For all fj ∈ r we have
+V a∗(f1) · · ·a∗(fn)Ω =
+: φ(f1) · · ·φ(fn) : .
+(A.2)
+A proof of Theorem A.6 can be found in Theorems I.6 and I.11 in [26]. For the con-
+venience of the reader, we shall outline a proof below.
+First, we need a few lemmas.
+For random variables f1, · · · , fk with finite moments we define the formal power series for
+α ∈ Ck by
+: exp(αf) : =
+∞
+�
+n∈Nk
+0
+αn : f n :
+n!
+.
+(A.3)
+Lemma A.7. Let f1, ..., fk be random variables with finite moments on a probability mea-
+sure space (M, µ). Then for all α ∈ Ck the following holds
+(a) ⟨: exp(αf) :⟩ = 1
+(b) : exp(αf) := exp(αf)⟨exp(αf)⟩−1
+32
+
+(c) If f is a Gaussian random variable, then (A.3) converges in L1(M, dµ) and
+: exp(αf) := exp(αf) exp
+�
+−1
+2
+�
+i,j
+αiαj⟨fifj⟩
+�
+.
+Proof. (a) This follows from (i) and (ii) of Definition A.5. (b) By (iii) of Definition A.5, we
+find
+∂
+∂fj : exp(αf) := αj : exp(αf) :. Thus
+∂
+∂fj : exp(αf) : exp(−αf) = 0 and so : exp(αf) :
+exp(−αf) = C for some constant C. Thus from (a) it follows that C = ⟨exp(αf)⟩−1.
+(c) The L1 convergence follows from dominated convergence. Using that f is Gaussian
+one finds ⟨exp(αf)⟩ = exp( 1
+2
+�
+i,j αiαj⟨fifj⟩) (e.g. by calculating the Fourier transform for
+α = it, with t ∈ Rk, and then using analytic continuation). Thus (c) follows from (b).
+The following Lemma is from [26, Theorem I.3, Corollary I.4].
+Lemma A.8. The following holds.
+(a) If f and g are Gaussian random variables, then for m, n ∈ N0
+⟨: f n :: gm :⟩ = δn,mn!⟨fg⟩n.
+(b) If f1, ..., fn and g1, ..., gm are Gaussian random variables and n ̸= m, then
+⟨: f1 · · ·fn :: g1 · · · gm :⟩ = 0.
+(c) If f1, ..., fk are Gaussian random variables with ⟨fifj⟩ = δi,j, then for n, m ∈ Nk
+0
+⟨: f n :: f m :⟩ = δn,mn! .
+Proof. (a). By (c) of Lemma A.7 we find
+: exp(αf) :: exp(βg) : = exp(αf + βg) exp
+�
+−1
+2
+�
+α2⟨f 2⟩ + β2⟨g2⟩
+��
+=: exp(αf + βg) : exp (αβ⟨fg⟩) .
+Thus by (a) of Lemma A.7
+⟨: exp(αf) :: exp(βg) :⟩ = exp (αβ⟨fg⟩) .
+Thus (a) now follows by expanding exponentials and equating coefficients. (b,c) follow
+from the multinomial theorem and (a).
+Lemma A.9. Let φ be a Gaussian random process indexed by the real Hilbert space r. Let
+Γn(r) = linC{: φ(f1) · · ·φ(fn) :
+|
+f1, ..., fn ∈ r}
+cl,
+n ∈ N
+and Γ0(r) = C. Then the following holds.
+33
+
+(a) Γn(r) ⊥ Γm(r) for n ̸= m.
+(b) L2(M, dµ) = �∞
+n=0 Γn(r).
+Proof. (a) This follows from (b) of Lemma A.8. (b) For any f ∈ r, a direct computation
+shows that the formal power series : eiφ(f) : converges in L2(M, dµ). We shall denote the
+limit by the same symbol. Thus by definition �∞
+n=0 Γn(r) contains : eiφ(f) : and so eiφ(f) in
+view of (c) of Lemma A.7. In particular, for any F ∈ S(Rn) and f1, ..., fn ∈ r we find that
+F(φ(f1), · · · , φ(fn)) = (2π)−n/2
+�
+�F(t) exp(
+n
+�
+j=1
+tjφ(fj))dnt
+(A.4)
+is in �∞
+n=0 Γn(r). But the set of random variables of the form as on the left hand side of
+(A.4) are dense in L2(M, dµ) by the assumptions of an indexed Gaussian random process.
+Thus (b) follows.
+Proof of Theorem A.6. First we show uniqueness. To this end we define for f ∈ rC the
+operator φF(f) in Fs(rC) by
+φF(f) = a∗(f) + a(f)
+cl.
+(A.5)
+We claim that for any m ∈ N0 the set
+{φF(f1) · · · φF(fn)Ω : fi ∈ D, n = 0, 1, ..., m}
+is dense in �m
+n=0 Sn(r⊗n
+C ). To show this, we use induction in m. The claim clearly holds
+for m = 0. Suppose it holds for m. Then multiplying out, we find
+φF(f1) · · ·φF(fm+1)Ω = a∗(f1) · · ·a∗(fm+1)Ω + h,
+where h ∈ �m
+n=0 Sn(r⊗n
+C ). Since the linear span of a∗(f1) · · ·a∗(fm+1)Ω is dense in Sm+1(r⊗n
+C )
+the claim follows for m + 1. Since
+V φF(f1) · · · φF(fn)Ω = (V φF(f1)V −1) · · ·(V φF(fn)V −1)V Ω,
+properties (i) and (ii) determine the action of V uniquely on a dense set.
+Let us now show existence. First choose an o.n.b. B of r. Define V by V Ω = 1 and
+V a∗(f1) · · · a∗(fn)Ω =
+: φ(f1) · · ·φ(fn) :,
+where fj ∈ B (this is well defined by the symmetry property of the Wick product) and
+extend it by linearity. It is straight forward to see that the map V is an isometry using on the
+one hand side the canonical commutation relations for creation and annihilation operators
+in Fock space and on the other hand Lemma A.8. Surjectivity, and hence unitarity, follows
+from Lemma A.9. Obviously, V satisfies (i) by construction. Let us now show, that it
+34
+
+satisfies (a) and hence (ii). Using the definition, (A.5), and the canonical commutation
+relations we find for fj ∈ B
+φF(f1)a∗(f1)n1 · · · a∗(fk)nkΩ
+(A.6)
+= a∗(f1)n1+1 · · · a∗(fk)nkΩ + n1a∗(f1)n1−1 · · · a∗(fk)nkΩ.
+On the other hand we will show that
+φ(f1) : φ(f1)n1 · · · φ(fk)nk :
+(A.7)
+= : φ(f1)n1+1 · · · φ(fk)nk : +n1 : φ(f1)n1−1 · · · φ(fk)nk : .
+To see (A.7), we first note that using (c) of Lemma A.7 we obtain
+φ(f1) : exp(
+n
+�
+j=1
+αjφ(fj)) : =
+� ∂
+∂α1
++ α1
+�
+: exp(
+n
+�
+j=1
+αjφ(fj)) : .
+(A.8)
+Now expanding (A.8) in a power series, calculating the derivative, and equating coefficients,
+we obtain (A.7). Thus it follows in view of (A.6), (A.7), and from the definition of V that
+for all f ∈ B
+V (a∗(f) + a∗(f))
+clV −1 = φ(f).
+(A.9)
+This implies (a) (and hence (ii)) by linearity and continuity.
+Clearly, (c) follows from
+uniqueness of the above construction and multi-linearity. To show (b) observe that from
+(A.2) we find for any fj ∈ r that
+J V Γ(J)a∗(f1) · · · a∗(fn)Ω = J V a∗(Jf1) · · · a∗(Jfn))Ω
+= J V a∗(f1) · · · a∗(fn))Ω = J : φ(f1) · · ·φ(fn) :
+= : φ(f1) · · · φ(fn) : = V a∗(f1) · · · a∗(fn)Ω.
+Thus by density and C-linearity it follows that J V Γ(J) = V . Thus (b) follows, since
+J−1 = J.
+B
+An Application of Minlos’ theorem
+In this appendix we will prove Theorems 7.1 and 7.3.
+For this we shall introduce the
+following definitions from [26]. Let us first recall the definition
+c(f) = e− 1
+4 B(f,f)
+for f ∈ S with B defined in (7.2).
+Lemma B.1. The following holds.
+35
+
+(i) c(0) = 1.
+(ii) f �→ c(f) is continuous.
+(iii) For any f1, ...., fn ∈ S and z1, ..., zn ∈ C we have
+n
+�
+i,j=1
+zizjc(fi − fj) ≥ 0
+.
+Proof. (i) This follows from B(0, 0) = 0. (ii) It is straight forward to see that f �→ B(f, f)
+is continuous on S, and hence also the function c : f �→ exp(−1
+4B(f, f)). (iii) Let V =
+linR{f1, ..., fn}. Then there exists a basis (ej)j=1,...,m of V , with dual basis (bj)m
+j=1, such
+that B(ei, ej) = λiδi,j with λ1 = · · · = λp = 1 and λp+1 = · · · λm = 0 for some 1 ≤ p ≤ m.
+Using that the Fourier transform of a Gaussian is a Gaussian we find for any f ∈ V with
+fj = bj(f)
+c(f) = e− 1
+4B(f,f) = e− 1
+4
+�p
+j=1 f2
+j = (π)−p/2
+�
+e−i �p
+j= yjbj(f)e− �p
+j=1 y2
+j dpy.
+So positivity of c(f) now follows from Bochner’s theorem [23, Theorem IX.9].
+Proof of Theorem 7.1. The existence and uniqueness of the measure ν follows in view of
+Lemma B.1 from Minlos theorem [9, Theorem 3.4.2] see also [1,2,3,22,28]. To this end, we
+extend the seminorms (7.1) to S as follows. For f = (f1, f2, f3) ∈ S we define ∥f∥α,β :=
+∥f1∥α,β + ∥f2∥α,β + ∥f3∥α,β. Then it is straight forward to see that S with these seminorms
+is a nuclear space.
+(a) This follows since for f ∈ S and each t ∈ R we have by (7.6)
+�
+exp(itϕ(f))dν = exp(−1
+4t2B(f, f)),
+and so ϕ(f) is a Gaussian random variable with mean zero, see [26]. (b) This follows from
+(a) and linearity (7.5), see [26]. (c) We argue similarly as in [28]. First observe that for all
+measurable sets E we have
+∀ǫ > 0, ∃C a cylinder set,
+ν(C△E) < ǫ.
+(B.1)
+Here, △ stands for the symmetric difference. To this end, let E be the set of all measurable
+E which satisfy (B.1). It is straight forward to verify that E is a σ-algebra containing all
+cylinder sets. Hence E equals the set of all measurable sets. It follows by definition of the
+integral that {1Ω(ϕ(f1), ..., ϕ(fn)) : Ω ⊂ Rn Borel measurable, f1, ..., fn ∈ S} is dense in
+L2(S′, dν). Now it is well known that S(Rn; C) is dense in L1(Rn, dµC), where µC denotes
+Gaussian measure with covariance C (with possibly matrix elements which are infinite).
+This shows the density. (d) If f ∈ S with P �f = 0, then B(f, f) = 0, so ϕ(f) is by (a) a
+Gaussian random variable with variance zero. Thus for all f ∈ S with P �f = 0 it follows
+36
+
+that ϕ(f) = 0 almost everywhere. Now let h ∈ S(R3; R). Then ∇h ∈ S and for all T ∈ S′
+we have
+ϕ(∇h)(T) = 0 ⇔ T(∇h) = 0 ⇔ (∇ · T)(h) = 0.
+Since P �
+∇h = 0, we find (∇ · T)(h) = 0 for almost all T ∈ S′. Since S(R3; R) is separable,
+there exists a countable dense subset Q. It follows that for almost all T ∈ S′ we have
+(∇ · T)(h) = 0 for all h ∈ Q. Since ∇ · T is continuous it follows that for almost all T ∈ S′
+we have (∇ · T)(h) = 0 for all h ∈ S(R3; R). This shows the claim.
+As an immediate consequence of Theorem 7.1 we obtain the following lemma, which we
+shall use for the proof of Theorem 7.3.
+Lemma B.2. Let hB denote the real Hilbert space obtained by the completion of the inner
+product space (S0, B(·, ·)) with the imbedding ι : S0 → hB having dense range. Let v ∈ hB,
+and let (vn)n∈N be a Cauchy sequence in S0 such that ι(vn) → v. Then the following limit
+exists in L2(S′, dν)
+ϕ(v) := lim
+n→∞ ϕ(vn),
+is independent of the Cauchy sequence. Furthermore, ϕ(v) is a Gaussian random process
+indexed by hB with (S′, ν) the probability measure space of the random process.
+Proof. First observe that (S0, B(·, ·)) is indeed an inner product space, since ∇ · f = 0
+implies P �f = �f.
+Clearly, ϕ(vn) is a Cauchy sequence in L2(S′, dν), since
+�
+|ϕ(vn) −
+ϕ(vm)|2dν = 1
+2B(vn − vm, vn − vm) by Theorem 7.1 (a), and hence converges to a unique
+limit. With regard to Definition A.2 the statement of the last sentence is straight forward
+to show using Theorem 7.1 and the fact that limits of Gaussians are Gaussian.
+Proof of Theorem 7.3. The map iω : (S0, B(·, ·)) → {v ∈ v : Imv = 0} is an isometry
+of real inner product spaces, which follows directly from the definitions.
+Furthermore,
+iω has dense range.
+To see this, observe that for any real v ∈ v there exists by well
+known construction a real vn ∈ S such that vn → v in the L2(R3; C3) norm. Now define
+wn = (ω1/2(1 − χn)P ˆvn)∨ for χ ∈ C∞
+c (R3; [0, 1]) with χ = 1 on B1/2(0) and χ = 0 outside
+of B1(0), and χn(x) = χ(nx). Then it is straight forward to see that wn ∈ S0 and (by
+unitarity of the Fourier transform and dominated convergence)
+∥iωwn − v∥ = ∥((1 − χn)P ˆvn)∨ − v∥ = ∥((1 − χn)P ˆvn − ˆv∥ = ∥((1 − χn)P ˆvn − P ˆv∥
+≤ ∥χnP ˆv∥ + ∥(1 − χn)P(ˆvn − ˆv)∥ ≤ ∥χnP ˆv∥ + ∥ˆvn − ˆv∥ → 0,
+as n → ∞, by construction. This shows that iω has dense range. So the map iω extends
+to hB the closure of (S0, B(·, ·)) and yields a bijective isometry hB → {v ∈ v : Imv = 0}.
+It follows using Lemma B.2 that ϕ ◦ i−1
+ω
+is a Gaussian random process indexed by {v ∈ v :
+Imv = 0} with probability measure space (S′, ν). Thus it follows from Theorem A.6 that
+there exists a unique unitary transformation Vv : Fs(v) → L2(S′, dν) with VvΩ = 1 and
+37
+
+Vv(a∗(h) + a(h))V −1
+v
+= ϕ(h) for all h ∈ iωS0 (since {v ∈ v : Imv = 0}C = v and iωS0 is
+dense in {v ∈ v : Imv = 0}). This shows the first part of the theorem. The last statement
+of the theorem now follows form part (b) of Theorem A.6.
+References
+[1] V. I. Bogachev, Measure theory. Vol. I, II, Springer-Verlag, Berlin, 2007. MR 2267655
+[2] V. I. Bogachev and O. G. Smolyanov, Topological vector spaces and their applications,
+Springer Monographs in Mathematics, Springer, Cham, 2017. MR 3616849
+[3] N. Bourbaki, ´El´ements de math´ematique. Fasc. XXXV. Livre VI: Int´egration. Chapitre
+IX: Int´egration sur les espaces topologiques s´epar´es, Actualit´es Scientifiques et Indus-
+trielles [Current Scientific and Industrial Topics], No. 1343, Hermann, Paris, 1969. MR
+0276436
+[4] C. Cohen-Tannoudji, G. Grynberg, and J. Dupont-Roc, Atom-photon interactions:
+Basic processes and applications, Wiley, New York, 1992.
+[5] Charles Fefferman, J¨urg Fr¨ohlich, and Gian Michele Graf, Stability of ultraviolet-cutoff
+quantum electrodynamics with non-relativistic matter, Comm. Math. Phys. 190 (1997),
+no. 2, 309–330. MR 1489574
+[6] J. Fr¨ohlich, Application of commutator theorems to the integration of representations
+of Lie algebras and commutation relations, Comm. Math. Phys. 54 (1977), no. 2,
+135–150. MR 473909
+[7] J. Glimm and A. Jaffe, Collected papers vol.1: Quantum field theory and statistical
+mechanics: Expositions, Contemporary Physicists, Birkh¨auser Boston, 1985.
+[8] James Glimm and Arthur Jaffe, Collected papers. Vol. 2, Birkh¨auser Boston, Inc.,
+Boston, MA, 1985, Constructive quantum field theory. Selected papers, Reprint of
+articles published 1968–1980. MR 947959
+[9]
+, Quantum physics, second ed., Springer-Verlag, New York, 1987, A functional
+integral point of view. MR 887102
+[10] David Hasler and Ira Herbst, Absence of ground states for a class of translation invari-
+ant models of non-relativistic QED, Comm. Math. Phys. 279 (2008), no. 3, 769–787.
+MR 2386727
+[11]
+, On the self-adjointness and domain of Pauli-Fierz type Hamiltonians, Rev.
+Math. Phys. 20 (2008), no. 7, 787–800. MR 2436496
+38
+
+[12]
+, Convergent expansions in non-relativistic qed: analyticity of the ground state,
+J. Funct. Anal. 261 (2011), no. 11, 3119–3154. MR 2835993
+[13]
+, Ground states in the spin boson model, Ann. Henri Poincar´e 12 (2011), no. 4,
+621–677. MR 2787765
+[14]
+, A vanishing theorem for operators in Fock space, Lett. Math. Phys. 101
+(2012), no. 2, 223–237. MR 2947962
+[15] David Hasler and Markus Lange, Degenerate perturbation theory for models of quantum
+field theory with symmetries, 2022.
+[16] F. Hiroshima and H. Spohn, Ground state degeneracy of the Pauli-Fierz Hamiltonian
+with spin, Adv. Theor. Math. Phys. 5 (2001), no. 6, 1091–1104. MR 1926665
+[17] Fumio Hiroshima, Fiber Hamiltonians in non-relativistic quantum electrodynamics, J.
+Funct. Anal. 252 (2007), no. 1, 314–355. MR 2357359
+[18] Hendrik A. Kramers, Th´eorie g´en´erale de la rotation paramagn´etique dans les cristaux,
+Proceedings Koninklijke Akademie van Wetenschappen 33 (1930), 959–972.
+[19] Michael Loss, Tadahiro Miyao, and Herbert Spohn, Lowest energy states in nonrela-
+tivistic QED: atoms and ions in motion, J. Funct. Anal. 243 (2007), no. 2, 353–393.
+MR 2289693
+[20]
+, Kramers degeneracy theorem in nonrelativistic QED, Lett. Math. Phys. 89
+(2009), no. 1, 21–31. MR 2520177
+[21]
+, Time reversal symmetries and properties of ground states in nonrelativistic
+QED, Applications of renormalization group methods in mathematical sciences, RIMS
+Kˆokyˆuroku Bessatsu, B21, Res. Inst. Math. Sci. (RIMS), Kyoto, 2010, pp. 35–44. MR
+2792021
+[22] R. A. Minlos, Generalized random processes and their extension to a measure, Selected
+Transl. Math. Statist. and Prob., Vol. 3, Amer. Math. Soc., Providence, R.I., 1963,
+pp. 291–313. MR 0154317
+[23] Michael Reed and Barry Simon, Methods of modern mathematical physics. II. Fourier
+analysis, self-adjointness, Academic Press [Harcourt Brace Jovanovich, Publishers],
+New York-London, 1975. MR 0493420
+[24]
+, Methods of modern mathematical physics. I, second ed., Academic Press, Inc.
+[Harcourt Brace Jovanovich, Publishers], New York, 1980, Functional analysis. MR
+751959
+39
+
+[25] Israel Michael Sigal, Ground state and resonances in the standard model of the non-
+relativistic QED, J. Stat. Phys. 134 (2009), no. 5-6, 899–939. MR 2518974
+[26] Barry Simon, The P(φ)2 Euclidean (quantum) field theory, Princeton University Press,
+Princeton, N.J., 1974, Princeton Series in Physics. MR 0489552
+[27] Herbert Spohn, Dynamics of charged particles and their radiation field, Cambridge
+University Press, Cambridge, 2004. MR 2097788
+[28] Yasuo Umemura, Measures on infinite dimensional vector spaces, Publ. Res. Inst.
+Math. Sci. Ser. A 1 (1965), 1–47. MR 0187273
+[29] E. Wigner, Ueber die operation der zeitumkehr in der quantenmechanik, Nachrichten
+von der Gesellschaft der Wissenschaften zu G¨ottingen, Mathematisch-Physikalische
+Klasse 1932 (1932), 546–559.
+40
+
diff --git a/KdFAT4oBgHgl3EQfvx7k/content/tmp_files/load_file.txt b/KdFAT4oBgHgl3EQfvx7k/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..19989326b01fd4d2dc76aa23fdb576c022915e77
--- /dev/null
+++ b/KdFAT4oBgHgl3EQfvx7k/content/tmp_files/load_file.txt
@@ -0,0 +1,1309 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf,len=1308
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='08678v1  [math-ph]  20 Jan 2023  Symmetries in non-relativistic quantum  electrodynamics  David Hasler1∗and Markus Lange2†  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Department of Mathematics, Friedrich Schiller University Jena  Jena, Germany  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' German Aerospace Center (DLR), Institute for AI-Safety and Security  Sankt Augustin & Ulm, Germany  January 23, 2023  Abstract  We define symmetries in non-relativistic quantum electrodynamics, which have  the physical interpretation of rotation, parity and time reversal symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' We collect  transformation properties related to these symmetries in Fock space representation  as well as in the Schr¨odinger representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' As an application, we generalize and  improve theorems about Kramer’s degeneracy in non-relativistic quantum electrody-  namics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  1  Introduction  Symmetries are often used to analyze various properties of physical systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' In particular  in quantum mechanics symmetries are used to determine spectral properties of the Hamil-  tonian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' In this paper we study symmetries of non-relativistic quantum electrodynamics  (qed), which have the physical interpretation of rotation, parity and time reversal symme-  try.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' We give explicit formulas for these symmetries both in Fock space representation as  well as in the so called Schr¨odinger representation and apply these symmetries to prove  multiplicities of eigenvalues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  The transformation properties described in the present paper are of general interest in  non-relativistic qed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' In particular, in the Fock representation these symmetries are helpful  for operator theoretic renormalization analysis of non-relativistic qed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' On the one hand,  ∗E-mail: david.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='hasler@uni-jena.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='de  †E-mail: markus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='lange@dlr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='de  1  symmetries can be used to control marginal terms [12,13,14,25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' On the other hand sym-  metries allow the treatment of degenerate eigenvalues in the frame work of renormalization,  provided the symmetries act irreducibly on the eigenspace [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' In fact, the latter is the  main interest, which we had in mind, for collecting the transformation properties of the  aforementioned symmetries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  In physics literature continuous symmetries are often described by means of their in-  finitesimal generator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' That is, as a representation of the Lie-algebra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' For non-relativistic  qed the generators of the Lie-algebra of SU(2) are readily available in textbooks about  non-relativistic aspects of quantum electrodynamics [4, 27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' In this paper we express the  SU(2)-symmetry directly as a representation of the Lie-group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  As already mentioned, symmetries are helpful in the spectral analysis of Hamiltonian  operators of quantum mechanics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' For example the classical Kramers degeneracy theorem  states, that the eigenvalues of a time-reversal symmetric Hamiltonian describing an odd  number of spin 1/2-particles have even multiplicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Using a theorem of this type it was  shown in [20, 21] that Hamiltonians of non-relativistic qed, which describe odd number  of spin 1/2-particles have a doubly degenerate ground state, provided the external poten-  tial is symmetric with respect to parity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' In this paper we improve that result and show  that parity symmetry is not necessary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' This is of physical relevance, since potentials de-  scribing molecules with static nuclei, are not necessarily symmetric with respect to parity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Furthermore, we include external magnetic fields in the mathematical model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Finally, we  consider translation invariant systems and generalize degeneracy results for a single spin  1/2-particle [16,17] to atoms and molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Let us give a short outline of the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' In the next section we review the notion of  a symmetry in quantum mechanics and state an abstract version of Kramers degeneracy  theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' In Section 3 we introduce non-relativistic qed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' In Section 4 we define rotation,  parity, and time-reversal symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Moreover we collect various transformation properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  In Section 5 we study symmetry properties of Hamiltonians of non-relativistic qed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' In par-  ticular we show the aforementioned degeneracy theorems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' In Section 6 we study symmetry  properties of fibers of translationally invariant Hamiltonians of non-relativistic qed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' In Sec-  tion 7 we define rotation, parity, and time-reversal symmetry in the so called Schr¨odinger  representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  We show that the definitions in Schr¨odinger representation agree with  the definitions in Fock space representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' To show this, we use the canonical unitary  transformation mapping the Fock space representation to the Schr¨odinger representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  2  Symmetries in Quantum Mechanical Systems  In this section we collect some well-known definitions and properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Let V be a complex vector space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' A mapping A : V → V is called anti-  linear (or conjugate linear) if  (i) A(x + y) = Ax + Ay for all x, y ∈ V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  2  (ii) A(αx) = αAx, for all x ∈ V and α ∈ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  If H is a complex Hilbert space and T : H → H anti-linear, then the adjoint T ∗ : H → H  is defined by  ⟨T ∗x, y⟩ = ⟨Ty, x⟩  ,  ∀x, y ∈ H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  If H is a complex Hilbert space and S : H → H anti-linear, then S is called anti-unitary  if it is surjective and satisfies  ⟨Sx, Sy⟩ = ⟨y, x⟩  ,  ∀x, y ∈ H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  The assertions of the following Lemma are straightforward to verify.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' The following holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (a) Let Ci be anti-linear (anti-unitary) transformations on complex vector spaces Vi (Hilbert  spaces), i = 1, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Then C1 ⊗ C2 : V1 ⊗ V2 → V1 ⊗ V2 is also anti-linear (anti-unitary).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (b) If T : H → H is an anti-linear mapping on a Hilbert space H, then also T ∗ is  anti-linear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (c) If S is anti-unitary, then S is bijective and S∗S = 1 and SS∗ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Let S be a unitary or anti-unitary operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Let H be a densely defined  operator in H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' We call S a symmetry of H, if  SH = HS  when S is unitary, and  SH = H∗S  when S is anti-unitary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  The following theorem, whose formulation is from [20], can be viewed as an abstract  version of Kramer’s degeneracy theorem, [18,29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='4 (Abstract Kramers Degeneracy).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Let θ be a an anti-unitary symmetry of  a self-adjoint operator H and θ2 = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Then each eigenvalue of H is at least doubly  degenerate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Any eigenvalue of H with finite multiplicity has even multiplicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  The proof follows from the following lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Let J be an anti-unitary operator on a complex Hilbert space V with J2 = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Then the following holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (a) For any nonzero v ∈ V , also Jv is nonzero and v ⊥ Jv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (b) The Hilbert space V cannot have finite odd dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  3  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' (a) Since J(Jv) = J2v = −v, the vector Jv is nonzero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Since J is anti-unitary  ⟨v, Jv⟩ = ⟨JJv, Jv⟩ = −⟨v, Jv⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  So ⟨v, Jv⟩ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (b) We show by induction that V cannot have dimension 2n − 1 for n ∈ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Clearly, the  induction hypothesis holds true for n = 1 by (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Suppose the induction hypothesis holds  for n, and suppose V has dimension 2n + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Pick a nonzero v ∈ V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Then Jv ∈ V and  Jv ⊥ v by (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Thus W := {v, Jv}⊥ is a complex vector space, which has dimension 2n−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Since J2 = −1, it follows that J leaves the complex linear span linC{v, Jv} invariant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Since  J is anti-unitary, it leaves also W invariant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' But the complex vector space W together  with J|W contradict the induction hypothesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Proof of Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Let E be an eigenvalue of H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Since H is self-adjoint E is real.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' So θ  leaves the space V = ker(H − E) invariant, since (H − E)θψ = θ(H − E)ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Thus the first  and second statement follow from (b) of Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='5 with J = θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  3  Non-relativistic qed  For a complex Hilbert space H we denote the n-fold tensor product by  H⊗n :=  n  �  j=1  H  and we set H⊗0 := C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Let S{1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=',n} be the permutation group of the set {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', n}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' For each  σ ∈ S{1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=',n} we define an operator U(σ) on H⊗n by  U(σ)(ϕ1 ⊗ ϕ2 ⊗ · · · ⊗ ϕn) = ϕσ(1) ⊗ ϕσ(2) ⊗ · · · ⊗ ϕσ(n)  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='1)  for any ϕj ∈ H, j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', n, and extending it linearly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' This yields a bounded operator (of  norm one) on H⊗n so we can define Sn =  1  n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  �  σ∈S{1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=',n} U(σ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' We define the symmetric  n-fold tensor product of H by  H⊗sn := Sn  �  H⊗n�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Let Ds denote the representation space of SU(2) with dimension 2s + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' In this paper  we shall only consider the case s = 0, describing spinless particles, and the case s = 1  2,  describing particles with spin 1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  The model consists of N particles with spins sj ∈ {0, 1/2}, masses mj > 0, charges  qj ∈ R, values of the spin magnetic moments µj ∈ R, j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' By xj ∈ R3 we shall  denote the position of the j-the particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' The Hilbert space describing the non-relativistic  quantum mechanical matter is  Hmat =  N  �  j=1  L2(R3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Dsj).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  4  We note that the description of physical systems usually requires the restriction to a sub-  space determined by the particle statistics of identical particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' This will be considered  below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  If s = 0, let ˆsl = 0 for l = 1, 2, 3, and if s = 1/2, let ˆsl = 1  2σl for l = 1, 2, 3, where σl  denotes the l-th Pauli-matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Note that ˆs1, ˆs2 and ˆs3 are representations of the generators of su(2) in the  representation Ds = C2s+1, s ∈ {0, 1/2}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' They are linear maps in Ds satisfying  [ˆsj, ˆsk] =  3  �  l=1  iǫj,k,lˆsl,  ˆs∗  l = ˆsl, l = 1, 2, 3,  ˆs1 = ˆs1,  ˆs2 = −ˆs2,  ˆs3 = ˆs3,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='2)  where ǫj,k,l denotes the totally antisymmetric tensor in three dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  For j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', N and l = 1, 2, 3 we define  (�Sj)l =  � j−1  �  k=1  1IDsk  �  ⊗ ˆsl ⊗  �  N  �  k=j+1  1IDsk  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  For a Hilbert space h define the symmetric Fock space over h by  Fs(h) :=  ∞  �  n=0  h⊗sn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Thus we can identify ψ ∈ Fs(h) with a sequence of functions ψ = (ψ(0), ψ(1), ψ(2), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='.) such  that ψ(n) ∈ h⊗sn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' We introduce the set F0(h) := {ψ ∈ Fs(h) : ∃N, ∀n ≥ N, ψ(n) = 0} of  finite particle vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' For f ∈ h let a∗(f) denote the usual creation operator, which is a  densely defined closed linear operator which satisfies for η ∈ h⊗sn  a∗(f)η =  √  n + 1Sn+1(f ⊗ η).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='3)  Let a(f) denote the adjoint of the creation operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' If T be a symmetry in h, then Γ(T)  denotes the unique operator on F(h) such that on h⊗sn  Γ(T)|h⊗sn =  n  �  j=1  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  It is straight forward to see that also Γ(T) is a symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Let A be any self-adjoint  operator on H with domain of essential self-adjointness D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Let DA = {ψ ∈ F0(h) : ψ(n) ∈  ⊗n  k=1D for each n} and define dΓ(A) on DA ∩ h⊗sn as  A ⊗ 1 ⊗ · · · ⊗ 1 + 1 ⊗ A ⊗ · · · ⊗ 1 + · · · + 1 ⊗ · · · ⊗ 1 ⊗ A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  5  In [24, Section VIII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='10] it is shown that dΓ(A) is essentially self-adjoint on DA, and we  shall denote this self-adjoint extension again by dΓ(A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' It follows from the definitions that  for a symmetry T on h and f ∈ h  Γ(T)a#(f)Γ(T)∗ = a#(Tf),  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='4)  Γ(T)dΓ(A)Γ(T)∗ = dΓ(TAT ∗),  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='5)  where a# stands for a or a∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Let us now define operators acting on the composite Hilbert  space  H ⊗ Fs(h),  where H denotes a Hilbert space, which is used to describe the matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' For a bounded  linear operator G ∈ L(H, H ⊗ h) we define for ϕ ∈ H and η ∈ h⊗sn  a∗(G)(ϕ ⊗ η) =  √  n + 1(1 ⊗ Sn+1)((Gϕ) ⊗ η).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='6)  This extends by linearity to a closable operator in H ⊗ Fs(h), which we shall again denote  by a∗(G).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' We define a(G) = [a∗(G)]∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  In non-relativistic qed one consider the Fock space over g := L2(R3 × Z2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' In that case  we can identify ψ ∈ Fs(g) with a sequence of functions ψ = (ψ(0), ψ(1), ψ(2), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=') such that  ψ(n) ∈ L2  s((R3×Z2)n), where the subscript s stands for wave functions which are symmetric  with respect to interchange of components of the n-fold Cartesian product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Let Mf denote  the operator of multiplication by the function f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' We define  Hf = dΓ(Mω),  where the so-called dispersion relation ω : R3 → [0, ∞) is defined such that ω(k) = ω(k′)  whenever |k′| = |k|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Moreover define  Pf = dΓ(Mπj),  where πj : R3 → R with πj(k) = kj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Next we introduce creation and annihilation operators  in terms of operator valued distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' We define  DS := {ψ ∈ F0(g) : ψ(n) ∈ S((R3 × Z2)n)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  where S((R3 × Z2)n) denotes the space of smooth rapidly decaying functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' For each  (k, λ) ∈ R3 × Z2 we define an operator a(k, λ) on Fs(g) with domain DS by  (a(k, λ)ψ)n(k1, λ1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', kn, λn) =  √  n + 1ψn+1(k, λ, k1, λ1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', kn, λn).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  We define a∗(k, λ) in the sense of quadratic forms on DS × DS by  ⟨ψ1, a∗(k, λ)ψ2⟩ = ⟨a(k, λ)ψ1, ψ2⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  6  Then it is straight forward to see that  a∗(f) =  �  λ=1,2  �  R3 f(k, λ)a∗(k, λ)dk,  a(f) =  �  λ=1,2  �  R3 f(k, λ)a(k, λ)dk,  where the equalities are understood in the sense of quadratic forms and the integrals are  understood as weak integrals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Let us now relate the definition given in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='6) to integrals of  operator valued distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' To this end we use the natural embedding  I : L2(R3 × Z2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' L(Hmat)) → L(Hmat;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' L2(R3 × Z2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Hmat)) ∼= L(Hmat;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Hmat ⊗ g)  g �→ (ϕ �→ [(k, λ) �→ g(k, λ)ϕ]) ,  which is a bounded injection, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' [24, Theorem II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Then for g ∈ L2(R3 × Z2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' L(Hmat))  it is straight forward to show that  a∗(I(g)) =  �  λ=1,2  �  R3 g(k) ⊗ a∗(k, λ)dk,  a(I(g)) =  �  λ=1,2  �  R3 g(k)∗ ⊗ a(k, λ)dk  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='7)  in the sense of quadratic forms on Hmat ⊗DS, where the integral is a weak integral.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Hence-  forth we shall drop the tensor sign in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='7) if it is clear on which factor the operator  acts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' The definition of the vector potential involves the so called polarization vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' For  λ = 1, 2 we choose a measurable function  ε(·, λ) : S2 → R3  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='8)  on the 3-dimensional sphere S2 with the following properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' For each k ∈ S2 the vectors  (ε(k, 1), ε(k, 2), k) form an orthonormal basis of R3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' We extend ε(·, λ) to R3\\{0} by setting  ε(k, λ) := ε(k/|k|, λ) for all nonzero k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' We assume that we are given a measurable coupling  function κ : R3 → C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' We note that the Fourier transform of κ is real, if and only if  κ(k) = κ(−k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='9)  We define the coupling functions for l = 1, 2, 3 and x ∈ R3  g(ε)  x,l(k, λ) = εl(k, λ)  �  2ω(k)  κ(k)e−ik·x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  We can now define the field operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' If ω−1/2κ ∈ L2(R3), we define the magnetic vector  potential  Al(x) :=a(g(ε)  x,l) + a∗(g(ε)  x,l)  =  �  λ=1,2  �  R3  εl(k, λ)  �  2ω(k)  �  κ(k)eik·xa(k, λ) + κ(k)e−ik·xa∗(k, λ)  �  dk,  l = 1, 2, 3,  7  where in the second line we made use of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  If | · |ω−1/2κ ∈ L2(R3), we define the  quantized magnetic field  Bl(x) :=[∇ × A(x)]l  =  �  λ=1,2  �  R3  i[k × ε(k, λ)]l  �  2ω(k)  �  κ(k)eik·xa(k, λ) − κ(k)e−ik·xa∗(k, λ)  �  dk,  l = 1, 2, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  If ω1/2κ ∈ L2(R3), we define the quantized electric field  E⊥  l (x) :=a(−iωg(ε)  x,j) + a∗(−iωg(ε)  x,j)  =  �  λ=1,2  �  R3 iεl(k, λ)  �  ω(k)  2  �  κ(k)eik·xa(k, λ) − κ(k)e−ik·xa∗(k, λ)  �  dk,  l = 1, 2, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  The Hamiltonian acting in the Hilbert space  Hmat ⊗ Fs(g)  is given by  H =  N  �  j=1  �  (pj ⊗ 1 + qj(A(ˆxj) + Aext(ˆxj)))2 + µj �Sj · (B(ˆxj) + Bext(ˆxj))  �  + 1 ⊗ Hf + V (ˆx1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', ˆxN) ⊗ 1,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='10)  where ˆxj denotes the operator of multiplication with xj, the coordinates of the j-th particle,  and pj = −i∇xj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' We assume that V : R3N → R is a function and that Bext : R3 → R3 is a  function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Furthermore, we defined  Aext(x) := −  � (x − y) × Bext(y)  4π|x − y|3  dy,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='11)  cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Provided Bext is sufficiently regular and has sufficient decay, we can write  Aext(x) := −  � (x − y) × Bext(y)  4π|x − y|3  dy = ∇x ×  �  Bext(y)  4π|x − y|dy =  � ∇y × Bext(y)  4π|x − y|  dy, (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='12)  by calculating the derivative and using integration by parts, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' In particular, if  ∇ · Bext = 0, it follows that ∇ × Aext = Bext.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Physically, V is called the external potential, Bext the external magnetic field, Aext the  external magnetic vector potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' We assume that Bext is such that Aext in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='11) is well  defined for almost all x ∈ R3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Moreover, we assume that κ and ω are such that the fields  occurring in the Hamiltonian exist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Furthermore, we assume that κ, ω, V , and Bext are  such that the Hamiltonian is essentially self-adjoint on  ��N  j=1 C∞  c (R3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Dsj)  �  ⊗ F0(g), for  details we refer the reader to [23, Theorem X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='35, Theorem X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='34] and [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  8  4  Symmetries  In this subsection we define symmetries associated to rotations, space inversion and time  inversion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' To define these symmetries on Fock space it is convenient to identity h with the  space of so called divergence free vector fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' In this section we shall denote by F the  Fourier transform and by F −1 its inverse, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' for f ∈ L1(R3)  (Ff)(k) = (2π)−3/2  �  R3 e−ik·xf(x)dx,  (F −1f)(x) = (2π)−3/2  �  R3 eik·xf(k)dk,  where both transformations are canonically extended to L2(R3) by Plancherel’s theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='1  Space of divergent free vector fields  We introduce the space of divergence free vector fields  v := {v ∈ L2(R3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' C3) :  3  �  j=1  kj�vj(k) = 0 , a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' k ∈ R3}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Given a specific measurable choice for the polarization vectors (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='8) we obtain a canonical  identification with the one photon Hilbert space g = L2(R3 × Z2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' This is the content of  the following lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' For the polarization vector ε : S2 × Z2 → R3, as in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='8), the map  τε : g → v,  h �→  �  F −1 �  λ=1,2  εj(·, λ)h(·, λ)  �  j=1,2,3  ,  is unitary and its inverse acting on v ∈ v is determined by (τ −1  ε v)(k, λ) = ε(k, λ) · (Fv)(k)  for almost all (k, λ) ∈ R3 × {1, 2}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  For the proof we first note the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' For k ∈ R3 \\ {0} define  P(k)a,b := δab − kakb  |k|2 ,  a, b = 1, 2, 3,  k ̸= 0  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='1)  From the definition it follows that P(k)a,b = P(k)b,a, and that P(k) is equal to the projection  operator in C3 onto the subspace in C3, which is perpendicular to k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Thus from the  definition of the polarization vectors, (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='8), we infer that for k ∈ R3 \\ {0}  P(k)a,b =  �  λ=1,2  εa(k, λ)εb(k, λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='2)  9  Proof of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' The lemma follows from a straight forward calculation using the  properties of the polarization vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Let h ∈ g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Clearly, τε is well defined, since  k · F(τε(h))(k) = k · �  λ=1,2 ε(k, λ)h(k, λ) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' The map is an isometry, since  ∥τεh∥2 =  �  R3  3  �  j=1  �  λ,λ′=1,2  εj(k, λ)h(k, λ)εj(k, λ′)h(k, λ′)d3k  =  �  R3  �  λ,λ′=1,2  δλ,λ′h(k, λ)h(k, λ′)d3k = ∥h∥2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Furthermore for v ∈ v let (βǫv)(k, λ) = ε(k, λ) · (Fv)(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Then  F(τε(βεv)j)(k) =  �  λ=1,2  εj(k, λ)(βεv)(k, λ)  =  �  λ=1,2  εj(k, λ)  3  �  l=1  εl(k, λ) · (Fvl)(k)  = Fvj(k),  where we used that (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='2) and that v is divergence free.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' This shows the surjectivity of τε  and that its inverse is given by βε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Define for x ∈ R3 and a = 1, 2, 3 the function vx,a : R3 → C3 by  [vx,b(y)]a :=  1  (2π)3/2  �  R3 e−ik·(x−y)  κ(k)  �  2ω(k)  P(k)a,b dk,  y ∈ R3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='3)  The properties collected in the following lemma are straight forward to verify using the  definitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' We have the following properties for x ∈ R3 and b = 1, 2, 3  (a) vx,b ∈ v,  (b) vx,b = τεg(ε)  x,b,  τ −1  ε vx,b = g(ε)  x,b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  The next lemma will be needed to determine transformation properties of the field  energy and field momentum with respect to rotations, parity transformations, and time  reversal symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Let f : R3 → C be a measurable function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Then we have the following  properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (a) τεMfτ −1  ε  = F −1MfF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (b) For ϕ ∈ L2(R3) and S ∈ O(3) we define the transformation TSϕ = ϕ ◦ S−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Then  TSF = FTS,  TSF −1 = F −1TS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='4)  10  (c) Let TS be defined as in (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Then T −1  S  = TS−1 and  TSMfT −1  S  = Mf◦S−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='5)  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Part (a) follows from  (τεMfτ −1  ε v)j = F −1 �  λ=1,2  εj(·, λ)Mf(τ −1  ε v)(·, λ)  = F −1 �  λ=1,2  εj(·, λ)f(·)ε(·, λ) · (Fv)(·)  = F −1(MfFvj)  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='6)  (b) If ϕ ∈ S(R3), we find by the transformation formula for integrals for arbitrary S ∈ O(3)  (TSFϕ)(k) = (2π)−3/2  �  R3 e−i(S−1k)·xϕ(x)dx = (2π)−3/2  �  R3 e−ik·xϕ(S−1x)dx = (FTSϕ)(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='7)  So (b) follows by density and continuity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Part (c) is straight forward to verify.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  The following lemma will be needed to determine transformation properties of the  interaction with respect to rotations and parity transformations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Let S ∈ O(3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Then the following holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (a) For all k ∈ R3 we have P(Sk) = SP(k)ST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (b) For all x ∈ R3 and b = 1, 2, 3  3  �  c′=1  Sc,c′  �  R3 e−ik·(x−S−1y)  κ(k)  �  2ω(k)  Pb,c′(k)dk  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='8)  =  3  �  b′=1  Sb′,b  �  R3 e−ik·(Sx−y)κ(S−1k)  �  2ω(k)  Pb′,c(k)dk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='9)  (c) lf κ(S·) = κ(·), then for all x ∈ R3 and b = 1, 2, 3  Svx,b(S−1y) =  3  �  b′=1  Sb′,bvSx,b′(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='10)  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Part (a) is straight forward to verify using the definition (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' For x ∈ C3 and  k ∈ R3 \\ {0} we find for �k = k/|k|  P(Sk)x = x − S�k(S�k · x) = SSTx − S�k(�k · STx) = SP(k)STx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  11  (b) follows from a change of variables and (a)  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='8) =  3  �  c′=1  �  e−i(Sk)·(Sx−y)  κ(k)  �  2ω(k)  Pb,c′(k)Sc,c′dk  =  3  �  c′=1  �  e−ik·(Sx−y)κ(S−1k)  �  2ω(k)  Pb,c′(S−1k)Sc,c′dk = (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (c) Now (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='10) follows from (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='9) and the definition (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='2  Rotation Invariance  We introduce the so called canonical double covering homomorphism  π : SU(2) → SO(3),  U �→ π(U),  where π(U) is the unique element of SO(3) such that  UσmU∗ =  3  �  l=1  π(U)l,mσl,  m = 1, 2, 3,  with σ1, σ2, σ3 denoting the Pauli matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' On the one electron Hilbert space L2(R3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Ds)  we define  (Up,s(U)ψ)(x) = Ds(U)ψ(π(U)−1x),  where Ds denotes the representation of SU(2) with spin s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Similarly we define for v ∈ v  the transformation for R ∈ SO(3)  (Uv(R)v)(x) = Rv(R−1x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Moreover, we define  Ug(R) = τ −1  ǫ Uv(R)τǫ,  which depends on the choice of the polarization vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' For R ∈ SO(3) we define the  unitary mapping  Uf(R) = Γ(Ug(R)),  and for U ∈ SU(2) we define the unitary mappings  Umat(U) =  N  �  j=1  Up,sj(U)  U(U) = Umat(U) ⊗ Uf(π(U))  on the Hilbert spaces Hmat and Hmat ⊗Fs(g), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' This defines a representation of  SU(2) on these Hilbert spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' The next proposition collects elementary properties, which  follow directly from the definitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  12  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' The map Uf is a unitary representation of R ∈ SO(3), and the maps  Umat, and U are unitary representations of SU(2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Remark 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' By abuse of notation we denote the unitary representation Uf ◦ π on SU(2)  also by Uf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Let R ∈ SO(3) and κ(R·) = κ(·).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Then  (a)  Uf(R)A(x)U∗  f (R) = R−1A(Rx),  (b)  Uf(R)B(x)U∗  f (R) = R−1B(Rx),  (c)  Uf(R)E⊥(x)U∗  f (R) = R−1E⊥(Rx).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' We observe that for R ∈ SO(3) we find  (Uv(R)vx,b)(y) = Rvx,b(R−1y) =  3  �  b′=1  Rb′,bvRx,b′(y),  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='11)  where we used Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='4 (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Using Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='4) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='11) as well as Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='2 we obtain  Uf(R)a#(g(ε)  x,b)U∗  f (R) = a#(Ug(R)g(ε)  x,b) = a#(τ −1  ε Uv(R)τεg(ε)  x,b)  = a#(τ −1  ε Uv(R)vx,b) =  3  �  b′=1  Rb′,ba#(τ −1  ε vRx,b′)  =  3  �  b′=1  Rb′,ba#(g(ε)  Rx,b′)  This implies  Uf(R)Ab(x)U∗  f (R) =  3  �  b′=1  Rb′,bAb′(Rx).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Thus (a) follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Now (b) follows from (a) and by calculating the rotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' (c) Follows  similarly as (a) observing that ω is invariant under rotations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Let U ∈ SU(2) and R = π(U).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Then the following holds  (a)  U(U)ˆxjU(U)∗ = R−1ˆxj,  (b)  U(U)pjU(U)∗ = R−1pj,  (c)  U(U)�SjU(U)∗ = R−1 �Sj,  (d)  U(U)A(ˆxj)U(U)∗ = R−1A(ˆxj),  if κ(R·) = κ(·),  (e)  U(U)B(ˆxj)U(U)∗ = R−1B(ˆxj),  if κ(R·) = κ(·),  (f)  U(U)E⊥(ˆxj)U(U)∗ = R−1E⊥(ˆxj),  if κ(R·) = κ(·),  (g)  U(U)HfU(U)∗ = Hf,  (h)  U(U)PfU(U)∗ = R−1Pf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  13  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Parts (a), (b), and (c) are straight forward to verify.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Parts (d)-(f) follow from (a)  and Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Next we show (g) and (h).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Using Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='3 and the identity (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='5) we  find for any measurable f : R3 → R and U ∈ SU(2) with R = π(U)  U(U)dΓ(Mf)U(U)∗ = dΓ(τ −1  ε Uv(π(U))τεMfτ −1  ε U∗  v (π(U))τε)  = dΓ(τ −1  ε Uv(R)F −1MfFU∗  v (R)τε)  = dΓ(τ −1  ε F −1Mf◦R−1Fτε)  = dΓ(Mf◦R−1)  Now choosing f = ω or f : k �→ kj Parts (g) and (h) follow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  In the following proposition we give a formula for the action of the rotation transfor-  mation in g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' For R ∈ SO(3) define  DU  λ,λ′(R;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' k) := (R−1ε(k, λ)) · ε(R−1k, λ′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Then for R ∈ SO(3)  DU  λ,λ′(R−1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' k) = DU  λ′,λ(R;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Rk)  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='12)  and the following holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (a) For any h ∈ g  (Ug(R)h)(k, λ) =  �  λ′=1,2  DU  λ,λ′(R;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' k)h(R−1k, λ′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='13)  (b) In the sense of operator valued distributions for all (k, λ) ∈ R3 × Z2  Uf(R)a#(k, λ)Uf(R)∗ =  �  λ′=1,2  DU  λ,λ′(R−1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' k)a#(Rk, λ′)  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Equation (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='12) follows from a straight forward calculation using that the elements  of SO(3) preserve the inner product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Now we prove (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Using the property (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='4) of the  Fourier transform, we find  (Ug(R)h)(k, λ) = ε(k, λ) · F  �  F −1 �  λ′=1,2  Rε(·, λ′)h(·, λ′)  �  (R−1k)  =  �  λ′=1,2  ε(k, λ) · Rε(R−1k, λ′)h(R−1k, λ′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  14  (b) We have by linearity and (a)  �  λ=1,2  �  R3 h(k, λ)Uf(R)a∗(k, λ)U∗  f (R)dk = Uf(R)a∗(h)U∗  f (R) = a∗(Ug(R)h)  =  �  λ=1,2  �  R3(Ug(R)h)(k, λ)a∗(k, λ)dk  =  �  λ,λ′=1,2  �  R3 DU  λ,λ′(R;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' k)h(R−1k, λ′)a∗(k, λ)dk  =  �  λ,λ′=1,2  �  R3 DU  λ′,λ(R;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Rk)h(k, λ)a∗(Rk, λ′)dk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Since h ∈ g is arbitrary the claim follows for a∗(k, λ) in view of (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Taking adjoints  the claim then follows also for a(k, λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='3  Parity Symmetry  Parity is the operation x �→ −x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' On the particle space we define  Pp,s : L2(R3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Ds) → L2(R3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Ds),  ψ �→ (x �→ ψ(−x))  for s = 0, 1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' On the photon space we define  Pv : v → v,  v �→ (x �→ −v(−x)),  and  Pg = τ −1  ε Pvτε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  We define  Pmat =  N  �  j=1  Pp,sj,  Pf = Γ(Pg),  P = Pmat ⊗ Pf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' The maps Pmat, Pf and P are unitary and commute with the repre-  sentations Umat, Uf and U, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' The unitarity property is straight forward to verify.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' The commutativity follows from  the commutativity of Pp with Up and Pv with Uv, which are straight forward to verify.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Suppose κ(−·) = κ(·).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Then  (a)  PfA(x)P∗  f = −A(−x),  (b)  PfB(x)P∗  f = B(−x),  (c)  PfE⊥(x)P∗  f = −E(−x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  15  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' We observe that for S = −1I3×3 we find from (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='10)  (Pvvx,b)(y) = −vx,b(−y) = −v−x,b(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='14)  Now we find similar as in the proof of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='7 using Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='2 and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='14)  Pfa#(g(ε)  x,b))P∗  f = a#(Pgg(ε)  x,b) = a#(τ −1  ε Pvτεg(ε)  x,b)  = a#(τ −1  ε Pvvx,b) = a#(−τ −1  ε v−x,b)  = −a#(g(ε)  −x,b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  This implies  PfAb(x)P∗  f = −Ab(−x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Thus (a) follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Now (b) follows from (a) and by calculating the rotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' (c) Follows  similarly as in (a) observing that ω(−·) = ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  In view of the following proposition we see that P has the physical interpretation of  parity inversion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' P has satisfies the following properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (a)  PˆxjP = −ˆxj,  (b)  PpjP∗ = −pj,  (c)  P �SjP∗ = �Sj,  (d)  PA(ˆxj)P∗ = −A(ˆxj),  if κ(−·) = κ(·),  (e)  PB(ˆxj)P∗ = B(ˆxj),  if κ(−·) = κ(·),  (f)  PE⊥(ˆxj)P∗ = −E⊥(ˆxj),  if κ(−·) = κ(·),  (g)  PHfP∗ = Hf,  (h)  PPfP∗ = −Pf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' The proof is analogous to that of Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  In the following proposition we give a formula for the action of the parity in g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' The map Pg has the following properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Define  DP  λ,λ′(k) := −ε(k, λ) · ε(−k, λ′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Then DP  λ,λ′(k) = DP  λ′,λ(−k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (a) For any h ∈ g we have for almost all (k, λ) ∈ R3 × {1, 2}  (Pgh)(k, λ) =  �  λ′=1,2  DP  λ,λ′(k)h(−k, λ′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  16  (b) We have in the sense of operator valued distributions for all (k, λ) ∈ R3 × Z2  Pfa#(k, λ)P∗  f =  �  λ′=1,2  DP  λ,λ′(k)a#(−k, λ′)  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' The first statement follows from the symmetry of the scalar product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' (a) Using  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='4), we find  (Pgh)(k, λ) = ε(k, λ) · F  �  F −1 �  λ′=1,2  (−ε(·, λ′))h(·, λ′)  �  (−k)  =  �  λ′=1,2  (−ε(k, λ)) · ε(−k, λ′)h(−k, λ′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (b) We have by linearity and (a)  �  λ=1,2  �  h(k, λ)Pfa∗(k, λ)P∗  f dk = Pfa∗(h)P∗  f = a∗(Pgh)  =  �  λ=1,2  �  R3(Pgh)(λ, k)a∗(k, λ)dk  =  �  λ,λ′=1,2  �  R3 DP  λ,λ′(k)a∗(k, λ)h(−k, λ′)dk  =  �  λ,λ′=1,2  �  R3 DP  λ′,λ(−k)a∗(−k, λ′)h(k, λ′)dk  Since h ∈ g is arbitrary the claim follows for a∗(k, λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Taking adjoints the claim then  follows also for a(k, λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='4  Time reversal symmetry  We define time reversal symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Let K denote complex conjugation on L2(R3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Ds).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Define the operators  Tp,s :=  � K  ,  if  s = 0,  (Kσ2)  ,  if  s = 1/2  and  Tmat :=  N  �  j=1  Tp,sj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Let Kv denote complex conjugation in v, and let  Kg = τ −1  ε Kvτε  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='15)  17  denote its action on g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Next we define operator of time reversal on the quantum field  Tf := Γ(−Kg).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='16)  We define the operator of time reversal in the full Hilbert space by  T = Tmat ⊗ Tf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='17)  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' The maps Tmat, Tf, and T are anti-unitary operators, which commute  with the representations Umat, Uf, and U and the operators Pmat, Pf, and P, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  We have T 2  f = 1, and  T 2  mat = (−1)  �N  j=1 2sj,  T 2 = (−1)  �N  j=1 2sj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' The anti-unitarity is straight forward to verify on the one particle spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' On the  tensor product it then follows by Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' The commutativity can be seen by verifying  it on the one particle spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' The last statement follows from  T 2  mat =  N  �  j=1  (Tmat,sj)2  with (Tmat,0)2 = 1 and (Tmat,1/2)2 = (Kσ2)(Kσ2) = K2σ2(−σ2) = −1,  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Suppose κ(·) = κ(−·).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Then the following holds  (d)  TfA(x)T ∗  f = −A(x),  (e)  TfB(x)T ∗  f = −B(x),  (e)  TfE⊥(x)T ∗  f = E⊥(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' It follows directly from the definition, a trivial change of variables, and the assump-  tion about κ that  (Kvvx,b)(y) = vx,b(y) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='18)  Now we find using Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='2  Γ(−Kg)a∗(g(ε)  x,b)Γ(−Kg)∗ = a∗(−Kgg(ε)  x,b) = −a∗(τ −1  ε Kvτεg(ε)  x,b)  = −a∗(τ −1  ε Kvvx,b) = −a∗(τ −1  ε vx,b)  = −a∗(g(ε)  x,b)  This implies Tfa∗(g(ε)  x,b)T ∗  f = −a∗(g(ε)  x,b) and by taking adjoints Tfa(g(ε)  x,b)T ∗  f = −a(g(ε)  x,b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Hence  TfAb(x)T ∗  f = −Ab(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  This shows (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Now (b) follows from (a) and by calculating the rotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' (c) Follows  similarly as in (a) observing that iω changes sign when complex conjugating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  18  In view of the following proposition we see that T has the physical interpretation of  time reversal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Suppose κ(·) = κ(−·).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Then T is anti-unitary and satisfies the follow-  ing properties  (a)  T ˆxjT ∗ = ˆxj,  (b)  T pjT ∗ = −pj,  (c)  T �SjT ∗ = −�Sj,  (d)  T A(ˆxj)T ∗ = −A(ˆxj),  if κ(−·) = κ(·),  (e)  T B(ˆxj)T ∗ = −B(ˆxj),  if κ(−·) = κ(·),  (f)  T E⊥(ˆxj)T ∗ = E⊥(ˆxj),  if κ(−·) = κ(·),  (g)  T HfT ∗ = Hf,  (h)  T PfT ∗ = −Pf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Parts (a), (b), and (c) are straight forward to verify.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Parts (d), (e), and (f) follow  from Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Using Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='3 we find for any measurable f : R3 → R  TfdΓ(Mf)T ∗  f = dΓ(τ −1  ε KvτεMfτ −1  ε K∗  vτε)  = dΓ(τ −1  ε KvF −1MfFK∗  vτε)  = dΓ(τ −1  ε F −1Mf(−·)Fτε)  = dΓ(Mf(−·)),  where in the third equality we used that the Fourier transform satisfies the following prop-  erties Fϕ = Fϕ(−·) and F −1ϕ = F −1ϕ(−·) for ϕ ∈ L2(R3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Now choosing f = ω or  f : k �→ kj Parts (g) and (h) follow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  In the following proposition we give a formula for the action of the time reversal sym-  metry in g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' For h ∈ g we have for almost all (k, λ) ∈ R3 × {1, 2}  (Kgh)(k, λ) =  �  λ′=1,2  DT  λ,λ′(k)h(−k, λ′),  where DT  λ,λ′(k) := ε(k, λ)·ε(−k, λ′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Then DT  λ,λ′(k) = DT  λ′,λ(−k) and in the sense of operator  valued distributions for all (k, λ) ∈ R3 × Z2  Tfa#(k, λ)T ∗  f = −  �  λ′=1,2  DT  λ,λ′(k)a#(−k, λ′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  19  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Using for ϕ ∈ L2(R3) the following property of the Fourier transform F(F −1ϕ)(k) =  ϕ(−k), we find  (Kgh)(k, λ) = ǫ(k, λ) · F  �  F −1 �  λ′=1,2  ε(·, λ′)h(·, λ′)  �  (k)  =  �  λ′=1,2  ε(k, λ) · ε(−k, λ′)h(−k, λ′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  This shows the first identity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Using this, we find by anti-linearity  �  λ=1,2  �  h(k, λ)Tfa∗(k, λ)T ∗  f dk = Tfa∗(h)T ∗  f = a∗(−Kgh)  = −  �  λ=1,2  �  R3(Kgh)(λ, k)a∗(k, λ)dk  = −  �  λ,λ′=1,2  �  R3 h(−k, λ′)DT  λ,λ′(k)a∗(k, λ)dk  = −  �  λ,λ′=1,2  �  R3 h(k, λ)DT  λ′,λ(−k)a∗(−k, λ′)dk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Since h ∈ g is arbitrary the second identity follows for a∗(k, λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Taking adjoints the claim  then follows also for a(k, λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  5  Hamiltonians with Symmetries  In this section we consider Hamiltonians of non-relativistic qed, and discuss their symmetry  properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Suppose U ∈ SU(2), R = π(U), V (x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', xN) = V (Rx1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', RxN) for all  x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', xN ∈ R3, Bext(x) = RBext(R−1x) for all x ∈ R3, and κ(R·) = κ(·).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Then  U(U)HU(U)∗ = H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Using (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='11), properties of the cross product, a change of variables, and the sym-  metry properties of Bext we find  RAext(R−1x) = −  � (x − Ry) × RBext(y)  4π|x − Ry|3  dy = Aext(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Thus using Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='8  U(U)HU(U)∗  =  N  �  j=1  � 1  2mj  �  R−1pj + qj(R−1A(ˆxj) + Aext(R−1ˆxj))  �2 + µjR−1 �Sj · (R−1B(ˆxj) + Bext(R−1ˆxj))  �  + Hf + V (R−1ˆx1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', R−1ˆxN)  = H,  20  where in the last line we used the assumed properties of Bext and V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Suppose V (x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', xN) = V (−x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', −xN) for all x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', xN ∈ R3, Bext(·) =  Bext(−·), and κ(−·) = κ(·).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Then  PHP∗ = H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Using (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='11), the properties of the cross product, a change of variables, and the  symmetry properties of Bext we find  Aext(−x) = −  � (−(x − y)) × Bext(−y)  4π|x − y|3  dy = −Aext(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Thus we find from Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='12  PHP∗  =  N  �  j=1  � 1  2mj  (−pj − qjA(ˆxj) + qjAext(−ˆxj)))2 + µj �Sj · (B(ˆxj) + Bext(−ˆxj))  �  + Hf + V (−ˆx1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', −ˆxN)  = H,  where in the last line we used the assumed properties of Bext and V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Suppose Bext = 0 and κ(·) = κ(−·).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Then  T HT ∗ = H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' We find from Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='16  T HT ∗ =  N  �  j=1  � 1  2mj  (−pj − qjA(ˆxj))2 + µj �Sj · B(ˆxj)  �  + Hf + V (ˆx1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', ˆxN) = H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' If V (x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', xN) = V (−x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', −xN) for all x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', xN ∈ R3, Bext(·) =  −Bext(−·), and κ(·) = κ(−·) = κ(·).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Then  T PH(T P)∗ = H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Using (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='11), the properties of the cross product, a change of variables, and the  symmetry properties of Bext we find  Aext(−x) = −  � (−(x − y)) × Bext(−y)  4π|x − y|3  dy = Aext(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  21  Thus we find from Propositions 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='12 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='16  T PHP∗ T ∗  = T  �  N  �  j=1  � 1  2mj  (−pj − qjA(ˆxj) + qjAext(−ˆxj))2 + µj �Sj · (B(ˆxj) + Bext(−ˆxj))  �  + Hf + V (−ˆx1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', −ˆxN)  �  T ∗  =  N  �  j=1  � 1  2mj  (pj + qjA(ˆxj) + qjAext(ˆxj)))2 + µj �Sj(B(ˆxj) − Bext(−ˆxj))  �  + Hf + V (−ˆx1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', −ˆxN)  = H,  where we used the assumed properties of Bext and V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  As an application of the abstract Kramer theorem, we now show the following degen-  eracy result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Suppose �N  j=1 2sj is odd, and that at least one of the following two assump-  tions hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (i) Bext = 0 and κ(·) = κ(−·)  (ii) V (−x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', −xN) = V (x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', xN) and Bext(−x) = −Bext(x), and κ(·) = κ(−·) = κ(·).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Then, any eigenvalue of H is at least two fold degenerate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' If the multiplicity of an eigenvalue  is finite, it is even.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' In case (i) the assertion follows from Kramers degeneracy theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='4 for θ =  T , Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='14, and Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' In case (ii) the assertion follows from Kramers  degeneracy theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='4 for θ = T P, Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='14, and Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Remark 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (a) We note that Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='5 for the case N = 1, s1 = 1/2, and (i) with the additional  assumption V (−x) = V (x) was shown in [20, 21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Thus Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='5 relaxes the  unnecessary parity-symmetry assumption for the external potential V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' In fact, the  proof given in [20] uses the symmetry PT , while the proof in [21] uses the symmetry  T in the so called Schr¨odinger representation, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Section 7 of this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (b) Since the classical Kramer theorem uses time inversion symmetry it cannot be applied  to situations with external magnetic fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' However if one considers the anti-linear  symmetry PT one can include external magnetic fields, which satisfy a symmetry  condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' We note that the result (ii) also holds for an ordinary Schr¨odinger oper-  ator without any quantized electromagnetic field, as the proof also applies to such a  situation with a straight forward (trivial) modification of the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  22  Next we consider the restriction to symmetric subspaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' To this end we introduce  notation satisfying the following hypothesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Hypothesis A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' The set P = {p1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='., pL}, L ∈ N ∩ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', N}, is a partition of {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='., N}  such that on each element p ∈ P of the partition the numbers mj, sj, qj, and µj are equal  (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='10)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' The function τ maps P to {0, 1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' The potential V is symmetric with respect  to interchange of particle coordinates of particles which belong to the same element p ∈ P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Remark 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' The function τ in Hypothesis A is used to specify the statistics of identical  particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  The value 0 will be used to describe bosons while the value 1 will be used  describe fermions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' By physical laws, spin zero particles are bosons while spin 1/2 particles  are fermions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  For a finite set S we shall denote by SS the set of all permutations of the set S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' For  a subset S ⊂ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', N} and σ ∈ SS we denote by σ its extension to {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', N} by setting  it equal to the identity on {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='., N} \\ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Suppose the partition P satisfies Hypothesis A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Then for any p ∈ P and σ ∈ Sp it follows that U(σ), defined in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='1), leaves Hmat invariant,  and we can define the subspace  Hmat,P,τ = {ψ ∈ Hmat : ∀p ∈ P, ∀σ ∈ Sp, U(σ)ψ = sgn(σ)τ(p)ψ},  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='1)  where sgn(σ) defines the signum of the permutation σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Furthermore, it follows from the  definitions that U(σ) commutes with the symmetries Umat, Pmat, Tmat as well as the Hamil-  tonian H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' In particular, Hmat,P,τ ⊗ Fs(g) is an invariant subspace of H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Suppose that the partition P, the function τ and the potential V , satisfy  Hypothesis A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Suppose �N  j=1 2sj is odd, and (i) or (ii) of Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='5 holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Then, any  eigenvalue of H|Hmat,P,τ ⊗Fs(g) has even or infinite multiplicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Follows from the same proof as Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='5, by observing in addition that T and  P commute with U(σ) for any σ ∈ Sp and p ∈ P, and thus leave Hmat,P,τ invariant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Remark 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' We note that Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='8 for the special case P = {p} with p = {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='., N},  sj = 1/2 for all j ∈ p, and τ(p) = 1, and with the additional assumption that V is given  by the Coulomb potential of N electrons in the presence of the electric field of a nucleus  was shown in [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  6  Translationally invariant Hamiltonians  We write the Hamiltonian (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='10) acting in the Hilbert space Hmat ⊗ Fs(g) in the following  notation  H =  N  �  j=1  Tj + Hf + V (�x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', �xN),  Tj :=  1  2mj  (pj + qjA(�xj))2 + µj �Sj · B(�xj),  23  and we assume that there is no external magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Furthermore, we assume that the  potential V in the definition of the Hamiltonian (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='10) is translationally invariant, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', that  for all a ∈ R3  V (x1 + a, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', xN + a) = V (x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', xN).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='1)  Using the unitary transformation  U = exp(ixN · (Pf +  N−1  �  j=1  pj))  and a Fourier transform in the variable xN we can write  H =  � ⊕  R3 H(ξ)dξ,  where  H(ξ) :=  1  2mN  (ξ −  N−1  �  j=1  pj − Pf + qNA(0))2 + µN �SN · B(0) +  N−1  �  j=1  Tj + Hf + V (�x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', �xN−1, 0)  acts in  H′  mat ⊗ DsN ⊗ Fs(g),  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='2)  where  H′  mat :=  N−1  �  j=1  L2(R3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Dsj),  cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' [10,19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' We define U′  mat, P′  mat, and T ′  mat on H′  mat as in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' On (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='2) we define the  symmetries  U′(U) := U′  mat(U) ⊗ DsN(U) ⊗ Uf(π(U)),  U ∈ SU(2)  P′ := P′  mat ⊗ 1IDsN ⊗ Pf  T ′ := T ′  mat ⊗ T ′  p,s ⊗ Tf,  where we defined  T ′  p,s :=  � Ks  ,  if  s = 0,  (Ksσ2)  ,  if  s = 1/2  where Ks denotes complex conjugation on Ds = C2s+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Lemma 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Suppose V is translationally invariant, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (a) Let U ∈ SU(2), R = π(U), V (Rx1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', RxN, 0) = V (x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', xN, 0) for all xj ∈ R3, and  κ(·) = κ(R·).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Then for all ξ ∈ R3  U′(U)H(ξ)U′(U)∗ = H(Rξ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  24  (b) Let V (x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', xN−1, 0) = V (−x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', −xN−1, 0) for all xj ∈ R3 and κ(·) = κ(−·).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Then  for all ξ ∈ R3  P′H(ξ)P′∗ = H(−ξ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (c) If κ(·) = κ(−·), then for all ξ ∈ R3  T ′H(ξ)T ′∗ = H(−ξ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' The Lemma follows as a consequence of Lemmas 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='7, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='11, and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='15 and Proposi-  tions 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='8, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='12, and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='16, respectively, and their trivial adaption to (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Suppose V is translationally invariant and �N  j=1 2sj is odd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' If κ(·) = κ(−·)  each eigenvalue of H(0) has even or infinite multiplicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' If in addition V (x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', xN−1, 0) =  V (−x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', −xN−1, 0) for all xj ∈ R3 and κ(−·) = κ(·), then for all ξ ∈ R3 each eigenvalue  of H(ξ) has even or infinite multiplicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' The theorem follows as a consequence of Parts (c) and (b) of Lemma 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='1, The-  orem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  The first statement follows using the anti-linear symmetry T ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  The second  statement follows using the anti-linear symmetry P′T ′ and their commutativity property,  cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='14 and its trivial adaption to (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Next we consider quantum systems with identical particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' For notational simplicity,  we shall assume that there is a single particle which is distinguishable from the rest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' This is  satisfied for atoms, ions and many molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Otherwise, a further restriction to subspaces  would be necessary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Suppose V is translationally invariant and �N  j=1 2sj is odd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Suppose that  the partition P, the function τ and the potential V , satisfy Hypothesis A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Furthermore,  assume {N} ∈ P and let P′ = P \\ {{N}} and τ ′ = τ|P′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' If κ(·) = κ(−·) each eigenvalue  of H(0) when restricted to H′  mat,P′,τ ′ ⊗ DsN ⊗ Fs(g) has even or infinite multiplicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' If in  addition V (x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', xN−1, 0) = V (−x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', −xN−1, 0) for all xj ∈ R3 and κ(−·) = κ(·), then  each eigenvalue of H(ξ) when restricted to H′  mat,P′,τ ′ ⊗ DsN ⊗ Fs(g) has even or infinite  multiplicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Follows from the same proof as Theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='2, by observing in addition that T ′ and  P′ commute with U(σ) for any σ ∈ Sp and p ∈ P′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Remark 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' We note that the statement of Theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='2 was proven for the special case  where N = 1 and V = 0 for small coupling in [16] and for general coupling in [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Clearly,  Theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='3 covers the special case of N −1 electrons with spin 1/2 and a spinless nucleus  with pairwise Coulomb interactions (P = {{1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='., N − 1}, {N}}), cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Remark 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='2 in [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  We note that whereas ground states of fiber Hamiltonians describing electrons do not exist  for nonzero momentum [10], they are shown to exist for atoms and small absolute values  of the momentum [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  25  7  Schr¨odinger Representation  In this section we define rotation, parity and time reversal symmetry in the so called  Schr¨odinger representation of non-relativistic qed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  To this end, we recall the Schwartz  space of smooth functions of rapid decrease S(Rd;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' F), with F = R or F = C, which is the  set of infinitely differentiable F-valued functions f(x) on Rd for which  ∥f∥α,β = sup  x∈Rd |xα∂βf(x)| < ∞  (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='1)  for all α, β ∈ Nd  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Let S = S(R3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' R)3 equipped with the product topology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' The topological  dual space S′ can be identified with the set of all T ∈ S′(R3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' R)3, with T(f) = T1(f1) +  T2(f2) + T3(f3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  On S we define the symmetric positive semi-definite form  B(v, w) =  �  i,j  �  1  |k|ˆvi(k)Pi,j(k) ˆwj(k)d3k,  (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='2)  where we recall  P(k)a,b := δab − kakb  |k|2 ,  a, b = 1, 2, 3,  k ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='3)  Let  c(f) = e− 1  4 B(f,f)  for f ∈ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  By definition a cylinder set in S′ is a set  {T ∈ S′ : (T(f1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='., T(fn)) ∈ Ω},  where f1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', fn are n fixed elements in S and Ω is a fixed Borel set in Rn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' A cylinder  set measure on S′ is a measure, µ, on the σ-algebra, generated by the cylinder sets, with  µ(S′) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' By construction, each f ∈ S defines a measurable function ϕ(f) on S′ by  ϕ(f)(T) = T(f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='4)  In particular it follows that for all α, β ∈ R and f, g ∈ S  ϕ(αf + βg) = αϕ(f) + βϕ(g).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='5)  We shall use the following theorem, see [5,6,7,8,9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' There exists a unique cylinder set measure ν on S′ such that for all f ∈ S  exp(−1  4B(f, f)) =  �  exp(iϕ(f))dν  (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='6)  Furthermore, ν has the following properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  26  (a) For each f ∈ S the function ϕ(f) is a Gaussian random variable with mean zero and  variance 1  2B(f, f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (b) For f1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='fn ∈ S the random variables ϕ(f1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', ϕ(fn) are jointly Gaussian random  variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (c) Let U = {F(ϕ(f1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', ϕ(fn)) : F ∈ S(Rn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' C), f1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', fn ∈ S}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Then U is dense in  L2(S′, dν).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (d) If f ∈ S and P �f = 0, then ϕ(f) = 0 almost surely, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' In particular, for  almost all T = (T1, T2, T3) ∈ S′ we have ∇ · T = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  A proof of Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='1 will be given in Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Henceforth, we shall denote by ν  the unique measure on S′ satisfying (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Remark 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' We note that part (d) of Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='1 will not be needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Nevertheless it is  interesting in its own.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  To formulate the next theorem we define  S0 := {g ∈ S : ∇ · g = 0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  By ( · )  cl we shall denote the operator closure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' There exists a unique unitary transformation Vv : Fs(v) → L2(S′, dν) with  the following properties  (i) VvΩ = 1,  (ii) Vv(a∗(iωf) + a(iωf))  clV −1  v  = ϕ(f), for all f ∈ S0,  where iωf = (ω−1/2 ˆf)∨ and ϕ(f) is understood as a multiplication operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Moreover, we  have VvΓ(Kv) = JVv, where J denotes complex conjugation in L2(S′, dν).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  The proof of Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='3 will be given in Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Using Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='1 we obtain  immediately the following corollary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Corollary 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Let the notation be as in in Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' There exists a unique unitary  transformation Vg : Fs(g) → L2(S′, dν) with the following properties  (i) VgΩ = 1,  (ii) Vg(a∗(τ −1  ǫ iωf) + a(τ −1  ǫ iωf))  clV −1  g  = ϕ(f), for all f ∈ S0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Moreover, we have VgΓ(Kg) = JVg, where J denotes complex conjugation in L2(S′, dν).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  27  Next we define symmetries in Schr¨odinger representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' We will show in Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='6,  below, that they agree by the unitary transformations of Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='3 and Corollary 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='4  with the definitions in Fock space representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  We define for U ∈ SU(2) on S the  representation  (US(U)f)(x) = Rf(R−1x),  f ∈ S, x ∈ R3,  where R = π(U).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' We define for f ∈ S  (PSf)(x) = −f(−x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  As a consequence of the definition P−1  S  = PS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Then this defines by duality a transformation  on S′ by  (US′(U)T)(f) = T(US(U)−1f)  and  (PS′T)(f) = T(P−1  S f),  for all T ∈ S′ and f ∈ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' On L2(S′, dν) we define for any F ∈ L2(S′, dν)  (USch(U)F)(T) = F(US′(U)−1T),  U ∈ SU(2),  (PSchF)(T) = F(P−1  S′ T),  (KSchF)(T) = F(T)  (ΘSchF)(T) = F(−T)  for all T ∈ S′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Lemma 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Let U ∈ SU(2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' The measure ν is invariant with respect to US′(U) and  PS′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' The transformations USch(U), PSch are unitary transformations on L2(S′, dν).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' The  transformation KSch is an anti-unitary transformation on L2(S′, dν), which squares to one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  The measure ν is invariant with respect to −1S′, and ΘSch is a unitary transformation on  L2(S′, dν), which squares to one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Let G stand for US′(U) and PS′ and g for US(U) and PS, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Then G  leaves the set of cylinder sets invariant, and hence the σ-algebra generated by the cylinder  sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Since the form B is invariant with respect to G, so is the measure ν.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' To see this  define νG(A) = ν(G(A)) for any measurable set A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Then for any f ∈ S we find from the  definition of the integral  exp(−1  4B(f, f)) = exp(−1  4B(gf, gf)) =  �  exp(iϕ(gf))dν =  �  exp(i(G−1T)(f))dν(T)  =  �  exp(iT(f))dνG(T) =  �  exp(iϕ(f))dνG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Thus it follows ν = νG from the uniqueness property in Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Thus the unitarity  properties of USch(U) and PSch on L2(S′, dν) now follow by the definition of the integral as  a limit of simple functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' The anti-unitarity of KSch is obvious.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' The last statement about  ΘSch follows analogously as above with G = −1S′ and g = −1S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  28  The following theorem relates the symmetries in the Fock representation to the sym-  metries in the Schr¨odinger representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Let Vv and Vg be the unique unitary transformations satisfying (i) and (ii)  of Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='3 and Corollary 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='4, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Then the following identities hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (a) VgUf(U)V −1  g  = USch(U) and VvΓ(Uv(π(U))V −1  v  = USch(U), for U ∈ SU(2),  (b) VgPfV −1  g  = PSch and VvΓ(Pv)V −1  v  = PSch,  (c) VgΓ(Kg)V −1  g  = KSch and VvΓ(Kv)V −1  v  = KSch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (d) VgΓ(−1g)V −1  g  = ΘSch and VvΓ(−1v)V −1  v  = ΘSch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (e) VgTfV −1  g  = ΘSchKSch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' We only discuss the case for v, the case for g then follows using Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (a) Let W = USch(U)VvΓ(Uv(π(U))−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Then it follows from the definitions that WΩ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Furthermore, it follows for all f ∈ S0 using (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='4), the invariance of ω and Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='3 (ii)  W(a∗(iωf) + a(iωf))clW −1 = USch(U)Vv(a∗(iωUv(U)−1f) + a(iωUv(U)−1f))clV −1  v  USch(U)−1  = USch(U)ϕ(Uv(U)−1f)USch(U)−1 = ϕ(f),  (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='7)  where the last equality can be seen as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  For any F ∈ L2(S′, dν) we find with  F ′ := USch(U)−1F using Uv(U)f = US(U)f and inserting into the definitions, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='4),  that  (USch(U)(ϕ(Uv(U)−1f)F ′))(T) = (ϕ(US(U)−1f)F ′)(US′(U)−1T)  = (US′(U)−1T)(US(U)−1f)F ′(US′(U)−1T)  = T(f)F ′(US′(U)−1T) = ϕ(f)F(T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  This show the last equality in (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  It now follows from (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='7) that W = Vv by the  uniqueness statement of Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' This shows (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Now (b) is shown similarly as (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (c) Let W = KSchVvΓ(Kv).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Then it follows from the definitions that WΩ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Furthermore,  it follows for all f ∈ S0 using (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='4), the reality and symmetry assumptions of ω, and  Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='3 (ii) that  W(a∗(iωf) + a(iωf))clW −1 = KSchVv(a∗(Kviωf) + a(Kviωf))clV −1  v  K−1  Sch  = KSchVv(a∗(iωKvf) + a(iωKvf))clV −1  v  K−1  Sch  = KSchϕ(Kvf)K−1  Sch = ϕ(f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  As in (a) it now follows that W = Vv by the uniqueness statement of Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' This  shows (c), since K−1  v  = Kv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Now (d) follows analogously to (c) by considering W =  29  ΘSchVvΓ(−1v) and observing that  W(a∗(iωf) + a(iωf))clW −1 = ΘSchVv(a∗(−iωf) + a(−iωf))clV −1  v  Θ−1  Sch  = ΘSchVv(a∗(iω(−f)) + a(iω(−f))clV −1  v  Θ−1  Sch  = ΘSchϕ(−f)Θ−1  Sch = ϕ(f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Again by uniqueness W = Vv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' This shows (d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Finally, (e) follows from (c) and (d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Remark 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' We see from Subsection 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='4 and Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='6 that USch, PSch and TSch :=  ΘSchKSch correspond to the rotation, parity and time reversal symmetries in the Schr¨odinger  representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Alternatively, one could redefine the field operators in the Hamiltonian so  that KSch has the property of a time reversal symmetry, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Acknowledgements  Both authors acknowledge financial support by the Research Training Group (1523/2)  “Quantum and Gravitational Fields” when this project was initiated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Hasler wants  to thank I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Herbst for valuable discussions on the subject.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Lange also acknowledges  financial support from the European Research Council (ERC) under the European Union’s  Horizon 2020 research and innovation programme (ERC StG MaMBoQ, grant agreement  n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='802901).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  A  Gaussian Random Processes  In this appendix we review notations and results about so called Gaussian random pro-  cesses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' We follow [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' The main result is Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='6, which will be used in the proof of  Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='3 in Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' First we introduce the following definitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Definition A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Let (M, µ) be a probability measure space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Let V be a real vector space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  A random process indexed by V is a map φ from V to the random variables on M, so  that almost everywhere  φ(v + w) = φ(v) + φ(w)  ∀v, w ∈ V  φ(αv) = αφ(v)  ∀α ∈ R, ∀v ∈ V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  For a random variable Y on probability measure space (M, µ) we will use the notation  ⟨Y ⟩ :=  �  Y dµ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Definition A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Let r be a real Hilbert space with inner product ⟨·, ·⟩r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  A Gaussian  random process indexed by r is a random process φ indexed by r so that the following  holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  30  (a) The set {F(φ(v1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', φ(vn)) : v1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', vn ∈ r, F ∈ S(Rn)} is dense in L2(M, dµ), where  (M, µ) is the probability measure space of the random process φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (b) Each φ(v) is a Gaussian random variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (c) ⟨φ(v)φ(w)⟩ = 1  2⟨v, w⟩r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Remark A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (a) We note that in (a) of Definition A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='2, we use a different assumption than in the  definition of a Gaussian random process indexed by a Hilbert space in [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' However,  in view of [26, Lemma I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='5] this is equivalent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (b) One can show that two Gaussian random processes indexed by the same real Hilbert  space are unique up to isomorphisms of probability measure spaces, see for example  [26, Theorem I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (c) For any real Hilbert space r, a Gaussian process indexed by r exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' For a proof see  Theorem I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='9 in [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Let r be the complexification of r, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', rC = r ⊕r as a real Hilbert space with a complex  structure given by i(u, v) = (−v, u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' We define  J : rC → rC,  J(u, v) = (u, −v).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='1)  Then J is anti-linear and satisfies J2 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Without mention we shall imbed r in rC by  the map ι : u �→ (u, 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' For the operator introduced in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='3) we shall write for notational  convenience a#(f) = a#(ιf) for f ∈ r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Next we introduce the notion of Wick powers and Wick product of random variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  To this end we introduce the following multi-index notation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' For k ∈ N, n ∈ Nk  0 and  α, β ∈ Ck we define  αn =  k  �  j=1  αnj,  αβ =  k  �  j=1  αjβj,  |n| =  k  �  j=1  nj,  n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' =  k  �  j=1  nj!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Given a formal power series in random variables f1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', fk with finite moments on a measure  space (M, µ), which we denote by �  n∈Nk  0 anf n, where an ∈ C and  f n :=  k  �  j=1  f  nj  j ,  we define the formal derivative  ∂  ∂fi  �  n∈Nk  0  anf n =  �  n∈Nk  0  annif n−ei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  where ei ∈ Nk is defined such that all components vanish except the i-th, which equals 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  31  Remark A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' As in [26] we don’t identify two series which are identical by virtue of  substituting in specific arguments (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' f and f 2 are distinct as formal power series even if  f = 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Definition A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Let f1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', fk be random variables with finite moments on a measure space  (M, µ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' The Wick product : f n : is defined inductively in n = |n| by  (i) : f 0 : = 1, where 0 = (0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='., 0),  (ii) ⟨: f n :⟩ = 0 if n ̸= 0,  (iii)  ∂  ∂fi : f n : = ni : f n−ei :  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  The following theorem is the main theorem of this section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Let φ be a Gaussian random process indexed by a separable real Hilbert  space r on the probability measure space (M, µ), and let D be a dense subset of r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Then  there exists a unique unitary transformation V : Fs(rC) → L2(M, dµ) satisfying  (i) V Ω = 1  (ii) V (a∗(f) + a(f))clV −1 = φ(f) for all f ∈ D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Moreover, the following holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' We have  (a) V (a∗(f) + a(f))clV −1 = φ(f) holds for all f ∈ r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (b) J V = V Γ(J), where J is defined in (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='1) and J denotes ordinary complex conjuga-  tion in L2(M, dµ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (c) For all fj ∈ r we have  V a∗(f1) · · ·a∗(fn)Ω =  : φ(f1) · · ·φ(fn) : .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='2)  A proof of Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='6 can be found in Theorems I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='6 and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='11 in [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' For the con-  venience of the reader, we shall outline a proof below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  First, we need a few lemmas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  For random variables f1, · · · , fk with finite moments we define the formal power series for  α ∈ Ck by  : exp(αf) : =  ∞  �  n∈Nk  0  αn : f n :  n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='3)  Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Let f1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', fk be random variables with finite moments on a probability mea-  sure space (M, µ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Then for all α ∈ Ck the following holds  (a) ⟨: exp(αf) :⟩ = 1  (b) : exp(αf) := exp(αf)⟨exp(αf)⟩−1  32  (c) If f is a Gaussian random variable, then (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='3) converges in L1(M, dµ) and  : exp(αf) := exp(αf) exp  �  −1  2  �  i,j  αiαj⟨fifj⟩  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' (a) This follows from (i) and (ii) of Definition A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' (b) By (iii) of Definition A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='5, we  find  ∂  ∂fj : exp(αf) := αj : exp(αf) :.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Thus  ∂  ∂fj : exp(αf) : exp(−αf) = 0 and so : exp(αf) :  exp(−αf) = C for some constant C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Thus from (a) it follows that C = ⟨exp(αf)⟩−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (c) The L1 convergence follows from dominated convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Using that f is Gaussian  one finds ⟨exp(αf)⟩ = exp( 1  2  �  i,j αiαj⟨fifj⟩) (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' by calculating the Fourier transform for  α = it, with t ∈ Rk, and then using analytic continuation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Thus (c) follows from (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  The following Lemma is from [26, Theorem I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='3, Corollary I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' The following holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (a) If f and g are Gaussian random variables, then for m, n ∈ N0  ⟨: f n :: gm :⟩ = δn,mn!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='⟨fg⟩n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (b) If f1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', fn and g1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', gm are Gaussian random variables and n ̸= m, then  ⟨: f1 · · ·fn :: g1 · · · gm :⟩ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (c) If f1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', fk are Gaussian random variables with ⟨fifj⟩ = δi,j, then for n, m ∈ Nk  0  ⟨: f n :: f m :⟩ = δn,mn!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' By (c) of Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='7 we find  : exp(αf) :: exp(βg) : = exp(αf + βg) exp  �  −1  2  �  α2⟨f 2⟩ + β2⟨g2⟩  ��  =: exp(αf + βg) : exp (αβ⟨fg⟩) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Thus by (a) of Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='7  ⟨: exp(αf) :: exp(βg) :⟩ = exp (αβ⟨fg⟩) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Thus (a) now follows by expanding exponentials and equating coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' (b,c) follow  from the multinomial theorem and (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Let φ be a Gaussian random process indexed by the real Hilbert space r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Let  Γn(r) = linC{: φ(f1) · · ·φ(fn) :  |  f1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', fn ∈ r}  cl,  n ∈ N  and Γ0(r) = C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Then the following holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  33  (a) Γn(r) ⊥ Γm(r) for n ̸= m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (b) L2(M, dµ) = �∞  n=0 Γn(r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' (a) This follows from (b) of Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' (b) For any f ∈ r, a direct computation  shows that the formal power series : eiφ(f) : converges in L2(M, dµ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' We shall denote the  limit by the same symbol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Thus by definition �∞  n=0 Γn(r) contains : eiφ(f) : and so eiφ(f) in  view of (c) of Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' In particular, for any F ∈ S(Rn) and f1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', fn ∈ r we find that  F(φ(f1), · · · , φ(fn)) = (2π)−n/2  �  �F(t) exp(  n  �  j=1  tjφ(fj))dnt  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='4)  is in �∞  n=0 Γn(r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' But the set of random variables of the form as on the left hand side of  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='4) are dense in L2(M, dµ) by the assumptions of an indexed Gaussian random process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Thus (b) follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Proof of Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' First we show uniqueness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' To this end we define for f ∈ rC the  operator φF(f) in Fs(rC) by  φF(f) = a∗(f) + a(f)  cl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='5)  We claim that for any m ∈ N0 the set  {φF(f1) · · · φF(fn)Ω : fi ∈ D, n = 0, 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', m}  is dense in �m  n=0 Sn(r⊗n  C ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' To show this, we use induction in m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' The claim clearly holds  for m = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Suppose it holds for m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Then multiplying out, we find  φF(f1) · · ·φF(fm+1)Ω = a∗(f1) · · ·a∗(fm+1)Ω + h,  where h ∈ �m  n=0 Sn(r⊗n  C ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Since the linear span of a∗(f1) · · ·a∗(fm+1)Ω is dense in Sm+1(r⊗n  C )  the claim follows for m + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Since  V φF(f1) · · · φF(fn)Ω = (V φF(f1)V −1) · · ·(V φF(fn)V −1)V Ω,  properties (i) and (ii) determine the action of V uniquely on a dense set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Let us now show existence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' First choose an o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' B of r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Define V by V Ω = 1 and  V a∗(f1) · · · a∗(fn)Ω =  : φ(f1) · · ·φ(fn) :,  where fj ∈ B (this is well defined by the symmetry property of the Wick product) and  extend it by linearity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' It is straight forward to see that the map V is an isometry using on the  one hand side the canonical commutation relations for creation and annihilation operators  in Fock space and on the other hand Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Surjectivity, and hence unitarity, follows  from Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Obviously, V satisfies (i) by construction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Let us now show, that it  34  satisfies (a) and hence (ii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Using the definition, (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='5), and the canonical commutation  relations we find for fj ∈ B  φF(f1)a∗(f1)n1 · · · a∗(fk)nkΩ  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='6)  = a∗(f1)n1+1 · · · a∗(fk)nkΩ + n1a∗(f1)n1−1 · · · a∗(fk)nkΩ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  On the other hand we will show that  φ(f1) : φ(f1)n1 · · · φ(fk)nk :  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='7)  = : φ(f1)n1+1 · · · φ(fk)nk : +n1 : φ(f1)n1−1 · · · φ(fk)nk : .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  To see (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='7), we first note that using (c) of Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='7 we obtain  φ(f1) : exp(  n  �  j=1  αjφ(fj)) : =  � ∂  ∂α1  + α1  �  : exp(  n  �  j=1  αjφ(fj)) : .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='8)  Now expanding (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='8) in a power series, calculating the derivative, and equating coefficients,  we obtain (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Thus it follows in view of (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='6), (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='7), and from the definition of V that  for all f ∈ B  V (a∗(f) + a∗(f))  clV −1 = φ(f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='9)  This implies (a) (and hence (ii)) by linearity and continuity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Clearly, (c) follows from  uniqueness of the above construction and multi-linearity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' To show (b) observe that from  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='2) we find for any fj ∈ r that  J V Γ(J)a∗(f1) · · · a∗(fn)Ω = J V a∗(Jf1) · · · a∗(Jfn))Ω  = J V a∗(f1) · · · a∗(fn))Ω = J : φ(f1) · · ·φ(fn) :  = : φ(f1) · · · φ(fn) : = V a∗(f1) · · · a∗(fn)Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Thus by density and C-linearity it follows that J V Γ(J) = V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Thus (b) follows, since  J−1 = J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  B  An Application of Minlos’ theorem  In this appendix we will prove Theorems 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='1 and 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  For this we shall introduce the  following definitions from [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Let us first recall the definition  c(f) = e− 1  4 B(f,f)  for f ∈ S with B defined in (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' The following holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  35  (i) c(0) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (ii) f �→ c(f) is continuous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (iii) For any f1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='., fn ∈ S and z1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', zn ∈ C we have  n  �  i,j=1  zizjc(fi − fj) ≥ 0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' (i) This follows from B(0, 0) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' (ii) It is straight forward to see that f �→ B(f, f)  is continuous on S, and hence also the function c : f �→ exp(−1  4B(f, f)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' (iii) Let V =  linR{f1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', fn}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Then there exists a basis (ej)j=1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=',m of V , with dual basis (bj)m  j=1, such  that B(ei, ej) = λiδi,j with λ1 = · · · = λp = 1 and λp+1 = · · · λm = 0 for some 1 ≤ p ≤ m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Using that the Fourier transform of a Gaussian is a Gaussian we find for any f ∈ V with  fj = bj(f)  c(f) = e− 1  4B(f,f) = e− 1  4  �p  j=1 f2  j = (π)−p/2  �  e−i �p  j= yjbj(f)e− �p  j=1 y2  j dpy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  So positivity of c(f) now follows from Bochner’s theorem [23, Theorem IX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Proof of Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' The existence and uniqueness of the measure ν follows in view of  Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='1 from Minlos theorem [9, Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='2] see also [1,2,3,22,28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' To this end, we  extend the seminorms (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='1) to S as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' For f = (f1, f2, f3) ∈ S we define ∥f∥α,β :=  ∥f1∥α,β + ∥f2∥α,β + ∥f3∥α,β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Then it is straight forward to see that S with these seminorms  is a nuclear space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (a) This follows since for f ∈ S and each t ∈ R we have by (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='6)  �  exp(itϕ(f))dν = exp(−1  4t2B(f, f)),  and so ϕ(f) is a Gaussian random variable with mean zero, see [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' (b) This follows from  (a) and linearity (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='5), see [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' (c) We argue similarly as in [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' First observe that for all  measurable sets E we have  ∀ǫ > 0, ∃C a cylinder set,  ν(C△E) < ǫ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='1)  Here, △ stands for the symmetric difference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' To this end, let E be the set of all measurable  E which satisfy (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' It is straight forward to verify that E is a σ-algebra containing all  cylinder sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Hence E equals the set of all measurable sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' It follows by definition of the  integral that {1Ω(ϕ(f1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', ϕ(fn)) : Ω ⊂ Rn Borel measurable, f1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', fn ∈ S} is dense in  L2(S′, dν).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Now it is well known that S(Rn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' C) is dense in L1(Rn, dµC), where µC denotes  Gaussian measure with covariance C (with possibly matrix elements which are infinite).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  This shows the density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' (d) If f ∈ S with P �f = 0, then B(f, f) = 0, so ϕ(f) is by (a) a  Gaussian random variable with variance zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Thus for all f ∈ S with P �f = 0 it follows  36  that ϕ(f) = 0 almost everywhere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Now let h ∈ S(R3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Then ∇h ∈ S and for all T ∈ S′  we have  ϕ(∇h)(T) = 0 ⇔ T(∇h) = 0 ⇔ (∇ · T)(h) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Since P �  ∇h = 0, we find (∇ · T)(h) = 0 for almost all T ∈ S′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Since S(R3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' R) is separable,  there exists a countable dense subset Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' It follows that for almost all T ∈ S′ we have  (∇ · T)(h) = 0 for all h ∈ Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Since ∇ · T is continuous it follows that for almost all T ∈ S′  we have (∇ · T)(h) = 0 for all h ∈ S(R3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' This shows the claim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  As an immediate consequence of Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='1 we obtain the following lemma, which we  shall use for the proof of Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Let hB denote the real Hilbert space obtained by the completion of the inner  product space (S0, B(·, ·)) with the imbedding ι : S0 → hB having dense range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Let v ∈ hB,  and let (vn)n∈N be a Cauchy sequence in S0 such that ι(vn) → v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Then the following limit  exists in L2(S′, dν)  ϕ(v) := lim  n→∞ ϕ(vn),  is independent of the Cauchy sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Furthermore, ϕ(v) is a Gaussian random process  indexed by hB with (S′, ν) the probability measure space of the random process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' First observe that (S0, B(·, ·)) is indeed an inner product space, since ∇ · f = 0  implies P �f = �f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Clearly, ϕ(vn) is a Cauchy sequence in L2(S′, dν), since  �  |ϕ(vn) −  ϕ(vm)|2dν = 1  2B(vn − vm, vn − vm) by Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='1 (a), and hence converges to a unique  limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' With regard to Definition A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='2 the statement of the last sentence is straight forward  to show using Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='1 and the fact that limits of Gaussians are Gaussian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Proof of Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' The map iω : (S0, B(·, ·)) → {v ∈ v : Imv = 0} is an isometry  of real inner product spaces, which follows directly from the definitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Furthermore,  iω has dense range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  To see this, observe that for any real v ∈ v there exists by well  known construction a real vn ∈ S such that vn → v in the L2(R3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' C3) norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Now define  wn = (ω1/2(1 − χn)P ˆvn)∨ for χ ∈ C∞  c (R3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' [0, 1]) with χ = 1 on B1/2(0) and χ = 0 outside  of B1(0), and χn(x) = χ(nx).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Then it is straight forward to see that wn ∈ S0 and (by  unitarity of the Fourier transform and dominated convergence)  ∥iωwn − v∥ = ∥((1 − χn)P ˆvn)∨ − v∥ = ∥((1 − χn)P ˆvn − ˆv∥ = ∥((1 − χn)P ˆvn − P ˆv∥  ≤ ∥χnP ˆv∥ + ∥(1 − χn)P(ˆvn − ˆv)∥ ≤ ∥χnP ˆv∥ + ∥ˆvn − ˆv∥ → 0,  as n → ∞, by construction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' This shows that iω has dense range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' So the map iω extends  to hB the closure of (S0, B(·, ·)) and yields a bijective isometry hB → {v ∈ v : Imv = 0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  It follows using Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='2 that ϕ ◦ i−1  ω  is a Gaussian random process indexed by {v ∈ v :  Imv = 0} with probability measure space (S′, ν).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Thus it follows from Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='6 that  there exists a unique unitary transformation Vv : Fs(v) → L2(S′, dν) with VvΩ = 1 and  37  Vv(a∗(h) + a(h))V −1  v  = ϕ(h) for all h ∈ iωS0 (since {v ∈ v : Imv = 0}C = v and iωS0 is  dense in {v ∈ v : Imv = 0}).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' This shows the first part of the theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' The last statement  of the theorem now follows form part (b) of Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  References  [1] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Bogachev, Measure theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' I, II, Springer-Verlag, Berlin, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' MR 2267655  [2] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Bogachev and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Smolyanov, Topological vector spaces and their applications,  Springer Monographs in Mathematics, Springer, Cham, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' MR 3616849  [3] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Bourbaki, ´El´ements de math´ematique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Fasc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' XXXV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Livre VI: Int´egration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Chapitre  IX: Int´egration sur les espaces topologiques s´epar´es, Actualit´es Scientifiques et Indus-  trielles [Current Scientific and Industrial Topics], No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' 1343, Hermann, Paris, 1969.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' MR  0276436  [4] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Cohen-Tannoudji, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Grynberg, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Dupont-Roc, Atom-photon interactions:  Basic processes and applications, Wiley, New York, 1992.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  [5] Charles Fefferman, J¨urg Fr¨ohlich, and Gian Michele Graf, Stability of ultraviolet-cutoff  quantum electrodynamics with non-relativistic matter, Comm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' 190 (1997),  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' 2, 309–330.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' MR 1489574  [6] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Fr¨ohlich, Application of commutator theorems to the integration of representations  of Lie algebras and commutation relations, Comm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' 54 (1977), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' 2,  135–150.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' MR 473909  [7] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Glimm and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Jaffe, Collected papers vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='1: Quantum field theory and statistical  mechanics: Expositions, Contemporary Physicists, Birkh¨auser Boston, 1985.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  [8] James Glimm and Arthur Jaffe, Collected papers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' 2, Birkh¨auser Boston, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=',  Boston, MA, 1985, Constructive quantum field theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Selected papers, Reprint of  articles published 1968–1980.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' MR 947959  [9]  , Quantum physics, second ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', Springer-Verlag, New York, 1987, A functional  integral point of view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' MR 887102  [10] David Hasler and Ira Herbst, Absence of ground states for a class of translation invari-  ant models of non-relativistic QED, Comm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' 279 (2008), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' 3, 769–787.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  MR 2386727  [11]  , On the self-adjointness and domain of Pauli-Fierz type Hamiltonians, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' 20 (2008), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' 7, 787–800.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' MR 2436496  38  [12]  , Convergent expansions in non-relativistic qed: analyticity of the ground state,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Funct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' 261 (2011), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' 11, 3119–3154.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' MR 2835993  [13]  , Ground states in the spin boson model, Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Henri Poincar´e 12 (2011), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' 4,  621–677.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' MR 2787765  [14]  , A vanishing theorem for operators in Fock space, Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' 101  (2012), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' 2, 223–237.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' MR 2947962  [15] David Hasler and Markus Lange, Degenerate perturbation theory for models of quantum  field theory with symmetries, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  [16] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Hiroshima and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Spohn, Ground state degeneracy of the Pauli-Fierz Hamiltonian  with spin, Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' 5 (2001), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' 6, 1091–1104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' MR 1926665  [17] Fumio Hiroshima, Fiber Hamiltonians in non-relativistic quantum electrodynamics, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Funct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' 252 (2007), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' 1, 314–355.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' MR 2357359  [18] Hendrik A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Kramers, Th´eorie g´en´erale de la rotation paramagn´etique dans les cristaux,  Proceedings Koninklijke Akademie van Wetenschappen 33 (1930), 959–972.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  [19] Michael Loss, Tadahiro Miyao, and Herbert Spohn, Lowest energy states in nonrela-  tivistic QED: atoms and ions in motion, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Funct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' 243 (2007), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' 2, 353–393.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  MR 2289693  [20]  , Kramers degeneracy theorem in nonrelativistic QED, Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' 89  (2009), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' 1, 21–31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' MR 2520177  [21]  , Time reversal symmetries and properties of ground states in nonrelativistic  QED, Applications of renormalization group methods in mathematical sciences, RIMS  Kˆokyˆuroku Bessatsu, B21, Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Inst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' (RIMS), Kyoto, 2010, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' 35–44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' MR  2792021  [22] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Minlos, Generalized random processes and their extension to a measure, Selected  Transl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Statist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' and Prob.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' 3, Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', Providence, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', 1963,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' 291–313.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' MR 0154317  [23] Michael Reed and Barry Simon, Methods of modern mathematical physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Fourier  analysis, self-adjointness, Academic Press [Harcourt Brace Jovanovich, Publishers],  New York-London, 1975.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' MR 0493420  [24]  , Methods of modern mathematical physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' I, second ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', Academic Press, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  [Harcourt Brace Jovanovich, Publishers], New York, 1980, Functional analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' MR  751959  39  [25] Israel Michael Sigal, Ground state and resonances in the standard model of the non-  relativistic QED, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Stat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' 134 (2009), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' 5-6, 899–939.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' MR 2518974  [26] Barry Simon, The P(φ)2 Euclidean (quantum) field theory, Princeton University Press,  Princeton, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=', 1974, Princeton Series in Physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' MR 0489552  [27] Herbert Spohn, Dynamics of charged particles and their radiation field, Cambridge  University Press, Cambridge, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' MR 2097788  [28] Yasuo Umemura, Measures on infinite dimensional vector spaces, Publ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Inst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' A 1 (1965), 1–47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' MR 0187273  [29] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content=' Wigner, Ueber die operation der zeitumkehr in der quantenmechanik, Nachrichten  von der Gesellschaft der Wissenschaften zu G¨ottingen, Mathematisch-Physikalische  Klasse 1932 (1932), 546–559.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
+page_content='  40' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdFAT4oBgHgl3EQfvx7k/content/2301.08678v1.pdf'}
diff --git a/KtAyT4oBgHgl3EQf6Prq/vector_store/index.faiss b/KtAyT4oBgHgl3EQf6Prq/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..1cf15618d84b6ff9fb81dcbdf872973044ada148
--- /dev/null
+++ b/KtAyT4oBgHgl3EQf6Prq/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:05d8bc3ed94b65f70a49b1c1fb227f6144385d94fbd8f5cee6dafa0310bec8cb
+size 3801133
diff --git a/L9E4T4oBgHgl3EQfKAwg/content/tmp_files/2301.04925v1.pdf.txt b/L9E4T4oBgHgl3EQfKAwg/content/tmp_files/2301.04925v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7d9f2bb037a780315a567a27a33085202110fb37
--- /dev/null
+++ b/L9E4T4oBgHgl3EQfKAwg/content/tmp_files/2301.04925v1.pdf.txt
@@ -0,0 +1,2919 @@
+Measuring Corporate Digital Divide with web scraping: Evidence
+from Italy
+Leonardo Mazzonia,b, Fabio Pinellib and Massimo Riccabonib
+a University of Padua - Department of Economics and Management, Padua (Italy);
+bIMT School for Advanced Studies, Lucca (Italy)
+Abstract
+With the increasing pervasiveness of ICTs in the fabric of economic activities, the
+corporate digital divide has emerged as a new crucial topic to evaluate the IT
+competencies and the digital gap between firms and territories. Given the scarcity of
+available granular data to measure the phenomenon, most studies have used survey
+data. To bridge the empirical gap, we scrape the website homepage of 182 705 Italian
+firms, extracting ten features related to their digital footprint characteristics to
+develop a new corporate digital assessment index. Our results highlight a significant
+digital divide across dimensions, sectors and geographical locations of Italian firms,
+opening up new perspectives on monitoring and near-real-time data-driven analysis.
+Keywords: Digital Divide; Web-based indicators; Corporate web scraping; Digital
+footprint; Digital transformation
+Acknowledgements: The authors would like to thank the following projects for the
+financial support and comments received: Artes 4.0 -Advanced Robotics and enabling
+digital Technologies & Systems; ”Rinascita dei Borghi” funded by Eurispes (Institute
+for Political, Economic and Social Studies) and the Italian Ministry of Economy and
+Finance; ”Borghi, paesi, aree interne: infrastrutture, sostenibilit`a e qualit`a della vita”
+funded by the Italian Ministry of University and Research.
+Corresponding Author: Leonardo Mazzoni. Email: leonardo.mazzoni@imtlucca.it
+arXiv:2301.04925v1  [econ.GN]  12 Jan 2023
+
+1.
+Introduction
+Digital transformation has recently emerged as a driving force able to forge the strategic
+orientation of firms to grow and innovate by means of digital technologies and the
+relative capabilities built on them (Blanka, Krumay, and Rueckel, 2022; Verhoef
+et al., 2021; Volberda et al., 2021). With the increasing pervasiveness of ICTs in the
+fabric of economic activities (Antonelli, 2003; Baskerville, Myers, and Yoo, 2020), a
+heterogeneous response by individuals, firms and institutions has occurred, translating
+into different rates of adoption of, and proficiency with, digital tools. This phenomenon
+has been generally analyzed under the umbrella of the Digital Divide, a concept able to
+represent the gap in accessing IT infrastructure (Fink and Kenny, 2003). Afterwards,
+the capillary diffusion of ICTs contributed to extend the Digital Divide definition
+also in its usage, involving dedicated human resources and digital market providers
+(Corrocher and Ordanini, 2002; Kyriakidou, Michalakelis, and Sphicopoulos, 2011). In
+this respect, the literature on Digital Divide has not developed a homogenous corpus of
+analysis. New forms are rapidly emerging with growing attention to its specific aspects
+for industries, firms, and territorial levels (Ellinger, Lynch, and Hansen, 2003; Shakina,
+Parshakov, and Alsufiev, 2021; Lythreatis, Singh, and El-Kassar, 2022; Thonipara
+et al., 2022). Particularly, the corporate Digital Divide is a crucial emerging topic in
+the management literature for the consequences brought by the Industry 4.0 paradigm
+on the competencies to develop (Shakina, Parshakov, and Alsufiev, 2021). As yet,
+the literature on the Digital Divide has remained relatively silent on the mechanisms
+occurring at the firm level, with very few studies addressing this specific subject
+(Lythreatis, Singh, and El-Kassar, 2022). This can be attributed to the fact that the
+Corporate Digital Divide is still difficult to observe for the lack of accounting metrics
+able to provide information on IT investment or the implementation of information
+systems updating in the cognitive architecture of the firm (Vehovar et al., 2006; Tambe
+et al., 2020).
+A possible way out from data shortage on the digital behavior of firms came from the
+analysis of corporate websites (Blazquez and Domenech, 2018). Accordingly, corporate
+websites are the “digital footprint” of organizations and part of new codified knowledge,
+which is increasingly becoming accessible for researchers and analysts to study the
+performance of firms in complementary/additional ways, with respect to the more
+traditional data sources (Gok, Waterworth, and Shapira, 2015; Blazquez, Domenech,
+and Deb´on, 2018; Kinne and Resch, 2018). This is because websites represent the
+self-expression of strategic information to external stakeholders: the products/services
+commercialized, delivery modes, mission and vision, the internal competencies, the
+relationships with other companies and universities, research activities, their location
+and facilities (Youtie et al., 2012; Gok, Waterworth, and Shapira, 2015; Li et al., 2018;
+Saridakis et al., 2018; Pukelis and Stanciauskas, 2019). Moreover, new decision-making
+procedures, cost structures, organizational routines and digital operations have been
+2
+
+consequently introduced (Teece and Linden, 2017; Verhoef et al., 2021). This makes
+websites, especially corporate ones, an essential open data source not only to capture the
+visibility and reputation of the firm but also to study the broader digital competencies
+beyond them (Auger, 2005). Despite a firm may rely on software houses or external IT
+consultants to build their websites, the specific technical features that characterize them
+imply indirect agency to transform digital objects by means of “sensing capabilities”
+on the intrinsic value of digital technologies (Faulkner and Runde, 2009). Accordingly,
+some studies have exploited the characteristics of websites as wider signals of the digital
+awareness of firms (Wells, Valacich, and Hess, 2011; Abeysekera, 2019).
+Thanks to the recent evolution of web-scraping techniques (Arora et al., 2016;
+Axenbeck and Breithaupt, 2019; Arora et al., 2020), our aim is to leverage information
+extracted from the corporate website to study the corporate Digital Divide at a large
+scale, considering different firms’ characteristics (e.g., dimension, industry, age, and
+geographical context). More concretely, we scraped the websites of 182 705 Italian
+firms in the period 2020-2021, extracting ten features related to the technical libraries,
+performances, security level, speed, links and social media. Next, we analyzed corporate
+website features in combination with the relative corporate information. Instead of
+considering the contents of websites, we focused on the most “objective” IT features
+available, following the research line aimed to exploit new IT technologies as new
+economic-related proxies of digital capabilities (George et al., 2016; Brynjolfsson, Wang,
+and Zhang, 2021).
+We analyze the Italian case because of the well-known sharp socio-economic
+disparities between northern and southern regions (Daniele, 2021). Moreover, Italy is a
+unique case in Europe of an industrialized country lagging behind other EU countries
+in terms of digital readiness.1
+Our results highlight a significant corporate Digital Divide across firms’ attributes
+such as dimension, sector and age, and territorial characteristics where the firm is
+located, opening up new perspectives of monitoring and near-real-time data-driven
+analysis. Controlling for the impact of wide band our results still hold, paving the way
+for further empirical investigations.
+Previous research has spotted a shortcoming of studies in the analysis of corporate
+digital behaviour with large website samples (e.g., Lythreatis, Singh, and El-Kassar,
+2022). Our study contributes to fill this gap, nuancing the current understanding of
+firms’ Digitial Divide, by exploiting big open-source data directly extracted by corporate
+websites. The extracted features described a multifaceted phenomenon. Interestingly
+as evidenced by low correlation among different elements, the digital-related variables
+capture specific capabilities and justify this explorative analysis. However, in order
+to ensure comparability among firms (and of territories), we propose an aggregation
+of the ten features, interpreting and categorizing them according to a theoretical
+1See
+the
+results
+of
+the
+Digital
+Economy
+Society
+index
+available
+at:
+https://digital-strategy.ec.europa.eu/en/policies/desi.
+3
+
+building process based on the digital space(s) of the firm: technical capabilities, internal
+organizations,external stakeholder engagement, and digital culture.
+The paper is organized as follows. Section 2 reviews the literature on the economic
+and Digital Divide and the role of websites in measuring digital footprint. Section 3
+describes the data collection process and the methodology adopted. Section 4 displays
+the results of the empirical investigation of the Digital Divide phenomenon. Section 5
+discusses the findings, underlining the limitations of this work and concluding with
+final remarks.
+2.
+Literature review
+2.1.
+The Digital Divide notion: a corporate perspective
+The notion of the Digital Divide was initially coined as the different rates of adoption
+of ICTs of individuals and households (Fink and Kenny, 2003; Vehovar et al., 2006;
+Kyriakidou, Michalakelis, and Sphicopoulos, 2011). Then the massive diffusion of
+the internet has shifted the attention beyond the simple rate of adoption, reaching
+a further layer related to the usage of ICTs (Corrocher and Ordanini, 2002). The
+transition from the industrial society to the information economy(Castells, 1996) and
+the recent conceptualisation of “onlife” societies (Floridi, 2014) with the new role
+of ICTs as “reality shapers” (Baskerville, Myers, and Yoo, 2020) has magnified the
+relevance of this divide, as a reflection of the socio-economic gap between individuals,
+firms and territories. Accordingly, the meaning of the Digital Divide has become a
+multifaceted and more elaborated notion, including the developed skills and abilities to
+use technical tools (Fink and Kenny, 2003; Szeles, 2018; Matthess and Kunkel, 2020).
+This has allowed elaborating more on the competitiveness drivers of the digital economy,
+being ICTs firmly embedded in the fabric of socio-economic systems (Antonelli, 2003;
+Forman, 2005). Furthermore, with the advent of the Industry 4.0 paradigm in the
+last decade, the concept of the digital divide has furtherly increased its significance
+as a metric able to reflect economic performances (Shakina, Parshakov, and Alsufiev,
+2021). This is particularly relevant considering the growing pervasiveness of ICTs and
+the complementarity between physical and key enabling digital technologies in the
+production and consumption of goods and services (e.g., cloud computing, artificial
+intelligence) (Giustiziero et al., 2021). While there is a growing awareness of the digital
+performance of countries and regions, the notion of the Digital Divide registers very
+few contributions applied to the firms as units of analysis.
+As evidenced by recent contributions, digital transformation has noteworthy impacted
+firms’ structure, being a strategic transformation of organization and core capabilities
+of businesses enabled by digital technologies (Volberda et al., 2021). The rapid and
+unceasing technological change that occurred in the last decade has challenged the
+status quo of firms across industries, creating gaps for different rates of digital
+4
+
+awareness by managers and employees and diverse accumulation of digital-related
+skills (Blanka, Krumay, and Rueckel, 2022; Shakina, Parshakov, and Alsufiev, 2021).
+Internal routines and relationships with customers and suppliers have been radically
+altered, and unsurprisingly, the term co-creation is frequently applied to refer to
+collaboration between the various actors in business ecosystems in the value creation
+path (Warner and W¨ager, 2019; Liu et al., 2022). Bearing in mind this transformation,
+the traditional resource-based view of the firm paradigm (Barney, 1991; Wernerfelt,
+1984) has been profoundly impacted by digital technologies and their bundled use
+(Giustiziero et al., 2021). Accordingly, the development of new capabilities to favor
+business model adaptation to the new techno-economic scenario requires a digital
+sensing activity by the firm (Warner and W¨ager, 2019). The ubiquity of ICTs requires
+not only the ownership of specific resources but also the creation of specialized human
+resources to frame the new possibilities opened by digital affordance property, that
+is, the creation of endless reconfiguration by the use of the same inputs or a creative
+(re)combination of them (Giustiziero et al., 2021; Liu et al., 2022). All in all, while we
+have rather substantial theoretical evidence that digital transformation has impacted
+corporates’ structure and strategic approach, we are still struggling to provide detailed
+and fine-grained measures at the firm level (Tambe et al., 2020). In other words,
+we cannot evaluate firms’ response to the introduction of digital technologies and if
+they have developed adequate digital capabilities. Hence, the literature has remained
+relatively silent on the corporate Digital Divide level across different typologies of firms,
+operating in various industries, and localized in urban or peripheral contexts.
+The good news is that digital footprints left by organisations and individuals
+have recently become available data for empirical analyses, thanks to the diffusion
+in social sciences of methodologies such as web scraping (Li et al., 2018; Axenbeck
+and Breithaupt, 2019; Kinne and Axenbeck, 2020; Thonipara et al., 2022). In other
+words, considering information reported on the internet under the lenses of digital
+signalling theory (Wells, Valacich, and Hess, 2011; Abeysekera, 2019) allows relating
+the produced digital artifacts (as the characteristics of a corporate website) to a set
+of underlying digital capabilities (Ageeva et al., 2018). Recent studies have exploited
+this caveat, investigating the relationships within the innovation ecosystem between
+firms, universities, and institutions (Li et al., 2018), the digital layer of companies
+and the concept of proximity (Kr¨uger et al., 2020), the innovation performance of
+firms (Kinne and Axenbeck, 2020). Despite this growing popularity, researches on these
+new data sources are still very fragmented, with many exploratory analyses and many
+elements that may not be applicable in all settings (Hern´andez, Jim´enez, and Mart´ın,
+2009). With few exceptions (Kinne and Axenbeck, 2020; Kr¨uger et al., 2020; Thonipara
+et al., 2022), most of the analyses have concentrated on small samples, without the
+possibility of transforming these unstructured and very heterogeneous data sources
+into new potential tools to investigate economic performance at the systemic level.
+5
+
+2.2.
+The use of websites to measure the digital footprint of firms
+The wide adoption of websites among firms, including SMEs, represents an interesting
+potential information source to bridge the gap between the need to assess the digital
+performance of firms and the lack of granular indicators. This is possible for the
+strategic role played by websites in the information and knowledge economy.
+A website is a digital means able to reduce information asymmetry between two
+parts, facilitating corporate operations (delivery, customer care, internationalization)
+(Billon, Ezcurra, and F., 2009). Its maintenance, use, and development imply some
+extra costs for the firms. This candidates it as “near-costless measure of marketing”
+(Thonipara et al., 2022) and, more in general, as an effective proxy to capture the
+digital footprint of economic agents (Gok, Waterworth, and Shapira, 2015; Blazquez
+and Domenech, 2018; Heroux-Vaillancourt, Beaudry, and Rietsch, 2020; Kinne and
+Axenbeck, 2020). Websites are publicly available sources, manageable at any desired
+time, and represent a new form of codified knowledge to complement information sources
+on the firms’ performances (Blank, Graham, and Calvino, 2018; Kinne and Resch,
+2018). The embeddedness of websites into online environments and the introduction
+of e-commerce platforms have created completely new value delivery bidirectional
+channels (Saridakis et al., 2018; Verhoef et al., 2021). As a result, this has impacted
+a wide and heterogeneous set of industries. The massive use of websites offers some
+advantages in data collection in comparison to traditional methodologies due to their
+(i) “unobtrusiveness”, (ii) accessibility, (iii) temporal frequency, (iv) granularity, and
+(v) coverage (Mateos et al., 2001; Gok, Waterworth, and Shapira, 2015; Rasmussen and
+Thimm, 2015; Blazquez and Domenech, 2018; Kinne and Resch, 2018; Li et al., 2018).
+Unobtrusiveness derives from the capacity to directly gather the information reported
+without requiring the direct involvement of a firm or a set of them (e.g., surveys).
+This saves time collecting information and is less variable than a traditional survey.
+Accessibility stems from the open-access nature of websites as information sources and
+the reproducibility of the analysis. Websites, especially corporate websites, are updated
+for business reasons much more frequently than traditional information sources such as
+surveys (temporal frequency). Moreover, the information reported on a website has a
+much more customisable degree of granularity than traditional survey methodologies
+(even if with increasing post-processing works). Finally, the massive analysis of websites
+has the potential to extend coverage to almost the entire population of companies
+(with the absence of non-response), overcoming the limitations of traditional collection
+methods based on the selection of a representative sample. This makes it possible
+to detect common and recurring characteristics agnostically and to identify hidden
+peculiarities and specificities that remain under the tip of the iceberg. Extracting
+data directly from websites can present some problems regarding the reliability of
+the information. However, companies would face rather negative feedback from the
+clients and/or business partners with whom they interact if they would exaggerate
+or mystify the reality. Hence, the general trend within the literature is to treat this
+6
+
+information as truthful or at least documentable (Pukelis and Stanciauskas, 2019).
+Notwithstanding the availability of websites, some doubts emerge on the typology of
+firms detectable on the web. Companies very close to the market are most likely to be
+included in this group (e.g., B2C). However, we have less evidence for subcontractors or
+intermediaries (B2B), whose activities can remain in the shadow to respect the will of
+their final clients (e.g., respecting industrial secrets or preventing competition) (Pukelis
+and Stanciauskas, 2019). Encouraging signals, in this case, come from the requesting
+of certificates (as ISO) by value chain leaders that are pushing subcontractors and
+suppliers, in general, to show them as digital “business cards”. Still, available company
+websites are a convenience sample to investigate firm dynamics, and a proper procedure
+can be implemented to re-balance the available information across geographical areas
+and sectors. The difficulties of website data processing are related to their reliability
+and data mining procedures. There are still some technical problems with treating
+homogeneously website data, which for their nature are organized in several formats,
+with different dimensionality, and composed of non-textual parts (i.e., graphics and
+images) (Gok, Waterworth, and Shapira, 2015; Beaudry, H´eroux-Vaillancourt, and
+Rietsch, 2016; Heroux-Vaillancourt, Beaudry, and Rietsch, 2020).
+3.
+Data Collection and Methodology
+3.1.
+Data Collection
+From the AIDA database (Bureau van Dijk), we collected information about the
+website of Italian firms. Initially, we collected website URL information for 450 348
+firms covering the entire national territory.
+We implemented in python our crawler script using a combination of different
+libraries: requests2, scrapy3, beautifulsoup4, trafilatura5, builtwith6 and
+finally we also rely on the results of Google Lighthouse7. Next, we stored the results of
+the crawling activities on a MongoDB8 instance, a document-oriented NOSQL database
+that provided us the right flexibility to store and update the gathered information.
+Each firm’s features were stored in a single MongoDB document.
+The crawling activity has been carried out from January 2021 to March 2021, with
+a further update in September 2021. As a result, we were able to obtain valid content
+for 347 010 enterprises. The other home page URLs returned a timeout error or an
+HTTP code different from 200. Thus, we obtained a valid set of features for the 77% of
+the initial sample. Together with their home page URL, we considered information on
+2docs.python-requests.org
+3https://scrapy.org/
+4https://www.crummy.com/software/BeautifulSoup/bs4/doc/
+5https://trafilatura.readthedocs.io/en/latest/
+6https://pypi.org/project/builtwith/
+7https://developers.google.com/web/tools/lighthouse
+8https://www.mongodb.com/
+7
+
+firm characteristics, such as geographical localisation (regional - NUTS-2, provincial
+- NUTS-3 and municipal level), industry (NACE REV.2 digit), age, and size (micro,
+small, medium or large firm according to the number of employees). Therefore from
+the merging of website information with firms’ characteristics, we obtain a final sample
+of 182˙705 observations.
+3.2.
+Methodology
+The crawler activity was aimed at extracting different features related to each specific
+home page to describe: a) how the site is built (i.e., links, images, text, etc.) and b) how
+it relates to other online contents (e.g., security, link to social media, loading speed,
+etc.).
+We interpreted the economic meaning of each extracted feature elaborating on the
+existing literature (Mateos et al., 2001; Sanders and Galloway, 2013; Kr´ol and Zdonek,
+2020). For the present analysis, we considered ten features as follows
+• the length of the URL. Short URLs are easier to remember and are a sign of
+cleanliness and user-centricity. Moreover, they are more likely to be discovered;
+• Social media presence: Facebook, LinkedIn and Instagram. We consider
+three popular social media (Facebook, LinkedIn and Instagram), checking for the
+absence/presence of links to those social media. In fact, social media represent a
+new valuable tool for conducting digital marketing strategies;
+• The quality of internal links. The presence of unique inner links can be
+interpreted as a sign of a good level of navigability to increase the probability
+for users to remain longer on the websites, being correctly addressed towards
+contents more in line with their preferences;
+• The quality of external links. The higher presence of unique outer links can
+be interpreted as a strong sign of stakeholder engagement and embeddedness in
+the digital business ecosystem;
+• Quality of the technical frameworks. The adoption of modern web
+development standards ensures a better user experience and reflects more technical
+competencies. This metric is based on Google Lighthouse 9.
+• Request access time. A webpage with a low level of request time implies a
+good speed and a good level of usability, being also this metric at the basis of
+the adoption of a state-of-the-art technological stack development;
+• Website’s age. We estimated the age of each website, checking for its first
+year of presence in the Wayback Machine archive10. Older websites have been
+interpreted as part of the digital history and tradition of the firm;
+• Website security. The presence of a high-level security header represents a
+proxy of awareness towards the risks of cyberattacks. Nowadays, this represents
+9See https://github.com/GoogleChrome/lighthouse.
+10https://archive.org/web/.
+8
+
+a crucial strategic aspect for firms.
+In the following, we provide an explorative analysis of the extracted features.
+Figure 1 describes how our final dataset is distributed along three firm characteristics,
+namely industry, size, and age. On the top, we show the number of enterprises for NACE
+2-digit code. In our sample, most of the firms belong to categories C (manufacturing)
+and G (wholesale and retail trade). Notice that not all the industries have been included
+in this list; in fact, we select only the top 10 more frequent categories. The second
+plot shows the size distribution of firms. As expected, considering the known Italian
+industrial distribution, most of the firms in our dataset are micro and small enterprises,
+i.e., with less than 50 employees. At the bottom of figure 3, we report the age of the
+enterprises in 5-year bins. The results show a higher concentration of relatively young
+firms that have from 5 to 25 years old.
+To investigate the representativeness of the sample, we compare the data we extracted
+with the general composition of the Italian firms, as reported in ORBIS (Bureau Van
+Dick) and ISTAT. Concerning industry, we obtained representativeness that vary from
+5% of NACE sector I (Food and Accommodation) to 28% of sector J (Information and
+Communication), with a good level (22%) also for sector C (Manufacturing) (ISTAT,
+2020).
+Concerning size, we were able to capture 75% of the total number of big firms, with
+a decreasing coverage for smaller firms: 56% of medium firms, 31% of small firms and
+only 8% of micro firms (ISTAT, 2020).
+In relation to age, we find values in the range 1-6%, registering also in this case
+progressive representativeness going back in time, with the peak (6%) for the firms
+born in the period 2002 and 2006 (ORBIS, 2022).
+Figure 2 maps the features extracted by means of the crawling activity at NUTS-3
+regions (descriptive statistics are available in table 2). We report values corresponding
+to the three quantiles, i.e. 33%, 66% and 100%, where a darker color indicates higher
+values. Seven out of the ten extracted features, namely URL length, LinkedIn, quality
+of the internal links, quality of the technical frameworks, request access time, website
+age and website security) exhibit clear spatial differences across Italian NUTS-3 regions.
+As an example, The North-South divide in access time might be due to infrastructure
+problems since a fast broadband connection is more spread in the North than in the
+South. The spatial distribution of websites might correspond to earlier adoption of
+digital tools for Northern enterprises w.r.t. firms located in the South, thus indicating
+a more rooted digital mindset. More scattered territorial patterns are reported for
+external links and social media. Social media are of special interest for their different
+penetration degree revealed, suggesting a specific interpretation of their usage. The
+presence of Facebook can be interpreted as the diffusion of a more generic marketing
+culture, with a low level of specialisation. Instagram can be seen as the diffusion of
+specific marketing culture adopted by specific B2C industries that exploit images and
+videos (such as tourism, food, and culture). LinkedIn can be interpreted as the diffusion
+9
+
+Figure 1.: main features of selected Italian firms with a known physical and digital presence.
+Top: the number of analysed firms grouped by NACE 2 Digit code, middle: size distribution,
+Bottom: age distribution.
+of Human Resources culture and a proxy of more developed job markets, where relying
+on professional networks can support more concrete business activities.
+Interestingly, table 2 shows a low level of correlation between variables, with the
+10
+
+50000
+40000
+30000
+z
+20000
+10000
+1
+NACE Rev.2100000
+00008
+firms
+00009
+JO
+z
+40000
+20000
+0.
+micro
+small
+medium
+big
+Firm size30000
+25000
+Z 15000
+10000
+5000
+0
+(0, 5]
+[0s'st] [s'0t] [0'se][se'05] [05'sz] [s'0z][0z"s] [50]][01"s]
+>50
+Firm age (Year from 2022)N.Links IN
+N. links out
+Lenght URL
+LinkedIn
+Instagram
+Facebook
+Best practice
+Request access time
+Security
+Website age
+Figure 2.: the spatial distribution of corporate website features in Italy, at the level of NUTS-3
+regions (provinces). Features are classified in three quantiles from low (yellow) to high (dark
+blue) levels.
+only exception of correlation between social media (ca .5). This result supports our
+approach of collecting different indicators to capture a multifaceted topic such as the
+corporate digital divide.
+More in general, our explorative data analysis allows us to validate some
+characteristics of the enterprises included in our dataset built through the crawler.
+11
+
+Augsburg
+0.721
+Wi0.755
+Freiburg
+0.763
+0.785
+Ulm
+imBreisgau
+olc
+Munchewills
+Gyor
+Basel
+Salzburg
+elforto
+Osterreich
+Budapest
+Deb
+zurich
+SanktGallen
+Szombathely
+Alfoldes
+Besancon
+Tirof
+Steiermark
+Magyarorszag
+Eszak
+Schweiz
+Suisse/Svizzeral
+Dunantur
+Karnten
+Kecskemet
+Lausanne
+Maribor
+Svizra
+eve
+Szeged
+Pecs
+Arad
+Slovenija
+Zagreb
+Cy6oTMLa
+Anney
+Timisoa
+hamber
+Trieste
+Osijek
+BojBoduHa
+ezia
+Rijeka
+Banja Luka
+Tuzla
+beorpaa
+diSan
+Hrvatska
+ence
+Genova
+BosnaiHercegovinal
+Cp6wja
+-cote
+ino
+Mon
+Zadar
+zur
+bocHaw
+0
+Ancona
+XepyeroBMHa
+eHmpanHo
+Cpuja
+Mostar
+Crna Gora
+Kosoval
+LpHaropa
+Kosovo
+Shgiperid
+Kyn
+Ajaccio
+Veriore
+Ce
+Make
+Lath
+Bari
+Shqiperia
+GMTOJ
+Korce
+Brindisi
+Vlore
+ATTOKEVTPWH
+Aroiknon
+Autikns
+-MQKEOOVIO
+eddu
+cagliari
+Palermo
+Messip
+ATOM
+4
+ania
+dcusa
+nstantineAugsburg
+Freiburg
+0.008
+0.010
+0.011
+Wien
+0.019
+Ulm
+imBreisgau
+olc
+Munchewills
+Salzburg
+Gyor
+elforto
+Basel
+Osterreich
+Budapest
+Deb
+zurich
+SanktGallen
+Szombathely
+Alfoldes
+Besancon
+Tirof
+Steiermark
+Magyarorszag
+Eszak
+Schweizi
+Suisse/Svizzeral
+Dunantur
+Karnten
+Kecskemet
+Maribor
+ausanne
+Svizra
+eve
+Szeged
+Pecs
+Arad
+Slovenija
+Zagreb
+Cy6oTMLa
+Anneo
+Timisoa
+hamber
+Trieste
+Osijek
+BojBoduHa
+ezia
+Rijeka
+Banja Luka
+Tuzla
+beorpaa
+diSan
+Hrvatska
+ence
+Genova
+BosnaiHercegovinal
+Cp6wja
+-cote
+ino
+Zadar
+zur
+Mon
+bocHaw
+Ancona
+XepyeroBMHa
+eHmpanHo
+Cpuja
+Mostar
+Crna Gora
+Kosoval
+LpHaropa
+Kosovo
+Shgiperid
+Kyn
+Ajaccio
+Veriore
+Ce
+Make
+Bari
+Shqiperia
+GMTOJ
+in
+Korce
+Brindisi
+Vlore
+ATOKEVTPUH
+Aroiknon
+Autikns
+-MQKEOOVIO
+jeddt
+tagliari
+Palermo
+Messir
+ATOK
+4
+nEO
+nia
+dcusa
+nstantineAugsburg
+Freiburg
+0.40
+0.41
+0.43 Wien
+0.47
+Ulm
+olc
+imBreisgau
+Munchewills
+Salzburg
+Gyor
+elforto
+Basel
+Osterreich
+Budapest
+Deb
+zurich
+PSanktGallen
+Szombathely
+Alfoldes
+Besancon
+Tirof
+Steiermark
+Magyarorszag
+Eszak
+Schweizi
+Suisse/svizzeral
+Dunantur
+Karnten
+Kecskemet
+Maribor
+ausanne
+Svizra
+eve
+Szeged
+Pecs
+Arad
+Slovenija
+Zagreb
+Cy6oTMLa
+Anney
+Timisoa
+@
+hamberi
+Trieste
+Osijek
+BojBoduHa
+ezia
+Rijeka
+@
+Banja Luka
+Tuzla
+beorpaa
+diSan
+Hrvatska
+ence-
+Genova
+BosnaiHercegovina
+Cp6wja
+-cote
+ino
+Mon
+Zadar
+zur
+bocHaw
+Ancona
+XepyeroBMHa
+eHmoanHo
+Cpuja
+Mostar
+Crna Gora
+Kosoval
+LpHaropa
+Kosovo
+Shgiperid
+Kyn
+Ajaccio
+Veriore
+Ce
+Make
+Bari
+Shqiperia
+GMTOJ
+in
+Korce
+Brindisi
+Vlore
+ATOKEVTPWH
+Aroiknon
+Autikns
+-MQKEOOVIO
+eddur
+Cagliari
+Palermo
+Messip
+ATTOK
+nEO
+nia
+dcusa
+nstantineAugsburg
+Freiburg
+7.6
+9.4 -Wien
+10.7
+11.9
+Ulm
+olc
+imBreisgau
+Munchewills
+Salzburg
+Osterreich
+Gyor
+elforto
+Basel
+Budapest
+Deb
+zurich
+SanktGallen
+Szombathely
+Alfoldes
+Besancon
+Tirof
+Steiermark
+Magyarorszag
+Eszak
+Schweizi
+Suisse/Svizzeral
+Dunantur
+Karnten
+Kecskemet
+Lausanne
+Maribor
+Svizra
+eve
+Szeged
+Pecs
+Arad
+Slovenija
+Zagreb
+Cy6oTMLa
+Anney
+Timisoa
+hamber
+Trieste
+Osijek
+BojBoduHa
+ezia
+Rijeka
+Banja Luka
+Tuzla
+beorpaa
+diSan
+Hrvatska
+ence
+Genova
+BosnaiHercegovinal
+Cp6wja
+-cote
+ino
+Zadar
+zur
+Mon
+bocHaw
+ncona
+XepyeroBMHa
+LeHmpanHo
+Cpuja
+Mostar
+Crna Gora
+Kosoval
+LpHaropa
+Kosovo
+Shgiperid
+Kyn
+Ajaccio
+Veriore
+K
+Ce
+Make
+Lath
+Bari
+Shqiperia
+GMTOJ
+n
+Korce
+Brindisi
+Vlore
+ATOKEVTPWH
+Aroiknon
+Autikns
+FMAKEOOVIO
+eddu
+cagliari
+Palermo
+Messin
+ATOK
+nEO
+ania
+dcusa
+nstantineAugsburg
+25
+29
+31Wien
+Freiburg
+39
+Ulm
+imBreisgau
+olc
+Munchewills
+Gyor
+Basel
+Salzburg
+elforto
+Osterreich
+Budapest
+Deb
+zurich
+SanktGallen
+Szombathely
+Alfoldes
+Besancon
+Tirof
+Steiermark
+Magyarorszag
+Eszak
+Schweiz
+Suisse/Svizzeral
+Dunantur
+Karnten
+Kecskemet
+Lausanne
+Maribor
+Svizra
+eve
+Szeged
+Pecs
+Arad
+Slovenija
+Zagreb
+Cy6oTMLa
+Anney
+Timisoa
+hamber
+Trieste
+Osijek
+BojBoduHa
+ezia
+Rijeka
+Banja Luka
+Tuzla
+beorpaa
+diSan
+Hrvatska
+ence
+Genova
+BosnaiHercegovinal
+Cp6wja
+-cote
+ino
+Mon
+Zadar
+zur
+bocHaw
+ncona
+XepyeroBHa
+eHmpanHo
+Cpuja
+Mostar
+Crna Gora
+Kosoval
+LpHaropa
+Kosovo
+Shgiperid
+Kyn
+Ajaccio
+Veriore
+Ce
+Make
+Lath
+Bari
+Shqiperia
+GMTOJ
+ing
+Korce
+Brindisi
+Vlore
+ATTOKEVTPWH
+Aroiknon
+Autikns
+-MQKEOOVIO
+eddul
+Cagliari
+Palermo
+Messir
+ATOM
+4
+ania
+dcusa
+nstantineAugsburg
+Freiburg
+5.9
+7.3
+8.0
+Wien
+12.4
+Ulm
+tolc
+imBreisgau
+Munchewills
+Salzburg
+Osterreich
+Gyor
+elforto
+Basel
+Budapest
+Deb
+zurich
+PSanktGallen
+Szombathely
+Alfoldes
+Besancon
+Tirof
+Steiermark
+Magyarorszag
+Eszak
+Schweizi
+Suisse/svizzeral
+Dunantur
+Karnten
+Kecskemet
+Lausanne
+Maribor
+svizra
+eve
+Szeged
+Pecs
+Arad
+Slovenija
+Zagreb
+Cy6oTMLa
+Anney
+Timisoa
+@
+hamber
+Trieste
+Osijek
+BojBoduHa
+ezla
+Rijeka
+Banja Luka
+Tuzla
+beorpaa
+diSan
+Hrvatska
+ence
+Genova
+BosnaiHercegovina
+Cp6wja
+-cote
+ino
+Mon
+Zadar
+zur
+bocHaw
+0
+Ancona
+XepyeroBHa
+eHmpanHo
+Cpuja
+Mostar
+Crna Gora
+Kosoval
+LpHaropa
+Kosovo
+Shgiperid
+Kyn
+Ajaccio
+Veriore
+Ce
+Make
+Lath
+Bari
+Shqiperia
+GMTOJ
+inc
+Korce
+Brindisi
+Vlore
+ATTOKEVTPWH
+Aroiknon
+Autikns
+-MQKEOOVIO
+eddur
+cagliari
+Palermo
+Messir
+ATOM
+4
+ania
+dcusa
+nstantineAugsburg
+Freiburg
+0.125
+0.132
+0.136Vien
+0.151
+Ulm
+olo
+imBreisgau
+Munchewills
+Salzburg
+Osterreich
+Gyor
+elforto
+Basel
+Budapest
+Deb
+zurich
+SanktGallen
+Szombathely
+Alfoldes
+Besancon
+Tirof
+Steiermark
+Magyarorszag
+Eszak
+Schweiz
+Suisse/Svizzeral
+Dunantur
+Karnten
+Kecskemet
+Maribor
+ausanne
+Svizra
+eve
+Szeged
+Pecs
+Arad
+Slovenija
+Zagreb
+Cy6oTMLa
+Anney
+Timisoa
+hamberi
+Trieste
+Osijek
+BojBoduHa
+ezia
+Rijeka
+@
+Banja Luka
+Tuzla
+beorpaa
+diSan
+Hrvatska
+ence-
+Genova
+BosnaiHercegovina
+Cp6wja
+-cote
+ino
+Mon
+Zadar
+zur
+bocHaw
+0
+ncona
+XepyeroBMHa
+eHmpanHo
+Cpbuja
+Mostar
+Crna Gora
+Kosoval
+LpHaropa
+Kosovo
+Shgiperid
+Kyn
+Ajaccio
+Veriore
+Ce
+Make
+Bari
+Shqiperia
+GMTOJ
+inc
+Korce
+Brindisi
+Vlore
+ATTOKEVTPWH
+Aroiknon
+Autikns
+-MQKEOOVIO
+edduy
+Cagliari
+Palermo
+Messip
+ATOK
+4
+nEO
+ania
+acusa
+nstantineAugsburg
+Freiburg
+6
+14
+17 Wien
+30
+Ulm
+kolc
+imBreisgau
+Munchewills
+Osterreich
+Gyor
+Basel
+Salzburg
+elforto
+Budapest
+Deb
+zurich
+SanktGallen
+Szombathely
+Alfoldes
+Besancon
+Tirof
+Steiermark
+Magyarorszag
+Eszak
+Schweiz
+Suisse/Svizzeral
+Dunantur
+Karnten
+Kecskemet
+Lausanne
+Maribor
+Svizra
+eve
+Szeged
+Pecs
+Arad
+Slovenija
+Zagreb
+Cy6oTMLa
+Anney
+Timisoa
+hamber
+Trieste
+Osijek
+BojBoduHa
+ezla
+Rijeka
+Banja Luka
+Tuzla
+beorpaa
+diSan
+Hrvatska
+ence
+Genova
+BosnaiHercegovinal
+Cp6wja
+-cote
+ino
+Zadar
+zur
+Mon
+bocHaw
+ncona
+XepyeroBMHa
+eHmpanHo
+Cpuja
+Mostar
+Crna Gora
+Kosoval
+LpHaropa
+Kosovo
+Shgiperid
+Kyn
+Ajaccio
+Veriore
+Ce
+Make
+ath
+Bari
+Shqiperia
+GMTOJ
+inc
+Korce
+Brindisi
+Vlore
+ATOKEVTPUH
+Aroiknon
+Autikns
+-MQKEOOVIO
+eddu
+cagliari
+Palermo
+Messir
+ATOK
+4
+nEO
+ania
+acusa
+nstantineAugsburg
+18
+24
+W27n
+Freiburg
+36
+Ulm
+imBreisgau
+kolc
+Munchewills
+Osterreich
+Gyor
+Basel
+Salzburg
+elforto
+Budapest
+Deb
+zurich
+SanktGallen
+Szombathely
+Alfoldes
+Besancon
+Tirof
+Steiermark
+Magyarorszag
+Eszak
+Schweizi
+Suisse/Svizzeral
+Dunantur
+Karnten
+Kecskemet
+Maribor
+ausanne
+Svizra
+eve
+Szeged
+Pecs
+Arad
+Slovenija
+Zagreb
+Cy6oTMLa
+Anney
+Timisoa
+hamberi
+Trieste
+Osijek
+BojBoduHa
+ezla
+Rijeka
+Banja Luka
+Tuzla
+beorpaa
+diSan
+Hrvatska
+ence-
+Genova
+BosnaiHercegovinal
+Cp6wja
+-cote
+no
+Mon
+Zadar
+zur
+bocHaw
+0
+Ancona
+XepyeroBMHa
+eHmpanHo
+Cpuja
+Mostar
+Crna Gora
+Kosoval
+LpHaropa
+Kosovo
+Shgiperid
+Kyn
+Ajaccio
+Veriore
+Ce
+Make
+Lath
+Bari
+Shqiperia
+GMTOJ
+inc
+Korce
+Brindisi
+Vlore
+ATTOKEVTPWH
+Aroiknon
+Autikns
+-MQKEOOVIO
+eddul
+Palermo
+Messin
+ATOM
+4
+ania
+acusa
+nstantineAugsburg
+Freiburg
+42
+54 
+-Wien
+Ulm
+59
+72
+Kolc
+imBreisgau
+Munchewills
+Salzburg
+Osterreich
+Gyor
+elforto
+Basel
+Budapest
+Deb
+zurich
+PSanktGallen
+Szombathely
+Alfoldes
+Besancon
+Tirof
+Steiermark
+Magyarorszag
+Eszak
+Schweizi
+Suisse/svizzeral
+Dunantur
+Karnten
+Kecskemet
+Maribor
+ausanne
+Svizra
+eve
+Szeged
+Pecs
+Arad
+Slovenija
+Zagreb
+Cy6oTMLa
+Anney
+Timisoa
+@
+hamberi
+Trieste
+Osijek
+BojBoduHa
+ezia
+Rijeka
+@
+Banja Luka
+Tuzla
+beorpaa
+diSan
+Hrvatska
+ence-
+Genova
+BosnaiHercegovina
+Cp6wja
+-cote
+ino
+Mon
+Zadar
+zur
+bocHaw
+ncona
+XepyeroBMHa
+eHmpanHo
+Cpuja
+Mostar
+Crna Gora
+Kosoval
+LpHaropa
+Kosovo
+Shgiperid
+Kyn
+Ajaccio
+Veriore
+Ce
+Make
+Lath
+Bari
+Shqiperia
+GMTOJ
+inc
+Korce
+Brindisi
+Vlore
+ATTOKEVTPWH
+Aroiknon
+Autikns
+-MQKEOOVIO
+eddur
+Cagliari
+Palermo
+Messip
+ATOK
+4
+nEO
+ania
+acusa
+nstantinemin
+max
+mean
+std
+unique links in
+0.000
+4885.000
+27.473
+48.921
+unique links out
+0.000
+15814.000
+6.942
+42.228
+best-practices
+0.380
+1.000
+0.837
+0.103
+length url
+4.000
+105.000
+19.214
+5.436
+Facebook
+0.000
+1.000
+0.461
+0.498
+Instagram
+0.000
+1.000
+0.219
+0.414
+LinkedIn
+0.000
+1.000
+0.159
+0.366
+years old
+0.000
+25.000
+10.308
+7.455
+request time
+0.127
+502.262
+5.265
+9.418
+security header int
+0.000
+15.000
+6.268
+1.941
+Table 1.: Descriptive statistics of the features of the corporate websites of interest
+As a result, we rely on 182 705 firms out of the initial sample (composed of 347 010
+firms) because a consistent number of firms showed missing values for employment,
+a useful indicator to categorize the size of each firm in different groups. To analyse
+the relationship between firms’ characteristics and corporate websites we run a set of
+simple OLS regressions with the following specification:
+y = α + β1xf + β2xt + ϵ
+where y represents one of the ten Digital Dimensions (i.e., one of the relevant features of
+the corporate websites), and xf is the vector that represents the relevant characteristics
+of the firm: age, industry and size. In each regression, we include a set of controls for
+the area in which the firm is located, represented by xt. This is because, beyond the
+specific patterns detectable by the traditional characteristics of the firm, the notion of
+corporate Digital Divide can be influenced (and captured) also by the place where the
+firm is located (e.g. a common available IT infrastructure or the diffusion of digital
+means to run a business activity varies between urban and rural areas and from the
+North to the South). In this regard, to avoid possible mispecifications of the model,
+(since some features of corporate websites, such as the request access time might depend
+on the wide band coverage of the area where the firm is located), we control for the
+possible impact of the wide band. The wide band data are obtained as open data from
+the Italian Authority for Communications Guarantees11. The data represent, for each
+Italian census area, the ratio of households reached by broadband with a speed greater
+than 30mbs over the total number of households in that area.
+11https://maps.agcom.it/
+12
+
+unique links in
+unique links out
+best-practices
+Instagram
+LinkedIn
+Facebook
+years old
+security header int
+request time
+length url
+unique links in
+1.000
+0.018
+-0.042
+0.151
+0.104
+0.179
+0.078
+-0.053
+-0.009
+-0.023
+unique links out
+0.018
+1.000
+-0.005
+0.073
+0.062
+0.087
+0.022
+-0.013
+0.001
+-0.003
+best-practices
+-0.042
+-0.005
+1.000
+0.038
+0.055
+0.008
+-0.038
+-0.055
+-0.011
+-0.026
+Instagram
+0.151
+0.073
+0.038
+1.000
+0.178
+0.524
+0.007
+-0.032
+0.006
+-0.004
+LinkedIn
+0.104
+0.062
+0.055
+0.178
+1.000
+0.293
+0.080
+-0.074
+-0.040
+-0.096
+Facebook
+0.179
+0.087
+0.008
+0.524
+0.293
+1.000
+0.002
+-0.033
+0.001
+0.023
+years old
+0.078
+0.022
+-0.038
+0.007
+0.080
+0.002
+1.000
+-0.056
+-0.060
+-0.167
+security header int
+-0.053
+-0.013
+-0.055
+-0.032
+-0.074
+-0.033
+-0.056
+1.000
+0.769
+0.072
+request time
+-0.009
+0.001
+-0.011
+0.006
+-0.040
+0.001
+-0.060
+0.769
+1.000
+0.075
+length url
+-0.023
+-0.003
+-0.026
+-0.004
+-0.096
+0.023
+-0.167
+0.072
+0.075
+1.000
+Table 2.: Correlation matrix between the ten corporate website features
+13
+
+4.
+Results
+4.1.
+Regression results
+In this section, we discuss the results of the regression analysis for the ten digital-related
+features of corporate websites. Table 3 summarizes the results for the analysis of the
+Digital Divide across different dimensions of Italian firms: size, sector, age and location.
+Micro firms show a negative and significant effect for unique links internal to the
+company, with more attention to internal navigability shown by medium and big firms.
+External links are not significant in micro firms, while we find a positive and significant
+effect for medium and large firms as a sign of more attention devoted to external
+stakeholders in terms of connection and reachability. Best practice has a positive
+and significant effect only on medium-sized firms, with no effect on big firms. This
+counterintuitive result could be interpreted as a sign of lower marginal utility in having
+libraries at the state of the art for big firms.
+Social media variables have all a significant effect across dimensions, with a negative
+sign for micro and a progressive value of the magnitude effect, with the highest value
+for big firms.
+Age, as a proxy of digital experience, tends to be more relevant in big firms, which,
+on average, understood the importance of creating a website many years before.
+Security, speed (request time), and the length of the URL should be interpreted in
+the inverted direction as lower request times and shorter URL improve the accessibility
+of corporate websites.
+We analyze the impact of the corporate Digital Divide also across NUTS-2 digit
+sectors. We take as a sector of reference in terms of quality, Information and
+Communication (“J”), for its direct involvement in the coding procedure or the
+marked attention to the quality of websites, as a fundamental tool to communicate with
+customers. A positive and significant effect is found in the wholesale and retail trade
+(“G”) for the unique internal and external links, confirming the importance of internal
+navigability and external connections for B2C activities. Concerning best practice, a
+positive and significant effect is detected in the sectors “M” (Professional, Scientific
+and Technical activities and “J” (Information and Communication), supporting the
+idea that, on average, firms in those sectors are better informed about the importance
+of high-quality technical libraries. Social Media seems to have different behaviors,
+according to their business functions, confirming the exploratory mapping reported in
+section 3. Accordingly, Instagram and Facebook have seems to play an important role
+in Accommodation and Food Service Activities (sector “I”), as free channels to engage
+with tourism. LinkedIn, more oriented to attracting highly skilled profiles, seems to
+have a bigger impact on sectors with highly specialized knowledge.
+Security Header and request time should be interpreted in the opposite direction, so
+negative and significant effects are signs of firms being more aware of the importance
+of adopting cyber security practices and frameworks able to ensure an adequate level
+14
+
+of speed.
+Age accounts for the years since the date of foundation. A negative and significant
+effect for unique links, best practices and social media is a sign that older firms have a
+worse performance than more digital-born companies.
+The geography of the corporate Digital Divide also presents sharp evidence of the
+fact that urban contexts offer the higher marginal utility of digital means usage for
+firms operating in dynamic and dense economic systems, where firms can exploit the
+network effect (Forman, Goldfarb, and Greenstein, 2005). The geographical location is
+also another important feature that reveals how the Digital Divide is the reverse coin
+of the economic development of territories. North and South dummies show opposite
+behavior. This supports the idea that more industrialized regions, prevalently located
+in the north, are favorable environments for the adoption of digital strategies and the
+relative adoption of skills and investment more than in the south.
+In all the regressions we control for the effect of the wide band, supposing that
+some digital web proxies could be shadowed by a high-quality web infrastructure.
+Disentangling the infrastructural effect is not a trivial task. Accordingly, websites can
+rely on external hosts or local servers. In the first case, the reactivity of the different
+webpages can be related to the quality of the website. In the last case, we can observe
+a good level of wide band coverage with low-quality websites, but also the opposite
+might occur. All in all, we find only four significant values for the impact of wide band
+out of ten regressions. This result is very important since it confirms that with our
+approach to collect multiple features of corporate websites we are able to detect the
+digital footprint of firms beyond the quality of shared web infrastructure.
+4.2.
+Corporate Digital Assessment Index
+Our findings show a multifaceted composite picture, revealing how Digital Divide is
+present across different firms’ dimensions.
+A major problem in measuring the corporate Digital Divide with such a data-driven
+approach is the absence of a theoretical framework to classify the typology of proxies
+into well-defined digital capabilities.
+A very specific research stream narrows on this, analysing the quality of websites as
+a proxy of organisations’ behavior (Mateos et al., 2001; Gok, Waterworth, and Shapira,
+2015; Axenbeck and Breithaupt, 2019; Kinne and Axenbeck, 2020). Analysing the
+quality of websites is a complex task for the presence of several unstructured pieces of
+information that need to be framed into logical theoretical schemes to understand their
+potential economic value. Moreover, it is not trivial to find synthetic measures able to
+capture the multifaceted characteristics of websites, considering also how a high degree
+of customisation makes it difficult to establish ”objective” accountable criteria (Kr´ol
+and Zdonek, 2020).
+Within this literature, Mateos et al. (2001) provide one of the first single index,
+15
+
+unique links in
+unique links out
+best-practices
+Instagram
+LinkedIn
+Facebook
+years old
+security header int
+request time
+length url
+Constant
+0.005***
+(0.000)
+0.000***
+(0.000)
+0.771***
+(0.002)
+-0.965***
+(0.027)
+-1.810***
+(0.032)
+0.376***
+(0.022)
+0.406***
+(0.003)
+0.415***
+(0.001)
+0.010***
+(0.000)
+0.143***
+(0.000)
+Micro firm
+-0.001***
+(0.000)
+-0.000***
+(0.000)
+-0.005***
+(0.001)
+-0.236***
+(0.013)
+-0.576***
+(0.016)
+-0.136***
+(0.011)
+-0.093***
+(0.002)
+0.012***
+(0.001)
+0.001***
+(0.000)
+0.002***
+(0.000)
+Mid-sized firm
+0.002***
+(0.000)
+0.000***
+(0.000)
+0.006***
+(0.001)
+0.322***
+(0.023)
+0.654***
+(0.023)
+0.196***
+(0.020)
+0.074***
+(0.003)
+-0.013***
+(0.001)
+-0.001***
+(0.000)
+-0.002***
+(0.000)
+Large firm
+0.005***
+(0.000)
+0.000***
+(0.000)
+0.003
+(0.003)
+0.505***
+(0.042)
+1.113***
+(0.040)
+0.339***
+(0.038)
+0.109***
+(0.005)
+-0.029***
+(0.002)
+-0.001
+(0.000)
+-0.002**
+(0.001)
+Agriculture, forestry and fishing (A)
+-0.001**
+(0.000)
+-0.000
+(0.000)
+0.001
+(0.003)
+0.694***
+(0.049)
+-0.575***
+(0.090)
+0.260***
+(0.047)
+0.031***
+(0.007)
+-0.007*
+(0.003)
+-0.000
+(0.000)
+-0.003**
+(0.001)
+Manufacturing (C)
+-0.000***
+(0.000)
+-0.000**
+(0.000)
+-0.001
+(0.001)
+-0.134***
+(0.020)
+0.272***
+(0.023)
+-0.494***
+(0.016)
+0.099***
+(0.002)
+-0.002*
+(0.001)
+-0.000**
+(0.000)
+-0.015***
+(0.000)
+Construction (F)
+-0.001***
+(0.000)
+-0.000***
+(0.000)
+-0.002
+(0.002)
+-0.804***
+(0.031)
+-0.194***
+(0.033)
+-0.653***
+(0.022)
+-0.012***
+(0.003)
+0.010***
+(0.001)
+0.001***
+(0.000)
+-0.004***
+(0.000)
+Wholesale and retail trade (G)
+0.003***
+(0.000)
+0.000***
+(0.000)
+-0.005***
+(0.001)
+0.300***
+(0.019)
+-0.002
+(0.024)
+0.033*
+(0.016)
+0.061***
+(0.002)
+0.001
+(0.001)
+0.001***
+(0.000)
+-0.010***
+(0.000)
+Transportation (H)
+-0.002***
+(0.000)
+-0.000
+(0.000)
+-0.009***
+(0.002)
+-0.763***
+(0.044)
+-0.287***
+(0.046)
+-0.735***
+(0.031)
+0.022***
+(0.004)
+0.007***
+(0.002)
+0.000
+(0.000)
+-0.003***
+(0.001)
+Accomodation and food service (I)
+-0.001***
+(0.000)
+0.000
+(0.000)
+-0.015***
+(0.002)
+0.904***
+(0.024)
+-1.411***
+(0.052)
+0.741***
+(0.023)
+0.045***
+(0.003)
+-0.002
+(0.001)
+-0.001***
+(0.000)
+0.009***
+(0.001)
+Information and communication (J)
+0.001***
+(0.000)
+0.000***
+(0.000)
+0.005**
+(0.002)
+-0.262***
+(0.029)
+1.275***
+(0.028)
+-0.133***
+(0.023)
+0.070***
+(0.003)
+-0.019***
+(0.001)
+-0.002***
+(0.000)
+-0.027***
+(0.001)
+Financial and insurance activities (K)
+-0.001*
+(0.000)
+-0.000
+(0.000)
+0.003
+(0.004)
+-0.982***
+(0.080)
+0.723***
+(0.059)
+-0.709***
+(0.051)
+0.017*
+(0.007)
+-0.017***
+(0.003)
+-0.003***
+(0.000)
+-0.009***
+(0.001)
+Real estate activities (L)
+0.001
+(0.000)
+0.000*
+(0.000)
+-0.011***
+(0.003)
+0.168***
+(0.043)
+0.263***
+(0.052)
+0.036
+(0.036)
+0.084***
+(0.005)
+-0.002
+(0.002)
+-0.001
+(0.000)
+0.001
+(0.001)
+Professional, scientific & technical activities (M)
+-0.000
+(0.000)
+0.000
+(0.000)
+0.008***
+(0.002)
+-0.212***
+(0.027)
+1.137***
+(0.027)
+-0.385***
+(0.022)
+0.039***
+(0.003)
+-0.014***
+(0.001)
+-0.002***
+(0.000)
+-0.018***
+(0.000)
+Urban area
+0.000***
+(0.000)
+0.000**
+(0.000)
+0.001
+(0.001)
+0.130***
+(0.013)
+0.170***
+(0.015)
+0.052***
+(0.011)
+0.003
+(0.002)
+-0.002
+(0.001)
+-0.000
+(0.000)
+-0.002***
+(0.000)
+North
+0.000
+(0.000)
+-0.000
+(0.000)
+0.011***
+(0.001)
+-0.102***
+(0.015)
+0.288***
+(0.018)
+-0.201***
+(0.012)
+0.019***
+(0.002)
+-0.008***
+(0.001)
+-0.001***
+(0.000)
+-0.005***
+(0.000)
+South
+0.000***
+(0.000)
+-0.000
+(0.000)
+-0.008***
+(0.001)
+0.067***
+(0.018)
+-0.109***
+(0.023)
+0.162***
+(0.015)
+-0.045***
+(0.002)
+0.014***
+(0.001)
+0.002***
+(0.000)
+0.001**
+(0.000)
+Firm age
+-0.000***
+(0.000)
+0.000
+(0.000)
+-0.000***
+(0.000)
+-0.013***
+(0.000)
+-0.009***
+(0.000)
+-0.010***
+(0.000)
+0.000**
+(0.000)
+-0.000
+(0.000)
+0.000***
+(0.000)
+Wide band
+0.000**
+(0.000)
+0.000
+(0.000)
+0.001
+(0.001)
+0.043*
+(0.017)
+0.131***
+(0.020)
+0.015
+(0.014)
+-0.004*
+(0.002)
+0.002
+(0.001)
+0.000
+(0.000)
+-0.000
+(0.000)
+R-squared:
+0.028
+0.002
+0.005
+0.037
+0.078
+0.035
+0.071
+0.013
+0.009
+0.041
+Adj. R-squared:
+0.027
+0.002
+0.005
+0.071
+0.013
+0.009
+0.041
+N. of Observations
+182,705
+182,705
+182,705
+182,705
+182,705
+182,705
+182,705
+182,705
+182,705
+182,705
+Table 3.: regression results considering as dependent variables the website feature extracted. Notice that for the features Instagram, Linkedin and
+Facebook, we use the Logit model and consequently, we report the relative Pseudo R-squared.
+16
+
+called Web Assessment Index (WAI).12
+Elaborating on this literature from the point of view of the digital strategy of the
+firm, we interpreted and classified the extracted features into four different aspects
+related to the digital strategy of the firm:
+(1) stakeholder engagement
+(2) technical capabilities
+(3) internal organisation
+(4) digital culture
+Stakeholder engagement includes the capabilities of the firm to establish links and
+connections with external stakeholders, such as customers and suppliers. Technical
+capabilities account for the competencies of the firm to build a state-of-the-art digital
+framework in terms of Libraries, security and speed. Internal organisation represents
+the ability of the firm to coherently and purposefully orchestrate internal information
+flows. Digital Culture stands for the historical trajectory in which the firm is inserted
+(awareness of the importance of web as a strategic resource).
+Aggregating these four indicators, we propose a synthetic index to capture the
+Corporate digital divide with a single dimension.
+To build our index, we normalize the variables with a MinMax technique, inverting
+the scale of the values where necessary (the length of the URL, Facebook, request
+time, and security header) for the purpose of interpretability. Then, we calculated the
+Corporate Digital Assessment Index (CoDAI) as the weighted sum of each element, as
+follows:
+CoDAI = (Stakeholder Engagement/2) + (Technical Capabilities/3) + (Internal Organization/2) + (Digital Culture)
+(1)
+Table 4 shows the dimensions and indicators we used to build the CoDAI. Table 4
+summarizes the regression results for the analysis of the determinants of the CoDAI
+and its four dimensions. Our proposal shows the expected significance level for firm
+dimension, with the prominence of big firms in comparison to medium and micro. We
+find interesting results also across sectors. For instance, the case of wholesale and
+retail trade (G) shows a positive and significant effect for what concerns stakeholder
+engagement, but a negative and significant effect for the technical capabilities subpart.
+Wideband is significant only for stakeholder engagement. This could be explained by
+12The authors built their index on universities’ websites, considering four dimensions of analysis: site content,
+speed, accessibility and navigability. While the first two are quite straightforward, the last two need to be
+explicitly framed. As underlined also by Vaughan (2004), accessibility has been proxied respectively by search
+engine indexes and popularity (the number of external links can imply more traffic). Navigability has been
+mainly measured as the number of steps (clicks) to access relevant information for the user. Other measures
+have been introduced as usability, which can be seen as an extension of navigability, more oriented to the
+convenience of users to navigate the website for several reasons, such as easiness, responsivity, and aesthetic
+reasons, which have become crucial especially in the last years to retain and acquire users (Mateos et al., 2001;
+Dickinger and Stangl, 2013; Kr´ol and Zdonek, 2020).
+17
+
+Indicator
+Dimension
+Quality of external links
+Stakeholder Engagement
+Facebook
+Instagram
+Linkedin
+Best Practice
+Technical Capabilities
+Security
+Speed
+URL’s length
+Internal Organization
+Quality of internal links
+Website’s age
+Digital Culture
+Table 4.: Corporate Digital Assessment Index (CoDAI): indicators and dimensions.
+the fact that the majority of the proxies, employed to realize such as category, rely
+on the adoption of external platforms. With no surprise, we find a negative effect for
+three out of four sub-dimensions of the CoDAI concerning the age of the firm. This
+could be interpreted as a more reactive digital behavior of newborn digital firms in
+comparison to more experienced ones.
+Furthermore, the relevance of our proposed framework is evident if we compare
+the results of our CoDAI with the simple sum of the ten indicators (see table 6 in
+the appendix). When we use a simple sum, we can notice how some of the Digital
+Divide aspects previously pointed out, tend to become blurry and difficult to interpret.
+For instance, the industrial prominence of Accommodation and food service (I) is in
+contrast with previous findings on the ICT sector. In addition, the South and North
+geographical areas signs are inverted and the wideband variable becomes positive and
+significant.
+To highlight the sharp corporate Digital Divide of Italy we map the results of our
+CoDAI across NUTS regions. Figure 3 displays three rough geographical clusters,
+representative of the three main areas of Italy: North, Centre and South (see also figure
+4 in the appendix for the map at municipal level). This result is noteworthy as confirms
+the traditional North-South economic divide, using also a novel set of web-related
+measures.
+5.
+Final Discussion
+Nowadays, the astonishing pervasiveness of ICTs in production and consumption
+processes has revolutionized how firms operate and strategize. As in every technological
+transformation, the time and quality of adoption of digital means have created a
+corporate Digital Divide between more structured and digital-oriented firms and more
+traditional ones. Staying behind this new paradigm has several consequences for
+the future of small businesses, which characterize the industrial structure of “digital
+latecomers” such as Italy. Moreover, no industry is immune to the increasing birth of
+18
+
+stakeholder eng.
+technical capabilities
+digital culture
+internal organization
+CoDAI
+Constant
+0.827***
+(0.006)
+2.346***
+(0.002)
+0.252***
+(0.003)
+0.862***
+(0.001)
+1.672***
+(0.003)
+Micro firms
+-0.076***
+(0.003)
+-0.018***
+(0.001)
+-0.049***
+(0.001)
+-0.003***
+(0.000)
+-0.075***
+(0.002)
+Mid-sized firms
+0.119***
+(0.005)
+0.020***
+(0.002)
+0.040***
+(0.003)
+0.004***
+(0.000)
+0.079***
+(0.003)
+Large firms
+0.221***
+(0.010)
+0.033***
+(0.004)
+0.058***
+(0.005)
+0.007***
+(0.001)
+0.128***
+(0.006)
+NACE sector A
+0.029*
+(0.012)
+0.009
+(0.005)
+-0.028***
+(0.006)
+0.003*
+(0.001)
+-0.017*
+(0.007)
+NACE sector C
+0.132***
+(0.004)
+0.002
+(0.002)
+0.064***
+(0.002)
+0.015***
+(0.000)
+0.105***
+(0.003)
+NACE sector F
+0.033***
+(0.005)
+-0.014***
+(0.002)
+-0.022***
+(0.003)
+0.002***
+(0.000)
+-0.018***
+(0.003)
+Nace sector G
+0.047***
+(0.004)
+-0.008***
+(0.002)
+0.037***
+(0.002)
+0.013***
+(0.000)
+0.053***
+(0.003)
+NACE sector H
+0.039***
+(0.008)
+-0.017***
+(0.003)
+-0.001
+(0.004)
+0.001
+(0.001)
+0.004
+(0.005)
+NACE sector I
+-0.074***
+(0.006)
+-0.011***
+(0.002)
+0.051***
+(0.003)
+-0.009***
+(0.001)
+0.024***
+(0.004)
+NACE sector J
+0.201***
+(0.006)
+0.026***
+(0.002)
+0.079***
+(0.003)
+0.028***
+(0.001)
+0.152***
+(0.004)
+NACE sector K
+0.149***
+(0.013)
+0.023***
+(0.005)
+0.011
+(0.007)
+0.008***
+(0.001)
+0.060***
+(0.008)
+NACE sector L
+0.050***
+(0.009)
+-0.008*
+(0.004)
+0.048***
+(0.005)
+-0.000
+(0.001)
+0.058***
+(0.006)
+NACE sector M
+0.238***
+(0.006)
+0.023***
+(0.002)
+0.048***
+(0.003)
+0.018***
+(0.001)
+0.124***
+(0.003)
+Urban area
+0.030***
+(0.003)
+0.003**
+(0.001)
+0.004**
+(0.001)
+0.003***
+(0.000)
+0.014***
+(0.002)
+North
+0.067***
+(0.003)
+0.020***
+(0.001)
+0.007***
+(0.002)
+0.005***
+(0.000)
+0.033***
+(0.002)
+South
+-0.038***
+(0.004)
+-0.024***
+(0.002)
+-0.030***
+(0.002)
+-0.001*
+(0.000)
+-0.048***
+(0.002)
+Firm age
+-0.001***
+(0.000)
+-0.000***
+(0.000)
+0.007***
+(0.000)
+-0.000***
+(0.000)
+0.006***
+(0.000)
+Wide band
+0.018***
+(0.004)
+-0.001
+(0.001)
+-0.001
+(0.002)
+0.000
+(0.000)
+0.003
+(0.002)
+R-squared:
+0.049
+0.014
+0.17
+0.043
+0.168
+Adj. R-squared:
+0.048
+0.014
+0.17
+0.043
+0.168
+N. of observations
+182,705
+182,705
+182,705
+182,705
+182,705
+Table 5.: regression results considering the CoDAI and its components as dependent variables.
+For a legend of NACE sectors see table 3
+.
+hybrid cyber-physical systems which disrupt how products are designed, realized and
+delivered.
+With few exceptions, the extant literature mapped the digital divide phenomenon
+using data on broadband access, neglecting the role of digital tools and the relative
+competencies built on it.
+With this paper, we continue along the research stream on the use of web scraping to
+identify digital economy phenomena (Gok, Waterworth, and Shapira, 2015; Blazquez,
+Domenech, and Deb´on, 2018; Axenbeck and Breithaupt, 2019; Heroux-Vaillancourt,
+Beaudry, and Rietsch, 2020; Kinne and Axenbeck, 2020; Kr¨uger et al., 2020; Thonipara
+et al., 2022).
+In particular, this explorative work introduces a novel way to map and evaluate the
+19
+
+Figure 3.: The distribution of the CoDAI across Italian regions (NUTS3).
+corporate digital divide at the granular level, overcoming the country-level perspective.
+Leveraging the potentiality of web scraping techniques, we inquire about the corporate
+Digital Divide, extracting, storing and analysing a set of website features related to
+the digital footprints of 182 705 Italian firms. We purposefully focus only on technical
+features as less manipulable in comparison to content and experience and with a less
+degree of variability.
+To improve the comparability of our results across firms, we introduce a Corporate
+Digital Assessment Index (CoDAI), interpreting the results across four distinctive
+aspects of the digital strategy of the firm. The CoDAI and its four dimensions confirm
+the main drivers of the corporate Digital Divide highligted in the literature: we find a
+prominence of big firms, active in ICT-related fields and localized in more industrialized
+20
+
+Augsburg
+Freiburg
+Ulm
+1.69
+1.78
+Wien
+1-87
+1.95
+imBreisgau
+olc
+Munchewills
+Belforto
+Basel
+Salzburg
+Osterreich
+Gvor
+Budapest
+De
+Zurich
+SanktGallen
+Besancon
+Tirof
+Steiermark
+Szombathely
+Alfoldes
+Magyarorszag
+Schweiz/
+Eszak
+Suisse/Svizzeral
+Karnten
+Dundntij
+Lausanne
+Maribor
+Kecskemet
+Svizra
+neve
+Szeged
+Slovenija
+Pecs
+Ara
+Annecy
+Zagreb
+Cy60TMLa
+Timiso
+chamber
+Trieste
+ezia
+Osijek,
+Bojeoduna
+Rijeka
+Tuzla
+beorpaA
+Banja Luka
+vence
+diSan
+Hrvatska
+Genova
+BosnaiHercegovina/
+Cp6wja
+es-Cote
+ino
+Azur
+Mon
+Zadar
+bOCHaM
+Ancona
+XepueroBHa
+Lempanh
+Cp6uja
+-Mostar
+Crna Gora
+Kosova
+LipHaropa
+Kosovo
+Shgiperia
+Veriore
+Ky
+Ajaccio
+Ce
+Mak
+Bari
+inc
+Shgiperia
+GMTC
+Brindisi
+Korce
+Vlore
+ATTOKEVTPO
+Atoikno
+HrtEipo
+AutiKr
+-MAKESOV
+inppa.
+Cagliari
+Palermo
+Messir
+ATTO
+ne
+ania
+onstantine
+esndurban contexts.
+Notwithstanding the relevance of our contribution to the analysis of the corporate
+Digital Divide, this work is not free of limits. The literature on the economic
+interpretation of websites and digital means is still in its infancy. Therefore, the
+iterative dialogue between empirical testing and theoretical building offers food for
+thought for multidisciplinary research between economics, management, and data
+science.
+In particular, the relevant elements of a website are changing with an impressive
+frequency. In this regard, multimedia elements (e.g., images, videos and sounds) have
+skyrocketed as means of communication thanks to the introduction of new technological
+enablers (e.g., high-speed broadband), as well as website design has become an important
+method to establish a website quality (Rasmussen and Thimm, 2015). In addition, also
+considering the myriad of legal and business services that have progressively emerged
+thanks to cloud computing, websites are more and more part of the wider ecosystem.
+This research opens up new perspectives of data-driven digital monitoring, possibly
+extending the analysis to more extensive samples of firms across countries, for instance,
+using the same approach for all firms in ORBIS. The building of proxies able to
+capture, in economic terms, the digital behaviour of firms represents an essential
+tool for policymakers. The firm’s digital footprint is an important measure to define
+targeted policies and development strategies for its replicability, unobtrusiveness,
+frequent updating, extension to new website information, and industrial benchmarking.
+In particular, the Italian National Recovery and Resilience Plan (named“NRRP”)
+established to help the country to recover from the Covid-19 pandemic has 21% of the
+total funds dedicated to digitalisation (with actions such as fastest connection through
+ultra-broadband, incentives for the adoption of innovative technologies by the private
+sector, revitalisation of touristic and cultural sectors) 13. The building of new tools and
+methodologies, such as the ones we provide with this work, able to identify laggard
+territories and NUTS-3 regions, represents a crucial step in an era in which policies
+are more and more data-driven. With the awareness of the limit and potentiality of
+our analysis, we contribute to this research stream with an innovative and original
+approach, which joint public-private strategic partnerships can further leverage.
+13see https://www.governo.it/it/approfondimento/le-missioni-e-le-componenti-del-pnrr/16700.
+21
+
+References
+Abeysekera, I. 2019. “How best to communicate intangible resources on websites to
+inform corporate-growth reputation of small entrepreneurial businesses.” Journal of
+Small Business Management 57 (3): 738–756.
+Ageeva, E., TC Melewar, C. Foroudi, P.and Dennis, and Z. Jin. 2018. “Examining
+the influence of corporate website favorability on corporate image and corporate
+reputation: Findings from fsQCA.” Journal of Business Research 89: 287–304.
+Antonelli, C. 2003. “The digital divide: understanding the economics of new information
+and communication technology in the global economy.” Information Economics and
+Policy 15 (2): 173–199.
+Arora, S. K., Y. Li, J. Youtie, and P. Shapira. 2016. “Using the wayback machine
+to mine websites in the social sciences: A methodological resource.” Journal of the
+Association for Information Science and Technology 67 (8): 1904–1915.
+Arora, Sanjay K., Yin Li, Jan Youtie, and Philip Shapira. 2020. “Measuring
+dynamic capabilities in new ventures: exploring strategic change in US green goods
+manufacturing using website data.” The Journal of Technology Transfer 45 (5):
+1451–1480.
+Auger, P. 2005. “The impact of interactivity and design sophistication on the
+performance of commercial websites for small businesses.” Journal of Small Business
+Management 43 (2): 119–137.
+Axenbeck, J., and P. Breithaupt. 2019. Web-based innovation indicators: Which firm
+website characteristics relate to firm-level innovation activity? ZEW Discussion
+Papers 19-063. ZEW - Leibniz Centre for European Economic Research. https:
+//ideas.repec.org/p/zbw/zewdip/19063.html.
+Barney, Jay B. 1991. “Firm Resources and Sustained Competitive Advantage.” Journal
+of Management. 17 (1): 99–120.
+Baskerville, R. L., M. D. Myers, and Y. Yoo. 2020. “Digital First: The Ontological
+Reversal and New Challenges for Information Systems Research.” MIS Quarterly 44
+(2): 509–523.
+Beaudry, C., M. H´eroux-Vaillancourt, and C. Rietsch. 2016. “Validation of a web
+mining technique to measure innovation in high technology Canadian industries.”
+1–25.
+Billon, M., R. Ezcurra, and Lera-L´opez F. 2009. “Spatial Effects in Website Adoption
+by Firms in European Regions.” Growth and Change 40 (1): 54–84.
+Blank, G., M. Graham, and C. Calvino. 2018. “Local geographies of digital inequality.
+Social Science Computer Review.” Social Science Computer Revie 36 (1): 82–102.
+Blanka, C., B. Krumay, and D. Rueckel. 2022. “The interplay of digital transformation
+and employee competency: A design science approach.” Technological Forecasting
+and Social Change 178 (C).
+Blazquez, D., and J. Domenech. 2018. “Big Data sources and methods for social and
+22
+
+economic analyses.” Technological Forecasting and Social Change 130 (C): 99–113.
+Blazquez, D., J. Domenech, and A. Deb´on. 2018. “Do corporate websites’ changes
+reflect firms’ survival?” Online Information Review 42 (6): 956–970.
+Brynjolfsson, E., C. Wang, and X. Zhang. 2021. “The economics of IT and digitization:
+Eight questions for research.” MIS Quarterly 45 (1): 473–477.
+Castells, M. 1996. he Rise of the Network Society, The Information Age: Economy,
+Society and Culture. Malden, MA; Oxford, UK: Blackwell.
+Corrocher, N., and A. Ordanini. 2002. “Measuring the digital divide: a framework for
+the analysis of cross-country differences.” Journal of Information technology 17 (1):
+9–19.
+Daniele, V. 2021. “Territorial disparities in labour productivity, wages and prices in
+Italy: What does the data show?” European Urban and Regional Studies 28 (4):
+431–449.
+Dickinger, A., and B. Stangl. 2013. “Website performance and behavioral consequences:
+A formative measurement approach.” Journal of Business Research 66 (6): 771–777.
+Ellinger, A. E., D. F. Lynch, and J. D. Hansen. 2003. “Firm size, web site content,
+and financial performance in the transportation industry.” Industrial Marketing
+Management 32 (3): 177–185.
+Faulkner, P., and J. Runde. 2009. “On the identity of technological objects and user
+innovations in function.” Academy of Management Review 34 (3): 442–462.
+Fink, C., and J. Kenny, C. 2003. “W(h)ither the Digital Divide?” info, The journal of
+policy, regulation and strategy for telecommunications 5 (6): 15–24.
+Floridi, L. 2014. The Fourth Revolution: How the Infosphere is Reshaping Human
+Reality. Oxford University Press UK.
+Forman, C. 2005. “The Corporate Digital Divide: Determinants of Internet Adoption.”
+Management Science 51 (4): 641–654.
+Forman, C., A. Goldfarb, and S. Greenstein. 2005. “How did location affect adoption
+of the commercial Internet? Global village vs. urban leadership. Journal of urban
+Economics.” Journal of urban Economics 58 (3): 389–420.
+George, G., E. C Osinga, D. Lavie, and B. A Scott. 2016. “Big data and data
+science methods for management research.” Academy of Management Journal 59
+(5): 1493–1507.
+Giustiziero, G., T. Kretschmer, D. Somaya, and B. Wu. 2021. “Hyperspecialization and
+hyperscaling: A resource-based theory of the digital firm.” Strategic Management
+Journal .
+Gok, A., A. Waterworth, and P. Shapira. 2015. “Use of web mining in studying
+innovation.” Scientometrics 102 (1): 653–671.
+Hern´andez, B., J. Jim´enez, and M. J. Mart´ın. 2009. “Key website factors in e-business
+strategy.” International Journal of Information Management 29 (5): 362–371.
+Heroux-Vaillancourt, M., C. Beaudry, and C. Rietsch. 2020. “Using web content analysis
+to create innovation indicators - What do we really measure?” Quantitative Science
+23
+
+Studies 1 (4): 1601–1637.
+Kinne, J., and J. Axenbeck. 2020. “Web mining for innovation ecosystem mapping: a
+framework and a large-scale pilot study.” Scientometrics 125 (3): 2011–2041.
+Kinne, J., and B. Resch. 2018. “Generating Big Spatial Data on Firm Innovation
+Activity from Text-mined Firm Websites.” GI Forum - Journal for Geographic
+Information Science 6 (1): 82–89.
+Kr´ol, K., and D. Zdonek. 2020. “Aggregated indices in Website quality assessment.”
+Future Internet 12 (4): 72.
+Kr¨uger, M., J. Kinne, D. Lenz, and B. Resch. 2020. The digital layer: How innovative
+firms relate on the web. ZEW Discussion Papers 20-003. ZEW - Leibniz Centre for
+European Economic Research.
+Kyriakidou, V., C. Michalakelis, and T. Sphicopoulos. 2011. “Digital divide gap
+convergence in Europe.” Technology in Society 33 (3): 265–270.
+Li, Y., S. Arora, J. Youtie, and P. Shapira. 2018. “Using web mining to explore Triple
+Helix influences on growth in small and mid-size firms.” Technovation 76: 3–14.
+Liu, Y., J. Dong, L. Mei, and R. Shen. 2022. “Digital innovation and performance of
+manufacturing firms: An affordance perspective.” Technovation 102458.
+Lythreatis, Sophie, Sanjay Kumar Singh, and Abdul-Nasser El-Kassar. 2022. “The
+digital divide: A review and future research agenda.” Technological Forecasting and
+Social Change 175 (C).
+Mateos, M. B., A. C. Mera, F. J. M. Gonz´alez, and ´O. R. G L´opez. 2001. “A new Web
+assessment index: Spanish universities analysis.” Internet research 11 (3): 226–234.
+Matthess, M., and S. Kunkel. 2020. “Structural change and digitalization in developing
+countries: Conceptually linking the two transformations.” Technology in Society 63.
+Pukelis, L., and V. Stanciauskas. 2019. sing Internet Data to Complement Traditional
+Innovation Indicators. Technical Report. Public Policy and Management Institute
+(PPMI). URL:https://www.ippapublicpolicy.org/file/paper/5d073ea805eb6.
+pdf.
+Rasmussen, K. B., and H. Thimm. 2015. “Circumventing nonresponse-upgrading
+traditional company survey data with unobtrusive data from company websites.”
+ulletin of Sociological Methodology 127 (1): 85–96.
+Sanders, J. W., and L. Galloway. 2013. “Rural small firms’ website quality in transition
+and market economies.” Journal of Small Business and Enterprise Development 20
+(4): 788–806.
+Saridakis, G., Y. Lai, A. M. Mohammed, and J. M. Hansen. 2018. “Industry
+characteristics, stages of E-commerce communications and entrepreneurs and SMEs
+revenue growth.” Technological Forecasting and Social Change 128 (C): 56–66.
+Shakina, E., P. Parshakov, and A. Alsufiev. 2021. “Rethinking the corporate digital
+divide: The complementarity of technologies and the demand for digital skills.”
+Technological Forecasting and Social Change 162 (C).
+Szeles, M. R. 2018. “New insights from a multilevel approach to the regional digital
+24
+
+divide in the European Union.” Telecommunications Policy 42 (6): 452–463.
+Tambe, P., L. Hitt, D. Rock, and E. Brynjolfsson. 2020. Digital Capital and Superstar
+Firms. NBER Working Papers 28285. National Bureau of Economic Research, Inc.
+https://ideas.repec.org/p/nbr/nberwo/28285.html.
+Teece, D. J., and G. Linden. 2017. “Business models, value capture and the digital
+enterprise.” Journal of Organization Design 6 (1): 1–14.
+Thonipara, A., G. Sternberg, R., T. Proeger, and L. Haefner. 2022. “Digital divide, craft
+firms’ websites and urban-rural disparities—empirical evidence from a web-scraping
+approach.” Review of Regional Research 1–14.
+Vaughan, L. 2004. “Exploring website features for business information.” Scientometrics
+61 (3): 467–477.
+Vehovar, V., P. Sicherl, T. H¨using, and V. Dolnicar. 2006. “Methodological Challenges
+of Digital Divide Measurements.” Inf. Soc. 22: 279–290.
+Verhoef, P. C., T. Broekhuizen, Y. Bart, A. Bhattacharya, J. Q. Dong, N. Fabian,
+and M Haenlein. 2021. “Digital transformation: A multidisciplinary reflection and
+research agenda.” Journal of Business Research 122 (C): 889–901.
+Volberda, H.W, S. Khanagha, C. Baden-Fuller, O. R Mihalache, and J. Birkinshaw.
+2021. “Strategizing in a digital world: Overcoming cognitive barriers, reconfiguring
+routines and introducing new organizational forms.” Long Range Planning 54 (5):
+102110.
+Warner, K. SR, and M. W¨ager. 2019. “Building dynamic capabilities for digital
+transformation: An ongoing process of strategic renewal.” Long range planning 52
+(3): 326–349.
+Wells, J. D., J. S Valacich, and T. J Hess. 2011. “What signal are you sending? How
+website quality influences perceptions of product quality and purchase intentions.”
+MIS quarterly 373–396.
+Wernerfelt, B. 1984. “A resource based view of the firm.” Strategic management journal
+5 (2): 171–180.
+Youtie, J., D. Hicks, P. Shapira, and Horsley. 2012. “Pathways from discovery to
+commercialisation: using web sources to track small and medium-sized enterprise
+strategies in emerging nanotechnologies.” Technology Analysis and Strategic
+Management 24 (10): 981–995.
+25
+
+6.
+Appendix
+sum of the ten indicators
+Constant
+2.601***
+(0.011)
+Micro firm
+-0.178***
+(0.006)
+Mid-sized firm
+0.244***
+(0.010)
+Large firm
+0.416***
+(0.019)
+A
+0.115***
+(0.023)
+C
+-0.064***
+(0.008)
+G
+0.088***
+(0.008)
+F
+-0.299***
+(0.011)
+H
+-0.321***
+(0.015)
+I
+0.311***
+(0.011)
+J
+0.172***
+(0.011)
+M
+0.071***
+(0.011)
+K
+-0.205***
+(0.024)
+L
+0.101***
+(0.018)
+Urban area
+0.055***
+(0.005)
+North
+-0.026***
+(0.006)
+South
+0.019*
+(0.008)
+Firm age
+0.001***
+(0.000)
+Wide band
+0.027***
+(0.007)
+R-squared:
+0.038
+Adj. R-squared:
+0.038
+N. of Observations
+182705
+Table 6.: OLS regression results. The dependent variable is the sum of the values of the ten
+indicators of the corporate web sites.
+26
+
+Figure 4.: The distribution of the CoDAI across Italian municipalities.
+27
+
+Augsburg
+r
+Bratislava
+Munchen
+Budapest
+Debrecer
+Szombathel
+Magyarorszag
+Oradea
+Szegec
+Sloyentija
+Pecs
+rad
+Zagreb
+FCy60TMLa
+Timisoara
+Osijek
+esita
+ania Luka
+beorpaa
+Sar
+Hrvatska
+BosnaiHercegovina
+Cp6wja
+Zadar
+bocHaM
+XeperoBMHa
+LpHaropa
+Kosovo
+Shgiperia
\ No newline at end of file
diff --git a/L9E4T4oBgHgl3EQfKAwg/content/tmp_files/load_file.txt b/L9E4T4oBgHgl3EQfKAwg/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f258a34b38e872e97662440337f92314e3e44833
--- /dev/null
+++ b/L9E4T4oBgHgl3EQfKAwg/content/tmp_files/load_file.txt
@@ -0,0 +1,2628 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf,len=2627
+page_content='Measuring Corporate Digital Divide with web scraping: Evidence  from Italy  Leonardo Mazzonia,b, Fabio Pinellib and Massimo Riccabonib  a University of Padua - Department of Economics and Management, Padua (Italy);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  bIMT School for Advanced Studies, Lucca (Italy)  Abstract  With the increasing pervasiveness of ICTs in the fabric of economic activities, the  corporate digital divide has emerged as a new crucial topic to evaluate the IT  competencies and the digital gap between firms and territories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Given the scarcity of  available granular data to measure the phenomenon, most studies have used survey  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' To bridge the empirical gap, we scrape the website homepage of 182 705 Italian  firms, extracting ten features related to their digital footprint characteristics to  develop a new corporate digital assessment index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Our results highlight a significant  digital divide across dimensions, sectors and geographical locations of Italian firms,  opening up new perspectives on monitoring and near-real-time data-driven analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Keywords: Digital Divide;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Web-based indicators;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Corporate web scraping;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Digital  footprint;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Digital transformation  Acknowledgements: The authors would like to thank the following projects for the  financial support and comments received: Artes 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='0 -Advanced Robotics and enabling  digital Technologies & Systems;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' ”Rinascita dei Borghi” funded by Eurispes (Institute  for Political, Economic and Social Studies) and the Italian Ministry of Economy and  Finance;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' ”Borghi, paesi, aree interne: infrastrutture, sostenibilit`a e qualit`a della vita”  funded by the Italian Ministry of University and Research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Corresponding Author: Leonardo Mazzoni.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Email: leonardo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='mazzoni@imtlucca.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='it  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='04925v1  [econ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='GN]  12 Jan 2023  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Introduction  Digital transformation has recently emerged as a driving force able to forge the strategic  orientation of firms to grow and innovate by means of digital technologies and the  relative capabilities built on them (Blanka, Krumay, and Rueckel, 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Verhoef  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Volberda et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' With the increasing pervasiveness of ICTs in the  fabric of economic activities (Antonelli, 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Baskerville, Myers, and Yoo, 2020), a  heterogeneous response by individuals, firms and institutions has occurred, translating  into different rates of adoption of, and proficiency with, digital tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' This phenomenon  has been generally analyzed under the umbrella of the Digital Divide, a concept able to  represent the gap in accessing IT infrastructure (Fink and Kenny, 2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Afterwards,  the capillary diffusion of ICTs contributed to extend the Digital Divide definition  also in its usage, involving dedicated human resources and digital market providers  (Corrocher and Ordanini, 2002;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Kyriakidou, Michalakelis, and Sphicopoulos, 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' In  this respect, the literature on Digital Divide has not developed a homogenous corpus of  analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' New forms are rapidly emerging with growing attention to its specific aspects  for industries, firms, and territorial levels (Ellinger, Lynch, and Hansen, 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Shakina,  Parshakov, and Alsufiev, 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Lythreatis, Singh, and El-Kassar, 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Thonipara  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Particularly, the corporate Digital Divide is a crucial emerging topic in  the management literature for the consequences brought by the Industry 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='0 paradigm  on the competencies to develop (Shakina, Parshakov, and Alsufiev, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' As yet,  the literature on the Digital Divide has remained relatively silent on the mechanisms  occurring at the firm level, with very few studies addressing this specific subject  (Lythreatis, Singh, and El-Kassar, 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' This can be attributed to the fact that the  Corporate Digital Divide is still difficult to observe for the lack of accounting metrics  able to provide information on IT investment or the implementation of information  systems updating in the cognitive architecture of the firm (Vehovar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Tambe  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  A possible way out from data shortage on the digital behavior of firms came from the  analysis of corporate websites (Blazquez and Domenech, 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Accordingly, corporate  websites are the “digital footprint” of organizations and part of new codified knowledge,  which is increasingly becoming accessible for researchers and analysts to study the  performance of firms in complementary/additional ways, with respect to the more  traditional data sources (Gok, Waterworth, and Shapira, 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Blazquez, Domenech,  and Deb´on, 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Kinne and Resch, 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' This is because websites represent the  self-expression of strategic information to external stakeholders: the products/services  commercialized, delivery modes, mission and vision, the internal competencies, the  relationships with other companies and universities, research activities, their location  and facilities (Youtie et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Gok, Waterworth, and Shapira, 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Saridakis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Pukelis and Stanciauskas, 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Moreover, new decision-making  procedures, cost structures, organizational routines and digital operations have been  2  consequently introduced (Teece and Linden, 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Verhoef et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' This makes  websites, especially corporate ones, an essential open data source not only to capture the  visibility and reputation of the firm but also to study the broader digital competencies  beyond them (Auger, 2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Despite a firm may rely on software houses or external IT  consultants to build their websites, the specific technical features that characterize them  imply indirect agency to transform digital objects by means of “sensing capabilities”  on the intrinsic value of digital technologies (Faulkner and Runde, 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Accordingly,  some studies have exploited the characteristics of websites as wider signals of the digital  awareness of firms (Wells, Valacich, and Hess, 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Abeysekera, 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Thanks to the recent evolution of web-scraping techniques (Arora et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Axenbeck and Breithaupt, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Arora et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2020), our aim is to leverage information  extracted from the corporate website to study the corporate Digital Divide at a large  scale, considering different firms’ characteristics (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', dimension, industry, age, and  geographical context).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' More concretely, we scraped the websites of 182 705 Italian  firms in the period 2020-2021, extracting ten features related to the technical libraries,  performances, security level, speed, links and social media.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Next, we analyzed corporate  website features in combination with the relative corporate information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Instead of  considering the contents of websites, we focused on the most “objective” IT features  available, following the research line aimed to exploit new IT technologies as new  economic-related proxies of digital capabilities (George et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Brynjolfsson, Wang,  and Zhang, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  We analyze the Italian case because of the well-known sharp socio-economic  disparities between northern and southern regions (Daniele, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Moreover, Italy is a  unique case in Europe of an industrialized country lagging behind other EU countries  in terms of digital readiness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='1  Our results highlight a significant corporate Digital Divide across firms’ attributes  such as dimension, sector and age, and territorial characteristics where the firm is  located, opening up new perspectives of monitoring and near-real-time data-driven  analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Controlling for the impact of wide band our results still hold, paving the way  for further empirical investigations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Previous research has spotted a shortcoming of studies in the analysis of corporate  digital behaviour with large website samples (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', Lythreatis, Singh, and El-Kassar,  2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Our study contributes to fill this gap, nuancing the current understanding of  firms’ Digitial Divide, by exploiting big open-source data directly extracted by corporate  websites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' The extracted features described a multifaceted phenomenon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Interestingly  as evidenced by low correlation among different elements, the digital-related variables  capture specific capabilities and justify this explorative analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' However, in order  to ensure comparability among firms (and of territories), we propose an aggregation  of the ten features, interpreting and categorizing them according to a theoretical  1See  the  results  of  the  Digital  Economy  Society  index  available  at:  https://digital-strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='europa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='eu/en/policies/desi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  3  building process based on the digital space(s) of the firm: technical capabilities, internal  organizations,external stakeholder engagement, and digital culture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  The paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Section 2 reviews the literature on the economic  and Digital Divide and the role of websites in measuring digital footprint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Section 3  describes the data collection process and the methodology adopted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Section 4 displays  the results of the empirical investigation of the Digital Divide phenomenon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Section 5  discusses the findings, underlining the limitations of this work and concluding with  final remarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Literature review  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  The Digital Divide notion: a corporate perspective  The notion of the Digital Divide was initially coined as the different rates of adoption  of ICTs of individuals and households (Fink and Kenny, 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Vehovar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Kyriakidou, Michalakelis, and Sphicopoulos, 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Then the massive diffusion of  the internet has shifted the attention beyond the simple rate of adoption, reaching  a further layer related to the usage of ICTs (Corrocher and Ordanini, 2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' The  transition from the industrial society to the information economy(Castells, 1996) and  the recent conceptualisation of “onlife” societies (Floridi, 2014) with the new role  of ICTs as “reality shapers” (Baskerville, Myers, and Yoo, 2020) has magnified the  relevance of this divide, as a reflection of the socio-economic gap between individuals,  firms and territories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Accordingly, the meaning of the Digital Divide has become a  multifaceted and more elaborated notion, including the developed skills and abilities to  use technical tools (Fink and Kenny, 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Szeles, 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Matthess and Kunkel, 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  This has allowed elaborating more on the competitiveness drivers of the digital economy,  being ICTs firmly embedded in the fabric of socio-economic systems (Antonelli, 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Forman, 2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Furthermore, with the advent of the Industry 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='0 paradigm in the  last decade, the concept of the digital divide has furtherly increased its significance  as a metric able to reflect economic performances (Shakina, Parshakov, and Alsufiev,  2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' This is particularly relevant considering the growing pervasiveness of ICTs and  the complementarity between physical and key enabling digital technologies in the  production and consumption of goods and services (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', cloud computing, artificial  intelligence) (Giustiziero et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' While there is a growing awareness of the digital  performance of countries and regions, the notion of the Digital Divide registers very  few contributions applied to the firms as units of analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  As evidenced by recent contributions, digital transformation has noteworthy impacted  firms’ structure, being a strategic transformation of organization and core capabilities  of businesses enabled by digital technologies (Volberda et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' The rapid and  unceasing technological change that occurred in the last decade has challenged the  status quo of firms across industries, creating gaps for different rates of digital  4  awareness by managers and employees and diverse accumulation of digital-related  skills (Blanka, Krumay, and Rueckel, 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Shakina, Parshakov, and Alsufiev, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Internal routines and relationships with customers and suppliers have been radically  altered, and unsurprisingly, the term co-creation is frequently applied to refer to  collaboration between the various actors in business ecosystems in the value creation  path (Warner and W¨ager, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Bearing in mind this transformation,  the traditional resource-based view of the firm paradigm (Barney, 1991;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Wernerfelt,  1984) has been profoundly impacted by digital technologies and their bundled use  (Giustiziero et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Accordingly, the development of new capabilities to favor  business model adaptation to the new techno-economic scenario requires a digital  sensing activity by the firm (Warner and W¨ager, 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' The ubiquity of ICTs requires  not only the ownership of specific resources but also the creation of specialized human  resources to frame the new possibilities opened by digital affordance property, that  is, the creation of endless reconfiguration by the use of the same inputs or a creative  (re)combination of them (Giustiziero et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' All in all, while we  have rather substantial theoretical evidence that digital transformation has impacted  corporates’ structure and strategic approach, we are still struggling to provide detailed  and fine-grained measures at the firm level (Tambe et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' In other words,  we cannot evaluate firms’ response to the introduction of digital technologies and if  they have developed adequate digital capabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Hence, the literature has remained  relatively silent on the corporate Digital Divide level across different typologies of firms,  operating in various industries, and localized in urban or peripheral contexts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  The good news is that digital footprints left by organisations and individuals  have recently become available data for empirical analyses, thanks to the diffusion  in social sciences of methodologies such as web scraping (Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Axenbeck  and Breithaupt, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Kinne and Axenbeck, 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Thonipara et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' In other  words, considering information reported on the internet under the lenses of digital  signalling theory (Wells, Valacich, and Hess, 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Abeysekera, 2019) allows relating  the produced digital artifacts (as the characteristics of a corporate website) to a set  of underlying digital capabilities (Ageeva et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Recent studies have exploited  this caveat, investigating the relationships within the innovation ecosystem between  firms, universities, and institutions (Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2018), the digital layer of companies  and the concept of proximity (Kr¨uger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2020), the innovation performance of  firms (Kinne and Axenbeck, 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Despite this growing popularity, researches on these  new data sources are still very fragmented, with many exploratory analyses and many  elements that may not be applicable in all settings (Hern´andez, Jim´enez, and Mart´ın,  2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' With few exceptions (Kinne and Axenbeck, 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Kr¨uger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Thonipara  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2022), most of the analyses have concentrated on small samples, without the  possibility of transforming these unstructured and very heterogeneous data sources  into new potential tools to investigate economic performance at the systemic level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  The use of websites to measure the digital footprint of firms  The wide adoption of websites among firms, including SMEs, represents an interesting  potential information source to bridge the gap between the need to assess the digital  performance of firms and the lack of granular indicators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' This is possible for the  strategic role played by websites in the information and knowledge economy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  A website is a digital means able to reduce information asymmetry between two  parts, facilitating corporate operations (delivery, customer care, internationalization)  (Billon, Ezcurra, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Its maintenance, use, and development imply some  extra costs for the firms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' This candidates it as “near-costless measure of marketing”  (Thonipara et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2022) and, more in general, as an effective proxy to capture the  digital footprint of economic agents (Gok, Waterworth, and Shapira, 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Blazquez  and Domenech, 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Heroux-Vaillancourt, Beaudry, and Rietsch, 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Kinne and  Axenbeck, 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Websites are publicly available sources, manageable at any desired  time, and represent a new form of codified knowledge to complement information sources  on the firms’ performances (Blank, Graham, and Calvino, 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Kinne and Resch,  2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' The embeddedness of websites into online environments and the introduction  of e-commerce platforms have created completely new value delivery bidirectional  channels (Saridakis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Verhoef et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' As a result, this has impacted  a wide and heterogeneous set of industries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' The massive use of websites offers some  advantages in data collection in comparison to traditional methodologies due to their  (i) “unobtrusiveness”, (ii) accessibility, (iii) temporal frequency, (iv) granularity, and  (v) coverage (Mateos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2001;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Gok, Waterworth, and Shapira, 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Rasmussen and  Thimm, 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Blazquez and Domenech, 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Kinne and Resch, 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Unobtrusiveness derives from the capacity to directly gather the information reported  without requiring the direct involvement of a firm or a set of them (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', surveys).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  This saves time collecting information and is less variable than a traditional survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Accessibility stems from the open-access nature of websites as information sources and  the reproducibility of the analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Websites, especially corporate websites, are updated  for business reasons much more frequently than traditional information sources such as  surveys (temporal frequency).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Moreover, the information reported on a website has a  much more customisable degree of granularity than traditional survey methodologies  (even if with increasing post-processing works).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Finally, the massive analysis of websites  has the potential to extend coverage to almost the entire population of companies  (with the absence of non-response), overcoming the limitations of traditional collection  methods based on the selection of a representative sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' This makes it possible  to detect common and recurring characteristics agnostically and to identify hidden  peculiarities and specificities that remain under the tip of the iceberg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Extracting  data directly from websites can present some problems regarding the reliability of  the information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' However, companies would face rather negative feedback from the  clients and/or business partners with whom they interact if they would exaggerate  or mystify the reality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Hence, the general trend within the literature is to treat this  6  information as truthful or at least documentable (Pukelis and Stanciauskas, 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Notwithstanding the availability of websites, some doubts emerge on the typology of  firms detectable on the web.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Companies very close to the market are most likely to be  included in this group (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', B2C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' However, we have less evidence for subcontractors or  intermediaries (B2B), whose activities can remain in the shadow to respect the will of  their final clients (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', respecting industrial secrets or preventing competition) (Pukelis  and Stanciauskas, 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Encouraging signals, in this case, come from the requesting  of certificates (as ISO) by value chain leaders that are pushing subcontractors and  suppliers, in general, to show them as digital “business cards”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Still, available company  websites are a convenience sample to investigate firm dynamics, and a proper procedure  can be implemented to re-balance the available information across geographical areas  and sectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' The difficulties of website data processing are related to their reliability  and data mining procedures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' There are still some technical problems with treating  homogeneously website data, which for their nature are organized in several formats,  with different dimensionality, and composed of non-textual parts (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', graphics and  images) (Gok, Waterworth, and Shapira, 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Beaudry, H´eroux-Vaillancourt, and  Rietsch, 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Heroux-Vaillancourt, Beaudry, and Rietsch, 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Data Collection and Methodology  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Data Collection  From the AIDA database (Bureau van Dijk), we collected information about the  website of Italian firms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Initially, we collected website URL information for 450 348  firms covering the entire national territory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  We implemented in python our crawler script using a combination of different  libraries: requests2, scrapy3, beautifulsoup4, trafilatura5, builtwith6 and  finally we also rely on the results of Google Lighthouse7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Next, we stored the results of  the crawling activities on a MongoDB8 instance, a document-oriented NOSQL database  that provided us the right flexibility to store and update the gathered information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Each firm’s features were stored in a single MongoDB document.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  The crawling activity has been carried out from January 2021 to March 2021, with  a further update in September 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' As a result, we were able to obtain valid content  for 347 010 enterprises.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' The other home page URLs returned a timeout error or an  HTTP code different from 200.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Thus, we obtained a valid set of features for the 77% of  the initial sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Together with their home page URL, we considered information on  2docs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='python-requests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='org  3https://scrapy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='org/  4https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='crummy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='com/software/BeautifulSoup/bs4/doc/  5https://trafilatura.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='readthedocs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='io/en/latest/  6https://pypi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='org/project/builtwith/  7https://developers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='google.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='com/web/tools/lighthouse  8https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='mongodb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='com/  7  firm characteristics, such as geographical localisation (regional - NUTS-2, provincial  NUTS-3 and municipal level), industry (NACE REV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='2 digit), age, and size (micro,  small, medium or large firm according to the number of employees).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Therefore from  the merging of website information with firms’ characteristics, we obtain a final sample  of 182˙705 observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Methodology  The crawler activity was aimed at extracting different features related to each specific  home page to describe: a) how the site is built (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', links, images, text, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=') and b) how  it relates to other online contents (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', security, link to social media, loading speed,  etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  We interpreted the economic meaning of each extracted feature elaborating on the  existing literature (Mateos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2001;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Sanders and Galloway, 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Kr´ol and Zdonek,  2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' For the present analysis, we considered ten features as follows  the length of the URL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Short URLs are easier to remember and are a sign of  cleanliness and user-centricity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Moreover, they are more likely to be discovered;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Social media presence: Facebook, LinkedIn and Instagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' We consider  three popular social media (Facebook, LinkedIn and Instagram), checking for the  absence/presence of links to those social media.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' In fact, social media represent a  new valuable tool for conducting digital marketing strategies;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  The quality of internal links.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' The presence of unique inner links can be  interpreted as a sign of a good level of navigability to increase the probability  for users to remain longer on the websites, being correctly addressed towards  contents more in line with their preferences;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  The quality of external links.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' The higher presence of unique outer links can  be interpreted as a strong sign of stakeholder engagement and embeddedness in  the digital business ecosystem;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Quality of the technical frameworks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' The adoption of modern web  development standards ensures a better user experience and reflects more technical  competencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' This metric is based on Google Lighthouse 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Request access time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' A webpage with a low level of request time implies a  good speed and a good level of usability, being also this metric at the basis of  the adoption of a state-of-the-art technological stack development;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Website’s age.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' We estimated the age of each website, checking for its first  year of presence in the Wayback Machine archive10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Older websites have been  interpreted as part of the digital history and tradition of the firm;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Website security.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' The presence of a high-level security header represents a  proxy of awareness towards the risks of cyberattacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Nowadays, this represents  9See https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='com/GoogleChrome/lighthouse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  10https://archive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='org/web/.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  8  a crucial strategic aspect for firms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  In the following, we provide an explorative analysis of the extracted features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Figure 1 describes how our final dataset is distributed along three firm characteristics,  namely industry, size, and age.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' On the top, we show the number of enterprises for NACE  2-digit code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' In our sample, most of the firms belong to categories C (manufacturing)  and G (wholesale and retail trade).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Notice that not all the industries have been included  in this list;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' in fact, we select only the top 10 more frequent categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' The second  plot shows the size distribution of firms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' As expected, considering the known Italian  industrial distribution, most of the firms in our dataset are micro and small enterprises,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', with less than 50 employees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' At the bottom of figure 3, we report the age of the  enterprises in 5-year bins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' The results show a higher concentration of relatively young  firms that have from 5 to 25 years old.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  To investigate the representativeness of the sample, we compare the data we extracted  with the general composition of the Italian firms, as reported in ORBIS (Bureau Van  Dick) and ISTAT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Concerning industry, we obtained representativeness that vary from  5% of NACE sector I (Food and Accommodation) to 28% of sector J (Information and  Communication), with a good level (22%) also for sector C (Manufacturing) (ISTAT,  2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Concerning size, we were able to capture 75% of the total number of big firms, with  a decreasing coverage for smaller firms: 56% of medium firms, 31% of small firms and  only 8% of micro firms (ISTAT, 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  In relation to age, we find values in the range 1-6%, registering also in this case  progressive representativeness going back in time, with the peak (6%) for the firms  born in the period 2002 and 2006 (ORBIS, 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Figure 2 maps the features extracted by means of the crawling activity at NUTS-3  regions (descriptive statistics are available in table 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' We report values corresponding  to the three quantiles, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 33%, 66% and 100%, where a darker color indicates higher  values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Seven out of the ten extracted features, namely URL length, LinkedIn, quality  of the internal links, quality of the technical frameworks, request access time, website  age and website security) exhibit clear spatial differences across Italian NUTS-3 regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  As an example, The North-South divide in access time might be due to infrastructure  problems since a fast broadband connection is more spread in the North than in the  South.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' The spatial distribution of websites might correspond to earlier adoption of  digital tools for Northern enterprises w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' firms located in the South, thus indicating  a more rooted digital mindset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' More scattered territorial patterns are reported for  external links and social media.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Social media are of special interest for their different  penetration degree revealed, suggesting a specific interpretation of their usage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' The  presence of Facebook can be interpreted as the diffusion of a more generic marketing  culture, with a low level of specialisation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Instagram can be seen as the diffusion of  specific marketing culture adopted by specific B2C industries that exploit images and  videos (such as tourism, food, and culture).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' LinkedIn can be interpreted as the diffusion  9  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=': main features of selected Italian firms with a known physical and digital presence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Top: the number of analysed firms grouped by NACE 2 Digit code, middle: size distribution,  Bottom: age distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  of Human Resources culture and a proxy of more developed job markets, where relying  on professional networks can support more concrete business activities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Interestingly, table 2 shows a low level of correlation between variables, with the  10  50000  40000  30000  z  20000  10000  1  NACE Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='2100000  00008  firms  00009  JO  z  40000  20000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  micro  small  medium  big  Firm size30000  25000  Z 15000  10000  5000  0  (0, 5]  [0s\'st] [s\'0t] [0\'se][se\'05] [05\'sz] [s\'0z][0z"s] [50]][01"s]  >50  Firm age (Year from 2022)N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Links IN  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' links out  Lenght URL  LinkedIn  Instagram  Facebook  Best practice  Request access time  Security  Website age  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=': the spatial distribution of corporate website features in Italy, at the level of NUTS-3  regions (provinces).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Features are classified in three quantiles from low (yellow) to high (dark  blue) levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  only exception of correlation between social media (ca .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' This result supports our  approach of collecting different indicators to capture a multifaceted topic such as the  corporate digital divide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  More in general, our explorative data analysis allows us to validate some  characteristics of the enterprises included in our dataset built through the crawler.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  11  Augsburg  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='721  Wi0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='755  Freiburg  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='763  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='785  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Ulm  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='imBreisgau  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='olc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Munchewills  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Gyor  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Basel  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Salzburg  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='elforto  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Osterreich  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Budapest  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Deb  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='zurich  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='SanktGallen  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Szombathely  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Alfoldes  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Besancon  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Tirof  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Steiermark  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Magyarorszag  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Eszak  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Schweiz  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Suisse/Svizzeral  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Dunantur  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Karnten  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kecskemet  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Lausanne  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Maribor  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Svizra  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='eve  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Szeged  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Pecs  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Arad  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Slovenija  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Zagreb  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Cy6oTMLa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Anney  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Timisoa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='hamber  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Trieste  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Osijek  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='BojBoduHa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ezia  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Rijeka  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Banja Luka  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Tuzla  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='beorpaa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='diSan  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Hrvatska  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ence  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Genova  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='BosnaiHercegovinal  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Cp6wja  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='cote  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ino  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Mon  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Zadar  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='zur  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='bocHaw  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Ancona  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='XepyeroBMHa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='eHmpanHo  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Cpuja  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Mostar  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Crna Gora  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kosoval  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='LpHaropa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kosovo  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Shgiperid  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kyn  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Ajaccio  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Veriore  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Ce  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Make  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Lath  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Bari  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Shqiperia  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='GMTOJ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Korce  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Brindisi  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Vlore  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ATTOKEVTPWH  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Aroiknon  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Autikns  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='MQKEOOVIO  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='eddu  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='cagliari  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Palermo  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Messip  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ATOM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ania  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='dcusa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='nstantineAugsburg  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Freiburg  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='008  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='010  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='011  Wien  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='019  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Ulm  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='imBreisgau  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='olc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Munchewills  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Salzburg  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Gyor  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='elforto  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Basel  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Osterreich  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Budapest  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Deb  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='zurich  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='SanktGallen  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Szombathely  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Alfoldes  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Besancon  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Tirof  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Steiermark  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Magyarorszag  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Eszak  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Schweizi  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Suisse/Svizzeral  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Dunantur  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Karnten  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kecskemet  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Maribor  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ausanne  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Svizra  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='eve  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Szeged  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Pecs  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Arad  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Slovenija  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Zagreb  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Cy6oTMLa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Anneo  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Timisoa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='hamber  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Trieste  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Osijek  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='BojBoduHa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ezia  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Rijeka  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Banja Luka  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Tuzla  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='beorpaa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='diSan  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Hrvatska  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ence  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Genova  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='BosnaiHercegovinal  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Cp6wja  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='cote  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ino  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Zadar  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='zur  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Mon  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='bocHaw  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Ancona  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='XepyeroBMHa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='eHmpanHo  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Cpuja  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Mostar  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Crna Gora  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kosoval  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='LpHaropa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kosovo  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Shgiperid  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kyn  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Ajaccio  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Veriore  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Ce  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Make  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Bari  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Shqiperia  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='GMTOJ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='in  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Korce  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Brindisi  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Vlore  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ATOKEVTPUH  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Aroiknon  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Autikns  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='MQKEOOVIO  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='jeddt  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='tagliari  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Palermo  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Messir  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ATOK  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='nEO  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='nia  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='dcusa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='nstantineAugsburg  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Freiburg  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='40  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='41  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='43 Wien  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='47  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Ulm  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='olc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='imBreisgau  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Munchewills  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Salzburg  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Gyor  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='elforto  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Basel  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Osterreich  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Budapest  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Deb  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='zurich  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='PSanktGallen  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Szombathely  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Alfoldes  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Besancon  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Tirof  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Steiermark  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Magyarorszag  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Eszak  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Schweizi  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Suisse/svizzeral  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Dunantur  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Karnten  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kecskemet  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Maribor  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ausanne  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Svizra  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='eve  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Szeged  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Pecs  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Arad  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Slovenija  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Zagreb  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Cy6oTMLa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Anney  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Timisoa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='@  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='hamberi  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Trieste  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Osijek  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='BojBoduHa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ezia  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Rijeka  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='@  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Banja Luka  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Tuzla  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='beorpaa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='diSan  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Hrvatska  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ence-  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Genova  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='BosnaiHercegovina  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Cp6wja  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='cote  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ino  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Mon  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Zadar  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='zur  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='bocHaw  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Ancona  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='XepyeroBMHa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='eHmoanHo  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Cpuja  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Mostar  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Crna Gora  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kosoval  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='LpHaropa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kosovo  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Shgiperid  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kyn  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Ajaccio  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Veriore  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Ce  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Make  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Bari  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Shqiperia  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='GMTOJ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='in  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Korce  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Brindisi  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Vlore  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ATOKEVTPWH  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Aroiknon  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Autikns  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='MQKEOOVIO  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='eddur  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Cagliari  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Palermo  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Messip  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ATTOK  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='nEO  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='nia  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='dcusa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='nstantineAugsburg  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Freiburg  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='6  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='4 -Wien  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='7  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Ulm  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='olc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='imBreisgau  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Munchewills  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Salzburg  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Osterreich  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Gyor  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='elforto  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Basel  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Budapest  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Deb  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='zurich  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='SanktGallen  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Szombathely  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Alfoldes  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Besancon  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Tirof  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Steiermark  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Magyarorszag  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Eszak  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Schweizi  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Suisse/Svizzeral  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Dunantur  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Karnten  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kecskemet  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Lausanne  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Maribor  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Svizra  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='eve  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Szeged  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Pecs  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Arad  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Slovenija  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Zagreb  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Cy6oTMLa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Anney  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Timisoa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='hamber  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Trieste  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Osijek  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='BojBoduHa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ezia  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Rijeka  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Banja Luka  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Tuzla  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='beorpaa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='diSan  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Hrvatska  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ence  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Genova  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='BosnaiHercegovinal  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Cp6wja  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='cote  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ino  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Zadar  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='zur  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Mon  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='bocHaw  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ncona  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='XepyeroBMHa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='LeHmpanHo  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Cpuja  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Mostar  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Crna Gora  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kosoval  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='LpHaropa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kosovo  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Shgiperid  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kyn  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Ajaccio  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Veriore  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='K  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Ce  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Make  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Lath  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Bari  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Shqiperia  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='GMTOJ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='n  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Korce  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Brindisi  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Vlore  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ATOKEVTPWH  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Aroiknon  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Autikns  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='FMAKEOOVIO  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='eddu  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='cagliari  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Palermo  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Messin  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ATOK  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='nEO  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ania  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='dcusa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='nstantineAugsburg  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='31Wien  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Freiburg  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='39  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Ulm  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='imBreisgau  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='olc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Munchewills  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Gyor  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Basel  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Salzburg  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='elforto  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Osterreich  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Budapest  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Deb  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='zurich  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='SanktGallen  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Szombathely  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Alfoldes  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Besancon  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Tirof  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Steiermark  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Magyarorszag  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Eszak  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Schweiz  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Suisse/Svizzeral  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Dunantur  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Karnten  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kecskemet  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Lausanne  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Maribor  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Svizra  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='eve  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Szeged  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Pecs  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Arad  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Slovenija  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Zagreb  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Cy6oTMLa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Anney  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Timisoa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='hamber  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Trieste  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Osijek  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='BojBoduHa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ezia  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Rijeka  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Banja Luka  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Tuzla  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='beorpaa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='diSan  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Hrvatska  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ence  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Genova  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='BosnaiHercegovinal  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Cp6wja  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='cote  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ino  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Mon  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Zadar  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='zur  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='bocHaw  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ncona  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='XepyeroBHa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='eHmpanHo  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Cpuja  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Mostar  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Crna Gora  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kosoval  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='LpHaropa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kosovo  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Shgiperid  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kyn  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Ajaccio  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Veriore  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Ce  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Make  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Lath  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Bari  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Shqiperia  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='GMTOJ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ing  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Korce  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Brindisi  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Vlore  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ATTOKEVTPWH  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Aroiknon  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Autikns  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='MQKEOOVIO  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='eddul  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Cagliari  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Palermo  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Messir  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ATOM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ania  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='dcusa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='nstantineAugsburg  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Freiburg  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='9  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='3  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='0  Wien  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Ulm  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='tolc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='imBreisgau  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Munchewills  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Salzburg  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Osterreich  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Gyor  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='elforto  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Basel  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Budapest  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Deb  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='zurich  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='PSanktGallen  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Szombathely  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Alfoldes  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Besancon  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Tirof  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Steiermark  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Magyarorszag  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Eszak  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Schweizi  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Suisse/svizzeral  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Dunantur  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Karnten  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kecskemet  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Lausanne  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Maribor  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='svizra  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='eve  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Szeged  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Pecs  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Arad  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Slovenija  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Zagreb  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Cy6oTMLa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Anney  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Timisoa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='@  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='hamber  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Trieste  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Osijek  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='BojBoduHa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ezla  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Rijeka  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Banja Luka  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Tuzla  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='beorpaa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='diSan  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Hrvatska  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ence  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Genova  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='BosnaiHercegovina  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Cp6wja  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='cote  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ino  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Mon  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Zadar  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='zur  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='bocHaw  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Ancona  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='XepyeroBHa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='eHmpanHo  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Cpuja  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Mostar  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Crna Gora  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kosoval  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='LpHaropa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kosovo  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Shgiperid  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kyn  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Ajaccio  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Veriore  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Ce  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Make  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Lath  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Bari  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Shqiperia  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='GMTOJ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='inc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Korce  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Brindisi  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Vlore  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ATTOKEVTPWH  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Aroiknon  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Autikns  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='MQKEOOVIO  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='eddur  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='cagliari  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Palermo  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Messir  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ATOM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ania  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='dcusa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='nstantineAugsburg  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Freiburg  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='125  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='132  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='136Vien  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='151  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Ulm  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='olo  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='imBreisgau  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Munchewills  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Salzburg  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Osterreich  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Gyor  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='elforto  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Basel  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Budapest  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Deb  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='zurich  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='SanktGallen  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Szombathely  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Alfoldes  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Besancon  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Tirof  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Steiermark  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Magyarorszag  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Eszak  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Schweiz  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Suisse/Svizzeral  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Dunantur  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Karnten  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kecskemet  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Maribor  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ausanne  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Svizra  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='eve  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Szeged  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Pecs  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Arad  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Slovenija  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Zagreb  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Cy6oTMLa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Anney  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Timisoa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='hamberi  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Trieste  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Osijek  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='BojBoduHa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ezia  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Rijeka  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='@  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Banja Luka  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Tuzla  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='beorpaa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='diSan  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Hrvatska  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ence-  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Genova  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='BosnaiHercegovina  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Cp6wja  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='cote  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ino  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Mon  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Zadar  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='zur  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='bocHaw  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ncona  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='XepyeroBMHa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='eHmpanHo  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Cpbuja  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Mostar  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Crna Gora  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kosoval  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='LpHaropa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kosovo  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Shgiperid  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kyn  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Ajaccio  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Veriore  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Ce  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Make  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Bari  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Shqiperia  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='GMTOJ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='inc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Korce  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Brindisi  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Vlore  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ATTOKEVTPWH  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Aroiknon  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Autikns  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='MQKEOOVIO  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='edduy  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Cagliari  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Palermo  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Messip  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ATOK  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='nEO  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ania  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='acusa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='nstantineAugsburg  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Freiburg  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='17 Wien  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Ulm  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='kolc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='imBreisgau  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Munchewills  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Osterreich  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Gyor  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Basel  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Salzburg  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='elforto  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Budapest  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Deb  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='zurich  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='SanktGallen  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Szombathely  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Alfoldes  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Besancon  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Tirof  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Steiermark  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Magyarorszag  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Eszak  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Schweiz  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Suisse/Svizzeral  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Dunantur  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Karnten  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kecskemet  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Lausanne  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Maribor  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Svizra  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='eve  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Szeged  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Pecs  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Arad  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Slovenija  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Zagreb  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Cy6oTMLa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Anney  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Timisoa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='hamber  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Trieste  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Osijek  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='BojBoduHa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ezla  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Rijeka  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Banja Luka  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Tuzla  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='beorpaa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='diSan  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Hrvatska  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ence  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Genova  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='BosnaiHercegovinal  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Cp6wja  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='cote  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ino  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Zadar  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='zur  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Mon  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='bocHaw  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ncona  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='XepyeroBMHa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='eHmpanHo  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Cpuja  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Mostar  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Crna Gora  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kosoval  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='LpHaropa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kosovo  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Shgiperid  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kyn  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Ajaccio  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Veriore  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Ce  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Make  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ath  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Bari  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Shqiperia  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='GMTOJ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='inc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Korce  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Brindisi  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Vlore  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ATOKEVTPUH  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Aroiknon  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Autikns  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='MQKEOOVIO  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='eddu  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='cagliari  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Palermo  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Messir  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ATOK  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='nEO  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ania  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='acusa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='nstantineAugsburg  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='24  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='W27n  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Freiburg  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='36  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Ulm  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='imBreisgau  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='kolc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Munchewills  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Osterreich  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Gyor  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Basel  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Salzburg  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='elforto  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Budapest  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Deb  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='zurich  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='SanktGallen  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Szombathely  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Alfoldes  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Besancon  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Tirof  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Steiermark  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Magyarorszag  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Eszak  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Schweizi  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Suisse/Svizzeral  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Dunantur  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Karnten  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kecskemet  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Maribor  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ausanne  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Svizra  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='eve  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Szeged  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Pecs  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Arad  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Slovenija  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Zagreb  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Cy6oTMLa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Anney  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Timisoa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='hamberi  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Trieste  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Osijek  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='BojBoduHa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ezla  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Rijeka  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Banja Luka  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Tuzla  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='beorpaa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='diSan  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Hrvatska  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ence-  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Genova  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='BosnaiHercegovinal  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Cp6wja  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='cote  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='no  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Mon  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Zadar  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='zur  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='bocHaw  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Ancona  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='XepyeroBMHa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='eHmpanHo  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Cpuja  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Mostar  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Crna Gora  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kosoval  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='LpHaropa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kosovo  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Shgiperid  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kyn  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Ajaccio  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Veriore  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Ce  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Make  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Lath  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Bari  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Shqiperia  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='GMTOJ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='inc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Korce  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Brindisi  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Vlore  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ATTOKEVTPWH  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Aroiknon  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Autikns  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='MQKEOOVIO  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='eddul  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Palermo  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Messin  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ATOM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ania  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='acusa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='nstantineAugsburg  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Freiburg  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='42  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='54  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Wien  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Ulm  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='59  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='72  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kolc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='imBreisgau  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Munchewills  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Salzburg  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Osterreich  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Gyor  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='elforto  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Basel  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Budapest  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Deb  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='zurich  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='PSanktGallen  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Szombathely  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Alfoldes  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Besancon  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Tirof  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Steiermark  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Magyarorszag  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Eszak  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Schweizi  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Suisse/svizzeral  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Dunantur  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Karnten  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kecskemet  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Maribor  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ausanne  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Svizra  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='eve  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Szeged  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Pecs  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Arad  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Slovenija  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Zagreb  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Cy6oTMLa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Anney  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Timisoa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='@  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='hamberi  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Trieste  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Osijek  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='BojBoduHa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ezia  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Rijeka  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='@  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Banja Luka  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Tuzla  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='beorpaa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='diSan  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Hrvatska  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ence-  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Genova  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='BosnaiHercegovina  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Cp6wja  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='cote  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ino  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Mon  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Zadar  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='zur  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='bocHaw  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ncona  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='XepyeroBMHa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='eHmpanHo  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Cpuja  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Mostar  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Crna Gora  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kosoval  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='LpHaropa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kosovo  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Shgiperid  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Kyn  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Ajaccio  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Veriore  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Ce  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Make  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Lath  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Bari  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Shqiperia  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='GMTOJ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='inc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Korce  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Brindisi  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Vlore  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ATTOKEVTPWH  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Aroiknon  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Autikns  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='MQKEOOVIO  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='eddur  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Cagliari  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Palermo  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='Messip  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ATOK  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='nEO  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ania  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='acusa  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='nstantinemin  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='max  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='mean  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='std  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='unique links in  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  4885.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='473  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='921  unique links out  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  15814.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='942  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='228  best-practices  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='380  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='837  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='103  length url  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='214  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='436  Facebook  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='461  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='498  Instagram  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='219  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='414  LinkedIn  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='159  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='366  years old  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='308  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='455  request time  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='127  502.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='262  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='265  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='418  security header int  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='268  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='941  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=': Descriptive statistics of the features of the corporate websites of interest  As a result, we rely on 182 705 firms out of the initial sample (composed of 347 010  firms) because a consistent number of firms showed missing values for employment,  a useful indicator to categorize the size of each firm in different groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' To analyse  the relationship between firms’ characteristics and corporate websites we run a set of  simple OLS regressions with the following specification:  y = α + β1xf + β2xt + ϵ  where y represents one of the ten Digital Dimensions (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', one of the relevant features of  the corporate websites), and xf is the vector that represents the relevant characteristics  of the firm: age, industry and size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' In each regression, we include a set of controls for  the area in which the firm is located, represented by xt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' This is because, beyond the  specific patterns detectable by the traditional characteristics of the firm, the notion of  corporate Digital Divide can be influenced (and captured) also by the place where the  firm is located (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' a common available IT infrastructure or the diffusion of digital  means to run a business activity varies between urban and rural areas and from the  North to the South).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' In this regard, to avoid possible mispecifications of the model,  (since some features of corporate websites, such as the request access time might depend  on the wide band coverage of the area where the firm is located), we control for the  possible impact of the wide band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' The wide band data are obtained as open data from  the Italian Authority for Communications Guarantees11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' The data represent, for each  Italian census area, the ratio of households reached by broadband with a speed greater  than 30mbs over the total number of households in that area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  11https://maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='agcom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='it/  12  unique links in  unique links out  best-practices  Instagram  LinkedIn  Facebook  years old  security header int  request time  length url  unique links in  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='018  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='042  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='151  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='104  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='179  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='078  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='053  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='009  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='023  unique links out  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='018  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='073  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='062  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='087  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='022  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='013  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003  best-practices  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='042  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='005  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='038  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='055  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='008  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='038  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='055  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='011  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='026  Instagram  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='151  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='073  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='038  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='178  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='524  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='007  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='032  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='006  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='004  LinkedIn  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='104  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='062  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='055  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='178  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='293  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='080  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='074  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='040  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='096  Facebook  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='179  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='087  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='008  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='524  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='293  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='033  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='023  years old  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='078  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='022  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='038  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='007  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='080  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='056  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='060  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='167  security header int  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='053  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='013  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='055  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='032  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='074  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='033  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='056  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='769  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='072  request time  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='009  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='011  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='006  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='040  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='060  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='769  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='075  length url  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='023  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='026  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='004  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='096  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='023  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='167  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='072  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='075  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=': Correlation matrix between the ten corporate website features  13  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Results  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Regression results  In this section, we discuss the results of the regression analysis for the ten digital-related  features of corporate websites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Table 3 summarizes the results for the analysis of the  Digital Divide across different dimensions of Italian firms: size, sector, age and location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Micro firms show a negative and significant effect for unique links internal to the  company, with more attention to internal navigability shown by medium and big firms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  External links are not significant in micro firms, while we find a positive and significant  effect for medium and large firms as a sign of more attention devoted to external  stakeholders in terms of connection and reachability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Best practice has a positive  and significant effect only on medium-sized firms, with no effect on big firms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' This  counterintuitive result could be interpreted as a sign of lower marginal utility in having  libraries at the state of the art for big firms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Social media variables have all a significant effect across dimensions, with a negative  sign for micro and a progressive value of the magnitude effect, with the highest value  for big firms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Age, as a proxy of digital experience, tends to be more relevant in big firms, which,  on average, understood the importance of creating a website many years before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Security, speed (request time), and the length of the URL should be interpreted in  the inverted direction as lower request times and shorter URL improve the accessibility  of corporate websites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  We analyze the impact of the corporate Digital Divide also across NUTS-2 digit  sectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' We take as a sector of reference in terms of quality, Information and  Communication (“J”), for its direct involvement in the coding procedure or the  marked attention to the quality of websites, as a fundamental tool to communicate with  customers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' A positive and significant effect is found in the wholesale and retail trade  (“G”) for the unique internal and external links, confirming the importance of internal  navigability and external connections for B2C activities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Concerning best practice, a  positive and significant effect is detected in the sectors “M” (Professional, Scientific  and Technical activities and “J” (Information and Communication), supporting the  idea that, on average, firms in those sectors are better informed about the importance  of high-quality technical libraries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Social Media seems to have different behaviors,  according to their business functions, confirming the exploratory mapping reported in  section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Accordingly, Instagram and Facebook have seems to play an important role  in Accommodation and Food Service Activities (sector “I”), as free channels to engage  with tourism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' LinkedIn, more oriented to attracting highly skilled profiles, seems to  have a bigger impact on sectors with highly specialized knowledge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Security Header and request time should be interpreted in the opposite direction, so  negative and significant effects are signs of firms being more aware of the importance  of adopting cyber security practices and frameworks able to ensure an adequate level  14  of speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Age accounts for the years since the date of foundation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' A negative and significant  effect for unique links, best practices and social media is a sign that older firms have a  worse performance than more digital-born companies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  The geography of the corporate Digital Divide also presents sharp evidence of the  fact that urban contexts offer the higher marginal utility of digital means usage for  firms operating in dynamic and dense economic systems, where firms can exploit the  network effect (Forman, Goldfarb, and Greenstein, 2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' The geographical location is  also another important feature that reveals how the Digital Divide is the reverse coin  of the economic development of territories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' North and South dummies show opposite  behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' This supports the idea that more industrialized regions, prevalently located  in the north, are favorable environments for the adoption of digital strategies and the  relative adoption of skills and investment more than in the south.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  In all the regressions we control for the effect of the wide band, supposing that  some digital web proxies could be shadowed by a high-quality web infrastructure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Disentangling the infrastructural effect is not a trivial task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Accordingly, websites can  rely on external hosts or local servers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' In the first case, the reactivity of the different  webpages can be related to the quality of the website.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' In the last case, we can observe  a good level of wide band coverage with low-quality websites, but also the opposite  might occur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' All in all, we find only four significant values for the impact of wide band  out of ten regressions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' This result is very important since it confirms that with our  approach to collect multiple features of corporate websites we are able to detect the  digital footprint of firms beyond the quality of shared web infrastructure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Corporate Digital Assessment Index  Our findings show a multifaceted composite picture, revealing how Digital Divide is  present across different firms’ dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  A major problem in measuring the corporate Digital Divide with such a data-driven  approach is the absence of a theoretical framework to classify the typology of proxies  into well-defined digital capabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  A very specific research stream narrows on this, analysing the quality of websites as  a proxy of organisations’ behavior (Mateos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2001;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Gok, Waterworth, and Shapira,  2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Axenbeck and Breithaupt, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Kinne and Axenbeck, 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Analysing the  quality of websites is a complex task for the presence of several unstructured pieces of  information that need to be framed into logical theoretical schemes to understand their  potential economic value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Moreover, it is not trivial to find synthetic measures able to  capture the multifaceted characteristics of websites, considering also how a high degree  of customisation makes it difficult to establish ”objective” accountable criteria (Kr´ol  and Zdonek, 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Within this literature, Mateos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' (2001) provide one of the first single index,  15  unique links in  unique links out  best-practices  Instagram  LinkedIn  Facebook  years old  security header int  request time  length url  Constant  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='005***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='771***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='965***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='027)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='810***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='032)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='376***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='022)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='406***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='415***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='010***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='143***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  Micro firm  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='005***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='236***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='013)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='576***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='016)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='136***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='011)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='093***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='012***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  Mid-sized firm  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='006***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='322***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='023)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='654***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='023)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='196***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='020)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='074***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='013***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  Large firm  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='005***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='505***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='042)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='113***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='040)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='339***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='038)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='109***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='005)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='029***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002**  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  Agriculture, forestry and fishing (A)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001**  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='694***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='049)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='575***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='090)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='260***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='047)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='031***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='007)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='007*  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003**  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  Manufacturing (C)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000**  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='134***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='020)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='272***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='023)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='494***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='016)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='099***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002*  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000**  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='015***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  Construction (F)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='804***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='031)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='194***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='033)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='653***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='022)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='012***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='010***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='004***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  Wholesale and retail trade (G)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='005***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='300***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='019)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='024)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='033*  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='016)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='061***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='010***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  Transportation (H)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='009***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='763***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='044)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='287***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='046)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='735***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='031)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='022***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='004)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='007***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  Accomodation and food service (I)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='015***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='904***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='024)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='411***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='052)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='741***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='023)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='045***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='009***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  Information and communication (J)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='005**  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='262***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='029)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='275***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='028)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='133***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='023)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='070***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='019***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='027***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  Financial and insurance activities (K)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001*  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='004)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='982***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='080)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='723***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='059)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='709***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='051)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='017*  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='007)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='017***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='009***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  Real estate activities (L)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000*  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='011***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='168***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='043)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='263***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='052)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='036  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='036)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='084***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='005)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  Professional, scientific & technical activities (M)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='008***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='212***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='027)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='137***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='027)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='385***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='022)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='039***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='014***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='018***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  Urban area  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000**  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='130***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='013)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='170***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='015)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='052***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='011)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  North  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='011***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='102***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='015)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='288***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='018)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='201***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='012)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='019***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='008***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='005***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  South  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='008***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='067***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='018)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='109***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='023)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='162***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='015)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='045***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='014***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001**  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  Firm age  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='013***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='009***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='010***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000**  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  Wide band  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000**  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='043*  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='017)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='131***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='020)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='015  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='014)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='004*  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  R-squared:  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='028  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='037  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='078  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='035  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='071  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='013  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='009  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='041  Adj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' R-squared:  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='027  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='071  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='013  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='009  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='041  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' of Observations  182,705  182,705  182,705  182,705  182,705  182,705  182,705  182,705  182,705  182,705  Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=': regression results considering as dependent variables the website feature extracted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Notice that for the features Instagram, Linkedin and  Facebook, we use the Logit model and consequently, we report the relative Pseudo R-squared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  16  called Web Assessment Index (WAI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='12  Elaborating on this literature from the point of view of the digital strategy of the  firm, we interpreted and classified the extracted features into four different aspects  related to the digital strategy of the firm:  (1) stakeholder engagement  (2) technical capabilities  (3) internal organisation  (4) digital culture  Stakeholder engagement includes the capabilities of the firm to establish links and  connections with external stakeholders, such as customers and suppliers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Technical  capabilities account for the competencies of the firm to build a state-of-the-art digital  framework in terms of Libraries, security and speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Internal organisation represents  the ability of the firm to coherently and purposefully orchestrate internal information  flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Digital Culture stands for the historical trajectory in which the firm is inserted  (awareness of the importance of web as a strategic resource).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Aggregating these four indicators, we propose a synthetic index to capture the  Corporate digital divide with a single dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  To build our index, we normalize the variables with a MinMax technique, inverting  the scale of the values where necessary (the length of the URL, Facebook, request  time, and security header) for the purpose of interpretability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Then, we calculated the  Corporate Digital Assessment Index (CoDAI) as the weighted sum of each element, as  follows:  CoDAI = (Stakeholder Engagement/2) + (Technical Capabilities/3) + (Internal Organization/2) + (Digital Culture)  (1)  Table 4 shows the dimensions and indicators we used to build the CoDAI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Table 4  summarizes the regression results for the analysis of the determinants of the CoDAI  and its four dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Our proposal shows the expected significance level for firm  dimension, with the prominence of big firms in comparison to medium and micro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' We  find interesting results also across sectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' For instance, the case of wholesale and  retail trade (G) shows a positive and significant effect for what concerns stakeholder  engagement, but a negative and significant effect for the technical capabilities subpart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Wideband is significant only for stakeholder engagement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' This could be explained by  12The authors built their index on universities’ websites, considering four dimensions of analysis: site content,  speed, accessibility and navigability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' While the first two are quite straightforward, the last two need to be  explicitly framed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' As underlined also by Vaughan (2004), accessibility has been proxied respectively by search  engine indexes and popularity (the number of external links can imply more traffic).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Navigability has been  mainly measured as the number of steps (clicks) to access relevant information for the user.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Other measures  have been introduced as usability, which can be seen as an extension of navigability, more oriented to the  convenience of users to navigate the website for several reasons, such as easiness, responsivity, and aesthetic  reasons, which have become crucial especially in the last years to retain and acquire users (Mateos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2001;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Dickinger and Stangl, 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Kr´ol and Zdonek, 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  17  Indicator  Dimension  Quality of external links  Stakeholder Engagement  Facebook  Instagram  Linkedin  Best Practice  Technical Capabilities  Security  Speed  URL’s length  Internal Organization  Quality of internal links  Website’s age  Digital Culture  Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=': Corporate Digital Assessment Index (CoDAI): indicators and dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  the fact that the majority of the proxies, employed to realize such as category, rely  on the adoption of external platforms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' With no surprise, we find a negative effect for  three out of four sub-dimensions of the CoDAI concerning the age of the firm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' This  could be interpreted as a more reactive digital behavior of newborn digital firms in  comparison to more experienced ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Furthermore, the relevance of our proposed framework is evident if we compare  the results of our CoDAI with the simple sum of the ten indicators (see table 6 in  the appendix).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' When we use a simple sum, we can notice how some of the Digital  Divide aspects previously pointed out, tend to become blurry and difficult to interpret.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  For instance, the industrial prominence of Accommodation and food service (I) is in  contrast with previous findings on the ICT sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' In addition, the South and North  geographical areas signs are inverted and the wideband variable becomes positive and  significant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  To highlight the sharp corporate Digital Divide of Italy we map the results of our  CoDAI across NUTS regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Figure 3 displays three rough geographical clusters,  representative of the three main areas of Italy: North, Centre and South (see also figure  4 in the appendix for the map at municipal level).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' This result is noteworthy as confirms  the traditional North-South economic divide, using also a novel set of web-related  measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Final Discussion  Nowadays, the astonishing pervasiveness of ICTs in production and consumption  processes has revolutionized how firms operate and strategize.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' As in every technological  transformation, the time and quality of adoption of digital means have created a  corporate Digital Divide between more structured and digital-oriented firms and more  traditional ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Staying behind this new paradigm has several consequences for  the future of small businesses, which characterize the industrial structure of “digital  latecomers” such as Italy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Moreover, no industry is immune to the increasing birth of  18  stakeholder eng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  technical capabilities  digital culture  internal organization  CoDAI  Constant  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='827***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='006)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='346***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='252***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='862***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='672***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003)  Micro firms  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='076***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='018***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='049***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='075***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002)  Mid-sized firms  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='119***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='005)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='020***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='040***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='004***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='079***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003)  Large firms  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='221***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='010)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='033***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='004)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='058***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='005)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='007***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='128***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='006)  NACE sector A  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='029*  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='012)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='009  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='005)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='028***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='006)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003*  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='017*  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='007)  NACE sector C  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='132***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='004)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='064***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='015***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='105***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003)  NACE sector F  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='033***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='005)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='014***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='022***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='018***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003)  Nace sector G  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='047***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='004)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='008***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='037***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='013***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='053***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003)  NACE sector H  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='039***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='008)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='017***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='004)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='004  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='005)  NACE sector I  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='074***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='006)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='011***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='051***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='009***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='024***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='004)  NACE sector J  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='201***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='006)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='026***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='079***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='028***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='152***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='004)  NACE sector K  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='149***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='013)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='023***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='005)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='011  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='007)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='008***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='060***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='008)  NACE sector L  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='050***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='009)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='008*  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='004)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='048***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='005)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='058***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='006)  NACE sector M  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='238***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='006)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='023***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='048***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='018***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='124***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003)  Urban area  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='030***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003**  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='004**  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='014***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002)  North  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='067***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='020***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='007***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='005***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='033***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002)  South  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='038***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='004)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='024***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='030***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001*  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='048***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002)  Firm age  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='007***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='006***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  Wide band  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='018***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='004)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='003  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='002)  R-squared:  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='049  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='014  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='17  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='043  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='168  Adj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' R-squared:  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='048  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='014  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='17  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='043  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='168  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' of observations  182,705  182,705  182,705  182,705  182,705  Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=': regression results considering the CoDAI and its components as dependent variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  For a legend of NACE sectors see table 3  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  hybrid cyber-physical systems which disrupt how products are designed, realized and  delivered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  With few exceptions, the extant literature mapped the digital divide phenomenon  using data on broadband access, neglecting the role of digital tools and the relative  competencies built on it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  With this paper, we continue along the research stream on the use of web scraping to  identify digital economy phenomena (Gok, Waterworth, and Shapira, 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Blazquez,  Domenech, and Deb´on, 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Axenbeck and Breithaupt, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Heroux-Vaillancourt,  Beaudry, and Rietsch, 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Kinne and Axenbeck, 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Kr¨uger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Thonipara  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  In particular, this explorative work introduces a novel way to map and evaluate the  19  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=': The distribution of the CoDAI across Italian regions (NUTS3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  corporate digital divide at the granular level, overcoming the country-level perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Leveraging the potentiality of web scraping techniques, we inquire about the corporate  Digital Divide, extracting, storing and analysing a set of website features related to  the digital footprints of 182 705 Italian firms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' We purposefully focus only on technical  features as less manipulable in comparison to content and experience and with a less  degree of variability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  To improve the comparability of our results across firms, we introduce a Corporate  Digital Assessment Index (CoDAI), interpreting the results across four distinctive  aspects of the digital strategy of the firm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' The CoDAI and its four dimensions confirm  the main drivers of the corporate Digital Divide highligted in the literature: we find a  prominence of big firms, active in ICT-related fields and localized in more industrialized  20  Augsburg  Freiburg  Ulm  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='69  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='78  Wien  1-87  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='95  imBreisgau  olc  Munchewills  Belforto  Basel  Salzburg  Osterreich  Gvor  Budapest  De  Zurich  SanktGallen  Besancon  Tirof  Steiermark  Szombathely  Alfoldes  Magyarorszag  Schweiz/  Eszak  Suisse/Svizzeral  Karnten  Dundntij  Lausanne  Maribor  Kecskemet  Svizra  neve  Szeged  Slovenija  Pecs  Ara  Annecy  Zagreb  Cy60TMLa  Timiso  chamber  Trieste  ezia  Osijek,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Bojeoduna  Rijeka  Tuzla  beorpaA  Banja Luka  vence  diSan  Hrvatska  Genova  BosnaiHercegovina/  Cp6wja  es-Cote  ino  Azur  Mon  Zadar  bOCHaM  Ancona  XepueroBHa  Lempanh  Cp6uja  Mostar  Crna Gora  Kosova  LipHaropa  Kosovo  Shgiperia  Veriore  Ky  Ajaccio  Ce  Mak  Bari  inc  Shgiperia  GMTC  Brindisi  Korce  Vlore  ATTOKEVTPO  Atoikno  HrtEipo  AutiKr  MAKESOV  inppa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Cagliari  Palermo  Messir  ATTO  ne  ania  onstantine  esndurban contexts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Notwithstanding the relevance of our contribution to the analysis of the corporate  Digital Divide, this work is not free of limits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' The literature on the economic  interpretation of websites and digital means is still in its infancy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Therefore, the  iterative dialogue between empirical testing and theoretical building offers food for  thought for multidisciplinary research between economics, management, and data  science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  In particular, the relevant elements of a website are changing with an impressive  frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' In this regard, multimedia elements (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', images, videos and sounds) have  skyrocketed as means of communication thanks to the introduction of new technological  enablers (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', high-speed broadband), as well as website design has become an important  method to establish a website quality (Rasmussen and Thimm, 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' In addition, also  considering the myriad of legal and business services that have progressively emerged  thanks to cloud computing, websites are more and more part of the wider ecosystem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  This research opens up new perspectives of data-driven digital monitoring, possibly  extending the analysis to more extensive samples of firms across countries, for instance,  using the same approach for all firms in ORBIS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' The building of proxies able to  capture, in economic terms, the digital behaviour of firms represents an essential  tool for policymakers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' The firm’s digital footprint is an important measure to define  targeted policies and development strategies for its replicability, unobtrusiveness,  frequent updating, extension to new website information, and industrial benchmarking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  In particular, the Italian National Recovery and Resilience Plan (named“NRRP”)  established to help the country to recover from the Covid-19 pandemic has 21% of the  total funds dedicated to digitalisation (with actions such as fastest connection through  ultra-broadband, incentives for the adoption of innovative technologies by the private  sector, revitalisation of touristic and cultural sectors) 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' The building of new tools and  methodologies, such as the ones we provide with this work, able to identify laggard  territories and NUTS-3 regions, represents a crucial step in an era in which policies  are more and more data-driven.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' With the awareness of the limit and potentiality of  our analysis, we contribute to this research stream with an innovative and original  approach, which joint public-private strategic partnerships can further leverage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  13see https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='governo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='it/it/approfondimento/le-missioni-e-le-componenti-del-pnrr/16700.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  21  References  Abeysekera, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “How best to communicate intangible resources on websites to  inform corporate-growth reputation of small entrepreneurial businesses.” Journal of  Small Business Management 57 (3): 738–756.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Ageeva, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', TC Melewar, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Foroudi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='and Dennis, and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Jin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Examining  the influence of corporate website favorability on corporate image and corporate  reputation: Findings from fsQCA.” Journal of Business Research 89: 287–304.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Antonelli, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “The digital divide: understanding the economics of new information  and communication technology in the global economy.” Information Economics and  Policy 15 (2): 173–199.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Arora, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Youtie, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Shapira.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Using the wayback machine  to mine websites in the social sciences: A methodological resource.” Journal of the  Association for Information Science and Technology 67 (8): 1904–1915.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Arora, Sanjay K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', Yin Li, Jan Youtie, and Philip Shapira.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Measuring  dynamic capabilities in new ventures: exploring strategic change in US green goods  manufacturing using website data.” The Journal of Technology Transfer 45 (5):  1451–1480.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Auger, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “The impact of interactivity and design sophistication on the  performance of commercial websites for small businesses.” Journal of Small Business  Management 43 (2): 119–137.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Axenbeck, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Breithaupt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Web-based innovation indicators: Which firm  website characteristics relate to firm-level innovation activity?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' ZEW Discussion  Papers 19-063.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' ZEW - Leibniz Centre for European Economic Research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' https:  //ideas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='repec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='org/p/zbw/zewdip/19063.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='html.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Barney, Jay B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 1991.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Firm Resources and Sustained Competitive Advantage.” Journal  of Management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 17 (1): 99–120.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Baskerville, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Myers, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Yoo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Digital First: The Ontological  Reversal and New Challenges for Information Systems Research.” MIS Quarterly 44  (2): 509–523.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Beaudry, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' H´eroux-Vaillancourt, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Rietsch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Validation of a web  mining technique to measure innovation in high technology Canadian industries.”  1–25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Billon, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Ezcurra, and Lera-L´opez F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Spatial Effects in Website Adoption  by Firms in European Regions.” Growth and Change 40 (1): 54–84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Blank, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Graham, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Calvino.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Local geographies of digital inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Social Science Computer Review.” Social Science Computer Revie 36 (1): 82–102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Blanka, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Krumay, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Rueckel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “The interplay of digital transformation  and employee competency: A design science approach.” Technological Forecasting  and Social Change 178 (C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Blazquez, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Domenech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Big Data sources and methods for social and  22  economic analyses.” Technological Forecasting and Social Change 130 (C): 99–113.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Blazquez, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Domenech, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Deb´on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Do corporate websites’ changes  reflect firms’ survival?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Online Information Review 42 (6): 956–970.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Brynjolfsson, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Wang, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “The economics of IT and digitization:  Eight questions for research.” MIS Quarterly 45 (1): 473–477.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Castells, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' he Rise of the Network Society, The Information Age: Economy,  Society and Culture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Malden, MA;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Oxford, UK: Blackwell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Corrocher, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Ordanini.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Measuring the digital divide: a framework for  the analysis of cross-country differences.” Journal of Information technology 17 (1):  9–19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Daniele, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Territorial disparities in labour productivity, wages and prices in  Italy: What does the data show?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' European Urban and Regional Studies 28 (4):  431–449.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Dickinger, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Stangl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Website performance and behavioral consequences:  A formative measurement approach.” Journal of Business Research 66 (6): 771–777.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Ellinger, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Lynch, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Hansen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Firm size, web site content,  and financial performance in the transportation industry.” Industrial Marketing  Management 32 (3): 177–185.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Faulkner, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Runde.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “On the identity of technological objects and user  innovations in function.” Academy of Management Review 34 (3): 442–462.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Fink, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Kenny, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “W(h)ither the Digital Divide?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' info, The journal of  policy, regulation and strategy for telecommunications 5 (6): 15–24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Floridi, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' The Fourth Revolution: How the Infosphere is Reshaping Human  Reality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Oxford University Press UK.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Forman, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “The Corporate Digital Divide: Determinants of Internet Adoption.”  Management Science 51 (4): 641–654.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Forman, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Goldfarb, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Greenstein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “How did location affect adoption  of the commercial Internet?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Global village vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' urban leadership.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Journal of urban  Economics.” Journal of urban Economics 58 (3): 389–420.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  George, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' C Osinga, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Lavie, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' A Scott.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Big data and data  science methods for management research.” Academy of Management Journal 59  (5): 1493–1507.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Giustiziero, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Kretschmer, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Somaya, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Wu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Hyperspecialization and  hyperscaling: A resource-based theory of the digital firm.” Strategic Management  Journal .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Gok, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Waterworth, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Shapira.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Use of web mining in studying  innovation.” Scientometrics 102 (1): 653–671.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Hern´andez, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Jim´enez, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Mart´ın.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Key website factors in e-business  strategy.” International Journal of Information Management 29 (5): 362–371.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Heroux-Vaillancourt, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Beaudry, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Rietsch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Using web content analysis  to create innovation indicators - What do we really measure?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Quantitative Science  23  Studies 1 (4): 1601–1637.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Kinne, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Axenbeck.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Web mining for innovation ecosystem mapping: a  framework and a large-scale pilot study.” Scientometrics 125 (3): 2011–2041.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Kinne, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Resch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Generating Big Spatial Data on Firm Innovation  Activity from Text-mined Firm Websites.” GI Forum - Journal for Geographic  Information Science 6 (1): 82–89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Kr´ol, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Zdonek.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Aggregated indices in Website quality assessment.”  Future Internet 12 (4): 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Kr¨uger, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Kinne, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Lenz, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Resch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' The digital layer: How innovative  firms relate on the web.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' ZEW Discussion Papers 20-003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' ZEW - Leibniz Centre for  European Economic Research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Kyriakidou, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Michalakelis, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Sphicopoulos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Digital divide gap  convergence in Europe.” Technology in Society 33 (3): 265–270.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Arora, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Youtie, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Shapira.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Using web mining to explore Triple  Helix influences on growth in small and mid-size firms.” Technovation 76: 3–14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Dong, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Mei, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Shen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Digital innovation and performance of  manufacturing firms: An affordance perspective.” Technovation 102458.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Lythreatis, Sophie, Sanjay Kumar Singh, and Abdul-Nasser El-Kassar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “The  digital divide: A review and future research agenda.” Technological Forecasting and  Social Change 175 (C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Mateos, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Mera, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Gonz´alez, and ´O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' G L´opez.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “A new Web  assessment index: Spanish universities analysis.” Internet research 11 (3): 226–234.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Matthess, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Kunkel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Structural change and digitalization in developing  countries: Conceptually linking the two transformations.” Technology in Society 63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Pukelis, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Stanciauskas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' sing Internet Data to Complement Traditional  Innovation Indicators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Technical Report.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Public Policy and Management Institute  (PPMI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' URL:https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='ippapublicpolicy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='org/file/paper/5d073ea805eb6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  pdf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Rasmussen, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Thimm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Circumventing nonresponse-upgrading  traditional company survey data with unobtrusive data from company websites.”  ulletin of Sociological Methodology 127 (1): 85–96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Sanders, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Galloway.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Rural small firms’ website quality in transition  and market economies.” Journal of Small Business and Enterprise Development 20  (4): 788–806.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Saridakis, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Lai, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Mohammed, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Hansen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Industry  characteristics, stages of E-commerce communications and entrepreneurs and SMEs  revenue growth.” Technological Forecasting and Social Change 128 (C): 56–66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Shakina, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Parshakov, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Alsufiev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Rethinking the corporate digital  divide: The complementarity of technologies and the demand for digital skills.”  Technological Forecasting and Social Change 162 (C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Szeles, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “New insights from a multilevel approach to the regional digital  24  divide in the European Union.” Telecommunications Policy 42 (6): 452–463.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Tambe, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Hitt, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Rock, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Brynjolfsson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Digital Capital and Superstar  Firms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' NBER Working Papers 28285.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' National Bureau of Economic Research, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  https://ideas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='repec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='org/p/nbr/nberwo/28285.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='html.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Teece, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Linden.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Business models, value capture and the digital  enterprise.” Journal of Organization Design 6 (1): 1–14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Thonipara, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Sternberg, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Proeger, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Haefner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Digital divide, craft  firms’ websites and urban-rural disparities—empirical evidence from a web-scraping  approach.” Review of Regional Research 1–14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Vaughan, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Exploring website features for business information.” Scientometrics  61 (3): 467–477.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Vehovar, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Sicherl, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' H¨using, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Dolnicar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Methodological Challenges  of Digital Divide Measurements.” Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 22: 279–290.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Verhoef, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Broekhuizen, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Bart, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Bhattacharya, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Dong, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Fabian,  and M Haenlein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Digital transformation: A multidisciplinary reflection and  research agenda.” Journal of Business Research 122 (C): 889–901.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Volberda, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='W, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Khanagha, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Baden-Fuller, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' R Mihalache, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Birkinshaw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Strategizing in a digital world: Overcoming cognitive barriers, reconfiguring  routines and introducing new organizational forms.” Long Range Planning 54 (5):  102110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Warner, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' SR, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' W¨ager.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Building dynamic capabilities for digital  transformation: An ongoing process of strategic renewal.” Long range planning 52  (3): 326–349.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Wells, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' S Valacich, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' J Hess.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “What signal are you sending?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' How  website quality influences perceptions of product quality and purchase intentions.”  MIS quarterly 373–396.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Wernerfelt, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 1984.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “A resource based view of the firm.” Strategic management journal  5 (2): 171–180.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Youtie, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=', D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Hicks, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' Shapira, and Horsley.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' “Pathways from discovery to  commercialisation: using web sources to track small and medium-sized enterprise  strategies in emerging nanotechnologies.” Technology Analysis and Strategic  Management 24 (10): 981–995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  25  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  Appendix  sum of the ten indicators  Constant  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='601***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='011)  Micro firm  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='178***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='006)  Mid-sized firm  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='244***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='010)  Large firm  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='416***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='019)  A  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='115***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='023)  C  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='064***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='008)  G  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='088***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='008)  F  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='299***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='011)  H  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='321***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='015)  I  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='311***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='011)  J  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='172***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='011)  M  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='071***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='011)  K  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='205***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='024)  L  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='101***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='018)  Urban area  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='055***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='005)  North  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='026***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='006)  South  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='019*  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='008)  Firm age  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='001***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='000)  Wide band  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='027***  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='007)  R-squared:  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='038  Adj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' R-squared:  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='038  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' of Observations  182705  Table 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=': OLS regression results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=' The dependent variable is the sum of the values of the ten  indicators of the corporate web sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  26  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content=': The distribution of the CoDAI across Italian municipalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
+page_content='  27  Augsburg  r  Bratislava  Munchen  Budapest  Debrecer  Szombathel  Magyarorszag  Oradea  Szegec  Sloyentija  Pecs  rad  Zagreb  FCy60TMLa  Timisoara  Osijek  esita  ania Luka  beorpaa  Sar  Hrvatska  BosnaiHercegovina  Cp6wja  Zadar  bocHaM  XeperoBMHa  LpHaropa  Kosovo  Shgiperia' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E4T4oBgHgl3EQfKAwg/content/2301.04925v1.pdf'}
diff --git a/L9FLT4oBgHgl3EQfMi8T/vector_store/index.faiss b/L9FLT4oBgHgl3EQfMi8T/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..41365dd099ade1c03cbd4636027b2febe74bd91b
--- /dev/null
+++ b/L9FLT4oBgHgl3EQfMi8T/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:bd8283c821d7824771916b684b8a31d924c45f3f1357c766c556c3d7745d9cae
+size 7471149
diff --git a/L9FLT4oBgHgl3EQfMi8T/vector_store/index.pkl b/L9FLT4oBgHgl3EQfMi8T/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..d5b6f488f288c980363ead71f0b8748c5b442835
--- /dev/null
+++ b/L9FLT4oBgHgl3EQfMi8T/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:100ac76ff1bcb8a0db075b825e18ef2f2b1da83e1f6e6fe7c62ede2d6e4d264e
+size 245105
diff --git a/LdAyT4oBgHgl3EQf6fqP/vector_store/index.faiss b/LdAyT4oBgHgl3EQf6fqP/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..e4901a15a3f15f2eaaa67f6509ce6146e5305340
--- /dev/null
+++ b/LdAyT4oBgHgl3EQf6fqP/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3c227d4dcd6f305eaac01a78fa3d1ef2d73b5bb9291b67b43a17d994fe0dd01e
+size 13631533
diff --git a/MdAzT4oBgHgl3EQfkv0u/content/tmp_files/2301.01535v1.pdf.txt b/MdAzT4oBgHgl3EQfkv0u/content/tmp_files/2301.01535v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e77a56747d2c799e8ce1f452c9c5e208e8d7866b
--- /dev/null
+++ b/MdAzT4oBgHgl3EQfkv0u/content/tmp_files/2301.01535v1.pdf.txt
@@ -0,0 +1,7753 @@
+arXiv:2301.01535v1  [math.AT]  4 Jan 2023
+THE SQUARING OPERATION AND THE HIT PROBLEM
+FOR THE POLYNOMIAL ALGEBRA IN A TYPE
+OF GENERIC DEGREE
+NGUYỄN SUM
+Abstract. Let Pk be the graded polynomial algebra F2[x1, x2, . . . , xk] with
+the degree of each generator xi being 1, where F2 denote the prime field of
+two elements.
+The hit problem of Frank Peterson asks for a minimal generating set for
+the polynomial algebra Pk as a module over the mod-2 Steenrod algebra A.
+Equivalently, we want to find a vector space basis for F2 ⊗A Pk in each degree.
+In this paper, we study a generating set for the kernel of Kameko’s squaring
+operation �
+Sq
+0
+∗ : F2 ⊗A Pk −→ F2 ⊗A Pk in a so-called generic degree. By using
+this result, we explicitly compute the hit problem for k = 5 in respective
+generic degree.
+(In memory of Professor Reginald Wood)
+1. Introduction
+Denote by Pk := F2[x1, x2, . . . , xk] the polynomial algebra over the field of two
+elements, F2, in k generators x1, x2, . . . , xk, each of degree 1. This algebra arises as
+the cohomology with coefficients in F2 of a classifying space of an elementary abelian
+2-group Vk of rank k. Therefore, Pk is a module over the mod-2 Steenrod algebra, A.
+The action of A on Pk is determined by the elementary properties of the Steenrod
+squares Sqi and subject to the Cartan formula Sqn(fg) = �n
+i=0 Sqi(f)Sqn−i(g),
+for f, g ∈ Pk (see Steenrod and Epstein [17]).
+A polynomial f in Pk is called hit if it can be written as a finite sum f =
+�
+i>0 Sqi(hi) for suitable polynomials hi ∈ Pk. That means f belongs to A+Pk,
+where A+ denotes the augmentation ideal in A.
+We study the Peterson hit problem of determining a minimal set of generators
+for the polynomial algebra Pk as a module over the Steenrod algebra. Equivalently,
+we want to find a vector space basis for the quotient
+QPk := Pk/A+Pk = F2 ⊗A Pk.
+The Peterson hit problem is an open problem in Algebraic Topology. It was
+first studied by Peterson [7], Priddy [10], Singer [15] and Wood [25], who showed
+its relation to several classical problems respectively in cobordism theory, modular
+representation theory of general linear groups, Adams spectral sequence for the
+2010 Mathematics Subject Classification. Primary 55S10; Secondary 55S05.
+Key words and phrases. Steenrod algebra, Peterson hit problem, polynomial algebra.
+The author was supported in part by the National Foundation for Science and Technology
+Development (NAFOSTED) of Viet Nam under the grant number 101.04-2017.05.
+1
+
+2
+NGUYỄN SUM
+stable homotopy of spheres, and stable homotopy type of classifying spaces of finite
+groups. Then, this problem was studied by Carlisle and Wood [1], Crabb and Hub-
+buck [2], Kameko [3, 4], Mothebe [5], Nam [6], Peterson [8], Repka and Selick [11],
+Silverman [12], Silverman and Singer [14], Singer [16], Walker and Wood [21, 22],
+Wood [26] and others.
+Let GLk be the general linear group over the field F2. Since Vk is an F2-vector
+space of dimension k, this group acts naturally on Vk and therefore on the coho-
+mology Pk of BVk. The two actions of A and GLk upon Pk commute with each
+other. Hence, there is an inherited action of GLk on QPk.
+The vector space QPk was explicitly calculated by Peterson [7] for k = 1, 2, by
+Kameko [3] for k = 3 and by Kameko [4] and the present author [19] for k = 4,
+unknown in general. Recently, the hit problem and its applications to represen-
+tations of general linear groups have been presented in the monographs of Walker
+and Wood [23, 24].
+For a positive integer n, by µ(n) one means the smallest number r for which it
+is possible to write n = �
+1⩽i⩽r(2ui − 1) with ui > 0. By a simple computation,
+we can see that µ(n) = s if and only if there exists a unique sequence of integers
+d1 > d2 > . . . > ds−1 ⩾ ds > 0 such that
+n = 2d1 + 2d2 + . . . + 2ds−1 + 2ds − s =
+�
+1⩽i⩽s
+(2di − 1),
+(1.1)
+(see e.g.
+[20, Lemma 2] for a proof).
+From this it implies n − s is even and
+µ( n−s
+2 ) ⩽ s.
+Based on the results of Wood [25] and Kameko [3, Theorem 4.2], the hit problem
+is reduced to the case of degree n of the form (1.1) with µ(n) = s < k.
+The hit problem in the case of degree n of the form (1.1) with s = k − 1, was
+studied by Crabb and Hubbuck [2], Nam [6], Repka and Selick [11], Walker and
+Wood [22] and the present author [18, 19].
+For s = k − 2, in [18], we studied the kernel of Kameko’s squaring operation
+�
+Sq
+0
+∗ : QPk → QPk. This operation is induced by the F2-linear map ϕ : Pk → Pk,
+given by
+ϕ(x) =
+�
+y,
+if x = x1x2 . . . xky2,
+0,
+otherwise,
+for any monomial x ∈ Pk. Note that ϕ is a homomorphism of GLk-modules but
+it is not an A-homomorphism. However, ϕSq2t = Sqtϕ and ϕSq2t+1 = 0 for any
+non-negative integer t. So, for each positive integer n such that n − k is even, ϕ
+induced a homomorphism of GLk-modules:
+(�
+Sq
+0
+∗)(k,n) := �
+Sq
+0
+∗ : (QPk)n → (QPk) n−k
+2 .
+Here and in what follows, we denote by (Pk)n the subspace of Pk consisting of
+the homogeneous polynomials of degree n in Pk and (QPk)n the subspace of QPk
+consisting of all the classes represented by the elements in (Pk)n.
+Since (�
+Sq
+0
+∗)(k,n) is a homomorphism of GLk-modules, Ker(�
+Sq
+0
+∗)(k,n) gives a rep-
+resentation of GLk. We have gave a prediction for the dimension of Ker(�
+Sq
+0
+∗)(k,n)
+in this case.
+
+THE SQUARING OPERATION AND THE HIT PROBLEM
+3
+Conjecture 1.1 (See [18]). Let n = �k−2
+i=1 (2di − 1) with di positive integers. If
+di−2 − di−1 > i for 3 ⩽ i ⩽ k − 1 and dk−2 > k ⩾ 3, then
+dim Ker(�
+Sq
+0
+∗)(k,n) =
+�
+3⩽i⩽k
+(2i − 1).
+This conjecture is true for k ⩽ 4 and unknown for k ⩾ 5.
+In [18, 19], we have studied the hit problem in case of the degree n with µ(n) =
+s = k −1 by using the strictly inadmissible monomials and Singer’s criterion in [16]
+on hit monomials. However, these tools are not enough to study this problem in
+the case of the degree n with µ(n) = s = k − 2.
+In this paper, based on Silverman’s criterion in [13] on hit polynomials, we
+introduce the notion of strongly inadmissible monomial to construct a generating
+set for the kernel of Kameko’s squaring operation.
+One of our main results is
+Theorem 3.3.3 in Section 3 which provides the upper bound on the dimension of
+Ker(�
+Sq
+0
+∗)(k,n). By using this result, we verify Conjecture 1.1 for k = 5. We prove
+the following.
+Theorem 1.2. Let n = 2d+s+t + 2d+s + 2d − 3 with d, s, t non-negative integers.
+If d ⩾ 6 and t, s ⩾ 4, then
+dim Ker(�
+Sq
+0
+∗)(5,n) = (23 − 1)(24 − 1)(25 − 1) = 3255.
+(1.2)
+Thus, Conjecture 1.1 is true for k = 5. Based on Theorem 1.2 and our result in
+[19, Theoren 1.4], one gets the following.
+Corollary 1.3. Let n be as in Theorem 1.2. If d ⩾ 6 and s, t ⩾ 4, then
+dim(QP5)n = 4(23 − 1)(24 − 1)(25 − 1) = 13020.
+We can see in Section 4 that using the notion of strongly inadmissible monomial
+can overcome many difficulties encountered if using the notion of strictly inadmissi-
+ble monomial. Thus, the notion of strongly inadmissible monomial can be a useful
+tool in progressing the study of the Peterson hit problem.
+This paper is organized as follows. In Section 2, we recall some needed informa-
+tion on the admissible monomials in Pk and criterions of Singer [16] and Silverman
+[13] on hit monomials. In Section 3, we present the results for a generating set
+of the kernel of Kameko’s squaring operation. As an application of the results of
+Section 3, in Section 4, we prove that Conjecture 1.1 is true for k = 5. Finally, in
+Section 5 we list the needed admissible monomials of degree 3(2d − 1) in P5.
+2. Preliminaries
+In this section, we recall some results from Kameko [3], Singer [16], Silverman [13]
+and our work [19] which will be used in the next sections.
+2.1. The weight vector and the admissible monomials.
+Notation 2.1.1. In the paper, we use the following notations.
+Nk = {1, 2, . . ., k},
+XJ = Xj1,j2,...,js =
+�
+j∈Nk\J
+xj,
+J = {j1, j2, . . . , js} ⊂ Nk.
+In particular, we have X∅ = x1x2 . . . xk, Xj = x1 . . . ˆxj . . . xk, 1 ⩽ j ⩽ k, XNk = 1.
+
+4
+NGUYỄN SUM
+Denote by αi(a) the i-th coefficient in dyadic expansion of a non-negative integer
+a. That means
+a = α0(a)20 + α1(a)21 + α2(a)22 + . . . ,
+for αi(a) = 0 or 1 and i ⩾ 0. Denote by α(a) the number of 1’s in dyadic expansion
+of a.
+Let x = xa1
+1 xa2
+2 . . . xak
+k
+∈ Pk. We denote νj(x) = aj, 1 ⩽ j ⩽ k and ν(x) =
+max{νj(x) : 1 ⩽ j ⩽ k}. We set
+Ji(x) = {j ∈ Nk : αi(νj(x)) = 0},
+for i ⩾ 0. Then, we have
+x =
+�
+i⩾0
+X2i
+Ji(x).
+Definition 2.1.2. A weight vector ω is a sequence of non-negative integers (ω1, ω2,
+. . . , ωi, . . .) such that ωi = 0 for i ≫ 0. For any monomial x in Pk, we define two
+sequences associated with x by
+ω(x) = (ω1(x), ω2(x), . . . , ωi(x), . . .),
+σ(x) = (ν1(x), ν2(x), . . . , νk(x)),
+where ωi(x) = �
+1⩽j⩽k αi−1(νj(x)) = deg XJi−1(x), i ⩾ 1. The sequences ω(x) and
+σ(x) are respectively called the weight vector and the exponent vector of x.
+The sets of the weight vectors and the exponent vectors are given the left lexi-
+cographical order.
+For a weight vector ω = (ω1, ω2, . . .), define deg ω = �
+i>0 2i−1ωi and the length
+ℓ(ω) = max{i : ωi > 0}. Then, we write ω = (ω1, ω2, . . . , ωr) if ℓ(ω) = r. For a
+weight vector η = (η1, η2, . . .), we define the concatenation of weight vectors
+ω|η = (ω1, . . . , ωr, η1, η2, . . .)
+if ℓ(ω) = r and (a)|b = (a)|(a)| . . . |(a), (b times of (a)’s), where a, b are positive
+integers. We denote Pk(ω) the subspace of Pk spanned by monomials y such that
+deg y = deg ω and ω(y) ⩽ ω, and by P −
+k (ω) the subspace of Pk(ω) spanned by
+monomials y such that ω(y) < ω.
+Denote by A+
+s the subspace of A spanned by all Sqj with 1 ⩽ j < 2s.
+Definition 2.1.3. For ω a weight vector and f, g two polynomials of the same
+degree in Pk, we define
+i) f ≡ g if and only if f + g ∈ A+Pk. If f ≡ 0, then f is said to be hit.
+ii) f ≡ω g if and only if f + g ∈ A+Pk + P −
+k (ω).
+iii) f ≃(s,ω) g if and only if f + g ∈ A+
+s Pk + P −
+k (ω).
+Obviously, the relations ≡, ≡ω and ≃(s,ω) are equivalence ones. Since A+
+0 Pk = 0,
+f ≃(0,ω) g if and only if f + g ∈ P −
+k (ω).
+For x a monomial in Pk and ω = ω(x), we denote x ≃s g if and only if x ≃(s,ω(x))
+g.
+Denote by QPk(ω) the quotient of Pk(ω) by the equivalence relation ≡ω. Fol-
+lowing [20], we have
+(QPk)n ∼=
+�
+deg ω=n
+QPk(ω).
+(2.1)
+
+THE SQUARING OPERATION AND THE HIT PROBLEM
+5
+For any polynomial f in Pk, we denote [f] the class in QPk represented by f.
+For a subset S ⊂ Pk, we denote [S] = {[f] : f ∈ S} ⊂ QPk. If f ∈ Pk(ω) and
+S ⊂ Pk(ω), then we denote by [f]ω the class in QPk(ω) represented by f and
+[S]ω = {[f]ω : f ∈ S} ⊂ QPk(ω).
+We recall some elementary properties on the action of the Steenrod squares on
+Pk.
+Proposition 2.1.4. Let f be a homogeneous polynomial in Pk.
+i) If i > deg f, then Sqi(f) = 0. If i = deg f, then Sqi(f) = f 2.
+ii) If i is not divisible by 2s, then Sqi(f 2s) = 0 while Sqr2s(f 2s) = (Sqr(f))2s.
+Proposition 2.1.5 (Kameko [3, Lemma 3.1]). Let x be a monomial in Pk and
+n, s be positive integers such that 0 < n < 2s. If v is a monomial in Pk which
+appears as a term in the polynomial Sqn(x), then there is an index i ⩽ s such that
+ωi(v) < ωi(x) and ω(v) < ω(x).
+Definition 2.1.6. Let x, y be monomials of the same degree in Pk. We define
+x < y if and only if one of the following holds:
+i) ω(x) < ω(y);
+ii) ω(x) = ω(y) and σ(x) < σ(y).
+Definition 2.1.7. A monomial x is said to be inadmissible if there exist monomials
+y1, y2, . . . , yr such that yj < x for j = 1, 2, . . . , r and x ≡ �r
+j=1 yj.
+A monomial x is said to be admissible if it is not inadmissible.
+Obviously, the set of all the admissible monomials of degree n in Pk is a minimal
+set of A-generators for Pk in degree n.
+Definition 2.1.8. A monomial x is said to be strictly inadmissible if and only
+if there exist monomials y1, y2, . . . , yr such that yj < x, for j = 1, 2, . . . , r and
+x ≃s
+�r
+j=1 yj with s = max{i : ωi(x) > 0}.
+It is easy to see that if x is strictly inadmissible, then it is inadmissible. The
+following theorem is a modification of a result in [3].
+Theorem 2.1.9 (Kameko [3], Sum [18]). For any monomials x, y, w in Pk such
+that ωi(x) = 0 for i > r > 0, ωs(w) ̸= 0 and ωi(w) = 0 for i > s > 0, we have
+i) If w is inadmissible, then so is xw2r.
+ii) If w is strictly inadmissible, then so is xw2ry2r+s.
+Proposition 2.1.10 (See [18]). Let x be an admissible monomial in Pk and let i0
+be a positive integer. Then we have
+i) If ωi0(x) = 0, then ωi(x) = 0 for all i > i0.
+ii) If ωi0(x) < k, then ωi(x) < k for all i > i0.
+For 1 ⩽ i ⩽ k, define a homomorphism fi : Pk−1 → Pk of A-algebras by
+substituting
+fi(xu) =
+�
+xu,
+if 1 ⩽ u < i,
+xu+1,
+if i ⩽ u < k.
+(2.2)
+Proposition 2.1.11 (See Mothebe and Uys [5]). Let i, d be positive integers such
+that 1 ⩽ i ⩽ k. If w is an admissible monomial in Pk−1, then x2d−1
+i
+fi(w) is also
+an admissible monomial in Pk.
+
+6
+NGUYỄN SUM
+2.2. Some criterions on the hit polynomials.
+Firstly, we recall Singer’s criterion on hit monomials in Pk.
+Definition 2.2.1. A monomial z in Pk is called a spike if νj(z) = 2sj − 1 for sj a
+non-negative integer and j = 1, 2, . . ., k. If z is a spike with s1 > s2 > . . . > sr−1 ⩾
+sr > 0 and sj = 0 for j > r, then it is called the minimal spike.
+Note that if µ(n) = s, then n is of the form (1.1) and z = �s
+i=1 x2di −1
+i
+is the
+minimal spike of degree n. It is easy to show that a spike of degree n is the minimal
+spike if its weight vector order is minimal with respect to other spikes of degree n.
+The following is a criterion for hit monomials in Pk.
+Theorem 2.2.2 (See Singer [16]). Suppose x ∈ Pk is a monomial of degree n,
+where µ(n) ⩽ k. Let z be the minimal spike of degree n. If ω(x) < ω(z), then x is
+hit.
+We remark that this criterion is not enough to determine all hit monomials.
+For example, it can be shown that x15
+1 x3
+2x3
+3 is the minimal spike of degee 21 and
+x1x5
+2x5
+3x5
+4x5
+5 is hit, but ω(x1x5
+2x5
+3x5
+4x5
+5) = (5, 0, 4, 0) > (3, 3, 1, 1) = ω(x15
+1 x3
+2x3
+3). So,
+we need Silverman’s criterion for hit polynomials in Pk.
+Theorem 2.2.3 (See Silverman [13, Theorem 1.2]). Let p be a polynomial of the
+form fg2m for some homogeneous polynomials f and g. If deg f < (2m−1)µ(deg g),
+then p is hit.
+This result leads to a criterion in terms of the minimal spike which strengthens
+Theorem 2.2.2.
+Theorem 2.2.4 (See Walker and Wood [23, Theorem 14.1.3]). Let x ∈ Pk be a
+monomial of degree n, where µ(n) ⩽ k and let z be the minimal spike of degree n.
+If there is an index h such that �h
+i=1 2i−1ωi(x) < �h
+i=1 2i−1ωi(z), then x is hit.
+For 1 ⩽ r ⩽ k, we set
+P 0
+s = ⟨{x = xa1
+1 xa2
+2 . . . xas
+s
+: a1a2 . . . as = 0}⟩,
+P +
+s = ⟨{x = xa1
+1 xa2
+2 . . . xas
+s
+: a1a2 . . . as > 0}⟩.
+It is easy to see that P 0
+s and P +
+s
+are the A-submodules of Pk, Ps = P 0
+s ⊕ P +
+s
+and QPs = QP 0
+s ⊕ QP +
+s , where QP 0
+s = P 0
+s /A+P 0
+s and QP +
+s = P +
+s /A+P +
+s .
+For J = (j1, j2, . . . , js) : 1 ⩽ j1 < . . . < js ⩽ k, we define a monomorphism
+θJ : Ps → Pk of A-algebras by substituting θJ(xu) = xju for 1 ⩽ u ⩽ s. It is easy
+to see that, for any weight vector ω of degree n,
+QθJ(P +
+s )(ω) ∼= QP +
+s (ω) and (QθJ(P +
+s ))n ∼= (QP +
+s )n
+for 1 ⩽ s ⩽ k, where QθJ(P +
+s ) = θJ(P +
+s )/A+θJ(P +
+s ). So, by a simple computation
+using Theorem 2.2.2 and (2.1), we get the following.
+Proposition 2.2.5 (See Walker and Wood [23, Proposition 6.2.9]). For a weight
+vector ω of degree n, we have direct summand decompositions of the F2-vector spaces
+QPk(ω) =
+�
+µ(n)⩽s⩽k
+�
+ℓ(J)=s
+QθJ(P +
+s )(ω),
+
+THE SQUARING OPERATION AND THE HIT PROBLEM
+7
+where ℓ(J) is the length of J. Consequently,
+dim QPk(ω) =
+�
+µ(n)⩽s⩽k
+�k
+s
+�
+dim QP +
+s (ω),
+dim(QPk)n =
+�
+µ(n)⩽s⩽k
+�k
+s
+�
+dim(QP +
+s )n.
+Notation 2.2.6. From now on, we denote by Bk(n) the set of all admissible mono-
+mials of degree n in Pk, B0
+k(n) = Bk(n) ∩ P 0
+k , B+
+k (n) = Bk(n) ∩ P +
+k . For a weight
+vector ω of degree n, we set Bk(ω) = Bk(n) ∩ Pk(ω), B+
+k (ω) = B+
+k (n) ∩ Pk(ω).
+Then, [B0
+k(n)], [B+
+k (n)], [Bk(ω)]ω and [B+
+k (ω)]ω are respectively the bases of the
+F2-vector spaces (QP 0
+k )n, (QP +
+k )n, QPk(ω) and QP +
+k (ω) := QPk(ω) ∩ QP +
+k .
+For any (i; I) with I = (i1, i2, . . . , ir), 1 ⩽ i < i1 < i2 < . . . < ir ⩽ k, 0 ⩽ r < k,
+define a homomorphism p(i;I) : Pk → Pk−1 of algebras by substituting
+p(i;I)(xj) =
+
+
+
+
+
+xj,
+if 1 ⩽ j < i,
+�r
+t=1 xit−1,
+if j = i,
+xj−1,
+if i < j ⩽ k.
+(2.3)
+Then p(i;I) is a homomorphism of A-modules. These homomorphisms will be used
+in the proof of Theorem 4.2.
+3. On the kernel of Kameko’s squaring operation
+In this section, we consider n = �k−2
+i=1 (2di − 1) with di positive integers such
+that d1 > d2 > . . . > dk−3 ⩾ d := dk−2 > 0, k ⩾ 4, m = �k−3
+i=1 (2di−d − 1) = βd
+k(n),
+where the function βk : Z → Z is defined by βk(t) = t−k+2
+2
+if t − k + 2 is even and
+βk(t) = 0 if t − k + 2 is odd. Note that µ(n) = k − 2 and this degree is used in
+Conjecture 1.1 on the dimension of the kernel of Kameko’s squaring operation
+(�
+Sq
+0
+∗)(k,n) : (QPk)n → (QPk) n−k
+2 .
+The main result of the section is Theorem 3.3.3 that provides an upper bound
+for the dimension of Ker((�
+Sq
+0
+∗)(k,n)).
+Firstly, we prove some properties of monomials in Ker((�
+Sq
+0
+∗)(k,n)) from which we
+can reduce the computations to the case of weight vector (k−2)|d. In Subsection 3.2,
+we present the notion of strongly inadmissible monomial and prove Proposition 3.2.4
+that is used instead of Theorem 2.1.9. Note that the notion of strongly inadmissible
+monomial is weaker than the one of strictly inadmissible monomial, so using this
+notion can overcome many difficulties encountered if using the notion of strictly
+inadmissible monomial. In Subsection 3.3, we prove our main result by using the
+results in the previous subsections.
+3.1. Some properties of monomials in Ker((�
+Sq
+0
+∗)(k,n)).
+In this subsection we present some properties of the admissible monomials in
+the kernel of Kameko’s squaring operation that allow us to reduce the study of this
+subspace to the case of weight vector (k − 2)|d.
+Lemma 3.1.1. If x is an admissible monomial of degree n in Pk such that [x] ∈
+Ker((�
+Sq
+0
+∗)(k,n)), then ωi(x) = k − 2 for 1 ⩽ i ⩽ dk−2.
+
+8
+NGUYỄN SUM
+Proof. Note that z = �k−2
+t=1 x2dt−1
+t
+is the minimal spike of degree n and ωi(z) = k−2
+for 1 ⩽ i ⩽ dk−2. Since x is admissible, [x] ̸= 0. If ω1(x) = k − 1, then x = Xjy2
+with y a monomial of degree n−k+1
+2
+= βk(n)+ 1
+2, however this is not an integer. So,
+by Theorem 2.2.2, we have either ω1(x) = k − 2 or ω1(x) = k. If ω1(x) = k, then
+x = X∅y2 with y a monomial in Pk. Since x is admissible, by Theorem 2.1.9, y is
+also admissible. Hence, (�
+Sq
+0
+∗)(k,n)([x]) = [y] ̸= 0. This contradicts the hypothesis
+that x ∈ Ker((�
+Sq
+0
+∗)(k,n)), hence ω1(x) = k − 2. Then, we have x = Xj,ℓy2 with
+1 ⩽ j < ℓ ⩽ k and y an admissible monomial of degree βk(n) = �k−2
+i=1 (2di−1 − 1).
+Since ω1(y) ̸= k − 1, using Theorem 2.2.2 and Proposition 2.1.10 we get ω2(x) =
+ω1(y) = k − 2. By repeating the above argument we obtain ωi(x) = k − 2 for
+1 ⩽ i ⩽ dk−2. The lemma is proved.
+□
+Lemma 3.1.2. If x is a monomial of degree n in Pk such that [x] ∈ Ker((�
+Sq
+0
+∗)(k,n)),
+then x ≡ � ¯x with ¯x monomials in Pk such that ωi(¯x) = k − 2, for 1 ⩽ i ⩽ dk−2.
+Proof. If ω1(x) < k − 2, then by Theorem 2.2.2, x is hit, hence the lemma holds.
+Suppose ω1(x) = k − 2 and let s > 1 be the smallest index such that ωs(x) ̸= k − 2.
+If ωs(x) < k − 2, then by Theorem 2.2.2, x is hit, hence the lemma holds. Since
+ω1(x) ̸= k − 1, we obtain ωs(x) = k.
+Then we have x = wy2s−2 �
+t⩾s X2t
+Jt(x),
+where w = �s−3
+t=0 X2t
+Jt(x), y = XJs−2(x)X2
+Js−1(x) = XJs−2(x)X2
+∅ = X3
+u,vx2
+ux2
+v with
+1 ⩽ u < v ⩽ k. It is easy to see that
+y =
+�
+i̸=u,v
+X3
+i,u,vxux2
+vx4
+i + Sq1(X3
+u,vxux2
+v).
+(3.1)
+By combining Proposition 2.1.4 and the Cartan formula, we have
+w(Sq1(X3
+u,vxux2
+v))2s−2 = wSq2s−2 �
+(X3
+u,vxux2
+v)2s−2�
+= Sq2s−2 �
+w(X3
+u,vxux2
+v)2s−2�
++ Sq2s−2(w)(X3
+u,vxux2
+v)2s−2.
+Let ¯w be a monomial which appears as a term in Sq2s−2(w).
+By Proposition
+2.1.5, ω( ¯w) < ω(w) = (k − 2)|s−2. Hence, using Theorem 2.2.2 we see that the
+polynomial w(Sq1(X3
+u,vxux2
+v))2s−2 �
+t⩾s X2t
+Jt(x) is hit. So, from the relation (3.1) we
+obtain x ≡ �
+i̸=u,v x(i,u,v), where
+x(i,u,v) =
+�
+0⩽t⩽s−3
+X2t
+Jt(x)(X3
+i,u,vxux2
+vx4
+i )2s−2 �
+t⩾s
+X2t
+Jt(x).
+A simple computation shows that ωt(x(i,u,v)) = k − 2 for 1 ⩽ t ⩽ s. By repeating
+this argument we see that the lemma is true in this case.
+If ω1(x) = k, then x = X∅y2 with y a monomial in Pk.
+Then, we have
+(�
+Sq
+0
+∗)(k,n)([x]) = [y] = 0.
+Hence, y = �
+r>0 Sqr(gr) with suitable polynomial
+gr in Pk. Then, by using Proposition 2.1.4 and the Cartan formula, we get
+x = X∅y2 =
+�
+r>0
+X∅Sq2r(g2
+r)
+=
+�
+r>0
+Sq2r(X∅g2
+r) +
+�
+r>0
+r
+�
+t=1
+Sq2t(X∅)(Sqr−t(gr))2.
+
+THE SQUARING OPERATION AND THE HIT PROBLEM
+9
+Since deg(X∅) = k, Sq2t(X∅) = 0 for 2t > k. If 2t ⩽ k and w is a monomial which
+appears as a term of Sq2t(X∅), then ω1(w) = k −2t ⩽ k −2. Hence, from the above
+equality and Theorem 2.2.2, we get x ≡ � x′ with x′ monomials in (Pk)n such that
+ω1(x′) = k − 2. The lemma is proved.
+□
+From this lemma, it suffices to consider monomials x such that ωi(x) = k − 2
+for 1 ⩽ i ⩽ d = dk−2. Then
+x =
+d
+�
+t=1
+X2d−t
+it,jt y2d,
+where 1 ⩽ it < jt ⩽ k, 1 ⩽ t ⩽ d and y ∈ (Pk)m. Note that ω(x) = (k − 2)|d|ω(y).
+Lemma 3.1.3. Let x be a monomial of degree (k − 2)(2d − 1). If ω1(x) < k and
+there is r > d such that ωr(x) > 0, then x ∈ P −
+k ((k − 2)|d) + A+
+d Pk.
+Proof. If ω1(x) < k − 2, then x ∈ P −
+k ((k − 2)|d), hence the lemma holds. Since
+ω1(x) ̸= k − 1, if ω1(x) ⩾ k − 2, then ω1(x) = k − 2. Let s be the smallest index
+such that ωs(x) > k − 2. Since ωs(x) ̸= k − 1, we have ωs(x) = k. If s ⩾ d, then
+(k − 2)(2d − 1) = deg x ⩾ (k − 2)(2d − 1) + 2t−1ωt(x) > (k − 2)(2d − 1). This is
+a contradiction, so s < d. If there is 1 < r < s such that ωr(x) < k − 2, then
+x ∈ P −
+k ((k − 2)|d), so the lemma holds. Suppose ωr(x) = k − 2 for 1 ⩽ r < s and
+XJs−2(x) = Xu,v for 1 ⩽ u < v ⩽ k. Then, we have
+X2
+Js−1(x)XJs−2(x) = X3
+u,vx2
+ux2
+v =
+�
+i̸=u,v
+X3
+i,u,vx4
+i xux2
+v + Sq1(X3
+u,vxux2
+v).
+By an argument analogous to the one in the proof of Lemma 3.1.2, we get
+x =
+�
+i̸=u,v
+x(i,u,v)
+mod(P −
+k ((k − 2)|d) + A+
+d Pk),
+where
+x(i,u,v) =
+s−3
+�
+t=0
+X2t
+Jt(x)(X3
+i,u,vxux2
+vx4
+i )2s−2 �
+t⩾s
+X2t
+Jt(x).
+It is easy to see that ωt(x(i,u,v)) = k − 2 for 1 ⩽ t ⩽ s and ωr(x(i,u,v)) > 0 for
+suitable r > d. By repeating this argument we obtain
+x =
+�
+¯x
+mod(P −
+k ((k − 2)|d) + A+
+d Pk)
+with ¯x monomials such that ωt(¯x) ⩽ k − 2 for 1 ⩽ t ⩽ d and ωr(¯x) > 0 for suitable
+r > d. Then we have �d
+i=1 2i−1ωi(¯x) < deg ¯x = (k − 2)(2d − 1). Hence, there is
+an index u ⩽ d such that ωt(¯x) = k − 2 for 1 ⩽ t < u, ωu(¯x) < k − 2, therefore
+¯x ∈ P −
+k ((k − 2)|d). The lemma is proved.
+□
+3.2. The strongly inadmissible monomials.
+In this subsection, we introduce the notion of strongly inadmissible monomial in
+Pk and use it to study the kernel of Kemeko’s squaring operation. We can see in
+Section 4 that the use of strongly inadmissible monomial is more convenience than
+that of the strictly inadmissible monomial because it can overcome many difficulties
+encountered if using the notion of strictly inadmissible monomial.
+
+10
+NGUYỄN SUM
+Definition 3.2.1. Let n be a positive integer and z be the minimal spike of degree
+n. Denote by P(k,n) the subspace of Pk spanned by all monomials x of degree n
+such that
+h
+�
+j=1
+ωj(x) <
+h
+�
+j=1
+ωj(z),
+for some index h ⩾ 1.
+Definition 3.2.2. A monomial x of degree n in Pk is said to be strongly inad-
+missible if there exist monomials y1, y2, . . . , yt of the same weight vector ω(x) such
+that yu < x, 1 ⩽ u ⩽ t and
+x ≃s y1 + y2 + . . . + yt mod(P(k,n)),
+where s = max{i : ωi(x) > 0}.
+Obviously, if x is strictly inadmissible, then it is strongly inadmissible.
+By
+using Theorem 2.2.4, we see that if g ∈ P(k,n) then g ∈ A+Pk. Hence, if x is
+strongly inadmissible then it is inadmissible. However, if g /∈ A+
+s Pk, then x is not
+strictly inadmissible. Therefore, it is more convenient to use the notion of a strongly
+inadmissible monomial than to use the one of a strictly inadmissible monomial.
+For example, let x = x1x3
+2x6
+3x6
+4x5
+5 be the monomial of weight vector (3)|3 in P5.
+We have
+x = x1x3
+2x5
+3x6
+4x6
+5 + x1x3
+2x6
+3x5
+4x6
+5 + x1x5
+2x5
+3x5
+4x5
+5
++ Sq1(x2
+1x3
+2x5
+3x5
+4x5
+5) + Sq2(x1x3
+2x5
+3x5
+4x5
+5) mod(P −
+5 ((3)|3)),
+where x1x5
+2x5
+3x5
+4x5
+5 ∈ P(5,21), hence x is strongly inadmissible. It is easy to see that
+x1x5
+2x5
+3x5
+4x5
+5 = Sq2(x1x3
+2x5
+3x5
+4x5
+5 + x1x5
+2x3
+3x5
+4x5
+5 + x1x5
+2x5
+3x3
+4x5
+5 + x1x5
+2x5
+3x5
+4x3
+5)
++ Sq8(x1x3
+2x3
+3x3
+4x3
+5) mod(P −
+5 ((3)|3)) ∈ A+
+4 P5 + P −
+5 ((3)|3).
+If x is strictly inadmissible, then x1x5
+2x5
+3x5
+4x5
+5 ∈ A+
+3 P5 + P −
+5 ((3)|3). However, we
+have been unable to prove this.
+For a positive integer a, denote by α(a) the number of ones in dyadic expansion
+of a and by ζ(a) the greatest integer u such that a is divisible by 2u. That means
+a = 2ζ(a)b with b an odd integer. We set δ(a) = a − α(a) − ζ(a).
+Proposition 3.2.3. Let d be a positive integer. If z∗ is the minimal spike of degree
+nd := (k − 2)(2d − 1) and d > δ(k − 2), then ωi(z∗) = k − 2 for 1 ⩽ i ⩽ d − δ(k − 2)
+and ωi(z∗) < k − 2 for i > d − δ(k − 2).
+Proof. Set s = α(k − 2). We have k − 2 = 2t1 + 2t2 + . . . + 2ts−1 + 2ts, where
+t1 > t2 > . . . > ts−1 > ts = ζ(k − 2) ⩾ 0. Then, we obtain
+(k − 2)(2d − 1) = 2d+t1 + 2d+t2 + . . . + 2d+ts−1 + 2d+ts − k + 2
+=
+�
+1⩽i⩽k−2
+(2ei − 1),
+where
+ei =
+
+
+
+d + ti,
+1 ⩽ i < s,
+d + ts − i + s − 1, s ⩽ i ⩽ k − 3,
+d + ts − k + s + 2, i = k − 2.
+
+THE SQUARING OPERATION AND THE HIT PROBLEM
+11
+It is easy to see that e1 > e2 > . . . > ek−3 = ek−2 = d − δ(k − 2) > 0. Hence
+z∗ = �k−2
+i=1 x2ei−1
+i
+is the minimal spike of degree nd = (k−2)(2d−1), ωj(z∗) = k−2
+for 1 ⩽ j ⩽ ek−2 and ωi(z∗) < k − 2 for i > d − δ(k − 2). The proposition is
+proved.
+□
+The following is a modification of Theorem 2.1.9.
+Proposition 3.2.4. Let c, d, e be positive integers and let u, w, y ∈ Pk be mono-
+mials such that ω(u) = (k − 2)|c, ω(w) = (k − 2)|d and ω(y) = (k − 2)|e. If w is
+strongly inadmissible, then so is uw2cy2c+d.
+Proof. Note that the weight vector of uw2cy2c+d is (k−2)|c+d+e. Since w is strongly
+inadmissible, there exist monomials y1, y2, . . . , yt of the same weight vector (k−2)|d,
+g1 ∈ P −
+k ((k − 2)|d) and g2 ∈ P(k,nd) such that yi < w for i = 1, 2, . . . , t and
+w = y1 + y2 + . . . + yt + g1 + g2 +
+�
+1⩽j<2d
+Sqj(hj),
+where hj are suitable polynomials in Pk and nd = (k−2)(2d −1). Since j2c < 2c+d,
+by using Proposition 2.1.4 and the Cartan formula we have
+(Sqj(hj))2cy2c+d = Sqj2c(h2c
+j )y2c+d = Sqj2c �
+h2c
+j y2c+d�
+.
+Then, combining the Cartan formula and Proposition 2.1.4, we get
+u(Sqj(hj))2cy2c+d = Sqj2c �
+uh2c
+j y2c+d�
++
+�
+1⩽r⩽j
+Sqr2c(u)
+�
+Sqj−r(hjy2d)
+�2c
+.
+Suppose v is a monomial which appears as a term of Sqr2c(u). By Proposition
+2.1.5, we have ω(v) < ω(u) = (k − 2)|c. Hence,
+�
+1⩽r⩽j
+Sqr2c(u)
+�
+Sqj−r(hjy2d)
+�2c
+∈ P −
+k ((k − 2)|c+d+e),
+for 1 ⩽ j < 2d. Combining the above equalities gives
+uw2cy2c+d =
+�
+1⩽i⩽t
+uy2c
+i y2c+d + ug2c
+1 y2c+d + ug2c
+2 y2c+d
++
+�
+1⩽j<2d
+Sqj2c �
+uh2c
+j y2c+d�
+mod(P −
+k ((k − 2)|c+d+e)).
+Since ω(u) = (k − 2)|c, we can easily check that uy2c
+i y2c+d < uw2cy2c+d for 1 ⩽
+i ⩽ t, ug2c
+1 y2c+d ∈ P −
+k ((k − 2)|c+d+e) and ug2c
+2 y2c+d ∈ P(k,nc+d+e) with nc+d+e =
+(k − 2)(2c+d+e − 1). Hence, the last equality implies that uw2cy2c+d is strongly
+inadmissible.
+□
+Lemma 3.2.5. Let f, g ∈ (Pk)nd be homogeneous polynomials with nd = (k −
+2)(2d −1), and let y ∈ (Pk)m be a monomial. If f ≃(d,(k−2)|d) g mod(P(k,nd)), then
+fy2d ≡ gy2d.
+Proof. Note that z = �k−2
+i=1 x2di −1 is the minimal spike of degree n and ωt(z) = k−2
+for 1 ⩽ t ⩽ d. Suppose
+f = g + g1 +
+�
+1⩽j<2d
+Sqj(hj),
+
+12
+NGUYỄN SUM
+where g1 ∈ P(k,nd) and suitable polynomials hj ∈ Pk. By Proposition 2.1.4 and the
+Cartan formula,
+Sqj(hj)y2d = Sqj(hjy2d), 1 ⩽ j < 2d.
+By Definition 3.2.2, if a monomial w appears as a term of the polynomial g1, then
+there is an integer h ⩾ 1, such that
+h
+�
+i=1
+2i−1ωi(w) <
+h
+�
+i=1
+2i−1ωi(z∗),
+where z∗ is determined as in Proposition 3.2.3. If h ⩽ d, then using Proposition
+3.2.3 we have �h
+i=1 2i−1ωi(z∗) ⩽ (k − 2)(2h − 1) = �h
+i=1 2i−1ωi(z). If h > d, then
+h
+�
+i=1
+2i−1ωi(z∗) ⩽ deg(z∗) = (k − 2)(2d − 1) <
+h
+�
+i=1
+2i−1ωi(z).
+By Theorem 2.2.4, wy2d is hit, hence the polynomial g1y2d is hit. This implies
+fy2d ≡ gy2d. The lemma is proved.
+□
+3.3. A construction for A-generators of Ker((�
+Sq
+0
+∗)(k,n)).
+Notation 3.3.1. Let S be a finite sequence of positive integers.
+Then, there
+are positive integers c0, c1, . . . , cr and s0, s1, . . . , sr such that si+1 ̸= si and S =
+(s0)|c0|(s1)|c1| . . . |(sr)|cr. We define rl(S) = c1 +c2 +. . .+cr, the reduced length of
+S. For example, with S = (2, 2, 3, 1, 1, 1) = (2)|2|(3)|1|(1)|3, we have c0 = 2, c1 =
+1, c2 = 3, hence rl(S) = c1 + c2 = 4.
+Denote by PSeqd
+k the set of all pairs (I, J ) of sequences I = (i1, i2, . . . , id),
+J = (j1, j2, . . . , jd), where it, jt are integers such that 1 ⩽ it < jt ⩽ k, for 1 ⩽ t ⩽ d,
+and by PIncd
+k the set of all (I, J ) ∈ PSeqd
+k such that i1 ⩽ i2 ⩽ . . . ⩽ id and
+j1 ⩽ j2 ⩽ . . . ⩽ jd. By convention, PSeq0
+k = ∅. For (I, J ) ∈ PSeqd
+k, we denote
+X(I,J ) =
+�
+1⩽t⩽d
+X2d−t
+it,jt ∈ Pk((k − 2)|d) ⊂ (Pk)(k−2)(2d−1).
+Definition 3.3.2. Let d0 be a positive integer, d0 > 2, and B be a subset of PIncd0
+k .
+The set B is said to be compatible with (k − 2)|d0 if the following conditions hold:
+i) For any (I, J ) ∈ B, rl(I) ⩽ d0 − 2 and rl(J ) ⩽ d0 − 2,
+ii) For any (H, K) ∈ PSeqd0
+k , we have
+X(H,K) ≃d0
+min K
+�
+u=min H+1
+�
+(I,J )∈Bu
+X(I,J ) mod(P(k,nd0)),
+(3.2)
+where Bu is a set of some pairs (I, J ) ∈ B such that min I = min H, min J = u
+and nd0 = (k − 2)(2d0 − 1).
+From the result in [18, Proposition 5.2.1] we see that the set
+B4 = {(I, J ) ∈ PSeq5
+4 : X(I,J ) ∈ B4((2)|5)} ⊂ PInc5
+4
+is compatible with (2)|5.
+
+THE SQUARING OPERATION AND THE HIT PROBLEM
+13
+For 1 ⩽ i < j ⩽ k, denote f(i,j) = fifj−1 : Pk−2
+fj−1
+−→ Pk−1
+fi
+−→ Pk. Here fi and
+fj−1 are defined by (2.2). More precisely,
+f(i,j)(xt) =
+
+
+
+
+
+xt,
+if 1 ⩽ t < i,
+xt+1,
+if i ⩽ t < j − 2,
+xt+2,
+if j − 2 ⩽ t ⩽ k − 2.
+The main result of this section is the following.
+Theorem 3.3.3. Let d0 be a positive integer, d0 > 2, and let k ⩾ 4, n =
+�k−2
+i=1 (2di − 1) with di positive integers such that d1 > d2 > . . . > dk−3 ⩾ dk−2 =
+d ⩾ d0. Denote m = �k−3
+i=1 (2di−d − 1) = βd
+k(n) with βk(n) = n−k+2
+2
+. Suppose the
+set B ⊂ PIncd0
+k is compatible with (k − 2)|d0. Then,
+B :=
+�
+(I,J )∈B
+�
+X(I,J )(Xi,j)2d−2d0 (f(i,j)(y))2d : y ∈ Bk−2(m)
+�
+is a set of generators for Ker(�
+Sq
+0)(k,n), where i = min I = i1, j = min J = j1
+and Bk−2(m) is the set of all the admissible monomials of the degree m in Pk−2.
+Consequently, dim Ker(�
+Sq
+0)(k,n) ⩽ |B| dim(QPk−2)m.
+We need the following lemmas for the proof of the theorem.
+Lemma 3.3.4. Let n, m, d0 and B be as in Theorem 3.3.3. Let y0 be a monomial
+in (Pk)m0−1 with m0 = �k−2
+i=1 (2di−d0 − 1) = βd0
+k (n), yu = y0xu for 1 ⩽ u ⩽ k, and
+(I, J ) ∈ B, i = min I, j = min J . Then we have
+X(I,J )y2d0
+i
+≡
+�
+1⩽u<k
+u̸=i,j
+�
+(U,V)∈Bu
+X(U,V)y2d0
+u
+,
+(3.3)
+X(I,J )y2d0
+j
+≡
+�
+2⩽v⩽k
+v̸=i,j
+�
+(U,V)∈Cv
+X(U,V)y2d0
+v
+,
+(3.4)
+where Bu is a set of some (U, V) ∈ B such that min U = u for u < i and min U = i
+for u > i; Cv is a set of some (U, V) ∈ B such that min V = v for v < j and
+min V = j for v > j.
+Proof. By the Cartan formula, we have Sq1(Xj) = �
+u̸=j Xu,jx2
+u and Sq1(Xjy2
+0) =
+Sq1(Xj)y2
+0. Hence, we obtain
+Xi,jy2
+i =
+�
+1⩽u<j
+u̸=i
+Xu,jy2
+u +
+�
+j<u⩽k
+Xj,uy2
+u + Sq1(Xjy2
+0).
+Since (I, J ) ∈ B ⊂ PIncd0
+k , we have X(I,J ) = X(I\i,J \j)(Xi,j)2d0−1 with i = i1, j =
+j1, and
+X(I\i,J \j)(Xu,j)2d0−1 =
+� X(u|(I\i),J ),
+if u < j,
+X(j|(I\i),u|(J \j)), if u > j.
+By using the Cartan formula, Proposition 2.1.4 and Theorem 2.2.2 we see that the
+polynomial X(I\i,J \j)(Sq1(Xjy2
+0))2d0−1 is hit. So, we get
+X(I,J )y2d0
+i
+≡
+�
+1⩽u<j
+u̸=i
+X(u|(I\i),J )y2d0
+u
++
+�
+j<u⩽k
+X(j|(I\i),u|(J \j))y2d0
+u
+.
+
+14
+NGUYỄN SUM
+Since rl(I) < d0 − 1 and rl(J ) < d0 − 1, we have min(u|(I \ i)) = u for u < i,
+min(j|(I \ i)) = min(u|(I \ i)) = i for i < u < j and min(u|(J \ j)) = j for u > j.
+Hence the relation (3.3) follows from the condition (3.2) of B in Definition 3.3.2
+and Lemma 3.2.5.
+The relation (3.4) is proved by a similar computation.
+□
+Lemma 3.3.5. Let n, d0, m0 be as in Lemma 3.3.4 and let P1
+k(n) denote the
+subspace of (Pk)n spanned by all monomials of the form X(I,J )(fi(y))2d0 with
+(I, J ) ∈ B, i = min I and y ∈ (Pk−1)m0. Then Ker(�
+Sq
+0)(k,n) ⊂ [P1
+k(n)].
+Proof. Let x be a monomial of degree n such that [x] ∈ Ker(�
+Sq
+0)(k,n). By using
+Lemmas 3.1.1 and 3.1.2, we can assume that ωi(x) = k − 2, for 1 ⩽ i ⩽ d. Then,
+x = �d
+t=1 X2d−t
+αt,δt ¯y2d, where αt, δt are integers such that 1 ⩽ αt < δt ⩽ k, for
+1 ⩽ t ⩽ d, and ¯y is a monomial of degree m = βd
+k(n) in Pk. Since d ⩾ d0, we set
+H = (α1, α2, . . . , αd0), K = (δ1, δ2, . . . , δd0), then we have x = X(H,K)˜y2d0 , where
+˜y = �d
+t=d0+1 X2d−t
+αt,δt ¯y2d is the monomial of degree m0 in Pk. By the condition of
+the set B in Definition 3.3.2, the monomial X(H,K) is of the form (3.2). Hence, by
+using Lemma 3.2.5, one gets
+x = X(H,K)˜y2d0 ≡
+min K
+�
+u=min H+1
+�
+(I,J )∈Bu
+X(I,J )˜y2d0
+where Bu is as in Definition 3.2.2.
+For i = min H, we have ˜y = xa
+i fi(y) with
+a a non-negative integer and y ∈ (Pk−1)m0−a. We prove the lemma by proving
+[X(I,J )(xa
+i fi(y))2d0 ] ∈ [P1
+k(n)] for all (I, J ) ∈ Bu, i < u ⩽ min K. We prove this
+claim by double induction on (a, i).
+If a = 0, then the claim is true for all 1 ⩽ i < k. Suppose a > 0 and the claim
+is true for (a − 1, i) with 1 ⩽ i < min J .
+For i = 1, by using Lemma 3.3.4 with y0 = xa−1
+1
+f1(y), we get
+X(I,J )(xa
+1f1(y))2d0 ≡
+�
+2⩽t⩽k
+t̸=min J
+�
+(U,V)∈B(t,1)
+X(U,V)(xa−1
+1
+f1(xt−1y))2d0,
+(3.5)
+where B(t,1) is a set of some (U, V) ∈ B such that min U = 1. By the inductive
+hypothesis, [X(U,V)(xa−1
+1
+f1(xt−1y))2d0 ] ∈ [P1
+k(n)] for all (U, V) ∈ B(t,1) with 1 <
+t ̸= min J . Hence, the claim is true for (a, 1).
+Suppose i > 1 and the claim is true for all (a′, t), 1 ⩽ t < i, and for (a − 1, i).
+By applying Lemma 3.3.4 for y0 = xa−1
+i
+fi(y), we have
+X(I,J )(xa
+i fi(y))2d0 ≡
+�
+1⩽t<i
+�
+(U,V)∈B(t,i)
+X(U,V)(xtxa−1
+i
+fi(y))2d0
++
+�
+i<t⩽k
+t̸=min J
+�
+(U,V)∈B(t,i)
+X(U,V)(xa−1
+i
+fi(xt−1y))2d0 ,
+(3.6)
+where B(t,i) is a set of some (U, V) ∈ B such that min U = t for t < i and min U = i
+for t > i. From the relation (3.6) and the inductive hypothesis, we see that our
+claim is true for (a, i). This completes the proof.
+□
+We now prove Theorem 3.3.3.
+
+THE SQUARING OPERATION AND THE HIT PROBLEM
+15
+Proof of Theorem 3.3.3. Denote by ⟨[B]⟩ the subspace of (QPk)n spanned by the
+set [B]. We prove that Ker(�
+Sq
+0)(k,n) ⊂ ⟨[B]⟩. By using Lemma 3.3.5, we need
+only to prove that [X(I,J )(fi(y∗))2d] ∈ ⟨[B]⟩ for all (I, J ) ∈ B with min I = i and
+y∗ ∈ (Pk−1)m0, where m0 = �k−2
+t=1 (2dt−d0 − 1) = βd0(n).
+Set j = min J , we have fi(y∗) = xb
+jf(i,j)(y) with b a non-negative integer and
+y ∈ (Pk−2)m0−b. We prove [X(I,J )(xb
+jf(i,j)(y))2d] ∈ ⟨[B]⟩ by double induction on
+(b, j).
+If b = 0, then y ∈ (Pk−2)m0. Since ωu(y) = k − 2 for 1 ⩽ u ⩽ d − d0, we
+get y = Y 2d−d0−1(˜y)2d−d0, with ˜y ∈ (Pk−2)m and Y = x1x2 . . . xk−2. Note that
+f(i,j)(Y ) = Xi,j, hence f(i,j)(y) = X2d−d0−1
+i,j
+(f(i,j)(˜y))2d−d0 . Since Bk−2(m) is a set
+of A-generators for (Pk−2)m, there are z1, z2, . . . , zr ∈ Bk−2(m) such that
+˜y ≡ z1 + z2 + . . . + zr +
+�
+t>0
+Sqt(ht),
+where ht are suitable polynomials in Pk−2. Set p = X(I,J )(Xi,j)2d−2d0. By using
+Proposition 2.1.4 and the Cartan formula, we have
+p(Sqt(f(i,j)(ht))2d = pSqt2d �
+(f(i,j)(ht))2d�
+= Sqt2d �
+p(f(i,j)(ht))2d�
++
+�
+1⩽ℓ⩽t
+Sqℓ2d(p)
+�
+Sqt−ℓ(f(i,j)(ht)
+�2d
+.
+(3.7)
+Suppose w is a monomial which appears as a term in the polynomial Sqℓ2d(p). By
+Proposition 2.1.5 we have ω(w) < ω(p) = (k−2)|d. Hence, using Theorem 2.2.2 and
+(3.7), we see that the polynomial p(Sqt(f(i,j)(ht))2d is hit. Since f(i,j) : Pk−2 → Pk
+is a homomorphism of A-algebras, we get
+�
+X(I,J )(f(i,j)(y))2d�
+=
+�
+1⩽u⩽r
+�
+X(I,J )(Xi,j)2d−2d0(f(i,j)(zu))2d�
+∈ ⟨[B]⟩.
+Hence, our claim is true for (0, j), i < j ⩽ k. We assume b > 0 and our claim holds
+for (b − 1, j) with i < j ⩽ k.
+For j = 2, we have i = 1. By applying Lemma 3.3.4 for y0 = xb−1
+2
+f(1,2)(y) we
+obtain
+X(I,J )(xb
+2f(1,2)(y))2d0 ≡
+�
+3⩽t⩽k
+�
+(U,V)∈Bt
+X(U,V)(xb−1
+2
+f(1,2)(xt−2y))2d0 ,
+where Bt is a set of some (U, V) ∈ B such that min V = 2. The last equality and
+the inductive hypothesis imply our claim for (b, 2).
+Suppose j > 2 and the claim holds for all (b′, t) with 1 ⩽ i < t < j and for
+(b − 1, j). By using Lemma 3.3.4 with y0 = xb−1
+j
+f(i,j)(y), we have
+X(I,J )(xb
+jf(i,j)(y))2d0 ≡
+�
+1⩽t<i
+�
+(U,V)∈B∗
+t
+X(U,V)(fi(xtxb−1
+j−1y))2d0
++
+�
+i<t<j
+�
+(U,V)∈B∗
+t
+X(U,V)(fi(xt−1xb−1
+j−1y))2d0
++
+�
+j<t⩽k
+�
+(U,V)∈B∗
+t
+X(U,V)(xb−1
+j
+f(i,j)(xt−2y))2d0 ,
+
+16
+NGUYỄN SUM
+where B∗
+t is a set of some (U, V) ∈ B such that min V = i for t < i, min V = t
+for i < t < j and min V = j for t > j. From the last equality and the inductive
+hypothesis, our claim is true for (b, j). The theorem is proved.
+□
+4. An application to the case k = 5
+In this section, we prove one of our main results, Theorem 1.2, that gives an
+affirmative answer to Conjecture 1.1 for k = 5. To do this, we explicitly determine
+the set B5((3)|d) of all the admissible monomials of weight vector (3)|d for d ⩾ 5. By
+combining this result and Theorem 3.3.3 one gets an upper bound for the dimension
+of the kernel of Kameko’s squaring operation in the degree n = 2d+t+u+2d+t+2d−3
+with d > 5 and t, u ⩾ 4. By using Theorem 4.1 below, we show that this upper
+bound is also a lower bound.
+Theorem 4.1 (See Walker and Wood [24, Proposition 24.5.1]). Let k ⩾ 3 and
+n = �k−2
+i=1 (2di − 1) with di positive integers. If di − di+1 ⩾ 4 for 1 ⩽ i ⩽ k − 3 and
+dk−2 ⩾ 5, then
+dim(QPk)n ⩾ (k − 1)
+�
+3⩽i⩽k
+(2i − 1).
+(4.1)
+From the results of Kameko [3, Theorem 8.1] and our work [19, Proposition 2.5.1]
+we see that if d ⩾ 4, then QP +
+3 ((3)|d) = ⟨[(x1x2x3)2d−1](3)|d⟩ and QP +
+4 ((3)|d) =
+⟨{[wd,u](3)|d : 1 ⩽ u ⩽ 11}⟩, where wd,u are determined as in Section 5.
+By applying Proposition 2.2.5, we get dim QP 0
+5 ((3)|d) =
+�5
+3
+�
++ 11
+�5
+4
+�
+= 65. So,
+we need only to determine QP +
+5 ((3)|d).
+Theorem 4.2. Let d be an integer. If d ⩾ 5, then QP +
+5 ((3)|d) is an F2-vector space
+of dimension 90 with a basis consisting the classes represented by the admissible
+monomials ad,t, 1 ⩽ t ⩽ 90, which are determined as in Section 5. Consequently,
+dim QP5((3)|d) = 155 for any d ⩾ 5.
+In [20, Proposition 1], we have proved that for any weight vector ω, QPk(ω) is
+an GLk-module. Hence, Theorem 4.2 gives a representation of dimension 155 of
+the general group GL5.
+The theorem is proved by induction on d. The proof is based on Proposition 3.2.4
+and suitable strongly inadmissible monomials of weight vector (3)|d with 2 ⩽ d ⩽ 5.
+Moreover, to prove the theorem for d = 5, we need to use suitable sets of generators
+for QP5((3)|d) with 1 ⩽ d ⩽ 4.
+4.1. Generating sets for QP5((3)|d) with d ⩽ 4.
+Proposition 4.1.1. We have
+i) B5((3)|1) = {Xα,β : 1 ⩽ α < β ⩽ 5}. Hence, dim QP5((3)|1) = 10.
+ii) B+
+5 ((3)|2) is the set of the monomials a2,t, 1 ⩽ t ⩽ 15, which are determine
+as follows:
+1. x1x2x2
+3x2
+4x3
+5
+2. x1x2x2
+3x3
+4x2
+5
+3. x1x2x3
+3x2
+4x2
+5
+4. x1x2
+2x3x2
+4x3
+5
+5. x1x2
+2x3x3
+4x2
+5
+6. x1x2
+2x2
+3x4x3
+5
+7. x1x2
+2x2
+3x3
+4x5
+8. x1x2
+2x3
+3x4x2
+5
+9. x1x2
+2x3
+3x2
+4x5
+10. x1x3
+2x3x2
+4x2
+5
+11. x1x3
+2x2
+3x4x2
+5
+12. x1x3
+2x2
+3x2
+4x5
+13. x3
+1x2x3x2
+4x2
+5
+14. x3
+1x2x2
+3x4x2
+5
+15. x3
+1x2x2
+3x2
+4x5.
+Consequently, dim QP5((3)|2) = 55.
+
+THE SQUARING OPERATION AND THE HIT PROBLEM
+17
+Lemma 4.1.2. Let i1, i2, j1, j2 ∈ Nk such that i1 < j1, i2 < j2.
+i) If either i1 > i2 or i1 = i2 and j1 > j2, then X2
+i1,j1Xi2,j2 is strictly inadmissi-
+ble.
+ii) If j1 > j2 and i, j ∈ Nk, i < j, then the monomial X4
+i1,j1X2
+i2,j2Xi,j is strictly
+inadmissible.
+iii) If either i1 < i2 ⩽ j1 or i1 = i2, j1 ̸= j2, then X4
+i1,j1X3
+i2,j2 is strictly inad-
+missible.
+iv) If either i1 < i2 or i1 = i2 and j1 ⩽ j2, then X8
+i1,j1X7
+i2,j2 is strictly inadmis-
+sible.
+Proof. For simplicity, we prove Part ii). The others can be proved by a similar
+computation.
+If i1 = i2 = i, then x = X2
+i1,j1Xi2,j2 = xj1x2
+j2X3
+i,j1,j2. We have
+x = x2
+j1xj2X3
+i,j1,j2 +
+�
+t̸=i,j1,j2
+xj1xj2x4
+tX3
+i,j1,j2,j + Sq1(xj1xj2X3
+i,j1,j2,j).
+This equality shows that x is strictly inadmissible. By Theorem 2.1.9, x2Xi,j is
+also strictly inadmissible.
+Suppose i1 < i2. Then x = xi1x2
+i2x2
+j2xj1X3
+i1,i2,j1,j2. We have
+xi1x2
+i2x2
+j2xj1 = xi1xi2x2
+j2x2
+j1 + xi1x2
+i2xj2x2
+j1
++ Sq1(x2
+i1xi2xj2xj1) + Sq2(xi1xi2xj2xj1).
+So, by using the Cartan formula, we get
+x = xi1xi2x2
+j2x2
+j1X3
+i1,i2,j1,j2 + xi1x2
+i2xj2x2
+j1X3
+i1,i2,j1,j2 + A + B + C,
+where
+A = x2
+i1xi2xj1xj2Sq1(X3
+i1,i2,j1,j2) + Sq1(xi1xi2xj1xj2)Sq1(X3
+i1,i2,j1,j2),
+B = xi1xi2xj1xj2Sq2(X3
+i1,i2,j1,j2),
+C = Sq1(x2
+i1xi2xj1xj2X3
+i1,i2,j1,j2) + Sq2(xi1xi2xj1xj2X3
+i1,i2,j1,j2).
+A simple computation shows that Xi,jA2 ∈ P −
+k ((k−2)|3), Xi,jB2 ∈ P −
+k ((k−2)|3)+
+A+
+1 P5 and Xi,jC2 ∈ P −
+k ((k − 2)|3) + A+
+3 P5. Hence, the monomial x2Xi,j is strictly
+inadmissible.
+□
+Proof of Proposition 4.1.1. For d = 1, if x ∈ P5((3)|1), then ω(x) = (3)|1 if and
+only if x = Xα,β with 1 ⩽ α < β ⩽ 5. Since Xα,β is admissible, we see that the
+first of Proposition 4.1.1 is true.
+From the results in Kameko [3, Theorem 8.1] and our work [19, Proposition 5.2.1],
+we have |B+
+3 ((3)|2)| = 1 and |B+
+4 ((3)|2)| = 6.
+Hence, by applying Proposition
+2.2.5, we get dim QP 0
+5 ((3)|2) =
+�5
+3
+�
++ 6
+�5
+4
+�
+= 40. So, we need only to determine
+QP +
+5 ((3)|2). We can check that if x ∈ P +
+5 ((3)|2) and x ̸= a2,t for all t, 1 ⩽ t ⩽ 15,
+then x = X2
+i1,j1Xi2,j2 with i1 > i2. By Lemma 4.1.2(i), x is inadmissible.
+We observe that for 1 ⩽ t ⩽ 15, a2,t = xifi(b2,t) with b2,t an admissible monomial
+of degree 8 in P4 and 1 ⩽ i ⩽ 5. By Proposition 2.1.11, a2,t is admissible. The
+proposition is proved.
+□
+Consider the case d = 3. From the results in Kameko [3, Theorem 8.1] and our
+work [19, Proposition 5.4.2], we have |B+
+3 ((3)|3)| = 1 and |B+
+4 ((3)|3)| = 10. So, by
+
+18
+NGUYỄN SUM
+using Proposition 2.2.5, we get dim QP 0
+5 ((3)|3) =
+�5
+3
+�
++ 10
+�5
+4
+�
+= 60. We need to
+compute QP +
+5 ((3)|3).
+We denote by A(3) the set of the monomials a3,t, 1 ⩽ t ⩽ 50, which are given in
+Section 5 for d = 3 and five monomials:
+a3,51 = x3
+1x3
+2x4
+3x4
+4x7
+5
+a3,52 = x3
+1x3
+2x4
+3x7
+4x4
+5
+a3,53 = x3
+1x3
+2x7
+3x4
+4x4
+5
+a3,54 = x3
+1x7
+2x3
+3x4
+4x4
+5
+a3,55 = x7
+1x3
+2x3
+3x4
+4x4
+5.
+Proposition 4.1.3. B+
+5 ((3)|3) ⊂ A(3) ∪ C(3), where C(3) is the set of the mono-
+mials a3,t, 56 ⩽ t ⩽ 70, which are determined as follows:
+56. x1x3
+2x5
+3x6
+4x6
+5
+57. x1x3
+2x6
+3x5
+4x6
+5
+58. x1x6
+2x3
+3x5
+4x6
+5
+59. x3
+1x2x5
+3x6
+4x6
+5
+60. x3
+1x2x6
+3x5
+4x6
+5
+61. x3
+1x5
+2x3x6
+4x6
+5
+62. x3
+1x5
+2x6
+3x4x6
+5
+63. x3
+1x5
+2x2
+3x5
+4x6
+5
+64. x3
+1x3
+2x4
+3x5
+4x6
+5
+65. x3
+1x3
+2x5
+3x4
+4x6
+5
+66. x3
+1x3
+2x5
+3x6
+4x4
+5
+67. x3
+1x4
+2x3
+3x5
+4x6
+5
+68. x3
+1x5
+2x3
+3x4
+4x6
+5
+69. x3
+1x5
+2x3
+3x6
+4x4
+5
+70. x3
+1x5
+2x6
+3x3
+4x4
+5.
+We prepare some lemmas for the proof of this proposition.
+Lemma 4.1.4. Let w is one of the monomials: x1x6
+2x6
+3x4, x1x2
+2x6
+3x5
+4, x1x6
+2x2
+3x5
+4,
+x1x6
+2x3
+3x4
+4, x3
+1x4
+2x3x6
+4, x3
+1x4
+2x5
+3x2
+4, x3
+1x5
+2x4
+3x2
+4, x3
+1x4
+2x3
+3x4
+4, x3
+1x4
+2x4
+3x3
+4. Then, the mono-
+mial x7
+i fi(w), 1 ⩽ i ⩽ 5, is strictly inadmissible.
+Proof. By using the Cartan formula, we have
+x1x6
+2x6
+3x4 = x1x5
+2x6
+3x2
+4 + x1x6
+2x5
+3x2
+4 + Sq1(x2
+1x5
+2x5
+3x4)
++ Sq2(x1x5
+2x5
+3x4) mod(P −
+4 ((2)|3)),
+x1x2
+2x6
+3x5
+4 = x1x2x6
+3x6
+4 + x1x2
+2x5
+3x6
+4 + Sq1(x2
+1x2x5
+3x5
+4)
++ Sq2(x1x2x5
+3x5
+4) mod(P −
+4 ((2)|3)),
+x1x6
+2x2
+3x5
+4 = x1x5
+2x2
+3x6
+4 + x1x6
+2x3x6
+4 + Sq1(x2
+1x5
+2x3x5
+4)
++ Sq2(x1x5
+2x3x5
+4) mod(P −
+4 ((2)|3)),
+x1x6
+2x3
+3x4
+4 = x1x3
+2x4
+3x6
+4 + x1x3
+2x6
+3x4
+4 + x1x4
+2x3
+3x6
+4 + x1x4
+2x6
+3x3
+4 + x1x6
+2x2
+3x5
+4
++ Sq1(x2
+1x5
+2x3
+3x3
+4 + x2
+1x3
+2x5
+3x3
+4 + x2
+1x3
+2x3
+3x5
+4) + Sq2(x1x5
+2x3
+3x3
+4
++ x1x3
+2x5
+3x3
+4 + x1x3
+2x3
+3x5
+4 + x1x6
+2x2
+3x3
+4) mod(P −
+4 ((2)|3)),
+x3
+1x4
+2x3x6
+4 = x2
+1x3
+2x4
+3x5
+4 + x2
+1x5
+2x4
+3x3
+4 + x3
+1x2
+2x4
+3x5
+4 + x3
+1x3
+2x4
+3x4
+4
++ Sq1(x3
+1x3
+2x4
+3x3
+4 + x3
+1x4
+2x3x5
+4) + Sq2(x2
+1x3
+2x4
+3x3
+4 + x5
+1x2
+2x2
+3x3
+4)
++ Sq4(x3
+1x2
+2x2
+3x3
+4) mod(P −
+4 ((2)|3)),
+x3
+1x4
+2x5
+3x2
+4 = x3
+1x2
+2x5
+3x4
+4 + x3
+1x4
+2x3
+3x4
+4
++ Sq2(x5
+1x2
+2x3
+3x2
+4) + Sq4(x3
+1x2
+2x3
+3x2
+4) mod(P −
+4 ((2)|3)),
+x3
+1x5
+2x4
+3x2
+4 = x3
+1x3
+2x4
+3x4
+4 + x3
+1x5
+2x2
+3x4
+4
++ Sq2(x5
+1x3
+2x2
+3x2
+4) + Sq4(x3
+1x3
+2x2
+3x2
+4) mod(P −
+4 ((2)|3)),
+x3
+1x4
+2x3
+3x4
+4 = x2
+1x3
+2x5
+3x4
+4 + x2
+1x5
+2x3
+3x4
+4 + x3
+1x3
+2x4
+3x4
+4
++ Sq1(x3
+1x3
+2x3
+3x4
+4) + Sq2(x2
+1x3
+2x3
+3x4
+4) mod(P −
+4 ((2)|3)),
+x3
+1x4
+2x4
+3x3
+4 = x2
+1x3
+2x4
+3x5
+4 + x2
+1x5
+2x4
+3x3
+4 + x3
+1x3
+2x4
+3x4
+4
++ Sq1(x3
+1x3
+2x4
+3x3
+4) + Sq2(x2
+1x3
+2x4
+3x3
+4) mod(P −
+4 ((2)|3)).
+
+THE SQUARING OPERATION AND THE HIT PROBLEM
+19
+From the above equalities we see that there is a positive integer r such that
+w = y1 + y2 + . . . + yr + Sq1(g1) + Sq2(g2) + Sq4(g3) mod(P −
+4 ((2)|3)),
+where yt are monomials of weight vector (2)|3 in P4, yt < w with 1 ⩽ t ⩽ r and
+g1, g2, g3 are suitable polynomials in P4. Using the Cartan formula and Lemma
+3.1.3 we get
+x7
+i fi(w) = x7
+i fi(y1) + x7
+i fi(y2) + . . . + x7
+i fi(yr) mod(P −
+5 ((3)|3) + A+
+3 P5).
+Since x7
+i fi(yt) < x7
+i fi(w) for 1 ⩽ t ⩽ r, the monomial x7
+i fi(w) is strictly inadmissi-
+ble. The lemma is proved.
+□
+Lemma 4.1.5.
+i) The following monomials are strictly inadmissible:
+x1x6
+2x3
+3x6
+4x5
+5
+x1x6
+2x6
+3x3
+4x5
+5
+x3
+1x5
+2x5
+3x2
+4x6
+5
+x3
+1x5
+2x5
+3x6
+4x2
+5
+x3
+1x5
+2x6
+3x5
+4x2
+5
+x3
+1x4
+2x5
+3x3
+4x6
+5
+x3
+1x4
+2x5
+3x6
+4x3
+5
+x3
+1x5
+2x4
+3x3
+4x6
+5
+x3
+1x5
+2x4
+3x6
+4x3
+5
+x3
+1x5
+2x6
+3x4
+4x3
+5.
+ii) The following monomials are strongly inadmissible:
+x1x3
+2x6
+3x6
+4x5
+5
+x3
+1x2x6
+3x6
+4x5
+5
+x3
+1x5
+2x6
+3x6
+4x5
+x3
+1x5
+2x2
+3x6
+4x5
+5
+x3
+1x5
+2x6
+3x2
+4x5
+5.
+Proof. Based on the Cartan formula we have
+x1x6
+2x3
+3x6
+4x5
+5 = x1x3
+2x5
+3x6
+4x6
+5 + x1x3
+2x6
+3x5
+4x6
+5 + x1x3
+2x6
+3x6
+4x5
+5 + x1x5
+2x3
+3x6
+4x6
+5
++ x1x6
+2x3
+3x5
+4x6
+5 + Sq1(x2
+1x3
+2x5
+3x5
+4x5
+5 + x2
+1x5
+2x3
+3x5
+4x5
+5)
++ Sq2(x1x3
+2x5
+3x5
+4x5
+5 + x1x5
+2x3
+3x5
+4x5
+5) mod(P −
+5 ((3)|3)),
+x1x6
+2x6
+3x3
+4x5
+5 = x1x3
+2x5
+3x6
+4x6
+5 + x1x3
+2x6
+3x5
+4x6
+5 + x1x3
+2x6
+3x6
+4x5
+5 + x1x5
+2x6
+3x3
+4x6
+5
++ x1x6
+2x5
+3x3
+4x6
+5 + Sq1(x2
+1x3
+2x5
+3x5
+4x5
+5 + x2
+1x5
+2x5
+3x3
+4x5
+5)
++ Sq2(x1x3
+2x5
+3x5
+4x5
+5 + x1x5
+2x5
+3x3
+4x5
+5) mod(P −
+5 ((3)|3)),
+x3
+1x5
+2x5
+3x2
+4x6
+5 = x3
+1x3
+2x5
+3x4
+4x6
+5 + x3
+1x5
+2x3
+3x4
+4x6
+5 + Sq1(x3
+1x3
+2x3
+3x4x10
+5 )
++ Sq2(x5
+1x3
+2x3
+3x2
+4x6
+5) + Sq4(x3
+1x3
+2x3
+3x2
+4x6
+5) mod(P −
+5 ((3)|3)),
+x3
+1x5
+2x5
+3x6
+4x2
+5 = x3
+1x3
+2x5
+3x6
+4x4
+5 + x3
+1x5
+2x3
+3x6
+4x4
+5 + Sq1(x3
+1x3
+2x3
+3x9
+4x2
+5)
++ Sq2(x5
+1x3
+2x3
+3x6
+4x2
+5) + Sq4(x3
+1x3
+2x3
+3x6
+4x2
+5) mod(P −
+5 ((3)|3)),
+x3
+1x5
+2x6
+3x5
+4x2
+5 = x3
+1x3
+2x6
+3x5
+4x4
+5 + x3
+1x5
+2x6
+3x3
+4x4
+5 + Sq1(x3
+1x3
+2x9
+3x3
+4x2
+5)
++ Sq2(x5
+1x3
+2x6
+3x3
+4x2
+5) + Sq4(x3
+1x3
+2x6
+3x3
+4x2
+5) mod(P −
+5 ((3)|3)),
+x3
+1x4
+2x5
+3x3
+4x6
+5 = x3
+1x2
+2x5
+3x5
+4x6
+5 + x3
+1x4
+2x3
+3x5
+4x6
+5 + Sq1(x3
+1x2x3
+3x3
+4x10
+5 )
++ Sq2(x5
+1x2
+2x3
+3x3
+4x6
+5) + Sq4(x3
+1x2
+2x3
+3x3
+4x6
+5) mod(P −
+5 ((3)|3)),
+x3
+1x4
+2x5
+3x6
+4x3
+5 = x3
+1x2
+2x5
+3x6
+4x5
+5 + x3
+1x4
+2x3
+3x6
+4x5
+5 + Sq1(x3
+1x2x3
+3x10
+4 x3
+5)
++ Sq2(x5
+1x2
+2x3
+3x6
+4x3
+5) + Sq4(x3
+1x2
+2x3
+3x6
+4x3
+5) mod(P −
+5 ((3)|3)),
+x3
+1x5
+2x4
+3x3
+4x6
+5 = x3
+1x3
+2x4
+3x5
+4x6
+5 + x3
+1x5
+2x2
+3x5
+4x6
+5 + Sq1(x3
+1x3
+2x3x3
+4x10
+5 )
++ Sq2(x5
+1x3
+2x2
+3x3
+4x6
+5) + Sq4(x3
+1x3
+2x2
+3x3
+4x6
+5) mod(P −
+5 ((3)|3)),
+x3
+1x5
+2x4
+3x6
+4x3
+5 = x3
+1x3
+2x4
+3x6
+4x5
+5 + x3
+1x5
+2x2
+3x6
+4x5
+5 + Sq1(x3
+1x3
+2x3x10
+4 x3
+5)
++ Sq2(x5
+1x3
+2x2
+3x6
+4x3
+5) + Sq4(x3
+1x3
+2x2
+3x6
+4x3
+5) mod(P −
+5 ((3)|3)),
+x3
+1x5
+2x6
+3x4
+4x3
+5 = x3
+1x3
+2x6
+3x4
+4x5
+5 + x3
+1x5
+2x6
+3x2
+4x5
+5 + Sq1(x3
+1x3
+2x9
+3x2
+4x3
+5)
+
+20
+NGUYỄN SUM
++ Sq2(x5
+1x3
+2x6
+3x2
+4x3
+5) + Sq4(x3
+1x3
+2x6
+3x2
+4x3
+5) mod(P −
+5 ((3)|3)).
+Part i) follows from the above equalities. We prove Part ii). For w = x1x3
+2x6
+3x6
+4x5
+5,
+we have
+w = x1x3
+2x5
+3x6
+4x6
+5 + x1x3
+2x6
+3x5
+4x6
+5 + x1x5
+2x5
+3x5
+4x5
+5
++ Sq1(x2
+1x3
+2x5
+3x5
+4x5
+5) + Sq2(x1x3
+2x5
+3x5
+4x5
+5) mod(P −
+5 ((3)|3)),
+where x1x3
+2x5
+3x6
+4x6
+5, x1x3
+2x6
+3x5
+4x6
+5 < w and x1x5
+2x5
+3x5
+4x5
+5 ∈ P(5,21). Hence, the mono-
+mial w is strongly inadmissible. By a similar computation we have
+x3
+1x2x6
+3x6
+4x5
+5 = x3
+1x2x5
+3x6
+4x6
+5 + x3
+1x2x6
+3x5
+4x6
+5 + x5
+1x2x5
+3x5
+4x5
+5
++ Sq1(x3
+1x2
+2x5
+3x5
+4x5
+5) + Sq2(x3
+1x2x5
+3x5
+4x5
+5) mod(P −
+5 ((3)|3)),
+x3
+1x5
+2x6
+3x6
+4x5 = x3
+1x5
+2x5
+3x6
+4x2
+5 + x3
+1x5
+2x6
+3x5
+4x2
+5 + x5
+1x5
+2x5
+3x5
+4x5
++ Sq1(x3
+1x6
+2x5
+3x5
+4x5) + Sq2(x3
+1x5
+2x5
+3x5
+4x5) mod(P −
+5 ((3)|3)),
+x3
+1x5
+2x2
+3x6
+4x5
+5 = x3
+1x5
+2x3x6
+4x6
+5 + x3
+1x5
+2x2
+3x5
+4x6
+5 + x5
+1x5
+2x3x5
+4x5
+5
++ Sq1(x3
+1x6
+2x3x5
+4x5
+5) + Sq2(x3
+1x5
+2x3x5
+4x5
+5) mod(P −
+5 ((3)|3)),
+x3
+1x5
+2x6
+3x2
+4x5
+5 = x3
+1x5
+2x5
+3x2
+4x6
+5 + x3
+1x5
+2x6
+3x4x6
+5 + x5
+1x5
+2x5
+3x4x5
+5
++ Sq1(x3
+1x6
+2x5
+3x4x5
+5) + Sq2(x3
+1x5
+2x5
+3x4x5
+5) mod(P −
+5 ((3)|3)).
+Since x5
+1x2x5
+3x5
+4x5
+5, x5
+1x5
+2x5
+3x5
+4x5, x5
+1x5
+2x3x5
+4x5
+5, x5
+1x5
+2x5
+3x4x5
+5 ∈ P(5,21), Part ii) follows
+from the above equalities. The lemma is completely proved.
+□
+Proof of Proposition 4.1.3. We can see that if x ∈ P +
+5 ((3)|3) and x ̸= a3,t for all
+t, 1 ⩽ t ⩽ 70, then either x is one of the monomials as given in Lemmas 4.1.4,
+4.1.5, or x is of the form X4
+i,jX2
+i1,j1Xi2,j2 with i1 > i2. Hence, by Lemma 4.1.2(i)
+and Theorem 2.1.9, x is inadmissible. The proposition is proved.
+□
+Consider the case d = 4. From the results in Kameko [3, Theorem 8.1] and
+our work [19, Propositon 5.4.2], we get |B+
+3 ((3)|4)| = 1 and |B+
+4 ((3)|4)| = 11. By
+Proposition 2.2.5, dim QP5((3)|4) =
+�5
+3
+�
++ 11
+�5
+4
+�
+= 65. We need to determine the
+set B+
+5 ((3)|4).
+Denote by A(4) the set of the monomials a4,t, 1 ⩽ t ⩽ 55, which are determined
+as in Section 5 for d = 4.
+Proposition 4.1.6. B+
+5 ((3)|4) ⊂ A(4) ∪ C(4), where C(4) is the set of the mono-
+mials a4,t, 56 ⩽ t ⩽ 89, which are determined as in Section 5 for d = 4, and the
+following monomials:
+a4,90 = x3
+1x7
+2x8
+3x13
+4 x14
+5
+a4,91 = x7
+1x3
+2x8
+3x13
+4 x14
+5
+a4,92 = x7
+1x7
+2x8
+3x9
+4x14
+5
+a4,93 = x7
+1x7
+2x9
+3x8
+4x14
+5
+a4,94 = x7
+1x7
+2x9
+3x10
+4 x12
+5 .
+We need the following lemma for the proof of this proposition.
+Lemma 4.1.7. If v is one of the monomials: x1x7
+2x10
+3 x12
+4 , x7
+1x2x10
+3 x12
+4 , x3
+1x3
+2x12
+3 x12
+4 ,
+x3
+1x5
+2x8
+3x14
+4 , x3
+1x5
+2x14
+3 x8
+4, x7
+1x7
+2x8
+3x8
+4, then the monomial x15
+i fi(x), 1 ⩽ i ⩽ 5, is strictly
+inadmissible.
+Proof. Based on the Cartan formula we have
+x1x7
+2x10
+3 x12
+4 = x1x4
+2x11
+3 x14
+4 + x1x6
+2x11
+3 x12
+4 + x1x7
+2x8
+3x14
+4
++ Sq1(x2
+1x7
+2x7
+3x13
+4 + x2
+1x7
+2x9
+3x11
+4 + x2
+1x9
+2x7
+3x11
+4 )
+
+THE SQUARING OPERATION AND THE HIT PROBLEM
+21
++ Sq2(x1x7
+2x7
+3x13
+4 + x1x7
+2x9
+3x11
+4 + x1x9
+2x7
+3x11
+4 )
++ Sq4(x1x4
+2x7
+3x14
+4 + x1x6
+2x7
+3x12
+4 ) mod(P −
+4 ((2)|4)),
+x7
+1x2x10
+3 x12
+4 = x4
+1x2x11
+3 x14
+4 + x6
+1x2x11
+3 x12
+4 + x7
+1x2x8
+3x14
+4
++ Sq1(x7
+1x2
+2x7
+3x13
+4 + x7
+1x2
+2x9
+3x11
+4 + x9
+1x2
+2x7
+3x11
+4 )
++ Sq2(x7
+1x2x7
+3x13
+4 + x7
+1x2x9
+3x11
+4 + x9
+1x2x7
+3x11
+4 )
++ Sq4(x4
+1x2x7
+3x14
+4 + x6
+1x2x7
+3x12
+4 ) mod(P −
+4 ((2)|4)),
+x3
+1x3
+2x12
+3 x12
+4 = x2
+1x3
+2x12
+3 x13
+4 + x2
+1x5
+2x12
+3 x11
+4 + x2
+1x8
+2x13
+3 x7
+4
++ Sq1(x3
+1x3
+2x12
+3 x11
+4 + x3
+1x8
+2x11
+3 x7
+4) + Sq2(x2
+1x3
+2x12
+3 x11
+4
++ x2
+1x8
+2x11
+3 x7
+4) + Sq4(x3
+1x4
+2x12
+3 x7
+4) mod(P −
+4 ((2)|4)),
+x3
+1x5
+2x8
+3x14
+4 = x2
+1x5
+2x9
+3x14
+4 + x3
+1x4
+2x9
+3x14
+4 + Sq1(x3
+1x3
+2x5
+3x18
+4
++ x3
+1x3
+2x9
+3x14
+4 ) + Sq2(x2
+1x3
+2x9
+3x14
+4 + x5
+1x3
+2x6
+3x14
+4 )
++ Sq4(x3
+1x3
+2x6
+3x14
+4 ) mod(P −
+4 ((2)|4)),
+x3
+1x5
+2x14
+3 x8
+4 = x2
+1x5
+2x14
+3 x9
+4 + x3
+1x4
+2x14
+3 x9
+4 + Sq1(x3
+1x3
+2x14
+3 x9
+4
++ x3
+1x3
+2x17
+3 x6
+4) + Sq2(x2
+1x3
+2x14
+3 x9
+4 + x5
+1x3
+2x14
+3 x6
+4)
++ Sq4(x3
+1x3
+2x14
+3 x6
+4) mod(P −
+4 ((2)|4)),
+x7
+1x7
+2x8
+3x8
+4 = x4
+1x7
+2x8
+3x11
+4 + x4
+1x11
+2 x8
+3x7
+4 + x5
+1x6
+2x8
+3x11
+4 + x5
+1x10
+2 x8
+3x7
+4
++ x7
+1x6
+2x8
+3x9
+4 + Sq1(x7
+1x7
+2x8
+3x7
+4) + Sq2(x7
+1x6
+2x8
+3x7
+4)
++ Sq4(x4
+1x7
+2x8
+3x7
+4 + x5
+1x6
+2x8
+3x7
+4) mod(P −
+4 ((2)|4)).
+From the above equalities we see that there is a positive integer s such that
+v = u1 + u2 + . . . + us + Sq1(h1) + Sq2(h2) + Sq4(h3) mod(P −
+4 ((2)|4)),
+where ut are monomials of weight vector (2)|4 in P4, ut < v with 1 ⩽ t ⩽ s and
+h1, h2, h3 are suitable polynomials in P4. Using the Cartan formula and Lemma
+3.1.3 we get
+x15
+i fi(v) = x15
+i fi(u1) + x15
+i fi(u2) + . . . + x15
+i fi(us) mod(P −
+5 ((3)|4) + A+
+4 P5).
+Since x15
+i fi(ut) < x15
+i fi(v) for 1 ⩽ t ⩽ s, the monomial x15
+i fi(v) is strictly inadmis-
+sible. The lemma is proved.
+□
+Lemma 4.1.8.
+i) The following monomials are strictly inadmissible:
+x3
+1x5
+2x9
+3x14
+4 x14
+5
+x3
+1x5
+2x14
+3 x9
+4x14
+5
+x3
+1x7
+2x11
+3 x12
+4 x12
+5
+x3
+1x7
+2x13
+3 x8
+4x14
+5
+x3
+1x7
+2x13
+3 x14
+4 x8
+5
+x3
+1x12
+2 x3
+3x13
+4 x14
+5
+x7
+1x3
+2x11
+3 x12
+4 x12
+5
+x7
+1x3
+2x13
+3 x8
+4x14
+5
+x7
+1x3
+2x13
+3 x14
+4 x8
+5
+x7
+1x7
+2x9
+3x14
+4 x8
+5
+x7
+1x9
+2x7
+3x10
+4 x12
+5
+x7
+1x11
+2 x3
+3x12
+4 x12
+5
+x7
+1x11
+2 x5
+3x8
+4x14
+5
+x7
+1x11
+2 x5
+3x14
+4 x8
+5
+x7
+1x11
+2 x13
+3 x6
+4x8
+5.
+ii) The following monomials are strongly inadmissible:
+x3
+1x5
+2x14
+3 x11
+4 x12
+5
+x3
+1x13
+2 x6
+3x11
+4 x12
+5
+x3
+1x13
+2 x7
+3x10
+4 x12
+5
+x3
+1x13
+2 x14
+3 x3
+4x12
+5 .
+Proof. By a direct computation using the Cartan formula, we have
+x3
+1x5
+2x9
+3x14
+4 x14
+5 = x2
+1x3
+2x13
+3 x13
+4 x14
+5 + x2
+1x5
+2x11
+3 x13
+4 x14
+5 + x3
+1x3
+2x12
+3 x13
+4 x14
+5
++ x3
+1x4
+2x11
+3 x13
+4 x14
+5 + Sq1(x3
+1x3
+2x7
+3x13
+4 x18
+5 + x3
+1x3
+2x7
+3x17
+4 x14
+5
+
+22
+NGUYỄN SUM
++ x3
+1x3
+2x11
+3 x13
+4 x14
+5 ) + Sq2(x2
+1x3
+2x11
+3 x13
+4 x14
+5 + x5
+1x3
+2x7
+3x14
+4 x14
+5 )
++ Sq4(x3
+1x3
+2x7
+3x14
+4 x14
+5 ) mod(P −
+5 ((3)|4)),
+x3
+1x5
+2x14
+3 x9
+4x14
+5 = x2
+1x3
+2x13
+3 x13
+4 x14
+5 + x2
+1x5
+2x13
+3 x11
+4 x14
+5 + x3
+1x3
+2x13
+3 x12
+4 x14
+5
++ x3
+1x4
+2x13
+3 x11
+4 x14
+5 + Sq1(x3
+1x3
+2x13
+3 x7
+4x18
+5 + x3
+1x3
+2x13
+3 x11
+4 x14
+5
++ x3
+1x3
+2x17
+3 x7
+4x14
+5 ) + Sq2(x2
+1x3
+2x13
+3 x11
+4 x14
+5 + x5
+1x3
+2x14
+3 x7
+4x14
+5 )
++ Sq4(x3
+1x3
+2x14
+3 x7
+4x14
+5 ) mod(P −
+5 ((3)|4)),
+x3
+1x7
+2x11
+3 x12
+4 x12
+5 = x2
+1x7
+2x11
+3 x12
+4 x13
+5 + x2
+1x7
+2x13
+3 x12
+4 x11
+5 + x3
+1x7
+2x12
+3 x10
+4 x13
+5
++ x3
+1x7
+2x10
+3 x12
+4 x13
+5 + Sq1(x3
+1x7
+2x11
+3 x12
+4 x12
+5 + x3
+1x11
+2 x9
+3x10
+4 x11
+5 )
++ Sq2(x2
+1x7
+2x11
+3 x12
+4 x11
+5 + x5
+1x7
+2x10
+3 x10
+4 x11
+5 )
++ Sq4(x3
+1x7
+2x10
+3 x10
+4 x11
+5 ) mod(P −
+5 ((3)|4)),
+x3
+1x7
+2x13
+3 x8
+4x14
+5 = x2
+1x7
+2x13
+3 x9
+4x14
+5 + x3
+1x5
+2x11
+3 x12
+4 x14
+5 + x3
+1x5
+2x13
+3 x10
+4 x14
+5
++ x3
+1x7
+2x9
+3x12
+4 x14
+5 + x3
+1x7
+2x12
+3 x9
+4x14
+5 + Sq1(x3
+1x7
+2x7
+3x5
+4x22
+5
++ x3
+1x7
+2x7
+3x9
+4x18
+5 + x3
+1x7
+2x11
+3 x5
+4x18
+5 + x3
+1x7
+2x11
+3 x9
+4x14
+5 )
++ Sq2(x2
+1x7
+2x7
+3x5
+4x22
+5 + x2
+1x7
+2x11
+3 x9
+4x14
+5 + x5
+1x7
+2x7
+3x6
+4x18
+5
++ x5
+1x7
+2x7
+3x10
+4 x14
+5 + x5
+1x7
+2x11
+3 x6
+4x14
+5 )
++ Sq4(x3
+1x5
+2x7
+3x12
+4 x14
+5 + x3
+1x5
+2x13
+3 x6
+4x14
+5 + x3
+1x11
+2 x7
+3x6
+4x14
+5 )
++ Sq8(x3
+1x7
+2x7
+3x6
+4x14
+5 ) mod(P −
+5 ((3)|4)),
+x3
+1x7
+2x13
+3 x14
+4 x8
+5 = x2
+1x7
+2x13
+3 x14
+4 x9
+5 + x3
+1x5
+2x11
+3 x14
+4 x12
+5 + x3
+1x5
+2x13
+3 x14
+4 x10
+5
++ x3
+1x7
+2x9
+3x14
+4 x12
+5 + x3
+1x7
+2x12
+3 x14
+4 x9
+5 + Sq1(x3
+1x7
+2x7
+3x17
+4 x10
+5
++ x3
+1x7
+2x7
+3x21
+4 x6
+5 + x3
+1x7
+2x11
+3 x14
+4 x9
+5 + x3
+1x7
+2x11
+3 x17
+4 x6
+5)
++ Sq2(x2
+1x7
+2x7
+3x21
+4 x6
+5 + x2
+1x7
+2x11
+3 x14
+4 x9
+5 + x5
+1x7
+2x7
+3x14
+4 x10
+5
++ x5
+1x7
+2x7
+3x18
+4 x6
+5 + x5
+1x7
+2x11
+3 x14
+4 x6
+5)
++ Sq4(x3
+1x5
+2x7
+3x14
+4 x12
+5 + x3
+1x5
+2x13
+3 x14
+4 x6
+5 + x3
+1x11
+2 x7
+3x14
+4 x6
+5)
++ Sq8(x3
+1x7
+2x7
+3x14
+4 x6
+5) mod(P −
+5 ((3)|4)),
+x3
+1x12
+2 x3
+3x13
+4 x14
+5 = x2
+1x11
+2 x5
+3x13
+4 x14
+5 + x2
+1x13
+2 x3
+3x13
+4 x14
+5 + x3
+1x9
+2x5
+3x14
+4 x14
+5
++ x3
+1x11
+2 x4
+3x13
+4 x14
+5 + Sq1(x3
+1x7
+2x3
+3x13
+4 x18
+5 + x3
+1x7
+2x3
+3x17
+4 x14
+5
++ x3
+1x11
+2 x3
+3x13
+4 x14
+5 ) + Sq2(x2
+1x11
+2 x3
+3x13
+4 x14
+5 + x5
+1x7
+2x3
+3x14
+4 x14
+5 )
++ Sq4(x3
+1x7
+2x3
+3x14
+4 x14
+5 ) mod(P −
+5 ((3)|4)),
+x7
+1x3
+2x11
+3 x12
+4 x12
+5 = x7
+1x2
+2x11
+3 x12
+4 x13
+5 + x7
+1x2
+2x13
+3 x12
+4 x11
+5 + x7
+1x3
+2x12
+3 x10
+4 x13
+5
++ x7
+1x3
+2x10
+3 x12
+4 x13
+5 + Sq1(x7
+1x3
+2x11
+3 x12
+4 x12
+5 + x11
+1 x3
+2x9
+3x10
+4 x11
+5 )
++ Sq2(x7
+1x2
+2x11
+3 x12
+4 x11
+5 + x7
+1x5
+2x10
+3 x10
+4 x11
+5 )
++ Sq4(x7
+1x3
+2x10
+3 x10
+4 x11
+5 ) mod(P −
+5 ((3)|4)),
+x7
+1x3
+2x13
+3 x8
+4x14
+5 = x5
+1x3
+2x11
+3 x12
+4 x14
+5 + x5
+1x3
+2x13
+3 x10
+4 x14
+5 + x7
+1x2
+2x13
+3 x9
+4x14
+5
++ x7
+1x3
+2x9
+3x12
+4 x14
+5 + x7
+1x3
+2x12
+3 x9
+4x14
+5 + Sq1(x7
+1x3
+2x7
+3x5
+4x22
+5
++ x7
+1x3
+2x7
+3x9
+4x18
+5 + x7
+1x3
+2x11
+3 x5
+4x18
+5 + x7
+1x3
+2x11
+3 x9
+4x14
+5 )
+
+THE SQUARING OPERATION AND THE HIT PROBLEM
+23
++ Sq2(x7
+1x2
+2x7
+3x5
+4x22
+5 + x7
+1x2
+2x11
+3 x9
+4x14
+5 + x7
+1x5
+2x7
+3x6
+4x18
+5
++ x7
+1x5
+2x7
+3x10
+4 x14
+5 + x7
+1x5
+2x11
+3 x6
+4x14
+5 ) + Sq4(x5
+1x3
+2x7
+3x12
+4 x14
+5
++ x5
+1x3
+2x13
+3 x6
+4x14
+5 + x11
+1 x3
+2x7
+3x6
+4x14
+5 )
++ Sq8(x7
+1x3
+2x7
+3x6
+4x14
+5 ) mod(P −
+5 ((3)|4)),
+x7
+1x3
+2x13
+3 x14
+4 x8
+5 = x7
+1x2
+2x13
+3 x14
+4 x9
+5 + x5
+1x3
+2x11
+3 x14
+4 x12
+5 + x5
+1x3
+2x13
+3 x14
+4 x10
+5
++ x7
+1x3
+2x9
+3x14
+4 x12
+5 + x7
+1x3
+2x12
+3 x14
+4 x9
+5 + Sq1(x7
+1x3
+2x7
+3x17
+4 x10
+5
++ x7
+1x3
+2x7
+3x21
+4 x6
+5 + x7
+1x3
+2x11
+3 x14
+4 x9
+5 + x7
+1x3
+2x11
+3 x17
+4 x6
+5)
++ Sq2(x7
+1x2
+2x7
+3x21
+4 x6
+5 + x7
+1x2
+2x11
+3 x14
+4 x9
+5 + x7
+1x5
+2x7
+3x14
+4 x10
+5
++ x7
+1x5
+2x7
+3x18
+4 x6
+5 + x7
+1x5
+2x11
+3 x14
+4 x6
+5) + Sq4(x5
+1x3
+2x7
+3x14
+4 x12
+5
++ x5
+1x3
+2x13
+3 x14
+4 x6
+5 + x11
+1 x3
+2x7
+3x14
+4 x6
+5)
++ Sq8(x7
+1x3
+2x7
+3x14
+4 x6
+5) mod(P −
+5 ((3)|4)),
+x7
+1x7
+2x9
+3x14
+4 x8
+5 = x4
+1x7
+2x12
+3 x11
+4 x11
+5 + x4
+1x11
+2 x12
+3 x7
+4x11
+5 + x5
+1x3
+2x12
+3 x11
+4 x14
+5
++ x5
+1x6
+2x12
+3 x11
+4 x11
+5 + x5
+1x7
+2x9
+3x14
+4 x10
+5 + x5
+1x7
+2x10
+3 x11
+4 x12
+5
++ x5
+1x7
+2x10
+3 x14
+4 x9
+5 + x5
+1x10
+2 x12
+3 x7
+4x11
+5 + x5
+1x11
+2 x6
+3x14
+4 x9
+5
++ x5
+1x11
+2 x9
+3x14
+4 x6
+5 + x5
+1x11
+2 x10
+3 x7
+4x12
+5 + x7
+1x3
+2x12
+3 x9
+4x14
+5
++ x7
+1x5
+2x9
+3x14
+4 x10
+5 + x7
+1x5
+2x10
+3 x11
+4 x12
+5 + x7
+1x6
+2x12
+3 x9
+4x11
+5
++ x7
+1x7
+2x8
+3x14
+4 x9
+5 + x7
+1x7
+2x9
+3x8
+4x14
+5 + x7
+1x7
+2x9
+3x10
+4 x12
+5
++ Sq1(x7
+1x5
+2x12
+3 x7
+4x13
+5 + x7
+1x7
+2x9
+3x8
+4x13
+5 + x7
+1x7
+2x9
+3x9
+4x12
+5
++ x7
+1x7
+2x12
+3 x7
+4x11
+5 + x7
+1x10
+2 x5
+3x13
+4 x9
+5) + Sq2(x7
+1x3
+2x5
+3x22
+4 x6
+5
++ x7
+1x3
+2x6
+3x7
+4x20
+5 + x7
+1x3
+2x12
+3 x7
+4x14
+5 + x7
+1x6
+2x12
+3 x7
+4x11
+5
++ x7
+1x7
+2x6
+3x14
+4 x9
+5 + x7
+1x7
+2x9
+3x14
+4 x6
+5 + x7
+1x7
+2x10
+3 x7
+4x12
+5
++ x7
+1x7
+2x10
+3 x8
+4x11
+5 + x7
+1x9
+2x5
+3x13
+4 x9
+5 + x7
+1x9
+2x6
+3x11
+4 x10
+5
++ x9
+1x9
+2x3
+3x13
+4 x9
+5) + Sq4(x4
+1x7
+2x12
+3 x7
+4x11
+5 + x5
+1x3
+2x12
+3 x7
+4x14
+5
++ x5
+1x6
+2x12
+3 x7
+4x11
+5 + x5
+1x7
+2x6
+3x14
+4 x9
+5 + x5
+1x7
+2x9
+3x14
+4 x6
+5
++ x5
+1x7
+2x10
+3 x7
+4x12
+5 + x11
+1 x5
+2x5
+3x14
+4 x6
+5 + x11
+1 x5
+2x6
+3x7
+4x12
+5 )
++ Sq8(x7
+1x5
+2x5
+3x14
+4 x6
+5 + x7
+1x5
+2x6
+3x7
+4x12
+5 ) mod(P −
+5 ((3)|4)),
+x7
+1x9
+2x7
+3x10
+4 x12
+5 = x4
+1x7
+2x11
+3 x11
+4 x12
+5 + x4
+1x11
+2 x7
+3x11
+4 x12
+5 + x5
+1x7
+2x11
+3 x10
+4 x12
+5
++ x5
+1x11
+2 x7
+3x10
+4 x12
+5 + x7
+1x7
+2x8
+3x11
+4 x12
+5 + x7
+1x7
+2x9
+3x10
+4 x12
+5
++ x7
+1x8
+2x7
+3x11
+4 x12
+5 + Sq1(x7
+1x7
+2x7
+3x11
+4 x12
+5 ) + Sq2(x7
+1x7
+2x7
+3x10
+4 x12
+5 )
++ Sq4(x4
+1x7
+2x7
+3x11
+4 x12
+5 + x5
+1x7
+2x7
+3x10
+4 x12
+5 ) mod(P −
+5 ((3)|4)),
+x7
+1x11
+2 x3
+3x12
+4 x12
+5 = x5
+1x7
+2x8
+3x11
+4 x14
+5 + x5
+1x11
+2 x8
+3x7
+4x14
+5 + x7
+1x9
+2x4
+3x11
+4 x14
+5
++ x7
+1x10
+2 x3x13
+4 x14
+5 + x7
+1x10
+2 x3
+3x12
+4 x13
+5 + x7
+1x10
+2 x5
+3x12
+4 x11
+5
++ x7
+1x11
+2 x3x12
+4 x14
+5 + x7
+1x11
+2 x2
+3x12
+4 x13
+5 + Sq1(x7
+1x7
+2x3x7
+4x22
+5
++ x7
+1x7
+2x3x11
+4 x18
+5 + x7
+1x7
+2x3x10
+4 x19
+5 + x7
+1x7
+2x3x18
+4 x11
+5
++ x7
+1x11
+2 x3x7
+4x18
+5 + x7
+1x11
+2 x3x11
+4 x14
+5 + x7
+1x11
+2 x3
+3x12
+4 x11
+5
+
+24
+NGUYỄN SUM
++ x7
+1x11
+2 x4
+3x9
+4x13
+5 ) + Sq2(x7
+1x7
+2x2
+3x13
+4 x14
+5 + x7
+1x10
+2 x3x11
+4 x14
+5
++ x7
+1x10
+2 x3
+3x12
+4 x11
+5 + x7
+1x13
+2 x2
+3x7
+4x14
+5 + x7
+1x13
+2 x2
+3x10
+4 x11
+5 )
++ Sq4(x5
+1x7
+2x4
+3x11
+4 x14
+5 + x5
+1x11
+2 x4
+3x7
+4x14
+5
++ x11
+1 x7
+2x2
+3x7
+4x14
+5 + x11
+1 x7
+2x2
+3x10
+4 x11
+5 )
++ Sq8(x7
+1x7
+2x2
+3x7
+4x14
+5 + x7
+1x7
+2x2
+3x10
+4 x11
+5 ) mod(P −
+5 ((3)|4)),
+x7
+1x11
+2 x5
+3x8
+4x14
+5 = x5
+1x7
+2x9
+3x10
+4 x14
+5 + x5
+1x11
+2 x9
+3x6
+4x14
+5 + x7
+1x9
+2x5
+3x10
+4 x14
+5
++ x7
+1x10
+2 x5
+3x9
+4x14
+5 + x7
+1x11
+2 x4
+3x9
+4x14
+5 + Sq1(x7
+1x7
+2x3
+3x5
+4x22
+5
++ x7
+1x7
+2x3
+3x9
+4x18
+5 + x7
+1x11
+2 x3
+3x5
+4x18
+5 + x7
+1x11
+2 x3
+3x9
+4x14
+5 )
++ Sq2(x7
+1x7
+2x2
+3x5
+4x22
+5 + x7
+1x7
+2x3
+3x12
+4 x14
+5 + x7
+1x10
+2 x3
+3x9
+4x14
+5
++ x7
+1x13
+2 x3
+3x6
+4x14
+5 ) + Sq4(x5
+1x7
+2x5
+3x10
+4 x14
+5 + x5
+1x11
+2 x5
+3x6
+4x14
+5
++ x11
+1 x7
+2x3
+3x6
+4x14
+5 ) + Sq8(x7
+1x7
+2x3
+3x6
+4x14
+5 ) mod(P −
+5 ((3)|4)),
+x7
+1x11
+2 x5
+3x14
+4 x8
+5 = x5
+1x7
+2x9
+3x14
+4 x10
+5 + x5
+1x11
+2 x9
+3x14
+4 x6
+5 + x7
+1x9
+2x5
+3x14
+4 x10
+5
++ x7
+1x10
+2 x5
+3x14
+4 x9
+5 + x7
+1x11
+2 x4
+3x14
+4 x9
+5 + Sq1(x7
+1x7
+2x3
+3x18
+4 x9
+5
++ x7
+1x7
+2x3
+3x22
+4 x5
+5 + x7
+1x11
+2 x3
+3x14
+4 x9
+5 + x7
+1x11
+2 x3
+3x18
+4 x5
+5)
++ Sq2(x7
+1x7
+2x2
+3x22
+4 x5
+5 + x7
+1x7
+2x3
+3x14
+4 x12
+5 + x7
+1x10
+2 x3
+3x14
+4 x9
+5
++ x7
+1x13
+2 x3
+3x14
+4 x6
+5) + Sq4(x5
+1x7
+2x5
+3x14
+4 x10
+5 + x5
+1x11
+2 x5
+3x14
+4 x6
+5
++ x11
+1 x7
+2x3
+3x14
+4 x6
+5) + Sq8(x7
+1x7
+2x3
+3x14
+4 x6
+5) mod(P −
+5 ((3)|4)),
+x7
+1x11
+2 x13
+3 x6
+4x8
+5 = x7
+1x7
+2x12
+3 x9
+4x10
+5 + x7
+1x7
+2x13
+3 x10
+4 x8
+5 + x7
+1x9
+2x13
+3 x6
+4x10
+5
++ x7
+1x9
+2x13
+3 x10
+4 x6
+5 + x7
+1x10
+2 x13
+3 x6
+4x9
+5 + x7
+1x10
+2 x13
+3 x9
+4x6
+5
++ x7
+1x11
+2 x12
+3 x6
+4x9
+5 + x7
+1x11
+2 x12
+3 x9
+4x6
+5 + x7
+1x11
+2 x13
+3 x4
+4x10
+5
++ Sq1(x7
+1x7
+2x11
+3 x9
+4x10
+5 + x7
+1x7
+2x19
+3 x5
+4x6
+5 + x7
+1x11
+2 x11
+3 x6
+4x9
+5
++ x7
+1x11
+2 x11
+3 x9
+4x6
+5) + Sq2(x7
+1x7
+2x11
+3 x6
+4x12
+5 + x7
+1x7
+2x11
+3 x12
+4 x6
+5
++ x7
+1x7
+2x18
+3 x5
+4x6
+5 + x7
+1x7
+2x19
+3 x4
+4x6
+5 + x7
+1x10
+2 x11
+3 x6
+4x9
+5
++ x7
+1x10
+2 x11
+3 x9
+4x6
+5 + x7
+1x13
+2 x11
+3 x6
+4x6
+5)
++ Sq4(x5
+1x7
+2x13
+3 x6
+4x10
+5 + x5
+1x7
+2x13
+3 x10
+4 x6
+5 + x5
+1x11
+2 x13
+3 x6
+4x6
+5
++ x11
+1 x7
+2x11
+3 x6
+4x6
+5 + x11
+1 x7
+2x13
+3 x4
+4x6
+5)
++ Sq8(x7
+1x7
+2x11
+3 x6
+4x6
+5 + x7
+1x7
+2x13
+3 x4
+4x6
+5) mod(P −
+5 ((3)|4)).
+Hence Part i) is proved. We now prove Part ii). We have
+x3
+1x5
+2x14
+3 x11
+4 x12
+5 = x2
+1x3
+2x13
+3 x14
+4 x13
+5 + x2
+1x5
+2x13
+3 x14
+4 x11
+5 + x3
+1x3
+2x13
+3 x14
+4 x12
+5
++ x3
+1x3
+2x14
+3 x13
+4 x12
+5 + x3
+1x4
+2x13
+3 x14
+4 x11
+5 + x3
+1x5
+2x13
+3 x14
+4 x10
+5
++ x5
+1x5
+2x13
+3 x13
+4 x9
+5 + Sq1(x3
+1x3
+2x13
+3 x14
+4 x11
+5 + x3
+1x3
+2x13
+3 x18
+4 x7
+5
++ x3
+1x3
+2x17
+3 x11
+4 x10
+5 + x3
+1x3
+2x17
+3 x14
+4 x7
+5 + x3
+1x6
+2x13
+3 x13
+4 x9
+5)
++ Sq2(x2
+1x3
+2x13
+3 x14
+4 x11
+5 + x3
+1x5
+2x13
+3 x13
+4 x9
+5
++ x5
+1x3
+2x14
+3 x11
+4 x10
+5 + x5
+1x3
+2x14
+3 x14
+4 x7
+5)
++ Sq4(x3
+1x3
+2x14
+3 x11
+4 x10
+5 + x3
+1x3
+2x14
+3 x14
+4 x7
+5) mod(P −
+5 ((3)|4)),
+
+THE SQUARING OPERATION AND THE HIT PROBLEM
+25
+where x5
+1x5
+2x13
+3 x13
+4 x9
+5 ∈ P(5,45). Hence, this equality shows that x3
+1x5
+2x14
+3 x11
+4 x12
+5
+is
+strongly inadmissible.
+x3
+1x13
+2 x6
+3x11
+4 x12
+5 = x3
+1x7
+2x8
+3x14
+4 x13
+5 + x3
+1x7
+2x12
+3 x14
+4 x9
+5 + x3
+1x9
+2x6
+3x14
+4 x13
+5
++ x3
+1x9
+2x12
+3 x14
+4 x7
+5 + x3
+1x11
+2 x6
+3x13
+4 x12
+5 + x3
+1x13
+2 x4
+3x14
+4 x11
+5
++ x3
+1x13
+2 x5
+3x14
+4 x10
+5 + x5
+1x13
+2 x5
+3x13
+4 x9
+5 + Sq1(x3
+1x7
+2x5
+3x18
+4 x11
+5
++ x3
+1x7
+2x9
+3x18
+4 x7
+5 + x3
+1x11
+2 x5
+3x18
+4 x7
+5 + x3
+1x11
+2 x9
+3x11
+4 x10
+5
++ x3
+1x14
+2 x5
+3x13
+4 x9
+5) + Sq2(x3
+1x13
+2 x5
+3x13
+4 x9
+5 + x5
+1x7
+2x6
+3x14
+4 x11
+5
++ x5
+1x7
+2x10
+3 x14
+4 x7
+5 + x5
+1x11
+2 x6
+3x11
+4 x10
+5 + x5
+1x11
+2 x6
+3x14
+4 x7
+5)
++ Sq4(x3
+1x7
+2x6
+3x14
+4 x11
+5 + x3
+1x7
+2x10
+3 x14
+4 x7
+5 + x3
+1x11
+2 x6
+3x11
+4 x10
+5
++ x3
+1x11
+2 x6
+3x14
+4 x7
+5 + x3
+1x13
+2 x4
+3x14
+4 x7
+5) mod(P −
+5 ((3)|4)).
+Since x5
+1x13
+2 x5
+3x13
+4 x9
+5 ∈ P(5,45), the monomial x3
+1x13
+2 x6
+3x11
+4 x12
+5 is strongly inadmissible.
+For w = x3
+1x13
+2 x7
+3x10
+4 x12
+5 , we have
+w = x2
+1x7
+2x13
+3 x10
+4 x13
+5 + x2
+1x7
+2x13
+3 x12
+4 x11
+5 + x2
+1x7
+2x14
+3 x9
+4x13
+5 + x2
+1x13
+2 x7
+3x9
+4x14
+5
++ x2
+1x13
+2 x7
+3x10
+4 x13
+5 + x2
+1x13
+2 x7
+3x12
+4 x11
+5 + x2
+1x13
+2 x9
+3x7
+4x14
+5 + x2
+1x13
+2 x10
+3 x7
+4x13
+5
++ x2
+1x13
+2 x12
+3 x7
+4x11
+5 + x3
+1x7
+2x8
+3x13
+4 x14
+5 + x3
+1x7
+2x10
+3 x13
+4 x12
+5 + x3
+1x7
+2x13
+3 x8
+4x14
+5
++ x3
+1x7
+2x14
+3 x9
+4x12
+5 + x3
+1x8
+2x7
+3x13
+4 x14
+5 + x3
+1x8
+2x13
+3 x7
+4x14
+5 + x3
+1x10
+2 x7
+3x13
+4 x12
+5
++ x3
+1x10
+2 x13
+3 x7
+4x12
+5 + x3
+1x13
+2 x4
+3x11
+4 x14
+5 + x3
+1x13
+2 x6
+3x11
+4 x12
+5 + x3
+1x13
+2 x7
+3x8
+4x14
+5 + g
++ Sq1(x3
+1x7
+2x7
+3x9
+4x18
+5 + x3
+1x7
+2x7
+3x14
+4 x13
+5 + x3
+1x7
+2x9
+3x7
+4x18
+5 + x3
+1x7
+2x9
+3x14
+4 x11
+5
++ x3
+1x7
+2x13
+3 x10
+4 x11
+5 + x3
+1x7
+2x14
+3 x7
+4x13
+5 + x3
+1x9
+2x7
+3x7
+4x18
+5 + x3
+1x9
+2x7
+3x14
+4 x11
+5
++ x3
+1x9
+2x14
+3 x7
+4x11
+5 + x3
+1x14
+2 x7
+3x7
+4x13
+5 + x3
+1x14
+2 x7
+3x9
+4x11
+5 + x3
+1x14
+2 x9
+3x7
+4x11
+5
++ x4
+1x7
+2x7
+3x13
+4 x13
+5 + x4
+1x7
+2x9
+3x13
+4 x11
+5 + x4
+1x7
+2x13
+3 x7
+4x13
+5 + x4
+1x7
+2x13
+3 x9
+4x11
+5
++ x4
+1x9
+2x7
+3x13
+4 x11
+5 + x4
+1x9
+2x13
+3 x7
+4x11
+5 ) + Sq2(x2
+1x7
+2x7
+3x14
+4 x13
+5 + x2
+1x7
+2x9
+3x14
+4 x11
+5
++ x2
+1x7
+2x13
+3 x10
+4 x11
+5 + x2
+1x7
+2x14
+3 x7
+4x13
+5 + x2
+1x9
+2x7
+3x14
+4 x11
+5 + x2
+1x9
+2x14
+3 x7
+4x11
+5
++ x2
+1x13
+2 x7
+3x7
+4x14
+5 + x2
+1x13
+2 x7
+3x10
+4 x11
+5 + x2
+1x13
+2 x10
+3 x7
+4x11
+5 + x5
+1x7
+2x7
+3x7
+4x17
+5
++ x5
+1x7
+2x7
+3x11
+4 x13
+5 + x5
+1x7
+2x9
+3x11
+4 x11
+5 + x5
+1x7
+2x11
+3 x7
+4x13
+5 + x5
+1x7
+2x11
+3 x9
+4x11
+5
++ x5
+1x9
+2x7
+3x11
+4 x11
+5 + x5
+1x9
+2x11
+3 x7
+4x11
+5 + x5
+1x11
+2 x7
+3x7
+4x13
+5 + x5
+1x11
+2 x7
+3x9
+4x11
+5
++ x5
+1x11
+2 x9
+3x7
+4x11
+5 ) + Sq4(x3
+1x7
+2x7
+3x7
+4x17
+5 + x3
+1x7
+2x7
+3x11
+4 x13
+5 + x3
+1x7
+2x9
+3x11
+4 x11
+5
++ x3
+1x7
+2x11
+3 x7
+4x13
+5 + x3
+1x7
+2x11
+3 x9
+4x11
+5 + x3
+1x9
+2x7
+3x11
+4 x11
+5 + x3
+1x9
+2x11
+3 x7
+4x11
+5
++ x3
+1x11
+2 x7
+3x7
+4x13
+5 + x3
+1x11
+2 x7
+3x9
+4x11
+5 + x3
+1x11
+2 x9
+3x7
+4x11
+5
++ x3
+1x13
+2 x4
+3x7
+4x14
+5 + x3
+1x13
+2 x6
+3x7
+4x12
+5 ) mod(P −
+5 ((3)|4)),
+where
+g = x3
+1x7
+2x9
+3x9
+4x17
+5 + x3
+1x9
+2x7
+3x9
+4x17
+5 + x3
+1x9
+2x9
+3x7
+4x17
+5
++ x3
+1x9
+2x9
+3x11
+4 x13
+5 + x3
+1x9
+2x11
+3 x9
+4x13
+5 + x3
+1x11
+2 x9
+3x9
+4x13
+5 ∈ P(5,45).
+Hence, w is strongly inadmissible.
+x3
+1x13
+2 x14
+3 x3
+4x12
+5 = x3
+1x7
+2x14
+3 x8
+4x13
+5 + x3
+1x7
+2x14
+3 x12
+4 x9
+5 + x3
+1x9
+2x14
+3 x6
+4x13
+5
+
+26
+NGUYỄN SUM
++ x3
+1x9
+2x14
+3 x12
+4 x7
+5 + x3
+1x11
+2 x14
+3 x4
+4x13
+5 + x3
+1x11
+2 x14
+3 x5
+4x12
+5
++ x3
+1x13
+2 x13
+3 x6
+4x10
+5 + x3
+1x13
+2 x14
+3 x2
+4x13
+5 + x5
+1x13
+2 x13
+3 x5
+4x9
+5
++ Sq1(x3
+1x7
+2x17
+3 x6
+4x11
+5 + x3
+1x7
+2x17
+3 x10
+4 x7
+5 + x3
+1x11
+2 x17
+3 x2
+4x11
+5
++ x3
+1x11
+2 x17
+3 x3
+4x10
+5 + x3
+1x11
+2 x17
+3 x6
+4x7
+5 + x3
+1x14
+2 x13
+3 x5
+4x9
+5)
++ Sq2(x3
+1x13
+2 x13
+3 x5
+4x9
+5 + x5
+1x7
+2x14
+3 x6
+4x11
+5 + x5
+1x7
+2x14
+3 x10
+4 x7
+5
++ x5
+1x11
+2 x14
+3 x2
+4x11
+5 + x5
+1x11
+2 x14
+3 x3
+4x10
+5 + x5
+1x11
+2 x14
+3 x6
+4x7
+5)
++ Sq4(x3
+1x7
+2x14
+3 x6
+4x11
+5 + x3
+1x7
+2x14
+3 x10
+4 x7
+5 + x3
+1x11
+2 x14
+3 x2
+4x11
+5
++ x3
+1x11
+2 x14
+3 x3
+4x10
+5 + x3
+1x11
+2 x14
+3 x6
+4x7
+5
++ x3
+1x13
+2 x14
+3 x4
+4x7
+5) mod(P −
+5 ((3)|4)).
+Since x5
+1x13
+2 x13
+3 x5
+4x9
+5 ∈ P(5,45), the monomial x3
+1x13
+2 x14
+3 x3
+4x12
+5 is strongly inadmissible.
+The lemma is completely proved.
+□
+Proof of Proposition 4.1.6. Let x ∈ P +
+5 ((3)|4) be an admissible monomial, then
+x = Xi,jy2 with 1 ⩽ i < j ⩽ k. Since x is admissible, by Theorem 2.1.9, y is
+admissible. We can see that if z ∈ A(3) ∪ C(3) such that Xi,jz2 ∈ P +
+5 ((3)|4) and
+Xi,jz2 ̸= a4,t for all t, 1 ⩽ t ⩽ 94, then either Xi,jz2 is one of the monomials
+as given in Lemmas 4.1.2(iv), 4.1.7, 4.1.8, or Xi,jz2 is of the form uv2r, where u
+is a monomial as given in one of Lemmas 4.1.2, 4.1.4, 4.1.5 and r is a suitable
+positive integer. Hence, by Propositions 3.2.3 and 3.2.4, Xi,jz2 is inadmissible.
+Since x = Xi,jy2 and y is admissible, we have x = a4,t for some t, 1 ⩽ t ⩽ 94.
+Hence, B+
+5 ((3)|4) ⊂ A(4) ∪ C(4). The proposition follows.
+□
+4.2. Proofs of Theorems 4.2 and 1.2.
+By a similar computation as given in the previous lemmas, one get the following.
+Lemma 4.2.1.
+i) The following monomials are strictly inadmissible:
+x3
+1x7
+2x24
+3 x29
+4 x30
+5
+x7
+1x3
+2x24
+3 x29
+4 x30
+5
+x7
+1x7
+2x25
+3 x26
+4 x28
+5
+x15
+1 x15
+2 x17
+3 x18
+4 x28
+5 .
+ii) The following monomials are strongly inadmissible:
+x3
+1x15
+2 x21
+3 x26
+4 x28
+5
+x15
+1 x3
+2x21
+3 x26
+4 x28
+5 .
+Proof. By using the Cartan formula, we obtain
+x3
+1x7
+2x24
+3 x29
+4 x30
+5 = x2
+1x7
+2x25
+3 x29
+4 x30
+5 + x2
+1x9
+2x23
+3 x29
+4 x30
+5 + x3
+1x4
+2x27
+3 x29
+4 x30
+5
++ x3
+1x5
+2x25
+3 x30
+4 x30
+5 + Sq1(x3
+1x7
+2x15
+3 x29
+4 x38
+5 + x3
+1x7
+2x15
+3 x33
+4 x34
+5
++ x3
+1x7
+2x15
+3 x37
+4 x30
+5 + x3
+1x7
+2x19
+3 x29
+4 x34
+5 + x3
+1x7
+2x19
+3 x33
+4 x30
+5
++ x3
+1x7
+2x23
+3 x29
+4 x30
+5 ) + Sq2(x2
+1x7
+2x15
+3 x29
+4 x38
+5 + x2
+1x7
+2x15
+3 x37
+4 x30
+5
++ x2
+1x7
+2x23
+3 x29
+4 x30
+5 + x5
+1x7
+2x15
+3 x30
+4 x34
+5 + x5
+1x7
+2x15
+3 x34
+4 x30
+5
++ x5
+1x7
+2x19
+3 x30
+4 x30
+5 ) + Sq4(x3
+1x4
+2x23
+3 x29
+4 x30
+5 + x3
+1x5
+2x21
+3 x30
+4 x30
+5
++ x3
+1x11
+2 x15
+3 x30
+4 x30
+5 ) + Sq8(x3
+1x7
+2x15
+3 x30
+4 x30
+5 ) mod(P −
+5 ((3)|5)),
+x7
+1x3
+2x24
+3 x29
+4 x30
+5 = x4
+1x3
+2x27
+3 x29
+4 x30
+5 + x5
+1x2
+2x27
+3 x29
+4 x30
+5 + x5
+1x3
+2x25
+3 x30
+4 x30
+5
++ x7
+1x2
+2x25
+3 x29
+4 x30
+5 + Sq1(x7
+1x3
+2x15
+3 x29
+4 x38
+5 + x7
+1x3
+2x15
+3 x33
+4 x34
+5
+
+THE SQUARING OPERATION AND THE HIT PROBLEM
+27
++ x7
+1x3
+2x15
+3 x37
+4 x30
+5 + x7
+1x3
+2x19
+3 x29
+4 x34
+5 + x7
+1x3
+2x19
+3 x33
+4 x30
+5
++ x7
+1x3
+2x23
+3 x29
+4 x30
+5 ) + Sq2(x7
+1x2
+2x15
+3 x29
+4 x38
+5 + x7
+1x2
+2x15
+3 x37
+4 x30
+5
++ x7
+1x2
+2x23
+3 x29
+4 x30
+5 + x7
+1x5
+2x15
+3 x30
+4 x34
+5 + x7
+1x5
+2x15
+3 x34
+4 x30
+5
++ x7
+1x5
+2x19
+3 x30
+4 x30
+5 ) + Sq4(x4
+1x3
+2x23
+3 x29
+4 x30
+5 + x5
+1x2
+2x23
+3 x29
+4 x30
+5
++ x5
+1x3
+2x21
+3 x30
+4 x30
+5 + x11
+1 x3
+2x15
+3 x30
+4 x30
+5 )
++ Sq8(x7
+1x3
+2x15
+3 x30
+4 x30
+5 ) mod(P −
+5 ((3)|5)),
+x7
+1x7
+2x25
+3 x26
+4 x28
+5 = x4
+1x7
+2x28
+3 x27
+4 x27
+5 + x4
+1x11
+2 x28
+3 x23
+4 x27
+5 + x5
+1x3
+2x27
+3 x30
+4 x28
+5
++ x5
+1x3
+2x28
+3 x27
+4 x30
+5 + x5
+1x6
+2x28
+3 x27
+4 x27
+5 + x5
+1x10
+2 x28
+3 x23
+4 x27
+5
++ x5
+1x11
+2 x19
+3 x30
+4 x28
+5 + x5
+1x11
+2 x22
+3 x27
+4 x28
+5 + x5
+1x11
+2 x26
+3 x23
+4 x28
+5
++ x7
+1x3
+2x25
+3 x30
+4 x28
+5 + x7
+1x3
+2x28
+3 x25
+4 x30
+5 + x7
+1x5
+2x26
+3 x27
+4 x28
+5
++ x7
+1x6
+2x28
+3 x25
+4 x27
+5 + x7
+1x7
+2x24
+3 x27
+4 x28
+5 + x7
+1x7
+2x25
+3 x24
+4 x30
+5
++ Sq1(x7
+1x5
+2x28
+3 x23
+4 x29
+5 + x7
+1x7
+2x21
+3 x29
+4 x28
+5 + x7
+1x7
+2x25
+3 x24
+4 x29
+5
++ x7
+1x7
+2x25
+3 x25
+4 x28
+5 + x7
+1x7
+2x28
+3 x23
+4 x27
+5 ) + Sq2(x7
+1x3
+2x22
+3 x23
+4 x36
+5
++ x7
+1x3
+2x23
+3 x30
+4 x28
+5 + x7
+1x3
+2x28
+3 x23
+4 x30
+5 + x7
+1x6
+2x28
+3 x23
+4 x27
+5
++ x7
+1x7
+2x19
+3 x30
+4 x28
+5 + x7
+1x7
+2x22
+3 x27
+4 x28
+5 + x7
+1x7
+2x26
+3 x23
+4 x28
+5
++ x7
+1x7
+2x26
+3 x24
+4 x27
+5 ) + Sq4(x4
+1x7
+2x28
+3 x23
+4 x27
+5 + x5
+1x3
+2x23
+3 x30
+4 x28
+5
++ x5
+1x3
+2x28
+3 x23
+4 x30
+5 + x5
+1x6
+2x28
+3 x23
+4 x27
+5 + x5
+1x7
+2x19
+3 x30
+4 x28
+5
++ x5
+1x7
+2x22
+3 x27
+4 x28
+5 + x5
+1x7
+2x26
+3 x23
+4 x28
+5
++ x11
+1 x5
+2x22
+3 x23
+4 x28
+5 + x11
+1 x5
+2x25
+3 x30
+4 x28
+5 )
++ Sq8(x7
+1x5
+2x22
+3 x23
+4 x28
+5 + x7
+1x5
+2x25
+3 x30
+4 x28
+5 ) mod(P −
+5 ((3)|5)),
+x15
+1 x15
+2 x17
+3 x18
+4 x28
+5 = x8
+1x15
+2 x23
+3 x19
+4 x28
+5 + x8
+1x23
+2 x15
+3 x19
+4 x28
+5 + x9
+1x15
+2 x23
+3 x18
+4 x28
+5
++ x9
+1x23
+2 x15
+3 x18
+4 x28
+5 + x11
+1 x12
+2 x23
+3 x19
+4 x28
+5 + x11
+1 x13
+2 x23
+3 x18
+4 x28
+5
++ x11
+1 x20
+2 x15
+3 x19
+4 x28
+5 + x11
+1 x21
+2 x15
+3 x18
+4 x28
+5 + x15
+1 x12
+2 x19
+3 x19
+4 x28
+5
++ x15
+1 x13
+2 x19
+3 x18
+4 x28
+5 + x15
+1 x15
+2 x16
+3 x19
+4 x28
+5 + Sq1(x15
+1 x15
+2 x15
+3 x19
+4 x28
+5 )
++ Sq2(x15
+1 x15
+2 x15
+3 x18
+4 x28
+5 ) + Sq4(x15
+1 x12
+2 x15
+3 x19
+4 x28
+5
++ x15
+1 x13
+2 x15
+3 x18
+4 x28
+5 ) + Sq8(x8
+1x15
+2 x15
+3 x19
+4 x28
+5 + x9
+1x15
+2 x15
+3 x18
+4 x28
+5
++ x11
+1 x12
+2 x15
+3 x19
+4 x28
+5 + x11
+1 x13
+2 x15
+3 x18
+4 x28
+5 ) mod(P −
+5 ((3)|5)).
+Part i) follows from the above equalities.
+We prove Part ii). We have
+x3
+1x15
+2 x21
+3 x26
+4 x28
+5 = x2
+1x15
+2 x21
+3 x25
+4 x30
+5 + x2
+1x15
+2 x21
+3 x26
+4 x29
+5 + x2
+1x15
+2 x21
+3 x28
+4 x27
+5
++ x2
+1x21
+2 x15
+3 x25
+4 x30
+5 + x2
+1x21
+2 x15
+3 x26
+4 x29
+5 + x2
+1x21
+2 x15
+3 x28
+4 x27
+5
++ x3
+1x8
+2x23
+3 x29
+4 x30
+5 + x3
+1x10
+2 x23
+3 x29
+4 x28
+5 + x3
+1x13
+2 x23
+3 x24
+4 x30
+5
++ x3
+1x13
+2 x23
+3 x26
+4 x28
+5 + x3
+1x15
+2 x16
+3 x29
+4 x30
+5 + x3
+1x15
+2 x18
+3 x29
+4 x28
+5
++ x3
+1x15
+2 x21
+3 x24
+4 x30
+5 + g1 + Sq1(x3
+1x15
+2 x15
+3 x25
+4 x34
+5
++ x3
+1x15
+2 x15
+3 x30
+4 x29
+5 + x3
+1x15
+2 x17
+3 x23
+4 x34
+5 + x3
+1x15
+2 x17
+3 x30
+4 x27
+5
+
+28
+NGUYỄN SUM
++ x3
+1x15
+2 x22
+3 x23
+4 x29
+5 + x3
+1x15
+2 x22
+3 x25
+4 x27
+5 + x3
+1x17
+2 x15
+3 x23
+4 x34
+5
++ x3
+1x17
+2 x15
+3 x30
+4 x27
+5 + x3
+1x17
+2 x19
+3 x23
+4 x30
+5 + x3
+1x17
+2 x19
+3 x26
+4 x27
+5
++ x3
+1x19
+2 x17
+3 x23
+4 x30
+5 + x3
+1x19
+2 x17
+3 x26
+4 x27
+5 + x3
+1x22
+2 x15
+3 x23
+4 x29
+5
++ x3
+1x22
+2 x15
+3 x25
+4 x27
+5 + x4
+1x15
+2 x15
+3 x29
+4 x29
+5 + x4
+1x15
+2 x17
+3 x29
+4 x27
+5
++ x4
+1x17
+2 x15
+3 x29
+4 x27
+5 ) + Sq2(x5
+1x15
+2 x19
+3 x25
+4 x27
+5 + x5
+1x15
+2 x19
+3 x23
+4 x29
+5
++ x5
+1x15
+2 x15
+3 x27
+4 x29
+5 + x5
+1x15
+2 x15
+3 x23
+4 x33
+5 + x5
+1x17
+2 x15
+3 x27
+4 x27
+5
++ x5
+1x15
+2 x17
+3 x27
+4 x27
+5 + x5
+1x19
+2 x15
+3 x23
+4 x29
+5 + x5
+1x19
+2 x15
+3 x25
+4 x27
+5
++ x2
+1x15
+2 x17
+3 x30
+4 x27
+5 + x2
+1x15
+2 x21
+3 x26
+4 x27
+5 + x2
+1x17
+2 x15
+3 x30
+4 x27
+5
++ x2
+1x21
+2 x15
+3 x26
+4 x27
+5 + x2
+1x15
+2 x15
+3 x30
+4 x29
+5 + x2
+1x15
+2 x21
+3 x23
+4 x30
+5
++ x2
+1x21
+2 x15
+3 x23
+4 x30
+5 ) + Sq4(x3
+1x15
+2 x19
+3 x25
+4 x27
+5 + x3
+1x15
+2 x19
+3 x23
+4 x29
+5
++ x3
+1x15
+2 x15
+3 x27
+4 x29
+5 + x3
+1x15
+2 x15
+3 x23
+4 x33
+5 + x3
+1x17
+2 x15
+3 x27
+4 x27
+5
++ x3
+1x15
+2 x17
+3 x27
+4 x27
+5 + x3
+1x19
+2 x15
+3 x23
+4 x29
+5 + x3
+1x19
+2 x15
+3 x25
+4 x27
+5 )
++ Sq8(x3
+1x8
+2x15
+3 x29
+4 x30
+5 + x3
+1x10
+2 x15
+3 x29
+4 x28
+5 + x3
+1x13
+2 x15
+3 x24
+4 x30
+5
++ x3
+1x13
+2 x15
+3 x26
+4 x28
+5 ) mod(P −
+5 ((3)|5)),
+where
+g1 = x3
+1x17
+2 x19
+3 x27
+4 x27
+5 + x3
+1x19
+2 x17
+3 x27
+4 x27
+5 + x3
+1x15
+2 x17
+3 x25
+4 x33
+5 + x3
+1x17
+2 x15
+3 x25
+4 x33
+5
++ x3
+1x17
+2 x17
+3 x23
+4 x33
+5 + x3
+1x17
+2 x17
+3 x27
+4 x29
+5 + x3
+1x17
+2 x21
+3 x25
+4 x27
+5 + x3
+1x21
+2 x17
+3 x25
+4 x27
+5
++ x3
+1x17
+2 x21
+3 x23
+4 x29
+5 + x3
+1x21
+2 x17
+3 x23
+4 x29
+5 ∈ P(5,93).
+Hence, the monomial x3
+1x15
+2 x21
+3 x26
+4 x28
+5 is strongly inadmissible.
+By a similar computation, we get
+x15
+1 x3
+2x21
+3 x26
+4 x28
+5 = x8
+1x3
+2x23
+3 x29
+4 x30
+5 + x10
+1 x3
+2x23
+3 x29
+4 x28
+5 + x13
+1 x2
+2x23
+3 x25
+4 x30
+5
++ x13
+1 x2
+2x23
+3 x26
+4 x29
+5 + x13
+1 x2
+2x23
+3 x28
+4 x27
+5 + x13
+1 x3
+2x23
+3 x24
+4 x30
+5
++ x13
+1 x3
+2x23
+3 x26
+4 x28
+5 + x15
+1 x2
+2x21
+3 x25
+4 x30
+5 + x15
+1 x2
+2x21
+3 x26
+4 x29
+5
++ x15
+1 x2
+2x21
+3 x28
+4 x27
+5 + x15
+1 x3
+2x16
+3 x29
+4 x30
+5 + x15
+1 x3
+2x18
+3 x29
+4 x28
+5
++ x15
+1 x3
+2x21
+3 x24
+4 x30
+5 + g2 + Sq1(x15
+1 x3
+2x15
+3 x25
+4 x34
+5
++ x15
+1 x3
+2x15
+3 x30
+4 x29
+5 + x15
+1 x3
+2x17
+3 x23
+4 x34
+5 + x15
+1 x3
+2x17
+3 x30
+4 x27
+5
++ x15
+1 x3
+2x22
+3 x23
+4 x29
+5 + x15
+1 x3
+2x22
+3 x25
+4 x27
+5 + x15
+1 x4
+2x15
+3 x29
+4 x29
+5
++ x15
+1 x4
+2x17
+3 x29
+4 x27
+5 + x17
+1 x3
+2x15
+3 x23
+4 x34
+5 + x17
+1 x3
+2x15
+3 x30
+4 x27
+5
++ x17
+1 x3
+2x19
+3 x23
+4 x30
+5 + x17
+1 x3
+2x19
+3 x26
+4 x27
+5 + x17
+1 x4
+2x15
+3 x29
+4 x27
+5
++ x19
+1 x3
+2x17
+3 x23
+4 x30
+5 + x19
+1 x3
+2x17
+3 x26
+4 x27
+5 + x22
+1 x3
+2x15
+3 x23
+4 x29
+5
++ x22
+1 x3
+2x15
+3 x25
+4 x27
+5 ) + Sq2(x15
+1 x2
+2x15
+3 x30
+4 x29
+5 + x15
+1 x2
+2x17
+3 x30
+4 x27
+5
++ x15
+1 x2
+2x21
+3 x23
+4 x30
+5 + x15
+1 x2
+2x21
+3 x26
+4 x27
+5 + x15
+1 x5
+2x15
+3 x23
+4 x33
+5
++ x15
+1 x5
+2x15
+3 x27
+4 x29
+5 + x15
+1 x5
+2x17
+3 x27
+4 x27
+5 + x15
+1 x5
+2x19
+3 x23
+4 x29
+5
++ x15
+1 x5
+2x19
+3 x25
+4 x27
+5 + x17
+1 x2
+2x15
+3 x30
+4 x27
+5 + x17
+1 x5
+2x15
+3 x27
+4 x27
+5
++ x19
+1 x5
+2x15
+3 x23
+4 x29
+5 + x19
+1 x5
+2x15
+3 x25
+4 x27
+5 + x21
+1 x2
+2x15
+3 x23
+4 x30
+5
+
+THE SQUARING OPERATION AND THE HIT PROBLEM
+29
++ x21
+1 x2
+2x15
+3 x26
+4 x27
+5 ) + Sq4(x15
+1 x3
+2x15
+3 x23
+4 x33
+5 + x15
+1 x3
+2x15
+3 x27
+4 x29
+5
++ x15
+1 x3
+2x17
+3 x27
+4 x27
+5 + x15
+1 x3
+2x19
+3 x23
+4 x29
+5 + x15
+1 x3
+2x19
+3 x25
+4 x27
+5
++ x17
+1 x3
+2x15
+3 x27
+4 x27
+5 + x19
+1 x3
+2x15
+3 x23
+4 x29
+5 + x19
+1 x3
+2x15
+3 x25
+4 x27
+5 )
++ Sq8(x8
+1x3
+2x15
+3 x29
+4 x30
+5 + x10
+1 x3
+2x15
+3 x29
+4 x28
+5 + x13
+1 x2
+2x15
+3 x25
+4 x30
+5
++ x13
+1 x2
+2x15
+3 x26
+4 x29
+5 + x13
+1 x2
+2x15
+3 x28
+4 x27
+5 + x13
+1 x3
+2x15
+3 x24
+4 x30
+5
++ x13
+1 x3
+2x15
+3 x26
+4 x28
+5 ) mod(P −
+5 ((3)|5)),
+where
+g2 = x15
+1 x3
+2x17
+3 x25
+4 x33
+5 + x17
+1 x3
+2x15
+3 x25
+4 x33
+5 + x17
+1 x3
+2x17
+3 x23
+4 x33
+5 + x17
+1 x3
+2x17
+3 x27
+4 x29
+5
++ x17
+1 x3
+2x19
+3 x27
+4 x27
+5 + x17
+1 x3
+2x21
+3 x23
+4 x29
+5 + x17
+1 x3
+2x21
+3 x25
+4 x27
+5 + x19
+1 x3
+2x17
+3 x27
+4 x27
+5
++ x21
+1 x3
+2x17
+3 x23
+4 x29
+5 + x21
+1 x3
+2x17
+3 x25
+4 x27
+5 ∈ P(5,93).
+The above equalities show that the monomial x15
+1 x3
+2x21
+3 x26
+4 x28
+5
+is strongly inadmis-
+sible. The lemma is completely proved.
+□
+Proof of Theorem 4.2. Denote A(d) = {ad,t : 1 ⩽ t ⩽ 55} and C(d) = {ad,t : 56 ⩽
+t ⩽ 90}, where ad,t, 1 ⩽ t ⩽ 90, are determined as in Section 5. We prove that
+B+
+5 ((3)|d) ⊂ A(d) ∪ C(d) by induction on d ⩾ 5.
+Let x ∈ P +
+5 ((3)|d) be an admissible monomial. Then, ω(x) = (3)|d and x =
+Xi,jy2 with y a monomial in P5((3)|d−1) and 1 ⩽ i < j ⩽ 5. Since x is admissible,
+by Theorem 2.1.9, y is also admissible.
+Let d = 5 and z ∈ A(4) ∪ C(4) ∪ B0
+5((3)|4). Based on Theorem 2.1.9 we can
+check that if Xi,jz2 ∈ P +
+5 ((3)|5) and Xi,jz2 ̸= a5,t for all t, 1 ⩽ t ⩽ 90, then
+either Xi,jz2 is one of the monomials as given in Lemma 4.2.1, or Xi,jz2 is of
+the form uv2r, where u is a monomial as given in one of Lemmas 4.1.2, 4.1.4,
+4.1.5, 4.1.7, 4.1.8, v is a monomial in P5 and r is a suitable integer. Hence, by
+Proposition 3.2.4, Xi,jz2 is inadmissible. Since x = Xi,jy2 is admissible and y ∈
+B5((3)|4) ⊂ A(4)∪C(4)∪B0
+5((3)|4), we have x = a5,t for some t, 1 ⩽ t ⩽ 90. Hence,
+B+
+5 ((3)|5) ⊂ A(5) ∪ C(5).
+Suppose d > 5 and B+
+5 ((3)|d−1) ⊂ A(d − 1) ∪ C(d − 1). Let z ∈ A(d − 1) ∪
+C(d − 1) ∪ B0
+5((3)|d−1). It is not difficult to check that if Xi,jz2 ∈ P +
+5 ((3)|d) and
+Xi,jz2 ̸= ad,t for all t, 1 ⩽ t ⩽ 90, then Xi,jz2 is of the form uw2s, where u is
+a monomial as given in one of Lemmas 4.1.2, 4.1.4, 4.1.5, 4.1.7, 4.1.8, 4.2.1, w
+is a monomial in P5 and s is a suitable integer. By Proposition 3.2.4, Xi,jz2 is
+inadmissible. Since x = Xi,jy2 and y is admissible, we have x = ad,t for some
+t, 1 ⩽ t ⩽ 90. That means B+
+5 ((3)|d) ⊂ A(d) ∪ C(d).
+Now we prove that the set [A(d)∪C(d)](3)|d is linearly independent in QP5((3)|d).
+Consider ⟨[A(d)](3)|d⟩ ⊂ QP5((3)|d) and ⟨[C(d)](3)|d⟩ ⊂ QP5((3)|d). It is easy to see
+that for 1 ⩽ t ⩽ 55, ad,t = x2d−1
+i
+fi(bd,t) with bd,t an admissible monomial of degree
+2(2d−1) in P4 and 1 ⩽ i ⩽ 5. By Proposition 2.1.11, ad,t is admissible. This implies
+dim⟨[A(d)](3)|d⟩ = 55. Since ν(ad,t) = 2d − 1 for 1 ⩽ t ⩽ 55 and ν(ad,t) < 2d − 1
+for 56 ⩽ t ⩽ 90, we obtain ⟨[A(d)](3)|d⟩ ∩ ⟨[C(d)](3)|d⟩ = {0}. Hence, we need only
+to prove the set [C(d)](3)|d is linearly independent in QP5((3)|d). Suppose there is
+a linear relation
+S :=
+�
+56⩽t⩽90
+γtad,t ≡(3)|d 0,
+(4.2)
+
+30
+NGUYỄN SUM
+where γt ∈ F2. We denote γJ = �
+t∈J γt for any J ⊂ {t ∈ N : 56 ⩽ t ⩽ 90}.
+Let wd,u, 1 ⩽ u ⩽ 11, be as in Section 5 and the homomorphism p(i;I) : P5 → P4
+which is defined by (2.3) for k = 5. From our work [9, Lemma 3.5], we see that
+p(i;I) passes to a homomorphism from QP5((3)|d) to QP4((3)|d). By applying p(i;j),
+1 ⩽ i < j ⩽ 5, to (4.2), we obtain
+p(1;2)(S) ≡(3)|d γ{58,68}wd,7 + γ62wd,10 ≡(3)|d 0,
+p(1;3)(S) ≡(3)|d γ{57,65}wd,6 + γ59wd,7 ≡(3)|d 0,
+p(1;4)(S) ≡(3)|d γ{56,61,66,70,72,77}wd,5 + γ60wd,7 ≡(3)|d 0,
+p(1;5)(S) ≡(3)|d γ{56,57,58,59,60,62,67,71,73,74,78}wd,4 + γ61wd,7 ≡(3)|d 0,
+p(2;3)(S) ≡(3)|d γ{64,65,68,69,76}wd,6 + γ80wd,7 ≡(3)|d 0,
+p(2;4)(S) ≡(3)|d γ{63,66,82,83}wd,5 + γ81wd,7 ≡(3)|d 0,
+p(2;5)(S) ≡(3)|d γ{63,64,67,80,81,84,85}wd,4 + γ82wd,7 ≡(3)|d 0,
+p(3;4)(S) ≡(3)|d γ{75,76,77,79,87,88,89}wd,5 + γ86wd,7 ≡(3)|d 0,
+p(3;5)(S) ≡(3)|d γ{75,78,86}wd,4 + γ87wd,7 ≡(3)|d 0,
+p(4;5)(S) ≡(3)|d γ79wd,4 + γ89wd,7 ≡(3)|d 0.
+From these equalities, we get γ59 = γ60 = γ61 = γ62 = γ79 = γ80 = γ81 = γ82 =
+γ86 = γ87 = γ89 = 0, γ65 = γ57, γ68 = γ58, γ78 = γ75. Then, by applying the
+homomorphism p(1;(u,v)), 2 ⩽ u < v ⩽ 4, to (4.2), we get
+p(1;(2,3))(S) ≡(3)|d γ64wd,6 + γ69wd,7 + γ76wd,10 ≡(3)|d 0,
+p(1;(2,4))(S) ≡(3)|d γ{56,58,63,66,70,71,72,77,83}wd,5 + γ70wd,7 + γ77wd,10 ≡(3)|d 0,
+p(1;(3,4))(S) ≡(3)|d γ{63,64,67,84,85}wd,3 + γ{56,57,66,69,70,72,73,75,76,77,83,88,90}wd,5
++ γ{66,74,83}wd,6 + γ72wd,7 ≡(3)|d 0.
+Computing from these above equalities gives γ64 = γ69 = γ70 = γ72 = γ76 = γ77 = 0
+and γ58 = γ57, γ66 = γ56, γ88 = γ75. Now, by applying p(1;(u,5)), 2 ⩽ u ⩽ 4, to
+(4.2), we obtain
+p(1;(2,5))(S) ≡(3)|d γ{56,57,63,67,71,73,74,75,84,85,90}wd,4 + γ71wd,7 + γ75wd,10 ≡(3)|d 0,
+p(1;(3,5))(S) ≡(3)|d γ{56,63,83}wd,2 + γ{56,57,67,71,73,74,84}wd,4
++ γ{67,74,84}wd,6 + γ73wd,7 ≡(3)|d 0,
+p(1;(4,5))(S) ≡(3)|d γ{67,71,73,74,85,90}wd,4 + γ{67,71,73,85,90}wd,5 + γ74wd,7 ≡(3)|d 0.
+By computing from the above equalities we get γt = 0 for all t, 56 ⩽ t ⩽ 90. The
+theorem is proved.
+□
+We need the following for the proof of Theorem 1.2.
+Proposition 4.2.2. The set
+B5 = {(I, J ) ∈ PSeq6
+5 : X(I,J ) ∈ B5((3)|6)} ⊂ PInc6
+5
+is compatible with (3)|6.
+Proof. Let (H, K) ∈ PSeq6
+5. We prove X(H,K) is of the form (3.2) for k = 5 and
+B = B5. We prove the claim by induction on X(H,K) with respect to the order
+as given in Definition 2.1.6. Obviously, this claim is true if X(H,K) is admissible.
+Suppose X(H,K) is inadmissible and the claim is true for all (U, V) ∈ PSeq6
+5 such
+
+THE SQUARING OPERATION AND THE HIT PROBLEM
+31
+that X(U,V) < X(H,K). From the proofs of Propositions 4.1.1, 4.1.3, 4.1.6 and the
+proof of Theorem 4.2 we see that X(H,K) = uw2cy2c+d, where u is a monomial of
+weight vector (3)|c, y is a monomial of weight vector (3)|e and w is a monomial of
+weight vector (3)|d as given in one of Lemmas 4.1.2, 4.1.4, 4.1.5, 4.1.7, 4.1.8, 4.2.1.
+Here c, e ⩾ 0, 2 ⩽ d ⩽ 5 and c + d + e = 6. Hence, there are (H1, K1) ∈ PSeqc
+5,
+(H2, K2) ∈ PSeqd
+5, (H3, K3) ∈ PSeqe
+5 such that u = X(H1,K1), w = X(H2,K2),
+y = X(H3,K3) and H = H1|H2|H3, K = K1|K2|K3. From the proofs of Lemmas
+4.1.2, 4.1.4, 4.1.5, 4.1.7, 4.1.8, 4.2.1 we see that
+w = X(H2,K2) =
+�
+(S,T )∈Bw
+X(S,T ) + g mod(P −
+5 ((3)|d) + A+
+d P5),
+where Bw is a set of suitable pairs (S, T ) ∈ PSeqd
+5 such that min S = min H2,
+min T ⩽ min K2, X(S,T ) < w and g ∈ P(5,nd) with nd = 3(2d − 1). Using the proof
+of Proposition 3.2.4 we obtain
+X(H,K) =
+�
+(S,T )∈Bw
+uX2c
+(S,T )y2c+d + ug2cy2c+d mod(P −
+5 ((3)|6) + A+
+6 P5),
+where ug2cy2c+d ∈ P(5,n6), uX2c
+(S,T )y2c+d = X(U,V) < X(H,K) with U = H1|S|H3,
+V = K1|T |K3. Since min S = min H2, min T ⩽ min K2, we have min U = min H,
+min V ⩽ min K. The proposition now follows from the inductive hypothesis.
+□
+Proof of Theorem 1.2. Let n = 2d+s+t + 2d+s + 2d − 3 and m = 2s+t + 2s − 2. We
+have n−5
+2
+= 2d−1+s+t + 2d−1+s + 2d−2 + 2d−2 − 4. By Theorems 1.3 and 1.4 in [19],
+if d ⩾ 6, s ⩾ 4 and t ⩾ 4, then
+dim(QP5) n−5
+2
+= (25 − 1) dim(QP4)2s+t+1+2s+1−2 = 3(23 − 1)(24 − 1)(25 − 1).
+Kameko’s squaring operation (�
+Sq
+0)(5,n) : (QP5)n −→ (QP5) n−5
+2
+is an epimorphism,
+hence by using Theorem 4.1, we get
+4(23 − 1)(24 − 1)(25 − 1) ⩽ dim(QP5)n = dim Ker(�
+Sq
+0)(5,n) + dim(QP5) n−5
+2
+= dim Ker(�
+Sq
+0)(5,n) + 3(23 − 1)(24 − 1)(25 − 1).
+This implies dim Ker(�
+Sq
+0)(5,n) ⩾ (23 − 1)(24 − 1)(25 − 1).
+By Proposition 4.2.2, the set B5 ⊂ PInc6
+5 is compatible with (3)|6 and |B5| =
+|B5((3)|6)| = 155. By applying Theorem 3.3.3, we obtain
+dim Ker(�
+Sq
+0)(5,n) ⩽ |B5| dim(QP3)m = 155 dim(QP3)m.
+From Kameko [3, Theorem 8.1], we have dim(QP3)m = 21 for any s, t ⩾ 2. Hence,
+we get
+dim Ker(�
+Sq
+0)(5,n) ⩽ 155 dim(QP3)m
+= 155 × 21 = (23 − 1)(24 − 1)(25 − 1).
+Thus, dim Ker(�
+Sq
+0)(5,n) = (23 − 1)(24 − 1)(25 − 1), for any d ⩾ 6 and s, t ⩾ 4. The
+theorem is proved.
+□
+Combining this result and Theorem 1.6 in [18] one gets the following, which is
+numbered as Corollary 1.3 in the introduction.
+
+32
+NGUYỄN SUM
+Corollary 4.2.3. Let n be as in Theorem 1.2. If d ⩾ 6 and s, t ⩾ 4, then
+dim(QP5)n = 4(23 − 1)(24 − 1)(25 − 1) = 13020.
+Consequently, the inequality (4.1) is an equality for k = 5 and d ⩾ 6.
+5. Appendix
+In this section, we list the admissible monomials of weight vector (3)d in Pk with
+k ⩽ 5.
+From the results of Kameko [3, Theorem 8.1] and our work [19, Proposition 5.4.2]
+we see that if d ⩾ 4, then B+
+3 ((3)|d) = {(x1x2x3)2d−1} and B+
+4 ((3)|d) = {wu =
+wd,u : 1 ⩽ u ⩽ 11}, where
+w1 = x1x2d−2
+2
+x2d−1
+3
+x2d−1
+4
+w2 = x1x2d−1
+2
+x2d−2
+3
+x2d−1
+4
+w3 = x1x2d−1
+2
+x2d−1
+3
+x2d−2
+4
+w4 = x3
+1x2d−3
+2
+x2d−2
+3
+x2d−1
+4
+w5 = x3
+1x2d−3
+2
+x2d−1
+3
+x2d−2
+4
+w6 = x3
+1x2d−1
+2
+x2d−3
+3
+x2d−2
+4
+w7 = x7
+1x2d−5
+2
+x2d−3
+3
+x2d−2
+4
+w8 = x2d−1
+1
+x2x2d−2
+3
+x2d−1
+4
+w9 = x2d−1
+1
+x2x2d−1
+3
+x2d−2
+4
+w10 = x2d−1
+1
+x3
+2x2d−3
+3
+x2d−2
+4
+w11 = x2d−1
+1
+x2d−1
+2
+x3x2d−2
+4
+The sets B4((3)|d) and B0
+5((3)|d) are determined by using Proposition 2.2.5.
+For any d ⩾ 5, B+
+5 ((3)|d) = {at = ad,t : 1 ⩽ t ⩽ 90}, where
+a1 = x1x2x2d−2
+3
+x2d−2
+4
+x2d−1
+5
+a2 = x1x2x2d−2
+3
+x2d−1
+4
+x2d−2
+5
+a3 = x1x2x2d−1
+3
+x2d−2
+4
+x2d−2
+5
+a4 = x1x2
+2x2d−4
+3
+x2d−1
+4
+x2d−1
+5
+a5 = x1x2
+2x2d−3
+3
+x2d−2
+4
+x2d−1
+5
+a6 = x1x2
+2x2d−3
+3
+x2d−1
+4
+x2d−2
+5
+a7 = x1x2
+2x2d−1
+3
+x2d−4
+4
+x2d−1
+5
+a8 = x1x2
+2x2d−1
+3
+x2d−3
+4
+x2d−2
+5
+a9 = x1x2
+2x2d−1
+3
+x2d−1
+4
+x2d−4
+5
+a10 = x1x3
+2x2d−4
+3
+x2d−2
+4
+x2d−1
+5
+a11 = x1x3
+2x2d−4
+3
+x2d−1
+4
+x2d−2
+5
+a12 = x1x3
+2x2d−2
+3
+x2d−4
+4
+x2d−1
+5
+a13 = x1x3
+2x2d−2
+3
+x2d−1
+4
+x2d−4
+5
+a14 = x1x3
+2x2d−1
+3
+x2d−4
+4
+x2d−2
+5
+a15 = x1x3
+2x2d−1
+3
+x2d−2
+4
+x2d−4
+5
+a16 = x1x2d−2
+2
+x3x2d−2
+4
+x2d−1
+5
+a17 = x1x2d−2
+2
+x3x2d−1
+4
+x2d−2
+5
+a18 = x1x2d−2
+2
+x2d−1
+3
+x4x2d−2
+5
+a19 = x1x2d−1
+2
+x3x2d−2
+4
+x2d−2
+5
+a20 = x1x2d−1
+2
+x2
+3x2d−4
+4
+x2d−1
+5
+a21 = x1x2d−1
+2
+x2
+3x2d−3
+4
+x2d−2
+5
+a22 = x1x2d−1
+2
+x2
+3x2d−1
+4
+x2d−4
+5
+a23 = x1x2d−1
+2
+x3
+3x2d−4
+4
+x2d−2
+5
+a24 = x1x2d−1
+2
+x3
+3x2d−2
+4
+x2d−4
+5
+a25 = x1x2d−1
+2
+x2d−2
+3
+x4x2d−2
+5
+a26 = x1x2d−1
+2
+x2d−1
+3
+x2
+4x2d−4
+5
+a27 = x3
+1x2x2d−4
+3
+x2d−2
+4
+x2d−1
+5
+a28 = x3
+1x2x2d−4
+3
+x2d−1
+4
+x2d−2
+5
+a29 = x3
+1x2x2d−2
+3
+x2d−4
+4
+x2d−1
+5
+a30 = x3
+1x2x2d−2
+3
+x2d−1
+4
+x2d−4
+5
+a31 = x3
+1x2x2d−1
+3
+x2d−4
+4
+x2d−2
+5
+a32 = x3
+1x2x2d−1
+3
+x2d−2
+4
+x2d−4
+5
+a33 = x3
+1x2d−3
+2
+x2
+3x2d−4
+4
+x2d−1
+5
+a34 = x3
+1x2d−3
+2
+x2
+3x2d−1
+4
+x2d−4
+5
+a35 = x3
+1x2d−3
+2
+x2d−1
+3
+x2
+4x2d−4
+5
+a36 = x3
+1x2d−1
+2
+x3x2d−4
+4
+x2d−2
+5
+a37 = x3
+1x2d−1
+2
+x3x2d−2
+4
+x2d−4
+5
+a38 = x3
+1x2d−1
+2
+x2d−3
+3
+x2
+4x2d−4
+5
+a39 = x2d−1
+1
+x2x3x2d−2
+4
+x2d−2
+5
+a40 = x2d−1
+1
+x2x2
+3x2d−4
+4
+x2d−1
+5
+a41 = x2d−1
+1
+x2x2
+3x2d−3
+4
+x2d−2
+5
+a42 = x2d−1
+1
+x2x2
+3x2d−1
+4
+x2d−4
+5
+a43 = x2d−1
+1
+x2x3
+3x2d−4
+4
+x2d−2
+5
+a44 = x2d−1
+1
+x2x3
+3x2d−2
+4
+x2d−4
+5
+
+THE SQUARING OPERATION AND THE HIT PROBLEM
+33
+a45 = x2d−1
+1
+x2x2d−2
+3
+x4x2d−2
+5
+a46 = x2d−1
+1
+x2x2d−1
+3
+x2
+4x2d−4
+5
+a47 = x2d−1
+1
+x3
+2x3x2d−4
+4
+x2d−2
+5
+a48 = x2d−1
+1
+x3
+2x3x2d−2
+4
+x2d−4
+5
+a49 = x2d−1
+1
+x3
+2x2d−3
+3
+x2
+4x2d−4
+5
+a50 = x2d−1
+1
+x2d−1
+2
+x3x2
+4x2d−4
+5
+a51 = x3
+1x5
+2x2d−6
+3
+x2d−4
+4
+x2d−1
+5
+a52 = x3
+1x5
+2x2d−6
+3
+x2d−1
+4
+x2d−4
+5
+a53 = x3
+1x5
+2x2d−1
+3
+x2d−6
+4
+x2d−4
+5
+a54 = x3
+1x2d−1
+2
+x5
+3x2d−6
+4
+x2d−4
+5
+a55 = x2d−1
+1
+x3
+2x5
+3x2d−6
+4
+x2d−4
+5
+a56 = x1x3
+2x2d−3
+3
+x2d−2
+4
+x2d−2
+5
+a57 = x1x3
+2x2d−2
+3
+x2d−3
+4
+x2d−2
+5
+a58 = x1x6
+2x2d−5
+3
+x2d−3
+4
+x2d−2
+5
+a59 = x1x7
+2x2d−6
+3
+x2d−3
+4
+x2d−2
+5
+a60 = x1x7
+2x2d−5
+3
+x2d−4
+4
+x2d−2
+5
+a61 = x1x7
+2x2d−5
+3
+x2d−2
+4
+x2d−4
+5
+a62 = x1x2d−2
+2
+x3
+3x2d−3
+4
+x2d−2
+5
+a63 = x3
+1x2x2d−3
+3
+x2d−2
+4
+x2d−2
+5
+a64 = x3
+1x2x2d−2
+3
+x2d−3
+4
+x2d−2
+5
+a65 = x3
+1x3
+2x2d−4
+3
+x2d−3
+4
+x2d−2
+5
+a66 = x3
+1x3
+2x2d−3
+3
+x2d−4
+4
+x2d−2
+5
+a67 = x3
+1x3
+2x2d−3
+3
+x2d−2
+4
+x2d−4
+5
+a68 = x3
+1x4
+2x2d−5
+3
+x2d−3
+4
+x2d−2
+5
+a69 = x3
+1x5
+2x2d−6
+3
+x2d−3
+4
+x2d−2
+5
+a70 = x3
+1x5
+2x2d−5
+3
+x2d−4
+4
+x2d−2
+5
+a71 = x3
+1x5
+2x2d−5
+3
+x2d−2
+4
+x2d−4
+5
+a72 = x3
+1x7
+2x2d−7
+3
+x2d−4
+4
+x2d−2
+5
+a73 = x3
+1x7
+2x2d−7
+3
+x2d−2
+4
+x2d−4
+5
+a74 = x3
+1x7
+2x2d−3
+3
+x2d−6
+4
+x2d−4
+5
+a75 = x3
+1x2d−3
+2
+x3x2d−2
+4
+x2d−2
+5
+a76 = x3
+1x2d−3
+2
+x2
+3x2d−3
+4
+x2d−2
+5
+a77 = x3
+1x2d−3
+2
+x3
+3x2d−4
+4
+x2d−2
+5
+a78 = x3
+1x2d−3
+2
+x3
+3x2d−2
+4
+x2d−4
+5
+a79 = x3
+1x2d−3
+2
+x2d−2
+3
+x4x2d−2
+5
+a80 = x7
+1x2x2d−6
+3
+x2d−3
+4
+x2d−2
+5
+a81 = x7
+1x2x2d−5
+3
+x2d−4
+4
+x2d−2
+5
+a82 = x7
+1x2x2d−5
+3
+x2d−2
+4
+x2d−4
+5
+a83 = x7
+1x3
+2x2d−7
+3
+x2d−4
+4
+x2d−2
+5
+a84 = x7
+1x3
+2x2d−7
+3
+x2d−2
+4
+x2d−4
+5
+a85 = x7
+1x3
+2x2d−3
+3
+x2d−6
+4
+x2d−4
+5
+a86 = x7
+1x2d−5
+2
+x3x2d−4
+4
+x2d−2
+5
+a87 = x7
+1x2d−5
+2
+x3x2d−2
+4
+x2d−4
+5
+a88 = x7
+1x2d−5
+2
+x5
+3x2d−6
+4
+x2d−4
+5
+a89 = x7
+1x2d−5
+2
+x2d−3
+3
+x2
+4x2d−4
+5
+a90 = x7
+1x11
+2 x2d−11
+3
+x2d−6
+4
+x2d−4
+5
+Acknowledgment
+The first version of this work was written while the author was visiting the
+Vietnam Institute for Advanced Study in Mathematics (VIASM). He would like to
+thank the VIASM for supporting the visit and hospitality.
+The author is very grateful to the referee for his valuable comments and sugges-
+tions which helped to improve the quality of the paper.
+References
+[1] D. P. Carlisle and R. M. W. Wood, The boundedness conjecture for the action of the Steen-
+rod algebra on polynomials, in: N. Ray and G. Walker (ed.), Adams Memorial Symposium
+on Algebraic Topology 2, (Manchester, 1990), in: London Math. Soc. Lecture Notes Ser.,
+Cambridge Univ. Press, Cambridge, vol. 176, 1992, pp. 203-216, MR1232207.
+[2] M. C. Crabb and J. R. Hubbuck, Representations of the homology of BV and the Steenrod
+algebra II, in: Algebraic Topology: New Trend in Localization and Periodicity, (Sant Feliu
+de Guíxols, 1994), in: Progr. Math., Birkh¨auser Verlag, Basel, Switzerland, vol. 136, 1996,
+pp. 143-154, MR1397726.
+[3] M. Kameko, Products of projective spaces as Steenrod modules, PhD Thesis, The Johns
+Hopkins University, ProQuest LLC, Ann Arbor, MI, 1990, 29 pp., MR2638633.
+[4] M. Kameko, Generators of the cohomology of BV4, Toyama University, Japan, Preprint,
+2003, 8 pp.
+[5] M. F. Mothebe and L. Uys, Some relations between admissible monomials for the polynomial
+algebra, Int. J. Math. Math. Sci. 2015, Art. ID 235806, 7 pp., MR3388909.
+
+34
+NGUYỄN SUM
+[6] T. N. Nam, A-générateurs génériques pour l’algèbre polynomiale, Adv. Math. 186 (2004)
+334-362, MR2073910.
+[7] F. P. Peterson, Generators of H∗(RP ∞ × RP ∞) as a module over the Steenrod algebra,
+Abstracts Amer. Math. Soc. No. 833 (1987) 55-89.
+[8] F. P. Peterson, A-generators for certain polynomial algebras, Math. Proc. Cambridge Philos.
+Soc. 105 (1989) 311–312, MR0974987.
+[9] Đ. V. Phúc and N. Sum, On the generators of the polynomial algebra as a module over the
+Steenrod algebra, C. R. Acad. Sci. Paris, Ser. I 353 (2015), 1035-1040, MR3419856.
+[10] S. Priddy, On characterizing summands in the classifying space of a group, I, Amer. Jour.
+Math. 112 (1990) 737-748, MR1073007.
+[11] J. Repka and P. Selick, On the subalgebra of H∗((RP ∞)n; F2) annihilated by Steenrod oper-
+ations, J. Pure Appl. Algebra 127 (1998) 273-288, MR1617199.
+[12] J. H. Silverman, Hit polynomials and the canonical anti-automorphism of the Steenrod alge-
+bra, Proc. Amer. Math. Soc. 123 (1995) 627-637, MR1254854.
+[13] J. H. Silverman, Hit polynomials and conjugation in the dual Steenrod algebra, Math. Proc.
+Cambridge Philos. Soc. 123 (1998) 531-547, MR1607993.
+[14] J. H. Silverman and W. M. Singer, On the action of Steenrod squares on polynomial algebras
+II, J. Pure Appl. Algebra 98 (1995) 95-103, MR1317001.
+[15] W. M. Singer, The transfer in homological algebra, Math. Zeit. 202 (1989) 493-523,
+MR1022818.
+[16] W. M. Singer, On the action of the Steenrod squares on polynomial algebras, Proc. Amer.
+Math. Soc. 111 (1991) 577-583, MR1045150.
+[17] N. E. Steenrod and D. B. A. Epstein, Cohomology operations, Ann. of Math. Stud. vol. 50,
+Princeton Univ. Press, Princeton, N.J 1962, MR0145525.
+[18] N. Sum, The negative answer to Kameko’s conjecture on the hit problem, Adv. Math. 225
+(2010) 2365-2390, MR2680169.
+[19] N. Sum, On the Peterson hit problem, Adv. Math. 274 (2015) 432-489, MR3318156.
+[20] N. Sum, The squaring operation and the Singer algebraic transfer, Vietnam J. Math. 49
+(2021), 1079-1096, MR4319539.
+[21] G. Walker and R. M. W. Wood, Weyl modules and the mod 2 Steenrod algebra, J. Algebra
+311 (2007) 840-858, MR2314738.
+[22] G. Walker and R. M. W. Wood, Flag modules and the hit problem for the Steenrod algebra,
+Math. Proc. Cambridge Philos. Soc. 147 (2009) 143-171, MR2507313.
+[23] G. Walker and R. M. W. Wood, Polynomials and the mod 2 Steenrod algebra, Vol. 1: The
+Peterson hit problem, London Mathematical Society Lecture Note Series 441, Cambridge
+University Press, 2018, MR3729477.
+[24] G. Walker and R. M. W. Wood, Polynomials and the mod 2 Steenrod algebra. Vol. 2. Repre-
+sentations of GL(n, F2), London Mathematical Society Lecture Note Series, 442. Cambridge
+University Press, 2018, MR3729478.
+[25] R. M. W. Wood, Steenrod squares of polynomials and the Peterson conjecture, Math. Proc.
+Cambridge Phil. Soc. 105 (1989) 307-309, MR0974986.
+[26] R. M. W. Wood, Problems in the Steenrod algebra, Bull. London Math. Soc. 30 (1998) 449-
+517, MR1643834.
+Department of Mathematics and Applications, Sài Gòn University, 273 An Dương
+Vương, District 5, Hồ Chí Minh city, Viet Nam
+Email address: nguyensum@sgu.edu.vn
+
diff --git a/MdAzT4oBgHgl3EQfkv0u/content/tmp_files/load_file.txt b/MdAzT4oBgHgl3EQfkv0u/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a14fafe2396f7e71d763ea6131619d358af7ede3
--- /dev/null
+++ b/MdAzT4oBgHgl3EQfkv0u/content/tmp_files/load_file.txt
@@ -0,0 +1,5439 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf,len=5438
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='01535v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='AT]  4 Jan 2023  THE SQUARING OPERATION AND THE HIT PROBLEM  FOR THE POLYNOMIAL ALGEBRA IN A TYPE  OF GENERIC DEGREE  NGUYỄN SUM  Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Let Pk be the graded polynomial algebra F2[x1, x2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' , xk] with  the degree of each generator xi being 1, where F2 denote the prime field of  two elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  The hit problem of Frank Peterson asks for a minimal generating set for  the polynomial algebra Pk as a module over the mod-2 Steenrod algebra A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Equivalently, we want to find a vector space basis for F2 ⊗A Pk in each degree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  In this paper, we study a generating set for the kernel of Kameko’s squaring  operation �  Sq  0  ∗ : F2 ⊗A Pk −→ F2 ⊗A Pk in a so-called generic degree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' By using  this result, we explicitly compute the hit problem for k = 5 in respective  generic degree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  (In memory of Professor Reginald Wood)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Introduction  Denote by Pk := F2[x1, x2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' , xk] the polynomial algebra over the field of two  elements, F2, in k generators x1, x2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' , xk, each of degree 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' This algebra arises as  the cohomology with coefficients in F2 of a classifying space of an elementary abelian  2-group Vk of rank k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Therefore, Pk is a module over the mod-2 Steenrod algebra, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  The action of A on Pk is determined by the elementary properties of the Steenrod  squares Sqi and subject to the Cartan formula Sqn(fg) = �n  i=0 Sqi(f)Sqn−i(g),  for f, g ∈ Pk (see Steenrod and Epstein [17]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  A polynomial f in Pk is called hit if it can be written as a finite sum f =  �  i>0 Sqi(hi) for suitable polynomials hi ∈ Pk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' That means f belongs to A+Pk,  where A+ denotes the augmentation ideal in A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  We study the Peterson hit problem of determining a minimal set of generators  for the polynomial algebra Pk as a module over the Steenrod algebra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Equivalently,  we want to find a vector space basis for the quotient  QPk := Pk/A+Pk = F2 ⊗A Pk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  The Peterson hit problem is an open problem in Algebraic Topology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' It was  first studied by Peterson [7], Priddy [10], Singer [15] and Wood [25], who showed  its relation to several classical problems respectively in cobordism theory, modular  representation theory of general linear groups, Adams spectral sequence for the  2010 Mathematics Subject Classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Primary 55S10;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Secondary 55S05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Key words and phrases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Steenrod algebra, Peterson hit problem, polynomial algebra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  The author was supported in part by the National Foundation for Science and Technology  Development (NAFOSTED) of Viet Nam under the grant number 101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='04-2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  1  2  NGUYỄN SUM  stable homotopy of spheres, and stable homotopy type of classifying spaces of finite  groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Then, this problem was studied by Carlisle and Wood [1], Crabb and Hub-  buck [2], Kameko [3, 4], Mothebe [5], Nam [6], Peterson [8], Repka and Selick [11],  Silverman [12], Silverman and Singer [14], Singer [16], Walker and Wood [21, 22],  Wood [26] and others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Let GLk be the general linear group over the field F2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Since Vk is an F2-vector  space of dimension k, this group acts naturally on Vk and therefore on the coho-  mology Pk of BVk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' The two actions of A and GLk upon Pk commute with each  other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Hence, there is an inherited action of GLk on QPk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  The vector space QPk was explicitly calculated by Peterson [7] for k = 1, 2, by  Kameko [3] for k = 3 and by Kameko [4] and the present author [19] for k = 4,  unknown in general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Recently, the hit problem and its applications to represen-  tations of general linear groups have been presented in the monographs of Walker  and Wood [23, 24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  For a positive integer n, by µ(n) one means the smallest number r for which it  is possible to write n = �  1⩽i⩽r(2ui − 1) with ui > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' By a simple computation,  we can see that µ(n) = s if and only if there exists a unique sequence of integers  d1 > d2 > .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' > ds−1 ⩾ ds > 0 such that  n = 2d1 + 2d2 + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' + 2ds−1 + 2ds − s =  �  1⩽i⩽s  (2di − 1),  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1)  (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  [20, Lemma 2] for a proof).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  From this it implies n − s is even and  µ( n−s  2 ) ⩽ s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Based on the results of Wood [25] and Kameko [3, Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2], the hit problem  is reduced to the case of degree n of the form (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1) with µ(n) = s < k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  The hit problem in the case of degree n of the form (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1) with s = k − 1, was  studied by Crabb and Hubbuck [2], Nam [6], Repka and Selick [11], Walker and  Wood [22] and the present author [18, 19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  For s = k − 2, in [18], we studied the kernel of Kameko’s squaring operation  �  Sq  0  ∗ : QPk → QPk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' This operation is induced by the F2-linear map ϕ : Pk → Pk,  given by  ϕ(x) =  �  y,  if x = x1x2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' xky2,  0,  otherwise,  for any monomial x ∈ Pk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Note that ϕ is a homomorphism of GLk-modules but  it is not an A-homomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' However, ϕSq2t = Sqtϕ and ϕSq2t+1 = 0 for any  non-negative integer t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' So, for each positive integer n such that n − k is even, ϕ  induced a homomorphism of GLk-modules:  (�  Sq  0  ∗)(k,n) := �  Sq  0  ∗ : (QPk)n → (QPk) n−k  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Here and in what follows, we denote by (Pk)n the subspace of Pk consisting of  the homogeneous polynomials of degree n in Pk and (QPk)n the subspace of QPk  consisting of all the classes represented by the elements in (Pk)n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Since (�  Sq  0  ∗)(k,n) is a homomorphism of GLk-modules, Ker(�  Sq  0  ∗)(k,n) gives a rep-  resentation of GLk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' We have gave a prediction for the dimension of Ker(�  Sq  0  ∗)(k,n)  in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  THE SQUARING OPERATION AND THE HIT PROBLEM  3  Conjecture 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 (See [18]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Let n = �k−2  i=1 (2di − 1) with di positive integers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' If  di−2 − di−1 > i for 3 ⩽ i ⩽ k − 1 and dk−2 > k ⩾ 3, then  dim Ker(�  Sq  0  ∗)(k,n) =  �  3⩽i⩽k  (2i − 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  This conjecture is true for k ⩽ 4 and unknown for k ⩾ 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  In [18, 19], we have studied the hit problem in case of the degree n with µ(n) =  s = k −1 by using the strictly inadmissible monomials and Singer’s criterion in [16]  on hit monomials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' However, these tools are not enough to study this problem in  the case of the degree n with µ(n) = s = k − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  In this paper, based on Silverman’s criterion in [13] on hit polynomials, we  introduce the notion of strongly inadmissible monomial to construct a generating  set for the kernel of Kameko’s squaring operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  One of our main results is  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 in Section 3 which provides the upper bound on the dimension of  Ker(�  Sq  0  ∗)(k,n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' By using this result, we verify Conjecture 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 for k = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' We prove  the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Let n = 2d+s+t + 2d+s + 2d − 3 with d, s, t non-negative integers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  If d ⩾ 6 and t, s ⩾ 4, then  dim Ker(�  Sq  0  ∗)(5,n) = (23 − 1)(24 − 1)(25 − 1) = 3255.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2)  Thus, Conjecture 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 is true for k = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Based on Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 and our result in  [19, Theoren 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4], one gets the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Corollary 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Let n be as in Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' If d ⩾ 6 and s, t ⩾ 4, then  dim(QP5)n = 4(23 − 1)(24 − 1)(25 − 1) = 13020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  We can see in Section 4 that using the notion of strongly inadmissible monomial  can overcome many difficulties encountered if using the notion of strictly inadmissi-  ble monomial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Thus, the notion of strongly inadmissible monomial can be a useful  tool in progressing the study of the Peterson hit problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  This paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' In Section 2, we recall some needed informa-  tion on the admissible monomials in Pk and criterions of Singer [16] and Silverman  [13] on hit monomials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' In Section 3, we present the results for a generating set  of the kernel of Kameko’s squaring operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' As an application of the results of  Section 3, in Section 4, we prove that Conjecture 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 is true for k = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Finally, in  Section 5 we list the needed admissible monomials of degree 3(2d − 1) in P5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Preliminaries  In this section, we recall some results from Kameko [3], Singer [16], Silverman [13]  and our work [19] which will be used in the next sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' The weight vector and the admissible monomials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Notation 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' In the paper, we use the following notations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Nk = {1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=', k},  XJ = Xj1,j2,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=',js =  �  j∈Nk\\J  xj,  J = {j1, j2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' , js} ⊂ Nk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  In particular, we have X∅ = x1x2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' xk, Xj = x1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' ˆxj .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' xk, 1 ⩽ j ⩽ k, XNk = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  4  NGUYỄN SUM  Denote by αi(a) the i-th coefficient in dyadic expansion of a non-negative integer  a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' That means  a = α0(a)20 + α1(a)21 + α2(a)22 + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' ,  for αi(a) = 0 or 1 and i ⩾ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Denote by α(a) the number of 1’s in dyadic expansion  of a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Let x = xa1  1 xa2  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' xak  k  ∈ Pk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' We denote νj(x) = aj, 1 ⩽ j ⩽ k and ν(x) =  max{νj(x) : 1 ⩽ j ⩽ k}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' We set  Ji(x) = {j ∈ Nk : αi(νj(x)) = 0},  for i ⩾ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Then, we have  x =  �  i⩾0  X2i  Ji(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' A weight vector ω is a sequence of non-negative integers (ω1, ω2,  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' , ωi, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=') such that ωi = 0 for i ≫ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' For any monomial x in Pk, we define two  sequences associated with x by  ω(x) = (ω1(x), ω2(x), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' , ωi(x), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' ),  σ(x) = (ν1(x), ν2(x), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' , νk(x)),  where ωi(x) = �  1⩽j⩽k αi−1(νj(x)) = deg XJi−1(x), i ⩾ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' The sequences ω(x) and  σ(x) are respectively called the weight vector and the exponent vector of x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  The sets of the weight vectors and the exponent vectors are given the left lexi-  cographical order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  For a weight vector ω = (ω1, ω2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' ), define deg ω = �  i>0 2i−1ωi and the length  ℓ(ω) = max{i : ωi > 0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Then, we write ω = (ω1, ω2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' , ωr) if ℓ(ω) = r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' For a  weight vector η = (η1, η2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' ), we define the concatenation of weight vectors  ω|η = (ω1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' , ωr, η1, η2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=')  if ℓ(ω) = r and (a)|b = (a)|(a)| .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' |(a), (b times of (a)’s), where a, b are positive  integers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' We denote Pk(ω) the subspace of Pk spanned by monomials y such that  deg y = deg ω and ω(y) ⩽ ω, and by P −  k (ω) the subspace of Pk(ω) spanned by  monomials y such that ω(y) < ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Denote by A+  s the subspace of A spanned by all Sqj with 1 ⩽ j < 2s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' For ω a weight vector and f, g two polynomials of the same  degree in Pk, we define  i) f ≡ g if and only if f + g ∈ A+Pk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' If f ≡ 0, then f is said to be hit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  ii) f ≡ω g if and only if f + g ∈ A+Pk + P −  k (ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  iii) f ≃(s,ω) g if and only if f + g ∈ A+  s Pk + P −  k (ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Obviously, the relations ≡, ≡ω and ≃(s,ω) are equivalence ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Since A+  0 Pk = 0,  f ≃(0,ω) g if and only if f + g ∈ P −  k (ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  For x a monomial in Pk and ω = ω(x), we denote x ≃s g if and only if x ≃(s,ω(x))  g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Denote by QPk(ω) the quotient of Pk(ω) by the equivalence relation ≡ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Fol-  lowing [20], we have  (QPk)n ∼=  �  deg ω=n  QPk(ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1)  THE SQUARING OPERATION AND THE HIT PROBLEM  5  For any polynomial f in Pk, we denote [f] the class in QPk represented by f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  For a subset S ⊂ Pk, we denote [S] = {[f] : f ∈ S} ⊂ QPk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' If f ∈ Pk(ω) and  S ⊂ Pk(ω), then we denote by [f]ω the class in QPk(ω) represented by f and  [S]ω = {[f]ω : f ∈ S} ⊂ QPk(ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  We recall some elementary properties on the action of the Steenrod squares on  Pk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Let f be a homogeneous polynomial in Pk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  i) If i > deg f, then Sqi(f) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' If i = deg f, then Sqi(f) = f 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  ii) If i is not divisible by 2s, then Sqi(f 2s) = 0 while Sqr2s(f 2s) = (Sqr(f))2s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 (Kameko [3, Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Let x be a monomial in Pk and  n, s be positive integers such that 0 < n < 2s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' If v is a monomial in Pk which  appears as a term in the polynomial Sqn(x), then there is an index i ⩽ s such that  ωi(v) < ωi(x) and ω(v) < ω(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Let x, y be monomials of the same degree in Pk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' We define  x < y if and only if one of the following holds:  i) ω(x) < ω(y);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  ii) ω(x) = ω(y) and σ(x) < σ(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' A monomial x is said to be inadmissible if there exist monomials  y1, y2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' , yr such that yj < x for j = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' , r and x ≡ �r  j=1 yj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  A monomial x is said to be admissible if it is not inadmissible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Obviously, the set of all the admissible monomials of degree n in Pk is a minimal  set of A-generators for Pk in degree n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' A monomial x is said to be strictly inadmissible if and only  if there exist monomials y1, y2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' , yr such that yj < x, for j = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' , r and  x ≃s  �r  j=1 yj with s = max{i : ωi(x) > 0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  It is easy to see that if x is strictly inadmissible, then it is inadmissible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' The  following theorem is a modification of a result in [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='9 (Kameko [3], Sum [18]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' For any monomials x, y, w in Pk such  that ωi(x) = 0 for i > r > 0, ωs(w) ̸= 0 and ωi(w) = 0 for i > s > 0, we have  i) If w is inadmissible, then so is xw2r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  ii) If w is strictly inadmissible, then so is xw2ry2r+s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='10 (See [18]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Let x be an admissible monomial in Pk and let i0  be a positive integer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Then we have  i) If ωi0(x) = 0, then ωi(x) = 0 for all i > i0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  ii) If ωi0(x) < k, then ωi(x) < k for all i > i0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  For 1 ⩽ i ⩽ k, define a homomorphism fi : Pk−1 → Pk of A-algebras by  substituting  fi(xu) =  �  xu,  if 1 ⩽ u < i,  xu+1,  if i ⩽ u < k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2)  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='11 (See Mothebe and Uys [5]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Let i, d be positive integers such  that 1 ⩽ i ⩽ k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' If w is an admissible monomial in Pk−1, then x2d−1  i  fi(w) is also  an admissible monomial in Pk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  6  NGUYỄN SUM  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Some criterions on the hit polynomials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Firstly, we recall Singer’s criterion on hit monomials in Pk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' A monomial z in Pk is called a spike if νj(z) = 2sj − 1 for sj a  non-negative integer and j = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=', k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' If z is a spike with s1 > s2 > .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' > sr−1 ⩾  sr > 0 and sj = 0 for j > r, then it is called the minimal spike.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Note that if µ(n) = s, then n is of the form (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1) and z = �s  i=1 x2di −1  i  is the  minimal spike of degree n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' It is easy to show that a spike of degree n is the minimal  spike if its weight vector order is minimal with respect to other spikes of degree n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  The following is a criterion for hit monomials in Pk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 (See Singer [16]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Suppose x ∈ Pk is a monomial of degree n,  where µ(n) ⩽ k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Let z be the minimal spike of degree n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' If ω(x) < ω(z), then x is  hit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  We remark that this criterion is not enough to determine all hit monomials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  For example, it can be shown that x15  1 x3  2x3  3 is the minimal spike of degee 21 and  x1x5  2x5  3x5  4x5  5 is hit, but ω(x1x5  2x5  3x5  4x5  5) = (5, 0, 4, 0) > (3, 3, 1, 1) = ω(x15  1 x3  2x3  3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' So,  we need Silverman’s criterion for hit polynomials in Pk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 (See Silverman [13, Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Let p be a polynomial of the  form fg2m for some homogeneous polynomials f and g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' If deg f < (2m−1)µ(deg g),  then p is hit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  This result leads to a criterion in terms of the minimal spike which strengthens  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 (See Walker and Wood [23, Theorem 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Let x ∈ Pk be a  monomial of degree n, where µ(n) ⩽ k and let z be the minimal spike of degree n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  If there is an index h such that �h  i=1 2i−1ωi(x) < �h  i=1 2i−1ωi(z), then x is hit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  For 1 ⩽ r ⩽ k, we set  P 0  s = ⟨{x = xa1  1 xa2  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' xas  s  : a1a2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' as = 0}⟩,  P +  s = ⟨{x = xa1  1 xa2  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' xas  s  : a1a2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' as > 0}⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  It is easy to see that P 0  s and P +  s  are the A-submodules of Pk, Ps = P 0  s ⊕ P +  s  and QPs = QP 0  s ⊕ QP +  s , where QP 0  s = P 0  s /A+P 0  s and QP +  s = P +  s /A+P +  s .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  For J = (j1, j2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' , js) : 1 ⩽ j1 < .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' < js ⩽ k, we define a monomorphism  θJ : Ps → Pk of A-algebras by substituting θJ(xu) = xju for 1 ⩽ u ⩽ s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' It is easy  to see that, for any weight vector ω of degree n,  QθJ(P +  s )(ω) ∼= QP +  s (ω) and (QθJ(P +  s ))n ∼= (QP +  s )n  for 1 ⩽ s ⩽ k, where QθJ(P +  s ) = θJ(P +  s )/A+θJ(P +  s ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' So, by a simple computation  using Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1), we get the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 (See Walker and Wood [23, Proposition 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='9]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' For a weight  vector ω of degree n, we have direct summand decompositions of the F2-vector spaces  QPk(ω) =  �  µ(n)⩽s⩽k  �  ℓ(J)=s  QθJ(P +  s )(ω),  THE SQUARING OPERATION AND THE HIT PROBLEM  7  where ℓ(J) is the length of J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Consequently,  dim QPk(ω) =  �  µ(n)⩽s⩽k  �k  s  �  dim QP +  s (ω),  dim(QPk)n =  �  µ(n)⩽s⩽k  �k  s  �  dim(QP +  s )n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Notation 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' From now on, we denote by Bk(n) the set of all admissible mono-  mials of degree n in Pk, B0  k(n) = Bk(n) ∩ P 0  k , B+  k (n) = Bk(n) ∩ P +  k .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' For a weight  vector ω of degree n, we set Bk(ω) = Bk(n) ∩ Pk(ω), B+  k (ω) = B+  k (n) ∩ Pk(ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Then, [B0  k(n)], [B+  k (n)], [Bk(ω)]ω and [B+  k (ω)]ω are respectively the bases of the  F2-vector spaces (QP 0  k )n, (QP +  k )n, QPk(ω) and QP +  k (ω) := QPk(ω) ∩ QP +  k .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  For any (i;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' I) with I = (i1, i2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' , ir), 1 ⩽ i < i1 < i2 < .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' < ir ⩽ k, 0 ⩽ r < k,  define a homomorphism p(i;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='I) : Pk → Pk−1 of algebras by substituting  p(i;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='I)(xj) =  \uf8f1  \uf8f4  \uf8f2  \uf8f4  \uf8f3  xj,  if 1 ⩽ j < i,  �r  t=1 xit−1,  if j = i,  xj−1,  if i < j ⩽ k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3)  Then p(i;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='I) is a homomorphism of A-modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' These homomorphisms will be used  in the proof of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' On the kernel of Kameko’s squaring operation  In this section, we consider n = �k−2  i=1 (2di − 1) with di positive integers such  that d1 > d2 > .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' > dk−3 ⩾ d := dk−2 > 0, k ⩾ 4, m = �k−3  i=1 (2di−d − 1) = βd  k(n),  where the function βk : Z → Z is defined by βk(t) = t−k+2  2  if t − k + 2 is even and  βk(t) = 0 if t − k + 2 is odd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Note that µ(n) = k − 2 and this degree is used in  Conjecture 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 on the dimension of the kernel of Kameko’s squaring operation  (�  Sq  0  ∗)(k,n) : (QPk)n → (QPk) n−k  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  The main result of the section is Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 that provides an upper bound  for the dimension of Ker((�  Sq  0  ∗)(k,n)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Firstly, we prove some properties of monomials in Ker((�  Sq  0  ∗)(k,n)) from which we  can reduce the computations to the case of weight vector (k−2)|d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' In Subsection 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2,  we present the notion of strongly inadmissible monomial and prove Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  that is used instead of Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Note that the notion of strongly inadmissible  monomial is weaker than the one of strictly inadmissible monomial, so using this  notion can overcome many difficulties encountered if using the notion of strictly  inadmissible monomial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' In Subsection 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3, we prove our main result by using the  results in the previous subsections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Some properties of monomials in Ker((�  Sq  0  ∗)(k,n)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  In this subsection we present some properties of the admissible monomials in  the kernel of Kameko’s squaring operation that allow us to reduce the study of this  subspace to the case of weight vector (k − 2)|d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' If x is an admissible monomial of degree n in Pk such that [x] ∈  Ker((�  Sq  0  ∗)(k,n)), then ωi(x) = k − 2 for 1 ⩽ i ⩽ dk−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  8  NGUYỄN SUM  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Note that z = �k−2  t=1 x2dt−1  t  is the minimal spike of degree n and ωi(z) = k−2  for 1 ⩽ i ⩽ dk−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Since x is admissible, [x] ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' If ω1(x) = k − 1, then x = Xjy2  with y a monomial of degree n−k+1  2  = βk(n)+ 1  2, however this is not an integer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' So,  by Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2, we have either ω1(x) = k − 2 or ω1(x) = k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' If ω1(x) = k, then  x = X∅y2 with y a monomial in Pk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Since x is admissible, by Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='9, y is  also admissible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Hence, (�  Sq  0  ∗)(k,n)([x]) = [y] ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' This contradicts the hypothesis  that x ∈ Ker((�  Sq  0  ∗)(k,n)), hence ω1(x) = k − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Then, we have x = Xj,ℓy2 with  1 ⩽ j < ℓ ⩽ k and y an admissible monomial of degree βk(n) = �k−2  i=1 (2di−1 − 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Since ω1(y) ̸= k − 1, using Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 and Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='10 we get ω2(x) =  ω1(y) = k − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' By repeating the above argument we obtain ωi(x) = k − 2 for  1 ⩽ i ⩽ dk−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' The lemma is proved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  □  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' If x is a monomial of degree n in Pk such that [x] ∈ Ker((�  Sq  0  ∗)(k,n)),  then x ≡ � ¯x with ¯x monomials in Pk such that ωi(¯x) = k − 2, for 1 ⩽ i ⩽ dk−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' If ω1(x) < k − 2, then by Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2, x is hit, hence the lemma holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Suppose ω1(x) = k − 2 and let s > 1 be the smallest index such that ωs(x) ̸= k − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  If ωs(x) < k − 2, then by Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2, x is hit, hence the lemma holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Since  ω1(x) ̸= k − 1, we obtain ωs(x) = k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Then we have x = wy2s−2 �  t⩾s X2t  Jt(x),  where w = �s−3  t=0 X2t  Jt(x), y = XJs−2(x)X2  Js−1(x) = XJs−2(x)X2  ∅ = X3  u,vx2  ux2  v with  1 ⩽ u < v ⩽ k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' It is easy to see that  y =  �  i̸=u,v  X3  i,u,vxux2  vx4  i + Sq1(X3  u,vxux2  v).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1)  By combining Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 and the Cartan formula, we have  w(Sq1(X3  u,vxux2  v))2s−2 = wSq2s−2 �  (X3  u,vxux2  v)2s−2�  = Sq2s−2 �  w(X3  u,vxux2  v)2s−2�  + Sq2s−2(w)(X3  u,vxux2  v)2s−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Let ¯w be a monomial which appears as a term in Sq2s−2(w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  By Proposition  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5, ω( ¯w) < ω(w) = (k − 2)|s−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Hence, using Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 we see that the  polynomial w(Sq1(X3  u,vxux2  v))2s−2 �  t⩾s X2t  Jt(x) is hit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' So, from the relation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1) we  obtain x ≡ �  i̸=u,v x(i,u,v), where  x(i,u,v) =  �  0⩽t⩽s−3  X2t  Jt(x)(X3  i,u,vxux2  vx4  i )2s−2 �  t⩾s  X2t  Jt(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  A simple computation shows that ωt(x(i,u,v)) = k − 2 for 1 ⩽ t ⩽ s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' By repeating  this argument we see that the lemma is true in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  If ω1(x) = k, then x = X∅y2 with y a monomial in Pk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Then, we have  (�  Sq  0  ∗)(k,n)([x]) = [y] = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Hence, y = �  r>0 Sqr(gr) with suitable polynomial  gr in Pk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Then, by using Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 and the Cartan formula, we get  x = X∅y2 =  �  r>0  X∅Sq2r(g2  r)  =  �  r>0  Sq2r(X∅g2  r) +  �  r>0  r  �  t=1  Sq2t(X∅)(Sqr−t(gr))2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  THE SQUARING OPERATION AND THE HIT PROBLEM  9  Since deg(X∅) = k, Sq2t(X∅) = 0 for 2t > k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' If 2t ⩽ k and w is a monomial which  appears as a term of Sq2t(X∅), then ω1(w) = k −2t ⩽ k −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Hence, from the above  equality and Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2, we get x ≡ � x′ with x′ monomials in (Pk)n such that  ω1(x′) = k − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' The lemma is proved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  □  From this lemma, it suffices to consider monomials x such that ωi(x) = k − 2  for 1 ⩽ i ⩽ d = dk−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Then  x =  d  �  t=1  X2d−t  it,jt y2d,  where 1 ⩽ it < jt ⩽ k, 1 ⩽ t ⩽ d and y ∈ (Pk)m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Note that ω(x) = (k − 2)|d|ω(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Let x be a monomial of degree (k − 2)(2d − 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' If ω1(x) < k and  there is r > d such that ωr(x) > 0, then x ∈ P −  k ((k − 2)|d) + A+  d Pk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' If ω1(x) < k − 2, then x ∈ P −  k ((k − 2)|d), hence the lemma holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Since  ω1(x) ̸= k − 1, if ω1(x) ⩾ k − 2, then ω1(x) = k − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Let s be the smallest index  such that ωs(x) > k − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Since ωs(x) ̸= k − 1, we have ωs(x) = k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' If s ⩾ d, then  (k − 2)(2d − 1) = deg x ⩾ (k − 2)(2d − 1) + 2t−1ωt(x) > (k − 2)(2d − 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' This is  a contradiction, so s < d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' If there is 1 < r < s such that ωr(x) < k − 2, then  x ∈ P −  k ((k − 2)|d), so the lemma holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Suppose ωr(x) = k − 2 for 1 ⩽ r < s and  XJs−2(x) = Xu,v for 1 ⩽ u < v ⩽ k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Then, we have  X2  Js−1(x)XJs−2(x) = X3  u,vx2  ux2  v =  �  i̸=u,v  X3  i,u,vx4  i xux2  v + Sq1(X3  u,vxux2  v).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  By an argument analogous to the one in the proof of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2, we get  x =  �  i̸=u,v  x(i,u,v)  mod(P −  k ((k − 2)|d) + A+  d Pk),  where  x(i,u,v) =  s−3  �  t=0  X2t  Jt(x)(X3  i,u,vxux2  vx4  i )2s−2 �  t⩾s  X2t  Jt(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  It is easy to see that ωt(x(i,u,v)) = k − 2 for 1 ⩽ t ⩽ s and ωr(x(i,u,v)) > 0 for  suitable r > d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' By repeating this argument we obtain  x =  �  ¯x  mod(P −  k ((k − 2)|d) + A+  d Pk)  with ¯x monomials such that ωt(¯x) ⩽ k − 2 for 1 ⩽ t ⩽ d and ωr(¯x) > 0 for suitable  r > d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Then we have �d  i=1 2i−1ωi(¯x) < deg ¯x = (k − 2)(2d − 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Hence, there is  an index u ⩽ d such that ωt(¯x) = k − 2 for 1 ⩽ t < u, ωu(¯x) < k − 2, therefore  ¯x ∈ P −  k ((k − 2)|d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' The lemma is proved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  □  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' The strongly inadmissible monomials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  In this subsection, we introduce the notion of strongly inadmissible monomial in  Pk and use it to study the kernel of Kemeko’s squaring operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' We can see in  Section 4 that the use of strongly inadmissible monomial is more convenience than  that of the strictly inadmissible monomial because it can overcome many difficulties  encountered if using the notion of strictly inadmissible monomial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  10  NGUYỄN SUM  Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Let n be a positive integer and z be the minimal spike of degree  n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Denote by P(k,n) the subspace of Pk spanned by all monomials x of degree n  such that  h  �  j=1  ωj(x) <  h  �  j=1  ωj(z),  for some index h ⩾ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' A monomial x of degree n in Pk is said to be strongly inad-  missible if there exist monomials y1, y2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' , yt of the same weight vector ω(x) such  that yu < x, 1 ⩽ u ⩽ t and  x ≃s y1 + y2 + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' + yt mod(P(k,n)),  where s = max{i : ωi(x) > 0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Obviously, if x is strictly inadmissible, then it is strongly inadmissible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  By  using Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4, we see that if g ∈ P(k,n) then g ∈ A+Pk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Hence, if x is  strongly inadmissible then it is inadmissible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' However, if g /∈ A+  s Pk, then x is not  strictly inadmissible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Therefore, it is more convenient to use the notion of a strongly  inadmissible monomial than to use the one of a strictly inadmissible monomial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  For example, let x = x1x3  2x6  3x6  4x5  5 be the monomial of weight vector (3)|3 in P5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  We have  x = x1x3  2x5  3x6  4x6  5 + x1x3  2x6  3x5  4x6  5 + x1x5  2x5  3x5  4x5  5  + Sq1(x2  1x3  2x5  3x5  4x5  5) + Sq2(x1x3  2x5  3x5  4x5  5) mod(P −  5 ((3)|3)),  where x1x5  2x5  3x5  4x5  5 ∈ P(5,21), hence x is strongly inadmissible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' It is easy to see that  x1x5  2x5  3x5  4x5  5 = Sq2(x1x3  2x5  3x5  4x5  5 + x1x5  2x3  3x5  4x5  5 + x1x5  2x5  3x3  4x5  5 + x1x5  2x5  3x5  4x3  5)  + Sq8(x1x3  2x3  3x3  4x3  5) mod(P −  5 ((3)|3)) ∈ A+  4 P5 + P −  5 ((3)|3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  If x is strictly inadmissible, then x1x5  2x5  3x5  4x5  5 ∈ A+  3 P5 + P −  5 ((3)|3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' However, we  have been unable to prove this.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  For a positive integer a, denote by α(a) the number of ones in dyadic expansion  of a and by ζ(a) the greatest integer u such that a is divisible by 2u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' That means  a = 2ζ(a)b with b an odd integer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' We set δ(a) = a − α(a) − ζ(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Let d be a positive integer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' If z∗ is the minimal spike of degree  nd := (k − 2)(2d − 1) and d > δ(k − 2), then ωi(z∗) = k − 2 for 1 ⩽ i ⩽ d − δ(k − 2)  and ωi(z∗) < k − 2 for i > d − δ(k − 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Set s = α(k − 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' We have k − 2 = 2t1 + 2t2 + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' + 2ts−1 + 2ts, where  t1 > t2 > .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' > ts−1 > ts = ζ(k − 2) ⩾ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Then, we obtain  (k − 2)(2d − 1) = 2d+t1 + 2d+t2 + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' + 2d+ts−1 + 2d+ts − k + 2  =  �  1⩽i⩽k−2  (2ei − 1),  where  ei =  \uf8f1  \uf8f2  \uf8f3  d + ti,  1 ⩽ i < s,  d + ts − i + s − 1, s ⩽ i ⩽ k − 3,  d + ts − k + s + 2, i = k − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  THE SQUARING OPERATION AND THE HIT PROBLEM  11  It is easy to see that e1 > e2 > .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' > ek−3 = ek−2 = d − δ(k − 2) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Hence  z∗ = �k−2  i=1 x2ei−1  i  is the minimal spike of degree nd = (k−2)(2d−1), ωj(z∗) = k−2  for 1 ⩽ j ⩽ ek−2 and ωi(z∗) < k − 2 for i > d − δ(k − 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' The proposition is  proved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  □  The following is a modification of Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Let c, d, e be positive integers and let u, w, y ∈ Pk be mono-  mials such that ω(u) = (k − 2)|c, ω(w) = (k − 2)|d and ω(y) = (k − 2)|e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' If w is  strongly inadmissible, then so is uw2cy2c+d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Note that the weight vector of uw2cy2c+d is (k−2)|c+d+e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Since w is strongly  inadmissible, there exist monomials y1, y2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' , yt of the same weight vector (k−2)|d,  g1 ∈ P −  k ((k − 2)|d) and g2 ∈ P(k,nd) such that yi < w for i = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' , t and  w = y1 + y2 + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' + yt + g1 + g2 +  �  1⩽j<2d  Sqj(hj),  where hj are suitable polynomials in Pk and nd = (k−2)(2d −1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Since j2c < 2c+d,  by using Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 and the Cartan formula we have  (Sqj(hj))2cy2c+d = Sqj2c(h2c  j )y2c+d = Sqj2c �  h2c  j y2c+d�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Then, combining the Cartan formula and Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4, we get  u(Sqj(hj))2cy2c+d = Sqj2c �  uh2c  j y2c+d�  +  �  1⩽r⩽j  Sqr2c(u)  �  Sqj−r(hjy2d)  �2c  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Suppose v is a monomial which appears as a term of Sqr2c(u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' By Proposition  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5, we have ω(v) < ω(u) = (k − 2)|c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Hence,  �  1⩽r⩽j  Sqr2c(u)  �  Sqj−r(hjy2d)  �2c  ∈ P −  k ((k − 2)|c+d+e),  for 1 ⩽ j < 2d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Combining the above equalities gives  uw2cy2c+d =  �  1⩽i⩽t  uy2c  i y2c+d + ug2c  1 y2c+d + ug2c  2 y2c+d  +  �  1⩽j<2d  Sqj2c �  uh2c  j y2c+d�  mod(P −  k ((k − 2)|c+d+e)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Since ω(u) = (k − 2)|c, we can easily check that uy2c  i y2c+d < uw2cy2c+d for 1 ⩽  i ⩽ t, ug2c  1 y2c+d ∈ P −  k ((k − 2)|c+d+e) and ug2c  2 y2c+d ∈ P(k,nc+d+e) with nc+d+e =  (k − 2)(2c+d+e − 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Hence, the last equality implies that uw2cy2c+d is strongly  inadmissible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  □  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Let f, g ∈ (Pk)nd be homogeneous polynomials with nd = (k −  2)(2d −1), and let y ∈ (Pk)m be a monomial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' If f ≃(d,(k−2)|d) g mod(P(k,nd)), then  fy2d ≡ gy2d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Note that z = �k−2  i=1 x2di −1 is the minimal spike of degree n and ωt(z) = k−2  for 1 ⩽ t ⩽ d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Suppose  f = g + g1 +  �  1⩽j<2d  Sqj(hj),  12  NGUYỄN SUM  where g1 ∈ P(k,nd) and suitable polynomials hj ∈ Pk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' By Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 and the  Cartan formula,  Sqj(hj)y2d = Sqj(hjy2d), 1 ⩽ j < 2d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  By Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2, if a monomial w appears as a term of the polynomial g1, then  there is an integer h ⩾ 1, such that  h  �  i=1  2i−1ωi(w) <  h  �  i=1  2i−1ωi(z∗),  where z∗ is determined as in Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' If h ⩽ d, then using Proposition  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 we have �h  i=1 2i−1ωi(z∗) ⩽ (k − 2)(2h − 1) = �h  i=1 2i−1ωi(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' If h > d, then  h  �  i=1  2i−1ωi(z∗) ⩽ deg(z∗) = (k − 2)(2d − 1) <  h  �  i=1  2i−1ωi(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  By Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4, wy2d is hit, hence the polynomial g1y2d is hit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' This implies  fy2d ≡ gy2d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' The lemma is proved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  □  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' A construction for A-generators of Ker((�  Sq  0  ∗)(k,n)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Notation 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Let S be a finite sequence of positive integers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Then, there  are positive integers c0, c1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' , cr and s0, s1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' , sr such that si+1 ̸= si and S =  (s0)|c0|(s1)|c1| .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' |(sr)|cr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' We define rl(S) = c1 +c2 +.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+cr, the reduced length of  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' For example, with S = (2, 2, 3, 1, 1, 1) = (2)|2|(3)|1|(1)|3, we have c0 = 2, c1 =  1, c2 = 3, hence rl(S) = c1 + c2 = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Denote by PSeqd  k the set of all pairs (I, J ) of sequences I = (i1, i2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' , id),  J = (j1, j2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' , jd), where it, jt are integers such that 1 ⩽ it < jt ⩽ k, for 1 ⩽ t ⩽ d,  and by PIncd  k the set of all (I, J ) ∈ PSeqd  k such that i1 ⩽ i2 ⩽ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' ⩽ id and  j1 ⩽ j2 ⩽ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' ⩽ jd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' By convention, PSeq0  k = ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' For (I, J ) ∈ PSeqd  k, we denote  X(I,J ) =  �  1⩽t⩽d  X2d−t  it,jt ∈ Pk((k − 2)|d) ⊂ (Pk)(k−2)(2d−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Let d0 be a positive integer, d0 > 2, and B be a subset of PIncd0  k .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  The set B is said to be compatible with (k − 2)|d0 if the following conditions hold:  i) For any (I, J ) ∈ B, rl(I) ⩽ d0 − 2 and rl(J ) ⩽ d0 − 2,  ii) For any (H, K) ∈ PSeqd0  k , we have  X(H,K) ≃d0  min K  �  u=min H+1  �  (I,J )∈Bu  X(I,J ) mod(P(k,nd0)),  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2)  where Bu is a set of some pairs (I, J ) ∈ B such that min I = min H, min J = u  and nd0 = (k − 2)(2d0 − 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  From the result in [18, Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1] we see that the set  B4 = {(I, J ) ∈ PSeq5  4 : X(I,J ) ∈ B4((2)|5)} ⊂ PInc5  4  is compatible with (2)|5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  THE SQUARING OPERATION AND THE HIT PROBLEM  13  For 1 ⩽ i < j ⩽ k, denote f(i,j) = fifj−1 : Pk−2  fj−1  −→ Pk−1  fi  −→ Pk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Here fi and  fj−1 are defined by (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' More precisely,  f(i,j)(xt) =  \uf8f1  \uf8f4  \uf8f2  \uf8f4  \uf8f3  xt,  if 1 ⩽ t < i,  xt+1,  if i ⩽ t < j − 2,  xt+2,  if j − 2 ⩽ t ⩽ k − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  The main result of this section is the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Let d0 be a positive integer, d0 > 2, and let k ⩾ 4, n =  �k−2  i=1 (2di − 1) with di positive integers such that d1 > d2 > .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' > dk−3 ⩾ dk−2 =  d ⩾ d0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Denote m = �k−3  i=1 (2di−d − 1) = βd  k(n) with βk(n) = n−k+2  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Suppose the  set B ⊂ PIncd0  k is compatible with (k − 2)|d0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Then,  B :=  �  (I,J )∈B  �  X(I,J )(Xi,j)2d−2d0 (f(i,j)(y))2d : y ∈ Bk−2(m)  �  is a set of generators for Ker(�  Sq  0)(k,n), where i = min I = i1, j = min J = j1  and Bk−2(m) is the set of all the admissible monomials of the degree m in Pk−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Consequently, dim Ker(�  Sq  0)(k,n) ⩽ |B| dim(QPk−2)m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  We need the following lemmas for the proof of the theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Let n, m, d0 and B be as in Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Let y0 be a monomial  in (Pk)m0−1 with m0 = �k−2  i=1 (2di−d0 − 1) = βd0  k (n), yu = y0xu for 1 ⩽ u ⩽ k, and  (I, J ) ∈ B, i = min I, j = min J .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Then we have  X(I,J )y2d0  i  ≡  �  1⩽u<k  u̸=i,j  �  (U,V)∈Bu  X(U,V)y2d0  u  ,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3)  X(I,J )y2d0  j  ≡  �  2⩽v⩽k  v̸=i,j  �  (U,V)∈Cv  X(U,V)y2d0  v  ,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4)  where Bu is a set of some (U, V) ∈ B such that min U = u for u < i and min U = i  for u > i;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Cv is a set of some (U, V) ∈ B such that min V = v for v < j and  min V = j for v > j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' By the Cartan formula, we have Sq1(Xj) = �  u̸=j Xu,jx2  u and Sq1(Xjy2  0) =  Sq1(Xj)y2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Hence, we obtain  Xi,jy2  i =  �  1⩽u<j  u̸=i  Xu,jy2  u +  �  j<u⩽k  Xj,uy2  u + Sq1(Xjy2  0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Since (I, J ) ∈ B ⊂ PIncd0  k , we have X(I,J ) = X(I\\i,J \\j)(Xi,j)2d0−1 with i = i1, j =  j1, and  X(I\\i,J \\j)(Xu,j)2d0−1 =  � X(u|(I\\i),J ),  if u < j,  X(j|(I\\i),u|(J \\j)), if u > j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  By using the Cartan formula, Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 and Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 we see that the  polynomial X(I\\i,J \\j)(Sq1(Xjy2  0))2d0−1 is hit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' So, we get  X(I,J )y2d0  i  ≡  �  1⩽u<j  u̸=i  X(u|(I\\i),J )y2d0  u  +  �  j<u⩽k  X(j|(I\\i),u|(J \\j))y2d0  u  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  14  NGUYỄN SUM  Since rl(I) < d0 − 1 and rl(J ) < d0 − 1, we have min(u|(I \\ i)) = u for u < i,  min(j|(I \\ i)) = min(u|(I \\ i)) = i for i < u < j and min(u|(J \\ j)) = j for u > j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Hence the relation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3) follows from the condition (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2) of B in Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  and Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  The relation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4) is proved by a similar computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  □  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Let n, d0, m0 be as in Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 and let P1  k(n) denote the  subspace of (Pk)n spanned by all monomials of the form X(I,J )(fi(y))2d0 with  (I, J ) ∈ B, i = min I and y ∈ (Pk−1)m0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Then Ker(�  Sq  0)(k,n) ⊂ [P1  k(n)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Let x be a monomial of degree n such that [x] ∈ Ker(�  Sq  0)(k,n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' By using  Lemmas 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2, we can assume that ωi(x) = k − 2, for 1 ⩽ i ⩽ d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Then,  x = �d  t=1 X2d−t  αt,δt ¯y2d, where αt, δt are integers such that 1 ⩽ αt < δt ⩽ k, for  1 ⩽ t ⩽ d, and ¯y is a monomial of degree m = βd  k(n) in Pk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Since d ⩾ d0, we set  H = (α1, α2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' , αd0), K = (δ1, δ2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' , δd0), then we have x = X(H,K)˜y2d0 , where  ˜y = �d  t=d0+1 X2d−t  αt,δt ¯y2d is the monomial of degree m0 in Pk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' By the condition of  the set B in Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2, the monomial X(H,K) is of the form (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Hence, by  using Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5, one gets  x = X(H,K)˜y2d0 ≡  min K  �  u=min H+1  �  (I,J )∈Bu  X(I,J )˜y2d0  where Bu is as in Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  For i = min H, we have ˜y = xa  i fi(y) with  a a non-negative integer and y ∈ (Pk−1)m0−a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' We prove the lemma by proving  [X(I,J )(xa  i fi(y))2d0 ] ∈ [P1  k(n)] for all (I, J ) ∈ Bu, i < u ⩽ min K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' We prove this  claim by double induction on (a, i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  If a = 0, then the claim is true for all 1 ⩽ i < k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Suppose a > 0 and the claim  is true for (a − 1, i) with 1 ⩽ i < min J .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  For i = 1, by using Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 with y0 = xa−1  1  f1(y), we get  X(I,J )(xa  1f1(y))2d0 ≡  �  2⩽t⩽k  t̸=min J  �  (U,V)∈B(t,1)  X(U,V)(xa−1  1  f1(xt−1y))2d0,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5)  where B(t,1) is a set of some (U, V) ∈ B such that min U = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' By the inductive  hypothesis, [X(U,V)(xa−1  1  f1(xt−1y))2d0 ] ∈ [P1  k(n)] for all (U, V) ∈ B(t,1) with 1 <  t ̸= min J .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Hence, the claim is true for (a, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Suppose i > 1 and the claim is true for all (a′, t), 1 ⩽ t < i, and for (a − 1, i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  By applying Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 for y0 = xa−1  i  fi(y), we have  X(I,J )(xa  i fi(y))2d0 ≡  �  1⩽t<i  �  (U,V)∈B(t,i)  X(U,V)(xtxa−1  i  fi(y))2d0  +  �  i<t⩽k  t̸=min J  �  (U,V)∈B(t,i)  X(U,V)(xa−1  i  fi(xt−1y))2d0 ,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='6)  where B(t,i) is a set of some (U, V) ∈ B such that min U = t for t < i and min U = i  for t > i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' From the relation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='6) and the inductive hypothesis, we see that our  claim is true for (a, i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' This completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  □  We now prove Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  THE SQUARING OPERATION AND THE HIT PROBLEM  15  Proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Denote by ⟨[B]⟩ the subspace of (QPk)n spanned by the  set [B].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' We prove that Ker(�  Sq  0)(k,n) ⊂ ⟨[B]⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' By using Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5, we need  only to prove that [X(I,J )(fi(y∗))2d] ∈ ⟨[B]⟩ for all (I, J ) ∈ B with min I = i and  y∗ ∈ (Pk−1)m0, where m0 = �k−2  t=1 (2dt−d0 − 1) = βd0(n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Set j = min J , we have fi(y∗) = xb  jf(i,j)(y) with b a non-negative integer and  y ∈ (Pk−2)m0−b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' We prove [X(I,J )(xb  jf(i,j)(y))2d] ∈ ⟨[B]⟩ by double induction on  (b, j).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  If b = 0, then y ∈ (Pk−2)m0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Since ωu(y) = k − 2 for 1 ⩽ u ⩽ d − d0, we  get y = Y 2d−d0−1(˜y)2d−d0, with ˜y ∈ (Pk−2)m and Y = x1x2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' xk−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Note that  f(i,j)(Y ) = Xi,j, hence f(i,j)(y) = X2d−d0−1  i,j  (f(i,j)(˜y))2d−d0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Since Bk−2(m) is a set  of A-generators for (Pk−2)m, there are z1, z2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' , zr ∈ Bk−2(m) such that  ˜y ≡ z1 + z2 + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' + zr +  �  t>0  Sqt(ht),  where ht are suitable polynomials in Pk−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Set p = X(I,J )(Xi,j)2d−2d0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' By using  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 and the Cartan formula, we have  p(Sqt(f(i,j)(ht))2d = pSqt2d �  (f(i,j)(ht))2d�  = Sqt2d �  p(f(i,j)(ht))2d�  +  �  1⩽ℓ⩽t  Sqℓ2d(p)  �  Sqt−ℓ(f(i,j)(ht)  �2d  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='7)  Suppose w is a monomial which appears as a term in the polynomial Sqℓ2d(p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' By  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 we have ω(w) < ω(p) = (k−2)|d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Hence, using Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 and  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='7), we see that the polynomial p(Sqt(f(i,j)(ht))2d is hit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Since f(i,j) : Pk−2 → Pk  is a homomorphism of A-algebras, we get  �  X(I,J )(f(i,j)(y))2d�  =  �  1⩽u⩽r  �  X(I,J )(Xi,j)2d−2d0(f(i,j)(zu))2d�  ∈ ⟨[B]⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Hence, our claim is true for (0, j), i < j ⩽ k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' We assume b > 0 and our claim holds  for (b − 1, j) with i < j ⩽ k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  For j = 2, we have i = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' By applying Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 for y0 = xb−1  2  f(1,2)(y) we  obtain  X(I,J )(xb  2f(1,2)(y))2d0 ≡  �  3⩽t⩽k  �  (U,V)∈Bt  X(U,V)(xb−1  2  f(1,2)(xt−2y))2d0 ,  where Bt is a set of some (U, V) ∈ B such that min V = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' The last equality and  the inductive hypothesis imply our claim for (b, 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Suppose j > 2 and the claim holds for all (b′, t) with 1 ⩽ i < t < j and for  (b − 1, j).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' By using Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 with y0 = xb−1  j  f(i,j)(y), we have  X(I,J )(xb  jf(i,j)(y))2d0 ≡  �  1⩽t<i  �  (U,V)∈B∗  t  X(U,V)(fi(xtxb−1  j−1y))2d0  +  �  i<t<j  �  (U,V)∈B∗  t  X(U,V)(fi(xt−1xb−1  j−1y))2d0  +  �  j<t⩽k  �  (U,V)∈B∗  t  X(U,V)(xb−1  j  f(i,j)(xt−2y))2d0 ,  16  NGUYỄN SUM  where B∗  t is a set of some (U, V) ∈ B such that min V = i for t < i, min V = t  for i < t < j and min V = j for t > j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' From the last equality and the inductive  hypothesis, our claim is true for (b, j).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' The theorem is proved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  □  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' An application to the case k = 5  In this section, we prove one of our main results, Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2, that gives an  affirmative answer to Conjecture 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 for k = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' To do this, we explicitly determine  the set B5((3)|d) of all the admissible monomials of weight vector (3)|d for d ⩾ 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' By  combining this result and Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 one gets an upper bound for the dimension  of the kernel of Kameko’s squaring operation in the degree n = 2d+t+u+2d+t+2d−3  with d > 5 and t, u ⩾ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' By using Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 below, we show that this upper  bound is also a lower bound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 (See Walker and Wood [24, Proposition 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Let k ⩾ 3 and  n = �k−2  i=1 (2di − 1) with di positive integers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' If di − di+1 ⩾ 4 for 1 ⩽ i ⩽ k − 3 and  dk−2 ⩾ 5, then  dim(QPk)n ⩾ (k − 1)  �  3⩽i⩽k  (2i − 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1)  From the results of Kameko [3, Theorem 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1] and our work [19, Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1]  we see that if d ⩾ 4, then QP +  3 ((3)|d) = ⟨[(x1x2x3)2d−1](3)|d⟩ and QP +  4 ((3)|d) =  ⟨{[wd,u](3)|d : 1 ⩽ u ⩽ 11}⟩, where wd,u are determined as in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  By applying Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5, we get dim QP 0  5 ((3)|d) =  �5  3  �  + 11  �5  4  �  = 65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' So,  we need only to determine QP +  5 ((3)|d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Let d be an integer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' If d ⩾ 5, then QP +  5 ((3)|d) is an F2-vector space  of dimension 90 with a basis consisting the classes represented by the admissible  monomials ad,t, 1 ⩽ t ⩽ 90, which are determined as in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Consequently,  dim QP5((3)|d) = 155 for any d ⩾ 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  In [20, Proposition 1], we have proved that for any weight vector ω, QPk(ω) is  an GLk-module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Hence, Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 gives a representation of dimension 155 of  the general group GL5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  The theorem is proved by induction on d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' The proof is based on Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  and suitable strongly inadmissible monomials of weight vector (3)|d with 2 ⩽ d ⩽ 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Moreover, to prove the theorem for d = 5, we need to use suitable sets of generators  for QP5((3)|d) with 1 ⩽ d ⩽ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Generating sets for QP5((3)|d) with d ⩽ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' We have  i) B5((3)|1) = {Xα,β : 1 ⩽ α < β ⩽ 5}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Hence, dim QP5((3)|1) = 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  ii) B+  5 ((3)|2) is the set of the monomials a2,t, 1 ⩽ t ⩽ 15, which are determine  as follows:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' x1x2x2  3x2  4x3  5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' x1x2x2  3x3  4x2  5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' x1x2x3  3x2  4x2  5  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' x1x2  2x3x2  4x3  5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' x1x2  2x3x3  4x2  5  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' x1x2  2x2  3x4x3  5  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' x1x2  2x2  3x3  4x5  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' x1x2  2x3  3x4x2  5  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' x1x2  2x3  3x2  4x5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' x1x3  2x3x2  4x2  5  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' x1x3  2x2  3x4x2  5  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' x1x3  2x2  3x2  4x5  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' x3  1x2x3x2  4x2  5  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' x3  1x2x2  3x4x2  5  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' x3  1x2x2  3x2  4x5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Consequently, dim QP5((3)|2) = 55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  THE SQUARING OPERATION AND THE HIT PROBLEM  17  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Let i1, i2, j1, j2 ∈ Nk such that i1 < j1, i2 < j2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  i) If either i1 > i2 or i1 = i2 and j1 > j2, then X2  i1,j1Xi2,j2 is strictly inadmissi-  ble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  ii) If j1 > j2 and i, j ∈ Nk, i < j, then the monomial X4  i1,j1X2  i2,j2Xi,j is strictly  inadmissible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  iii) If either i1 < i2 ⩽ j1 or i1 = i2, j1 ̸= j2, then X4  i1,j1X3  i2,j2 is strictly inad-  missible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  iv) If either i1 < i2 or i1 = i2 and j1 ⩽ j2, then X8  i1,j1X7  i2,j2 is strictly inadmis-  sible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' For simplicity, we prove Part ii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' The others can be proved by a similar  computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  If i1 = i2 = i, then x = X2  i1,j1Xi2,j2 = xj1x2  j2X3  i,j1,j2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' We have  x = x2  j1xj2X3  i,j1,j2 +  �  t̸=i,j1,j2  xj1xj2x4  tX3  i,j1,j2,j + Sq1(xj1xj2X3  i,j1,j2,j).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  This equality shows that x is strictly inadmissible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' By Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='9, x2Xi,j is  also strictly inadmissible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Suppose i1 < i2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Then x = xi1x2  i2x2  j2xj1X3  i1,i2,j1,j2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' We have  xi1x2  i2x2  j2xj1 = xi1xi2x2  j2x2  j1 + xi1x2  i2xj2x2  j1  + Sq1(x2  i1xi2xj2xj1) + Sq2(xi1xi2xj2xj1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  So, by using the Cartan formula, we get  x = xi1xi2x2  j2x2  j1X3  i1,i2,j1,j2 + xi1x2  i2xj2x2  j1X3  i1,i2,j1,j2 + A + B + C,  where  A = x2  i1xi2xj1xj2Sq1(X3  i1,i2,j1,j2) + Sq1(xi1xi2xj1xj2)Sq1(X3  i1,i2,j1,j2),  B = xi1xi2xj1xj2Sq2(X3  i1,i2,j1,j2),  C = Sq1(x2  i1xi2xj1xj2X3  i1,i2,j1,j2) + Sq2(xi1xi2xj1xj2X3  i1,i2,j1,j2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  A simple computation shows that Xi,jA2 ∈ P −  k ((k−2)|3), Xi,jB2 ∈ P −  k ((k−2)|3)+  A+  1 P5 and Xi,jC2 ∈ P −  k ((k − 2)|3) + A+  3 P5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Hence, the monomial x2Xi,j is strictly  inadmissible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  □  Proof of Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' For d = 1, if x ∈ P5((3)|1), then ω(x) = (3)|1 if and  only if x = Xα,β with 1 ⩽ α < β ⩽ 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Since Xα,β is admissible, we see that the  first of Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 is true.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  From the results in Kameko [3, Theorem 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1] and our work [19, Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1],  we have |B+  3 ((3)|2)| = 1 and |B+  4 ((3)|2)| = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Hence, by applying Proposition  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5, we get dim QP 0  5 ((3)|2) =  �5  3  �  + 6  �5  4  �  = 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' So, we need only to determine  QP +  5 ((3)|2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' We can check that if x ∈ P +  5 ((3)|2) and x ̸= a2,t for all t, 1 ⩽ t ⩽ 15,  then x = X2  i1,j1Xi2,j2 with i1 > i2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' By Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2(i), x is inadmissible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  We observe that for 1 ⩽ t ⩽ 15, a2,t = xifi(b2,t) with b2,t an admissible monomial  of degree 8 in P4 and 1 ⩽ i ⩽ 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' By Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='11, a2,t is admissible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' The  proposition is proved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  □  Consider the case d = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' From the results in Kameko [3, Theorem 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1] and our  work [19, Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2], we have |B+  3 ((3)|3)| = 1 and |B+  4 ((3)|3)| = 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' So, by  18  NGUYỄN SUM  using Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5, we get dim QP 0  5 ((3)|3) =  �5  3  �  + 10  �5  4  �  = 60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' We need to  compute QP +  5 ((3)|3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  We denote by A(3) the set of the monomials a3,t, 1 ⩽ t ⩽ 50, which are given in  Section 5 for d = 3 and five monomials:  a3,51 = x3  1x3  2x4  3x4  4x7  5  a3,52 = x3  1x3  2x4  3x7  4x4  5  a3,53 = x3  1x3  2x7  3x4  4x4  5  a3,54 = x3  1x7  2x3  3x4  4x4  5  a3,55 = x7  1x3  2x3  3x4  4x4  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' B+  5 ((3)|3) ⊂ A(3) ∪ C(3), where C(3) is the set of the mono-  mials a3,t, 56 ⩽ t ⩽ 70, which are determined as follows:  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' x1x3  2x5  3x6  4x6  5  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' x1x3  2x6  3x5  4x6  5  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' x1x6  2x3  3x5  4x6  5  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' x3  1x2x5  3x6  4x6  5  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' x3  1x2x6  3x5  4x6  5  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' x3  1x5  2x3x6  4x6  5  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' x3  1x5  2x6  3x4x6  5  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' x3  1x5  2x2  3x5  4x6  5  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' x3  1x3  2x4  3x5  4x6  5  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' x3  1x3  2x5  3x4  4x6  5  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' x3  1x3  2x5  3x6  4x4  5  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' x3  1x4  2x3  3x5  4x6  5  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' x3  1x5  2x3  3x4  4x6  5  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' x3  1x5  2x3  3x6  4x4  5  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' x3  1x5  2x6  3x3  4x4  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  We prepare some lemmas for the proof of this proposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Let w is one of the monomials: x1x6  2x6  3x4, x1x2  2x6  3x5  4, x1x6  2x2  3x5  4,  x1x6  2x3  3x4  4, x3  1x4  2x3x6  4, x3  1x4  2x5  3x2  4, x3  1x5  2x4  3x2  4, x3  1x4  2x3  3x4  4, x3  1x4  2x4  3x3  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Then, the mono-  mial x7  i fi(w), 1 ⩽ i ⩽ 5, is strictly inadmissible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' By using the Cartan formula,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' we have  x1x6  2x6  3x4 = x1x5  2x6  3x2  4 + x1x6  2x5  3x2  4 + Sq1(x2  1x5  2x5  3x4)  + Sq2(x1x5  2x5  3x4) mod(P −  4 ((2)|3)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  x1x2  2x6  3x5  4 = x1x2x6  3x6  4 + x1x2  2x5  3x6  4 + Sq1(x2  1x2x5  3x5  4)  + Sq2(x1x2x5  3x5  4) mod(P −  4 ((2)|3)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  x1x6  2x2  3x5  4 = x1x5  2x2  3x6  4 + x1x6  2x3x6  4 + Sq1(x2  1x5  2x3x5  4)  + Sq2(x1x5  2x3x5  4) mod(P −  4 ((2)|3)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  x1x6  2x3  3x4  4 = x1x3  2x4  3x6  4 + x1x3  2x6  3x4  4 + x1x4  2x3  3x6  4 + x1x4  2x6  3x3  4 + x1x6  2x2  3x5  4  + Sq1(x2  1x5  2x3  3x3  4 + x2  1x3  2x5  3x3  4 + x2  1x3  2x3  3x5  4) + Sq2(x1x5  2x3  3x3  4  + x1x3  2x5  3x3  4 + x1x3  2x3  3x5  4 + x1x6  2x2  3x3  4) mod(P −  4 ((2)|3)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  x3  1x4  2x3x6  4 = x2  1x3  2x4  3x5  4 + x2  1x5  2x4  3x3  4 + x3  1x2  2x4  3x5  4 + x3  1x3  2x4  3x4  4  + Sq1(x3  1x3  2x4  3x3  4 + x3  1x4  2x3x5  4) + Sq2(x2  1x3  2x4  3x3  4 + x5  1x2  2x2  3x3  4)  + Sq4(x3  1x2  2x2  3x3  4) mod(P −  4 ((2)|3)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  x3  1x4  2x5  3x2  4 = x3  1x2  2x5  3x4  4 + x3  1x4  2x3  3x4  4  + Sq2(x5  1x2  2x3  3x2  4) + Sq4(x3  1x2  2x3  3x2  4) mod(P −  4 ((2)|3)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  x3  1x5  2x4  3x2  4 = x3  1x3  2x4  3x4  4 + x3  1x5  2x2  3x4  4  + Sq2(x5  1x3  2x2  3x2  4) + Sq4(x3  1x3  2x2  3x2  4) mod(P −  4 ((2)|3)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  x3  1x4  2x3  3x4  4 = x2  1x3  2x5  3x4  4 + x2  1x5  2x3  3x4  4 + x3  1x3  2x4  3x4  4  + Sq1(x3  1x3  2x3  3x4  4) + Sq2(x2  1x3  2x3  3x4  4) mod(P −  4 ((2)|3)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  x3  1x4  2x4  3x3  4 = x2  1x3  2x4  3x5  4 + x2  1x5  2x4  3x3  4 + x3  1x3  2x4  3x4  4  + Sq1(x3  1x3  2x4  3x3  4) + Sq2(x2  1x3  2x4  3x3  4) mod(P −  4 ((2)|3)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  THE SQUARING OPERATION AND THE HIT PROBLEM  19  From the above equalities we see that there is a positive integer r such that  w = y1 + y2 + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' + yr + Sq1(g1) + Sq2(g2) + Sq4(g3) mod(P −  4 ((2)|3)),  where yt are monomials of weight vector (2)|3 in P4, yt < w with 1 ⩽ t ⩽ r and  g1, g2, g3 are suitable polynomials in P4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Using the Cartan formula and Lemma  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 we get  x7  i fi(w) = x7  i fi(y1) + x7  i fi(y2) + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' + x7  i fi(yr) mod(P −  5 ((3)|3) + A+  3 P5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Since x7  i fi(yt) < x7  i fi(w) for 1 ⩽ t ⩽ r, the monomial x7  i fi(w) is strictly inadmissi-  ble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' The lemma is proved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  □  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  i) The following monomials are strictly inadmissible:  x1x6  2x3  3x6  4x5  5  x1x6  2x6  3x3  4x5  5  x3  1x5  2x5  3x2  4x6  5  x3  1x5  2x5  3x6  4x2  5  x3  1x5  2x6  3x5  4x2  5  x3  1x4  2x5  3x3  4x6  5  x3  1x4  2x5  3x6  4x3  5  x3  1x5  2x4  3x3  4x6  5  x3  1x5  2x4  3x6  4x3  5  x3  1x5  2x6  3x4  4x3  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  ii) The following monomials are strongly inadmissible:  x1x3  2x6  3x6  4x5  5  x3  1x2x6  3x6  4x5  5  x3  1x5  2x6  3x6  4x5  x3  1x5  2x2  3x6  4x5  5  x3  1x5  2x6  3x2  4x5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Based on the Cartan formula we have  x1x6  2x3  3x6  4x5  5 = x1x3  2x5  3x6  4x6  5 + x1x3  2x6  3x5  4x6  5 + x1x3  2x6  3x6  4x5  5 + x1x5  2x3  3x6  4x6  5  + x1x6  2x3  3x5  4x6  5 + Sq1(x2  1x3  2x5  3x5  4x5  5 + x2  1x5  2x3  3x5  4x5  5)  + Sq2(x1x3  2x5  3x5  4x5  5 + x1x5  2x3  3x5  4x5  5) mod(P −  5 ((3)|3)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  x1x6  2x6  3x3  4x5  5 = x1x3  2x5  3x6  4x6  5 + x1x3  2x6  3x5  4x6  5 + x1x3  2x6  3x6  4x5  5 + x1x5  2x6  3x3  4x6  5  + x1x6  2x5  3x3  4x6  5 + Sq1(x2  1x3  2x5  3x5  4x5  5 + x2  1x5  2x5  3x3  4x5  5)  + Sq2(x1x3  2x5  3x5  4x5  5 + x1x5  2x5  3x3  4x5  5) mod(P −  5 ((3)|3)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  x3  1x5  2x5  3x2  4x6  5 = x3  1x3  2x5  3x4  4x6  5 + x3  1x5  2x3  3x4  4x6  5 + Sq1(x3  1x3  2x3  3x4x10  5 )  + Sq2(x5  1x3  2x3  3x2  4x6  5) + Sq4(x3  1x3  2x3  3x2  4x6  5) mod(P −  5 ((3)|3)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  x3  1x5  2x5  3x6  4x2  5 = x3  1x3  2x5  3x6  4x4  5 + x3  1x5  2x3  3x6  4x4  5 + Sq1(x3  1x3  2x3  3x9  4x2  5)  + Sq2(x5  1x3  2x3  3x6  4x2  5) + Sq4(x3  1x3  2x3  3x6  4x2  5) mod(P −  5 ((3)|3)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  x3  1x5  2x6  3x5  4x2  5 = x3  1x3  2x6  3x5  4x4  5 + x3  1x5  2x6  3x3  4x4  5 + Sq1(x3  1x3  2x9  3x3  4x2  5)  + Sq2(x5  1x3  2x6  3x3  4x2  5) + Sq4(x3  1x3  2x6  3x3  4x2  5) mod(P −  5 ((3)|3)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  x3  1x4  2x5  3x3  4x6  5 = x3  1x2  2x5  3x5  4x6  5 + x3  1x4  2x3  3x5  4x6  5 + Sq1(x3  1x2x3  3x3  4x10  5 )  + Sq2(x5  1x2  2x3  3x3  4x6  5) + Sq4(x3  1x2  2x3  3x3  4x6  5) mod(P −  5 ((3)|3)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  x3  1x4  2x5  3x6  4x3  5 = x3  1x2  2x5  3x6  4x5  5 + x3  1x4  2x3  3x6  4x5  5 + Sq1(x3  1x2x3  3x10  4 x3  5)  + Sq2(x5  1x2  2x3  3x6  4x3  5) + Sq4(x3  1x2  2x3  3x6  4x3  5) mod(P −  5 ((3)|3)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  x3  1x5  2x4  3x3  4x6  5 = x3  1x3  2x4  3x5  4x6  5 + x3  1x5  2x2  3x5  4x6  5 + Sq1(x3  1x3  2x3x3  4x10  5 )  + Sq2(x5  1x3  2x2  3x3  4x6  5) + Sq4(x3  1x3  2x2  3x3  4x6  5) mod(P −  5 ((3)|3)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  x3  1x5  2x4  3x6  4x3  5 = x3  1x3  2x4  3x6  4x5  5 + x3  1x5  2x2  3x6  4x5  5 + Sq1(x3  1x3  2x3x10  4 x3  5)  + Sq2(x5  1x3  2x2  3x6  4x3  5) + Sq4(x3  1x3  2x2  3x6  4x3  5) mod(P −  5 ((3)|3)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  x3  1x5  2x6  3x4  4x3  5 = x3  1x3  2x6  3x4  4x5  5 + x3  1x5  2x6  3x2  4x5  5 + Sq1(x3  1x3  2x9  3x2  4x3  5)  20  NGUYỄN SUM  + Sq2(x5  1x3  2x6  3x2  4x3  5) + Sq4(x3  1x3  2x6  3x2  4x3  5) mod(P −  5 ((3)|3)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Part i) follows from the above equalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' We prove Part ii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' For w = x1x3  2x6  3x6  4x5  5,  we have  w = x1x3  2x5  3x6  4x6  5 + x1x3  2x6  3x5  4x6  5 + x1x5  2x5  3x5  4x5  5  + Sq1(x2  1x3  2x5  3x5  4x5  5) + Sq2(x1x3  2x5  3x5  4x5  5) mod(P −  5 ((3)|3)),  where x1x3  2x5  3x6  4x6  5, x1x3  2x6  3x5  4x6  5 < w and x1x5  2x5  3x5  4x5  5 ∈ P(5,21).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Hence, the mono-  mial w is strongly inadmissible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' By a similar computation we have  x3  1x2x6  3x6  4x5  5 = x3  1x2x5  3x6  4x6  5 + x3  1x2x6  3x5  4x6  5 + x5  1x2x5  3x5  4x5  5  + Sq1(x3  1x2  2x5  3x5  4x5  5) + Sq2(x3  1x2x5  3x5  4x5  5) mod(P −  5 ((3)|3)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  x3  1x5  2x6  3x6  4x5 = x3  1x5  2x5  3x6  4x2  5 + x3  1x5  2x6  3x5  4x2  5 + x5  1x5  2x5  3x5  4x5  + Sq1(x3  1x6  2x5  3x5  4x5) + Sq2(x3  1x5  2x5  3x5  4x5) mod(P −  5 ((3)|3)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  x3  1x5  2x2  3x6  4x5  5 = x3  1x5  2x3x6  4x6  5 + x3  1x5  2x2  3x5  4x6  5 + x5  1x5  2x3x5  4x5  5  + Sq1(x3  1x6  2x3x5  4x5  5) + Sq2(x3  1x5  2x3x5  4x5  5) mod(P −  5 ((3)|3)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  x3  1x5  2x6  3x2  4x5  5 = x3  1x5  2x5  3x2  4x6  5 + x3  1x5  2x6  3x4x6  5 + x5  1x5  2x5  3x4x5  5  + Sq1(x3  1x6  2x5  3x4x5  5) + Sq2(x3  1x5  2x5  3x4x5  5) mod(P −  5 ((3)|3)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Since x5  1x2x5  3x5  4x5  5, x5  1x5  2x5  3x5  4x5, x5  1x5  2x3x5  4x5  5, x5  1x5  2x5  3x4x5  5 ∈ P(5,21), Part ii) follows  from the above equalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' The lemma is completely proved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  □  Proof of Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' We can see that if x ∈ P +  5 ((3)|3) and x ̸= a3,t for all  t, 1 ⩽ t ⩽ 70, then either x is one of the monomials as given in Lemmas 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4,  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5, or x is of the form X4  i,jX2  i1,j1Xi2,j2 with i1 > i2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Hence, by Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2(i)  and Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='9, x is inadmissible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' The proposition is proved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  □  Consider the case d = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' From the results in Kameko [3, Theorem 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1] and  our work [19, Propositon 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2], we get |B+  3 ((3)|4)| = 1 and |B+  4 ((3)|4)| = 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' By  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5, dim QP5((3)|4) =  �5  3  �  + 11  �5  4  �  = 65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' We need to determine the  set B+  5 ((3)|4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Denote by A(4) the set of the monomials a4,t, 1 ⩽ t ⩽ 55, which are determined  as in Section 5 for d = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' B+  5 ((3)|4) ⊂ A(4) ∪ C(4), where C(4) is the set of the mono-  mials a4,t, 56 ⩽ t ⩽ 89, which are determined as in Section 5 for d = 4, and the  following monomials:  a4,90 = x3  1x7  2x8  3x13  4 x14  5  a4,91 = x7  1x3  2x8  3x13  4 x14  5  a4,92 = x7  1x7  2x8  3x9  4x14  5  a4,93 = x7  1x7  2x9  3x8  4x14  5  a4,94 = x7  1x7  2x9  3x10  4 x12  5 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  We need the following lemma for the proof of this proposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' If v is one of the monomials: x1x7  2x10  3 x12  4 , x7  1x2x10  3 x12  4 , x3  1x3  2x12  3 x12  4 ,  x3  1x5  2x8  3x14  4 , x3  1x5  2x14  3 x8  4, x7  1x7  2x8  3x8  4, then the monomial x15  i fi(x), 1 ⩽ i ⩽ 5, is strictly  inadmissible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Based on the Cartan formula we have  x1x7  2x10  3 x12  4 = x1x4  2x11  3 x14  4 + x1x6  2x11  3 x12  4 + x1x7  2x8  3x14  4  + Sq1(x2  1x7  2x7  3x13  4 + x2  1x7  2x9  3x11  4 + x2  1x9  2x7  3x11  4 )  THE SQUARING OPERATION AND THE HIT PROBLEM  21  + Sq2(x1x7  2x7  3x13  4 + x1x7  2x9  3x11  4 + x1x9  2x7  3x11  4 )  + Sq4(x1x4  2x7  3x14  4 + x1x6  2x7  3x12  4 ) mod(P −  4 ((2)|4)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  x7  1x2x10  3 x12  4 = x4  1x2x11  3 x14  4 + x6  1x2x11  3 x12  4 + x7  1x2x8  3x14  4  + Sq1(x7  1x2  2x7  3x13  4 + x7  1x2  2x9  3x11  4 + x9  1x2  2x7  3x11  4 )  + Sq2(x7  1x2x7  3x13  4 + x7  1x2x9  3x11  4 + x9  1x2x7  3x11  4 )  + Sq4(x4  1x2x7  3x14  4 + x6  1x2x7  3x12  4 ) mod(P −  4 ((2)|4)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  x3  1x3  2x12  3 x12  4 = x2  1x3  2x12  3 x13  4 + x2  1x5  2x12  3 x11  4 + x2  1x8  2x13  3 x7  4  + Sq1(x3  1x3  2x12  3 x11  4 + x3  1x8  2x11  3 x7  4) + Sq2(x2  1x3  2x12  3 x11  4  + x2  1x8  2x11  3 x7  4) + Sq4(x3  1x4  2x12  3 x7  4) mod(P −  4 ((2)|4)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  x3  1x5  2x8  3x14  4 = x2  1x5  2x9  3x14  4 + x3  1x4  2x9  3x14  4 + Sq1(x3  1x3  2x5  3x18  4  + x3  1x3  2x9  3x14  4 ) + Sq2(x2  1x3  2x9  3x14  4 + x5  1x3  2x6  3x14  4 )  + Sq4(x3  1x3  2x6  3x14  4 ) mod(P −  4 ((2)|4)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  x3  1x5  2x14  3 x8  4 = x2  1x5  2x14  3 x9  4 + x3  1x4  2x14  3 x9  4 + Sq1(x3  1x3  2x14  3 x9  4  + x3  1x3  2x17  3 x6  4) + Sq2(x2  1x3  2x14  3 x9  4 + x5  1x3  2x14  3 x6  4)  + Sq4(x3  1x3  2x14  3 x6  4) mod(P −  4 ((2)|4)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  x7  1x7  2x8  3x8  4 = x4  1x7  2x8  3x11  4 + x4  1x11  2 x8  3x7  4 + x5  1x6  2x8  3x11  4 + x5  1x10  2 x8  3x7  4  + x7  1x6  2x8  3x9  4 + Sq1(x7  1x7  2x8  3x7  4) + Sq2(x7  1x6  2x8  3x7  4)  + Sq4(x4  1x7  2x8  3x7  4 + x5  1x6  2x8  3x7  4) mod(P −  4 ((2)|4)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  From the above equalities we see that there is a positive integer s such that  v = u1 + u2 + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' + us + Sq1(h1) + Sq2(h2) + Sq4(h3) mod(P −  4 ((2)|4)),  where ut are monomials of weight vector (2)|4 in P4, ut < v with 1 ⩽ t ⩽ s and  h1, h2, h3 are suitable polynomials in P4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Using the Cartan formula and Lemma  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 we get  x15  i fi(v) = x15  i fi(u1) + x15  i fi(u2) + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' + x15  i fi(us) mod(P −  5 ((3)|4) + A+  4 P5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Since x15  i fi(ut) < x15  i fi(v) for 1 ⩽ t ⩽ s, the monomial x15  i fi(v) is strictly inadmis-  sible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' The lemma is proved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  □  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='i) The following monomials are strictly inadmissible:  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  ii) The following monomials are strongly inadmissible:  x3  1x5  2x14  3 x11  4 x12  5  x3  1x13  2 x6  3x11  4 x12  5  x3  1x13  2 x7  3x10  4 x12  5  x3  1x13  2 x14  3 x3  4x12  5 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' By a direct computation using the Cartan formula,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' we have  x3  1x5  2x9  3x14  4 x14  5 = x2  1x3  2x13  3 x13  4 x14  5 + x2  1x5  2x11  3 x13  4 x14  5 + x3  1x3  2x12  3 x13  4 x14  5  + x3  1x4  2x11  3 x13  4 x14  5 + Sq1(x3  1x3  2x7  3x13  4 x18  5 + x3  1x3  2x7  3x17  4 x14  5  22  NGUYỄN SUM  + x3  1x3  2x11  3 x13  4 x14  5 ) + Sq2(x2  1x3  2x11  3 x13  4 x14  5 + x5  1x3  2x7  3x14  4 x14  5 )  + Sq4(x3  1x3  2x7  3x14  4 x14  5 ) mod(P −  5 ((3)|4)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  x3  1x5  2x14  3 x9  4x14  5 = x2  1x3  2x13  3 x13  4 x14  5 + x2  1x5  2x13  3 x11  4 x14  5 + x3  1x3  2x13  3 x12  4 x14  5  + x3  1x4  2x13  3 x11  4 x14  5 + Sq1(x3  1x3  2x13  3 x7  4x18  5 + x3  1x3  2x13  3 x11  4 x14  5  + x3  1x3  2x17  3 x7  4x14  5 ) + Sq2(x2  1x3  2x13  3 x11  4 x14  5 + x5  1x3  2x14  3 x7  4x14  5 )  + Sq4(x3  1x3  2x14  3 x7  4x14  5 ) mod(P −  5 ((3)|4)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  x3  1x7  2x11  3 x12  4 x12  5 = x2  1x7  2x11  3 x12  4 x13  5 + x2  1x7  2x13  3 x12  4 x11  5 + x3  1x7  2x12  3 x10  4 x13  5  + x3  1x7  2x10  3 x12  4 x13  5 + Sq1(x3  1x7  2x11  3 x12  4 x12  5 + x3  1x11  2 x9  3x10  4 x11  5 )  + Sq2(x2  1x7  2x11  3 x12  4 x11  5 + x5  1x7  2x10  3 x10  4 x11  5 )  + Sq4(x3  1x7  2x10  3 x10  4 x11  5 ) mod(P −  5 ((3)|4)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 = x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + Sq1(x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 )  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ Sq2(x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 )  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ Sq4(x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 )  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ Sq8(x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ) mod(P −  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ((3)|4)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 = x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + Sq1(x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ Sq2(x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ Sq4(x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ Sq8(x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5) mod(P −  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ((3)|4)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  x3  1x12  2 x3  3x13  4 x14  5 = x2  1x11  2 x5  3x13  4 x14  5 + x2  1x13  2 x3  3x13  4 x14  5 + x3  1x9  2x5  3x14  4 x14  5  + x3  1x11  2 x4  3x13  4 x14  5 + Sq1(x3  1x7  2x3  3x13  4 x18  5 + x3  1x7  2x3  3x17  4 x14  5  + x3  1x11  2 x3  3x13  4 x14  5 ) + Sq2(x2  1x11  2 x3  3x13  4 x14  5 + x5  1x7  2x3  3x14  4 x14  5 )  + Sq4(x3  1x7  2x3  3x14  4 x14  5 ) mod(P −  5 ((3)|4)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  x7  1x3  2x11  3 x12  4 x12  5 = x7  1x2  2x11  3 x12  4 x13  5 + x7  1x2  2x13  3 x12  4 x11  5 + x7  1x3  2x12  3 x10  4 x13  5  + x7  1x3  2x10  3 x12  4 x13  5 + Sq1(x7  1x3  2x11  3 x12  4 x12  5 + x11  1 x3  2x9  3x10  4 x11  5 )  + Sq2(x7  1x2  2x11  3 x12  4 x11  5 + x7  1x5  2x10  3 x10  4 x11  5 )  + Sq4(x7  1x3  2x10  3 x10  4 x11  5 ) mod(P −  5 ((3)|4)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 = x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + Sq1(x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 )  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='THE SQUARING OPERATION AND THE HIT PROBLEM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ Sq2(x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ) + Sq4(x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 )  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ Sq8(x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ) mod(P −  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ((3)|4)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 = x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + Sq1(x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ Sq2(x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5) + Sq4(x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ Sq8(x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5) mod(P −  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ((3)|4)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 = x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ Sq1(x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5) + Sq2(x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5) + Sq4(x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 )  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ Sq8(x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ) mod(P −  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ((3)|4)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  x7  1x9  2x7  3x10  4 x12  5 = x4  1x7  2x11  3 x11  4 x12  5 + x4  1x11  2 x7  3x11  4 x12  5 + x5  1x7  2x11  3 x10  4 x12  5  + x5  1x11  2 x7  3x10  4 x12  5 + x7  1x7  2x8  3x11  4 x12  5 + x7  1x7  2x9  3x10  4 x12  5  + x7  1x8  2x7  3x11  4 x12  5 + Sq1(x7  1x7  2x7  3x11  4 x12  5 ) + Sq2(x7  1x7  2x7  3x10  4 x12  5 )  + Sq4(x4  1x7  2x7  3x11  4 x12  5 + x5  1x7  2x7  3x10  4 x12  5 ) mod(P −  5 ((3)|4)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 = x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x3x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x3x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + Sq1(x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x3x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x3x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x3x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x3x18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x3x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x3x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='24  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='NGUYỄN SUM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ) + Sq2(x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x3x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 )  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ Sq4(x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 )  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ Sq8(x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ) mod(P −  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ((3)|4)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 = x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + Sq1(x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 )  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ Sq2(x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ) + Sq4(x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ) + Sq8(x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ) mod(P −  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ((3)|4)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 = x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + Sq1(x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ Sq2(x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5) + Sq4(x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5) + Sq8(x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5) mod(P −  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ((3)|4)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 = x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ Sq1(x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5) + Sq2(x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ Sq4(x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ Sq8(x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5) mod(P −  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ((3)|4)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Hence Part i) is proved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' We now prove Part ii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' We have  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 = x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + Sq1(x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ Sq2(x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ Sq4(x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5) mod(P −  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ((3)|4)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  THE SQUARING OPERATION AND THE HIT PROBLEM  25  where x5  1x5  2x13  3 x13  4 x9  5 ∈ P(5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='45).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Hence, this equality shows that x3  1x5  2x14  3 x11  4 x12  5  is  strongly inadmissible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + Sq1(x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5) + Sq2(x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ Sq4(x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5) mod(P −  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ((3)|4)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Since x5  1x13  2 x5  3x13  4 x9  5 ∈ P(5,45), the monomial x3  1x13  2 x6  3x11  4 x12  5 is strongly inadmissible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  For w = x3  1x13  2 x7  3x10  4 x12  5 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' we have  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='w = x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + g  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ Sq1(x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ) + Sq2(x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ) + Sq4(x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ) mod(P −  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ((3)|4)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  where  g = x3  1x7  2x9  3x9  4x17  5 + x3  1x9  2x7  3x9  4x17  5 + x3  1x9  2x9  3x7  4x17  5  + x3  1x9  2x9  3x11  4 x13  5 + x3  1x9  2x11  3 x9  4x13  5 + x3  1x11  2 x9  3x9  4x13  5 ∈ P(5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='45).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Hence, w is strongly inadmissible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='NGUYỄN SUM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ Sq1(x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ Sq2(x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ Sq4(x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5) mod(P −  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ((3)|4)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Since x5  1x13  2 x13  3 x5  4x9  5 ∈ P(5,45), the monomial x3  1x13  2 x14  3 x3  4x12  5 is strongly inadmissible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  The lemma is completely proved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  □  Proof of Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Let x ∈ P +  5 ((3)|4) be an admissible monomial, then  x = Xi,jy2 with 1 ⩽ i < j ⩽ k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Since x is admissible, by Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='9, y is  admissible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' We can see that if z ∈ A(3) ∪ C(3) such that Xi,jz2 ∈ P +  5 ((3)|4) and  Xi,jz2 ̸= a4,t for all t, 1 ⩽ t ⩽ 94, then either Xi,jz2 is one of the monomials  as given in Lemmas 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2(iv), 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='7, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='8, or Xi,jz2 is of the form uv2r, where u  is a monomial as given in one of Lemmas 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 and r is a suitable  positive integer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Hence, by Propositions 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4, Xi,jz2 is inadmissible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Since x = Xi,jy2 and y is admissible, we have x = a4,t for some t, 1 ⩽ t ⩽ 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Hence, B+  5 ((3)|4) ⊂ A(4) ∪ C(4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' The proposition follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  □  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Proofs of Theorems 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  By a similar computation as given in the previous lemmas, one get the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  i) The following monomials are strictly inadmissible:  x3  1x7  2x24  3 x29  4 x30  5  x7  1x3  2x24  3 x29  4 x30  5  x7  1x7  2x25  3 x26  4 x28  5  x15  1 x15  2 x17  3 x18  4 x28  5 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  ii) The following monomials are strongly inadmissible:  x3  1x15  2 x21  3 x26  4 x28  5  x15  1 x3  2x21  3 x26  4 x28  5 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' By using the Cartan formula,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' we obtain  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x24  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 = x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + Sq1(x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x38  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x33  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x34  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x37  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x34  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x33  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ) + Sq2(x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x38  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x37  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x34  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x34  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ) + Sq4(x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ) + Sq8(x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ) mod(P −  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ((3)|5)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x24  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 = x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + Sq1(x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x38  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x33  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x34  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='THE SQUARING OPERATION AND THE HIT PROBLEM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x37  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x34  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x33  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ) + Sq2(x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x38  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x37  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x34  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x34  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ) + Sq4(x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 )  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ Sq8(x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ) mod(P −  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ((3)|5)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 = x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x24  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x24  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ Sq1(x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x24  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ) + Sq2(x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x36  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x24  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ) + Sq4(x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 )  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ Sq8(x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ) mod(P −  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ((3)|5)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 = x8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + Sq1(x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 )  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ Sq2(x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ) + Sq4(x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ) + Sq8(x8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ) mod(P −  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ((3)|5)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Part i) follows from the above equalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  We prove Part ii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' We have  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 = x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x24  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x24  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + g1 + Sq1(x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x34  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x34  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='NGUYỄN SUM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x34  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ) + Sq2(x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x33  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ) + Sq4(x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x33  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 )  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ Sq8(x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x24  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ) mod(P −  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ((3)|5)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  where  g1 = x3  1x17  2 x19  3 x27  4 x27  5 + x3  1x19  2 x17  3 x27  4 x27  5 + x3  1x15  2 x17  3 x25  4 x33  5 + x3  1x17  2 x15  3 x25  4 x33  5  + x3  1x17  2 x17  3 x23  4 x33  5 + x3  1x17  2 x17  3 x27  4 x29  5 + x3  1x17  2 x21  3 x25  4 x27  5 + x3  1x21  2 x17  3 x25  4 x27  5  + x3  1x17  2 x21  3 x23  4 x29  5 + x3  1x21  2 x17  3 x23  4 x29  5 ∈ P(5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='93).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Hence, the monomial x3  1x15  2 x21  3 x26  4 x28  5 is strongly inadmissible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  By a similar computation,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' we get  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 = x8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x24  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x24  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + g2 + Sq1(x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x34  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x34  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x34  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ) + Sq2(x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x33  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='THE SQUARING OPERATION AND THE HIT PROBLEM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ) + Sq4(x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x33  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 )  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ Sq8(x8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 + x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x24  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='+ x13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 x26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 x28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ) mod(P −  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5 ((3)|5)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  where  g2 = x15  1 x3  2x17  3 x25  4 x33  5 + x17  1 x3  2x15  3 x25  4 x33  5 + x17  1 x3  2x17  3 x23  4 x33  5 + x17  1 x3  2x17  3 x27  4 x29  5  + x17  1 x3  2x19  3 x27  4 x27  5 + x17  1 x3  2x21  3 x23  4 x29  5 + x17  1 x3  2x21  3 x25  4 x27  5 + x19  1 x3  2x17  3 x27  4 x27  5  + x21  1 x3  2x17  3 x23  4 x29  5 + x21  1 x3  2x17  3 x25  4 x27  5 ∈ P(5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='93).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  The above equalities show that the monomial x15  1 x3  2x21  3 x26  4 x28  5  is strongly inadmis-  sible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' The lemma is completely proved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  □  Proof of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Denote A(d) = {ad,t : 1 ⩽ t ⩽ 55} and C(d) = {ad,t : 56 ⩽  t ⩽ 90}, where ad,t, 1 ⩽ t ⩽ 90, are determined as in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' We prove that  B+  5 ((3)|d) ⊂ A(d) ∪ C(d) by induction on d ⩾ 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Let x ∈ P +  5 ((3)|d) be an admissible monomial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Then, ω(x) = (3)|d and x =  Xi,jy2 with y a monomial in P5((3)|d−1) and 1 ⩽ i < j ⩽ 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Since x is admissible,  by Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='9, y is also admissible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Let d = 5 and z ∈ A(4) ∪ C(4) ∪ B0  5((3)|4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Based on Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='9 we can  check that if Xi,jz2 ∈ P +  5 ((3)|5) and Xi,jz2 ̸= a5,t for all t, 1 ⩽ t ⩽ 90, then  either Xi,jz2 is one of the monomials as given in Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1, or Xi,jz2 is of  the form uv2r, where u is a monomial as given in one of Lemmas 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4,  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='7, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='8, v is a monomial in P5 and r is a suitable integer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Hence, by  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4, Xi,jz2 is inadmissible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Since x = Xi,jy2 is admissible and y ∈  B5((3)|4) ⊂ A(4)∪C(4)∪B0  5((3)|4), we have x = a5,t for some t, 1 ⩽ t ⩽ 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Hence,  B+  5 ((3)|5) ⊂ A(5) ∪ C(5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Suppose d > 5 and B+  5 ((3)|d−1) ⊂ A(d − 1) ∪ C(d − 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Let z ∈ A(d − 1) ∪  C(d − 1) ∪ B0  5((3)|d−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' It is not difficult to check that if Xi,jz2 ∈ P +  5 ((3)|d) and  Xi,jz2 ̸= ad,t for all t, 1 ⩽ t ⩽ 90, then Xi,jz2 is of the form uw2s, where u is  a monomial as given in one of Lemmas 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='7, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='8, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1, w  is a monomial in P5 and s is a suitable integer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' By Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4, Xi,jz2 is  inadmissible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Since x = Xi,jy2 and y is admissible, we have x = ad,t for some  t, 1 ⩽ t ⩽ 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' That means B+  5 ((3)|d) ⊂ A(d) ∪ C(d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Now we prove that the set [A(d)∪C(d)](3)|d is linearly independent in QP5((3)|d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Consider ⟨[A(d)](3)|d⟩ ⊂ QP5((3)|d) and ⟨[C(d)](3)|d⟩ ⊂ QP5((3)|d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' It is easy to see  that for 1 ⩽ t ⩽ 55, ad,t = x2d−1  i  fi(bd,t) with bd,t an admissible monomial of degree  2(2d−1) in P4 and 1 ⩽ i ⩽ 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' By Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='11, ad,t is admissible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' This implies  dim⟨[A(d)](3)|d⟩ = 55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Since ν(ad,t) = 2d − 1 for 1 ⩽ t ⩽ 55 and ν(ad,t) < 2d − 1  for 56 ⩽ t ⩽ 90, we obtain ⟨[A(d)](3)|d⟩ ∩ ⟨[C(d)](3)|d⟩ = {0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Hence, we need only  to prove the set [C(d)](3)|d is linearly independent in QP5((3)|d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Suppose there is  a linear relation  S :=  �  56⩽t⩽90  γtad,t ≡(3)|d 0,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2)  30  NGUYỄN SUM  where γt ∈ F2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' We denote γJ = �  t∈J γt for any J ⊂ {t ∈ N : 56 ⩽ t ⩽ 90}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Let wd,u, 1 ⩽ u ⩽ 11, be as in Section 5 and the homomorphism p(i;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='I) : P5 → P4  which is defined by (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3) for k = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' From our work [9, Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5], we see that  p(i;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='I) passes to a homomorphism from QP5((3)|d) to QP4((3)|d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' By applying p(i;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='j),  1 ⩽ i < j ⩽ 5, to (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2), we obtain  p(1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2)(S) ≡(3)|d γ{58,68}wd,7 + γ62wd,10 ≡(3)|d 0,  p(1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3)(S) ≡(3)|d γ{57,65}wd,6 + γ59wd,7 ≡(3)|d 0,  p(1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4)(S) ≡(3)|d γ{56,61,66,70,72,77}wd,5 + γ60wd,7 ≡(3)|d 0,  p(1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5)(S) ≡(3)|d γ{56,57,58,59,60,62,67,71,73,74,78}wd,4 + γ61wd,7 ≡(3)|d 0,  p(2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3)(S) ≡(3)|d γ{64,65,68,69,76}wd,6 + γ80wd,7 ≡(3)|d 0,  p(2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4)(S) ≡(3)|d γ{63,66,82,83}wd,5 + γ81wd,7 ≡(3)|d 0,  p(2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5)(S) ≡(3)|d γ{63,64,67,80,81,84,85}wd,4 + γ82wd,7 ≡(3)|d 0,  p(3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4)(S) ≡(3)|d γ{75,76,77,79,87,88,89}wd,5 + γ86wd,7 ≡(3)|d 0,  p(3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5)(S) ≡(3)|d γ{75,78,86}wd,4 + γ87wd,7 ≡(3)|d 0,  p(4;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5)(S) ≡(3)|d γ79wd,4 + γ89wd,7 ≡(3)|d 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  From these equalities, we get γ59 = γ60 = γ61 = γ62 = γ79 = γ80 = γ81 = γ82 =  γ86 = γ87 = γ89 = 0, γ65 = γ57, γ68 = γ58, γ78 = γ75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Then, by applying the  homomorphism p(1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='(u,v)), 2 ⩽ u < v ⩽ 4, to (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2), we get  p(1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='(2,3))(S) ≡(3)|d γ64wd,6 + γ69wd,7 + γ76wd,10 ≡(3)|d 0,  p(1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='(2,4))(S) ≡(3)|d γ{56,58,63,66,70,71,72,77,83}wd,5 + γ70wd,7 + γ77wd,10 ≡(3)|d 0,  p(1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='(3,4))(S) ≡(3)|d γ{63,64,67,84,85}wd,3 + γ{56,57,66,69,70,72,73,75,76,77,83,88,90}wd,5  + γ{66,74,83}wd,6 + γ72wd,7 ≡(3)|d 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Computing from these above equalities gives γ64 = γ69 = γ70 = γ72 = γ76 = γ77 = 0  and γ58 = γ57, γ66 = γ56, γ88 = γ75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Now, by applying p(1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='(u,5)), 2 ⩽ u ⩽ 4, to  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2), we obtain  p(1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='(2,5))(S) ≡(3)|d γ{56,57,63,67,71,73,74,75,84,85,90}wd,4 + γ71wd,7 + γ75wd,10 ≡(3)|d 0,  p(1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='(3,5))(S) ≡(3)|d γ{56,63,83}wd,2 + γ{56,57,67,71,73,74,84}wd,4  + γ{67,74,84}wd,6 + γ73wd,7 ≡(3)|d 0,  p(1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='(4,5))(S) ≡(3)|d γ{67,71,73,74,85,90}wd,4 + γ{67,71,73,85,90}wd,5 + γ74wd,7 ≡(3)|d 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  By computing from the above equalities we get γt = 0 for all t, 56 ⩽ t ⩽ 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' The  theorem is proved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  □  We need the following for the proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' The set  B5 = {(I, J ) ∈ PSeq6  5 : X(I,J ) ∈ B5((3)|6)} ⊂ PInc6  5  is compatible with (3)|6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Let (H, K) ∈ PSeq6  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' We prove X(H,K) is of the form (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2) for k = 5 and  B = B5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' We prove the claim by induction on X(H,K) with respect to the order  as given in Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Obviously, this claim is true if X(H,K) is admissible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Suppose X(H,K) is inadmissible and the claim is true for all (U, V) ∈ PSeq6  5 such  THE SQUARING OPERATION AND THE HIT PROBLEM  31  that X(U,V) < X(H,K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' From the proofs of Propositions 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='6 and the  proof of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 we see that X(H,K) = uw2cy2c+d, where u is a monomial of  weight vector (3)|c, y is a monomial of weight vector (3)|e and w is a monomial of  weight vector (3)|d as given in one of Lemmas 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='7, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='8, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Here c, e ⩾ 0, 2 ⩽ d ⩽ 5 and c + d + e = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Hence, there are (H1, K1) ∈ PSeqc  5,  (H2, K2) ∈ PSeqd  5, (H3, K3) ∈ PSeqe  5 such that u = X(H1,K1), w = X(H2,K2),  y = X(H3,K3) and H = H1|H2|H3, K = K1|K2|K3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' From the proofs of Lemmas  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='7, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='8, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1 we see that  w = X(H2,K2) =  �  (S,T )∈Bw  X(S,T ) + g mod(P −  5 ((3)|d) + A+  d P5),  where Bw is a set of suitable pairs (S, T ) ∈ PSeqd  5 such that min S = min H2,  min T ⩽ min K2, X(S,T ) < w and g ∈ P(5,nd) with nd = 3(2d − 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Using the proof  of Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 we obtain  X(H,K) =  �  (S,T )∈Bw  uX2c  (S,T )y2c+d + ug2cy2c+d mod(P −  5 ((3)|6) + A+  6 P5),  where ug2cy2c+d ∈ P(5,n6), uX2c  (S,T )y2c+d = X(U,V) < X(H,K) with U = H1|S|H3,  V = K1|T |K3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Since min S = min H2, min T ⩽ min K2, we have min U = min H,  min V ⩽ min K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' The proposition now follows from the inductive hypothesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  □  Proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Let n = 2d+s+t + 2d+s + 2d − 3 and m = 2s+t + 2s − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' We  have n−5  2  = 2d−1+s+t + 2d−1+s + 2d−2 + 2d−2 − 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' By Theorems 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4 in [19],  if d ⩾ 6, s ⩾ 4 and t ⩾ 4, then  dim(QP5) n−5  2  = (25 − 1) dim(QP4)2s+t+1+2s+1−2 = 3(23 − 1)(24 − 1)(25 − 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Kameko’s squaring operation (�  Sq  0)(5,n) : (QP5)n −→ (QP5) n−5  2  is an epimorphism,  hence by using Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1, we get  4(23 − 1)(24 − 1)(25 − 1) ⩽ dim(QP5)n = dim Ker(�  Sq  0)(5,n) + dim(QP5) n−5  2  = dim Ker(�  Sq  0)(5,n) + 3(23 − 1)(24 − 1)(25 − 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  This implies dim Ker(�  Sq  0)(5,n) ⩾ (23 − 1)(24 − 1)(25 − 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  By Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2, the set B5 ⊂ PInc6  5 is compatible with (3)|6 and |B5| =  |B5((3)|6)| = 155.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' By applying Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3, we obtain  dim Ker(�  Sq  0)(5,n) ⩽ |B5| dim(QP3)m = 155 dim(QP3)m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  From Kameko [3, Theorem 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1], we have dim(QP3)m = 21 for any s, t ⩾ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Hence,  we get  dim Ker(�  Sq  0)(5,n) ⩽ 155 dim(QP3)m  = 155 × 21 = (23 − 1)(24 − 1)(25 − 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Thus, dim Ker(�  Sq  0)(5,n) = (23 − 1)(24 − 1)(25 − 1), for any d ⩾ 6 and s, t ⩾ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' The  theorem is proved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  □  Combining this result and Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='6 in [18] one gets the following, which is  numbered as Corollary 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3 in the introduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  32  NGUYỄN SUM  Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Let n be as in Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' If d ⩾ 6 and s, t ⩾ 4, then  dim(QP5)n = 4(23 − 1)(24 − 1)(25 − 1) = 13020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Consequently, the inequality (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1) is an equality for k = 5 and d ⩾ 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Appendix  In this section, we list the admissible monomials of weight vector (3)d in Pk with  k ⩽ 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  From the results of Kameko [3, Theorem 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1] and our work [19, Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2]  we see that if d ⩾ 4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' then B+  3 ((3)|d) = {(x1x2x3)2d−1} and B+  4 ((3)|d) = {wu =  wd,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='u : 1 ⩽ u ⩽ 11},' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' where  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='w1 = x1x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='w2 = x1x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='w3 = x1x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='w4 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2d−3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='w5 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2d−3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='w6 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='w7 = x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2d−5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='w8 = x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='w9 = x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='w10 = x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2d−3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='w11 = x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x3x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='The sets B4((3)|d) and B0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5((3)|d) are determined by using Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  For any d ⩾ 5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' B+  5 ((3)|d) = {at = ad,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='t : 1 ⩽ t ⩽ 90},' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' where  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a1 = x1x2x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a2 = x1x2x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a3 = x1x2x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a4 = x1x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a5 = x1x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2d−3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a6 = x1x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2d−3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a7 = x1x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a8 = x1x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a9 = x1x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a10 = x1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a11 = x1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a12 = x1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a13 = x1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a14 = x1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a15 = x1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a16 = x1x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x3x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a17 = x1x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x3x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a18 = x1x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x4x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a19 = x1x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x3x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a20 = x1x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a21 = x1x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x2d−3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a22 = x1x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a23 = x1x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a24 = x1x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a25 = x1x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x4x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a26 = x1x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a27 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a28 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a29 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a30 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a31 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a32 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a33 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2d−3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a34 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2d−3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a35 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2d−3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a36 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x3x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a37 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x3x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a38 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a39 = x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2x3x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a40 = x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a41 = x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x2d−3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a42 = x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a43 = x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a44 = x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='THE SQUARING OPERATION AND THE HIT PROBLEM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='33  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a45 = x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x4x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a46 = x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a47 = x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x3x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a48 = x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x3x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a49 = x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2d−3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a50 = x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x3x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a51 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2d−6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a52 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2d−6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a53 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a54 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x2d−6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a55 = x2d−1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x2d−6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a56 = x1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2d−3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a57 = x1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a58 = x1x6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2d−5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a59 = x1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2d−6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a60 = x1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2d−5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a61 = x1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2d−5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a62 = x1x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x2d−3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a63 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2x2d−3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a64 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a65 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a66 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2d−3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a67 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2d−3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a68 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2d−5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a69 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2d−6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a70 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2d−5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a71 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2d−5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a72 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2d−7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a73 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2d−7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a74 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2d−3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a75 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2d−3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x3x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a76 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2d−3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x2d−3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a77 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2d−3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a78 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2d−3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a79 = x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2d−3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x4x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a80 = x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2x2d−6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a81 = x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2x2d−5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a82 = x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2x2d−5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a83 = x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2d−7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a84 = x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2d−7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a85 = x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2x2d−3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a86 = x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2d−5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x3x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a87 = x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2d−5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x3x2d−2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a88 = x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2d−5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3x2d−6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a89 = x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x2d−5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='a90 = x7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='1x11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='2 x2d−11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='x2d−4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='Acknowledgment  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='The first version of this work was written while the author was visiting the  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='Vietnam Institute for Advanced Study in Mathematics (VIASM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' He would like to  thank the VIASM for supporting the visit and hospitality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  The author is very grateful to the referee for his valuable comments and sugges-  tions which helped to improve the quality of the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  References  [1] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Carlisle and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Wood, The boundedness conjecture for the action of the Steen-  rod algebra on polynomials, in: N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Ray and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Walker (ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' ), Adams Memorial Symposium  on Algebraic Topology 2, (Manchester, 1990), in: London Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Lecture Notes Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=',  Cambridge Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Press, Cambridge, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' 176, 1992, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' 203-216, MR1232207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  [2] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Crabb and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Hubbuck, Representations of the homology of BV and the Steenrod  algebra II, in: Algebraic Topology: New Trend in Localization and Periodicity, (Sant Feliu  de Guíxols, 1994), in: Progr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=', Birkh¨auser Verlag, Basel, Switzerland, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' 136, 1996,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' 143-154, MR1397726.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  [3] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Kameko, Products of projective spaces as Steenrod modules, PhD Thesis, The Johns  Hopkins University, ProQuest LLC, Ann Arbor, MI, 1990, 29 pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=', MR2638633.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  [4] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Kameko, Generators of the cohomology of BV4, Toyama University, Japan, Preprint,  2003, 8 pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  [5] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Mothebe and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Uys, Some relations between admissible monomials for the polynomial  algebra, Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' 2015, Art.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' ID 235806, 7 pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=', MR3388909.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  34  NGUYỄN SUM  [6] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Nam, A-générateurs génériques pour l’algèbre polynomiale, Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' 186 (2004)  334-362, MR2073910.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  [7] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Peterson, Generators of H∗(RP ∞ × RP ∞) as a module over the Steenrod algebra,  Abstracts Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' 833 (1987) 55-89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  [8] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Peterson, A-generators for certain polynomial algebras, Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Cambridge Philos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' 105 (1989) 311–312, MR0974987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  [9] Đ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Phúc and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Sum, On the generators of the polynomial algebra as a module over the  Steenrod algebra, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Acad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Paris, Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' I 353 (2015), 1035-1040, MR3419856.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  [10] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Priddy, On characterizing summands in the classifying space of a group, I, Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Jour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' 112 (1990) 737-748, MR1073007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  [11] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Repka and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Selick, On the subalgebra of H∗((RP ∞)n;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' F2) annihilated by Steenrod oper-  ations, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Pure Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Algebra 127 (1998) 273-288, MR1617199.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  [12] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Silverman, Hit polynomials and the canonical anti-automorphism of the Steenrod alge-  bra, Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' 123 (1995) 627-637, MR1254854.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  [13] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Silverman, Hit polynomials and conjugation in the dual Steenrod algebra, Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Cambridge Philos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' 123 (1998) 531-547, MR1607993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  [14] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Silverman and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Singer, On the action of Steenrod squares on polynomial algebras  II, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Pure Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Algebra 98 (1995) 95-103, MR1317001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  [15] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Singer, The transfer in homological algebra, Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Zeit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' 202 (1989) 493-523,  MR1022818.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  [16] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Singer, On the action of the Steenrod squares on polynomial algebras, Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' 111 (1991) 577-583, MR1045150.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  [17] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Steenrod and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Epstein, Cohomology operations, Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' of Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Stud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' 50,  Princeton Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Press, Princeton, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='J 1962, MR0145525.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  [18] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Sum, The negative answer to Kameko’s conjecture on the hit problem, Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' 225  (2010) 2365-2390, MR2680169.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  [19] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Sum, On the Peterson hit problem, Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' 274 (2015) 432-489, MR3318156.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  [20] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Sum, The squaring operation and the Singer algebraic transfer, Vietnam J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' 49  (2021), 1079-1096, MR4319539.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  [21] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Walker and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Wood, Weyl modules and the mod 2 Steenrod algebra, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Algebra  311 (2007) 840-858, MR2314738.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  [22] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Walker and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Wood, Flag modules and the hit problem for the Steenrod algebra,  Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Cambridge Philos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' 147 (2009) 143-171, MR2507313.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  [23] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Walker and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Wood, Polynomials and the mod 2 Steenrod algebra, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' 1: The  Peterson hit problem, London Mathematical Society Lecture Note Series 441, Cambridge  University Press, 2018, MR3729477.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  [24] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Walker and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Wood, Polynomials and the mod 2 Steenrod algebra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Repre-  sentations of GL(n, F2), London Mathematical Society Lecture Note Series, 442.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Cambridge  University Press, 2018, MR3729478.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  [25] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Wood, Steenrod squares of polynomials and the Peterson conjecture, Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Cambridge Phil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' 105 (1989) 307-309, MR0974986.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  [26] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Wood, Problems in the Steenrod algebra, Bull.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' London Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content=' 30 (1998) 449-  517, MR1643834.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='  Department of Mathematics and Applications, Sài Gòn University, 273 An Dương  Vương, District 5, Hồ Chí Minh city, Viet Nam  Email address: nguyensum@sgu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
+page_content='vn' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAzT4oBgHgl3EQfkv0u/content/2301.01535v1.pdf'}
diff --git a/NtAyT4oBgHgl3EQfUPfO/content/tmp_files/2301.00123v1.pdf.txt b/NtAyT4oBgHgl3EQfUPfO/content/tmp_files/2301.00123v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1666702c33ee775fac4efc2746a1375805eebabe
--- /dev/null
+++ b/NtAyT4oBgHgl3EQfUPfO/content/tmp_files/2301.00123v1.pdf.txt
@@ -0,0 +1,1635 @@
+Velocity Laws for Bound States in Asymptotically AdS
+Geometries
+Dimitrios Giataganas
+1 Department of Physics,
+National Sun Yat-sen University,
+Kaohsiung 80424, Taiwan
+2 Center for Theoretical and Computational Physics,
+National Sun Yat-sen University
+Kaohsiung 80424, Taiwan
+3 Physics Division, National Center for Theoretical Sciences,
+Taipei 10617, Taiwan
+dimitrios.giataganas@mail.nsysu.edu.tw
+Abstract
+We study the behavior of heavy quark bound states in moving plasmas that are dual to
+theories with generic non-trivial renormalization group flows interpolating between an AdS
+geometry in the ultraviolet and infrared fixed points with broken symmetries. We investigate
+analytically the observables associated with the bound state and find their scaling exponents
+with respect to the Lorentz factor for ultrarelativistic motion. Despite having asymptotically
+an AdS geometry, the scaling is not universal and depends on geometric conditions of the
+Fefferman-Graham expansion in the near boundary regime, or equivalently on the order of the
+asymptotic background expansion that provides the leading contributions to the Wilson loops.
+arXiv:2301.00123v1  [hep-th]  31 Dec 2022
+
+1
+Introduction
+The Wilson loop operators contain important gauge invariant information about non-perturbative
+physics of gauge field theories. Their expectation value is an order parameter for the confining-
+deconfining phase transitions, where confinement indicates an area law. Additionally the Wilson
+loops above the crossover point of the hadronic state, in the finite temperature strongly coupled
+deconfined plasma state, are related to a number of different observables which have theoretical
+interest and some of them are in principle accessible in heavy ion experiments.
+The expectation values of Wilson loops contain ultraviolet divergences which can be realised
+in the holographic gravity dual theories from the infinite bulk to boundary proper distance
+where the Wilson loop surface extends, while in the field theory can be realized for example,
+as coming from propagators connecting coincident points at loop computations. In holography
+there is a rigorous renormalization formalism [1, 2, 3], established for static Wilson loops, which
+can be realised with the Legendre transform method, or equivalently with the holographic
+renormalization, or with the infinite mass subtraction. The latter scheme not only cancels the
+ultraviolet divergences but contributes certain infrared terms, which can be thought as part of
+the thermal masses of the infinite heavily bound state when the loops are orthogonal. Therefore
+the application of the mass renormalization gives the interaction energy of an extremely massive
+bound state in a strongly coupled environment. Non-static Wilson loops, or boosted static, have
+also been studied and can be thought as corresponding to moving bound states in a thermal
+strongly couple environment. Some of the renormalization schemes have been extended for
+this case successfully, for example [4, 5], despite the complications in the application of the
+mass renormalization due to the interactions of the color charged singlets in strongly coupled
+environments [6].
+It is known that the application of the mass renormalization scheme, leads to a critical value
+of the renormalized Wilson loop expectation value, beyond which the state does not exist. For
+instance, by fixing the scales of the theory, there exists a critical value for the size of the heavy
+quark bound state L, beyond which the bound state seizes to exist and becomes energetically
+non-favourable compared to the free state of its ingredients, the two infinite massive heavy
+quarks. L naturally depends on the scales of the theory and the velocity of motion. It has been
+found holographically that for ultrarelativistic velocities there is a characteristic power that
+the screening length depends on the Lorentz factor γ = 1/
+√
+1 − v2, which for AdS spacetimes
+is 1/4 when expressed in terms of the velocity Lmax ∼
+�
+1 − v2�1/4 [7], while for other type of
+spacetimes takes different values as expected, especially when other dimensionful scales of the
+theory are present [4, 8, 9, 10, 11].
+1
+
+In this work we investigate further the properties of the non-local observables dependence
+on the Lorentz factor and how much the degree of symmetry affect the studies. Our motivation
+is primarily of theoretical interest and our study includes a new type of approach based on
+the properties of the background’s asymptotic expansion, while working on the rest frame
+of the bound state. The holographic theories we consider have a non-trivial renormalization
+group flow.
+Their ultraviolet conformal fixed point is conformal and a Fefferman-Graham
+asymptotic expansion is applicable in the near boundary regime. Moreover, along the flow we
+allow rotational symmetry breaking, as a result the infrared fixed point is allowed in principle
+to have reduced symmetries. We point out that our approach is generic, we do not specify the
+holographic theory and our formalism and results are applicable for any asymptotically AdS
+theory with the mentioned symmetries. Example of such specific holographic theories with
+non-trivial renormalization group flows include [12, 13, 14].
+Our work can also be though to be motivated from recent developments on known strongly
+coupled systems and in particular of the quark-gluon plasma. It has been known for a long time
+that the suppression in the number of J/Ψ mesons [15] may be related to the high transverse
+momenta. Moreover, recent experimental results show that certain hadrons, for example the
+Λ-hyperons, which are produced in noncentral collisions exhibit nonzero spin polarization. This
+implies that the strongly coupled plasma is rotating and precise measurements suggest that it
+is the most vortical fluid observed to date [16]. Holographic dual models that describe such
+fast rotating plasmas, will exhibit breaking of the rotational symmetry due to the rotation at
+least on a plane. Candidates of such theories are ones that have been deformed by relevant
+and marginal operators, which can be still asymptotically AdS, while their infrared fixed point
+has broken symmetry due to a rotation and they can be included in our generic formalism
+as special cases. The Wilson loop scaling analysis in those theories could have extra minor
+computational complication but there is no obvious reason that the velocity dependence on the
+screening length changes for a rotating motion compared to that of a linear motion. In fact
+in the special case of AdS, the holographic analysis for rotating plasmas supports qualitative
+the quarkonium suppression observed in heavy ion collisions for linear and rotating motion in
+the same way. For the spinning bound states in thermal backgrounds their qualitative [6] and
+quantitative [17] dependence of the screening length on the velocity is consistent with the one
+reported for linear boosts. So we expect that our classification on the scaling powers we have
+done in this work applies in the case of rotation as well, with potentially modified classification
+conditions. Recently, there is an extensive effort in holography to understand bound states and
+other aspects of the fast rotating strongly coupled plasmas, for example [6, 18, 19, 20, 21, 22].
+It is worthy to note that the behavior of the critical temperature in presence of rotation has
+2
+
+been investigated with different type of approaches, see for example [23, 24, 25, 26], where the
+vast majority of these studies suggests lower critical temperature for the phase transitions and
+easier melting of the bound states, in agreement with the holographic findings. Notice that
+these observations are also in agreement with computations in strongly coupled theories where
+the rotational symmetry is broken by other mechanisms, for example via the backreaction of
+a strong external field, [27, 13, 28, 29, 30]. This alternatively suggests the breaking of the
+symmetry as one of the dominant causes for the suppression on the heavy quarks and the
+lowering of the critical temperature of the phase transitions.
+In our work we analyze analytically the quantities associated with the heavy bound state
+in the plasma wind for asymptotically AdS theories, and we find their scaling exponents with
+respect to the Lorentz factor for ultrarelativistic motion. Despite the fact that our theories are
+asymptotically AdS, we show that different velocity scaling powers are allowed for the Wilson
+loop observables. The different scalings are associated with different asymptotic background
+conditions we specify. As a result there is no universality in the scalings although the set of the
+scaling values is finite and discrete. Once the background satisfies an asymptotic condition, a
+unique scaling power is determined. The reason that a variety in scalings is possible, is that
+different background conditions correspond to higher order geometric contributions from the
+asymptotic expansion on the observables. In section 2, we rotate and boost the plasma that
+our dipole bound state is placed in order to set up our system in full generality. In section
+3, we examine Wilson lines in general holographic boosted backgrounds, then we apply the
+formalism in the asymptomatically expanded background in the ultrarelativistic limit. The
+observables we study for ultrarelativistic motion receive their leading contribution from the
+near boundary regime. In section 4, we compute the expectation value of the Wilson loop in
+generic holographic boosted spacetimes. Then we take the ultrarelativistic limit and assume
+asymptotically AdS geometries to find how the various quantities scale with the Lorentz factor.
+For instance, for the screening length we find Lmax ∼
+�
+1 − v2� 1
+2k , where k = 1, 2 depending
+on the asymptotic behavior of the metric. We find the conditions of the asymptotic expansion
+that are associated with each scaling power k and discuss their implications.
+2
+Gravitational Background: Rotation and Boost
+Let us assume a space that along the RG flow is allowed to have a potential breaking of
+rotational symmetry in d spatial dimensions, where the SO(d) boundary symmetry is broken
+along the flow to infrared to SO(d − d1) in the (⃗xi) plane and SO(d1) in the ( ⃗xj) plane. To
+set up our system we consider a dipole state of random orientation in the space. We examine
+3
+
+backgrounds of only radial dependence and therefore our analysis can be reduced without any
+loss of generality to a three-spatial dimensional configuration with an isotropic plane x1x2
+preserved along the whole renormalization group flow and a special direction x3 (d1 = 1) that
+breakes the rotational invariance in the bulk.
+The dipole experiences a wind of velocity v
+that lies say in a x1x3-plane, and forms an angle θ with the x3-direction. We align the new
+coordinate system at the orientation of the wind with an application of a rotation coordinate
+transformation of angle θ on x1x3 plane. Then we can perform a boost along the new aligned
+direction of the wind that coincides with one axis to eventually obtain the rotated boosted
+metric
+ds2 =
+˜g00(u)dt2 + ˜g11(u)d˜x2
+1 + ˜g22(u)d˜x2
+2 + ˜g33(u)d˜x2
+3 + ˜guu(u)du2
++2˜g01(u)d˜x0d˜x1 + 2˜g03(u)d˜x0d˜x3 + 2˜g13(u)d˜x1d˜x3 ,
+(2.1)
+where
+˜g00(u) = g00(u) cosh2 η +
+�
+g33(u)c2
+θ + g11(u)s2
+θ
+�
+sinh2 η ,
+˜g11(u) = g11(u)c2
+θ + g33(u)s2
+θ ,
+˜g33(u) = g00(u) sinh2 η +
+�
+g33(u)c2
+θ + g11(u)s2
+θ
+�
+cosh2 η ,
+˜g01(u) = 1
+2(g33(u) − g11(u)) sinh ηs2θ ,
+˜g13(u) = 1
+2(g11(u) − g33(u)) cosh ηs2θ ,
+˜g03(u) = −
+�
+g00(u) + g11(u) sin2 θ + g33(u)c2
+θ
+�
+sinh η cosh η .
+The tildes refer to the boosted rotated background metric and the metric elements ˜g that do
+not appear in the above expressions coincide with the initial holographic background ˜gij = gij.
+The rapidity η is given by the cosh2 η = γ2 = 1/
+�
+1 − v2�
+, where γ is the Lorentz factor and v
+is the velocity of the boost. The setup is particularly convenient to describe the direction of
+the hot wind and the dipole orientation in a generic space-time. For example, the angle θ = 0
+corresponds to having a wind blowing along the x3 direction, boosting therefore the system
+along the special anisotropic direction, while the angle θ = π/2 corresponds to having the wind
+within the transverse x1x2 plane and the boost of the systems happens there. When we refer
+to the dipole orientation is with respect to initial system before any boost and rotation. Notice
+that analysis is in the probe’s rest frame.
+3
+Velocity Laws for Wilson Lines
+Let us start by studying Wilson lines which correspond to free heavy colour charged singlets in
+the wind. To parametrize the string we fix it to the radial gauge while we embed the string of
+4
+
+single boundary endpoint (x1(σ), x3(σ)), taking into account the symmetry of the theory. The
+action reads
+S = −
+1
+2πα′
+�
+dσ
+�
+A0 + A1˜x1′(σ)2 + A3˜x3′(σ)2 + A13˜x1′(σ)˜x3′(σ) .
+(3.1)
+The functions Ai(θ, η, σ) are given by
+A0 = −˜gtt˜guu ,
+A1 = ˜g2
+01 − ˜g00˜g11 ,
+A3 = ˜g2
+03 − ˜g00˜g33 ,
+A13 = 2(˜g01˜g03 − ˜g00˜g13) , (3.2)
+where the metric elements are of the rotated boosted of the metric (2.1). It is straightforward to
+obtain the conjugate momenta Π1 = ∂L/∂˜x′
+1 and Π3 = ∂L/∂˜x′
+3, then we can solve the system
+of the two equations for ˜x′
+1 and ˜x′
+3 to obtain
+˜x′2
+1 =
+4A0(Π3A13 − 2Π1A3)2
+�
+A2
+13 − 4A1A3
+��
+4Π2
+1A3 − 4Π1Π3A13 + A2
+13 + 4A1
+�
+Π2
+3 − A3
+�� ,
+(3.3)
+˜x′2
+3 =
+4A0(Π1A13 − 2Π3A1)2
+�
+A2
+13 − 4A1A3
+��
+4Π2
+1A3 − 4Π1Π3A13 + A2
+13 + 4A1
+�
+Π2
+3 − A3
+�� .
+(3.4)
+The requirement of real solutions for the worldsheet, suggests that the momenta remain real
+along the full string. This imposes the existence of a horizon on the worldsheet, at a critical
+value uc that is given by solving the algebraic equations requiring the numerators and the
+denominators of (3.3), (3.4) to have coinciding zeros
+4A1A3 = A2
+13
+��
+u=uc ,
+Π1 = A13Π3
+2A3
+����
+u=uc
+,
+A13 = 2Π1Π3
+��
+u=uc .
+(3.5)
+Notice the simplicity of the above equations which also leads to a further simplification of the
+expressions of the momenta evaluated at uc
+Π2
+3 = A3
+��
+u=uc ,
+Π2
+1 = A2
+13
+4A3
+����
+u=uc
+.
+(3.6)
+It is useful to express the above conditions in terms of the initial holographic background
+elements, since they take a compact form
+Π2
+3 = −g00
+�
+g33c2
+θ + g11s2
+θ
+���
+u=uc ,
+Π2
+1 = −g00(g11 − g33)2s2
+2θ cosh2 η
+4
+�
+g33c2
+θ + g11s2
+θ
+�
+����
+u=uc
+.
+(3.7)
+Finally, the on-shell action comes by the substitution of (3.3) and (3.4) into the action (3.1)
+and can be written as
+S = −
+1
+2πα′
+�
+dσ
+�
+A0
+�
+A2
+13 − 4A1A3
+�
+A2
+13 + 4A1
+�
+Π2
+3 − A3
+�
++ 4Π2
+1A3 − 4Π1Π3A13
+,
+(3.8)
+which is related to the energy of the system. The system of our equations (3.3) and (3.4) is
+solvable analytically only in certain limits, otherwise a numerical treatment is required. Of
+particular interest is the ultra-relativistic limit, since the regime that plays a leading role is the
+near the boundary where we are allowed to investigate the system perturbatively.
+5
+
+3.1
+Worldsheet Horizon Equation and Conjugate Momenta
+The existence of the string worldsheet horizon is determined by (3.5), the equation can be
+written in the following form
+g11g33
+�
+g00 + v2�
+g33c2
+θ + g11s2
+θ
+��
+·
+��
+g11s2
+θ + g33c2
+θ
+��
+1 − v2��−1 = 0
+��
+u=uc .
+(3.9)
+where we include the denominator in order to comment on the asymptotic behavior of the
+solutions. This is an algebraic equation that determines the uc dependence on the velocity in
+the background under study. Even without knowing the exact background the equation the
+behavior of the criticality in the string worldsheet can be extracted. For zero or low velocity
+v ≃ 0, we have static quarks and the worldsheet critical value uc ≃ uh approaches the black hole
+horizon resulting to straight string solutions. For these velocities we essentially solve (3.9) for
+the blackening factor in g00. The opposite ultra-relativistic limit v → 1, leads the solution of eq.
+(3.9) to the boundary regime in order to compensate the infinity generated by the denominator.
+The equation (3.9) can be solved for g00
+g00 = −v2�
+g33c2
+θ + g11s2
+θ
+���
+u=uc ,
+(3.10)
+which directly simplifies the momenta (3.6)
+Π2
+1 = (g11 − g33)2s2
+2θ v2
+4(1 − v2)
+����
+u=uc
+,
+Π2
+3 =
+�
+g33c2
+θ + g11s2
+θ
+�2v2��
+u=uc ,
+(3.11)
+where the metric elements in the right hand side have still implicit dependence on the velocity
+via the uc solution of the algebraic equation (3.10).
+Nevertheless, from the equations (3.11) suffices to observe that for an isotropic holographic
+renormalization flow, Π1 = 0. To understand this notice that there is a rotation to align the
+direction of the wind along the ˜x3 direction. For isotropic theories, all three directions are
+equivalent, which means that the non-diagonal ˜gxi metric elements vanish and therefore only
+the momentum along the plasma wind is non-zero. At the same time Π3 becomes independent
+of θ and it is never zero for the same reason, after the rotation the wind blows always along the
+direction ˜x3. Moreover, even for a non-trivial anisotropic background when the motion happens
+exclusively along one of the axes x1 or x3 of the initial coordinate system, there is a vanishing
+Π1 momentum along the orthogonal axis, since the direction of the wind is along ˜x3.
+3.2
+Ultra-Relativistic Analysis
+As we have elaborated in the previous section v → 1 implies that uc → (boundary).
+Let
+us assume a space which is asymptotically AdS, and along the RG flow is allowed to have a
+potential breaking of rotational symmetry.
+6
+
+3.2.1
+Asymptotically AdS Renormalization Group Flows
+The near boundary expansion of the original theory takes the form
+ds2 = du
+u2 + γijdxidxj ,
+(3.12)
+with
+γij = 1
+u2
+�
+ηij + u2g(2)
+ij + u4�
+g(4)
+ij + h(4)
+ij log u
+�
++ . . .
+�
+.
+(3.13)
+In order to investigate the expansion in detail and to investigate all the cases let us distinguish
+the two type of motions with respect to the x3 direction.
+Motion for θ ̸= π/2 :
+For a motion outside the transverse plane, θ ̸= π/2, the momentum along ˜x1 reads directly
+from (3.11) without the need of solving the algebraic equation for uc since it is independent of
+it
+Π2
+1 ≃
+�
+g(2)
+11 − g(2)
+33
+�2
+sin2 2θ
+4(1 − v2)
+.
+(3.14)
+In contrast, the momentum along x3 depends on uc, so that (3.10) needs to be solved explicitly
+to give
+u2
+c ≃ 2
+�
+1 − v2�
+A(2)
+5
+,
+(3.15)
+where A(2)
+5
+is defined via
+A(2)
+5
+:= 2g(2)
+00 + g(2)
+11 + g(2)
+33 +
+�
+g(2)
+33 − g(2)
+11
+�
+c2θ .
+(3.16)
+Notice the uc ∼
+√
+1 − v2 dependence which is crucial in what follows and that the (3.15) is
+assumed for now to be regular. For example, if we had a fully isotropic geometry (3.15) would
+have been singular. The substitution of uc in equation (3.11) leads to the following expression
+for the remaining momentum
+Π2
+3 =
+A(2)
+5
+2
+4(1 − v2)2 .
+(3.17)
+The validity of the derived expressions rely on the condition that the expressions are regular
+otherwise higher order terms need to be considered, a case we examine later. To obtain even-
+tually the scaling of the action with the velocity, we substitute the momenta (3.14) and (3.17)
+to (3.8) to obtain
+2πα′Sθ̸= π
+2 ≃ −2
+� uc
+0
+du 1
+u2
+�
+1 −
+u2A(2)
+5
+4(1 − v2)
+�
+.
+(3.18)
+In order to extract the Lorentz factor dependence, we rescale u = us
+�
+1 − v2�1/2 so that we
+extract the v dependence of the critical point uc. Then the ultrarelativistic expansion scales
+7
+
+with the Lorentz factor as
+2πα′Sθ̸= π
+2 ≃ −2
+�
+1 − v2�− 1
+2
+� usc
+0
+dus
+1
+u2s
+�
+1 − 1
+4u2
+sA(2)
+5
+�
+(3.19)
+The action is integrated twice to count the energies of both free moving particles and the upper
+limit ucs is the rescaled worldsheet horizon. It serves as an upper bound in the integration since
+after this point the string is causally disconnected from the boundary. All the v dependence
+has been extracted outside the action and we conclude that Sθ̸= π
+2 ∼
+�
+1 − v2�− 1
+2 , when uc given
+by the equation (3.15) is regular.
+Let us examine backgrounds where the expression (3.15) is singular to show that the leading
+contributions comes from higher orders in the asymptotic expansion. For this to happen the
+holographic background has to satisfy
+A(2)
+5
+= 0 ,
+(3.20)
+which can occur only for a fixed angle θ or for an isotropic background. Let us again work with
+the generic case and for simplicity we assume that the leading leading logarithmic contributions
+are absent, h(4)
+ij = 0, or cancel each other in the expressions. Then the solution of the critical
+point of the worldsheet becomes
+u2
+c =
+√
+2
+√
+1 − v2
+�
+A(4)
+5
+,
+(3.21)
+where we have used the condition (3.20) and we require the above solution to be real. A(4)
+5
+is defined in the same way as A(2)
+5
+in (3.16) but with the next order terms.
+The leading
+contributions in the momenta now are found as
+Π2
+1 =
+�
+g(2)
+33 − g(2)
+11
+�2
+s2
+2θ
+4(1 − v2)
+,
+Π2
+3 =
+A(4)
+5
+2(1 − v2) ,
+(3.22)
+while the action takes the form
+Sθ̸= π
+2 ≃ −
+�
+1 − v2�− 1
+4
+2πα′
+� us
+0
+dus
+1
+us2
+�
+1 − 1
+16
+�
+4A(4)
+5
+−
+�
+g(4)
+00 + g(4)
+33
+�
++ (1 − c4θ)
+�
+g(2)
+33 − g(2)
+11
+�2��
+,
+(3.23)
+where we have rescaled the radial coordinate as us = u
+�
+1 − v2�1/4. We point out, that only the
+leading terms four our study are enough to determine the scaling.
+To summarize the findings so far, for motion with θ ̸= π/2, the free energy scales with the
+Lorentz factor as S ∼
+�
+1 − v2�− 1
+2 as long as the asymptotic condition A(2)
+5
+̸= 0 holds, where
+A(2)
+5
+is given by (3.16). Otherwise, if the background satisfies the above condition for A(2)
+5
+asymptotically, we obtain S ∼
+�
+1 − v2�− 1
+4 .
+8
+
+Motion for θ = π/2 :
+For the motion in the transverse plane, θ = π/2, we deal with more compact expressions.
+Working again in the leading order we obtain from the solution of (3.10) for the uc:
+u2
+c =
+1 − v2
+g(2)
+00 + g(2)
+11
+,
+(3.24)
+which results for the momenta
+Π1 = 0 ,
+Π2
+3 =
+�
+g(2)
+00 + g(2)
+11
+�2
+(1 − v2)2
+.
+(3.25)
+The action (3.8) in the near boundary regime comes by the use of the momenta (3.25) and the
+rescaling u = us
+√
+1 − v2 to isolate the velocity dependence and we obtain
+πα′Sθ= π
+2 ≃ −
+�
+1 − v2�− 1
+2
+� ucs
+0
+dus
+1
+u2s
+�
+1 − u2
+s
+g(2)
+00 + g(2)
+11
+2
+�
+.
+(3.26)
+The leading contribution changes when the equation (3.24) is singular for the holographic
+background. Then the leading order to the Wilson lines will be the next one in the asymptotic
+expansion. In this case the background satisfies
+g(2)
+00 + g(2)
+11 = 0 ,
+(3.27)
+and the worldsheet horizon is found by solving (3.10) and is equal to
+u2
+c ≃
+√
+1 − v2
+�
+g(4)
+00 + g(4)
+11
+.
+(3.28)
+The above expression is valid even with logarithmic terms present, as long as h(4)
+00 = h(4)
+11 .
+However, to simplify the presentation let us consider vanishing logarithmic contributions. The
+momentum Π3 takes the simple form
+Π2
+3 ≃ g(4)
+00 + g(4)
+11
+1 − v2
+.
+(3.29)
+The Lorentz scaling in the action can be found by rescaling u = us
+�
+1 − v2�1/4 where we obtain
+in the near boundary regime the divergent action as
+πα′Sθ= π
+2 ≃ −
+�
+1 − v2�− 1
+4
+� ucs
+0
+dus
+1 − u4
+s
+�
+g(4)
+00 + g(4)
+11
+�
+u2s
+�
+1 − 2u2s
+�
+g(4)
+00 + g(4)
+11
+�� .
+(3.30)
+In summary we find from equations (3.19), (3.23), (3.26) and (3.30), that S scales as S ∼
+�
+1 − v2�− 1
+2k , where k = 1, 2 and depends on the angle of motion and the asymptotic behavior.
+When the leading terms of the asymptotic expansion of the background satisfy (3.20) and (3.27)
+then k = 2 and the scalings read off the equation (3.23) and (3.30), otherwise k = 1 and the
+actions is given asymptotically by (3.19) and (3.26).
+9
+
+4
+Velocity laws for Wilson loops and the Screening Length
+In the previous section we have computed the leading contributions of the velocity for the
+singlets’ motion. In this section we compute the expectation value of the Wilson loop from
+where we read off the velocity dependence for the heavy bound state potential and for the
+screening length. We will apply the mass renormalization scheme, subtracting the free energy
+divergences of the bound state from the infinite masses of the singlets we derived in the previous
+section in order to extract the interaction energy of the bound state. We take the orientation
+of the dipole to be arbitrary with respect to the velocity of the plasma and the ˜xi coordinates.
+For the Wilson loop computation we fix the radial gauge and have the string embedded along
+the spatial directions (x1(u), x2(u), x3(u)). The string has a turning point at u0, and the action
+reads
+S = −
+1
+2πα′
+�
+dσ
+�
+A0 + A1˜x1′(σ)2 + A2˜x2′(σ)2 + A3˜x3′(σ)2 + A13˜x1′(σ)˜x3′(σ) ,
+(4.1)
+where the functions Ai(θ, η, σ) are given by (3.2) and additionally
+A2 = −˜g00˜g22 .
+(4.2)
+We can solve the system of the momenta Π1 = ∂L/∂˜x′
+1, Π2 = ∂L/∂˜x′
+2 and Π3 = ∂L/∂˜x′
+3 with
+respect to the derivatives of the coordinates to get
+˜x′
+1 = 2√A0A2(2Π1A3 − Π3A13)
+�
+−
+�
+A2
+13 − 4A1A3
+�
+D
+,
+˜x′
+2 =
+Π2
+�
+−A0
+�
+A2
+13 − 4A1A3
+�
+√A2D
+,
+(4.3)
+˜x′
+3 = 2√A0A2(2Π3A1 − Π1A13)
+�
+−
+�
+A2
+13 − 4A1A3
+�
+D
+,
+with a common denominator D which reads
+D = A2
+13
+�
+Π2
+2 − A2
+�
++ 4Π1Π3A13A2 − 4
+�
+Π2
+1A2A3 + A1
+�
+A2
+�
+Π2
+3 − A3
+�
++ Π2
+2A3
+��
+.
+(4.4)
+The boundary length of the state is
+(L1, L2, L3) = (Lsθdsφd, Lsθdcφd, Lcθd) ,
+(4.5)
+where (θd, φd) are the bound state orientation angles. To determine it we need to integrate the
+equations (4.3) as
+Li = 2
+� u0
+0
+˜xi dσ .
+(4.6)
+10
+
+By substituting the equations of motion (4.3) to the action (4.1) we can eliminate the derivatives
+and eventually express it in terms of the momenta
+S = − 1
+πα′
+� u0
+0
+dσ
+�
+−A0A2
+�
+A2
+13 − 4A1A3
+�
+D
+.
+(4.7)
+Our aim is to extract the dependence behavior of the interaction energy (4.7) on the Lorentz
+factor for non-trivial holographic renormalization group flows. The turning point of the string
+worldsheet is specified by solving the algebraic equation D = 0 given by the (4.4). The algebraic
+equation simplifies considerably for high and low velocities. At the limit of high velocities where
+our primary interest is, it reads
+g22
+�
+g00 + g33c2
+θ + g11s2
+θ
+��
+g11
+�
+Π2
+3g33 + g2
+00g33 + g00
+�
+Π2
+3 + g2
+33
+�
+c2
+θ
+�
++ g00g33
+�
+Π2
+3 + g2
+11
+�
+s2
+θ
+�
+(1 − v)2
+= 0,
+(4.8)
+with a solution for the turning point u0 that approaches the near boundary regime. So far, we
+have not made any approximations or assumptions and all the expression derived hold for any
+holographic background. To progress further so as to find the explicit velocity dependence, we
+apply the formalism on non-trivial RG holographic flows that are asymptotically AdS. Let us
+split the analysis again with respect to the direction of the wind and the values of angles θ.
+4.1
+Asymptotically AdS Renormalization Group Flows
+Motion for (θ ̸= π/2)
+The state’s boundary length integrals (4.6) in the asymptotic regime of the metric (3.12), after
+some algebra take the compact form
+Li ≃ 2
+� u0
+0
+du Πiu2
+√D0
+�
+�1 + u2
+�
+�si
+A(2)
+5
+4(1 − v2) + ˜si
+�
+g(2)
+33 − g(2)
+11
+�
+s2θ
+2
+√
+1 − v2
+�
+�
+�
+� ,
+(4.9)
+where s1 = s2 = s3/3 = −1 and ˜s1 = ˜s−1
+3
+= Π3/Π1 , ˜s2 = 0
+and the u−independent A(2)
+5
+has been defined in (3.16). Notice that in this section we omit terms in the expansion that will
+be proven to be subleading with the rescalings below. D0 is defined through the asymptotic
+expansion of D as
+D ≃
+4
+u12
+�
+1 − A(2)
+5
+1 − v2 u2 +
+�
+A(2)
+5
+2
+4(1 − v2)2 −
+3
+�
+i=1
+Π2
+i +
+C1
+1 − v2 + C2
+�
+u4
+�
+:=
+4
+u12 D0 ,
+(4.10)
+where Ci are u-independent terms that will be proven subleading in the subsequent analysis.
+The action for the bound state can be found from (4.7) by putting all the expansions together
+and reads
+S ≃ − 1
+πα′
+� u0
+0
+du
+1
+u2√D0
+�
+1 −
+3A(2)
+5
+4(1 − v2)u2
+�
+.
+(4.11)
+11
+
+At this stage we have to impose the natural requirement, [1, 2, 3, 6], to have an action with
+leading divergences that are canceled by the ultraviolet divergence of the infinite massive singlets
+(3.19), and that the momenta increase with the increase of the velocity. To extract the correct
+scaling dependence, we rescale u and Π at the ultrarelativistic limit as u = us
+√
+1 − v2 and
+Πi = Πs,i
+�
+1 − v2�−1. The energy now becomes in the rescaled us coordinates
+S ≃ − 1
+πα′
+1
+√
+1 − v2
+� us0
+0
+dus
+1
+u2s
+√Ds0
+�
+1 − 3A(2)
+5
+4
+u2
+s
+�
+≃ − 1
+πα′
+1
+√
+1 − v2
+� us0
+0
+dus
+�
+1
+u2s
++ A(2)
+5
+4
+�
+(4.12)
+and boundary lengths read from equation (4.9)
+Li ≃ 2
+�
+1 − v2� 1
+2 Πs,i
+� us0
+0
+dus
+u2
+s
+√Ds0
+�
+1 + si
+u2
+sA(2)
+5
+4
+�
+,
+(4.13)
+where notice that Ds0 is obtained from the rescaling in D0 of (4.10) and is v-independent
+Ds0 = 1 − A(2)
+5 u2
+s +
+�
+A(2)
+5
+2
+4
+−
+3
+�
+i=1
+Π2
+s,i
+�
+u4
+s .
+(4.14)
+The action (4.12) indeed has the same ultraviolet asymptotics with the Wilson line action (3.19)
+and the divergences cancel each other as expected.
+Notice that the integrands of Li in equations (4.13) are independent of the Lorentz factor
+and therefore Li ∼ (1 − v2)1/2. The strings under study have a maximum length that depends
+on the scales of the theory and in the ultrarelativistic limit this is obtained by finding the
+maximum possible distance that the bound state exist, merely by the maximization of (4.13).
+The velocity dependence has extracted outside the integrands in (4.13) and the integrals are
+bounded. Therefore the maximum separation between a bound quark-antiquark state, which
+is the screening length for the bound state, scales as Lmax ∼
+�
+1 − v2� 1
+2 .
+Let us assume that there exist a scenario for a certain angle that the condition A(2)
+5
+= 0,
+like the prior analysis of the singlet (3.20). We expect that the leading action divergences scales
+with the Lorentz factor as in (3.23). The asymptotic expansion of D becomes
+D ≃
+4
+u12
+�
+1 + u4
+�
+−
+A(4)
+5
+(1 − v2) −
+3
+�
+i=1
+Π2
+i +
+C1
+1 − v2 + C2
+��
+=
+4
+u12 D0 ,
+(4.15)
+where the Ci terms will be proved subleading and are not the same as in previous expressions
+where we have used the same notation. The boundary length now reads
+Li ≃ 2
+� u0
+0
+du Πiu2
+√D0
+�
+�
+�1 + ˜siu2
+�
+g(2)
+33 − g(2)
+11
+�
+s2θ
+2
+√
+1 − v2
++ u4
+�
+�
+�si
+A(4)
+5
+4(1 − v2) + ˆsi
+�
+g(2)
+33 − g(2)
+11
+�2
+(c4θ − 1)
+8(1 − v2)
+�
+�
+�
+�
+�
+� ,(4.16)
+12
+
+where ˆs1 = ˆs2 = 0 , ˆs3 = 1 and the subleading terms will be proven that do not contribute.
+The action takes the form
+S ≃ − 1
+πα′
+� u0
+0
+du
+1
+u2√D0
+�
+1 −
+3A(4)
+5
+4(1 − v2)u4
+�
+.
+(4.17)
+Acting as in previous cases, we rescale u = us
+�
+1 − v2�1/4 and then Πi needs to be rescaled as
+Πi = Πs,i
+�
+1 − v2�−1/2 to give the energy in the new redial coordinates
+S ≃ − 1
+πα′
+1
+(1 − v2)
+1
+4
+� us0
+0
+dus
+1
+u2s
+√Ds0
+�
+1 − 3A(4)
+5
+4
+u2
+s
+�
+.
+(4.18)
+where
+Ds0 = 1 − A(4)
+5 u4
+s −
+3
+�
+i=1
+Π2
+s,iu4
+s .
+(4.19)
+The leading contributions to the expression of Li close to the boundary become
+Li ≃ 2
+� us0
+0
+dus
+Πs,iu2
+s
+√Ds0
+�
+�
+�1 + u4
+s
+�
+�
+�si
+A6
+4 + ˆsi
+�
+g(2)
+33 − g(2)
+11
+�2
+(c4θ − 1)
+8
+�
+�
+�
+�
+�
+� ,
+(4.20)
+and therefore follows that Lmax ∼
+�
+1 − v2� 1
+4
+provided that the background satisfies A(2)
+5
+= 0
+for a motion along a certain angle and that the contributions of the logarithmic terms in the
+asymptotic expansion cancel each other or vanish.
+Motion for (θ = π/2)
+For motion within the transverse plane, θ = π/2, the computation is along the same lines. The
+asymptotic expansion of D is
+D ≃
+4
+u12
+�
+��1 −
+2
+�
+g(2)
+00 + g(2)
+11
+�
+1 − v2
+u2 +
+�
+�
+�
+�
+g(2)
+00 + g(2)
+11
+�2
+(1 − v2)2
+−
+3
+�
+i=1
+Π2
+i +
+C1
+1 − v2 + C2
+�
+�
+�u4
+�
+�� =
+4
+u12 D0 .
+(4.21)
+The state’s boundary length integrals (4.6) in the asymptotic regime of (3.12), after some
+algebra take the compact form
+Li ≃ 2
+� u0
+0
+du Πiu2
+√D0
+�
+�1 − siu2
+�
+g(2)
+00 + g(2)
+11
+�
+4(1 − v2)
+�
+� ,
+(4.22)
+where s1 = s2 = s3/3 = 1 as defined earlier. The action for the bound state reads
+S ≃ − 1
+πα′
+� u0
+0
+du
+1
+u2√D0
+�
+�
+�1 −
+3
+�
+g(2)
+00 + g(2)
+11
+�
+2(1 − v2)
+u2 +
+3
+�
+g(2)
+00 + g(2)
+11
+�2
+2(1 − v2)2
+u4
+�
+�
+� .
+(4.23)
+13
+
+We require for the action’s ultraviolet-divergences to get cancelled with the divergences of the
+infinite massive singlets (3.26). In the ultrarelativistic limit we rescale u and Πi, u = us
+√
+1 − v2
+and Πi = Πs,i
+�
+1 − v2�−1 to get the action for the bound state in new coordinates
+S ≃ − 1
+πα′
+1
+√
+1 − v2
+� us0
+0
+dus
+1
+u2s
+√Ds0
+�
+1 − 3
+2
+��
+g(2)
+00 + g(2)
+11
+�
+u2
+s +
+�
+g(2)
+00 + g(2)
+11
+�2
+u4
+s
+��
+,
+(4.24)
+extracting the right velocity dependence, where Ds0 in the rescaled coordinates reads
+Ds0 = 1 − 2
+�
+g(2)
+00 + g(2)
+11
+�
+u2
+s +
+�
+g(2)
+00 + g(2)
+11
+�2
+u4
+s −
+3
+�
+i=1
+Π2
+s,iu4
+s .
+(4.25)
+The boundary lengths in the rescaled radial coordinate are equal to
+Li ≃ 2
+�
+1 − v2� 1
+2
+� us0
+0
+dus
+Πi,su2
+s
+√Ds0
+�
+1 − 1
+4siu2
+s
+�
+g(2)
+00 + g(2)
+11
+��
+.
+(4.26)
+Therefore the screening length of the bound state scales as Lmax ∼
+�
+1 − v2� 1
+2 where we again
+observe the half-integer power.
+When the leading contributions come from the next term of the FG expansion we get a
+different power scaling. This happens when the asymptotic expansion of the metric satisfies
+g(2)
+00 = −g(2)
+11 . In this case D takes the form
+D ≃
+4
+u12
+�
+�1 +
+�
+�−
+2
+�
+g(4)
+00 + g(4)
+11
+�
+(1 − v2)
+−
+3
+�
+i=1
+Π2
+i + C2
+�
+�u4
+�
+� =
+4
+u12 D0 ,
+(4.27)
+and Li reads
+Li ≃ 2
+� u0
+0
+du Πiu2
+√D0
+�
+1 − u2ci +
+ki
+(1 − v2)
+�
+,
+(4.28)
+where ki and ci are u-independent terms. As has been mentioned earlier we omit terms that
+will be proven that do not affect the scaling. The action computation gives
+S ≃ − 1
+πα′
+� u0
+0
+du
+1
+u2√D0
+�
+�1 −
+3
+�
+g(4)
+00 + g(4)
+11
+�
+2(1 − v2)
+u2
+�
+� .
+(4.29)
+To extract the right asymptotic of the divergences matching the Wilson line action (3.30) we
+rescale the radial coordinate and the momenta as u = us
+�
+1 − v2�1/4 and Πi = Πs,i
+�
+1 − v2�−1/2.
+The action for the bound state becomes
+S ≃ − 1
+πα′
+1
+(1 − v2)1/4
+� us0
+0
+dus
+1
+u2s
+√Ds0
+�
+�1 −
+3
+�
+g(4)
+00 + g(4)
+11
+�
+2
+u2
+s
+�
+� ,
+(4.30)
+and the boundary length of the bound state scales as
+Li ≃ 2
+�
+1 − v2� 1
+4
+� us0
+0
+dus
+Πs,iu2
+s
+√Ds0
+,
+(4.31)
+14
+
+where the leading contributions of Ds0 are v-independent. Therefore with the same arguing
+we extract the dependence of the screening length to the bound state Lmax ∼
+�
+1 − v2� 1
+4 for
+θ = π/2 and g(2)
+00 = −g(2)
+11 , assuming that the logarithmic terms of the expansion vanish.
+In summary, we find
+Lmax ∼
+�
+1 − v2� 1
+2k
+(4.32)
+where k = 1, 2 depending on the direction of motion and the asymptotic behavior of the metric.
+k = 2 when the background conditions (3.20) and (3.27) are asymptotically satisfied for the
+corresponding direction of motion. Our analysis shows that theories dual to non-trivial RG flows
+which are asymptotically AdS and have a non-trivial renormalization group flow with broken
+rotational symmetry along the flow, are allowed to have bound states with a non-universal
+scaling dependence on the velocity, which we explicitly specify.
+Acknowledgments: The research work of D.G. is supported by the National Science and
+Technology Council (NSTC) of Taiwan with the Young Scholar Columbus Fellowship grant
+110-2636-M-110-008.
+References
+[1] J. M. Maldacena, Wilson loops in large N field theories, Phys.Rev.Lett. 80 (1998)
+4859–4862, [hep-th/9803002].
+[2] N. Drukker, D. J. Gross and H. Ooguri, Wilson loops and minimal surfaces, Phys. Rev.
+D60 (1999) 125006, [hep-th/9904191].
+[3] C.-S. Chu and D. Giataganas, UV-divergences of Wilson Loops for Gauge/Gravity
+Duality, JHEP 0812 (2008) 103, [0810.5729].
+[4] H. Liu, K. Rajagopal and U. A. Wiedemann, Wilson loops in heavy ion collisions and
+their calculation in AdS/CFT, JHEP 0703 (2007) 066, [hep-ph/0612168].
+[5] C.-S. Chu and D. Giataganas, Thermal bath in de Sitter space from holography, Phys.
+Rev. D 96 (2017) 026023, [1608.07431].
+[6] V. Giantsos and D. Giataganas, Holographic nonlocal rotating observables and their
+renormalization, Phys. Rev. D 106 (2022) 126012, [2209.04866].
+[7] H. Liu, K. Rajagopal and U. A. Wiedemann, An AdS/CFT Calculation of Screening in a
+Hot Wind, Phys.Rev.Lett. 98 (2007) 182301, [hep-ph/0607062].
+15
+
+[8] A. V. Sadofyev and Y. Yin, The charmonium dissociation in an “anomalous wind”,
+JHEP 01 (2016) 052, [1510.06760].
+[9] M. Chernicoff, D. Fernandez, D. Mateos and D. Trancanelli, Quarkonium dissociation by
+anisotropy, JHEP 1301 (2013) 170, [1208.2672].
+[10] M. Chernicoff, J. A. Garcia and A. Guijosa, The Energy of a Moving Quark-Antiquark
+Pair in an N=4 SYM Plasma, JHEP 0609 (2006) 068, [hep-th/0607089].
+[11] E. Caceres, M. Natsuume and T. Okamura, Screening length in plasma winds, JHEP
+0610 (2006) 011, [hep-th/0607233].
+[12] D. Mateos and D. Trancanelli, The anisotropic N=4 super Yang-Mills plasma and its
+instabilities, Phys.Rev.Lett. 107 (2011) 101601, [1105.3472].
+[13] D. Giataganas, U. G¨ursoy and J. F. Pedraza, Strongly-coupled anisotropic gauge theories
+and holography, Phys. Rev. Lett. 121 (2018) 121601, [1708.05691].
+[14] C. Hoyos, N. Jokela, J. M. Pen´ın and A. V. Ramallo, Holographic spontaneous
+anisotropy, JHEP 04 (2020) 062, [2001.08218].
+[15] NA50 collaboration, B. Alessandro et al., A New measurement of J/psi suppression in
+Pb-Pb collisions at 158-GeV per nucleon, Eur. Phys. J. C 39 (2005) 335–345,
+[hep-ex/0412036].
+[16] STAR collaboration, L. Adamczyk et al., Global Λ hyperon polarization in nuclear
+collisions: evidence for the most vortical fluid, Nature 548 (2017) 62–65, [1701.06657].
+[17] K. Peeters, J. Sonnenschein and M. Zamaklar, Holographic melting and related properties
+of mesons in a quark gluon plasma, Phys. Rev. D74 (2006) 106008, [hep-th/0606195].
+[18] M. Garbiso and M. Kaminski, Hydrodynamics of simply spinning black holes &
+hydrodynamics for spinning quantum fluids, JHEP 12 (2020) 112, [2007.04345].
+[19] J.-X. Chen and D.-F. Hou, Heavy quark potential and jet quenching parameter in a
+rotating D-instanton background, 2202.00888.
+[20] X. Chen, L. Zhang, D. Li, D. Hou and M. Huang, Gluodynamics and deconfinement
+phase transition under rotation from holography, JHEP 07 (2021) 132, [2010.14478].
+[21] A. A. Golubtsova, E. Gourgoulhon and M. K. Usova, Heavy quarks in rotating plasma via
+holography, Nucl. Phys. B 979 (2022) 115786, [2107.11672].
+16
+
+[22] A. A. Golubtsova and N. S. Tsegel’nik, Probing the holographic model of N = 4 SYM
+rotating quark-gluon plasma, 2211.11722.
+[23] Y. Jiang and J. Liao, Pairing Phase Transitions of Matter under Rotation, Phys. Rev.
+Lett. 117 (2016) 192302, [1606.03808].
+[24] Y. Fujimoto, K. Fukushima and Y. Hidaka, Deconfining Phase Boundary of Rapidly
+Rotating Hot and Dense Matter and Analysis of Moment of Inertia, Phys. Lett. B 816
+(2021) 136184, [2101.09173].
+[25] V. V. Braguta, A. Y. Kotov, D. D. Kuznedelev and A. A. Roenko, Influence of
+relativistic rotation on the confinement-deconfinement transition in gluodynamics, Phys.
+Rev. D 103 (2021) 094515, [2102.05084].
+[26] M. N. Chernodub, Inhomogeneous confining-deconfining phases in rotating plasmas,
+Phys. Rev. D 103 (2021) 054027, [2012.04924].
+[27] D. Giataganas, Probing strongly coupled anisotropic plasma, JHEP 1207 (2012) 031,
+[1202.4436].
+[28] U. Gursoy, Holographic QCD and magnetic fields, Eur. Phys. J. A 57 (2021) 247,
+[2104.02839].
+[29] D. Giataganas, Observables in Strongly Coupled Anisotropic Theories, PoS Corfu2012
+(2013) 122, [1306.1404].
+[30] K. B. Fadafan, D. Giataganas and H. Soltanpanahi, The Imaginary Part of the Static
+Potential in Strongly Coupled Anisotropic Plasma, JHEP 1311 (2013) 107, [1306.2929].
+17
+
diff --git a/NtAyT4oBgHgl3EQfUPfO/content/tmp_files/load_file.txt b/NtAyT4oBgHgl3EQfUPfO/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..67249548e50f0529c19aac9976d02de4dd941fb4
--- /dev/null
+++ b/NtAyT4oBgHgl3EQfUPfO/content/tmp_files/load_file.txt
@@ -0,0 +1,516 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf,len=515
+page_content='Velocity Laws for Bound States in Asymptotically AdS  Geometries  Dimitrios Giataganas  1 Department of Physics,  National Sun Yat-sen University,  Kaohsiung 80424, Taiwan  2 Center for Theoretical and Computational Physics,  National Sun Yat-sen University  Kaohsiung 80424, Taiwan  3 Physics Division, National Center for Theoretical Sciences,  Taipei 10617, Taiwan  dimitrios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='giataganas@mail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='nsysu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='tw  Abstract  We study the behavior of heavy quark bound states in moving plasmas that are dual to  theories with generic non-trivial renormalization group flows interpolating between an AdS  geometry in the ultraviolet and infrared fixed points with broken symmetries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' We investigate  analytically the observables associated with the bound state and find their scaling exponents  with respect to the Lorentz factor for ultrarelativistic motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Despite having asymptotically  an AdS geometry, the scaling is not universal and depends on geometric conditions of the  Fefferman-Graham expansion in the near boundary regime, or equivalently on the order of the  asymptotic background expansion that provides the leading contributions to the Wilson loops.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='00123v1  [hep-th]  31 Dec 2022  1  Introduction  The Wilson loop operators contain important gauge invariant information about non-perturbative  physics of gauge field theories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Their expectation value is an order parameter for the confining-  deconfining phase transitions, where confinement indicates an area law.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Additionally the Wilson  loops above the crossover point of the hadronic state, in the finite temperature strongly coupled  deconfined plasma state, are related to a number of different observables which have theoretical  interest and some of them are in principle accessible in heavy ion experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  The expectation values of Wilson loops contain ultraviolet divergences which can be realised  in the holographic gravity dual theories from the infinite bulk to boundary proper distance  where the Wilson loop surface extends, while in the field theory can be realized for example,  as coming from propagators connecting coincident points at loop computations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' In holography  there is a rigorous renormalization formalism [1, 2, 3], established for static Wilson loops, which  can be realised with the Legendre transform method, or equivalently with the holographic  renormalization, or with the infinite mass subtraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' The latter scheme not only cancels the  ultraviolet divergences but contributes certain infrared terms, which can be thought as part of  the thermal masses of the infinite heavily bound state when the loops are orthogonal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Therefore  the application of the mass renormalization gives the interaction energy of an extremely massive  bound state in a strongly coupled environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Non-static Wilson loops, or boosted static, have  also been studied and can be thought as corresponding to moving bound states in a thermal  strongly couple environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Some of the renormalization schemes have been extended for  this case successfully, for example [4, 5], despite the complications in the application of the  mass renormalization due to the interactions of the color charged singlets in strongly coupled  environments [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  It is known that the application of the mass renormalization scheme, leads to a critical value  of the renormalized Wilson loop expectation value, beyond which the state does not exist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' For  instance, by fixing the scales of the theory, there exists a critical value for the size of the heavy  quark bound state L, beyond which the bound state seizes to exist and becomes energetically  non-favourable compared to the free state of its ingredients, the two infinite massive heavy  quarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' L naturally depends on the scales of the theory and the velocity of motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' It has been  found holographically that for ultrarelativistic velocities there is a characteristic power that  the screening length depends on the Lorentz factor γ = 1/  √  1 − v2, which for AdS spacetimes  is 1/4 when expressed in terms of the velocity Lmax ∼  �  1 − v2�1/4 [7], while for other type of  spacetimes takes different values as expected, especially when other dimensionful scales of the  theory are present [4, 8, 9, 10, 11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  1  In this work we investigate further the properties of the non-local observables dependence  on the Lorentz factor and how much the degree of symmetry affect the studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Our motivation  is primarily of theoretical interest and our study includes a new type of approach based on  the properties of the background’s asymptotic expansion, while working on the rest frame  of the bound state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' The holographic theories we consider have a non-trivial renormalization  group flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  Their ultraviolet conformal fixed point is conformal and a Fefferman-Graham  asymptotic expansion is applicable in the near boundary regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Moreover, along the flow we  allow rotational symmetry breaking, as a result the infrared fixed point is allowed in principle  to have reduced symmetries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' We point out that our approach is generic, we do not specify the  holographic theory and our formalism and results are applicable for any asymptotically AdS  theory with the mentioned symmetries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Example of such specific holographic theories with  non-trivial renormalization group flows include [12, 13, 14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  Our work can also be though to be motivated from recent developments on known strongly  coupled systems and in particular of the quark-gluon plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' It has been known for a long time  that the suppression in the number of J/Ψ mesons [15] may be related to the high transverse  momenta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Moreover, recent experimental results show that certain hadrons, for example the  Λ-hyperons, which are produced in noncentral collisions exhibit nonzero spin polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' This  implies that the strongly coupled plasma is rotating and precise measurements suggest that it  is the most vortical fluid observed to date [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Holographic dual models that describe such  fast rotating plasmas, will exhibit breaking of the rotational symmetry due to the rotation at  least on a plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Candidates of such theories are ones that have been deformed by relevant  and marginal operators, which can be still asymptotically AdS, while their infrared fixed point  has broken symmetry due to a rotation and they can be included in our generic formalism  as special cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' The Wilson loop scaling analysis in those theories could have extra minor  computational complication but there is no obvious reason that the velocity dependence on the  screening length changes for a rotating motion compared to that of a linear motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' In fact  in the special case of AdS, the holographic analysis for rotating plasmas supports qualitative  the quarkonium suppression observed in heavy ion collisions for linear and rotating motion in  the same way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' For the spinning bound states in thermal backgrounds their qualitative [6] and  quantitative [17] dependence of the screening length on the velocity is consistent with the one  reported for linear boosts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' So we expect that our classification on the scaling powers we have  done in this work applies in the case of rotation as well, with potentially modified classification  conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Recently, there is an extensive effort in holography to understand bound states and  other aspects of the fast rotating strongly coupled plasmas, for example [6, 18, 19, 20, 21, 22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  It is worthy to note that the behavior of the critical temperature in presence of rotation has  2  been investigated with different type of approaches, see for example [23, 24, 25, 26], where the  vast majority of these studies suggests lower critical temperature for the phase transitions and  easier melting of the bound states, in agreement with the holographic findings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Notice that  these observations are also in agreement with computations in strongly coupled theories where  the rotational symmetry is broken by other mechanisms, for example via the backreaction of  a strong external field, [27, 13, 28, 29, 30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' This alternatively suggests the breaking of the  symmetry as one of the dominant causes for the suppression on the heavy quarks and the  lowering of the critical temperature of the phase transitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  In our work we analyze analytically the quantities associated with the heavy bound state  in the plasma wind for asymptotically AdS theories, and we find their scaling exponents with  respect to the Lorentz factor for ultrarelativistic motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Despite the fact that our theories are  asymptotically AdS, we show that different velocity scaling powers are allowed for the Wilson  loop observables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' The different scalings are associated with different asymptotic background  conditions we specify.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' As a result there is no universality in the scalings although the set of the  scaling values is finite and discrete.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Once the background satisfies an asymptotic condition, a  unique scaling power is determined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' The reason that a variety in scalings is possible, is that  different background conditions correspond to higher order geometric contributions from the  asymptotic expansion on the observables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' In section 2, we rotate and boost the plasma that  our dipole bound state is placed in order to set up our system in full generality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' In section  3, we examine Wilson lines in general holographic boosted backgrounds, then we apply the  formalism in the asymptomatically expanded background in the ultrarelativistic limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' The  observables we study for ultrarelativistic motion receive their leading contribution from the  near boundary regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' In section 4, we compute the expectation value of the Wilson loop in  generic holographic boosted spacetimes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Then we take the ultrarelativistic limit and assume  asymptotically AdS geometries to find how the various quantities scale with the Lorentz factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  For instance, for the screening length we find Lmax ∼  �  1 − v2� 1  2k , where k = 1, 2 depending  on the asymptotic behavior of the metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' We find the conditions of the asymptotic expansion  that are associated with each scaling power k and discuss their implications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  2  Gravitational Background: Rotation and Boost  Let us assume a space that along the RG flow is allowed to have a potential breaking of  rotational symmetry in d spatial dimensions, where the SO(d) boundary symmetry is broken  along the flow to infrared to SO(d − d1) in the (⃗xi) plane and SO(d1) in the ( ⃗xj) plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' To  set up our system we consider a dipole state of random orientation in the space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' We examine  3  backgrounds of only radial dependence and therefore our analysis can be reduced without any  loss of generality to a three-spatial dimensional configuration with an isotropic plane x1x2  preserved along the whole renormalization group flow and a special direction x3 (d1 = 1) that  breakes the rotational invariance in the bulk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  The dipole experiences a wind of velocity v  that lies say in a x1x3-plane, and forms an angle θ with the x3-direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' We align the new  coordinate system at the orientation of the wind with an application of a rotation coordinate  transformation of angle θ on x1x3 plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Then we can perform a boost along the new aligned  direction of the wind that coincides with one axis to eventually obtain the rotated boosted  metric  ds2 =  ˜g00(u)dt2 + ˜g11(u)d˜x2  1 + ˜g22(u)d˜x2  2 + ˜g33(u)d˜x2  3 + ˜guu(u)du2  +2˜g01(u)d˜x0d˜x1 + 2˜g03(u)d˜x0d˜x3 + 2˜g13(u)d˜x1d˜x3 ,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='1)  where  ˜g00(u) = g00(u) cosh2 η +  �  g33(u)c2  θ + g11(u)s2  θ  �  sinh2 η ,  ˜g11(u) = g11(u)c2  θ + g33(u)s2  θ ,  ˜g33(u) = g00(u) sinh2 η +  �  g33(u)c2  θ + g11(u)s2  θ  �  cosh2 η ,  ˜g01(u) = 1  2(g33(u) − g11(u)) sinh ηs2θ ,  ˜g13(u) = 1  2(g11(u) − g33(u)) cosh ηs2θ ,  ˜g03(u) = −  �  g00(u) + g11(u) sin2 θ + g33(u)c2  θ  �  sinh η cosh η .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  The tildes refer to the boosted rotated background metric and the metric elements ˜g that do  not appear in the above expressions coincide with the initial holographic background ˜gij = gij.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  The rapidity η is given by the cosh2 η = γ2 = 1/  �  1 − v2�  , where γ is the Lorentz factor and v  is the velocity of the boost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' The setup is particularly convenient to describe the direction of  the hot wind and the dipole orientation in a generic space-time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' For example, the angle θ = 0  corresponds to having a wind blowing along the x3 direction, boosting therefore the system  along the special anisotropic direction, while the angle θ = π/2 corresponds to having the wind  within the transverse x1x2 plane and the boost of the systems happens there.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' When we refer  to the dipole orientation is with respect to initial system before any boost and rotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Notice  that analysis is in the probe’s rest frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  3  Velocity Laws for Wilson Lines  Let us start by studying Wilson lines which correspond to free heavy colour charged singlets in  the wind.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' To parametrize the string we fix it to the radial gauge while we embed the string of  4  single boundary endpoint (x1(σ), x3(σ)), taking into account the symmetry of the theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' The  action reads  S = −  1  2πα′  �  dσ  �  A0 + A1˜x1′(σ)2 + A3˜x3′(σ)2 + A13˜x1′(σ)˜x3′(σ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='1)  The functions Ai(θ, η, σ) are given by  A0 = −˜gtt˜guu ,  A1 = ˜g2  01 − ˜g00˜g11 ,  A3 = ˜g2  03 − ˜g00˜g33 ,  A13 = 2(˜g01˜g03 − ˜g00˜g13) , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='2)  where the metric elements are of the rotated boosted of the metric (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' It is straightforward to  obtain the conjugate momenta Π1 = ∂L/∂˜x′  1 and Π3 = ∂L/∂˜x′  3, then we can solve the system  of the two equations for ˜x′  1 and ˜x′  3 to obtain  ˜x′2  1 =  4A0(Π3A13 − 2Π1A3)2  �  A2  13 − 4A1A3  ��  4Π2  1A3 − 4Π1Π3A13 + A2  13 + 4A1  �  Π2  3 − A3  �� ,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='3)  ˜x′2  3 =  4A0(Π1A13 − 2Π3A1)2  �  A2  13 − 4A1A3  ��  4Π2  1A3 − 4Π1Π3A13 + A2  13 + 4A1  �  Π2  3 − A3  �� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='4)  The requirement of real solutions for the worldsheet, suggests that the momenta remain real  along the full string.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' This imposes the existence of a horizon on the worldsheet, at a critical  value uc that is given by solving the algebraic equations requiring the numerators and the  denominators of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='3), (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='4) to have coinciding zeros  4A1A3 = A2  13  ��  u=uc ,  Π1 = A13Π3  2A3  ����  u=uc  ,  A13 = 2Π1Π3  ��  u=uc .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='5)  Notice the simplicity of the above equations which also leads to a further simplification of the  expressions of the momenta evaluated at uc  Π2  3 = A3  ��  u=uc ,  Π2  1 = A2  13  4A3  ����  u=uc  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='6)  It is useful to express the above conditions in terms of the initial holographic background  elements, since they take a compact form  Π2  3 = −g00  �  g33c2  θ + g11s2  θ  ���  u=uc ,  Π2  1 = −g00(g11 − g33)2s2  2θ cosh2 η  4  �  g33c2  θ + g11s2  θ  �  ����  u=uc  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='7)  Finally, the on-shell action comes by the substitution of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='3) and (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='4) into the action (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='1)  and can be written as  S = −  1  2πα′  �  dσ  �  A0  �  A2  13 − 4A1A3  �  A2  13 + 4A1  �  Π2  3 − A3  �  + 4Π2  1A3 − 4Π1Π3A13  ,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='8)  which is related to the energy of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' The system of our equations (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='3) and (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='4) is  solvable analytically only in certain limits, otherwise a numerical treatment is required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Of  particular interest is the ultra-relativistic limit, since the regime that plays a leading role is the  near the boundary where we are allowed to investigate the system perturbatively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='1  Worldsheet Horizon Equation and Conjugate Momenta  The existence of the string worldsheet horizon is determined by (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='5), the equation can be  written in the following form  g11g33  �  g00 + v2�  g33c2  θ + g11s2  θ  �� ��  g11s2  θ + g33c2  θ  ��  1 − v2��−1 = 0  ��  u=uc .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='9)  where we include the denominator in order to comment on the asymptotic behavior of the  solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' This is an algebraic equation that determines the uc dependence on the velocity in  the background under study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Even without knowing the exact background the equation the  behavior of the criticality in the string worldsheet can be extracted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' For zero or low velocity  v ≃ 0, we have static quarks and the worldsheet critical value uc ≃ uh approaches the black hole  horizon resulting to straight string solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' For these velocities we essentially solve (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='9) for  the blackening factor in g00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' The opposite ultra-relativistic limit v → 1, leads the solution of eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='9) to the boundary regime in order to compensate the infinity generated by the denominator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  The equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='9) can be solved for g00  g00 = −v2�  g33c2  θ + g11s2  θ  ���  u=uc ,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='10)  which directly simplifies the momenta (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='6)  Π2  1 = (g11 − g33)2s2  2θ v2  4(1 − v2)  ����  u=uc  ,  Π2  3 =  �  g33c2  θ + g11s2  θ  �2v2��  u=uc ,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='11)  where the metric elements in the right hand side have still implicit dependence on the velocity  via the uc solution of the algebraic equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  Nevertheless, from the equations (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='11) suffices to observe that for an isotropic holographic  renormalization flow, Π1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' To understand this notice that there is a rotation to align the  direction of the wind along the ˜x3 direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' For isotropic theories, all three directions are  equivalent, which means that the non-diagonal ˜gxi metric elements vanish and therefore only  the momentum along the plasma wind is non-zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' At the same time Π3 becomes independent  of θ and it is never zero for the same reason, after the rotation the wind blows always along the  direction ˜x3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Moreover, even for a non-trivial anisotropic background when the motion happens  exclusively along one of the axes x1 or x3 of the initial coordinate system, there is a vanishing  Π1 momentum along the orthogonal axis, since the direction of the wind is along ˜x3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='2  Ultra-Relativistic Analysis  As we have elaborated in the previous section v → 1 implies that uc → (boundary).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  Let  us assume a space which is asymptotically AdS, and along the RG flow is allowed to have a  potential breaking of rotational symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  6  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='1  Asymptotically AdS Renormalization Group Flows  The near boundary expansion of the original theory takes the form  ds2 = du  u2 + γijdxidxj ,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='12)  with  γij = 1  u2  �  ηij + u2g(2)  ij + u4�  g(4)  ij + h(4)  ij log u  �  + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='13)  In order to investigate the expansion in detail and to investigate all the cases let us distinguish  the two type of motions with respect to the x3 direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  Motion for θ ̸= π/2 :  For a motion outside the transverse plane, θ ̸= π/2, the momentum along ˜x1 reads directly  from (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='11) without the need of solving the algebraic equation for uc since it is independent of  it  Π2  1 ≃  �  g(2)  11 − g(2)  33  �2  sin2 2θ  4(1 − v2)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='14)  In contrast, the momentum along x3 depends on uc, so that (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='10) needs to be solved explicitly  to give  u2  c ≃ 2  �  1 − v2�  A(2)  5  ,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='15)  where A(2)  5  is defined via  A(2)  5  := 2g(2)  00 + g(2)  11 + g(2)  33 +  �  g(2)  33 − g(2)  11  �  c2θ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='16)  Notice the uc ∼  √  1 − v2 dependence which is crucial in what follows and that the (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='15) is  assumed for now to be regular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' For example, if we had a fully isotropic geometry (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='15) would  have been singular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' The substitution of uc in equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='11) leads to the following expression  for the remaining momentum  Π2  3 =  A(2)  5  2  4(1 − v2)2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='17)  The validity of the derived expressions rely on the condition that the expressions are regular  otherwise higher order terms need to be considered, a case we examine later.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' To obtain even-  tually the scaling of the action with the velocity, we substitute the momenta (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='14) and (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='17)  to (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='8) to obtain  2πα′Sθ̸= π  2 ≃ −2  � uc  0  du 1  u2  �  1 −  u2A(2)  5  4(1 − v2)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='18)  In order to extract the Lorentz factor dependence, we rescale u = us  �  1 − v2�1/2 so that we  extract the v dependence of the critical point uc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Then the ultrarelativistic expansion scales  7  with the Lorentz factor as  2πα′Sθ̸= π  2 ≃ −2  �  1 − v2�− 1  2  � usc  0  dus  1  u2s  �  1 − 1  4u2  sA(2)  5  �  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='19)  The action is integrated twice to count the energies of both free moving particles and the upper  limit ucs is the rescaled worldsheet horizon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' It serves as an upper bound in the integration since  after this point the string is causally disconnected from the boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' All the v dependence  has been extracted outside the action and we conclude that Sθ̸= π  2 ∼  �  1 − v2�− 1  2 , when uc given  by the equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='15) is regular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  Let us examine backgrounds where the expression (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='15) is singular to show that the leading  contributions comes from higher orders in the asymptotic expansion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' For this to happen the  holographic background has to satisfy  A(2)  5  = 0 ,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='20)  which can occur only for a fixed angle θ or for an isotropic background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Let us again work with  the generic case and for simplicity we assume that the leading leading logarithmic contributions  are absent, h(4)  ij = 0, or cancel each other in the expressions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Then the solution of the critical  point of the worldsheet becomes  u2  c =  √  2  √  1 − v2  �  A(4)  5  ,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='21)  where we have used the condition (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='20) and we require the above solution to be real.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' A(4)  5  is defined in the same way as A(2)  5  in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='16) but with the next order terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  The leading  contributions in the momenta now are found as  Π2  1 =  �  g(2)  33 − g(2)  11  �2  s2  2θ  4(1 − v2)  ,  Π2  3 =  A(4)  5  2(1 − v2) ,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='22)  while the action takes the form  Sθ̸= π  2 ≃ −  �  1 − v2�− 1  4  2πα′  � us  0  dus  1  us2  �  1 − 1  16  �  4A(4)  5  −  �  g(4)  00 + g(4)  33  �  + (1 − c4θ)  �  g(2)  33 − g(2)  11  �2��  ,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='23)  where we have rescaled the radial coordinate as us = u  �  1 − v2�1/4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' We point out, that only the  leading terms four our study are enough to determine the scaling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  To summarize the findings so far, for motion with θ ̸= π/2, the free energy scales with the  Lorentz factor as S ∼  �  1 − v2�− 1  2 as long as the asymptotic condition A(2)  5  ̸= 0 holds, where  A(2)  5  is given by (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Otherwise, if the background satisfies the above condition for A(2)  5  asymptotically, we obtain S ∼  �  1 − v2�− 1  4 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  8  Motion for θ = π/2 :  For the motion in the transverse plane, θ = π/2, we deal with more compact expressions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  Working again in the leading order we obtain from the solution of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='10) for the uc:  u2  c =  1 − v2  g(2)  00 + g(2)  11  ,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='24)  which results for the momenta  Π1 = 0 ,  Π2  3 =  �  g(2)  00 + g(2)  11  �2  (1 − v2)2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='25)  The action (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='8) in the near boundary regime comes by the use of the momenta (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='25) and the  rescaling u = us  √  1 − v2 to isolate the velocity dependence and we obtain  πα′Sθ= π  2 ≃ −  �  1 − v2�− 1  2  � ucs  0  dus  1  u2s  �  1 − u2  s  g(2)  00 + g(2)  11  2  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='26)  The leading contribution changes when the equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='24) is singular for the holographic  background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Then the leading order to the Wilson lines will be the next one in the asymptotic  expansion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' In this case the background satisfies  g(2)  00 + g(2)  11 = 0 ,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='27)  and the worldsheet horizon is found by solving (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='10) and is equal to  u2  c ≃  √  1 − v2  �  g(4)  00 + g(4)  11  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='28)  The above expression is valid even with logarithmic terms present, as long as h(4)  00 = h(4)  11 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  However, to simplify the presentation let us consider vanishing logarithmic contributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' The  momentum Π3 takes the simple form  Π2  3 ≃ g(4)  00 + g(4)  11  1 − v2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='29)  The Lorentz scaling in the action can be found by rescaling u = us  �  1 − v2�1/4 where we obtain  in the near boundary regime the divergent action as  πα′Sθ= π  2 ≃ −  �  1 − v2�− 1  4  � ucs  0  dus  1 − u4  s  �  g(4)  00 + g(4)  11  �  u2s  �  1 − 2u2s  �  g(4)  00 + g(4)  11  �� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='30)  In summary we find from equations (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='19), (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='23), (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='26) and (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='30), that S scales as S ∼  �  1 − v2�− 1  2k , where k = 1, 2 and depends on the angle of motion and the asymptotic behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  When the leading terms of the asymptotic expansion of the background satisfy (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='20) and (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='27)  then k = 2 and the scalings read off the equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='23) and (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='30), otherwise k = 1 and the  actions is given asymptotically by (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='19) and (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='26).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  9  4  Velocity laws for Wilson loops and the Screening Length  In the previous section we have computed the leading contributions of the velocity for the  singlets’ motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' In this section we compute the expectation value of the Wilson loop from  where we read off the velocity dependence for the heavy bound state potential and for the  screening length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' We will apply the mass renormalization scheme, subtracting the free energy  divergences of the bound state from the infinite masses of the singlets we derived in the previous  section in order to extract the interaction energy of the bound state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' We take the orientation  of the dipole to be arbitrary with respect to the velocity of the plasma and the ˜xi coordinates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  For the Wilson loop computation we fix the radial gauge and have the string embedded along  the spatial directions (x1(u), x2(u), x3(u)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' The string has a turning point at u0, and the action  reads  S = −  1  2πα′  �  dσ  �  A0 + A1˜x1′(σ)2 + A2˜x2′(σ)2 + A3˜x3′(σ)2 + A13˜x1′(σ)˜x3′(σ) ,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='1)  where the functions Ai(θ, η, σ) are given by (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='2) and additionally  A2 = −˜g00˜g22 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='2)  We can solve the system of the momenta Π1 = ∂L/∂˜x′  1, Π2 = ∂L/∂˜x′  2 and Π3 = ∂L/∂˜x′  3 with  respect to the derivatives of the coordinates to get  ˜x′  1 = 2√A0A2(2Π1A3 − Π3A13)  �  −  �  A2  13 − 4A1A3  �  D  ,  ˜x′  2 =  Π2  �  −A0  �  A2  13 − 4A1A3  �  √A2D  ,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='3)  ˜x′  3 = 2√A0A2(2Π3A1 − Π1A13)  �  −  �  A2  13 − 4A1A3  �  D  ,  with a common denominator D which reads  D = A2  13  �  Π2  2 − A2  �  + 4Π1Π3A13A2 − 4  �  Π2  1A2A3 + A1  �  A2  �  Π2  3 − A3  �  + Π2  2A3  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='4)  The boundary length of the state is  (L1, L2, L3) = (Lsθdsφd, Lsθdcφd, Lcθd) ,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='5)  where (θd, φd) are the bound state orientation angles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' To determine it we need to integrate the  equations (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='3) as  Li = 2  � u0  0  ˜xi dσ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='6)  10  By substituting the equations of motion (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='3) to the action (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='1) we can eliminate the derivatives  and eventually express it in terms of the momenta  S = − 1  πα′  � u0  0  dσ  �  −A0A2  �  A2  13 − 4A1A3  �  D  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='7)  Our aim is to extract the dependence behavior of the interaction energy (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='7) on the Lorentz  factor for non-trivial holographic renormalization group flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' The turning point of the string  worldsheet is specified by solving the algebraic equation D = 0 given by the (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' The algebraic  equation simplifies considerably for high and low velocities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' At the limit of high velocities where  our primary interest is, it reads  g22  �  g00 + g33c2  θ + g11s2  θ  ��  g11  �  Π2  3g33 + g2  00g33 + g00  �  Π2  3 + g2  33  �  c2  θ  �  + g00g33  �  Π2  3 + g2  11  �  s2  θ  �  (1 − v)2  = 0,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='8)  with a solution for the turning point u0 that approaches the near boundary regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' So far, we  have not made any approximations or assumptions and all the expression derived hold for any  holographic background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' To progress further so as to find the explicit velocity dependence, we  apply the formalism on non-trivial RG holographic flows that are asymptotically AdS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Let us  split the analysis again with respect to the direction of the wind and the values of angles θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='1  Asymptotically AdS Renormalization Group Flows  Motion for (θ ̸= π/2)  The state’s boundary length integrals (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='6) in the asymptotic regime of the metric (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='12), after  some algebra take the compact form  Li ≃ 2  � u0  0  du Πiu2  √D0  �  �1 + u2  �  �si  A(2)  5  4(1 − v2) + ˜si  �  g(2)  33 − g(2)  11  �  s2θ  2  √  1 − v2  �  �  �  � ,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='9)  where s1 = s2 = s3/3 = −1 and ˜s1 = ˜s−1  3  = Π3/Π1 , ˜s2 = 0  and the u−independent A(2)  5  has been defined in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Notice that in this section we omit terms in the expansion that will  be proven to be subleading with the rescalings below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' D0 is defined through the asymptotic  expansion of D as  D ≃  4  u12  �  1 − A(2)  5  1 − v2 u2 +  �  A(2)  5  2  4(1 − v2)2 −  3  �  i=1  Π2  i +  C1  1 − v2 + C2  �  u4  �  :=  4  u12 D0 ,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='10)  where Ci are u-independent terms that will be proven subleading in the subsequent analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  The action for the bound state can be found from (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='7) by putting all the expansions together  and reads  S ≃ − 1  πα′  � u0  0  du  1  u2√D0  �  1 −  3A(2)  5  4(1 − v2)u2  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='11)  11  At this stage we have to impose the natural requirement, [1, 2, 3, 6], to have an action with  leading divergences that are canceled by the ultraviolet divergence of the infinite massive singlets  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='19), and that the momenta increase with the increase of the velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' To extract the correct  scaling dependence, we rescale u and Π at the ultrarelativistic limit as u = us  √  1 − v2 and  Πi = Πs,i  �  1 − v2�−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' The energy now becomes in the rescaled us coordinates  S ≃ − 1  πα′  1  √  1 − v2  � us0  0  dus  1  u2s  √Ds0  �  1 − 3A(2)  5  4  u2  s  �  ≃ − 1  πα′  1  √  1 − v2  � us0  0  dus  �  1  u2s  + A(2)  5  4  �  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='12)  and boundary lengths read from equation (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='9)  Li ≃ 2  �  1 − v2� 1  2 Πs,i  � us0  0  dus  u2  s  √Ds0  �  1 + si  u2  sA(2)  5  4  �  ,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='13)  where notice that Ds0 is obtained from the rescaling in D0 of (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='10) and is v-independent  Ds0 = 1 − A(2)  5 u2  s +  �  A(2)  5  2  4  −  3  �  i=1  Π2  s,i  �  u4  s .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='14)  The action (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='12) indeed has the same ultraviolet asymptotics with the Wilson line action (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='19)  and the divergences cancel each other as expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  Notice that the integrands of Li in equations (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='13) are independent of the Lorentz factor  and therefore Li ∼ (1 − v2)1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' The strings under study have a maximum length that depends  on the scales of the theory and in the ultrarelativistic limit this is obtained by finding the  maximum possible distance that the bound state exist, merely by the maximization of (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  The velocity dependence has extracted outside the integrands in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='13) and the integrals are  bounded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Therefore the maximum separation between a bound quark-antiquark state, which  is the screening length for the bound state, scales as Lmax ∼  �  1 − v2� 1  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  Let us assume that there exist a scenario for a certain angle that the condition A(2)  5  = 0,  like the prior analysis of the singlet (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' We expect that the leading action divergences scales  with the Lorentz factor as in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='23).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' The asymptotic expansion of D becomes  D ≃  4  u12  �  1 + u4  �  −  A(4)  5  (1 − v2) −  3  �  i=1  Π2  i +  C1  1 − v2 + C2  ��  =  4  u12 D0 ,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='15)  where the Ci terms will be proved subleading and are not the same as in previous expressions  where we have used the same notation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' The boundary length now reads  Li ≃ 2  � u0  0  du Πiu2  √D0  �  �  �1 + ˜siu2  �  g(2)  33 − g(2)  11  �  s2θ  2  √  1 − v2  + u4  �  �  �si  A(4)  5  4(1 − v2) + ˆsi  �  g(2)  33 − g(2)  11  �2  (c4θ − 1)  8(1 − v2)  �  �  �  �  �  � ,(4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='16)  12  where ˆs1 = ˆs2 = 0 , ˆs3 = 1 and the subleading terms will be proven that do not contribute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  The action takes the form  S ≃ − 1  πα′  � u0  0  du  1  u2√D0  �  1 −  3A(4)  5  4(1 − v2)u4  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='17)  Acting as in previous cases, we rescale u = us  �  1 − v2�1/4 and then Πi needs to be rescaled as  Πi = Πs,i  �  1 − v2�−1/2 to give the energy in the new redial coordinates  S ≃ − 1  πα′  1  (1 − v2)  1  4  � us0  0  dus  1  u2s  √Ds0  �  1 − 3A(4)  5  4  u2  s  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='18)  where  Ds0 = 1 − A(4)  5 u4  s −  3  �  i=1  Π2  s,iu4  s .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='19)  The leading contributions to the expression of Li close to the boundary become  Li ≃ 2  � us0  0  dus  Πs,iu2  s  √Ds0  �  �  �1 + u4  s  �  �  �si  A6  4 + ˆsi  �  g(2)  33 − g(2)  11  �2  (c4θ − 1)  8  �  �  �  �  �  � ,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='20)  and therefore follows that Lmax ∼  �  1 − v2� 1  4  provided that the background satisfies A(2)  5  = 0  for a motion along a certain angle and that the contributions of the logarithmic terms in the  asymptotic expansion cancel each other or vanish.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  Motion for (θ = π/2)  For motion within the transverse plane, θ = π/2, the computation is along the same lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' The  asymptotic expansion of D is  D ≃  4  u12  �  ��1 −  2  �  g(2)  00 + g(2)  11  �  1 − v2  u2 +  �  �  �  �  g(2)  00 + g(2)  11  �2  (1 − v2)2  −  3  �  i=1  Π2  i +  C1  1 − v2 + C2  �  �  �u4  �  �� =  4  u12 D0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='21)  The state’s boundary length integrals (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='6) in the asymptotic regime of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='12), after some  algebra take the compact form  Li ≃ 2  � u0  0  du Πiu2  √D0  �  �1 − siu2  �  g(2)  00 + g(2)  11  �  4(1 − v2)  �  � ,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='22)  where s1 = s2 = s3/3 = 1 as defined earlier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' The action for the bound state reads  S ≃ − 1  πα′  � u0  0  du  1  u2√D0  �  �  �1 −  3  �  g(2)  00 + g(2)  11  �  2(1 − v2)  u2 +  3  �  g(2)  00 + g(2)  11  �2  2(1 − v2)2  u4  �  �  � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='23)  13  We require for the action’s ultraviolet-divergences to get cancelled with the divergences of the  infinite massive singlets (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='26).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' In the ultrarelativistic limit we rescale u and Πi, u = us  √  1 − v2  and Πi = Πs,i  �  1 − v2�−1 to get the action for the bound state in new coordinates  S ≃ − 1  πα′  1  √  1 − v2  � us0  0  dus  1  u2s  √Ds0  �  1 − 3  2  ��  g(2)  00 + g(2)  11  �  u2  s +  �  g(2)  00 + g(2)  11  �2  u4  s  ��  ,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='24)  extracting the right velocity dependence, where Ds0 in the rescaled coordinates reads  Ds0 = 1 − 2  �  g(2)  00 + g(2)  11  �  u2  s +  �  g(2)  00 + g(2)  11  �2  u4  s −  3  �  i=1  Π2  s,iu4  s .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='25)  The boundary lengths in the rescaled radial coordinate are equal to  Li ≃ 2  �  1 − v2� 1  2  � us0  0  dus  Πi,su2  s  √Ds0  �  1 − 1  4siu2  s  �  g(2)  00 + g(2)  11  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='26)  Therefore the screening length of the bound state scales as Lmax ∼  �  1 − v2� 1  2 where we again  observe the half-integer power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  When the leading contributions come from the next term of the FG expansion we get a  different power scaling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' This happens when the asymptotic expansion of the metric satisfies  g(2)  00 = −g(2)  11 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' In this case D takes the form  D ≃  4  u12  �  �1 +  �  �−  2  �  g(4)  00 + g(4)  11  �  (1 − v2)  −  3  �  i=1  Π2  i + C2  �  �u4  �  � =  4  u12 D0 ,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='27)  and Li reads  Li ≃ 2  � u0  0  du Πiu2  √D0  �  1 − u2ci +  ki  (1 − v2)  �  ,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='28)  where ki and ci are u-independent terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' As has been mentioned earlier we omit terms that  will be proven that do not affect the scaling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' The action computation gives  S ≃ − 1  πα′  � u0  0  du  1  u2√D0  �  �1 −  3  �  g(4)  00 + g(4)  11  �  2(1 − v2)  u2  �  � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='29)  To extract the right asymptotic of the divergences matching the Wilson line action (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='30) we  rescale the radial coordinate and the momenta as u = us  �  1 − v2�1/4 and Πi = Πs,i  �  1 − v2�−1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  The action for the bound state becomes  S ≃ − 1  πα′  1  (1 − v2)1/4  � us0  0  dus  1  u2s  √Ds0  �  �1 −  3  �  g(4)  00 + g(4)  11  �  2  u2  s  �  � ,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='30)  and the boundary length of the bound state scales as  Li ≃ 2  �  1 − v2� 1  4  � us0  0  dus  Πs,iu2  s  √Ds0  ,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='31)  14  where the leading contributions of Ds0 are v-independent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Therefore with the same arguing  we extract the dependence of the screening length to the bound state Lmax ∼  �  1 − v2� 1  4 for  θ = π/2 and g(2)  00 = −g(2)  11 , assuming that the logarithmic terms of the expansion vanish.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  In summary, we find  Lmax ∼  �  1 − v2� 1  2k  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='32)  where k = 1, 2 depending on the direction of motion and the asymptotic behavior of the metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  k = 2 when the background conditions (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='20) and (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='27) are asymptotically satisfied for the  corresponding direction of motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Our analysis shows that theories dual to non-trivial RG flows  which are asymptotically AdS and have a non-trivial renormalization group flow with broken  rotational symmetry along the flow, are allowed to have bound states with a non-universal  scaling dependence on the velocity, which we explicitly specify.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  Acknowledgments: The research work of D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' is supported by the National Science and  Technology Council (NSTC) of Taiwan with the Young Scholar Columbus Fellowship grant  110-2636-M-110-008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  References  [1] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Maldacena, Wilson loops in large N field theories, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' 80 (1998)  4859–4862, [hep-th/9803002].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  [2] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Drukker, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Gross and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Ooguri, Wilson loops and minimal surfaces, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  D60 (1999) 125006, [hep-th/9904191].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  [3] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Chu and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Giataganas, UV-divergences of Wilson Loops for Gauge/Gravity  Duality, JHEP 0812 (2008) 103, [0810.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='5729].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  [4] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Liu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Rajagopal and U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Wiedemann, Wilson loops in heavy ion collisions and  their calculation in AdS/CFT, JHEP 0703 (2007) 066, [hep-ph/0612168].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  [5] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Chu and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Giataganas, Thermal bath in de Sitter space from holography, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' D 96 (2017) 026023, [1608.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='07431].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  [6] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Giantsos and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Giataganas, Holographic nonlocal rotating observables and their  renormalization, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' D 106 (2022) 126012, [2209.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='04866].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  [7] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Liu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Rajagopal and U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Wiedemann, An AdS/CFT Calculation of Screening in a  Hot Wind, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' 98 (2007) 182301, [hep-ph/0607062].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  15  [8] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Sadofyev and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Yin, The charmonium dissociation in an “anomalous wind”,  JHEP 01 (2016) 052, [1510.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='06760].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  [9] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Chernicoff, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Fernandez, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Mateos and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Trancanelli, Quarkonium dissociation by  anisotropy, JHEP 1301 (2013) 170, [1208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='2672].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  [10] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Chernicoff, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Garcia and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Guijosa, The Energy of a Moving Quark-Antiquark  Pair in an N=4 SYM Plasma, JHEP 0609 (2006) 068, [hep-th/0607089].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  [11] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Caceres, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Natsuume and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Okamura, Screening length in plasma winds, JHEP  0610 (2006) 011, [hep-th/0607233].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  [12] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Mateos and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Trancanelli, The anisotropic N=4 super Yang-Mills plasma and its  instabilities, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' 107 (2011) 101601, [1105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='3472].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  [13] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Giataganas, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' G¨ursoy and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Pedraza, Strongly-coupled anisotropic gauge theories  and holography, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' 121 (2018) 121601, [1708.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='05691].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  [14] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Hoyos, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Jokela, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Pen´ın and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Ramallo, Holographic spontaneous  anisotropy, JHEP 04 (2020) 062, [2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='08218].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  [15] NA50 collaboration, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Alessandro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=', A New measurement of J/psi suppression in  Pb-Pb collisions at 158-GeV per nucleon, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' C 39 (2005) 335–345,  [hep-ex/0412036].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  [16] STAR collaboration, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Adamczyk et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=', Global Λ hyperon polarization in nuclear  collisions: evidence for the most vortical fluid, Nature 548 (2017) 62–65, [1701.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='06657].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  [17] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Peeters, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Sonnenschein and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Zamaklar, Holographic melting and related properties  of mesons in a quark gluon plasma, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' D74 (2006) 106008, [hep-th/0606195].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  [18] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Garbiso and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Kaminski, Hydrodynamics of simply spinning black holes &  hydrodynamics for spinning quantum fluids, JHEP 12 (2020) 112, [2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='04345].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  [19] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Chen and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Hou, Heavy quark potential and jet quenching parameter in a  rotating D-instanton background, 2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='00888.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  [20] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Chen, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Zhang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Li, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Hou and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Huang, Gluodynamics and deconfinement  phase transition under rotation from holography, JHEP 07 (2021) 132, [2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='14478].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  [21] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Golubtsova, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Gourgoulhon and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Usova, Heavy quarks in rotating plasma via  holography, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' B 979 (2022) 115786, [2107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='11672].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  16  [22] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Golubtsova and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Tsegel’nik, Probing the holographic model of N = 4 SYM  rotating quark-gluon plasma, 2211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='11722.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  [23] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Jiang and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Liao, Pairing Phase Transitions of Matter under Rotation, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' 117 (2016) 192302, [1606.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='03808].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  [24] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Fujimoto, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Fukushima and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Hidaka, Deconfining Phase Boundary of Rapidly  Rotating Hot and Dense Matter and Analysis of Moment of Inertia, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' B 816  (2021) 136184, [2101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='09173].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  [25] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Braguta, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Kotov, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Kuznedelev and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Roenko, Influence of  relativistic rotation on the confinement-deconfinement transition in gluodynamics, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' D 103 (2021) 094515, [2102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='05084].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  [26] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Chernodub, Inhomogeneous confining-deconfining phases in rotating plasmas,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' D 103 (2021) 054027, [2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='04924].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  [27] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Giataganas, Probing strongly coupled anisotropic plasma, JHEP 1207 (2012) 031,  [1202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='4436].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  [28] U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Gursoy, Holographic QCD and magnetic fields, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' A 57 (2021) 247,  [2104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='02839].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  [29] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Giataganas, Observables in Strongly Coupled Anisotropic Theories, PoS Corfu2012  (2013) 122, [1306.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='1404].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  [30] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Fadafan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Giataganas and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content=' Soltanpanahi, The Imaginary Part of the Static  Potential in Strongly Coupled Anisotropic Plasma, JHEP 1311 (2013) 107, [1306.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='2929].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
+page_content='  17' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NtAyT4oBgHgl3EQfUPfO/content/2301.00123v1.pdf'}
diff --git a/OdE2T4oBgHgl3EQfrAj4/content/2301.04046v1.pdf b/OdE2T4oBgHgl3EQfrAj4/content/2301.04046v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..050cb409769044ad5ccd738daa5a1c5dd75fc8dd
--- /dev/null
+++ b/OdE2T4oBgHgl3EQfrAj4/content/2301.04046v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7a2d5e94ec0b2a632e5f5c40030b952eddbbefb5690628687cd0a62ec14040b7
+size 1236753
diff --git a/OdE2T4oBgHgl3EQfrAj4/vector_store/index.faiss b/OdE2T4oBgHgl3EQfrAj4/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..65f74e0d431ace5d607f0d047a834c520eddf15b
--- /dev/null
+++ b/OdE2T4oBgHgl3EQfrAj4/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5ed23ffef0c1595090d10b8c4ba129852961695115c5f01c34599439e2462621
+size 7012397
diff --git a/P9FKT4oBgHgl3EQfhC52/content/tmp_files/2301.11836v1.pdf.txt b/P9FKT4oBgHgl3EQfhC52/content/tmp_files/2301.11836v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..70cac89b3f13a6d0b3dfb79c9981505247eeb4cb
--- /dev/null
+++ b/P9FKT4oBgHgl3EQfhC52/content/tmp_files/2301.11836v1.pdf.txt
@@ -0,0 +1,2030 @@
+arXiv:2301.11836v1  [astro-ph.SR]  27 Jan 2023
+Astronomy & Astrophysics manuscript no. aaagb3dfirstwind
+©ESO 2023
+January 30, 2023
+Global 3D radiation-hydrodynamical models of AGB stars
+with dust-driven winds
+Bernd Freytag and Susanne Höfner
+Theoretical Astrophysics, Department of Physics and Astronomy, Uppsala University, Box 516, SE-751 20 Uppsala, Sweden
+e-mail: Bernd.Freytag@physics.uu.se
+January 30, 2023
+ABSTRACT
+Context. Convection and mass loss by stellar winds are two dynamical processes that shape asymptotic giant branch (AGB) stars and
+their evolution. Observations and earlier 3D models indicate that giant convection cells cause high-contrast surface intensity patterns,
+and contribute to the origin of clumpy dust clouds.
+Aims. We study the formation and resulting properties of dust-driven winds from AGB stars, using new global 3D simulations.
+Methods. The dynamical stellar interiors, atmospheres, and wind acceleration zones of two M-type AGB stars were modeled with the
+CO5BOLD code. These first global 3D simulations are based on frequency-dependent gas opacities, and they feature time-dependent
+condensation and evaporation of silicate grains.
+Results. Convection and pulsations emerge self-consistently, allowing us to derive wind properties (e.g., mass-loss rates and outflow
+velocities), without relying on parameterized descriptions of these processes. In contrast to 1D models with purely radial pulsations,
+the shocks induced by convection and pulsation in the 3D models cover large parts, but not the entirety, of the sphere, leading to a
+patchy, nonspherical structure of the atmosphere. Since dust condensation critically depends on gas density, new dust clouds form
+mostly in the dense wakes of atmospheric shocks, where the grains can grow efficiently. The resulting clumpy distribution of newly
+formed dust leads to a complex 3D morphology of the extended atmosphere and wind-acceleration zone, with simultaneous infall and
+outflow regions close to the star. Highly nonspherical isotherms and short-lived cool pockets of gas in the stellar vicinity are prominent
+features. Efficient dust formation sets in closer to the star than spherical averages of the temperature indicate, in dense regions where
+grain growth rates are higher than average. This can lead to weak outflows in situations where corresponding 1D models do not
+produce winds. For stars where the overall conditions for dust formation and wind acceleration are favorable, it is unclear whether
+the resulting mass-loss rates will be higher or lower than in the 1D case. The increased efficiency of dust formation in high-density
+clumps may be offset by a low volume coverage of the forming clouds.
+Conclusions. A global 3D approach is essential to make progress in understanding dynamical processes in AGB stars, and, in partic-
+ular, to solve long-standing problems regarding mass loss.
+Key words. convection – shock waves – stars: AGB and post-AGB – stars: atmospheres – stars: oscillations (including pulsations)
+– stars: mass-loss
+1. Introduction
+During the late stages of evolution on the asymptotic giant
+branch (AGB), low- and intermediate-mass stars are strongly af-
+fected by large-scale dynamical processes. Convection and mass
+loss through stellar winds influence the evolution, appearance,
+and final fate of these stars. They cause an enrichment of the sur-
+rounding interstellar medium with nucleosynthesis products and
+dust. Large-amplitude, long-period pulsations play a critical role
+in the formation of the dust grains that drive the massive outflows
+of AGB stars through radiation pressure. The pulsations trigger
+atmospheric shock waves, which lift gas to distances where tem-
+peratures are sufficiently low to allow for condensation of sili-
+cates and other relevant solids (for a recent review on AGB mass
+loss, see Höfner & Olofsson 2018).
+The current theoretical picture of dynamical atmospheres
+and dust-driven winds of AGB stars is mainly derived from time-
+dependent spherically symmetric models (e.g., Winters et al.
+2000; Jeong et al. 2003; Höfner et al. 2003, 2016). Such simu-
+lations describe the varying radial profiles of densities, tempera-
+tures, velocities, and dust properties, accounting for the shock
+waves that are triggered by pulsation and propagate outward
+through the atmospheres. Radiation-hydrodynamical DARWIN
+models, combining frequency-dependent radiative transfer with
+nonequilibrium dust formation, suggest that the dust-driven
+winds of M-type AGB stars are initiated by photon scattering on
+Fe-free silicate grains (Höfner 2008b). Such particles are nearly
+transparent at visual and near-IR wavelengths (e.g., Jäger et al.
+2003; Zeidler et al. 2011), resulting in significantly less radia-
+tive heating by stellar photons and, consequently, smaller con-
+densation distances, than for their Fe-bearing counterparts (e.g.,
+Woitke 2006b; Höfner et al. 2022). In order to cause sufficient
+radiation pressure by pure scattering, however, these dust grains
+have to grow to rather large sizes (typical radii of about 0.1
+– 1 µm; comparable to wavelengths near the stellar flux maxi-
+mum). The existence of such large grains in the close stel-
+lar environment is consistent with spatially resolved observa-
+tions of scattered light around several nearby AGB stars (e.g.,
+Norris et al. 2012; Ohnaka et al. 2016, 2017).
+Over the past few decades, 1D dynamical models of AGB-
+star atmospheres and winds have given valuable insights into the
+critical physical processes and dust properties, as outlined above,
+and on the dependence of mass-loss rates on stellar parameters
+(e.g., Wachter et al. 2002; Bladh et al. 2015, 2019). The compu-
+Article number, page 1 of 14
+
+A&A proofs: manuscript no. aaagb3dfirstwind
+tational efficiency of such simulations has made it possible to
+generate large grids of models, but the computational domains
+usually do not include the regions of the star where the pulsations
+are excited. The effects of stellar pulsation on the atmosphere
+and wind are typically introduced through variable physical con-
+ditions at the inner boundary, just below the stellar photosphere.
+Periodic motions simulate the radial expansion and contraction
+of the star, accompanied by luminosity variations, in so-called
+piston models. In this approach, the periods and amplitudes of
+the variations are free parameters that need to be constrained by
+observations or models of the pulsating stellar interior.
+Producing realistic theoretical models of pulsating AGB
+stars, however, has turned out to be a difficult task. In re-
+cent years, progress has been made regarding lower ampli-
+tude overtone pulsation by applying a linear nonadiabatic ap-
+proach (e.g., Wood 2015; Trabucchi et al. 2017). Lately, using
+1D nonlinear pulsation models, Trabucchi et al. (2021) resolved
+some earlier discrepancies between predicted and observed ra-
+dial fundamental-mode periods of Mira variables.
+A basic problem with 1D stellar interior models is that
+they have to use a parameterized description of convection,
+which is an intrinsically 3D process. Classical descriptions such
+as mixing-length theory, with appropriately chosen parameters,
+work reasonably well in stellar evolution models. Regarding stel-
+lar pulsation, however, 1D recipes for treating convective energy
+transport are probably not adequate in the case of AGB stars,
+as they show strongly nonlinear, nonadiabatic, large-scale con-
+vective motions that couple to pulsation. Turbulent gas flows
+occur on scales comparable to the stellar radius, giving rise to
+pronounced surface intensity patterns (e.g., Schwarzschild 1975;
+Freytag & Höfner 2008; Freytag et al. 2017).
+In recent years, with the progress in high-angular-resolution
+observations, it has become possible to obtain spatially resolved
+data for a few nearby AGB stars. Imaging of stellar surface
+structures at near-IR wavelengths has revealed patterns in good
+agreement with convective surface structures in 3D models (e.g.,
+Paladini et al. 2018). Spatially resolved data in the submillime-
+ter regime show complex dynamical atmospheric structures with
+simultaneous inward and outward motions, as well as the coexis-
+tence of hot and cold gas (Khouri et al. 2016b; Vlemmings et al.
+2017). Nonspherical distributions of gas and dust in the close
+circumstellar environment are also seen in high-resolution im-
+ages at visual and infrared wavelengths (e.g., Ohnaka et al. 2016;
+Stewart et al. 2016; Wittkowski et al. 2017). Visual and near-IR
+scattered light images of circumstellar material have given infor-
+mation about the properties of dust clouds close to the star, and
+about the sizes of the dust grains within them (e.g., Norris et al.
+2012). Temporal monitoring shows changes in both atmospheric
+morphology and grain sizes over the course of weeks or months
+(e.g., Khouri et al. 2016a; Ohnaka et al. 2017).
+Global 3D radiation-hydrodynamical (RHD) models offer a
+promising way of solving existing problems with interior dy-
+namics (convection, pulsation) and, at the same time, gain-
+ing an understanding of the complex observed atmospheric
+structures. The pioneering AGB "star-in-a-box" models by
+Freytag & Höfner (2008) and Freytag et al. (2017), building on
+the capability of the CO5BOLD code to cover the entire outer
+convective envelope and atmosphere, indeed show both large-
+scale convection and self-excited radial pulsations with realistic
+periods. Recently, Ahmad et al. (2023) analyzed a much larger
+sample of global 3D CO5BOLD models of evolved stars, find-
+ing a good agreement of the results with the observed period-
+luminosity relations for AGB stars.
+An inhomogeneous distribution of atmospheric gas, as seen
+in observations, is a natural consequence of large-scale con-
+vective flows below the photosphere and the resulting net-
+work of atmospheric shock waves. The exploratory models of
+Freytag & Höfner (2008) and Höfner & Freytag (2019) indi-
+cated that the dynamical patterns in the gas will leave imprints
+on the dust in the close stellar environment, due to the density
+and temperature sensitivity of the grain growth process. How-
+ever, these earlier 3D simulations did not include the effects of
+radiation pressure on dust, and could therefore not predict the
+structure of the wind formation zone.
+In this paper, we present the first global 3D RHD simula-
+tions of dust-driven winds of AGB stars, exploring the interplay
+of convection, pulsation, atmospheric shocks, dust formation,
+and wind acceleration. In addition to the newly implemented ra-
+diative pressure on dust, these new models also feature a much
+larger computational domain, covering the inner wind region.
+This allows us to follow the emerging 3D structures to a dis-
+tance where the outflow is established, and to compute mass-loss
+rates. In Sect. 2, we give a brief overview of the basic physical
+assumptions and numerical methods. The results are presented
+in Sect. 3, and compared to observations in Sect. 4. Finally, a
+summary and conclusions are given in Sect. 5.
+2. Setup of global AGB-star models
+Below, we give a short summary of the physical and numer-
+ical properties of the CO5BOLD code, focusing on features
+that are relevant for the new simulations presented in this pa-
+per. More details can be found in our earlier papers on global
+AGB-star models (Freytag & Höfner 2008; Freytag et al. 2017;
+Höfner & Freytag 2019) and on the properties of wind-driving
+dust grains in M-type AGB stars (Höfner et al. 2016).
+2.1. General properties of the CO5BOLD models
+The CO5BOLD code (Freytag et al. 2012) numerically inte-
+grates the coupled nonlinear equations of compressible hydro-
+dynamics and nonlocal radiative energy transfer on a Cartesian
+grid. The hydrodynamics scheme is based on an approximate
+Riemann solver of Roe-type (see Freytag 2013), modified to
+account for the effects of ionization and gravity. The tabulated
+equation of state (assuming solar abundances) takes the ioniza-
+tion of hydrogen and helium, and the formation of H2 molecules
+into account. Gravitation is included as an external potential,
+with a general 1/r profile, that is smoothed in the central re-
+gion of the star. In this central volume, heat is added as a con-
+stant source term, corresponding to the stellar luminosity. A drag
+force is active in this core region only, to prevent dipolar flows
+traversing the entire star. All outer boundaries are open for the
+flow of matter and for radiation (see Freytag 2017, for some de-
+tails about boundary conditions in CO5BOLD).
+2.2. Computational domain and radiative transfer
+A global model describing the flow of gas and radiation from the
+convective stellar interior, through the dynamical atmosphere, to
+the dust formation region and wind-acceleration zone, needs to
+cover a wide range of physical conditions on different spatial
+and temporal scales. To keep computation times at a reasonable
+level, the spatial domain of the new global models is divided
+into two regions. An inner box, covering the star and its immedi-
+ate surroundings, features a more detailed description of radia-
+Article number, page 2 of 14
+
+Bernd Freytag and Susanne Höfner: Global 3D models of AGB stars with winds
+Table 1. Basic model parameters and derived quantities.
+model
+M⋆
+Menv
+L⋆
+n3
+x
+xouterbox
+xinnerbox
+CTfac
+tavg
+R⋆,smin
+Teff,smin
+log gsmin
+Ppuls
+(M⊙)
+(M⋆)
+(L⊙)
+(R⊙)
+(R⊙)
+(yr)
+(R⊙)
+(K)
+cgs
+(d)
+st28gm06n050
+1.0
+0.182
+7049
+5993
+4858
+2340
+0.75
+54.61
+351
+2823
+-0.656
+510
+st28gm06n052
+1.0
+0.181
+7030
+6793
+6386
+2640
+0.77
+57.78
+355
+2806
+-0.665
+545
+st28gm05n033
+1.5
+0.298
+6702
+5593
+3454
+1581
+0.72
+27.70
+304
+2993
+-0.358
+297
+Notes. The table shows the model name; the mass M⋆, used for the external potential; the envelope mass Menv, derived from integrating the mass
+density of all grid cells within the computational box; the average emitted luminosity L⋆; the model grid dimensions n3
+x; the edge length of the
+entire cubical computational box xouterbox; the edge length of the inner box with detailed radiation transport xinnerbox; the adjustable temperature-
+reduction factor CTfac in the outer layers; the time tavg, used for averaging the remaining quantities in this table; the radius R⋆,smin at the point with
+minimum entropy; the effective temperature Teff,smin at minimum entropy; the logarithm of the surface gravity log gsmin at minimum entropy; and
+the pulsation period Ppuls.
+tive transfer, which is critical for the modeling of temperature
+structures (see below) and a higher spatial resolution. It is sur-
+rounded by a larger outer box with a simplified radiative transfer
+and a coarser grid, beyond the main grain growth region, where
+the wind has been initiated and dynamical structures tend to be
+larger. Regarding hydrodynamics, there is no difference between
+the two boxes, except for the grid spacing. The inner box con-
+sists of cubical cells with a constant size. In the outer box, going
+outward, cells become incrementally larger along the axis direc-
+tions (typically by a few percent per step) and only those along
+the space diagonals retain a cubical shape, while their size in-
+creases.
+In the inner box, the nonlocal radiative energy transfer is
+solved with a short-characteristics scheme. Most of our earlier
+global 3D RHD simulations of AGB stars used tabulated gray
+gas opacities, which is sufficient for studies of interior proper-
+ties such as convection and pulsations, and to give a qualita-
+tive picture of the shock-dominated atmospheric dynamics (see
+Freytag et al. 2017). Simulations including dust formation, how-
+ever, require a refined modeling of the atmospheric temperature
+structure, which sets thresholds for the onset of dust condensa-
+tion and evaporation. This can be achieved by using frequency-
+dependent data, as discussed in Höfner & Freytag (2019). In the
+new models of dust-driven winds presented in this paper, we use
+a similar approach with three frequency bins, but we have re-
+done the iterative binning procedure for a larger region of the
+representative pressure-temperature structure, due to the larger
+computational box used here. The tables for atmospheric gas
+opacities used in the present models are based on COMA data
+(see Aringer 2000; Aringer et al. 2016), extended with OPAL
+data at temperatures above approximately 12 000 K. Scattering
+is treated as true absorption, that is to say, the scattering opacity
+is added to the absorption opacity, so that the source function can
+be computed from the local temperature alone.
+In the outer box, where the outflow is established and further
+grain growth is of minor importance, temperature plays a less
+critical role. Therefore, we use an approximate description, suf-
+ficient for the purpose of hydrodynamics, which is computation-
+ally much less costly than solving radiative transfer. The average
+radial temperature profile is assumed to be set by the radiative
+flux from the stellar surface, geometrically diluted with distance,
+which can be written as T(r) ∝ (L/r2)1/4, where L is the mean
+stellar luminosity and r the radial distance from the center. To
+minimize the jump in temperature from the inner box (with de-
+tailed radiative transfer, as described above), an adjustable factor
+CTfac (see Table 1) is included in the description of T(r). In each
+time step, the internal energy at each grid point in the outer lay-
+ers is adjusted, so that the actual temperature relaxes toward the
+approximate target temperature on a small but finite timescale
+(typically 104 s).
+2.3. Dust formation
+In the new global models with dust-driven winds, we use a time-
+dependent kinetic treatment of silicate formation and destruc-
+tion, adapted from the DARWIN models, as described in de-
+tail by Höfner et al. (2016). The dust grains grow by the ad-
+dition of abundant atoms and molecules from the gas phase,
+and they may shrink due to thermal evaporation from the grain
+surface. The growth of grains is triggered by the temperature
+falling below a critical value (depending on gas density; see
+Fig. 1 in Höfner et al. 2016). Conversely, when the temperature
+rises above this value, the grains start to shrink due to evapora-
+tion from the surface. At the relatively low densities in the stellar
+atmosphere, grain growth typically occurs on timescales that are
+comparable to those of gas dynamics and radiative flux varia-
+tions. Grain growth and evaporation may, therefore, proceed far
+from equilibrium, making a time-dependent treatment necessary.
+The condensation of wind-driving olivine-type silicate grains
+is assumed to proceed according to the net reaction
+2 Mg + SiO + 3 H2O −→ Mg2SiO4 + 3 H2 .
+(1)
+In principle, olivine-type silicates can be considered as a solid
+solution of Mg2SiO4 and Fe2SiO4, with a variable Fe/Mg ratio.
+However, as discussed by Höfner et al. (2022), the inclusion of
+Fe atoms in the growing grains is a secondary process, taking
+place after the wind has been triggered by Fe-free silicate dust.
+The Fe/Mg ratio remains low, due to a self-regulating feedback
+via the grain temperature, and due to rapidly falling densities in
+the outflow. The resulting effects on wind dynamics are small,
+and therefore we only consider the condensation of Fe-free sil-
+icates (Mg2SiO4) in the exploratory 3D wind models presented
+here.
+It should be noted that the kinetic treatment of grain growth
+used here does not describe nucleation, that is, the formation of
+the very first solid seed particles. Since nucleation rates and the
+chemical composition of seed particles in M-type AGB stars are
+still a matter of debate, the abundance of seed particles relative
+to hydrogen is treated as an input parameter (for a more detailed
+discussion see Höfner et al. 2016). It is assumed that these seed
+particles are readily available whenever conditions permit the
+condensation of silicate dust. They are tiny compared to the re-
+sulting dust grains, and they have no effect other than providing
+an initial condensation surface for grain growth.
+Article number, page 3 of 14
+
+A&A proofs: manuscript no. aaagb3dfirstwind
+2.4. Radiation pressure on dust
+In contrast to the pre-tabulated gas opacities (see Sect. 2.2), the
+dust opacities that cause radiative acceleration are calculated
+during the simulations, using the current grain radii that result
+from the equations describing dust condensation and evapora-
+tion (see Sect. 2.3). The total opacity of grains with radius agr in
+a volume element (cross section per volume) can be expressed
+as
+κacc(agr, λ) = πa2
+gr Qacc(agr, λ) nd ,
+(2)
+where nd is the corresponding number density of grains and λ
+represents the wavelength. The efficiency factor Qacc(agr, λ), de-
+fined as the ratio of radiative to geometrical cross section of a
+grain, contains contributions from true absorption and scatter-
+ing:
+Qacc = Qabs + (1 − gsca) Qsca ,
+(3)
+where gsca is an asymmetry factor describing deviations from
+isotropic scattering.
+In principle, the efficiency factors and gsca can be computed
+using Mie theory. In the exploratory 3D wind models presented
+here, however, we use a simplified description of Qacc, retaining
+the critical dependence on grain size, but treating the dependence
+on wavelength in an approximate way. We assume that the flux
+mean of the opacity determining radiative acceleration can be
+replaced by a monochromatic value at a wavelength close to the
+flux maximum, κacc(agr, λmax), where λmax ≈ 1µm, and we use a
+simple analytical approximation for Qacc as a function of grain
+radius:
+Qacc(agr, λmax) = min
+
+q1
+� agr
+λmax
+�
++ q4
+� agr
+λmax
+�4 , qmax
+ ,
+(4)
+introduced by Höfner (2008a). The term linear in grain radius
+represents true absorption for grains smaller than the wave-
+length under consideration, while scattering in that regime is ac-
+counted for by the term depending on the fourth power of the
+grain radius, which dominates for near-transparent Fe-free sili-
+cate grains. The fact that the efficiency factor approaches a con-
+stant value for grains much larger than the wavelength is taken
+into consideration by setting a maximum value qmax. Choosing
+q1 = 2.0 · 10−3, q4 = 4.68 · 102 and qmax = 1.0 at λmax = 1.08 µm
+gives a description that stays reasonably close to Qacc computed
+from full Mie theory, considering the level of the other approx-
+imations in the radiative transfer, and the fact that Qacc varies
+over several orders of magnitude within the grain-size range of
+interest (see Figs. 3 and 4 in Höfner 2008a).
+To compute the radiative force acting on the dust grains, the
+opacity κacc has to be multiplied with a factor describing the
+photon flux from the star. In an optically thin environment, this
+corresponds to a geometrically diluted flux from the stellar sur-
+face, decreasing with radial distance roughly as 1/r2 (assuming
+that the star can be approximated by a point source). However,
+if the optical depth of the circumstellar dust is not negligible,
+leading to a weakening of the local photon flux, this effect has
+to be taken into account, which is done by introducing a factor
+(1 − exp (−dτ)), where dτ is the local optical depth. We chose
+dτ = 0.02rκacc. This situation can arise during dust formation in
+small high-density regions in the wake of shocks, corresponding
+to typical length scales of a few percent of the radial distance r.
+In practice, however, the optical depth effects are usually negli-
+gible.
+Currently, radiation pressure is the only dust opacity effect
+taken into account. The Fe-free silicate grains are very trans-
+parent at near-IR wavelengths, where the stellar flux has its
+maximum, and the corresponding absorption coefficients are ne-
+glected when solving radiative energy transfer in the inner box
+to obtain the temperature structure. The dust grains are assumed
+to have the same temperature as the gas, which is mainly rele-
+vant for the thresholds for condensation and evaporation. This
+approximation is in line with the other simplifications concern-
+ing the dust component.
+2.5. Input parameters and resulting model properties
+In this paper we present a selection of new 3D AGB-star mod-
+els with dust-driven winds, demonstrating the effects of stellar
+and numerical parameters (see Table 1). Models st28gm06n050
+and st28gm06n052 are similar, except for the sizes of the in-
+ner and outer computational boxes, and the adjustable factor of
+the target temperature CTfac in the outer box, which ensures a
+smooth transition in temperature from the domain of detailed ra-
+diative transfer to the outer box (see Sect. 2.2). The mean radial
+structures of models st28gm06n050 and st28gm06n052, aver-
+aged over spherical shells and time, are shown in Fig. 1 (dashed
+black and solid red curves), demonstrating that box size and the
+simplified treatment of the radiative transfer in the outer box
+only have a minor effect on the resulting wind dynamics. In
+particular, the mean radial-velocity profiles are almost identi-
+cal for the two models. In the following, we focus our discus-
+sion on model st28gm06n052, which has both a larger inner and
+outer box, and therefore allows us to follow the development of
+3D structures in more detail, and to larger distances from the
+star. The blue curves in Fig. 1 show the mean radial structure of
+model st28gm05n033, which has a higher mass, a smaller ra-
+dius, and a higher effective temperature, compared to models
+st28gm06n050 and st28gm06n052. This leads to less favorable
+conditions for dust formation and wind acceleration, as is dis-
+cussed in Sect. 3.
+Table 1 summarizes the basic parameters and resulting global
+properties of the models. While the stellar mass M⋆ (control-
+ling the gravitational potential), as well as the resolution and the
+extent of the numerical grid, are pre-chosen fixed parameters,
+other model properties are determined after a simulation is fin-
+ished. The envelope mass Menv is calculated from the integrated
+density of all grid cells, averaged over time. We assume that the
+difference in mass is located in the compact, unresolved stellar
+core. The listed stellar luminosity is a time average of the to-
+tal luminosity emitted at the surface (very similar to the inserted
+luminosity of 7000 L⊙ in the core).
+The stellar radius is more difficult to determine and is less
+well defined due to the complex morphology of the extended at-
+mosphere. Here, we use a value corresponding to the point of
+minimum entropy near the photosphere, which has turned out to
+be a good choice in connection with the analysis of pulsation
+properties (Ahmad et al. 2023). We note that this definition is
+different from the one used in earlier papers (e.g., Freytag et al.
+2017; Höfner & Freytag 2019), where the radius was chosen
+as the point R⋆ where the spherically and temporally aver-
+aged temperature and luminosity fulfill ⟨L⟩Ω,t = 4πσR2
+⋆⟨T⟩4
+Ω,t.
+For the less massive and cooler models st28gm06n050 and
+st28gm06n052, the latter definition leads to values that are about
+10% larger, while both definitions give very similar values for
+model st28gm05n033, which has a more compact atmosphere
+Article number, page 4 of 14
+
+Bernd Freytag and Susanne Höfner: Global 3D models of AGB stars with winds
+Table 2. Dust and wind properties.
+model
+nd/nH
+˙M
+fMg
+agr
+(M⊙/yr)
+(µm)
+st28gm06n052
+3 · 10−16
+5 · 10−6
+0.5
+0.8
+st28gm05n033
+3 · 10−15
+5 · 10−8
+0.15
+0.2
+Notes. Listed here are the assumed seed particle abundance nd/nH, and
+the resulting temporal means of the mass-loss rate ˙M, the fraction of Mg
+condensed into grains fMg, and the grain radius agr at the outer bound-
+ary. When forming Mg2SiO4 grains in a gas of solar composition, the
+abundance of Mg is the limiting factor, since that element will be used
+up first. In the models described here, however, fMg is well below its
+maximum value of 1.
+(see Fig. 1, showing the mean radial density and temperature
+structures).
+In contrast to our earlier 3D simulations of AGB stars, the
+new models presented here predict mass-loss rates and properties
+of wind-driving dust grains (see Table 2). The dust properties are
+a direct result of solving the equations describing grain growth
+and evaporation (see Sect. 2.3). The mass-loss rate of a model is
+computed by averaging the mass flux across spherical shells and
+time.
+3. Results
+In this section, we describe in detail the emergence and evolution
+of atmospheric and circumstellar structures triggered by large-
+scale convective flows and stellar pulsation, and study the persis-
+tence of inhomogeneities in the gas and dust distributions during
+the onset of dust-driven outflows. In the following, we focus on
+the description of these phenomena in model st28gm06n052, us-
+ing the more massive and hotter model st28gm05n33 mainly to
+illustrate the influence of stellar parameters.
+3.1. Formation and evolution of dust clouds
+Figure 2 shows the evolving structures in model st28gm06n052
+for slices through the center of the star, at three instants of time
+(left to right). The top row of panels shows the gas density, illus-
+trating the strong contrast between the high values in the stellar
+interior (bright colors at the center of the image) and the thin
+circumstellar material, with a steep transition region in the inner
+atmosphere (it is important to note the logarithmic scale).
+In the second row of panels, showing radial velocity, these
+different zones can be distinguished by their dynamical behav-
+ior. The stellar interior (inside a radius of about 350 R⊙ from
+the center) is dominated by large-scale convective flows, corre-
+sponding to variable blue and red areas that represent outflows
+and inflows, respectively. In the atmosphere, the convective
+flows, together with radial pulsations, trigger strong, outward-
+propagating shock waves, seen as dark blue arc-like structures
+in the 2D slices. Beside these shock-accelerated regions, there
+are large areas where gas is falling back toward the star (appar-
+ent in red), since the inner atmosphere is gravitationally bound.
+The wind-acceleration region corresponds to the blue region in
+the outer parts of the model, indicating the outflow of matter. As
+discussed above, the stellar wind is driven by radiation pressure
+on dust. The grains collide with the surrounding gas particles
+and transfer outward-directed momentum, thereby initiating the
+wind.
+The bottom row of panels in Fig. 2 shows the silicate grain
+radius, with brighter colors indicating larger grains. The spatial
+0
+1000
+2000
+3000
+4000
+-16
+-14
+-12
+-10
+-8
+-6
+log(ρ/[g cm-3])
+st28gm06n052: M= 1.0 MO
+ •, L= 7029 LO
+ • , R=354 RO
+ • , xbox= 6386.1 RO
+ • 
+st28gm06n050: M= 1.0 MO
+ •, L= 7048 LO
+ • , R=350 RO
+ • , xbox= 4858.2 RO
+ • 
+st28gm05n033: M= 1.5 MO
+ •, L= 6701 LO
+ • , R=304 RO
+ • , xbox= 3454.1 RO
+ • 
+0
+1000
+2000
+3000
+4000
+0
+5
+10
+15
+20
+vradial [km s-1]
+0
+1000
+2000
+3000
+4000
+3.0
+3.5
+4.0
+4.5
+5.0
+log(T/[K])
+st28gm06n052: M= 1.0 MO
+ •, L= 7029 LO
+ • , R=354 RO
+ • , xbox= 6386.1 RO
+ • 
+st28gm06n050: M= 1.0 MO
+ •, L= 7048 LO
+ • , R=350 RO
+ • , xbox= 4858.2 RO
+ • 
+st28gm05n033: M= 1.5 MO
+ •, L= 6701 LO
+ • , R=304 RO
+ • , xbox= 3454.1 RO
+ • 
+0
+1000
+2000
+3000
+4000
+r [RO
+ • ]
+2×10-5
+4×10-5
+6×10-5
+8×10-5
+Radius of Mg2SiO4 grains [cm]
+Fig. 1. Mean radial structures of the models st28gm06n050 (dashed
+black curves), st28gm06n052 (red curves), and st28gm05n033 (blue
+curves). Shown are gas density, radial velocity, temperature, and sili-
+cate grain radius, averaged over spherical shells and time, and plotted
+against the distance from the stellar center. Averages are not only taken
+over spheres that fit completely into the cubical computational box, but
+also over partial spheres somewhat beyond, up to 1.5× xouterbox/2, omit-
+ting the regions close to the corners of the cube. The dotted red and
+blue curves in the radial-velocity panel represent the escape velocity as
+a function of distance for stellar masses of 1 M⊙ and 1.5 M⊙, respec-
+tively. For details, see Sects. 2.5 and 3.
+Article number, page 5 of 14
+
+A&A proofs: manuscript no. aaagb3dfirstwind
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+-3000
+-2000
+-1000
+0
+1000
+2000
+3000
+y [RO
+ • ]
+t=29.296 yr
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+t=29.962 yr
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+t=31.158 yr
+     
+ 
+ 
+ 
+ 
+ 
+log(ρ [g cm-3])
+-16
+-14
+-12
+-10
+-8
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+-3000
+-2000
+-1000
+0
+1000
+2000
+3000
+y [RO
+ • ]
+t=29.296 yr
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+t=29.962 yr
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+t=31.158 yr
+     
+ 
+ 
+ 
+ 
+ 
+vradial [km s-1]
+-20
+-10
+0
+10
+20
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+-3000
+-2000
+-1000
+0
+1000
+2000
+3000
+y [RO
+ • ]
+t=29.296 yr
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+t=29.962 yr
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+t=31.158 yr
+     
+ 
+ 
+ 
+ 
+ 
+log(T [K])
+2.5
+3.0
+3.5
+4.0
+4.5
+-3000 -2000 -1000
+0
+1000
+2000
+3000
+x [RO
+ • ]
+-3000
+-2000
+-1000
+0
+1000
+2000
+3000
+y [RO
+ • ]
+t=29.296 yr
+-3000 -2000 -1000
+0
+1000
+2000
+3000
+x [RO
+ • ]
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+t=29.962 yr
+-3000 -2000 -1000
+0
+1000
+2000
+3000
+x [RO
+ • ]
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+t=31.158 yr
+     
+ 
+ 
+ 
+ 
+ 
+ 
+Radius of Mg2SiO4 grains [cm]
+0
+2×10-5
+4×10-5
+6×10-5
+8×10-5
+1×10-4
+Fig. 2. Time sequences of density, radial velocity, temperature, and silicate grain radius for a slice through the center of the large 1 M⊙ model
+st28gm06n052. The snapshots are about 8 and 14 months apart, respectively (see the counter at the top of the panels). The orange line in the
+bottom panels indicates an isotherm of 1150 K.
+patterns in grain size reflect the effects of density and tempera-
+ture on the condensation process. Higher densities lead to faster,
+more efficient grain growth, and the brightest areas (largest
+grains) are found in the wakes of shock waves, which compress
+the gas. The central dark zone indicates the region where dust
+formation is prevented by high temperatures (see panels in row
+3). The over-plotted line in the grain-size panels represents an
+isotherm at 1150 K, corresponding roughly to the condensation
+temperature of the silicate grains.
+In the bottom right quadrant of the images, a new dust
+cloud (bright area in grain-size plots) is forming in the wake
+of an outward-propagating shock wave, which compresses the
+Article number, page 6 of 14
+
+Bernd Freytag and Susanne Höfner: Global 3D models of AGB stars with winds
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+-1500
+-1000
+-500
+0
+500
+1000
+1500
+y [RO
+ • ]
+t=22.772 yr
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+t=23.065 yr
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+t=23.664 yr
+     
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+log(ρ [g cm-3])
+-18
+-16
+-14
+-12
+-10
+-8
+-6
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+-1500
+-1000
+-500
+0
+500
+1000
+1500
+y [RO
+ • ]
+t=22.772 yr
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+t=23.065 yr
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+t=23.664 yr
+     
+ 
+ 
+ 
+ 
+ 
+vradial [km s-1]
+-20
+-10
+0
+10
+20
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+-1500
+-1000
+-500
+0
+500
+1000
+1500
+y [RO
+ • ]
+t=22.772 yr
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+t=23.065 yr
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+t=23.664 yr
+     
+ 
+ 
+ 
+ 
+ 
+ 
+log(T [K])
+2.5
+3.0
+3.5
+4.0
+4.5
+5.0
+-1500 -1000 -500
+0
+500
+1000 1500
+x [RO
+ • ]
+-1500
+-1000
+-500
+0
+500
+1000
+1500
+y [RO
+ • ]
+t=22.772 yr
+-1500 -1000 -500
+0
+500
+1000 1500
+x [RO
+ • ]
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+t=23.065 yr
+-1500 -1000 -500
+0
+500
+1000 1500
+x [RO
+ • ]
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+t=23.664 yr
+     
+ 
+ 
+ 
+ 
+ 
+Radius of Mg2SiO4 grains [cm]
+0
+1×10-5
+2×10-5
+3×10-5
+4×10-5
+Fig. 3. Time sequences of density, radial velocity, temperature, and silicate grain radius for a slice through the center of the 1.5 M⊙ model
+st28gm05n033. The snapshots are about 3.5 and 7 months apart, respectively (see the counter at the top of the panels). The orange line in the
+bottom panels indicates an isotherm of 1150 K.
+gas (blue arc in the radial velocity plots and brighter orange in
+the density plots). Initially appearing as a small bright region in
+the grain radius plot (bottom row, left panel), the cloud quickly
+grows in size, with its inner edge defined by the condensation
+temperature (middle panel), before being driven outward by ra-
+diation pressure (right panel). In the bottom left quadrant, an
+existing cloud that was formed earlier in a similar way, is ac-
+celerated outward by radiation pressure, leaving the model do-
+Article number, page 7 of 14
+
+A&A proofs: manuscript no. aaagb3dfirstwind
+main. Another outward-moving cloud can bee seen in the top
+left quadrant. The fact that the series of snapshots (covering
+about 22 months in total) shows several distinct dust clouds in-
+dicates that efficient dust formation events, triggered by shock
+waves, occur frequently. It should, however, be mentioned here
+that not all dust clouds survive and lead to an outflow of matter.
+In some cases, the variations in the radiative flux and the result-
+ing changes in atmospheric temperatures lead to dust evapora-
+tion, before the cloud is accelerated outward. This is consistent
+with the coexistence of inward and outward moving gas in the
+atmosphere, mentioned above.
+3.2. Overall morphology and wind properties
+The dependence of grain growth rates on density gives the stellar
+wind a patchy, time-variable start. As clumps of dusty gas move
+outward and merge into a general outflow, some degree of inho-
+mogeneity is preserved. Looking at Fig. 2, there are clear signs
+of a stellar wind in the outer regions of model st28gm06n052,
+with a dominant direction of the flow velocity away from the
+star. However, the density and dust-grain size still show imprints
+of the atmospheric shock waves that triggered dust condensation,
+and thereby the onset of the wind.
+The radial structure of model st28gm06n052, averaged over
+spherical shells and time, is shown in Fig. 1 (red curves). In the
+plots of the mean radial velocity, the time-dependent dynamics
+of the stellar interior and atmosphere averages out, and the dom-
+inant flow direction of the wind is clearly visible. After an initial
+phase of fast grain growth, dust condensation slows down, as
+density drops rapidly in the accelerating wind. At about 3000 R⊙
+(corresponding to about eight stellar radii), the average radial ve-
+locity of the flow exceeds the local escape velocity (dotted red
+line). When the outflow approaches a constant velocity further
+out, the density profile changes from a steep decline to the fa-
+miliar 1/r2 profile of a spherical wind with constant velocity.
+In Fig. 1, the time-averaged radial structures of models with
+different stellar parameters are compared. It is evident that model
+st28gm05n033 (blue curves), representing a more massive, hot-
+ter star with a smaller radius, shows a much steeper atmo-
+spheric density decrease. At a distance where temperatures are
+low enough for dust condensation, the difference in density com-
+pared to model st28gm06n052 is about two orders of magnitude,
+leading to much less efficient grain growth. Despite a higher
+seed-particle abundance in model st28gm05n033, the final de-
+gree of condensation is lower by about a factor of three, com-
+pared to the cooler, less massive model st28gm06n052, and the
+mass-loss rate is lower by about two orders of magnitude, corre-
+sponding to the difference in atmospheric gas densities.
+While the lower mass-loss rate of model st28gm05n033 can
+be explained by the lower atmospheric densities, it should also
+be mentioned here that the outflow of this hotter, more mas-
+sive model is much more variable, due to the low efficiency of
+grain growth. As is shown in Sect. 3.3, most of the mass loss in
+model st28gm05n033 occurs during a few strong events ("gusts"
+of wind). Therefore, the mean structures in Fig. 1 are less well
+defined than in the case of model st28gm06n052.
+This becomes apparent when taking a closer look at the mean
+radial-velocity curves. Model st28gm06n052 (red curve) shows
+the familiar pattern of a steady dust-driven wind: a steep ini-
+tial increase in radial velocity associated with the dust formation
+region, followed by a levelling off further out, where both the ra-
+diative pressure and gravitational attraction weaken with increas-
+ing distance from the star. In contrast, the blue curve representing
+model st28gm05n033 shows a non-monotonic pattern, following
+a steep initial increase and a local maximum at about 1700 R⊙.
+This point corresponds to the radius of the largest sphere fitting
+within the computational box (half of the edge length of the cu-
+bical box xouterbox, see Table 1). Beyond that point, the spatial
+averaging relies on the decreasing fractions of spherical surfaces
+contained in the box, until the largest distance, corresponding to
+1.5 × xouterbox/2, is reached. Computing representative averages
+for a gusty, inhomogeneous wind turns into a sampling prob-
+lem, as the coverage of angles decreases. As a consequence, the
+average wind velocity of model st28gm05n033 is not well con-
+strained. However, there is no doubt that material reaching the
+outer edge of the computational box will escape from the star,
+even if the average flow velocity does not exceed the local escape
+velocity (Fig. 1, dotted blue line). We note that the dynamics is
+not ballistic, and radiative acceleration continues to exceed grav-
+itational attraction, while both forces decrease with distance.
+Figure 3 shows evolving structures in model st28gm05n033
+at three instants, for slices through the center of the star. The
+less efficient dust condensation is illustrated by the grain radius
+plots (bottom row), with only one pronounced dust formation
+event, followed by outward acceleration, taking place in the bot-
+tom right quadrant. In contrast to the corresponding Fig. 2 for
+model st28gm06n052, the outer parts of model st28gm05n033
+mostly show a red color in the radial-velocity plots during the
+chosen time interval, indicating gas falling back toward the star,
+after the passing of shock waves. Since the computational box
+of model st28gm05n033 is smaller by about a factor of two,
+this region should be compared to the corresponding parts of
+model st28gm06n052, which also show large regions of infalling
+gas. The somewhat clumpy but continuous outflow of model
+st28gm06n052 (blue colors in the radial-velocity plots) is more
+clearly visible at larger distances, beyond about 2000 solar radii.
+3.3. Time variations of global properties
+Figures showing the evolution of structures, as discussed above,
+are essential for understanding the interplay of physical pro-
+cesses at work. However, to study the connection between radial
+pulsation, dust formation, and wind acceleration, and to see vari-
+ations in global properties as derived from spatially unresolved
+observations of AGB stars, we need a different approach.
+Figure 4 shows spherical averages of luminosity, radial ve-
+locity, and grain radius as a function of radial depth and time
+for the cooler, less massive model st28gm06n052. In the panel
+showing luminosity, we can distinguish two different regions:
+the dark area (indicating low radiative flux) below about 300 R⊙
+represents the deep stellar interior, where essentially all of the
+energy flux is carried by convection. Further out, in the atmo-
+sphere and circumstellar envelope, on the other hand, energy is
+mostly transported by the radiative flux, which shows more or
+less regular variations related to radial pulsations of the star.
+In the velocity panel, the radial pulsations are apparent as
+alternating blue and red vertical stripes in the stellar interior.
+In the inner atmosphere, the dynamics is dominated by strong
+pulsation-induced shocks that are propagating outward (dark
+blue stripes, pointing upward and to the right), separated by
+phases where gas falls back toward the stellar surface (red). The
+outermost part of the model corresponds to the dust-driven stel-
+lar wind, with an outward-directed flow velocity (blue). We note
+that the highest wind velocities (darkest blue colors) occur in
+the wake of strong shocks, which, in turn, are directly linked to
+stellar expansion phases due to the pulsations.
+The temperatures in the atmosphere and wind-acceleration
+region are mostly set by radiative processes, dominated by pho-
+Article number, page 8 of 14
+
+Bernd Freytag and Susanne Höfner: Global 3D models of AGB stars with winds
+10
+20
+30
+40
+50
+60
+500
+1000
+1500
+2000
+2500
+3000
+r [RO
+ • ]
+     
+ 
+ 
+ 
+ 
+ 
+L* [LO
+ •]
+0
+2000
+4000
+6000
+8000
+10
+20
+30
+40
+50
+60
+500
+1000
+1500
+2000
+2500
+3000
+r [RO
+ • ]
+     
+ 
+ 
+ 
+ 
+ 
+vradial [km s-1]
+-20
+-10
+0
+10
+20
+10
+20
+30
+40
+50
+60
+t [yr]
+500
+1000
+1500
+2000
+2500
+3000
+r [RO
+ • ]
+     
+ 
+ 
+ 
+ 
+ 
+ 
+Radius of Mg2SiO4 grains [cm]
+0
+2×10-5
+4×10-5
+6×10-5
+8×10-5
+1×10-4
+Fig. 4. Spherical averages of luminosity (integrated radiative flux), radial velocity, and grain radius in the large 1 M⊙ model st28gm06n052, as a
+function of radial distance and time. In the top and bottom panels, an isotherm with a temperature representative of silicate condensation is shown
+(1150 K) to demonstrate the interplay between variable radiative heating and the inner edges of dust layers. The red, orange, and green vertical
+bars indicate the instants selected for Figs. 2 and 6. The dark area in the lower part of the top panel represents the deep stellar interior, where most
+of the energy flux is transported by convection.
+tons emitted from the stellar surface. As the total radiative flux
+varies due to pulsations, so does the temperature in the dust-
+formation region. This effect is illustrated by an over-plotted
+isotherm (1150 K, typical silicate condensation temperature).
+During the luminosity minima, the atmosphere is coolest and
+the isotherm is closer to the center, meaning that the average
+distance from the star at which dust condensation is possible,
+is smallest. Since the density decreases steeply with the radial
+distance, the phases around luminosity minima are favorable for
+efficient dust condensation. This is apparent in the panel showing
+the grain radii, where pronounced dust formation events (bright
+areas) tend to coincide with deep minima in luminosity.
+A closer inspection shows that the regions of efficient grain
+growth (resulting in large grain radii) are typically closer to the
+star than the isothermal line, which roughly marks the conden-
+sation temperature of silicates. It should be pointed out that the
+radial distance of this line corresponds to a spherical mean, while
+the actual 2D isotherms in the 3D models are far from spherical.
+Figures 2 and 3 illustrate that efficient grain growth events tend
+to occur in high-density regions where lower temperatures pre-
+vail close to the star.
+Figure 5 shows spherical averages of luminosity, radial ve-
+locity, and grain radius as a function of radial depth and time for
+the warmer, more massive model st28gm05n033. In the radial-
+velocity plot, the alternating blue and red vertical stripes be-
+low about 300 R⊙ in the stellar interior indicate radial pulsa-
+tion, as discussed above for the other model. The velocity pat-
+tern both inside the star and in the inner atmosphere (propa-
+gating shocks, indicated by blue stripes pointing upward and
+to the right) looks somewhat more regular for this star with
+higher surface gravity. However, fewer of the global-scale atmo-
+spheric shock waves lead to efficient dust formation events (see
+Article number, page 9 of 14
+
+A&A proofs: manuscript no. aaagb3dfirstwind
+5
+10
+15
+20
+25
+30
+500
+1000
+1500
+r [RO
+ • ]
+     
+ 
+ 
+ 
+ 
+ 
+L* [LO
+ •]
+0
+2000
+4000
+6000
+8000
+5
+10
+15
+20
+25
+30
+500
+1000
+1500
+r [RO
+ • ]
+     
+ 
+ 
+ 
+ 
+ 
+vradial [km s-1]
+-20
+-10
+0
+10
+20
+5
+10
+15
+20
+25
+30
+t [yr]
+500
+1000
+1500
+r [RO
+ • ]
+     
+ 
+ 
+ 
+ 
+ 
+Radius of Mg2SiO4 grains [cm]
+0
+1×10-5
+2×10-5
+3×10-5
+4×10-5
+Fig. 5. Spherical averages of luminosity (integrated radiative flux), radial velocity, and grain radius in the 1.5 M⊙ model st28gm05n033, as a
+function of radial distance and time. In the top and bottom panels, an isotherm with a temperature representative of silicate condensation is shown
+(1150 K) to demonstrate the interplay between variable radiative heating and the inner edges of dust layers. The red, orange, and green vertical
+bars indicate the instants selected for Figs. 3 and 6. The dark area in the lower part of the top panel represents the deep stellar interior, where
+most of the energy flux is transported by convection. The plots are similar to the corresponding ones in Fig 4. However, it is important to note the
+differing spatial and temporal axes, and the different range in grain radii.
+the grain-radius panel), followed by outward acceleration of the
+gas-dust mixture. A majority of the pulsation-induced shocks are
+stopped by infalling material (red). We note, again, that the com-
+putational box is smaller than for model st28gm06n052, and the
+global flow direction in the outer parts of the model is not always
+directed outward (both blue and red colors can be found at the
+upper edge). This is consistent with the less efficient dust forma-
+tion and less dense outflow, as indicated by the spherically and
+temporally averaged structures shown in Fig. 1.
+4. Discussion
+4.1. Comparison with earlier 3D models and with 1D models
+Dynamical models and spatially resolved observations indicate
+that the extended atmospheres of AGB stars are characterized by
+a network of shock waves, triggered by large-scale convective
+flows and stellar pulsations. Our earlier 3D AGB-star models
+suggested that the resulting structures in atmospheric densities
+should lead to a patchy dust distribution in the circumstellar ma-
+terial close to the star (Höfner & Freytag 2019).1 While provid-
+1 For clarity, we point out that this effect is different from the intrin-
+sic instabilities of a circumstellar dust shell, as discussed by Woitke
+(2006a), occurring in 2D models that did not take processes in the star
+and their influences on the circumstellar environment into account.
+Article number, page 10 of 14
+
+Bernd Freytag and Susanne Höfner: Global 3D models of AGB stars with winds
+-600
+-400
+-200
+0
+200
+400
+600
+x [RO
+ • ]
+-600
+-400
+-200
+0
+200
+400
+600
+y [RO
+ • ]
+t=29.296 yr
+-600
+-400
+-200
+0
+200
+400
+600
+x [RO
+ • ]
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+t=29.962 yr
+-600
+-400
+-200
+0
+200
+400
+600
+x [RO
+ • ]
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+t=31.158 yr
+     
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+Normalized surface intensity
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+1.2
+1.4
+-600
+-400
+-200
+0
+200
+400
+600
+x [RO
+ • ]
+-600
+-400
+-200
+0
+200
+400
+600
+y [RO
+ • ]
+t=22.772 yr
+-600
+-400
+-200
+0
+200
+400
+600
+x [RO
+ • ]
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+t=23.065 yr
+-600
+-400
+-200
+0
+200
+400
+600
+x [RO
+ • ]
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+t=23.664 yr
+     
+ 
+ 
+ 
+ 
+ 
+Normalized surface intensity
+0.0
+0.5
+1.0
+1.5
+2.0
+Fig. 6. Time sequences of bolometric surface intensity for the large 1 M⊙ model st28gm06n052 (snapshots about 8 and 14 months apart, see
+the counter at the top of the panels) and the 1.5 M⊙ model st28gm05n033 (snapshots about 3.5 and 7 months apart). Only the inner part of
+computational box that contains the star is plotted, on the same scale for both models.
+ing an explanation for the origin of clumpy dust clouds observed
+around several nearby AGB stars, these earlier models did not
+include radiation pressure, and we could therefore not draw def-
+inite conclusions about atmospheric dynamics and the formation
+of a dust-driven stellar wind.
+In contrast, the new models presented in Sect. 3 account for
+the effects of radiation pressure on the silicate dust that forms
+in the stellar atmosphere, with grain growth rates depending
+on the densities of condensible material in the surrounding gas.
+Dust condensation is most efficient in the dense wakes of shock
+waves, and the basic cloud formation mechanism, which pre-
+cedes wind acceleration, is similar to our earlier 3D models.
+However, we note that the models presented here show more
+pronounced spatial variations in grain size, and the final degree
+of condensation in the outflow, when averaging over time, is far
+from complete (Table 2).
+Incomplete condensation is in line with results of 1D dust-
+driven wind models, where grain growth slows down drastically
+in the accelerating outflow due to rapidly falling densities. This
+typically leaves a significant fraction of condensible material in
+the gas phase (see, e.g., Höfner et al. 2016, 2022). Another fea-
+ture of the new 3D models that is reminiscent of 1D dust-driven
+wind models is the time-dependent behavior of spherically aver-
+aged quantities, as seen in Figs. 4 and 5. The spherical averaging
+highlights the role of radial stellar pulsations, related luminosity
+variations, and resulting large-scale atmospheric shock waves,
+which trigger dust formation events.
+As temperatures and gas densities vary along a shock front,
+in contrast to the situation in 1D models, the dust forms with
+different rates at different locations, leading to regions with very
+high, and others with low or zero, dust densities behind a shock.
+Depending on the statistics of the thermodynamic quantities, the
+net effect on the overall mass loss might be an increase or a de-
+crease, compared to 1D models. The stellar parameter sets of the
+3D models presented here were chosen to fall into two differ-
+ent regimes: according to results from 1D DARWIN simulations,
+model st28gm06n052 is expected to develop a pronounced dust-
+driven wind, while the 1D counterpart of model st28gm05n033
+fails to produce an outflow (see Bladh et al. 2019). In this context
+it is remarkable that the 1.5 M⊙ CO5BOLD model does develop
+a gusty, inhomogeneous wind with a low mass-loss rate, in con-
+trast to its wind-less DARWIN equivalent. This could be due to
+an intrinsically more efficient wind mechanism in the 3D mod-
+els, that is to say, more favorable conditions for dust formation in
+the inhomogeneous atmospheres, with cool dense pockets of gas
+close to the star. However, there are differences in the treatment
+of radiative transfer compared to the DARWIN models that may
+also affect the results and need to be investigated further, before
+more quantitative conclusions can be drawn (see Sect. 4.3).
+4.2. Observable properties
+Using averages of radial velocities and other quantities, taken
+over spherical shells, Freytag et al. (2017) identified radial pul-
+sation in a sample of 3D star-in-a-box models with different stel-
+Article number, page 11 of 14
+
+A&A proofs: manuscript no. aaagb3dfirstwind
+-3000 -2000 -1000
+0
+1000
+2000
+3000
+x [RO
+ • ]
+-3000
+-2000
+-1000
+0
+1000
+2000
+3000
+y [RO
+ • ]
+t=29.296 yr
+-3000 -2000 -1000
+0
+1000
+2000
+3000
+x [RO
+ • ]
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+t=29.962 yr
+-3000 -2000 -1000
+0
+1000
+2000
+3000
+x [RO
+ • ]
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+t=31.158 yr
+     
+ 
+ 
+ 
+ 
+ 
+ 
+Number of Mg2SiO4 monomers [cm-3]
+0
+2×106
+4×106
+6×106
+8×106
+1×107
+Fig. 7. Time sequence of silicate density, through the center of the large 1 M⊙ model st28gm06n052. The snapshots are about 8 and 14 months
+apart, respectively (see the counter at the top of the panels).
+lar parameters. The simulations show periods in good agree-
+ment with the observed P-L relation for Mira variables by
+Whitelock et al. (2009). Recently, Ahmad et al. (2023) analyzed
+the pulsation properties of a much larger set of global 3D models
+produced with the CO5BOLD code, including those presented
+here. The periods determined for models st28gm06n052 and
+st28gm05n033 are 545 and 297 days, respectively, bracketing
+the mean P-L relation derived by Whitelock et al. (2009), with
+both models falling inside the broad range of observed values.
+While the spherically averaged radial velocities show clear
+signs of radial stellar pulsations and dominantly outward-
+directed flow velocities in the outer parts of the models (see
+Figs. 4 and 5), the 2D slices demonstrate the complex nature
+of dynamics in the convective stellar interior and in the stellar
+atmosphere (Figs. 2 and 3). Convective motions, and possibly
+non-radial pulsations, cause shock waves on a wide range of an-
+gular scales. The shocks may merge or collide, leading to in-
+tricate density structures. Some shock waves trigger sufficient
+dust formation and radiative acceleration to overcome gravity,
+leading to an outflow. At the same time, other parts of the atmo-
+sphere show ballistic motions and material falling back toward
+the stellar surface. Both the density and the temperature in the
+atmosphere are strongly variable, and differ from the spherical
+structures expected in case of a purely radial pulsation. Recent
+submillimeter observations have given evidence of simultaneous
+inward and outward directed motions of atmospheric gas, and a
+complex morphology of the extended dynamical atmospheres of
+AGB stars, with coexisting warm and cool gas components (e.g.,
+Khouri et al. 2016b; Vlemmings et al. 2017).
+Paladini et al. (2018) presented H-band images of π1 Gruis
+(based on VLTI/PIONIER data), indicating large granulation
+cells on the stellar surface. The sizes of the observed surface
+structures are in good agreement with extrapolations of local 3D
+models for less evolved stars, and with qualitative predictions of
+global 3D AGB-star models. Figure 6 shows time sequences of
+the bolometric surface intensity for the large 1 M⊙ model and
+the 1.5 M⊙ model plotted on the same spatial scale (zoomed in
+on the star, which is small compared to the computational box).
+Both models have a similar mean luminosity, but the higher mass
+in model st28gm05n033, together with a slightly smaller radius,
+leads to a more well-defined stellar surface with much smaller
+structures. The lower surface gravity in model st28gm06n052,
+on the other hand, results in a much more extended atmosphere,
+favoring efficient dust formation. It should be noted here that the
+images show the bolometric intensity. For a detailed compari-
+son with observations, images in appropriate filter bands have to
+be computed (see Chiavassa et al. 2018, and references therein),
+which is an effort well beyond the scope of the present paper.
+However, the qualitative trends with stellar parameters can be
+expected to be similar to the bolometric images.
+Dust condensation is favored by high density, and therefore
+grain growth is most effective in the dense wakes of outward-
+propagating shocks, as illustrated by the sequence of grain-size
+plots in Fig. 2 for model st28gm06n052. Figure 7 shows the cor-
+responding plots of dust density (total number of monomers con-
+tained in dust grains per unit volume). This quantity can be re-
+garded as a simple proxy for dust emission in the mid-IR, where
+dust grains are small compared to the wavelengths, and the dust
+opacity (emission coefficient) is roughly proportional to the vol-
+ume occupied by the dust. The formation of a new dust cloud
+in the wake of a shock, followed by radiative acceleration away
+from the star, is clearly visible in the lower right quadrant. In
+contrast to the grain size, however, the density decreases as the
+cloud moves outward, as indicated by the darkening of the col-
+ors.
+4.3. Approximations and future improvements
+In current 1D DARWIN models, frequency-dependent radiative
+transfer is routinely computed at several hundred wavelength
+points, thereby achieving a good coverage of the spectral energy
+distribution, while simultaneously solving the equations of hy-
+drodynamics and dust formation (see Höfner et al. 2016, 2022).
+The much more computationally intensive 3D AGB-star models,
+however, are based on an opacity binning scheme, to account for
+non-gray effects (see Sect. 2.2). In this context, it is a nontrivial
+task to introduce dust opacities, which are not simply a function
+of current temperature and density as the pre-tabulated gas opac-
+ities are, but depend on grain sizes that result from nonequilib-
+rium condensation and evaporation processes, and are not known
+a priori.
+In the exploratory 3D "star-and-wind-in-a-box" models pre-
+sented here, we chose to represent the dust opacities relevant
+for radiation pressure by monochromatic values at a wavelength
+near the stellar flux maximum. Furthermore, considering the
+level of other approximations in the radiative transfer, we de-
+scribe the size-dependent efficiency factor for radiation pressure
+on dust grains by a simple analytical formula (see Sect. 2.4). The
+formula reproduces key features of Fe-free silicate dust, such as
+low absorption in the visual and near-IR, and a strong depen-
+Article number, page 12 of 14
+
+Bernd Freytag and Susanne Höfner: Global 3D models of AGB stars with winds
+dence of scattering on grain size for particles with radii smaller
+than the relevant wavelengths. It should give a qualitatively cor-
+rect picture of the dynamics, and the resulting wind velocities
+are, indeed, in the expected range. Nevertheless, we plan to re-
+place the simple formula with optical properties computed with
+Mie theory in future 3D models, similar to what is used in the
+1D DARWIN models.
+Another obvious difference compared to 1D wind models
+is the smaller overall size of the computational domain, ad-
+justed for an efficient use of computational resources. For model
+st28gm06n052, the box extends to distances where the stellar
+wind is well established and close to reaching its terminal veloc-
+ity. The more massive, somewhat hotter model st28gm05n033,
+with its smaller box, on the other hand, illustrates potential prob-
+lems with determining reliable average wind properties for stars
+with higher surface gravity and less favorable conditions for dust
+formation, leading to strongly inhomogeneous outflows with low
+mass-loss rates. In principle, the box of this particular model
+could have been extended to larger distances. In practice, how-
+ever, the model in its current form is sufficient to demonstrate the
+influence of key stellar parameters on the formation of a dust-
+driven wind.
+5. Conclusions
+In this paper we have presented the first global 3D RHD mod-
+els of AGB stars and their dust-driven winds, computed with the
+CO5BOLD code. The models allow us to follow the flow of mat-
+ter from the stellar interior, through the dynamical atmosphere,
+and into the wind-acceleration region, while taking nonequilib-
+rium dust formation and the interaction of matter with radiation
+into account. Convection and pulsations emerge self-consistently
+in the 3D models. Wind properties (e.g. mass-loss rates and out-
+flow velocities) can be derived without relying on parameterized
+descriptions of these interior dynamical processes, in contrast to
+current 1D wind models. Atmospheric shock waves, triggered by
+convective motions and pulsation, play a critical role in the con-
+densation of the dust grains, which drive the winds. A global 3D
+approach is essential to make progress in understanding dynami-
+cal processes in AGB stars, and to solve long-standing problems
+regarding mass loss.
+The giant convection cells, which are a characteristic feature
+of AGB stars, cause large-scale intensity patterns in the stellar
+photosphere, and leave their imprints on atmospheric temper-
+atures and densities. In contrast to 1D models with purely ra-
+dial pulsations and global spherical shocks fronts propagating
+outward through the atmosphere, the shocks induced by con-
+vection and pulsation in the 3D models cover large but finite
+regions. This leads to a patchy, nonspherical structure of the
+atmosphere. Since the efficiency of dust condensation depends
+critically on gas density, new dust clouds mostly emerge in the
+dense wakes of atmospheric shocks. The resulting clumpy dis-
+tribution of newly formed dust, together with radiative pressure
+being highly sensitive to grain sizes, leads to a complex 3D
+morphology of the extended atmosphere and wind-acceleration
+zone, with simultaneous infall and outflow regions close to the
+star.
+Genuine 3D effects in the models are strong deviations of
+isotherms from spherical symmetry and the intermittent forma-
+tion of cool pockets of gas in the stellar vicinity. Efficient dust
+formation tends to occur closer to the star than spherical averages
+of the temperature would indicate, in dense regions where grain
+growth rates are higher than average. This can lead to dust-driven
+outflows with low mass-loss rates in situations where 1D models
+with the same stellar parameters do not produce winds. In con-
+trast, for stars where the overall conditions for dust formation
+and wind acceleration are favorable, it is not obvious whether the
+resulting mass-loss rates will be higher or lower than in the 1D
+case. The increased efficiency of dust formation in high-density
+clumps may be set off by a low filling factor of these regions.
+The key features of the models (high-contrast convective sur-
+face patterns, complex velocity fields, clumpy dust clouds) are
+seen in observations of nearby AGB stars. Synthetic observables
+need to be computed from the dynamical 3D structures in order
+to compare the models to observations in more detail. The pro-
+duction of spectra and images in various wavelength regimes is
+under way, but this is a considerable, time-consuming effort, and
+results will be presented in future papers.
+Based on the first exploratory models discussed in this paper,
+we can mainly draw qualitative conclusions about the physics
+and 3D morphology of AGB-star atmospheres and winds, since
+the simulations include a number of approximations. Improve-
+ments regarding dust microphysics and the treatment of radia-
+tion pressure are planned for future models, to get a better quan-
+titative description of these aspects, and of the resulting wind
+properties.
+Eventually, it will be necessary to produce additional models,
+to explore how mass-loss rates depend on fundamental stellar
+parameters. However, 3D models are time-consuming to com-
+pute and analyze. Therefore, 1D models of dust-driven winds
+will continue to play an important role for the foreseeable future,
+as they can provide the wide coverage of stellar parameter com-
+binations required in stellar evolution models. Hopefully, knowl-
+edge gained from full 3D modeling can be used to improve 1D
+models, in particular regarding a better representation of pulsa-
+tion and convection effects on the stellar atmosphere and wind.
+Acknowledgements. This work is part of a project that has received funding from
+the European Research Council (ERC) under the European Union’s Horizon
+2020 research and innovation programme (Grant agreement No. 883867, project
+EXWINGS) and the Swedish Research Council (Vetenskapsrådet, grant num-
+ber 2019-04059). The computations were enabled by resources provided by the
+Swedish National Infrastructure for Computing (SNIC) partially funded by the
+Swedish Research Council through grant agreement no. 2018-05973. We thank
+the referee Jan Martin Winters for his insightful comments.
+References
+Ahmad, A., Freytag, B., & Höfner, S. 2023, A&A, 669, A49
+Aringer, B. 2000, PhD thesis, Univ. of Vienna, Univ. Wien
+Aringer, B., Girardi, L., Nowotny, W., Marigo, P., & Bressan, A. 2016, MNRAS,
+457, 3611
+Bladh, S., Höfner, S., Aringer, B., & Eriksson, K. 2015, A&A, 575, A105
+Bladh, S., Liljegren, S., Höfner, S., Aringer, B., & Marigo, P. 2019, A&A, 626,
+A100
+Chiavassa, A., Freytag, B., & Schultheis, M. 2018, A&A, 617, L1
+Freytag, B. 2013, Mem. Soc. Astron. Italiana Suppl., 24, 26
+Freytag, B. 2017, Mem. Soc. Astron. Italiana, 88, 12
+Freytag, B. & Höfner, S. 2008, A&A, 483, 571
+Freytag, B., Liljegren, S., & Höfner, S. 2017, A&A, 600, A137
+Freytag, B., Steffen, M., Ludwig, H.-G., et al. 2012, J.Comput.Phys., 231, 919
+Höfner, S. 2008a, Physica Scripta Volume T, 133, 014007
+Höfner, S. 2008b, A&A, 491, L1
+Höfner, S., Bladh, S., Aringer, B., & Ahuja, R. 2016, A&A, 594, A108
+Höfner, S., Bladh, S., Aringer, B., & Eriksson, K. 2022, A&A, 657, A109
+Höfner, S. & Freytag, B. 2019, A&A, 623, A158
+Höfner, S., Gautschy-Loidl, R., Aringer, B., & Jørgensen, U. G. 2003, A&A,
+399, 589
+Höfner, S. & Olofsson, H. 2018, A&A Rev., 26, 1
+Jäger, C., Dorschner, J., Mutschke, H., Posch, T., & Henning, T. 2003, A&A,
+408, 193
+Jeong, K. S., Winters, J. M., Le Bertre, T., & Sedlmayr, E. 2003, A&A, 407, 191
+Khouri, T., Maercker, M., Waters, L. B. F. M., et al. 2016a, A&A, 591, A70
+Khouri, T., Vlemmings, W. H. T., Ramstedt, S., et al. 2016b, MNRAS, 463, L74
+Article number, page 13 of 14
+
+A&A proofs: manuscript no. aaagb3dfirstwind
+Norris, B. R. M., Tuthill, P. G., Ireland, M. J., et al. 2012, Nature, 484, 220
+Ohnaka, K., Weigelt, G., & Hofmann, K.-H. 2016, A&A, 589, A91
+Ohnaka, K., Weigelt, G., & Hofmann, K.-H. 2017, A&A, 597, A20
+Paladini, C., Baron, F., Jorissen, A., et al. 2018, Nature, 553, 310
+Schwarzschild, M. 1975, ApJ, 195, 137
+Stewart, P. N., Tuthill, P. G., Nicholson, P. D., & Hedman, M. M. 2016, MNRAS,
+457, 1410
+Trabucchi, M., Wood, P. R., Montalbán, J., et al. 2017, ApJ, 847, 139
+Trabucchi, M., Wood, P. R., Mowlavi, N., et al. 2021, MNRAS, 500, 1575
+Vlemmings, W., Khouri, T., O’Gorman, E., et al. 2017, Nature Astronomy, 1,
+848
+Wachter, A., Schröder, K. P., Winters, J. M., Arndt, T. U., & Sedlmayr, E. 2002,
+A&A, 384, 452
+Whitelock, P. A., Menzies, J. W., Feast, M. W., et al. 2009, MNRAS, 394, 795
+Winters, J. M., Le Bertre, T., Jeong, K. S., Helling, C., & Sedlmayr, E. 2000,
+A&A, 361, 641
+Wittkowski, M., Hofmann, K. H., Höfner, S., et al. 2017, A&A, 601, A3
+Woitke, P. 2006a, A&A, 452, 537
+Woitke, P. 2006b, A&A, 460, L9
+Wood, P. R. 2015, MNRAS, 448, 3829
+Zeidler, S., Posch, T., Mutschke, H., Richter, H., & Wehrhan, O. 2011, A&A,
+526, A68
+Article number, page 14 of 14
+
diff --git a/P9FKT4oBgHgl3EQfhC52/content/tmp_files/load_file.txt b/P9FKT4oBgHgl3EQfhC52/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2840ec5328e2ba8d79ea8f07ef18359adf43e1bd
--- /dev/null
+++ b/P9FKT4oBgHgl3EQfhC52/content/tmp_files/load_file.txt
@@ -0,0 +1,830 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf,len=829
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='11836v1  [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='SR]  27 Jan 2023 Astronomy & Astrophysics manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' aaagb3dfirstwind ©ESO 2023 January 30, 2023 Global 3D radiation-hydrodynamical models of AGB stars with dust-driven winds Bernd Freytag and Susanne Höfner Theoretical Astrophysics, Department of Physics and Astronomy, Uppsala University, Box 516, SE-751 20 Uppsala, Sweden e-mail: Bernd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='Freytag@physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='uu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='se January 30, 2023 ABSTRACT Context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Convection and mass loss by stellar winds are two dynamical processes that shape asymptotic giant branch (AGB) stars and their evolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Observations and earlier 3D models indicate that giant convection cells cause high-contrast surface intensity patterns, and contribute to the origin of clumpy dust clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Aims.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' We study the formation and resulting properties of dust-driven winds from AGB stars, using new global 3D simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The dynamical stellar interiors, atmospheres, and wind acceleration zones of two M-type AGB stars were modeled with the CO5BOLD code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' These first global 3D simulations are based on frequency-dependent gas opacities, and they feature time-dependent condensation and evaporation of silicate grains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Convection and pulsations emerge self-consistently, allowing us to derive wind properties (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', mass-loss rates and outflow velocities), without relying on parameterized descriptions of these processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='  In contrast to 1D models with purely radial pulsations, the shocks induced by convection and pulsation in the 3D models cover large parts, but not the entirety, of the sphere, leading to a patchy, nonspherical structure of the atmosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Since dust condensation critically depends on gas density, new dust clouds form mostly in the dense wakes of atmospheric shocks, where the grains can grow efficiently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The resulting clumpy distribution of newly formed dust leads to a complex 3D morphology of the extended atmosphere and wind-acceleration zone, with simultaneous infall and outflow regions close to the star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Highly nonspherical isotherms and short-lived cool pockets of gas in the stellar vicinity are prominent features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Efficient dust formation sets in closer to the star than spherical averages of the temperature indicate, in dense regions where grain growth rates are higher than average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' This can lead to weak outflows in situations where corresponding 1D models do not produce winds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' For stars where the overall conditions for dust formation and wind acceleration are favorable, it is unclear whether the resulting mass-loss rates will be higher or lower than in the 1D case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The increased efficiency of dust formation in high-density clumps may be offset by a low volume coverage of the forming clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Conclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' A global 3D approach is essential to make progress in understanding dynamical processes in AGB stars, and, in partic- ular, to solve long-standing problems regarding mass loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='  Key words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' convection – shock waves – stars: AGB and post-AGB – stars: atmospheres – stars: oscillations (including pulsations) – stars: mass-loss 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Introduction During the late stages of evolution on the asymptotic giant branch (AGB), low- and intermediate-mass stars are strongly af- fected by large-scale dynamical processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Convection and mass loss through stellar winds influence the evolution, appearance, and final fate of these stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' They cause an enrichment of the sur- rounding interstellar medium with nucleosynthesis products and dust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Large-amplitude, long-period pulsations play a critical role in the formation of the dust grains that drive the massive outflows of AGB stars through radiation pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The pulsations trigger atmospheric shock waves, which lift gas to distances where tem- peratures are sufficiently low to allow for condensation of sili- cates and other relevant solids (for a recent review on AGB mass loss, see Höfner & Olofsson 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The current theoretical picture of dynamical atmospheres and dust-driven winds of AGB stars is mainly derived from time- dependent spherically symmetric models (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Winters et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2000;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Jeong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Höfner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2003, 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Such simu- lations describe the varying radial profiles of densities, tempera- tures, velocities, and dust properties, accounting for the shock waves that are triggered by pulsation and propagate outward through the atmospheres.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='  Radiation-hydrodynamical DARWIN models, combining frequency-dependent radiative transfer with nonequilibrium dust formation, suggest that the dust-driven winds of M-type AGB stars are initiated by photon scattering on Fe-free silicate grains (Höfner 2008b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Such particles are nearly transparent at visual and near-IR wavelengths (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Jäger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Zeidler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2011), resulting in significantly less radia- tive heating by stellar photons and, consequently, smaller con- densation distances, than for their Fe-bearing counterparts (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Woitke 2006b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Höfner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In order to cause sufficient radiation pressure by pure scattering, however, these dust grains have to grow to rather large sizes (typical radii of about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='1 – 1 µm;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' comparable to wavelengths near the stellar flux maxi- mum).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The existence of such large grains in the close stel- lar environment is consistent with spatially resolved observa- tions of scattered light around several nearby AGB stars (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Norris et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Ohnaka et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2016, 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Over the past few decades, 1D dynamical models of AGB- star atmospheres and winds have given valuable insights into the critical physical processes and dust properties, as outlined above, and on the dependence of mass-loss rates on stellar parameters (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Wachter et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2002;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Bladh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2015, 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The compu- Article number, page 1 of 14  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' aaagb3dfirstwind tational efficiency of such simulations has made it possible to generate large grids of models, but the computational domains usually do not include the regions of the star where the pulsations are excited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The effects of stellar pulsation on the atmosphere and wind are typically introduced through variable physical con- ditions at the inner boundary, just below the stellar photosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Periodic motions simulate the radial expansion and contraction of the star, accompanied by luminosity variations, in so-called piston models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In this approach, the periods and amplitudes of the variations are free parameters that need to be constrained by observations or models of the pulsating stellar interior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Producing realistic theoretical models of pulsating AGB stars, however, has turned out to be a difficult task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In re- cent years, progress has been made regarding lower ampli- tude overtone pulsation by applying a linear nonadiabatic ap- proach (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Wood 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Trabucchi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Lately, using 1D nonlinear pulsation models, Trabucchi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' (2021) resolved some earlier discrepancies between predicted and observed ra- dial fundamental-mode periods of Mira variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' A basic problem with 1D stellar interior models is that they have to use a parameterized description of convection, which is an intrinsically 3D process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='  Classical descriptions such as mixing-length theory, with appropriately chosen parameters, work reasonably well in stellar evolution models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Regarding stel- lar pulsation, however, 1D recipes for treating convective energy transport are probably not adequate in the case of AGB stars, as they show strongly nonlinear, nonadiabatic, large-scale con- vective motions that couple to pulsation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Turbulent gas flows occur on scales comparable to the stellar radius, giving rise to pronounced surface intensity patterns (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Schwarzschild 1975;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Freytag & Höfner 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Freytag et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In recent years, with the progress in high-angular-resolution observations, it has become possible to obtain spatially resolved data for a few nearby AGB stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Imaging of stellar surface structures at near-IR wavelengths has revealed patterns in good agreement with convective surface structures in 3D models (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Paladini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Spatially resolved data in the submillime- ter regime show complex dynamical atmospheric structures with simultaneous inward and outward motions, as well as the coexis- tence of hot and cold gas (Khouri et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2016b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Vlemmings et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Nonspherical distributions of gas and dust in the close circumstellar environment are also seen in high-resolution im- ages at visual and infrared wavelengths (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Ohnaka et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Stewart et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Wittkowski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='  Visual and near-IR scattered light images of circumstellar material have given infor- mation about the properties of dust clouds close to the star, and about the sizes of the dust grains within them (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Norris et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Temporal monitoring shows changes in both atmospheric morphology and grain sizes over the course of weeks or months (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Khouri et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2016a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Ohnaka et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Global 3D radiation-hydrodynamical (RHD) models offer a promising way of solving existing problems with interior dy- namics (convection, pulsation) and, at the same time, gain- ing an understanding of the complex observed atmospheric structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The pioneering AGB "star-in-a-box" models by Freytag & Höfner (2008) and Freytag et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' (2017), building on the capability of the CO5BOLD code to cover the entire outer convective envelope and atmosphere, indeed show both large- scale convection and self-excited radial pulsations with realistic periods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Recently, Ahmad et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' (2023) analyzed a much larger sample of global 3D CO5BOLD models of evolved stars, find- ing a good agreement of the results with the observed period- luminosity relations for AGB stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' An inhomogeneous distribution of atmospheric gas, as seen in observations, is a natural consequence of large-scale con- vective flows below the photosphere and the resulting net- work of atmospheric shock waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='  The exploratory models of Freytag & Höfner (2008) and Höfner & Freytag (2019) indi- cated that the dynamical patterns in the gas will leave imprints on the dust in the close stellar environment, due to the density and temperature sensitivity of the grain growth process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' How- ever, these earlier 3D simulations did not include the effects of radiation pressure on dust, and could therefore not predict the structure of the wind formation zone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In this paper, we present the first global 3D RHD simula- tions of dust-driven winds of AGB stars, exploring the interplay of convection, pulsation, atmospheric shocks, dust formation, and wind acceleration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In addition to the newly implemented ra- diative pressure on dust, these new models also feature a much larger computational domain, covering the inner wind region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' This allows us to follow the emerging 3D structures to a dis- tance where the outflow is established, and to compute mass-loss rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2, we give a brief overview of the basic physical assumptions and numerical methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The results are presented in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 3, and compared to observations in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Finally, a summary and conclusions are given in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Setup of global AGB-star models Below, we give a short summary of the physical and numer- ical properties of the CO5BOLD code, focusing on features that are relevant for the new simulations presented in this pa- per.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='  More details can be found in our earlier papers on global AGB-star models (Freytag & Höfner 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Freytag et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Höfner & Freytag 2019) and on the properties of wind-driving dust grains in M-type AGB stars (Höfner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' General properties of the CO5BOLD models The CO5BOLD code (Freytag et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2012) numerically inte- grates the coupled nonlinear equations of compressible hydro- dynamics and nonlocal radiative energy transfer on a Cartesian grid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The hydrodynamics scheme is based on an approximate Riemann solver of Roe-type (see Freytag 2013), modified to account for the effects of ionization and gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The tabulated equation of state (assuming solar abundances) takes the ioniza- tion of hydrogen and helium, and the formation of H2 molecules into account.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Gravitation is included as an external potential, with a general 1/r profile, that is smoothed in the central re- gion of the star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In this central volume, heat is added as a con- stant source term, corresponding to the stellar luminosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' A drag force is active in this core region only, to prevent dipolar flows traversing the entire star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' All outer boundaries are open for the flow of matter and for radiation (see Freytag 2017, for some de- tails about boundary conditions in CO5BOLD).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='  Computational domain and radiative transfer A global model describing the flow of gas and radiation from the convective stellar interior, through the dynamical atmosphere, to the dust formation region and wind-acceleration zone, needs to cover a wide range of physical conditions on different spatial and temporal scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' To keep computation times at a reasonable level, the spatial domain of the new global models is divided into two regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' An inner box, covering the star and its immedi- ate surroundings, features a more detailed description of radia- Article number, page 2 of 14  Bernd Freytag and Susanne Höfner: Global 3D models of AGB stars with winds Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Basic model parameters and derived quantities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' model M⋆ Menv L⋆ n3 x xouterbox xinnerbox CTfac tavg R⋆,smin Teff,smin log gsmin Ppuls (M⊙) (M⋆) (L⊙) (R⊙) (R⊙) (yr) (R⊙) (K) cgs (d) st28gm06n050 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='182 7049 5993 4858 2340 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='75 54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='61 351 2823 -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='656 510 st28gm06n052 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='181 7030 6793 6386 2640 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='77 57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='78 355 2806 -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='665 545 st28gm05n033 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='298 6702 5593 3454 1581 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='72 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='70 304 2993 -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='358 297 Notes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The table shows the model name;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' the mass M⋆, used for the external potential;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' the envelope mass Menv, derived from integrating the mass density of all grid cells within the computational box;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' the average emitted luminosity L⋆;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' the model grid dimensions n3 x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' the edge length of the entire cubical computational box xouterbox;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' the edge length of the inner box with detailed radiation transport xinnerbox;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' the adjustable temperature- reduction factor CTfac in the outer layers;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' the time tavg, used for averaging the remaining quantities in this table;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' the radius R⋆,smin at the point with minimum entropy;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' the effective temperature Teff,smin at minimum entropy;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' the logarithm of the surface gravity log gsmin at minimum entropy;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' and the pulsation period Ppuls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' tive transfer, which is critical for the modeling of temperature structures (see below) and a higher spatial resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='  It is sur- rounded by a larger outer box with a simplified radiative transfer and a coarser grid, beyond the main grain growth region, where the wind has been initiated and dynamical structures tend to be larger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Regarding hydrodynamics, there is no difference between the two boxes, except for the grid spacing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The inner box con- sists of cubical cells with a constant size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In the outer box, going outward, cells become incrementally larger along the axis direc- tions (typically by a few percent per step) and only those along the space diagonals retain a cubical shape, while their size in- creases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In the inner box, the nonlocal radiative energy transfer is solved with a short-characteristics scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Most of our earlier global 3D RHD simulations of AGB stars used tabulated gray gas opacities, which is sufficient for studies of interior proper- ties such as convection and pulsations, and to give a qualita- tive picture of the shock-dominated atmospheric dynamics (see Freytag et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Simulations including dust formation, how- ever, require a refined modeling of the atmospheric temperature structure, which sets thresholds for the onset of dust condensa- tion and evaporation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' This can be achieved by using frequency- dependent data, as discussed in Höfner & Freytag (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='  In the new models of dust-driven winds presented in this paper, we use a similar approach with three frequency bins, but we have re- done the iterative binning procedure for a larger region of the representative pressure-temperature structure, due to the larger computational box used here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The tables for atmospheric gas opacities used in the present models are based on COMA data (see Aringer 2000;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Aringer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2016), extended with OPAL data at temperatures above approximately 12 000 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Scattering is treated as true absorption, that is to say, the scattering opacity is added to the absorption opacity, so that the source function can be computed from the local temperature alone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In the outer box, where the outflow is established and further grain growth is of minor importance, temperature plays a less critical role.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Therefore, we use an approximate description, suf- ficient for the purpose of hydrodynamics, which is computation- ally much less costly than solving radiative transfer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The average radial temperature profile is assumed to be set by the radiative flux from the stellar surface, geometrically diluted with distance, which can be written as T(r) ∝ (L/r2)1/4, where L is the mean stellar luminosity and r the radial distance from the center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' To minimize the jump in temperature from the inner box (with de- tailed radiative transfer, as described above), an adjustable factor CTfac (see Table 1) is included in the description of T(r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='  In each time step, the internal energy at each grid point in the outer lay- ers is adjusted, so that the actual temperature relaxes toward the approximate target temperature on a small but finite timescale (typically 104 s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Dust formation In the new global models with dust-driven winds, we use a time- dependent kinetic treatment of silicate formation and destruc- tion, adapted from the DARWIN models, as described in de- tail by Höfner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The dust grains grow by the ad- dition of abundant atoms and molecules from the gas phase, and they may shrink due to thermal evaporation from the grain surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The growth of grains is triggered by the temperature falling below a critical value (depending on gas density;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 1 in Höfner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Conversely, when the temperature rises above this value, the grains start to shrink due to evapora- tion from the surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' At the relatively low densities in the stellar atmosphere, grain growth typically occurs on timescales that are comparable to those of gas dynamics and radiative flux varia- tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Grain growth and evaporation may, therefore, proceed far from equilibrium, making a time-dependent treatment necessary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The condensation of wind-driving olivine-type silicate grains is assumed to proceed according to the net reaction 2 Mg + SiO + 3 H2O −→ Mg2SiO4 + 3 H2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' (1) In principle, olivine-type silicates can be considered as a solid solution of Mg2SiO4 and Fe2SiO4, with a variable Fe/Mg ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='  However, as discussed by Höfner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' (2022), the inclusion of Fe atoms in the growing grains is a secondary process, taking place after the wind has been triggered by Fe-free silicate dust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The Fe/Mg ratio remains low, due to a self-regulating feedback via the grain temperature, and due to rapidly falling densities in the outflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The resulting effects on wind dynamics are small, and therefore we only consider the condensation of Fe-free sil- icates (Mg2SiO4) in the exploratory 3D wind models presented here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' It should be noted that the kinetic treatment of grain growth used here does not describe nucleation, that is, the formation of the very first solid seed particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Since nucleation rates and the chemical composition of seed particles in M-type AGB stars are still a matter of debate, the abundance of seed particles relative to hydrogen is treated as an input parameter (for a more detailed discussion see Höfner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' It is assumed that these seed particles are readily available whenever conditions permit the condensation of silicate dust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' They are tiny compared to the re- sulting dust grains, and they have no effect other than providing an initial condensation surface for grain growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Article number, page 3 of 14  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' aaagb3dfirstwind 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Radiation pressure on dust In contrast to the pre-tabulated gas opacities (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='2), the dust opacities that cause radiative acceleration are calculated during the simulations, using the current grain radii that result from the equations describing dust condensation and evapora- tion (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The total opacity of grains with radius agr in a volume element (cross section per volume) can be expressed as κacc(agr, λ) = πa2 gr Qacc(agr, λ) nd , (2) where nd is the corresponding number density of grains and λ represents the wavelength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The efficiency factor Qacc(agr, λ), de- fined as the ratio of radiative to geometrical cross section of a grain, contains contributions from true absorption and scatter- ing: Qacc = Qabs + (1 − gsca) Qsca , (3) where gsca is an asymmetry factor describing deviations from isotropic scattering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In principle, the efficiency factors and gsca can be computed using Mie theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In the exploratory 3D wind models presented here, however, we use a simplified description of Qacc, retaining the critical dependence on grain size, but treating the dependence on wavelength in an approximate way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='  We assume that the flux mean of the opacity determining radiative acceleration can be replaced by a monochromatic value at a wavelength close to the flux maximum, κacc(agr, λmax), where λmax ≈ 1µm, and we use a simple analytical approximation for Qacc as a function of grain radius: Qacc(agr, λmax) = min \uf8ee\uf8ef\uf8ef\uf8ef\uf8ef\uf8ef\uf8f0 \uf8eb\uf8ec\uf8ec\uf8ec\uf8ec\uf8ec\uf8edq1 � agr λmax � + q4 � agr λmax �4\uf8f6\uf8f7\uf8f7\uf8f7\uf8f7\uf8f7\uf8f8 , qmax \uf8f9\uf8fa\uf8fa\uf8fa\uf8fa\uf8fa\uf8fb , (4) introduced by Höfner (2008a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The term linear in grain radius represents true absorption for grains smaller than the wave- length under consideration, while scattering in that regime is ac- counted for by the term depending on the fourth power of the grain radius, which dominates for near-transparent Fe-free sili- cate grains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The fact that the efficiency factor approaches a con- stant value for grains much larger than the wavelength is taken into consideration by setting a maximum value qmax.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Choosing q1 = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='0 · 10−3, q4 = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='68 · 102 and qmax = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='0 at λmax = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='08 µm gives a description that stays reasonably close to Qacc computed from full Mie theory, considering the level of the other approx- imations in the radiative transfer, and the fact that Qacc varies over several orders of magnitude within the grain-size range of interest (see Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 3 and 4 in Höfner 2008a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' To compute the radiative force acting on the dust grains, the opacity κacc has to be multiplied with a factor describing the photon flux from the star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='  In an optically thin environment, this corresponds to a geometrically diluted flux from the stellar sur- face, decreasing with radial distance roughly as 1/r2 (assuming that the star can be approximated by a point source).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' However, if the optical depth of the circumstellar dust is not negligible, leading to a weakening of the local photon flux, this effect has to be taken into account, which is done by introducing a factor (1 − exp (−dτ)), where dτ is the local optical depth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' We chose dτ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='02rκacc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' This situation can arise during dust formation in small high-density regions in the wake of shocks, corresponding to typical length scales of a few percent of the radial distance r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In practice, however, the optical depth effects are usually negli- gible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Currently, radiation pressure is the only dust opacity effect taken into account.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The Fe-free silicate grains are very trans- parent at near-IR wavelengths, where the stellar flux has its maximum, and the corresponding absorption coefficients are ne- glected when solving radiative energy transfer in the inner box to obtain the temperature structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The dust grains are assumed to have the same temperature as the gas, which is mainly rele- vant for the thresholds for condensation and evaporation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' This approximation is in line with the other simplifications concern- ing the dust component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='  Input parameters and resulting model properties In this paper we present a selection of new 3D AGB-star mod- els with dust-driven winds, demonstrating the effects of stellar and numerical parameters (see Table 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Models st28gm06n050 and st28gm06n052 are similar, except for the sizes of the in- ner and outer computational boxes, and the adjustable factor of the target temperature CTfac in the outer box, which ensures a smooth transition in temperature from the domain of detailed ra- diative transfer to the outer box (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The mean radial structures of models st28gm06n050 and st28gm06n052, aver- aged over spherical shells and time, are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 1 (dashed black and solid red curves), demonstrating that box size and the simplified treatment of the radiative transfer in the outer box only have a minor effect on the resulting wind dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In particular, the mean radial-velocity profiles are almost identi- cal for the two models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In the following, we focus our discus- sion on model st28gm06n052, which has both a larger inner and outer box, and therefore allows us to follow the development of 3D structures in more detail, and to larger distances from the star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The blue curves in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 1 show the mean radial structure of model st28gm05n033, which has a higher mass, a smaller ra- dius, and a higher effective temperature, compared to models st28gm06n050 and st28gm06n052.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='  This leads to less favorable conditions for dust formation and wind acceleration, as is dis- cussed in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Table 1 summarizes the basic parameters and resulting global properties of the models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' While the stellar mass M⋆ (control- ling the gravitational potential), as well as the resolution and the extent of the numerical grid, are pre-chosen fixed parameters, other model properties are determined after a simulation is fin- ished.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The envelope mass Menv is calculated from the integrated density of all grid cells, averaged over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' We assume that the difference in mass is located in the compact, unresolved stellar core.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The listed stellar luminosity is a time average of the to- tal luminosity emitted at the surface (very similar to the inserted luminosity of 7000 L⊙ in the core).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The stellar radius is more difficult to determine and is less well defined due to the complex morphology of the extended at- mosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Here, we use a value corresponding to the point of minimum entropy near the photosphere, which has turned out to be a good choice in connection with the analysis of pulsation properties (Ahmad et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2023).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' We note that this definition is different from the one used in earlier papers (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Freytag et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Höfner & Freytag 2019), where the radius was chosen as the point R⋆ where the spherically and temporally aver- aged temperature and luminosity fulfill ⟨L⟩Ω,t = 4πσR2 ⋆⟨T⟩4 Ω,t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='  For the less massive and cooler models st28gm06n050 and st28gm06n052, the latter definition leads to values that are about 10% larger, while both definitions give very similar values for model st28gm05n033, which has a more compact atmosphere Article number, page 4 of 14  Bernd Freytag and Susanne Höfner: Global 3D models of AGB stars with winds Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Dust and wind properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' model nd/nH ˙M fMg agr (M⊙/yr) (µm) st28gm06n052 3 · 10−16 5 · 10−6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='8 st28gm05n033 3 · 10−15 5 · 10−8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='2 Notes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Listed here are the assumed seed particle abundance nd/nH, and the resulting temporal means of the mass-loss rate ˙M, the fraction of Mg condensed into grains fMg, and the grain radius agr at the outer bound- ary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' When forming Mg2SiO4 grains in a gas of solar composition, the abundance of Mg is the limiting factor, since that element will be used up first.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In the models described here, however, fMg is well below its maximum value of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 1, showing the mean radial density and temperature structures).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In contrast to our earlier 3D simulations of AGB stars, the new models presented here predict mass-loss rates and properties of wind-driving dust grains (see Table 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The dust properties are a direct result of solving the equations describing grain growth and evaporation (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The mass-loss rate of a model is computed by averaging the mass flux across spherical shells and time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Results In this section, we describe in detail the emergence and evolution of atmospheric and circumstellar structures triggered by large- scale convective flows and stellar pulsation, and study the persis- tence of inhomogeneities in the gas and dust distributions during the onset of dust-driven outflows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='  In the following, we focus on the description of these phenomena in model st28gm06n052, us- ing the more massive and hotter model st28gm05n33 mainly to illustrate the influence of stellar parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Formation and evolution of dust clouds Figure 2 shows the evolving structures in model st28gm06n052 for slices through the center of the star, at three instants of time (left to right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The top row of panels shows the gas density, illus- trating the strong contrast between the high values in the stellar interior (bright colors at the center of the image) and the thin circumstellar material, with a steep transition region in the inner atmosphere (it is important to note the logarithmic scale).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In the second row of panels, showing radial velocity, these different zones can be distinguished by their dynamical behav- ior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The stellar interior (inside a radius of about 350 R⊙ from the center) is dominated by large-scale convective flows, corre- sponding to variable blue and red areas that represent outflows and inflows, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In the atmosphere, the convective flows, together with radial pulsations, trigger strong, outward- propagating shock waves, seen as dark blue arc-like structures in the 2D slices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Beside these shock-accelerated regions, there are large areas where gas is falling back toward the star (appar- ent in red), since the inner atmosphere is gravitationally bound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='  The wind-acceleration region corresponds to the blue region in the outer parts of the model, indicating the outflow of matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' As discussed above, the stellar wind is driven by radiation pressure on dust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The grains collide with the surrounding gas particles and transfer outward-directed momentum, thereby initiating the wind.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The bottom row of panels in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2 shows the silicate grain radius, with brighter colors indicating larger grains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The spatial 0 1000 2000 3000 4000 -16 -14 -12 -10 -8 -6 log(ρ/[g cm-3]) st28gm06n052: M= 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='0 MO •, L= 7029 LO • , R=354 RO • , xbox= 6386.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='1 RO • st28gm06n050: M= 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='0 MO •, L= 7048 LO • , R=350 RO • , xbox= 4858.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='2 RO • st28gm05n033: M= 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='5 MO •, L= 6701 LO • , R=304 RO • , xbox= 3454.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='1 RO • 0 1000 2000 3000 4000 0 5 10 15 20 vradial [km s-1] 0 1000 2000 3000 4000 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='5 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='0 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='5 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='0 log(T/[K]) st28gm06n052: M= 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='0 MO •, L= 7029 LO • , R=354 RO • , xbox= 6386.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='1 RO • st28gm06n050: M= 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='0 MO •, L= 7048 LO • , R=350 RO • , xbox= 4858.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='2 RO • st28gm05n033: M= 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='5 MO •, L= 6701 LO • , R=304 RO • , xbox= 3454.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='1 RO • 0 1000 2000 3000 4000 r [RO • ] 2×10-5 4×10-5 6×10-5 8×10-5 Radius of Mg2SiO4 grains [cm] Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Mean radial structures of the models st28gm06n050 (dashed black curves), st28gm06n052 (red curves), and st28gm05n033 (blue curves).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Shown are gas density, radial velocity, temperature, and sili- cate grain radius, averaged over spherical shells and time, and plotted against the distance from the stellar center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='  Averages are not only taken over spheres that fit completely into the cubical computational box, but also over partial spheres somewhat beyond, up to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='5× xouterbox/2, omit- ting the regions close to the corners of the cube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The dotted red and blue curves in the radial-velocity panel represent the escape velocity as a function of distance for stellar masses of 1 M⊙ and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='5 M⊙, respec- tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' For details, see Sects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='5 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Article number, page 5 of 14  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' aaagb3dfirstwind  3000  2000  1000 0 1000 2000 3000 y [RO  ] t=29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='296 yr  t=29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='962 yr  t=31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='158 yr  log(ρ [g cm 3]) 16 14 12 10 8  3000  2000  1000 0 1000 2000 3000 y [RO  ] t=29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='296 yr  t=29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='962 yr  t=31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='158 yr  vradial [km s 1] 20 10  0  10  20  3000  2000  1000 0 1000 2000 3000 y [RO  ] t=29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='296 yr  t=29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='962 yr  t=31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='158 yr  log(T [K])  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='5  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='5 3000 2000 1000  0  1000  2000  3000  x [RO ] 3000 2000 1000  0  1000  2000  3000  y [RO ]  t=29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='296 yr 3000 2000 1000  0  1000  2000  3000  x [RO ]  t=29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='962 yr 3000 2000 1000  0  1000  2000  3000  x [RO ]  t=31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='158 yr  Radius of Mg2SiO4 grains [cm] 0 2×10-5 4×10-5 6×10-5 8×10-5 1×10-4 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Time sequences of density, radial velocity, temperature, and silicate grain radius for a slice through the center of the large 1 M⊙ model st28gm06n052.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The snapshots are about 8 and 14 months apart, respectively (see the counter at the top of the panels).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The orange line in the bottom panels indicates an isotherm of 1150 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' patterns in grain size reflect the effects of density and tempera- ture on the condensation process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Higher densities lead to faster, more efficient grain growth, and the brightest areas (largest grains) are found in the wakes of shock waves, which compress the gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The central dark zone indicates the region where dust formation is prevented by high temperatures (see panels in row 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The over-plotted line in the grain-size panels represents an isotherm at 1150 K, corresponding roughly to the condensation temperature of the silicate grains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In the bottom right quadrant of the images, a new dust cloud (bright area in grain-size plots) is forming in the wake of an outward-propagating shock wave, which compresses the Article number, page 6 of 14  Bernd Freytag and Susanne Höfner: Global 3D models of AGB stars with winds  1500  1000  500 0 500 1000 1500 y [RO  ] t=22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='772 yr  t=23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='065 yr  t=23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='664 yr  log(ρ [g cm 3]) 18 16 14 12 10 8 6  1500  1000  500 0 500 1000 1500 y [RO  ] t=22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='772 yr  t=23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='065 yr  t=23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='664 yr  vradial [km s 1] 20 10  0  10  20  1500  1000  500 0 500 1000 1500 y [RO  ] t=22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='772 yr  t=23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='065 yr  t=23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='664 yr  log(T [K])  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='5  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='0 1500 1000 500  0  500  1000 1500  x [RO ] 1500 1000 500  0  500  1000  1500  y [RO ]  t=22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='772 yr 1500 1000 500  0  500  1000 1500  x [RO ]  t=23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='065 yr 1500 1000 500  0  500  1000 1500  x [RO ]  t=23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='664 yr  Radius of Mg2SiO4 grains [cm] 0 1×10-5 2×10-5 3×10-5 4×10-5 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Time sequences of density, radial velocity, temperature, and silicate grain radius for a slice through the center of the 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='5 M⊙ model st28gm05n033.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The snapshots are about 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='5 and 7 months apart, respectively (see the counter at the top of the panels).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The orange line in the bottom panels indicates an isotherm of 1150 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' gas (blue arc in the radial velocity plots and brighter orange in the density plots).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Initially appearing as a small bright region in the grain radius plot (bottom row, left panel), the cloud quickly grows in size, with its inner edge defined by the condensation temperature (middle panel), before being driven outward by ra- diation pressure (right panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In the bottom left quadrant, an existing cloud that was formed earlier in a similar way, is ac- celerated outward by radiation pressure, leaving the model do- Article number, page 7 of 14  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' aaagb3dfirstwind main.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Another outward-moving cloud can bee seen in the top left quadrant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The fact that the series of snapshots (covering about 22 months in total) shows several distinct dust clouds in- dicates that efficient dust formation events, triggered by shock waves, occur frequently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' It should, however, be mentioned here that not all dust clouds survive and lead to an outflow of matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In some cases, the variations in the radiative flux and the result- ing changes in atmospheric temperatures lead to dust evapora- tion, before the cloud is accelerated outward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' This is consistent with the coexistence of inward and outward moving gas in the atmosphere, mentioned above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Overall morphology and wind properties The dependence of grain growth rates on density gives the stellar wind a patchy, time-variable start.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' As clumps of dusty gas move outward and merge into a general outflow, some degree of inho- mogeneity is preserved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Looking at Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2, there are clear signs of a stellar wind in the outer regions of model st28gm06n052, with a dominant direction of the flow velocity away from the star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' However, the density and dust-grain size still show imprints of the atmospheric shock waves that triggered dust condensation, and thereby the onset of the wind.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The radial structure of model st28gm06n052, averaged over spherical shells and time, is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 1 (red curves).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='  In the plots of the mean radial velocity, the time-dependent dynamics of the stellar interior and atmosphere averages out, and the dom- inant flow direction of the wind is clearly visible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' After an initial phase of fast grain growth, dust condensation slows down, as density drops rapidly in the accelerating wind.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' At about 3000 R⊙ (corresponding to about eight stellar radii), the average radial ve- locity of the flow exceeds the local escape velocity (dotted red line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' When the outflow approaches a constant velocity further out, the density profile changes from a steep decline to the fa- miliar 1/r2 profile of a spherical wind with constant velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 1, the time-averaged radial structures of models with different stellar parameters are compared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' It is evident that model st28gm05n033 (blue curves), representing a more massive, hot- ter star with a smaller radius, shows a much steeper atmo- spheric density decrease.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' At a distance where temperatures are low enough for dust condensation, the difference in density com- pared to model st28gm06n052 is about two orders of magnitude, leading to much less efficient grain growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Despite a higher seed-particle abundance in model st28gm05n033, the final de- gree of condensation is lower by about a factor of three, com- pared to the cooler, less massive model st28gm06n052, and the mass-loss rate is lower by about two orders of magnitude, corre- sponding to the difference in atmospheric gas densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='  While the lower mass-loss rate of model st28gm05n033 can be explained by the lower atmospheric densities, it should also be mentioned here that the outflow of this hotter, more mas- sive model is much more variable, due to the low efficiency of grain growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' As is shown in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='3, most of the mass loss in model st28gm05n033 occurs during a few strong events ("gusts" of wind).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Therefore, the mean structures in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 1 are less well defined than in the case of model st28gm06n052.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' This becomes apparent when taking a closer look at the mean radial-velocity curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Model st28gm06n052 (red curve) shows the familiar pattern of a steady dust-driven wind: a steep ini- tial increase in radial velocity associated with the dust formation region, followed by a levelling off further out, where both the ra- diative pressure and gravitational attraction weaken with increas- ing distance from the star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In contrast, the blue curve representing model st28gm05n033 shows a non-monotonic pattern, following a steep initial increase and a local maximum at about 1700 R⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' This point corresponds to the radius of the largest sphere fitting within the computational box (half of the edge length of the cu- bical box xouterbox, see Table 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Beyond that point, the spatial averaging relies on the decreasing fractions of spherical surfaces contained in the box, until the largest distance, corresponding to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='5 × xouterbox/2, is reached.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='  Computing representative averages for a gusty, inhomogeneous wind turns into a sampling prob- lem, as the coverage of angles decreases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' As a consequence, the average wind velocity of model st28gm05n033 is not well con- strained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' However, there is no doubt that material reaching the outer edge of the computational box will escape from the star, even if the average flow velocity does not exceed the local escape velocity (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 1, dotted blue line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' We note that the dynamics is not ballistic, and radiative acceleration continues to exceed grav- itational attraction, while both forces decrease with distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Figure 3 shows evolving structures in model st28gm05n033 at three instants, for slices through the center of the star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The less efficient dust condensation is illustrated by the grain radius plots (bottom row), with only one pronounced dust formation event, followed by outward acceleration, taking place in the bot- tom right quadrant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In contrast to the corresponding Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2 for model st28gm06n052, the outer parts of model st28gm05n033 mostly show a red color in the radial-velocity plots during the chosen time interval, indicating gas falling back toward the star, after the passing of shock waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Since the computational box of model st28gm05n033 is smaller by about a factor of two, this region should be compared to the corresponding parts of model st28gm06n052, which also show large regions of infalling gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='  The somewhat clumpy but continuous outflow of model st28gm06n052 (blue colors in the radial-velocity plots) is more clearly visible at larger distances, beyond about 2000 solar radii.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Time variations of global properties Figures showing the evolution of structures, as discussed above, are essential for understanding the interplay of physical pro- cesses at work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' However, to study the connection between radial pulsation, dust formation, and wind acceleration, and to see vari- ations in global properties as derived from spatially unresolved observations of AGB stars, we need a different approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Figure 4 shows spherical averages of luminosity, radial ve- locity, and grain radius as a function of radial depth and time for the cooler, less massive model st28gm06n052.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In the panel showing luminosity, we can distinguish two different regions: the dark area (indicating low radiative flux) below about 300 R⊙ represents the deep stellar interior, where essentially all of the energy flux is carried by convection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Further out, in the atmo- sphere and circumstellar envelope, on the other hand, energy is mostly transported by the radiative flux, which shows more or less regular variations related to radial pulsations of the star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In the velocity panel, the radial pulsations are apparent as alternating blue and red vertical stripes in the stellar interior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='  In the inner atmosphere, the dynamics is dominated by strong pulsation-induced shocks that are propagating outward (dark blue stripes, pointing upward and to the right), separated by phases where gas falls back toward the stellar surface (red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The outermost part of the model corresponds to the dust-driven stel- lar wind, with an outward-directed flow velocity (blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' We note that the highest wind velocities (darkest blue colors) occur in the wake of strong shocks, which, in turn, are directly linked to stellar expansion phases due to the pulsations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The temperatures in the atmosphere and wind-acceleration region are mostly set by radiative processes,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' dominated by pho- Article number,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' page 8 of 14  Bernd Freytag and Susanne Höfner: Global 3D models of AGB stars with winds 10 20 30 40 50 60 500 1000 1500 2000 2500 3000 r [RO • ]  L [LO ]  0  2000  4000  6000  8000  10  20  30  40  50  60  500  1000  1500  2000  2500  3000  r [RO ]  vradial [km s 1] 20 10  0  10  20  10  20  30  40  50  60  t [yr]  500  1000  1500  2000  2500  3000  r [RO ]  Radius of Mg2SiO4 grains [cm] 0 2×10-5 4×10-5 6×10-5 8×10-5 1×10-4 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Spherical averages of luminosity (integrated radiative flux), radial velocity, and grain radius in the large 1 M⊙ model st28gm06n052, as a function of radial distance and time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In the top and bottom panels, an isotherm with a temperature representative of silicate condensation is shown (1150 K) to demonstrate the interplay between variable radiative heating and the inner edges of dust layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The red, orange, and green vertical bars indicate the instants selected for Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2 and 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The dark area in the lower part of the top panel represents the deep stellar interior, where most of the energy flux is transported by convection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' tons emitted from the stellar surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' As the total radiative flux varies due to pulsations, so does the temperature in the dust- formation region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' This effect is illustrated by an over-plotted isotherm (1150 K, typical silicate condensation temperature).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' During the luminosity minima, the atmosphere is coolest and the isotherm is closer to the center, meaning that the average distance from the star at which dust condensation is possible, is smallest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Since the density decreases steeply with the radial distance, the phases around luminosity minima are favorable for efficient dust condensation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' This is apparent in the panel showing the grain radii, where pronounced dust formation events (bright areas) tend to coincide with deep minima in luminosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='  A closer inspection shows that the regions of efficient grain growth (resulting in large grain radii) are typically closer to the star than the isothermal line, which roughly marks the conden- sation temperature of silicates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' It should be pointed out that the radial distance of this line corresponds to a spherical mean, while the actual 2D isotherms in the 3D models are far from spherical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Figures 2 and 3 illustrate that efficient grain growth events tend to occur in high-density regions where lower temperatures pre- vail close to the star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Figure 5 shows spherical averages of luminosity, radial ve- locity, and grain radius as a function of radial depth and time for the warmer, more massive model st28gm05n033.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In the radial- velocity plot, the alternating blue and red vertical stripes be- low about 300 R⊙ in the stellar interior indicate radial pulsa- tion, as discussed above for the other model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The velocity pat- tern both inside the star and in the inner atmosphere (propa- gating shocks, indicated by blue stripes pointing upward and to the right) looks somewhat more regular for this star with higher surface gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' However, fewer of the global-scale atmo- spheric shock waves lead to efficient dust formation events (see Article number, page 9 of 14  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' aaagb3dfirstwind 5 10 15 20 25 30 500 1000 1500 r [RO • ]  L [LO ]  0  2000  4000  6000  8000  5  10  15  20  25  30  500  1000  1500  r [RO ]  vradial [km s 1] 20 10  0  10  20  5  10  15  20  25  30  t [yr]  500  1000  1500  r [RO ]  Radius of Mg2SiO4 grains [cm] 0 1×10-5 2×10-5 3×10-5 4×10-5 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Spherical averages of luminosity (integrated radiative flux), radial velocity, and grain radius in the 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='5 M⊙ model st28gm05n033, as a function of radial distance and time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In the top and bottom panels, an isotherm with a temperature representative of silicate condensation is shown (1150 K) to demonstrate the interplay between variable radiative heating and the inner edges of dust layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The red, orange, and green vertical bars indicate the instants selected for Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 3 and 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The dark area in the lower part of the top panel represents the deep stellar interior, where most of the energy flux is transported by convection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The plots are similar to the corresponding ones in Fig 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' However, it is important to note the differing spatial and temporal axes, and the different range in grain radii.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' the grain-radius panel), followed by outward acceleration of the gas-dust mixture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' A majority of the pulsation-induced shocks are stopped by infalling material (red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' We note, again, that the com- putational box is smaller than for model st28gm06n052, and the global flow direction in the outer parts of the model is not always directed outward (both blue and red colors can be found at the upper edge).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' This is consistent with the less efficient dust forma- tion and less dense outflow, as indicated by the spherically and temporally averaged structures shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Discussion 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='  Comparison with earlier 3D models and with 1D models Dynamical models and spatially resolved observations indicate that the extended atmospheres of AGB stars are characterized by a network of shock waves, triggered by large-scale convective flows and stellar pulsations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Our earlier 3D AGB-star models suggested that the resulting structures in atmospheric densities should lead to a patchy dust distribution in the circumstellar ma- terial close to the star (Höfner & Freytag 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='1 While provid- 1 For clarity, we point out that this effect is different from the intrin- sic instabilities of a circumstellar dust shell, as discussed by Woitke (2006a), occurring in 2D models that did not take processes in the star and their influences on the circumstellar environment into account.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Article number, page 10 of 14  Bernd Freytag and Susanne Höfner: Global 3D models of AGB stars with winds -600 -400 -200 0 200 400 600 x [RO • ] -600 -400 -200 0 200 400 600 y [RO • ] t=29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='296 yr -600 -400 -200 0 200 400 600 x [RO • ]  t=29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='962 yr 600 400 200  0  200  400  600  x [RO ]  t=31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='158 yr  Normalized surface intensity  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='4 600 400 200  0  200  400  600  x [RO ] 600 400 200  0  200  400  600  y [RO ]  t=22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='772 yr 600 400 200  0  200  400  600  x [RO ]  t=23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='065 yr 600 400 200  0  200  400  600  x [RO ]  t=23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='664 yr  Normalized surface intensity 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='0 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Time sequences of bolometric surface intensity for the large 1 M⊙ model st28gm06n052 (snapshots about 8 and 14 months apart, see the counter at the top of the panels) and the 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='5 M⊙ model st28gm05n033 (snapshots about 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='5 and 7 months apart).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Only the inner part of computational box that contains the star is plotted, on the same scale for both models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' ing an explanation for the origin of clumpy dust clouds observed around several nearby AGB stars, these earlier models did not include radiation pressure, and we could therefore not draw def- inite conclusions about atmospheric dynamics and the formation of a dust-driven stellar wind.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In contrast, the new models presented in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 3 account for the effects of radiation pressure on the silicate dust that forms in the stellar atmosphere, with grain growth rates depending on the densities of condensible material in the surrounding gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Dust condensation is most efficient in the dense wakes of shock waves, and the basic cloud formation mechanism, which pre- cedes wind acceleration, is similar to our earlier 3D models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' However, we note that the models presented here show more pronounced spatial variations in grain size, and the final degree of condensation in the outflow, when averaging over time, is far from complete (Table 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='  Incomplete condensation is in line with results of 1D dust- driven wind models, where grain growth slows down drastically in the accelerating outflow due to rapidly falling densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' This typically leaves a significant fraction of condensible material in the gas phase (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Höfner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2016, 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Another fea- ture of the new 3D models that is reminiscent of 1D dust-driven wind models is the time-dependent behavior of spherically aver- aged quantities, as seen in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 4 and 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The spherical averaging highlights the role of radial stellar pulsations, related luminosity variations, and resulting large-scale atmospheric shock waves, which trigger dust formation events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' As temperatures and gas densities vary along a shock front, in contrast to the situation in 1D models, the dust forms with different rates at different locations, leading to regions with very high, and others with low or zero, dust densities behind a shock.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Depending on the statistics of the thermodynamic quantities, the net effect on the overall mass loss might be an increase or a de- crease, compared to 1D models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The stellar parameter sets of the 3D models presented here were chosen to fall into two differ- ent regimes: according to results from 1D DARWIN simulations, model st28gm06n052 is expected to develop a pronounced dust- driven wind, while the 1D counterpart of model st28gm05n033 fails to produce an outflow (see Bladh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='  In this context it is remarkable that the 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='5 M⊙ CO5BOLD model does develop a gusty, inhomogeneous wind with a low mass-loss rate, in con- trast to its wind-less DARWIN equivalent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' This could be due to an intrinsically more efficient wind mechanism in the 3D mod- els, that is to say, more favorable conditions for dust formation in the inhomogeneous atmospheres, with cool dense pockets of gas close to the star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' However, there are differences in the treatment of radiative transfer compared to the DARWIN models that may also affect the results and need to be investigated further, before more quantitative conclusions can be drawn (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Observable properties Using averages of radial velocities and other quantities, taken over spherical shells, Freytag et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' (2017) identified radial pul- sation in a sample of 3D star-in-a-box models with different stel- Article number, page 11 of 14  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' aaagb3dfirstwind -3000 -2000 -1000 0 1000 2000 3000 x [RO • ] -3000 -2000 -1000 0 1000 2000 3000 y [RO • ] t=29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='296 yr -3000 -2000 -1000 0 1000 2000 3000 x [RO • ]  t=29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='962 yr 3000 2000 1000  0  1000  2000  3000  x [RO ]  t=31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='158 yr  Number of Mg2SiO4 monomers [cm-3] 0 2×106 4×106 6×106 8×106 1×107 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Time sequence of silicate density, through the center of the large 1 M⊙ model st28gm06n052.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The snapshots are about 8 and 14 months apart, respectively (see the counter at the top of the panels).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' lar parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The simulations show periods in good agree- ment with the observed P-L relation for Mira variables by Whitelock et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Recently, Ahmad et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' (2023) analyzed the pulsation properties of a much larger set of global 3D models produced with the CO5BOLD code, including those presented here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The periods determined for models st28gm06n052 and st28gm05n033 are 545 and 297 days, respectively, bracketing the mean P-L relation derived by Whitelock et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' (2009), with both models falling inside the broad range of observed values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' While the spherically averaged radial velocities show clear signs of radial stellar pulsations and dominantly outward- directed flow velocities in the outer parts of the models (see Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 4 and 5), the 2D slices demonstrate the complex nature of dynamics in the convective stellar interior and in the stellar atmosphere (Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2 and 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Convective motions, and possibly non-radial pulsations, cause shock waves on a wide range of an- gular scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The shocks may merge or collide, leading to in- tricate density structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Some shock waves trigger sufficient dust formation and radiative acceleration to overcome gravity, leading to an outflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='  At the same time, other parts of the atmo- sphere show ballistic motions and material falling back toward the stellar surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Both the density and the temperature in the atmosphere are strongly variable, and differ from the spherical structures expected in case of a purely radial pulsation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Recent submillimeter observations have given evidence of simultaneous inward and outward directed motions of atmospheric gas, and a complex morphology of the extended dynamical atmospheres of AGB stars, with coexisting warm and cool gas components (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Khouri et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2016b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Vlemmings et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Paladini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' (2018) presented H-band images of π1 Gruis (based on VLTI/PIONIER data), indicating large granulation cells on the stellar surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The sizes of the observed surface structures are in good agreement with extrapolations of local 3D models for less evolved stars, and with qualitative predictions of global 3D AGB-star models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Figure 6 shows time sequences of the bolometric surface intensity for the large 1 M⊙ model and the 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='5 M⊙ model plotted on the same spatial scale (zoomed in on the star, which is small compared to the computational box).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Both models have a similar mean luminosity, but the higher mass in model st28gm05n033, together with a slightly smaller radius, leads to a more well-defined stellar surface with much smaller structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The lower surface gravity in model st28gm06n052, on the other hand, results in a much more extended atmosphere, favoring efficient dust formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='  It should be noted here that the images show the bolometric intensity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' For a detailed compari- son with observations, images in appropriate filter bands have to be computed (see Chiavassa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2018, and references therein), which is an effort well beyond the scope of the present paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' However, the qualitative trends with stellar parameters can be expected to be similar to the bolometric images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Dust condensation is favored by high density, and therefore grain growth is most effective in the dense wakes of outward- propagating shocks, as illustrated by the sequence of grain-size plots in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2 for model st28gm06n052.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Figure 7 shows the cor- responding plots of dust density (total number of monomers con- tained in dust grains per unit volume).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' This quantity can be re- garded as a simple proxy for dust emission in the mid-IR, where dust grains are small compared to the wavelengths, and the dust opacity (emission coefficient) is roughly proportional to the vol- ume occupied by the dust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The formation of a new dust cloud in the wake of a shock, followed by radiative acceleration away from the star, is clearly visible in the lower right quadrant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In contrast to the grain size, however, the density decreases as the cloud moves outward, as indicated by the darkening of the col- ors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='  Approximations and future improvements In current 1D DARWIN models, frequency-dependent radiative transfer is routinely computed at several hundred wavelength points, thereby achieving a good coverage of the spectral energy distribution, while simultaneously solving the equations of hy- drodynamics and dust formation (see Höfner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2016, 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The much more computationally intensive 3D AGB-star models, however, are based on an opacity binning scheme, to account for non-gray effects (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In this context, it is a nontrivial task to introduce dust opacities, which are not simply a function of current temperature and density as the pre-tabulated gas opac- ities are, but depend on grain sizes that result from nonequilib- rium condensation and evaporation processes, and are not known a priori.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In the exploratory 3D "star-and-wind-in-a-box" models pre- sented here, we chose to represent the dust opacities relevant for radiation pressure by monochromatic values at a wavelength near the stellar flux maximum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Furthermore, considering the level of other approximations in the radiative transfer, we de- scribe the size-dependent efficiency factor for radiation pressure on dust grains by a simple analytical formula (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The formula reproduces key features of Fe-free silicate dust, such as low absorption in the visual and near-IR, and a strong depen- Article number, page 12 of 14  Bernd Freytag and Susanne Höfner: Global 3D models of AGB stars with winds dence of scattering on grain size for particles with radii smaller than the relevant wavelengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' It should give a qualitatively cor- rect picture of the dynamics, and the resulting wind velocities are, indeed, in the expected range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Nevertheless, we plan to re- place the simple formula with optical properties computed with Mie theory in future 3D models, similar to what is used in the 1D DARWIN models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Another obvious difference compared to 1D wind models is the smaller overall size of the computational domain, ad- justed for an efficient use of computational resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' For model st28gm06n052, the box extends to distances where the stellar wind is well established and close to reaching its terminal veloc- ity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The more massive, somewhat hotter model st28gm05n033, with its smaller box, on the other hand, illustrates potential prob- lems with determining reliable average wind properties for stars with higher surface gravity and less favorable conditions for dust formation, leading to strongly inhomogeneous outflows with low mass-loss rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In principle, the box of this particular model could have been extended to larger distances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In practice, how- ever, the model in its current form is sufficient to demonstrate the influence of key stellar parameters on the formation of a dust- driven wind.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='  Conclusions In this paper we have presented the first global 3D RHD mod- els of AGB stars and their dust-driven winds, computed with the CO5BOLD code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The models allow us to follow the flow of mat- ter from the stellar interior, through the dynamical atmosphere, and into the wind-acceleration region, while taking nonequilib- rium dust formation and the interaction of matter with radiation into account.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Convection and pulsations emerge self-consistently in the 3D models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Wind properties (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' mass-loss rates and out- flow velocities) can be derived without relying on parameterized descriptions of these interior dynamical processes, in contrast to current 1D wind models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Atmospheric shock waves, triggered by convective motions and pulsation, play a critical role in the con- densation of the dust grains, which drive the winds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' A global 3D approach is essential to make progress in understanding dynami- cal processes in AGB stars, and to solve long-standing problems regarding mass loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The giant convection cells, which are a characteristic feature of AGB stars, cause large-scale intensity patterns in the stellar photosphere, and leave their imprints on atmospheric temper- atures and densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In contrast to 1D models with purely ra- dial pulsations and global spherical shocks fronts propagating outward through the atmosphere, the shocks induced by con- vection and pulsation in the 3D models cover large but finite regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='  This leads to a patchy, nonspherical structure of the atmosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Since the efficiency of dust condensation depends critically on gas density, new dust clouds mostly emerge in the dense wakes of atmospheric shocks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The resulting clumpy dis- tribution of newly formed dust, together with radiative pressure being highly sensitive to grain sizes, leads to a complex 3D morphology of the extended atmosphere and wind-acceleration zone, with simultaneous infall and outflow regions close to the star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Genuine 3D effects in the models are strong deviations of isotherms from spherical symmetry and the intermittent forma- tion of cool pockets of gas in the stellar vicinity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Efficient dust formation tends to occur closer to the star than spherical averages of the temperature would indicate, in dense regions where grain growth rates are higher than average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' This can lead to dust-driven outflows with low mass-loss rates in situations where 1D models with the same stellar parameters do not produce winds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' In con- trast, for stars where the overall conditions for dust formation and wind acceleration are favorable, it is not obvious whether the resulting mass-loss rates will be higher or lower than in the 1D case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The increased efficiency of dust formation in high-density clumps may be set off by a low filling factor of these regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The key features of the models (high-contrast convective sur- face patterns, complex velocity fields, clumpy dust clouds) are seen in observations of nearby AGB stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='  Synthetic observables need to be computed from the dynamical 3D structures in order to compare the models to observations in more detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The pro- duction of spectra and images in various wavelength regimes is under way, but this is a considerable, time-consuming effort, and results will be presented in future papers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Based on the first exploratory models discussed in this paper, we can mainly draw qualitative conclusions about the physics and 3D morphology of AGB-star atmospheres and winds, since the simulations include a number of approximations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Improve- ments regarding dust microphysics and the treatment of radia- tion pressure are planned for future models, to get a better quan- titative description of these aspects, and of the resulting wind properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Eventually, it will be necessary to produce additional models, to explore how mass-loss rates depend on fundamental stellar parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' However, 3D models are time-consuming to com- pute and analyze.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Therefore, 1D models of dust-driven winds will continue to play an important role for the foreseeable future, as they can provide the wide coverage of stellar parameter com- binations required in stellar evolution models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Hopefully, knowl- edge gained from full 3D modeling can be used to improve 1D models, in particular regarding a better representation of pulsa- tion and convection effects on the stellar atmosphere and wind.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Acknowledgements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='  This work is part of a project that has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 883867, project EXWINGS) and the Swedish Research Council (Vetenskapsrådet, grant num- ber 2019-04059).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' The computations were enabled by resources provided by the Swedish National Infrastructure for Computing (SNIC) partially funded by the Swedish Research Council through grant agreement no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2018-05973.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' We thank the referee Jan Martin Winters for his insightful comments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' References Ahmad, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Freytag, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', & Höfner, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2023, A&A, 669, A49 Aringer, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2000, PhD thesis, Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' of Vienna, Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Wien Aringer, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Girardi, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Nowotny, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Marigo, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', & Bressan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2016, MNRAS, 457, 3611 Bladh, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Höfner, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Aringer, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', & Eriksson, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2015, A&A, 575, A105 Bladh, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Liljegren, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Höfner, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Aringer, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', & Marigo, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2019, A&A, 626, A100 Chiavassa, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Freytag, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', & Schultheis, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2018, A&A, 617, L1 Freytag, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2013, Mem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Italiana Suppl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', 24, 26 Freytag, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2017, Mem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' Italiana, 88, 12 Freytag, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' & Höfner, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2008, A&A, 483, 571 Freytag, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Liljegren, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', & Höfner, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2017, A&A, 600, A137 Freytag, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Steffen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Ludwig, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='  2012, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', 231, 919 Höfner, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2008a, Physica Scripta Volume T, 133, 014007 Höfner, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2008b, A&A, 491, L1 Höfner, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Bladh, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Aringer, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', & Ahuja, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2016, A&A, 594, A108 Höfner, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Bladh, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Aringer, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', & Eriksson, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2022, A&A, 657, A109 Höfner, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' & Freytag, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2019, A&A, 623, A158 Höfner, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Gautschy-Loidl, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Aringer, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', & Jørgensen, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2003, A&A, 399, 589 Höfner, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' & Olofsson, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2018, A&A Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', 26, 1 Jäger, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Dorschner, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Mutschke, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Posch, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', & Henning, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2003, A&A, 408, 193 Jeong, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Winters, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Le Bertre, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', & Sedlmayr, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2003, A&A, 407, 191 Khouri, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Maercker, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Waters, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2016a, A&A, 591, A70 Khouri, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Vlemmings, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Ramstedt, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2016b, MNRAS, 463, L74 Article number, page 13 of 14  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' aaagb3dfirstwind Norris, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Tuthill, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Ireland, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2012, Nature, 484, 220 Ohnaka, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Weigelt, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', & Hofmann, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2016, A&A, 589, A91 Ohnaka, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Weigelt, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', & Hofmann, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2017, A&A, 597, A20 Paladini, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Baron, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Jorissen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2018, Nature, 553, 310 Schwarzschild, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 1975, ApJ, 195, 137 Stewart, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Tuthill, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Nicholson, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', & Hedman, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2016, MNRAS, 457, 1410 Trabucchi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Wood, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Montalbán, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2017, ApJ, 847, 139 Trabucchi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Wood, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Mowlavi, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2021, MNRAS, 500, 1575 Vlemmings, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Khouri, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', O’Gorman, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2017, Nature Astronomy, 1, 848 Wachter, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Schröder, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Winters, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Arndt, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', & Sedlmayr, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2002, A&A, 384, 452 Whitelock, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Menzies, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Feast, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2009, MNRAS, 394, 795 Winters, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Le Bertre, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Jeong, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Helling, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', & Sedlmayr, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2000, A&A, 361, 641 Wittkowski, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Hofmann, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Höfner, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2017, A&A, 601, A3 Woitke, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2006a, A&A, 452, 537 Woitke, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2006b, A&A, 460, L9 Wood, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2015, MNRAS, 448, 3829 Zeidler, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Posch, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Mutschke, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', Richter, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=', & Wehrhan, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
+page_content=' 2011, A&A, 526, A68 Article number, page 14 of 14' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/P9FKT4oBgHgl3EQfhC52/content/2301.11836v1.pdf'}
diff --git a/RtE4T4oBgHgl3EQf_g5X/content/tmp_files/2301.05371v1.pdf.txt b/RtE4T4oBgHgl3EQf_g5X/content/tmp_files/2301.05371v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..adc452bde8aac9f03aabf040d930f2387075898b
--- /dev/null
+++ b/RtE4T4oBgHgl3EQf_g5X/content/tmp_files/2301.05371v1.pdf.txt
@@ -0,0 +1,973 @@
+Coherent subcycle optical shock from superluminal plasma wake
+H. Peng,1 T.W. Huang,1, ∗ K. Jiang,1 R. Li,1 C.N. Wu,1 M.Y.
+Yu,1 C. Riconda,2 S. Weber,3 C.T. Zhou,1, † and S.C. Ruan1, ‡
+1Shenzhen Key Laboratory of Ultraintense Laser and Advanced Material Technology,
+Center for Advanced Material Diagnostic Technology, and College of Engineering Physics,
+Shenzhen Technology University, Shenzhen 518118, China
+2LULI, Sorbonne Universit´e, CNRS, ´Ecole Polytechnique, CEA, F-75252 Paris, France
+3Extreme Light Infrastructure ERIC, ELI Beamlines Facility, 25241 Doln´ı Bˇreˇzany, Czech Republic
+(Dated: January 16, 2023)
+We propose a new mechanism for generating coherent subcycle optical pulse by directing a rel-
+ativistic electron beam (REB) into a plasma with a density up-ramp. The subcycle pulse is co-
+herently emitted by bubble-sheath electrons in REB-induced superluminal plasma wake.
+Using
+three-dimensional particle-in-cell and far-field time-domain radiation simulations as well as analyt-
+ical modeling, we show that an isolated subcycle optical shock can be produced at the Cherenkov
+angle.
+This radiation has ultra-short attosecond-scale duration and high intensity, and exhibits
+excellent directionality with ultra-low angular divergence and stable carrier envelope phase.
+Its
+central frequency can be easily tuned over a wide range, from the far-infrared to the ultra-violet, by
+adjusting the plasma and driver-beam density.
+High-energy subcycle radiation pulses are useful for
+many
+applications,
+including
+attosecond-scale
+spec-
+troscopy of living systems [1], ultrafast monitoring and
+control of molecules [2, 3], attosecond metrology of
+electron motion, petahertz signal processing [4–6], etc.
+Frequency-mixing [7, 8], pulse syntheses [9, 10], and para-
+metric amplification [11], etc.
+have been proposed for
+generating subcycle pulses, but these often need precise
+control and synchronization of the phases of the laser
+modes and the carrier envelops. The pulse energy is also
+limited. In relativistic laser-plasma interaction studies,
+intense few- and sub-cycle pulses can be generated from
+photon deceleration in plasma wakes [12, 13], coherent
+synchrotron emission from relativistic-laser interaction
+with nanofoil capacitor targets [14], seed pulse ampli-
+fication from interaction of foil with electron beam [15]
+or laser wakefield [16]. For many applications, it is de-
+sired to have high intensity, tunable frequency, stable car-
+rier envelope phase (CEP), and foremost a simple setup.
+However, to our best knowledge, currently there is not
+such a radiation source that possesses all of these desired
+properties simultaneously.
+As recently demonstrated by Vieira et al.[17], when
+a rarefied high-energy electron bunch is suitably modu-
+lated, its radiation can form a coherent optical shock at
+the Cherenkov angle. Prerequisites for this superradiance
+radiation, or generalized Cherenkov radiation (GCR), are
+that all the electrons in the bunch have similar trajecto-
+ries and are modulated with a superluminal phase, such
+that they form a superluminal radiation point (SRP)[17],
+whose speed stays constant above the light speed c. In
+this Letter, we found that the cusp-like rear of the su-
+perluminal wake bubble in plasma with up-ramped den-
+sity can be exploited as an SRP that leads to coherent
+GCR. As observed in three-dimensional (3D) particle-
+in-cell (PIC) and far-field time-domain radiation simula-
+tions, an isolated subcycle optical pulse in the form of a
+shock can be generated from a superluminal wake bubble
+of a relativistic electron beam(REB). Such radiation has
+many interesting and unique features: radiations from
+the involved electrons are phase-locked at the Cherenkov
+angle, it is CEP stable, as well as of subcycle attosecond-
+scale duration. It has also excellent directionality, namely
+at the Cherenkov angle with very small angular diver-
+gence, and high intensity that scales with the square of
+the propagation distance. In addition, the frequency can
+be readily tuned by adjusting the densities of the plasma
+and REB.
+As an intense laser or particle pulse propagates in
+plasma, it expels the affected plasma electrons, form-
+ing a positively charge channel bounded by the narrow
+sheath of the accumulated expelled electrons(hereinafter
+referred to as sheath electrons). The electrons return af-
+ter half a cycle of the plasma oscillation. In a plasma with
+density up(down)-ramp, the density in front of the driver
+pulse is higher(lower), so that the plasma oscillation fre-
+quency is higher(lower), the electrons return to the axis
+faster(slower) than the earlier ones, and the rear of the
+bubble(ROB) moves superluminally(subluminally)[18].
+When the sheath electrons reach the ROB, they have
+forward speed close to c and get reflected, with their
+transverse momentum vanishing at the ROB[19]. In a
+subluminal wakefield, these electrons can be captured,
+resulting in an accelerated electron beam with low emit-
+tance. In superluminal bubble wakefield, these electrons
+become a coherent GCR source, since they all have nearly
+the same trajectory. At the (superluminal) ROB, they
+have high energy and large trajectory curvature, leading
+to the intense radiation. The plasma density profile can
+be tailored for realizing a nearly constant ROB velocity.
+To verify the above process, 3D simulations are per-
+formed using the WarpX PIC code[20].
+To improve
+arXiv:2301.05371v1  [physics.plasm-ph]  13 Jan 2023
+
+2
+0
+9e10
+Er[V/m]
+I. Up Ramp
+II. Constant
+(f)
+1.8e11
+-9e10
+-1.8e11
+1000 1500 2000
+1.0
+ne/n0
+I. Up Ramp
+0
+10
+20
+30
+40
+-15
+0
+15
+I.
+II.
+0
+3
+6
+×1018
+cm− 3
+36
+31
+26
+ξ[µm]
+0
+15
+30
+x[µm]
+-1
+0
+1
+×1011
+V/m
+0
+30
+60
+90
+120
+ω/ωp0
+0
+5
+10
+|F F T(Ex)|
+A.U.
+0
+5
+10
+15
+20
+-6
+0
+6
+Ex[V/m ]
+× 1010
+(a)
+(b)
+(c)
+(d)
+(e)
+0
+500
+1.5
+ξ[µm]
+x[µm]
+z[µm]
+II. Constant
+t[fs]
+FIG. 1.
+3D PIC simulation results of subcycle pulse gen-
+eration from a superluminal plasma wake at z0 = 1000 µm,
+compared with that of a subluminal plasma wake, with no sig-
+nificant radiation generation. (a) Electron densities of Case
+I for an up-ramped plasma slab and Case II for a uniform
+(except at the front and back edges) plasma slab. (b) Wake
+densities in the x, ξ plane, where ξ = ct−z. The upper(lower)
+half is for Case I(II). (c) Electric field Ex of the subcycle pulse
+from the ROB in the upper x − ξ plane. (d) The temporal
+Ex profile from (c) along the emission angle of 74.0 mrad. (e)
+Spectrum of the subcycle pulse in arbitrary units (A.U.). (f)
+Radial electric field Er = Ex cos φ + Ey sin φ in a visualiza-
+tion of the subcycle pulse emitted from the ROB in Case I,
+where φ is the azimuthal angle and tan φ = y/x. Note no
+such optical shock is observed in Case II.
+the accuracy and prevent numerical Cherenkov insta-
+bilities, the modified finite-difference Maxwell-equations
+solver CKC[21] as well as the pseudo-spectral Maxwell-
+equations solver PSATD are used[22–24], and we found
+that they yield similar results.
+There are 512 × 512
+cells in the transverse (x, y) directions and 1664 cells
+in the axial (z) direction, with two electrons per cell.
+The immobile ions form a positive background. In the
+simulations, a moving window with speed c is used.
+The size of the simulation box is Lx = Ly = 32c/ωp0
+and Lz = 13c/ωp0, where ωp0 =
+�
+e2n0/ε0me is the
+plasma frequency with n0 = 1.5 × 1018 cm−3.
+A com-
+plete blowout wake is generated by a high-current REB
+of density nb = 16n0, whose normalized peak charge
+per unit length is Λ = 4πre
+� σr
+0
+drrnb = 4, where σr
+is the spot size of the beam and re is the classical elec-
+tron radius.
+The initial beam density is nb(r, ξ) = nb
+for r < σr and zl < z < zr, where σr = 0.5c/ωp0 and
+σz = zr −zl = 0.7c/ωp0.The REB has a relativistic factor
+of γb = 2500 and is assumed to have no energy spread.
+These parameters are similar to that of Ref. 19. Per-
+fectly matched layers are implemented at all boundaries
+to avoid reflection of electromagnetic waves.
+Fig. 1(a) shows the two types of plasma slabs. In Case
+I for an up-ramped plasma slab, the density from zi =
+500 µm to ze = 2000 µm is ne(z) = n0/[1 − (z − zi)/Lp]2,
+with Lp ∼ 8174.2 µm (so that ne is 1.5n0 at ze), and then
+sharp drops (within a distance 100 µm) to vacuum. Such
+a plasma density profile has often been used in previous
+simulations[25, 26] and can be realized in experiments
+by suitably tailoring gas capillaries[27]. In Case II, the
+plasma slab density is given by ne(z) = n0 =constant in
+100 µm < z < 2100 µm, with sharp drops (within 100 µm)
+to vacuum on both ends.
+Assuming the sheath electrons are expelled by the
+REB at td, after half a cycle of betatron oscillation
+tp = π/ωβ, where ωβ = ωp/2
+√
+Λ is the nonlinear os-
+cillation frequency[28, 29] and ωp(z) is the local plasma
+frequency, they form a ROB at tROB = td + tp[18]. Per-
+forming differentiation with respect to z gives:
+1
+vph
+= 1
+vd
++ dtp
+dz ,
+(1)
+vph(z, t) =
+vd
+1 − (2
+√
+Λvd/ω2p)dωp/dz
+,
+(2)
+where vph is the velocity of the ROB or the wake
+phase velocity and vd <∼ c is driver beam velocity.
+In
+Case I, vph = vd/(1 − α) ∼ 1.0021c, is superluminal
+and constant along the density up-ramp, where α =
+2
+√
+Λc/Lpωp0. The resulting Cherenkov radiation angle
+is θch = arccos(c/vph) ∼ 65.2 mrad. In Case II, vph = vd
+is subluminal. The wake bubbles for the two cases are
+shown in Fig.1(b).
+The ROB of Case I is slightly ad-
+vanced with respect to the one of Case II because of a
+superluminal velocity.
+In Case I, an isolated subcycle
+pulse is generated by the ROB and emitted along the
+density up-ramp, as depicted in Fig.1(c). As a represen-
+tative example, the radiation at z0 = 1000 µm is shown.
+The emission angle is ∼ 74.0 ± 2.0 mrad, very close to
+the theoretical value θch ∼ 65.2 mrad. The duration of
+the pulse is ∼ 581.4 as (FWHM) and the field peak value
+is 44.1 GV/m, the same order as that of the wakefield.
+As expected, the corresponding spectrum, shown in Fig.
+1(e), is broad with the cutoff frequency ωcut ∼ 120ωp0,
+or cutoff wavelength λcut ∼ 226.9 nm.
+The frequency
+at its maximum strength is ∼ 31.3ωp0, or wavelength
+∼ 870.7 nm. The radial electric field Er of the two cases
+
+5
+0
+5
+5
+(wn)
+5
+5
+5
+5
+5
+-5
+-40
+-35-30-25-20-15-10
+40
+-35-30-25-20-15-10-5
+z-ct(um)
+z-ct(um)3
+is shown in Fig. 1(f). The strong field of the driver elec-
+tron beam at ξ ∼ 5 µm expels the plasma electrons and
+forms the bubble.
+In Case I, around the high-density
+ROB at ξ ∼ 30.5 µm is a strong Coulomb field region,
+from which a subcycle radially-polarized electromagnetic
+pulse in form of an optical shock emerges. No such shock
+is generated in Case II.
+It is emphasized that the subcycle pulse can be al-
+ways generated as long as a plasma-density up-ramp ex-
+ists and the ROB is superluminal (see the Supplemen-
+tal Material[30] for detailed discussion).
+On the other
+hand, multiple bubbles can also be generated.
+The
+rear of the secondary bubbles can also emit subcycle
+radiation pulses, since the phase velocity of the wake-
+field behind the driver beam increases steadily accord-
+ing to Eq.(2)[31]. However, they are emitted with larger
+Cherenkov angles and are much weaker than that from
+the first bubble, and thus can be easily separated from
+the main subcycle pulse in the far field. The subcycle
+pulse from the second ROB is discussed in more detail in
+the Supplemental Material[30].
+15
+0
+15
+ξ[µm]
+0
+20
+40
+-15
+0
+15
+x[µm]
+-20
+-30
+-40
+z-z0[µm]
+-15
+0
+15
+x[µm]
+-15
+0
+15
+y[µm]
+-100
+-60
+-20
+20
+60
+t-z0/c[fs]
+(a)   Comoving Frame
+(b)     Lab Frame
+-15
+0
+15
+y[µm]
+βz
+γ
+ROB
+(c)   Velocities 
+-1
+1
+0
+1
+3
+2
+ξ[µm]
+ξ[µm]
+(d)    Relativistic Factor 
+35
+25
+15
+ 5
+35
+25
+15
+ 5
+γ
+βr
+βz, βr
+FIG. 2. Trajectories of the sheath electrons passing through
+the ROB at t = z0/c in the (a) moving and (b) labora-
+tory frames.
+Their axial and radial velocities as well as
+their relativistic factors are shown in (c) and (d), respec-
+tively, where the dotted lines mark the position of the ROB at
+ξ = ct − z ∼ 30.5 µm. Note that the variations of the velocity
+and energy of almost all sheath electrons overlap before they
+reach the ROB.
+To understand how the electron dynamics lead to sub-
+cycle radiation at the ROB, it is of interest to look at the
+trajectories of the sheath electrons and compute the far-
+field radiation based on the electron trajectories. In this
+case, quasi-3D cylindrical-geometry simulations for both
+cases are carried out using the FBPIC code[32], with 416
+cells along z, 12 particles per cell and other parameters
+the same. Although the longitudinal spatial resolution dz
+is reduced but it is still sufficient to resolve the electron
+dynamics involved. PIC codes in the cylindrical geome-
+try are commonly used to mitigate computing resource
+consumption of large-scale plasma wake simulations[33–
+35], here FBPIC significantly reduces the number of elec-
+trons to be analyzed, which in turn reduces the compu-
+tational burden of far-field radiation simulations as will
+be discussed next. Figs. 2(a) and (b) show the trajecto-
+ries of the sheath electrons of Case I at t = z0/c in the
+co-moving and lab frames, respectively. Notice that the
+trejectories in Case II (not shown) are very similar. The
+trajectories are mainly 2D in the r −z plane and they all
+follow the same pattern: starting at about ri ∼ 5.3 µm
+and form the narrow sheath defining the bubble bound-
+ary, with maximum radius rm ∼ 8.05 µm[28, 29]. As the
+REB propagates forward, the sheath electrons are even-
+tually pulled back by the charge separation field of the
+nearly immobile plasma ions in the channel and merge
+at the ROB, forming the bubble. The defocusing force
+from the radial electron current dominates, and reflects
+most electrons (few of them go across the axis)[19].
+The dynamics of about 400 typical sheath electrons are
+shown in Figs. 2(c)-(d). We can see that before they ar-
+rive at the ROB, their trajectories are almost the same.
+At the ROB they have high (near c) forward axial ve-
+locities, with their relativistic factors reaching γm ∼ 3.0.
+The radial velocities decrease to 0 at the ROB, where the
+electron trajectories have small curvature radius ρ and
+large deflection angle ψ > 1. The critical radiation fre-
+quency ωc ∝ γ3/ρ, and radiation power Prad ∝ γ4/ρ2 [36]
+both reach a local maximum at the ROB. The radiation
+pulse is confined to a narrow cone with angle ∆θ = 1/γ
+centered at ⃗β, thus the radiation at the ROB is mainly
+directed towards the forward direction. When the ROB
+is slightly superluminal, the sheath electrons generate a
+strong optical shock along the Cherenkov angle.
+Next we discuss the properties of far-field radiation,
+which is important for experimental observation and fur-
+ther applications of the radiation. With the aforemen-
+tioned configuration, the wiggler strength is K = γψ ≫
+1, so that the radiation from every involved electron is
+mainly confined in the same azimuthal φ − z plane in
+which this electron oscillates[37].
+On the other hand,
+as analyzed above, for dβz/dt ∼ 0 and βr ∼ 0, the
+sheath electron acceleration at the ROB is mainly along
+the radial direction: ˙⃗β = dβr/dt. Accordingly, we have
+⃗β ∼ (0, 0, βz), ˙⃗β ∼ (B cos φ, B sin φ, 0).
+The radiation
+direction is ⃗n = (sin θ cos ϕ, sin θ sin ϕ, cos θ), where B is
+the acceleration amplitude and θ is the opening angle of
+the radiation. The electric field on the far-field detector
+plane is[36]:
+⃗Edet =
+q
+4πε0
+⃗n × [(⃗n − ⃗β) × ˙⃗β]
+cR(1 − ⃗β · ⃗n)3
+,
+(3)
+where R is the distance from the electron to the de-
+tector plane.
+Thus, we have ⃗Edet ∝ −B cos θ(cos θ −
+βz)[⃗ex cos ϕ + ⃗ey sin ϕ] ∝ ⃗er, or that ⃗Edet is radially-
+
+4
+polarized, as expected due to the cylindrical symmetry.
+0
+2
+4
+6
+8
+t[fs]
+-150
+-75
+0
+75
+150
+θ[mrad ]
+-3
+0
+3
+Er
+-1.2
+0
+1.2
+× 108
+× 108
+V/m
+(a) Er (ϕ = 0)
+ϕ
+0 50 100
+θ[mrad]
+0
+π/2
+π
+3π/2
+× 1015
+V2/m 2
+(c)
+0
+0.66
+1.32
+0
+2
+4
+6
+8
+t[fs]
+-150
+-75
+0
+75
+150
+θ[mrad]
+-2
+0
+2
+× 107
+V/m
+(b)Er (ϕ = 0)
+ϕ
+0 50 100
+θ[mrad]
+0
+π/2
+π
+3π/2
+× 1013
+V2/m 2
+(d)
+0
+1.3
+2.6
+500
+1000
+1500
+2000
+z[µm]
+0.0
+0.5
+1.0
+Peak E2
+A.U.
+(f)
+500
+1000
+1500
+2000
+z[µm]
+-1
+0
+1
+2
+3
+βph − 1
+×10−3 (e)
+FIG. 3. Far-field radiation computation results: (a,b) time-
+resolved radiation Er on the azimuthal plane ϕ = 0 and (c,d)
+time-averaged radiation ⟨E2⟩ =
+�
+E2(t)dt/
+�
+dt on the θ − ϕ
+plane. (a,c) are from Case I and (b,d) are from Case II, re-
+spectively.
+The brown superimposed line in (a) is the 1D
+slice of 2D Er at θ = 72.7 mrad, at which angle Er obtains
+its maximum amplitude. It is labelled on the right axis. (e)
+Phase velocities of the first bubble. Broken lines are for Case
+I(purple) and Case II(green), obtained by tracing the first
+ROB in FBPIC simulations. Solid lines are the theoretical
+values of Case I(yellow): βph = vph/c = 1.0021 and Case
+II(red): βph = 1.
+(f)Peak radiation intensity E2 in arbi-
+trary units versus the propagation distance for Case I(orange
+squares) and Case II(red crosses). The solid line and broken
+line are the quadric and linear fit for the squares and crosses,
+respectively.
+A postprocessing far-field time-domain code FaTiDo
+was developed to compute the radiation based on the
+trajectories of the bulk electrons, as projected on a far-
+field spherical surface, similar to the RaDio module of the
+OSIRIS code [17]. In the FBPIC simulations, we trace a
+portion of the bulk electrons(randomly-picked) which are
+originally located from zi to ze and r < 1.5rm. About
+3.9 × 106 electrons and more than 104 time steps are
+considered in total in each case. FaTiDo reads the tra-
+jectories of the macro-electrons and computes the total
+radiation field emitted by the bulk electrons. A far-field
+spherical detector plane is set 1 m away from the origin,
+i.e. R = |⃗robs| = 1 m. The detector time axis is defined
+to completely cover the arrival time of the radiation from
+the ROB. The time resolution is dtf = 5 × 10−18 s = 5 as
+with Nt = 1600 time steps. The spherical detector θ − ϕ
+plane is resolved as Nθ × Nϕ observers, with Nθ = 128
+along θ, Nϕ = 32 along ϕ and θ ranging from 0 to
+150 mrad, ϕ from 0 to 2π, respectively. Note that com-
+puting far-field radiation by tracing macro-particles with
+large weight will greatly exaggerate the amplitude of in-
+coherent radiation, but not for the coherent radiation
+[38].
+The detailed information on the FaTiDo simula-
+tions can be found in the Supplemental Materials[30].
+The time-resolved as well as time-averaged far-field ra-
+diations are shown in Fig. 3. The results are consistent
+with the theory and near-field PIC simulations. For Case
+I, the radiations along the driver path are coherently
+phase-locked at the Cherenkov angle θ ∼ 72.7 mrad, a
+subcycle pulse is clearly seen in Fig.
+3(a), where the
+Ex(Er at ϕ = 0) temporal profile is almost the same as
+that in the near-field PIC simulation, and the duration ∼
+617.1 as(FWHM) is slightly longer. The time-integrated
+radiation is concentrated around the Cherenkov angle
+and forms a photon ring with very small angular diver-
+gence ∼ 5.7 mrad at FWHM. This is due to the fact that
+the superluminal phase velocity of the wakefield stays rel-
+atively constant, as can be seen in Fig. 3(e). Without the
+density ramp (Case II), the radiation is not phase-locked
+and incoherent, resulting in a much smaller amplitude
+and intensity, as shown in Figs. 3(b) and (d). The ra-
+diation is mainly directed towards +z, i.e. the velocity
+direction of the sheath electrons when they pass through
+the ROB. There is an intensity void in Fig.
+3(d), as
+the incoherent radiation is radially-polarized as explained
+above[39].
+To verify that the generalized superradiance is ob-
+tained here, FaTiDo simulations have been performed to
+give the peak intensity collected on the far-field detector
+plane as a function of the wake propagation distance. As
+shown in Fig. 3(f), in Case I the peak intensity shows a
+quadric dependence on the propagation distance, while
+the dependence is linear in Case II. These are signatures
+of superradiant radiation and incoherent radiation[17] re-
+spectively, noting that the number of the radiating elec-
+trons is approximately proportional to the propagation
+distance. The total energy of the subcycle pulse of Case
+I is ϵ =
+� ⃗S · d⃗σdt ≈ 11.5 µJ, where ⃗S = ( ⃗E × ⃗B)/µ0
+is the Poynting vector, d⃗σ = R2⃗n sin θ cos θdθdϕ is the
+surface element vector of the spherical detector and
+⃗B = (⃗n × ⃗E)/c[36].
+Thus, the conversion efficiency is
+η = ϵ/ϵb ≈ 5.2 × 10−5, where ϵb is the energy of the in-
+jected driver beam. It is noted that the pulse energy and
+conversion efficiency can be greatly improved by using a
+longer plasma slab while preserving the same density gra-
+dient as they scale with the square of the plasma length.
+Plasma slab length of the order of 10 centimeters can al-
+ready be realized in experiments[40]. This subcycle pulse
+generation scheme is highly robust with respect to the ex-
+act density profile shape, see Supplemental Material[30].
+The proposed method also allows to generate subcycle
+pulses with high frequency tunability. By adjusting the
+plasma and beam densities according to the law of scale
+conversion, while maintaining the same density profiles,
+
+5
+it is possible to tune the central frequency of the gener-
+ated pulse over a wide range. For example, our additional
+simulation results show that by increasing the plasma and
+beam densities by a factor of 100, it is possible to gener-
+ate an 87 nm ultra-violet subcycle pulse with a duration
+of about 60 as. Conversely, reducing the densities by a
+factor of 100 allows for central frequency tuning to the
+far-infrared regime at 8.7 µm, with a duration of around
+6 fs.
+Finally, it is worth noting that superluminal plasma
+wakes can also be driven by other methods, such as
+”flying focusing” lasers[41–43] or electron beams[44], or
+evolving electron beam drivers[45] in a homogeneous
+plasma. In this letter, we have limited our discussion to
+the case where a superluminal wake is driven in a plasma
+with a density up-ramp, but given the simplicity and
+generality of the process, it is expected that similar re-
+sults would be obtained using any of the aforementioned
+methods.
+In summary, we have proposed a new scheme for gener-
+ating coherent isolated, intense, CEP-stable subcycle ra-
+diation pulse from a superluminal plasma wake. The su-
+perradiance mechanism differs from existing ones, which
+require bunching the radiating particles in a spatial re-
+gion smaller than the radiation wavelength. In partic-
+ular, the far-field radiation has an excellent directional-
+ity, low angular divergence, and a well-defined wavefront
+and high frequency tunability, from the far-infrared to
+the ultra-violet.
+These attributes make the proposed
+method highly attractive for a variety of applications.
+It is worth noting that the necessary plasma and high-
+energy drivers are already available in current experimen-
+tal setups[46, 47], suggesting that subcycle superradiant
+pulses may already have been generated without being
+recognized.
+This work is supported by the National Natural
+Science Foundation of China (Grants No.12005148,
+No.12175154
+and
+No.11875092),
+the
+Natural
+Sci-
+ence Foundation of Top Talent of Shenzhen Tech-
+nology University (Grant No.
+2019010801001 and
+No.
+2019020801001)
+and
+Foundation
+of
+Science
+and Technology on Plasma Physics Laboratory(Grants
+No.6142A04200211).
+H.P. acknowledges H. Zhang,
+C.X.
+Zhu
+for
+discussions
+on
+code
+implementation.
+S.W. acknowledges support from the projects High
+Field
+Initiative
+(CZ.02.1.01/0.0/0.0/15 003/0000449)
+(HiFI)
+and
+Advanced
+research
+using
+high
+inten-
+sity
+laserproduced
+photons
+and
+particles
+(ADO-
+NIS)(CZ.02.1.01/0.0/0.0/16 019/0000789),
+both
+from
+European Regional Development Fund.
+∗ taiwu.huang@sztu.edu.cn
+† zcangtao@sztu.edu.cn
+‡ scruan@sztu.edu.cn
+[1] I. Pupeza, M. Huber, M. Trubetskov, W. Schweinberger,
+S. A. Hussain, C. Hofer, K. Fritsch, M. Poetzlberger,
+L. Vamos, E. Fill, et al., Field-resolved infrared spec-
+troscopy of biological systems, Nature 577, 52 (2020).
+[2] T. L. Cocker, D. Peller, P. Yu, J. Repp, and R. Huber,
+Tracking the ultrafast motion of a single molecule by fem-
+tosecond orbital imaging, Nature 539, 263 (2016).
+[3] D. Peller, L. Z. Kastner, T. Buchner, C. Roelcke, F. Al-
+brecht, N. Moll, R. Huber, and J. Repp, Sub-cycle
+atomic-scale forces coherently control a single-molecule
+switch, Nature 585, 58 (2020).
+[4] F. Krausz and M. I. Stockman, Attosecond metrology:
+from electron capture to future signal processing, Nat.
+Photonics 8, 205 (2014).
+[5] O. D. M¨ucke, Pick up speed, Nat. Phys. 12, 724 (2016).
+[6] F. Langer, C. P. Schmid, S. Schlauderer, M. Gmitra,
+J. Fabian, P. Nagler, C. Sch¨uller, T. Korn, P. Hawkins,
+J. Steiner, et al., Lightwave valleytronics in a monolayer
+of tungsten diselenide, Nature 557, 76 (2018).
+[7] P. Steinleitner, N. Nagl, M. Kowalczyk, J. Zhang, V. Per-
+vak, C. Hofer, A. Hudzikowski, J. Sotor, A. Weigel,
+F. Krausz, et al., Single-cycle infrared waveform control,
+Nat. Photonics 16, 512 (2022).
+[8] C. Manzoni, O. D. M¨ucke, G. Cirmi, S. Fang, J. Moses,
+S.-W. Huang, K.-H. Hong, G. Cerullo, and F. X. K¨artner,
+Coherent pulse synthesis:
+towards sub-cycle optical
+waveforms, Laser Photonics Rev. 9, 129 (2015).
+[9] G. M. Rossi, R. E. Mainz, Y. Yang, F. Scheiba, M. A.
+Silva-Toledo, S.-H. Chia, P. D. Keathley, S. Fang, O. D.
+M¨ucke, C. Manzoni, et al., Sub-cycle millijoule-level
+parametric waveform synthesizer for attosecond science,
+Nat. Photonics 14, 629 (2020).
+[10] Y. Yang, R. E. Mainz, G. M. Rossi, F. Scheiba, M. A.
+Silva-Toledo, P. D. Keathley, G. Cirmi, and F. X.
+K¨artner, Strong-field coherent control of isolated attosec-
+ond pulse generation, Nat. Commun. 12, 1 (2021).
+[11] Y.-C. Lin, Y. Nabekawa, and K. Midorikawa, Optical
+parametric amplification of sub-cycle shortwave infrared
+pulses, Nat. Commun. 11, 1 (2020).
+[12] Z. Nie, C.-H. Pai, J. Hua, C. Zhang, Y. Wu, Y. Wan,
+F. Li, J. Zhang, Z. Cheng, Q. Su, et al., Relativistic
+single-cycle tunable infrared pulses generated from a tai-
+lored plasma density structure, Nat. Photonics 12, 489
+(2018).
+[13] X.-L. Zhu, W.-Y. Liu, S.-M. Weng, M. Chen, Z.-M.
+Sheng, and J. Zhang, Generation of single-cycle relativis-
+tic infrared pulses at wavelengths above 20 µ m from
+density-tailored plasmas, Matter and Radiation at Ex-
+tremes 7, 014403 (2022).
+[14] X. Xu, Y. Zhang, H. Zhang, H. Lu, W. Zhou, C. Zhou,
+B. Dromey, S. Zhu, M. Zepf, X. He, et al., Production
+of 100-TW single attosecond x-ray pulse, Optica 7, 355
+(2020).
+[15] I. Thiele, E. Siminos, and T. F¨ul¨op, Electron beam driven
+generation of frequency-tunable isolated relativistic sub-
+cycle pulses, Phys. Rev. Lett. 122, 104803 (2019).
+[16] E. Siminos, I. Thiele, and C. Olofsson, Laser wake-
+field driven generation of isolated carrier-envelope-phase
+tunable intense subcycle pulses, Phys. Rev. Lett. 126,
+044801 (2021).
+[17] J. Vieira, M. Pardal, J. Mendon¸ca, and R. Fonseca, Gen-
+eralized superradiance for producing broadband coherent
+radiation with transversely modulated arbitrarily diluted
+
+6
+bunches, Nat. Phys. 17, 99 (2021).
+[18] M. P. Tooley,
+B. Ersfeld,
+S. R. Yoffe,
+A. Noble,
+E. Brunetti, Z. M. Sheng, M. R. Islam, and D. A.
+Jaroszynski, Towards attosecond high-energy electron
+bunches:
+Controlling self-injection in laser-wakefield
+accelerators through plasma-density modulation, Phys.
+Rev. Lett. 119, 044801 (2017).
+[19] X. L. Xu, F. Li, W. An, T. N. Dalichaouch, P. Yu, W. Lu,
+C. Joshi, and W. B. Mori, High quality electron bunch
+generation using a longitudinal density-tailored plasma-
+based
+accelerator
+in
+the
+three-dimensional
+blowout
+regime, Phys. Rev. Accel. Beams 20, 111303 (2017).
+[20] A. Myers, A. Almgren, L. D. Amorim, J. Bell, L. Fedeli,
+L. Ge, K. Gott, D. P. Grote, M. Hogan, A. Huebl,
+et al., Porting warpx to gpu-accelerated platforms, Par-
+allel Comput. 108, 102833 (2021).
+[21] B. M. Cowan, D. L. Bruhwiler, J. R. Cary, E. Cormier-
+Michel, and C. G. R. Geddes, Generalized algorithm for
+control of numerical dispersion in explicit time-domain
+electromagnetic simulations, Phys. Rev. ST Accel. Beams
+16, 041303 (2013).
+[22] G. Blaclard, H. Vincenti, R. Lehe, and J. L. Vay, Pseu-
+dospectral maxwell solvers for an accurate modeling of
+doppler harmonic generation on plasma mirrors with
+particle-in-cell codes, Phys. Rev. E 96, 033305 (2017).
+[23] H. Vincenti and J.-L. Vay, Ultrahigh-order maxwell
+solver with extreme scalability for electromagnetic pic
+simulations of plasmas, Comput. Phys. Commun. 228,
+22 (2018).
+[24] H. Vincenti, Achieving extreme light intensities using
+optically curved relativistic plasma mirrors, Phys. Rev.
+Lett. 123, 105001 (2019).
+[25] X. L. Xu, J. F. Hua, Y. P. Wu, C. J. Zhang, F. Li,
+Y. Wan, C.-H. Pai, W. Lu, W. An, P. Yu, M. J. Hogan,
+C. Joshi, and W. B. Mori, Physics of phase space match-
+ing for staging plasma and traditional accelerator compo-
+nents using longitudinally tailored plasma profiles, Phys.
+Rev. Lett. 116, 124801 (2016).
+[26] T. J. Mehrling, R. A. Fonseca, A. MartinezdelaOssa, and
+J. Vieira, Mitigation of the hose instability in plasma-
+wakefield accelerators, Phys. Rev. Lett. 118, 174801
+(2017).
+[27] L. Schaper, L. Goldberg, T. Kleinw¨achter, J.-P. Schwink-
+endorf, and J. Osterhoff, Longitudinal gas-density pro-
+filometry for plasma-wakefield acceleration targets, Nucl.
+Instrum. Meth. A 740, 208 (2014), proceedings of the
+first European Advanced Accelerator Concepts Work-
+shop 2013.
+[28] W. Lu, C. Huang, M. Zhou, M. Tzoufras, F. Tsung,
+W. Mori, and T. Katsouleas, A nonlinear theory for mul-
+tidimensional relativistic plasma wave wakefields, Phys.
+Plasmas 13, 056709 (2006).
+[29] W. Lu, C. Huang, M. Zhou, W. B. Mori, and T. Kat-
+souleas, Nonlinear theory for relativistic plasma wake-
+fields in the blowout regime, Phys. Rev. Lett. 96, 165002
+(2006).
+[30] See supplemental material for the detailed discussions on
+the effects of different density profiles on the generation
+of subcycle radiation pulse, the radiation from the sec-
+ond wake bubble and the far-field time-domain radiation
+calculation.
+[31] A. Pukhov, A. Golovanov, and I. Kostyukov, Efficient
+narrow-band terahertz radiation from electrostatic wake-
+fields in nonuniform plasmas, Phys. Rev. Lett. 127,
+175001 (2021).
+[32] R. Lehe, M. Kirchen, I. A. Andriyash, B. B. Godfrey, and
+J.-L. Vay, A spectral, quasi-cylindrical and dispersion-
+free particle-in-cell algorithm, Comput. Phys. Commun.
+203, 66 (2016).
+[33] W. Wang, K. Feng, L. Ke, C. Yu, Y. Xu, R. Qi, Y. Chen,
+Z. Qin, Z. Zhang, M. Fang, et al., Free-electron lasing
+at 27 nanometres based on a laser wakefield accelerator,
+Nature 595, 516 (2021).
+[34] R. Shalloo, S. Dann, J.-N. Gruse, C. Underwood, A. An-
+toine, C. Arran, M. Backhouse, C. Baird, M. Balcazar,
+N. Bourgeois, et al., Automation and control of laser
+wakefield accelerators using bayesian optimization, Nat.
+Commun. 11, 1 (2020).
+[35] L. T. Ke, K. Feng, W. T. Wang, Z. Y. Qin, C. H. Yu,
+Y. Wu, Y. Chen, R. Qi, Z. J. Zhang, Y. Xu, X. J. Yang,
+Y. X. Leng, J. S. Liu, R. X. Li, and Z. Z. Xu, Near-
+GeV electron beams at a few per-mille level from a laser
+wakefield accelerator via density-tailored plasma, Phys.
+Rev. Lett. 126, 214801 (2021).
+[36] J. D. Jackson, Classical electrodynamics (American As-
+sociation of Physics Teachers, 1999).
+[37] S. Corde, K. TaPhuoc , G. Lambert, R. Fitour, V. Malka,
+A. Rousse, A. Beck, and E. Lefebvre, Femtosecond x rays
+from laser-plasma accelerators, Rev. Mod. Phys. 85, 1
+(2013).
+[38] R.
+Pausch,
+A.
+Debus,
+A.
+Huebl,
+U.
+Schramm,
+K. Steiniger, R. Widera, and M. Bussmann, Quantita-
+tively consistent computation of coherent and incoherent
+radiation in particle-in-cell codes—a general form factor
+formalism for macro-particles, Nucl. Instrum. Meth. A
+909, 419 (2018).
+[39] Q. Zhan, Cylindrical vector beams:
+from mathemati-
+cal concepts to applications, Adv. Opt. Photonics 1, 1
+(2009).
+[40] A. J. Gonsalves, K. Nakamura, J. Daniels, C. Benedetti,
+C. Pieronek, T. C. H. deRaadt, S. Steinke, J. H.
+Bin, S. S. Bulanov, J. vanTilborg, C. G. R. Ged-
+des, C. B. Schroeder, C. Toth, E. Esarey, K. Swanson,
+L. Fan-Chiang, G. Bagdasarov, N. Bobrova, V. Gasilov,
+G. Korn, P. Sasorov, and W. P. Leemans, Petawatt laser
+guiding and electron beam acceleration to 8 GeV in a
+laser-heated capillary discharge waveguide, Phys. Rev.
+Lett. 122, 084801 (2019).
+[41] A. Sainte-Marie, O. Gobert, and F. Quere, Controlling
+the velocity of ultrashort light pulses in vacuum through
+spatio-temporal couplings, Optica 4, 1298 (2017).
+[42] C. Caizergues, S. Smartsev, V. Malka, and C. Thaury,
+Phase-locked laser-wakefield electron acceleration, Nat.
+Photonics 14, 475 (2020).
+[43] D. H. Froula, D. Turnbull, A. S. Davies, T. J. Kessler,
+D. Haberberger, J. P. Palastro, S.-W. Bahk, I. A. Begi-
+shev, R. Boni, S. Bucht, et al., Spatiotemporal control of
+laser intensity, Nat. Photonics 12, 262 (2018).
+[44] F. Li, T. N. Dalichaouch, J. R. Pierce, X. Xu, F. S.
+Tsung, W. Lu, C. Joshi, and W. B. Mori, Ultrabright
+electron bunch injection in a plasma wakefield driven by
+a superluminal flying focus electron beam, Phys. Rev.
+Lett. 128, 174803 (2022).
+[45] T. N. Dalichaouch, X. L. Xu, F. Li, A. Tableman, F. S.
+Tsung, W. An, and W. B. Mori, Generating high quality
+ultrarelativistic electron beams using an evolving elec-
+tron beam driver, Phys. Rev. Accel. Beams. 23, 021304
+(2020).
+
+7
+[46] Z. Nie, C.-H. Pai, J. Zhang, X. Ning, J. Hua, Y. He,
+Y. Wu, Q. Su, S. Liu, Y. Ma, et al., Photon deceler-
+ation in plasma wakes generates single-cycle relativistic
+tunable infrared pulses, Nat. Commun. 11, 1 (2020).
+[47] Y. Wu, J. Hua, Z. Zhou, J. Zhang, S. Liu, B. Peng,
+Y. Fang, X. Ning, Z. Nie, F. Li, et al., High-throughput
+injection–acceleration of electron bunches from a linear
+accelerator to a laser wakefield accelerator, Nat. Phys.
+17, 801 (2021).
+
diff --git a/RtE4T4oBgHgl3EQf_g5X/content/tmp_files/load_file.txt b/RtE4T4oBgHgl3EQf_g5X/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d2ca88a4253af7e117ca6979f46ce1336c73592b
--- /dev/null
+++ b/RtE4T4oBgHgl3EQf_g5X/content/tmp_files/load_file.txt
@@ -0,0 +1,850 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf,len=849
+page_content='Coherent subcycle optical shock from superluminal plasma wake  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Peng,1 T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Huang,1, ∗ K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Jiang,1 R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Li,1 C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Wu,1 M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  Yu,1 C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Riconda,2 S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Weber,3 C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Zhou,1, † and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Ruan1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' ‡  1Shenzhen Key Laboratory of Ultraintense Laser and Advanced Material Technology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  Center for Advanced Material Diagnostic Technology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' and College of Engineering Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  Shenzhen Technology University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Shenzhen 518118,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' China  2LULI,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Sorbonne Universit´e,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' CNRS,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' ´Ecole Polytechnique,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' CEA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' F-75252 Paris,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' France  3Extreme Light Infrastructure ERIC,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' ELI Beamlines Facility,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' 25241 Doln´ı Bˇreˇzany,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Czech Republic  (Dated: January 16,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' 2023)  We propose a new mechanism for generating coherent subcycle optical pulse by directing a rel-  ativistic electron beam (REB) into a plasma with a density up-ramp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' The subcycle pulse is co-  herently emitted by bubble-sheath electrons in REB-induced superluminal plasma wake.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  Using  three-dimensional particle-in-cell and far-field time-domain radiation simulations as well as analyt-  ical modeling, we show that an isolated subcycle optical shock can be produced at the Cherenkov  angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  This radiation has ultra-short attosecond-scale duration and high intensity, and exhibits  excellent directionality with ultra-low angular divergence and stable carrier envelope phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  Its  central frequency can be easily tuned over a wide range, from the far-infrared to the ultra-violet, by  adjusting the plasma and driver-beam density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  High-energy subcycle radiation pulses are useful for  many  applications,  including  attosecond-scale  spec-  troscopy of living systems [1], ultrafast monitoring and  control of molecules [2, 3], attosecond metrology of  electron motion, petahertz signal processing [4–6], etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  Frequency-mixing [7, 8], pulse syntheses [9, 10], and para-  metric amplification [11], etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  have been proposed for  generating subcycle pulses, but these often need precise  control and synchronization of the phases of the laser  modes and the carrier envelops.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' The pulse energy is also  limited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' In relativistic laser-plasma interaction studies,  intense few- and sub-cycle pulses can be generated from  photon deceleration in plasma wakes [12, 13], coherent  synchrotron emission from relativistic-laser interaction  with nanofoil capacitor targets [14], seed pulse ampli-  fication from interaction of foil with electron beam [15]  or laser wakefield [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' For many applications, it is de-  sired to have high intensity, tunable frequency, stable car-  rier envelope phase (CEP), and foremost a simple setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  However, to our best knowledge, currently there is not  such a radiation source that possesses all of these desired  properties simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  As recently demonstrated by Vieira et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' [17], when  a rarefied high-energy electron bunch is suitably modu-  lated, its radiation can form a coherent optical shock at  the Cherenkov angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Prerequisites for this superradiance  radiation, or generalized Cherenkov radiation (GCR), are  that all the electrons in the bunch have similar trajecto-  ries and are modulated with a superluminal phase, such  that they form a superluminal radiation point (SRP)[17],  whose speed stays constant above the light speed c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' In  this Letter, we found that the cusp-like rear of the su-  perluminal wake bubble in plasma with up-ramped den-  sity can be exploited as an SRP that leads to coherent  GCR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' As observed in three-dimensional (3D) particle-  in-cell (PIC) and far-field time-domain radiation simula-  tions, an isolated subcycle optical pulse in the form of a  shock can be generated from a superluminal wake bubble  of a relativistic electron beam(REB).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Such radiation has  many interesting and unique features: radiations from  the involved electrons are phase-locked at the Cherenkov  angle, it is CEP stable, as well as of subcycle attosecond-  scale duration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' It has also excellent directionality, namely  at the Cherenkov angle with very small angular diver-  gence, and high intensity that scales with the square of  the propagation distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' In addition, the frequency can  be readily tuned by adjusting the densities of the plasma  and REB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  As an intense laser or particle pulse propagates in  plasma, it expels the affected plasma electrons, form-  ing a positively charge channel bounded by the narrow  sheath of the accumulated expelled electrons(hereinafter  referred to as sheath electrons).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' The electrons return af-  ter half a cycle of the plasma oscillation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' In a plasma with  density up(down)-ramp, the density in front of the driver  pulse is higher(lower), so that the plasma oscillation fre-  quency is higher(lower), the electrons return to the axis  faster(slower) than the earlier ones, and the rear of the  bubble(ROB) moves superluminally(subluminally)[18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  When the sheath electrons reach the ROB, they have  forward speed close to c and get reflected, with their  transverse momentum vanishing at the ROB[19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' In a  subluminal wakefield, these electrons can be captured,  resulting in an accelerated electron beam with low emit-  tance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' In superluminal bubble wakefield, these electrons  become a coherent GCR source, since they all have nearly  the same trajectory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' At the (superluminal) ROB, they  have high energy and large trajectory curvature, leading  to the intense radiation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' The plasma density profile can  be tailored for realizing a nearly constant ROB velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  To verify the above process, 3D simulations are per-  formed using the WarpX PIC code[20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  To improve  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='05371v1  [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='plasm-ph]  13 Jan 2023  2  0  9e10  Er[V/m]  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Up Ramp  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Constant  (f)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='8e11  9e10  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='8e11  1000 1500 2000  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='0  ne/n0  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Up Ramp  0  10  20  30  40  15  0  15  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  0  3  6  ×1018  cm− 3  36  31  26  ξ[µm]  0  15  30  x[µm]  1  0  1  ×1011  V/m  0  30  60  90  120  ω/ωp0  0  5  10  |F F T(Ex)|  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  0  5  10  15  20  6  0  6  Ex[V/m ]  × 1010  (a)  (b)  (c)  (d)  (e)  0  500  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='5  ξ[µm]  x[µm]  z[µm]  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Constant  t[fs]  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  3D PIC simulation results of subcycle pulse gen-  eration from a superluminal plasma wake at z0 = 1000 µm,  compared with that of a subluminal plasma wake, with no sig-  nificant radiation generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' (a) Electron densities of Case  I for an up-ramped plasma slab and Case II for a uniform  (except at the front and back edges) plasma slab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' (b) Wake  densities in the x, ξ plane, where ξ = ct−z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' The upper(lower)  half is for Case I(II).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' (c) Electric field Ex of the subcycle pulse  from the ROB in the upper x − ξ plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' (d) The temporal  Ex profile from (c) along the emission angle of 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='0 mrad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' (e)  Spectrum of the subcycle pulse in arbitrary units (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' (f)  Radial electric field Er = Ex cos φ + Ey sin φ in a visualiza-  tion of the subcycle pulse emitted from the ROB in Case I,  where φ is the azimuthal angle and tan φ = y/x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Note no  such optical shock is observed in Case II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  the accuracy and prevent numerical Cherenkov insta-  bilities, the modified finite-difference Maxwell-equations  solver CKC[21] as well as the pseudo-spectral Maxwell-  equations solver PSATD are used[22–24], and we found  that they yield similar results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  There are 512 × 512  cells in the transverse (x, y) directions and 1664 cells  in the axial (z) direction, with two electrons per cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  The immobile ions form a positive background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' In the  simulations, a moving window with speed c is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  The size of the simulation box is Lx = Ly = 32c/ωp0  and Lz = 13c/ωp0, where ωp0 =  �  e2n0/ε0me is the  plasma frequency with n0 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='5 × 1018 cm−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  A com-  plete blowout wake is generated by a high-current REB  of density nb = 16n0, whose normalized peak charge  per unit length is Λ = 4πre  � σr  0  drrnb = 4, where σr  is the spot size of the beam and re is the classical elec-  tron radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  The initial beam density is nb(r, ξ) = nb  for r < σr and zl < z < zr, where σr = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='5c/ωp0 and  σz = zr −zl = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='7c/ωp0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='The REB has a relativistic factor  of γb = 2500 and is assumed to have no energy spread.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  These parameters are similar to that of Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Per-  fectly matched layers are implemented at all boundaries  to avoid reflection of electromagnetic waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' 1(a) shows the two types of plasma slabs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' In Case  I for an up-ramped plasma slab, the density from zi =  500 µm to ze = 2000 µm is ne(z) = n0/[1 − (z − zi)/Lp]2,  with Lp ∼ 8174.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='2 µm (so that ne is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='5n0 at ze), and then  sharp drops (within a distance 100 µm) to vacuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Such  a plasma density profile has often been used in previous  simulations[25, 26] and can be realized in experiments  by suitably tailoring gas capillaries[27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' In Case II, the  plasma slab density is given by ne(z) = n0 =constant in  100 µm < z < 2100 µm, with sharp drops (within 100 µm)  to vacuum on both ends.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  Assuming the sheath electrons are expelled by the  REB at td, after half a cycle of betatron oscillation  tp = π/ωβ, where ωβ = ωp/2  √  Λ is the nonlinear os-  cillation frequency[28, 29] and ωp(z) is the local plasma  frequency, they form a ROB at tROB = td + tp[18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Per-  forming differentiation with respect to z gives:  1  vph  = 1  vd  + dtp  dz ,  (1)  vph(z, t) =  vd  1 − (2  √  Λvd/ω2p)dωp/dz  ,  (2)  where vph is the velocity of the ROB or the wake  phase velocity and vd <∼ c is driver beam velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  In  Case I, vph = vd/(1 − α) ∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='0021c, is superluminal  and constant along the density up-ramp, where α =  2  √  Λc/Lpωp0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' The resulting Cherenkov radiation angle  is θch = arccos(c/vph) ∼ 65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='2 mrad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' In Case II, vph = vd  is subluminal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' The wake bubbles for the two cases are  shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='1(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  The ROB of Case I is slightly ad-  vanced with respect to the one of Case II because of a  superluminal velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  In Case I, an isolated subcycle  pulse is generated by the ROB and emitted along the  density up-ramp, as depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='1(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' As a represen-  tative example, the radiation at z0 = 1000 µm is shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  The emission angle is ∼ 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='0 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='0 mrad, very close to  the theoretical value θch ∼ 65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='2 mrad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' The duration of  the pulse is ∼ 581.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='4 as (FWHM) and the field peak value  is 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='1 GV/m, the same order as that of the wakefield.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  As expected, the corresponding spectrum, shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  1(e), is broad with the cutoff frequency ωcut ∼ 120ωp0,  or cutoff wavelength λcut ∼ 226.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='9 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  The frequency  at its maximum strength is ∼ 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='3ωp0, or wavelength  ∼ 870.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='7 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' The radial electric field Er of the two cases  5  0  5  5  (wn)  5  5  5  5  5  5  40  35-30-25-20-15-10  40  35-30-25-20-15-10-5  z-ct(um)  z-ct(um)3  is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' 1(f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' The strong field of the driver elec-  tron beam at ξ ∼ 5 µm expels the plasma electrons and  forms the bubble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  In Case I, around the high-density  ROB at ξ ∼ 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='5 µm is a strong Coulomb field region,  from which a subcycle radially-polarized electromagnetic  pulse in form of an optical shock emerges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' No such shock  is generated in Case II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  It is emphasized that the subcycle pulse can be al-  ways generated as long as a plasma-density up-ramp ex-  ists and the ROB is superluminal (see the Supplemen-  tal Material[30] for detailed discussion).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  On the other  hand, multiple bubbles can also be generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  The  rear of the secondary bubbles can also emit subcycle  radiation pulses, since the phase velocity of the wake-  field behind the driver beam increases steadily accord-  ing to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='(2)[31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' However, they are emitted with larger  Cherenkov angles and are much weaker than that from  the first bubble, and thus can be easily separated from  the main subcycle pulse in the far field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' The subcycle  pulse from the second ROB is discussed in more detail in  the Supplemental Material[30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  15  0  15  ξ[µm]  0  20  40  15  0  15  x[µm]  20  30  40  z-z0[µm]  15  0  15  x[µm]  15  0  15  y[µm]  100  60  20  20  60  t-z0/c[fs]  (a)   Comoving Frame  (b)     Lab Frame  15  0  15  y[µm]  βz  γ  ROB  (c)   Velocities  1  1  0  1  3  2  ξ[µm]  ξ[µm]  (d)    Relativistic Factor  35  25  15  5  35  25  15  5  γ  βr  βz, βr  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Trajectories of the sheath electrons passing through  the ROB at t = z0/c in the (a) moving and (b) labora-  tory frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  Their axial and radial velocities as well as  their relativistic factors are shown in (c) and (d), respec-  tively, where the dotted lines mark the position of the ROB at  ξ = ct − z ∼ 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='5 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Note that the variations of the velocity  and energy of almost all sheath electrons overlap before they  reach the ROB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  To understand how the electron dynamics lead to sub-  cycle radiation at the ROB, it is of interest to look at the  trajectories of the sheath electrons and compute the far-  field radiation based on the electron trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' In this  case, quasi-3D cylindrical-geometry simulations for both  cases are carried out using the FBPIC code[32], with 416  cells along z, 12 particles per cell and other parameters  the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Although the longitudinal spatial resolution dz  is reduced but it is still sufficient to resolve the electron  dynamics involved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' PIC codes in the cylindrical geome-  try are commonly used to mitigate computing resource  consumption of large-scale plasma wake simulations[33–  35], here FBPIC significantly reduces the number of elec-  trons to be analyzed, which in turn reduces the compu-  tational burden of far-field radiation simulations as will  be discussed next.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' 2(a) and (b) show the trajecto-  ries of the sheath electrons of Case I at t = z0/c in the  co-moving and lab frames, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Notice that the  trejectories in Case II (not shown) are very similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' The  trajectories are mainly 2D in the r −z plane and they all  follow the same pattern: starting at about ri ∼ 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='3 µm  and form the narrow sheath defining the bubble bound-  ary, with maximum radius rm ∼ 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='05 µm[28, 29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' As the  REB propagates forward, the sheath electrons are even-  tually pulled back by the charge separation field of the  nearly immobile plasma ions in the channel and merge  at the ROB, forming the bubble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' The defocusing force  from the radial electron current dominates, and reflects  most electrons (few of them go across the axis)[19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  The dynamics of about 400 typical sheath electrons are  shown in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' 2(c)-(d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' We can see that before they ar-  rive at the ROB, their trajectories are almost the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  At the ROB they have high (near c) forward axial ve-  locities, with their relativistic factors reaching γm ∼ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  The radial velocities decrease to 0 at the ROB, where the  electron trajectories have small curvature radius ρ and  large deflection angle ψ > 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' The critical radiation fre-  quency ωc ∝ γ3/ρ, and radiation power Prad ∝ γ4/ρ2 [36]  both reach a local maximum at the ROB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' The radiation  pulse is confined to a narrow cone with angle ∆θ = 1/γ  centered at ⃗β, thus the radiation at the ROB is mainly  directed towards the forward direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' When the ROB  is slightly superluminal, the sheath electrons generate a  strong optical shock along the Cherenkov angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  Next we discuss the properties of far-field radiation,  which is important for experimental observation and fur-  ther applications of the radiation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' With the aforemen-  tioned configuration, the wiggler strength is K = γψ ≫  1, so that the radiation from every involved electron is  mainly confined in the same azimuthal φ − z plane in  which this electron oscillates[37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  On the other hand,  as analyzed above, for dβz/dt ∼ 0 and βr ∼ 0, the  sheath electron acceleration at the ROB is mainly along  the radial direction: ˙⃗β = dβr/dt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Accordingly, we have  ⃗β ∼ (0, 0, βz), ˙⃗β ∼ (B cos φ, B sin φ, 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  The radiation  direction is ⃗n = (sin θ cos ϕ, sin θ sin ϕ, cos θ), where B is  the acceleration amplitude and θ is the opening angle of  the radiation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' The electric field on the far-field detector  plane is[36]:  ⃗Edet =  q  4πε0  ⃗n × [(⃗n − ⃗β) × ˙⃗β]  cR(1 − ⃗β · ⃗n)3  ,  (3)  where R is the distance from the electron to the de-  tector plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  Thus, we have ⃗Edet ∝ −B cos θ(cos θ −  βz)[⃗ex cos ϕ + ⃗ey sin ϕ] ∝ ⃗er, or that ⃗Edet is radially-  4  polarized, as expected due to the cylindrical symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  0  2  4  6  8  t[fs]  150  75  0  75  150  θ[mrad ]  3  0  3  Er  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='2  0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='2  × 108  × 108  V/m  (a) Er (ϕ = 0)  ϕ  0 50 100  θ[mrad]  0  π/2  π  3π/2  × 1015  V2/m 2  (c)  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='66  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='32  0  2  4  6  8  t[fs]  150  75  0  75  150  θ[mrad]  2  0  2  × 107  V/m  (b)Er (ϕ = 0)  ϕ  0 50 100  θ[mrad]  0  π/2  π  3π/2  × 1013  V2/m 2  (d)  0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='6  500  1000  1500  2000  z[µm]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='0  Peak E2  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  (f)  500  1000  1500  2000  z[µm]  1  0  1  2  3  βph − 1  ×10−3 (e)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Far-field radiation computation results: (a,b) time-  resolved radiation Er on the azimuthal plane ϕ = 0 and (c,d)  time-averaged radiation ⟨E2⟩ =  �  E2(t)dt/  �  dt on the θ − ϕ  plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' (a,c) are from Case I and (b,d) are from Case II, re-  spectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  The brown superimposed line in (a) is the 1D  slice of 2D Er at θ = 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='7 mrad, at which angle Er obtains  its maximum amplitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' It is labelled on the right axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' (e)  Phase velocities of the first bubble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Broken lines are for Case  I(purple) and Case II(green), obtained by tracing the first  ROB in FBPIC simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Solid lines are the theoretical  values of Case I(yellow): βph = vph/c = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='0021 and Case  II(red): βph = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  (f)Peak radiation intensity E2 in arbi-  trary units versus the propagation distance for Case I(orange  squares) and Case II(red crosses).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' The solid line and broken  line are the quadric and linear fit for the squares and crosses,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  A postprocessing far-field time-domain code FaTiDo  was developed to compute the radiation based on the  trajectories of the bulk electrons, as projected on a far-  field spherical surface, similar to the RaDio module of the  OSIRIS code [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' In the FBPIC simulations, we trace a  portion of the bulk electrons(randomly-picked) which are  originally located from zi to ze and r < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='5rm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' About  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='9 × 106 electrons and more than 104 time steps are  considered in total in each case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' FaTiDo reads the tra-  jectories of the macro-electrons and computes the total  radiation field emitted by the bulk electrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' A far-field  spherical detector plane is set 1 m away from the origin,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' R = |⃗robs| = 1 m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' The detector time axis is defined  to completely cover the arrival time of the radiation from  the ROB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' The time resolution is dtf = 5 × 10−18 s = 5 as  with Nt = 1600 time steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' The spherical detector θ − ϕ  plane is resolved as Nθ × Nϕ observers, with Nθ = 128  along θ, Nϕ = 32 along ϕ and θ ranging from 0 to  150 mrad, ϕ from 0 to 2π, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Note that com-  puting far-field radiation by tracing macro-particles with  large weight will greatly exaggerate the amplitude of in-  coherent radiation, but not for the coherent radiation  [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  The detailed information on the FaTiDo simula-  tions can be found in the Supplemental Materials[30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  The time-resolved as well as time-averaged far-field ra-  diations are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' The results are consistent  with the theory and near-field PIC simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' For Case  I, the radiations along the driver path are coherently  phase-locked at the Cherenkov angle θ ∼ 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='7 mrad, a  subcycle pulse is clearly seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  3(a), where the  Ex(Er at ϕ = 0) temporal profile is almost the same as  that in the near-field PIC simulation, and the duration ∼  617.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='1 as(FWHM) is slightly longer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' The time-integrated  radiation is concentrated around the Cherenkov angle  and forms a photon ring with very small angular diver-  gence ∼ 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='7 mrad at FWHM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' This is due to the fact that  the superluminal phase velocity of the wakefield stays rel-  atively constant, as can be seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' 3(e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Without the  density ramp (Case II), the radiation is not phase-locked  and incoherent, resulting in a much smaller amplitude  and intensity, as shown in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' 3(b) and (d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' The ra-  diation is mainly directed towards +z, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' the velocity  direction of the sheath electrons when they pass through  the ROB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' There is an intensity void in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  3(d), as  the incoherent radiation is radially-polarized as explained  above[39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  To verify that the generalized superradiance is ob-  tained here, FaTiDo simulations have been performed to  give the peak intensity collected on the far-field detector  plane as a function of the wake propagation distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' As  shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' 3(f), in Case I the peak intensity shows a  quadric dependence on the propagation distance, while  the dependence is linear in Case II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' These are signatures  of superradiant radiation and incoherent radiation[17] re-  spectively, noting that the number of the radiating elec-  trons is approximately proportional to the propagation  distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' The total energy of the subcycle pulse of Case  I is ϵ =  � ⃗S · d⃗σdt ≈ 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='5 µJ, where ⃗S = ( ⃗E × ⃗B)/µ0  is the Poynting vector, d⃗σ = R2⃗n sin θ cos θdθdϕ is the  surface element vector of the spherical detector and  ⃗B = (⃗n × ⃗E)/c[36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  Thus, the conversion efficiency is  η = ϵ/ϵb ≈ 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='2 × 10−5, where ϵb is the energy of the in-  jected driver beam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' It is noted that the pulse energy and  conversion efficiency can be greatly improved by using a  longer plasma slab while preserving the same density gra-  dient as they scale with the square of the plasma length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  Plasma slab length of the order of 10 centimeters can al-  ready be realized in experiments[40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' This subcycle pulse  generation scheme is highly robust with respect to the ex-  act density profile shape, see Supplemental Material[30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  The proposed method also allows to generate subcycle  pulses with high frequency tunability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' By adjusting the  plasma and beam densities according to the law of scale  conversion, while maintaining the same density profiles,  5  it is possible to tune the central frequency of the gener-  ated pulse over a wide range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' For example, our additional  simulation results show that by increasing the plasma and  beam densities by a factor of 100, it is possible to gener-  ate an 87 nm ultra-violet subcycle pulse with a duration  of about 60 as.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Conversely, reducing the densities by a  factor of 100 allows for central frequency tuning to the  far-infrared regime at 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='7 µm, with a duration of around  6 fs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  Finally, it is worth noting that superluminal plasma  wakes can also be driven by other methods, such as  ”flying focusing” lasers[41–43] or electron beams[44], or  evolving electron beam drivers[45] in a homogeneous  plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' In this letter, we have limited our discussion to  the case where a superluminal wake is driven in a plasma  with a density up-ramp, but given the simplicity and  generality of the process, it is expected that similar re-  sults would be obtained using any of the aforementioned  methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  In summary, we have proposed a new scheme for gener-  ating coherent isolated, intense, CEP-stable subcycle ra-  diation pulse from a superluminal plasma wake.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' The su-  perradiance mechanism differs from existing ones, which  require bunching the radiating particles in a spatial re-  gion smaller than the radiation wavelength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' In partic-  ular, the far-field radiation has an excellent directional-  ity, low angular divergence, and a well-defined wavefront  and high frequency tunability, from the far-infrared to  the ultra-violet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  These attributes make the proposed  method highly attractive for a variety of applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  It is worth noting that the necessary plasma and high-  energy drivers are already available in current experimen-  tal setups[46, 47], suggesting that subcycle superradiant  pulses may already have been generated without being  recognized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  This work is supported by the National Natural  Science Foundation of China (Grants No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='12005148,  No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='12175154  and  No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='11875092),  the  Natural  Sci-  ence Foundation of Top Talent of Shenzhen Tech-  nology University (Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  2019010801001 and  No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  2019020801001)  and  Foundation  of  Science  and Technology on Plasma Physics Laboratory(Grants  No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='6142A04200211).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' acknowledges H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Zhang,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  Zhu  for  discussions  on  code  implementation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' acknowledges support from the projects High  Field  Initiative  (CZ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='02.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='01/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='0/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='0/15 003/0000449)  (HiFI)  and  Advanced  research  using  high  inten-  sity  laserproduced  photons  and  particles  (ADO-  NIS)(CZ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='02.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='01/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='0/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='0/16 019/0000789),  both  from  European Regional Development Fund.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  ∗ taiwu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='huang@sztu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='cn  † zcangtao@sztu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='cn  ‡ scruan@sztu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='cn  [1] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Pupeza, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Huber, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Trubetskov, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Schweinberger,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Hussain, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Hofer, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Fritsch, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Poetzlberger,  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Vamos, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Fill, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=', Field-resolved infrared spec-  troscopy of biological systems, Nature 577, 52 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [2] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Cocker, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Peller, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Yu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Repp, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Huber,  Tracking the ultrafast motion of a single molecule by fem-  tosecond orbital imaging, Nature 539, 263 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [3] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Peller, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Kastner, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Buchner, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Roelcke, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Al-  brecht, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Moll, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Huber, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Repp, Sub-cycle  atomic-scale forces coherently control a single-molecule  switch, Nature 585, 58 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [4] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Krausz and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Stockman, Attosecond metrology:  from electron capture to future signal processing, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  Photonics 8, 205 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [5] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' M¨ucke, Pick up speed, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' 12, 724 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [6] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Langer, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Schmid, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Schlauderer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Gmitra,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Fabian, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Nagler, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Sch¨uller, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Korn, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Hawkins,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Steiner, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=', Lightwave valleytronics in a monolayer  of tungsten diselenide, Nature 557, 76 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [7] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Steinleitner, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Nagl, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Kowalczyk, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Zhang, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Per-  vak, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Hofer, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Hudzikowski, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Sotor, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Weigel,  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Krausz, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=', Single-cycle infrared waveform control,  Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Photonics 16, 512 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [8] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Manzoni, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' M¨ucke, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Cirmi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Fang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Moses,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Huang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Hong, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Cerullo, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' K¨artner,  Coherent pulse synthesis:  towards sub-cycle optical  waveforms, Laser Photonics Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' 9, 129 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [9] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Rossi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Mainz, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Yang, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Scheiba, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  Silva-Toledo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Chia, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Keathley, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Fang, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  M¨ucke, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Manzoni, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=', Sub-cycle millijoule-level  parametric waveform synthesizer for attosecond science,  Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Photonics 14, 629 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [10] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Yang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Mainz, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Rossi, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Scheiba, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  Silva-Toledo, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Keathley, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Cirmi, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  K¨artner, Strong-field coherent control of isolated attosec-  ond pulse generation, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' 12, 1 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [11] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Lin, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Nabekawa, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Midorikawa, Optical  parametric amplification of sub-cycle shortwave infrared  pulses, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' 11, 1 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [12] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Nie, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Pai, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Hua, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Wu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Wan,  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Zhang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Cheng, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Su, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=', Relativistic  single-cycle tunable infrared pulses generated from a tai-  lored plasma density structure, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Photonics 12, 489  (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [13] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Zhu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Liu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Weng, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Chen, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  Sheng, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Zhang, Generation of single-cycle relativis-  tic infrared pulses at wavelengths above 20 µ m from  density-tailored plasmas, Matter and Radiation at Ex-  tremes 7, 014403 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [14] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Xu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Zhang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Zhang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Lu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Zhou, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Zhou,  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Dromey, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Zhu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Zepf, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' He, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=', Production  of 100-TW single attosecond x-ray pulse, Optica 7, 355  (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [15] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Thiele, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Siminos, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' F¨ul¨op, Electron beam driven  generation of frequency-tunable isolated relativistic sub-  cycle pulses, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' 122, 104803 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [16] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Siminos, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Thiele, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Olofsson, Laser wake-  field driven generation of isolated carrier-envelope-phase  tunable intense subcycle pulses, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' 126,  044801 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [17] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Vieira, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Pardal, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Mendon¸ca, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Fonseca, Gen-  eralized superradiance for producing broadband coherent  radiation with transversely modulated arbitrarily diluted  6  bunches, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' 17, 99 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [18] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Tooley,  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Ersfeld,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Yoffe,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Noble,  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Brunetti, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Sheng, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Islam, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  Jaroszynski, Towards attosecond high-energy electron  bunches:  Controlling self-injection in laser-wakefield  accelerators through plasma-density modulation, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' 119, 044801 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [19] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Xu, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Li, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' An, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Dalichaouch, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Yu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Lu,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Joshi, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Mori, High quality electron bunch  generation using a longitudinal density-tailored plasma-  based  accelerator  in  the  three-dimensional  blowout  regime, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Accel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Beams 20, 111303 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [20] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Myers, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Almgren, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Amorim, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Bell, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Fedeli,  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Ge, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Gott, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Grote, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Hogan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Huebl,  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=', Porting warpx to gpu-accelerated platforms, Par-  allel Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' 108, 102833 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [21] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Cowan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Bruhwiler, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Cary, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Cormier-  Michel, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Geddes, Generalized algorithm for  control of numerical dispersion in explicit time-domain  electromagnetic simulations, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' ST Accel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Beams  16, 041303 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [22] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Blaclard, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Vincenti, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Lehe, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Vay, Pseu-  dospectral maxwell solvers for an accurate modeling of  doppler harmonic generation on plasma mirrors with  particle-in-cell codes, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' E 96, 033305 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [23] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Vincenti and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Vay, Ultrahigh-order maxwell  solver with extreme scalability for electromagnetic pic  simulations of plasmas, Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' 228,  22 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [24] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Vincenti, Achieving extreme light intensities using  optically curved relativistic plasma mirrors, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' 123, 105001 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [25] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Xu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Hua, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Wu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Zhang, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Li,  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Wan, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Pai, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Lu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' An, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Yu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Hogan,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Joshi, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Mori, Physics of phase space match-  ing for staging plasma and traditional accelerator compo-  nents using longitudinally tailored plasma profiles, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' 116, 124801 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [26] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Mehrling, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Fonseca, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' MartinezdelaOssa, and  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Vieira, Mitigation of the hose instability in plasma-  wakefield accelerators, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' 118, 174801  (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [27] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Schaper, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Goldberg, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Kleinw¨achter, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Schwink-  endorf, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Osterhoff, Longitudinal gas-density pro-  filometry for plasma-wakefield acceleration targets, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  Instrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Meth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' A 740, 208 (2014), proceedings of the  first European Advanced Accelerator Concepts Work-  shop 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [28] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Lu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Huang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Zhou, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Tzoufras, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Tsung,  W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Mori, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Katsouleas, A nonlinear theory for mul-  tidimensional relativistic plasma wave wakefields, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  Plasmas 13, 056709 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [29] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Lu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Huang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Zhou, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Mori, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Kat-  souleas, Nonlinear theory for relativistic plasma wake-  fields in the blowout regime, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' 96, 165002  (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [30] See supplemental material for the detailed discussions on  the effects of different density profiles on the generation  of subcycle radiation pulse, the radiation from the sec-  ond wake bubble and the far-field time-domain radiation  calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [31] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Pukhov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Golovanov, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Kostyukov, Efficient  narrow-band terahertz radiation from electrostatic wake-  fields in nonuniform plasmas, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' 127,  175001 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [32] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Lehe, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Kirchen, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Andriyash, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Godfrey, and  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Vay, A spectral, quasi-cylindrical and dispersion-  free particle-in-cell algorithm, Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  203, 66 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [33] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Wang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Feng, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Ke, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Yu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Xu, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Qi, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Chen,  Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Qin, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Zhang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Fang, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=', Free-electron lasing  at 27 nanometres based on a laser wakefield accelerator,  Nature 595, 516 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [34] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Shalloo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Dann, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='-N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Gruse, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Underwood, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' An-  toine, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Arran, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Backhouse, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Baird, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Balcazar,  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Bourgeois, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=', Automation and control of laser  wakefield accelerators using bayesian optimization, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' 11, 1 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [35] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Ke, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Feng, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Wang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Qin, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Yu,  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Wu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Chen, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Qi, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Xu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Yang,  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Leng, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Liu, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Li, and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Xu, Near-  GeV electron beams at a few per-mille level from a laser  wakefield accelerator via density-tailored plasma, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' 126, 214801 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [36] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Jackson, Classical electrodynamics (American As-  sociation of Physics Teachers, 1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [37] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Corde, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' TaPhuoc , G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Lambert, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Fitour, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Malka,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Rousse, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Beck, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Lefebvre, Femtosecond x rays  from laser-plasma accelerators, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' 85, 1  (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [38] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  Pausch,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  Debus,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  Huebl,  U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  Schramm,  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Steiniger, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Widera, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Bussmann, Quantita-  tively consistent computation of coherent and incoherent  radiation in particle-in-cell codes—a general form factor  formalism for macro-particles, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Instrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Meth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' A  909, 419 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [39] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Zhan, Cylindrical vector beams:  from mathemati-  cal concepts to applications, Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Photonics 1, 1  (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [40] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Gonsalves, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Nakamura, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Daniels, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Benedetti,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Pieronek, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' deRaadt, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Steinke, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  Bin, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Bulanov, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' vanTilborg, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Ged-  des, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Schroeder, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Toth, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Esarey, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Swanson,  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Fan-Chiang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Bagdasarov, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Bobrova, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Gasilov,  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Korn, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Sasorov, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Leemans, Petawatt laser  guiding and electron beam acceleration to 8 GeV in a  laser-heated capillary discharge waveguide, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' 122, 084801 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [41] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Sainte-Marie, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Gobert, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Quere, Controlling  the velocity of ultrashort light pulses in vacuum through  spatio-temporal couplings, Optica 4, 1298 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [42] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Caizergues, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Smartsev, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Malka, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Thaury,  Phase-locked laser-wakefield electron acceleration, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  Photonics 14, 475 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [43] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Froula, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Turnbull, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Davies, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Kessler,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Haberberger, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Palastro, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Bahk, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Begi-  shev, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Boni, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Bucht, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=', Spatiotemporal control of  laser intensity, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Photonics 12, 262 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [44] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Li, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Dalichaouch, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Pierce, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Xu, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  Tsung, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Lu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Joshi, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Mori, Ultrabright  electron bunch injection in a plasma wakefield driven by  a superluminal flying focus electron beam, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' 128, 174803 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [45] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Dalichaouch, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Xu, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Li, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Tableman, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  Tsung, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' An, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Mori, Generating high quality  ultrarelativistic electron beams using an evolving elec-  tron beam driver, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Accel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Beams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' 23, 021304  (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  7  [46] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Nie, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Pai, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Zhang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Ning, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Hua, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' He,  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Wu, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Su, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Ma, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=', Photon deceler-  ation in plasma wakes generates single-cycle relativistic  tunable infrared pulses, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' 11, 1 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  [47] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Wu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Hua, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Zhou, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Zhang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Liu, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Peng,  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Fang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Ning, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Nie, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Li, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=', High-throughput  injection–acceleration of electron bunches from a linear  accelerator to a laser wakefield accelerator, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
+page_content='  17, 801 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE4T4oBgHgl3EQf_g5X/content/2301.05371v1.pdf'}
diff --git a/S9FKT4oBgHgl3EQfkC7A/content/2301.11848v1.pdf b/S9FKT4oBgHgl3EQfkC7A/content/2301.11848v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..650ba76f348b12520e1279e4656222ce0e999880
--- /dev/null
+++ b/S9FKT4oBgHgl3EQfkC7A/content/2301.11848v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:070f25e90ba5c5bcf95166c99f57efb37bd028311c17dfc6083a022cc2f2f4b3
+size 713645
diff --git a/S9FKT4oBgHgl3EQfkC7A/vector_store/index.faiss b/S9FKT4oBgHgl3EQfkC7A/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..ea254aac606ade3c6f2705ad98ee2e40ff744d5b
--- /dev/null
+++ b/S9FKT4oBgHgl3EQfkC7A/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0c680f7751df8f1206cc138827aece434fd09a81726dfd51532605a512d44483
+size 2228269
diff --git a/S9FKT4oBgHgl3EQfkC7A/vector_store/index.pkl b/S9FKT4oBgHgl3EQfkC7A/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..de79f0c9ff5e8d666640ee39f42c8123e8c1e0e7
--- /dev/null
+++ b/S9FKT4oBgHgl3EQfkC7A/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a9c6b3ed41331d7f5800530d6880a0d1969567e029d6e0fa17ef9645bab73f49
+size 80151
diff --git a/SdA0T4oBgHgl3EQfD_9b/content/tmp_files/2301.02011v1.pdf.txt b/SdA0T4oBgHgl3EQfD_9b/content/tmp_files/2301.02011v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a588edad65c7f26d5675207b8a4b2fc8e5ef6d90
--- /dev/null
+++ b/SdA0T4oBgHgl3EQfD_9b/content/tmp_files/2301.02011v1.pdf.txt
@@ -0,0 +1,12586 @@
+Lattice Boltzmann for non-ideal fluids: Fundamentals and Practice
+S.A. Hosseinia, I.V. Karlina,∗
+aDepartment of Mechanical and Process Engineering, ETH Zurich, Zurich, 8092, Switzerland
+Abstract
+This contribution presents a comprehensive overview of of lattice Boltzmann models for non-ideal fluids, covering
+both theoretical concepts at both kinetic and macroscopic levels and more practical discussion of numerical nature.
+In that context, elements of kinetic theory of ideal gases are presented and discussed at length. Then a detailed dis-
+cussion of the lattice Boltzmann method for ideal gases from discretization to Galilean invariance issues and different
+collision models along with their effect on stability and consistency at the hydrodynamic level is presented. Exten-
+sion to non-ideal fluids is then introduced in the context of the kinetic theory of gases along with the corresponding
+thermodynamics at the macroscopic level, i.e. the van der Waals fluid, followed by an overview of different lattice
+Boltzmann based models for non-ideal fluids. After an in-depth discussion of different well-known issues and artifacts
+and corresponding solutions, the article finishes with a brief discussion on most recent applications of such models
+and extensions proposed in the literature towards non-isothermal and multi-component flows.
+Keywords: non-ideal fluids, lattice Boltzmann method, kinetic theory,
+PACS: 0000, 1111
+2000 MSC: 0000, 1111
+Contents
+1
+Introduction
+5
+2
+Elements of kinetic theory
+5
+2.1
+The Boltzmann transport equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+5
+2.1.1
+Binary collision: Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+6
+2.1.2
+Differential scattering cross-section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+7
+2.1.3
+Boltzmann’s collision integral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+8
+2.2
+Transport equations for molecular properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+11
+2.2.1
+Boltzmann’s transport theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+11
+2.2.2
+Invariants of collision. Conservation of mass, momentum and energy
+. . . . . . . . . . . . .
+12
+2.2.3
+Boltzmann’s H-theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+12
+2.2.4
+Equilibrium and local equilibrium. The Maxwell-Boltzmann distribution function . . . . . . .
+13
+3
+From Boltzmann equation to hydrodynamics
+14
+3.1
+Fields and fluxes
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+14
+3.2
+Balance equations for thirteen moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+15
+3.3
+Local equilibrium projection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+16
+3.4
+Dynamic correction to the local equilibrium projection
+. . . . . . . . . . . . . . . . . . . . . . . . .
+17
+3.4.1
+Estimates from the Maxwell-Boltzmann distribution
+. . . . . . . . . . . . . . . . . . . . . .
+17
+3.4.2
+Mean free path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+17
+∗Corresponding author
+Email address: ikarlin@ethz.ch (I.V. Karlin)
+Preprint submitted to Physics reports
+January 6, 2023
+arXiv:2301.02011v1  [physics.flu-dyn]  5 Jan 2023
+
+3.4.3
+Estimates from the Boltzmann collision integral . . . . . . . . . . . . . . . . . . . . . . . . .
+17
+3.4.4
+Reduced Boltzmann equation
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+18
+3.4.5
+Hydrodynamic limit
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+18
+3.4.6
+Elementary derivation of viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+19
+3.4.7
+Singularly perturbed Boltzmann equation . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+19
+3.4.8
+Normal solutions. The invariance principle
+. . . . . . . . . . . . . . . . . . . . . . . . . . .
+20
+3.4.9
+The Chapman–Enskog method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+21
+3.4.10 Euler’s compressible flow equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+21
+3.4.11 Navier-Stokes and Fourier compressible flow equations . . . . . . . . . . . . . . . . . . . . .
+22
+3.5
+Lifting the local equilibrium projection: BGK kinetic model
+. . . . . . . . . . . . . . . . . . . . . .
+28
+3.6
+Grad’s thirteen-moments projection
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+29
+3.6.1
+Grad’s thirteen-moments distribution function . . . . . . . . . . . . . . . . . . . . . . . . . .
+29
+3.6.2
+Grad’s thirteen-moments closure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+29
+3.6.3
+Grad’s thirteen-moments system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+31
+3.6.4
+Quasi-equilibrium projection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+32
+3.6.5
+Triangle entropy method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+33
+3.6.6
+Grad’s projections via triangle entropy method
+. . . . . . . . . . . . . . . . . . . . . . . . .
+34
+3.7
+Dynamic correction to Grad’s thirteen-moments projection: The R13 system . . . . . . . . . . . . . .
+37
+3.7.1
+Invariance defect of Grad’s thirteen-moments approximation . . . . . . . . . . . . . . . . . .
+37
+3.7.2
+The R13 distribution function
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+39
+3.7.3
+The R13 equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+40
+3.8
+Lifting of Grad’s and quasi-equilibrium projections: Kinetic models for simple fluid . . . . . . . . . .
+41
+3.8.1
+Quasi-equilibrium and related kinetic models . . . . . . . . . . . . . . . . . . . . . . . . . .
+41
+3.8.2
+Two relaxation times quasi-equilibrium models . . . . . . . . . . . . . . . . . . . . . . . . .
+43
+3.8.3
+Lifting the eight-moments Grad’s projection: Shakhov’s S-model
+. . . . . . . . . . . . . . .
+44
+3.8.4
+Lifting the ten-moments Grad’s projection.
+. . . . . . . . . . . . . . . . . . . . . . . . . . .
+44
+3.8.5
+Holway’s ellipsoidal-statistical kinetic model . . . . . . . . . . . . . . . . . . . . . . . . . .
+44
+3.9
+Summary: Projections, corrections and lifting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+45
+4
+Lattice Boltzmann for ideal fluid and related models
+46
+4.1
+Phase-space discretization
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+46
+4.1.1
+Hermite expansion and Gauss-Hermite quadrature
+. . . . . . . . . . . . . . . . . . . . . . .
+46
+4.1.2
+Product form equilibria and moment matching
+. . . . . . . . . . . . . . . . . . . . . . . . .
+48
+4.1.3
+Alternative to polynomial equilibria: Entropic equilibria . . . . . . . . . . . . . . . . . . . .
+49
+4.1.4
+Galilean invariance issues on standard lattices . . . . . . . . . . . . . . . . . . . . . . . . . .
+50
+4.2
+Space and time discretization: Integration along characteristics . . . . . . . . . . . . . . . . . . . . .
+55
+4.2.1
+Realization without force and correction term . . . . . . . . . . . . . . . . . . . . . . . . . .
+55
+4.2.2
+Correction for the diagonal components of the equilibrium third-order moments tensor . . . .
+56
+4.3
+Introduction of external body forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+57
+4.3.1
+Shan and Chen’s forcing scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+57
+4.3.2
+Luo’s scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+58
+4.3.3
+He et al’s scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+59
+4.3.4
+Guo’s scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+60
+4.3.5
+Kupershtokh’s scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+60
+4.4
+Stability of LB-BGK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+60
+4.4.1
+Isothermal closure: spurious bulk viscosity and stabilization of normal modes . . . . . . . . .
+61
+4.4.2
+Positivity of the discrete equilibria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+61
+4.4.3
+Linear stability of discrete solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+62
+4.5
+Extension of stability domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+65
+4.5.1
+Relaxation of discrete populations in alternate spaces . . . . . . . . . . . . . . . . . . . . . .
+65
+4.5.2
+Central moments-based decomposition
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+67
+4.5.3
+Closures for the relaxation rates: entropic . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+68
+2
+
+4.5.4
+The specific case of regularization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+70
+5
+Extension to non-ideal fluids
+72
+5.1
+Second-gradient theory and non-ideal fluids thermodynamics . . . . . . . . . . . . . . . . . . . . . .
+72
+5.1.1
+Non-ideal equation of state: van der Waals
+. . . . . . . . . . . . . . . . . . . . . . . . . . .
+72
+5.1.2
+Co-existence densities: Common-tangent construction . . . . . . . . . . . . . . . . . . . . .
+73
+5.1.3
+Co-existence densities: First-order transition and Maxwell construction . . . . . . . . . . . .
+74
+5.1.4
+Free energy of non-uniform non-ideal fluid . . . . . . . . . . . . . . . . . . . . . . . . . . .
+75
+5.1.5
+Gibbs equilibrium conditions for a flat interface . . . . . . . . . . . . . . . . . . . . . . . . .
+76
+5.1.6
+Korteweg stress tensor and second-gradient fluid balance equations
+. . . . . . . . . . . . . .
+77
+5.2
+Kinetic models for non-ideal fluid
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+78
+5.2.1
+Hard sphere potential: The Enskog model . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+78
+5.2.2
+Long-range interactions: Vlasov model . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+79
+5.2.3
+General Enkog-Vlasov-BGK kinetic framework for hydrodynamics . . . . . . . . . . . . . .
+80
+5.2.4
+Scaling and hydrdynamic limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+81
+5.3
+Overview of lattice Boltzmann models for non-ideal fluids
+. . . . . . . . . . . . . . . . . . . . . . .
+83
+5.3.1
+Shan and Chen’s pseudo-potential model
+. . . . . . . . . . . . . . . . . . . . . . . . . . . .
+84
+5.3.2
+Free energy model and derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+85
+5.4
+Bridging the scale gap: Principle of corresponding states . . . . . . . . . . . . . . . . . . . . . . . .
+86
+5.4.1
+Dimensional form of equations and restriction by the interface thickness . . . . . . . . . . . .
+86
+5.4.2
+Extension to realistic-sized systems: Rescaling interface thickness and the principle of corre-
+sponding states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+87
+5.5
+Numerical artifacts and issues of non-ideal lattice Boltzmann models . . . . . . . . . . . . . . . . . .
+89
+5.5.1
+Deviations in normal stress at interface: The issue of thermodynamic consistency . . . . . . .
+89
+5.5.2
+Fixed surface tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+91
+5.5.3
+The issue of spurious currents at interfaces
+. . . . . . . . . . . . . . . . . . . . . . . . . . .
+91
+5.5.4
+Galilean invariance of viscous dissipation rates and stability . . . . . . . . . . . . . . . . . .
+92
+5.6
+Improvements and enhanced models for non-ideal fluids
+. . . . . . . . . . . . . . . . . . . . . . . .
+94
+5.6.1
+Equations of state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+94
+5.6.2
+Partitioning of pressure contributions
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+98
+5.6.3
+Non-local thermodynamic pressure force contribution: Using mathematical identities to re-
+duce discretization errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
+5.6.4
+Higher order discretization: Leading order error and isotropy . . . . . . . . . . . . . . . . . . 101
+5.6.5
+Thickening interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
+5.6.6
+Independent control over surface tension
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
+5.6.7
+The discrete pressure tensor
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
+5.6.8
+Evaluating the effective surface tension
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
+5.7
+Fluid-solid interaction: wetting properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
+5.7.1
+Static contact angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
+5.7.2
+Contact angle hysteresis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
+5.8
+Assessment of thermo-physical properties of models
+. . . . . . . . . . . . . . . . . . . . . . . . . . 111
+5.8.1
+Speed of sound and compressibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
+5.8.2
+Meanfield scaling laws: Interface thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
+5.8.3
+Meanfield scaling laws: Surface tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
+5.8.4
+Meanfield scaling laws: Tolman length
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
+6
+Illustration of applications
+117
+6.1
+Drop interaction with solid substrates
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
+6.1.1
+Impact on non-wetting surfaces
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
+6.1.2
+Pancake bouncing
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
+6.1.3
+Other approaches to reduce contact time via macro-structures
+. . . . . . . . . . . . . . . . . 118
+6.2
+Flow in porous media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
+3
+
+6.2.1
+Water transport in proton exchange membrane fuel cells
+. . . . . . . . . . . . . . . . . . . . 120
+6.2.2
+Isothermal drying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
+7
+Extension to more complex physics
+123
+7.1
+Thermal flows with evaporation
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
+7.1.1
+The hybrid and passive scalar approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
+7.1.2
+The kinetic route . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
+7.2
+Multiple components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
+7.2.1
+Ternary free energy model of W¨ohrwag et al. . . . . . . . . . . . . . . . . . . . . . . . . . . 126
+7.2.2
+Mixtures with multi-component van der Waals equation of state . . . . . . . . . . . . . . . . 127
+7.2.3
+The multi-component pseudo-potential method . . . . . . . . . . . . . . . . . . . . . . . . . 128
+8
+Conclusion
+129
+Appendix A
+Hermite expansion
+129
+Appendix B
+Elements of the von Neumann formalism
+133
+Appendix C
+Hydrodynamic limit of the Enskog–Vlasov–BGK kinetic model
+135
+Appendix D
+Chapman–Enskog analysis of the lattice Boltzmann method for non-ideal fluids
+136
+4
+
+1. Introduction
+Non-ideal fluids are omnipresent in science and technology. From micro-droplets coalescing in clouds, to so-
+lidification or melting of alloys and diesel droplets evaporation and subsequent combustion, all involve multiple in-
+teracting phases and moving interfaces. This ubiquity fueled wide efforts focused on the development of predictive
+mathematical models and numerical tools for multi-phase flows. While significant attention has been focused on sharp
+interface methods requiring efficient tracking of the evolving and deforming interfaces, and imposing jump conditions
+[1, 2, 3, 4], the ever-growing range of temperatures and pressures involved in typical systems of interest is making ther-
+modynamic consistency of the computational models at interfaces essential. Dramatically different thermodynamic
+regimes are encountered in diesel engines during the compression phase, in aeronautical engines during take-off while
+most rocket engines operate in trans- and super-critical regimes, where the interface thickness becomes comparable
+to the flow scales. Nucleation and cavitation are yet another example, where the sharp interface limit does not hold
+and modifications to the classical nucleation theory [5], related to curvature-dependence of the surface tension, are
+required. In such cases, an accurate account of non-ideality of the fluid, including a finite interface thickness, is crucial
+for predictive numerical simulations of the flow physics. At a macorscopic level, a primer example for thermodynam-
+ics of non-ideal fluids is the second-gradient theory, first introduced by van der Waals for single-component fluids [6],
+leading to the Navier-Stokes equations supplemented with the Korteweg stress tensor [7], and is a starting point for
+numerical methods known as diffuse interface approach [8]. On the other hand, extension of the Boltzmann equation
+to dense gases within the Enskog hard-sphere collision model [9] and Vlasov mean-field approximation [10] provides
+a kinetic-theory basis for dynamics of non-ideal fluid [11].
+The lattice Boltzmann method (LBM), a discrete solver for the discrete Boltzmann equation ( discrete in phase space)
+is a numerical tool targeting the hydrodynamic balance equations (initially in the incompressible limit) that has expe-
+rienced noticeable growth in both popularity and ability to incorporate complex physics. Since the pioneering work
+of [12], the LBM gained popularity as a viable numerical tool targeting the hydrodynamic regime of non-ideal fluids.
+Different models for non-ideal fluid dynamics have been developed since and used for a wide variety of applications
+involving complex physics and geometries. The rapid growth, constant evolution of non-ideal fluid models within the
+context of the LBM and very large number of yearly publications in that area point to the need for a comprehensive
+document listing and discussing fundamentals, pitfalls, best practices and most recent developments. A couple of pub-
+lications have previously taken upon this task in previous years. While well-written and covering a number of topics
+related to implementation and numerics they do not treat of fundamentals and do not provide in-depth discussions .
+In the present contribution we aim to provide a comprehensive overview of the LBM for non-ideal fluids simulations.
+Given the relatively wide area of topics covered in the present document and depth of discussions, sections have been
+organised in a manner allowing readers to go directly to topics they are interested in without having to go through the
+document in its entirety. As such readers interested in an introduction to the kinetic theory can read section 2 while
+those looking for a more in-depth discussion can move on to section 3. Those with an interest only for the LBM can
+directly go to section 4. To give interested readers all necessary background to analyze and understand challenges
+and shortcomings of different models we start with a detailed introductory discussion covering different aspects of the
+kinetic theory of ideal gases. This is followed by a section covering all fundamental aspects of the lattice Boltzmann
+method for ideal gases covering discretization in phase-space physical space and time, incorporation of body forces,
+an overview of different collision operators and corresponding numerical and physical properties. Extension of the
+lattice Boltzmann method to non-ideal fluids is then discussed in details in section 5 where different models are re-
+viewed and a comprehensive discussion covering most important challenges is provided. Some of the most interesting
+and recent achievement in terms of application with LBMs for non-ideal fluids are then reviewed and discussed in
+section 6. This is followed by a section discussing interesting extensions of the iso-thermal non-ideal fluid solvers to
+compressible and multi-component fluids in section 7.
+2. Elements of kinetic theory
+2.1. The Boltzmann transport equation
+Following Boltzmann, we consider a gas consisting of a large number of identical particles of mass m = 1. The
+state of the gas is described by the distribution function,
+f(v, x, t),
+(1)
+5
+
+with the interpretation that the number of particles dN1 in a differential volume of phase space centered at (x, v) at
+time t is
+dN = f(v, x, t)d3vd3x.
+(2)
+We further assume that the gas is moderately dilute, that is, the particles mostly fly freely, and experience encounters
+(collisions) from time to time. Collisions with a participation of more than two particles at a time can be neglected,
+so we consider only binary collisions. More specifically, think of hard spheres of a diameter d. Then if N is the
+number of such spheres in a container of a volume V, we consider the case N → ∞ (”many particles”), V → ∞
+(”big container”) and d → 0 (”interaction range is short”), so that with both these limits we have N/V ∼ const (the
+average density of particles is finite). Furthermore, Nd3/V → 0 (total volume occupied by the particles is negligible
+to the volume of the container), but Nd2 ∼ const (total cross-section area is fixed, so that molecules will be able to
+”see” each other and collide). This is called the Boltzmann–Grad limit and is used to rigorously justify the domain of
+validity of the Boltzmann equation.
+With the above assumptions we can state that there will be two mechanisms which contribute to changing the
+distribution function in time and space: the free flight (or a modification thereof if long-range forces are present), and
+the binary collisions. Thus, we write,
+∂ f
+∂t + v · ∂f
+∂x + F
+m · ∂ f
+∂v = JB.
+(3)
+Here on the left we have the free flight operator (v · ∂/∂x) and we have also included an effect of action of large-scale
+forces such as gravity, (F/m)·∂/∂v. These two terms signify the net change of the number of particles in the element of
+the phase space volume d3vd3x centered at (v, x) due to flying in and out of particles and the change of their velocities
+through an acceleration caused by external forces.
+The term on the right hand side is called the collision integral, and which takes into account the change of the
+number of particles in the elementary volume d3vd3x through ”kicking out” a particle with the velocity about v when
+it collides with some other particle and alters the velocity, and through ”kicking in” a particle with the velocity v
+which is produced in a collision of two particles with some different velocities. Now we shall evaluate the effect of
+the binary collisions according to Boltzmann.
+2.1.1. Binary collision: Kinematics
+We need first to consider a purely mechanical part of the derivation, namely the collision of two particles. In this
+section, we shall neglect the long-range forces. Collision is vaguely understood as a relatively sharp change of the
+trajectories of the particles approaching each other from a distance. The range of the force which causes the sharp
+change of their trajectories is assumed short so that the particles approach each other along straight trajectories (it is
+best to think of hard spheres again); their encounter happens almost instantly, after which the molecules fly away from
+each other along the changed straight trajectories.
+We shall consider two molecules labeled ”1” and ”2”, their velocities before the collision in the lab frame are v1
+and v2, whereas after the collision they are denoted by primes, v′
+1 and v′
+2, respectively. Furthermore, we introduce the
+center-of-mass velocity G and the relative velocity g21, and similarly, after the collision, G′ and g′
+21,
+G = v1 + v2
+2
+,
+(4)
+g21 = v2 − v1,
+(5)
+G′ = v′
+1 + v′
+2
+2
+,
+(6)
+g′
+21 = v′
+2 − v′
+1.
+(7)
+The unit vector in the direction of the relative velocity g21 will be denoted e; correspondingly, e′ for the post-collision
+relative velocity g′
+21,
+e = v2 − v1
+|v2 − v1| = g21
+g21
+,
+(8)
+e′ = v′
+2 − v′
+1
+|v′
+2 − v′
+1| = g′
+21
+g′
+21
+.
+(9)
+6
+
+Thus, before and after the collision, the velocities of the molecules in the lab frame are, respectively,
+v1 = G − 1
+2g21e,
+(10)
+v2 = G + 1
+2g21e,
+(11)
+v′
+1 = G′ − 1
+2g′
+21e′,
+(12)
+v2 = G′ + 1
+2g′
+21e′.
+(13)
+Collision are further assumed to be elastic so that the momentum of the pair of molecules and their energy is conserved
+as the result of the collision (particle’s mass m = 1),
+v1 + v2 = v′
+1 + v′
+2,
+(14)
+|v1|2 + |v2|2 = |v′
+1|2 + |v′
+2|2.
+(15)
+These are 3 + 1 = 4 equations (three components of momentum conservation and one energy conservation) for 6
+unknowns (three components of v′ and three components of v′
+1). From the first equation, we infer that the center-of-
+mass momentum is conserved in the collision. From the second we get that the magnitude of the relative velocity does
+not change in the collision,
+G′ = G,
+(16)
+g′
+21 = g21.
+(17)
+The post-collision velocities in the lab frame are thus a two-parametric family is parameterized by a vector e′ belong-
+ing to a unit sphere, |e′|2 = 1:
+v′
+1 = v1 + v2
+2
+− |v2 − v1|
+2
+e′,
+(18)
+v′
+2 = v1 + v2
+2
++ |v2 − v1|
+2
+e′.
+(19)
+From these relation we see that the vector |e′| is a rotation of the relative velocity as the result of the collision.
+Deflection angle θ is the angle between e and e′,
+cos θ = e · e′.
+(20)
+2.1.2. Differential scattering cross-section
+We now shall move on, still in a pure mechanics mode, to considering a number of encounters. This is a scattering
+problem, familiar from classical mechanics. We shall further assume that molecules are interacting through a potential
+which depends only on the absolute distance between them, U(r1, r2) = U(|r2 − r1|) (central forces). In such a case
+the trajectories of both molecules are confined to a plane, which is orthogonal to the angular momentum (the latter is
+conserved for the central force interaction).
+The analysis is best done in the center-of-mass (CM) frame (co-moving with the center-of-mass velocity G). The
+problem then reduces to the scattering of a particle with a reduced mass m0 = m1m2/(m1 + m2) (m0 = m/2 in the case
+of equal masses of particles), moving with the velocity g21 on a fixed center. Trajectories of such particles look most
+simple: they are symmetric with respect to the line through the points of closest approach of the molecules and the
+center of force.
+Now we need to specify the two parameters to characterize the initial data for the scattering particle. For that we
+use the azimuth angle ϵ which fixes the orientation of the plane containing the trajectory with respect to an arbitrary
+fixed plane containing the center of force and parallel to g21, and the impact parameter b, defined as the distance
+between the line drawn by g21 and the parallel to it line containing the center of force.
+7
+
+Let us consider the incident jet of particles through the area between the two concentric circles of radii b and
+b + db, cut with the angle between ϵ and ϵ + dϵ,
+dAin = bdbdϵ.
+(21)
+The particles coming through the area dAin are scattered into the solid angle,
+dAout = d2e′ = sin θdθdϵ.
+(22)
+The differential scattering cross section α12 is defined as the ratio between these two areas,
+α12 = dAin
+dAout
+=
+bdbdϵ
+sin θdθdϵ .
+(23)
+Thus,
+bdbdϵ = α12d2e′,
+(24)
+where
+α21 =
+b
+��� ∂b
+∂θ
+���
+sin θ .
+(25)
+Note that we have written the absolute value of the derivative of the impact parameter with respect to the deflection
+angle because for repulsive force this function is negative (that is, with the decrease of the impact parameter the
+particle is ”turned back” by the potential, the deflection angle is increased).
+Differential scattering cross section thus represents intensity of the incoming flux of particles through the element
+of the cross-section in terms of the flux of scattered particles into the solid angle. Note that for the central forces,
+the dependence on the azimuth angle is irrelevant, and the differential scattering cross section depends only on the
+deflection angle θ and the magnitude of the relative velocity g21. For a specified central potential, the differential
+cross-section is computed by classical mechanics. We shall discuss a few relevant examples later, but for now we
+shall keep it unspecified.
+2.1.3. Boltzmann’s collision integral
+We shall now proceed with the evaluation of the rate of change of the distribution function, which we represent in
+a ”gain-loss” form,
+JB = J+
+B − J−
+B,
+(26)
+where
+• The loss,
+J−
+B(v1, x, t)d3v1d3xdt,
+(27)
+is the number of collisions of the type {v1, v2} → {v′
+1, v′
+2}, resulting in the loss of the particles of the type ”1”, in
+the infinitesimal volume of phase space d3v1dx, during the time between t and t + dt, and
+• The gain,
+J+
+B(v1, x, t)d3v1d3xdt,
+(28)
+is the number of collisions of the type {v′
+1, v′
+2} → {v1, v2}, resulting in the gain of the particles of the type ”1”, in
+the same infinitesimal phase space volume, for the same time duration.
+Note that when we say ”loss/gain”, we do not mean a particle is destroyed or created in the volume element dx; rather,
+we mean that a particle, which was in d3v1 before the collision, has changed its velocity ”too much” after the collision,
+so that is not within d3v1 any longer (loss), or that after a collision, the velocity of one of the particles changed in such
+a way that it now belongs to d3v1 (gain). So it is about the loss and gain in the element of the phase space d3v1d3x.
+For the evaluation of the rates J−
+B and J+
+B, Boltzmann assumed that any two particles which are about to collide,
+”do not know anything about each other”, neither with respect to their velocities, nor position. In other words, the
+molecular chaos assumption means that velocities of any of the two particles entering an encounter are un-correlated.
+With this assumption, we proceed as follows:
+8
+
+The loss. The number of the type ”2” particles which will encounter the dN1 = f(v1, x, t)d3v1d3x particles of type
+”1” can be written as,
+dN2 = f(v2, x, t)d3v2 (|v2 − v1|dt × bdbdϵ) .
+(29)
+Note the elementary collision volume in this expression, dVc = |v2 − v1|dt × bdbdϵ. The number of colliding pairs is
+thus estimated as,
+dN12 = dN1 × dN2 =
+�
+f(v1, x, t)d3v1d3x
+� �
+f(v2, x, t)|v2 − v1|bdbdϵd3v2dt
+�
+.
+(30)
+Notice that the number of pairs of interacting particles is estimated in this expression as a product of two one-particle
+distributions, dN12 ∼ f(v1, x, t) f(v2, x, t). This is implied by the molecular chaos assumption: if the colliding particles
+were assumed to be correlated, then we would need a distribution function of pairs of particles. With the results of
+the previous section, this expression can be written using the differential scattering cross section,
+dN12 =
+�
+f(v1, x, t) f(v2, x, t)|v2 − v1|α12d2e′d3v2
+�
+d3v1d3xdt.
+(31)
+Thus, the rate of loss of particles with velocities v1 is the sum (integral) of the above expression over all possible
+velocities v2 and over all the directions of post-collision relative velocity e′ (the surface of the three-dimensional unit
+sphere S 2):
+J−
+B(v1, x, t) = f(v1, x, t)
+�
+R3
+�
+S 2 f(v2, x, t)|v2 − v1|α12d2e′d3v2.
+(32)
+The gain. We now need to construct a similar expression for the rate with which the particles with the velocity v1 are
+produced as the result of collisions of pairs of particles with other velocities. The counting process is greatly simplified
+by the reversibility of mechanical motion. Indeed, Newton’s equations are reversible in the time. Therefore, if in the
+direct scattering the initial data for the velocities {v1, v2} was transformed into {v′
+1, v′
+2}, then we can take {v′
+1, v′
+2} as the
+initial data in another (reverse) scattering experiment, and the result of scattering will be known, it is {v1, v2}. Precisely
+this ability to interchange of the past and the future in a mechanical system (time-reversal) is what will be used to
+count all the pairs of particles which produce the desired velocity v1. We therefore do not need to start a counting
+from the beginning, as we just need to repeat all of the above by changing non-primed variables into primed variables,
+and vice versa. Note, however, that we still use the molecular chaos assumption when so doing. Thus, using the
+reversibility, we can write the number of pair collisions of the type {v′
+1, v′
+2} → {v1, v2},
+dN′
+12 = f(v′
+1, x, t) f(v′
+2, x, t)|v′
+2 − v′
+1|α′
+12d2ed3v′
+1d3v′
+2d3xdt.
+(33)
+This expression is transformed in three steps: As the magnitude of the relative velocity does not change as the result
+of collision, we have
+dN′
+12 = f(v′
+1, x, t) f(v′
+2, x, t)|v2 − v1|α′
+12d2ed3v′
+1d3v′
+2d3xdt.
+(34)
+Furthermore, the differential scattering cross section remains same under the inversion of the velocities,
+dN′
+12 = f(v′
+1, x, t) f(v′
+2, x, t)|v2 − v1|α12d2ed3v′
+1d3v′
+2d3xdt.
+(35)
+Finally, the element of the 2 + 3 + 3-dimensional volume, d2ed3v′
+1d3v′
+2 is transformed to the elementary volume
+d2e′d3v1d3v2. First, we compute the Jacobian of the transformation {v1, v2} → {G, g21},
+J = ∂(G, g21)
+∂(v1, v2) = 1.
+(36)
+Thus, by the definition of the transformation of the elementary volume which includes the determinant of the Jacobian,
+we have d3Gd3 g21 = |J|d3v1d3v2 = d3v1d3v2, and similarly, d3Gd3 g′
+21 = d3v′
+1d3v′
+2. On the other hand, d3g21 =
+g2
+21dg21d2e and d3 g′
+21 = g2
+21dg21d2e′. Combining these expressions, we have,
+d2ed3v′
+1d3v′
+2 = d2e′d3v1d3v2,
+(37)
+9
+
+and thus we obtain the final expression for dN′
+12 in the form,
+dN′
+12 =
+�
+f(v′
+1, x, t) f(v′
+2, x, t)|v2 − v1|α12d2e′d3v2
+�
+d3v1d3xdt.
+(38)
+As the result, we obtain the rate of gain after integration,
+J+
+B(v1, x, t) =
+�
+R3
+�
+S 2 f(v′
+1, x, t) f(v′
+2, x, t)|v2 − v1|α12d2e′d3v2.
+(39)
+Combining the results of the above estimate for the gain (39) and loss (32), we obtain the rate of change of the
+one-particle distribution function due to binary collisions,
+JB =
+�
+R3
+�
+S 2
+� f(v′
+1, x, t) f(v′
+2, x, t) − f(v1, x, t) f(v2, x, t)� K(|v2 − v1|, θ)e′d3v2,
+(40)
+where the post-collision velocities v′
+1 and v′
+2 are the functions of v1, v2 and e′, Eqs. (18) and (19), and where the
+function K is the collision kernel,
+K = |v2 − v1|α12(|v2 − v1|, θ).
+(41)
+This is the Boltzmann Stosszahlansatz or the Boltzmann collision integral.
+The collision kernel (41) depends on the magnitude of the relative velocity |v2 − v1| and on the deflection angle θ.
+Computation of K is a matter of studying the mechanical scattering problem. Here we mention two cases.
+Hard spheres. These are ”billiard balls” of a diameter d. In this case the differential cross-section does not depend
+on the relative velocity of colliding particles. By simple geometrical considerations we obtain
+α12 = d2
+4 , K = d2
+4 |v2 − v1|.
+(42)
+Inverse-power law potentials. For any interaction potential U(r), the dependence of the deflection angle on the impact
+parameter and the relative velocity is given in terms of a quadrature. We do not write it here. However, if the potential
+is inverse proportional to power of distance, U(r) ∼ r−n we can infer about the dependence of the differential scattering
+cross-sections on the velocity even without integrating Newton’s equations explicitly. It is sufficient to make use of
+similarity: if the potential of a mechanical system is a homogeneous function of order k, that is U(αr) = αkU(r), then
+the velocity and the geometric parameters of geometrically similar trajectories are related by
+� v
+V
+�
+=
+� l
+L
+�k/2
+,
+(43)
+where v, V and l, L are the velocity and characteristic length on two geometrically similar trajectories. This follows
+immediately from the invariance of Newton’s equations under the transformation of space and time r → αr, t →
+α(2−k)/2t. In our case k = −n, thus we have the following relation between the impact parameter and the relative
+velocity: b ∼ |v2 − v1|−2/n. This implies for the Boltzmann collision kernel
+K = a(θ)|v2 − v1|1−4/n,
+(44)
+where function a depends only on the deflection angle. We see that in the special case n = 4 (that is, for the molec-
+ular potential inverse proportional to the fourth power of the separation distance in three dimensions), the collision
+kernel depends only on the deflection angle but not on the relative velocity of particles. This is known as Maxwell’s
+molecules, and it was first shown by Maxwell that computations in that case greatly simplify. Finally, we mention that
+function a(θ) diverges as θ → 0 because of a large number of particles experiencing grazing collisions with almost no
+deflection. In practice, one often uses a cutoff angle to regularize this divergence. This works for most inverse-power
+law potentials but not for the Coulomb potential n = −1 where grazing collisions have to be treated in a different
+manner.
+Summarizing, we can trace the assumptions behind the derivation of the Boltzmann equation by looking once
+again at the structure of the Boltzmann collision integral (40):
+10
+
+1. The gas is assumed to be dilute so that only binary collisions of molecules are considered. This is reflected by
+the quadratic nonlinearity of the collision integral.
+2. Binary collisions are assumed to be local in time and space. That is, the duration of the collision and the
+effective range of interaction where the trajectories of the particles change appreciably are supposed to be much
+smaller than any other characteristic time/distance scales of the system. This is reflected by the fact that x and t
+are simply parameters in the collision integral, there is neither space or time derivative in there.
+3. Collisions are supposed to be elastic, which is reflected by the specific post-collision velocities v′
+1 and v′
+2; they
+are the implication of the momentum and energy conservation in the elastic collision.
+4. Micro-reversibility of the Newton’s equation of mechanical interaction is reflected by the structure of the colli-
+sion kernel; we have explicitly used it to count the pairs of colliding particles by tracing backward in time the
+scattering trajectories.
+5. The molecular chaos hypothesis is reflected by the specific structure of the gain and loss parts, quadratic in the
+distribution function.
+Notation convention. It is customary to use some abbreviation in writing the Boltzmann transport equation. First, we
+change the notation for the velocity, v1 → v and v2 → v1. Second, one usually drops the space and time arguments,
+and uses the abbreviations
+f(v, x, t) = f, f(v1, x, t) = f1, f(v′, x, t) = f ′, f(v′
+1, x, t) = f ′
+1.
+(45)
+With this, the Boltzmann collision integral (40) is written as,
+JB =
+�
+R3
+�
+S 2
+� f ′ f ′
+1 − f f1
+� Bd2e′d3v1,
+(46)
+while the Boltzmann transport equation in the absence of long-range forces becomes,
+∂t f + v · ∇f = JB,
+(47)
+where ∂t = ∂/∂t and ∇ = ∂/∂x are shorthand notation for the derivatives in time and space.
+2.2. Transport equations for molecular properties
+2.2.1. Boltzmann’s transport theorem
+A molecular (or microscopic) property can be thought as a generic function of the velocity ϕ(v), such as, for
+example ϕ = m (particle’s mass), ϕ = mv (particle’s momentum), ϕ = mv2/2 (kinetic energy of the particle) and
+so fort. With the help of the distribution function, we define the corresponding macroscopic densities (or fields) by
+averaging over the entire range of the microscopic velocities according to their distribution function,
+ρϕ(x, t) =
+�
+R3 ϕ(v) f(v, x, t)d3v.
+(48)
+We can also define the microscopic flux of any microscopic property by multiplying it with v so that the macroscopic
+flux jϕ is,
+jϕ(x, t) =
+�
+R3 vϕ(v) f(v, x, t)d3v.
+(49)
+When the distribution function evolves in time and space according to the Boltzmann equation, also all the macro-
+scopic densities and fluxes evolve due to f. The transport equation for any macroscopic density is obtained by
+multiplying the Boltzmann equation with the corresponding microscopic property and integrating over the velocities,
+∂tρϕ + ∇ · jϕ = Rϕ.
+(50)
+The left hand side of this equation contains the divergence of the flux jϕ, while the right hand side is the production
+rate due to collisions,
+Rϕ =
+�
+R3
+�
+R3
+�
+S 2 ϕ � f ′ f ′
+1 − f f1
+� Kd2e′d3v1d3v.
+(51)
+11
+
+This expression can be written in a more symmetric and telling form by using the symmetries of the with respect to
+renaming the particles, the time reversal and the combination thereof,
+d2e′d3v1d3v = d2e′d3vd3v1 = d2ed3v′
+1d3v′ = d2ed3v′d3v′
+1,
+so that
+Rϕ =
+�
+R3
+�
+R3
+�
+S 2 ϕ � f ′ f ′
+1 − f f1
+� Kd2e′d3v1d3v
+=
+�
+R3
+�
+R3
+�
+S 2 ϕ1
+� f ′ f ′
+1 − f f1
+� Kd2e′d3v1d3v,
+= −
+�
+R3
+�
+R3
+�
+S 2 ϕ′ � f ′ f ′
+1 − f f1
+� Kd2e′d3v1d3v,
+= −
+�
+R3
+�
+R3
+�
+S 2 ϕ′
+1
+� f ′ f ′
+1 − f f1
+� Kd2e′d3v1d3v.
+(52)
+Thus, we arrive at Boltzmann’s transport theorem: The production rate of any molecular property is written in the
+following symmetrized form,
+Rϕ = 1
+4
+�
+R3
+�
+R3
+�
+S 2(ϕ + ϕ1 − ϕ′ − ϕ′
+1) � f ′ f ′
+1 − f f1
+� Kd2e′d3v1d3v.
+(53)
+2.2.2. Invariants of collision. Conservation of mass, momentum and energy
+Immediate implication of the Boltzmann’s transport theorem is vanishing of the rate whenever the molecular
+property satisfies the condition,
+ϕ + ϕ1 − ϕ′ − ϕ′
+1 = 0.
+(54)
+Because each binary collision conserves the number of particles, their momentum (14) and kinetic energy (15), the
+most general solution to the collision invariants condition is a linear combination of five scalar quantities,
+ϕ ∈ Lin
+�
+1, v, v2�
+.
+(55)
+The conventional basis of the linear subspace (55) is built by five molecular properties m, mv and mv2/2, corresponding
+to macroscopic densities ρ, ρu and ρE, respectively, interpreted as the mass density, the momentum flux and the energy
+density,
+ρ(x, t) = m
+�
+R3 f(v, x, t)d3v,
+(56)
+ρu(x, t) = m
+�
+R3 v f(v, x, t)d3v,
+(57)
+ρE(x, t) = (m/2)
+�
+R3 v2 f(v, x, t)d3v.
+(58)
+Therefore, the corresponding terms Rϕ vanish, and the transport equations for these locally conserved fields become
+conventional statements of the local conservation. Under suitable boundary conditions (vanishing at infinity, peri-
+odic etc), this leads, after integration over the volume of the container, to the global mass, momentum and energy
+conservation.
+2.2.3. Boltzmann’s H-theorem
+Yet another implication of Boltzmann’s transport theorem is manifest when considering the following molecular
+property,
+ϕ = ln f(v, x, t) + 1.
+(59)
+12
+
+The corresponding production rate is,
+σB = 1
+4
+�
+R3
+�
+R3
+�
+S 2(ln f + ln f1 − ln f ′ − ln f ′
+1) � f ′ f ′
+1 − f f1
+� Kd2e′d3v1d3v
+= 1
+4
+�
+R3
+�
+R3
+�
+S 2 ln
+� f f1
+f ′ f ′
+1
+� � f ′ f ′
+1 − f f1
+� Kd2e′d3v1d3v.
+(60)
+Now we denote X = f f1, Y = f ′ f ′
+1, and notice that the function under integration, F = ln X
+Y (Y − X) ≤ 0 for any X > 0,
+Y > 0. Thus, for any f, the rate σ is non-positive,
+σB(x, t) ≤ 0.
+(61)
+Consider the following field, the Boltzmann H-function,
+H(x, t) =
+�
+R3 f(v, x, t) ln f(v, x, t)d3v.
+(62)
+The total H-function ¯H is obtained after integration of the density (62) over the volume V. Assuming suitable bound-
+ary conditions under which the flux of the H-function vanishes at the boundaries, we find, based on the non-positivity
+of the H-function production rate (60),
+d ¯H
+dt =
+�
+V
+σB(x, t)d3x ≤ 0.
+(63)
+This is the H-theorem proven by Boltzmann: H-function never increases due to the Boltzmann equation. This is the
+spectacular implication of the Boltzmann equation, as it describes irreversible behavior, and the H-function has to be
+related to the entropy of the system according to second law of thermodynamics (the non-decrease of the entropy with
+the time). Identification of the H-function with the entropy will be completed below.
+2.2.4. Equilibrium and local equilibrium. The Maxwell-Boltzmann distribution function
+The structure of the Boltzmann collision integral (40) implies that its zero-point, JB( f) = 0, is achieved on the
+family of local equilibrium distribution functions f eq(v, x, t), satisfying the detail balance condition,
+f eq′ f eq′
+1
+= f eq f eq
+1 ,
+(64)
+or, by taking the logarithm of this expression,
+ln f eq′ + ln f eq′
+1
+− ln f eq − ln f eq
+1 = 0.
+(65)
+Comparison to Eq. (54) shows that the logarithm of the local equilibrium distribution function is a linear combination
+of collision invariants,
+ln f eq ∈ {1, v, v2}.
+(66)
+Thus, the generic local equilibrium can be written as a five-parametric subset,
+f eq = A exp
+�
+−(v − λ)2
+2σ
+�
+.
+(67)
+We now turn to the definition of the density (56), the momentum (57) and the energy (58). For the latter, we assume a
+relation to the absolute temperature by the caloric equation of state of monatomic ideal gas,
+ρE = 3
+2ρRT + 1
+2ρu2,
+(68)
+where R is gas constant,
+R = RU
+µ ,
+(69)
+13
+
+with RU the universal gas constant and µ the molar mass. Using (67) in (56), (57) and (58), the parameters {A, λ, σ} are
+expressed in terms of the conventional parameters {ρ, u, T} upon evaluation of the Gauss integrals: A = (ρ/m) (2πRT)−3/2,
+λ = u and σ = RT. With this re-parameterization, the local equilibrium distribution function reads,
+f eq = n (2πRT)−3/2 exp
+�
+−(v − u)2
+2RT
+�
+,
+(70)
+where n = ρ/m is the number density. This is the local Maxwell-Boltzmann distribution function. Specification ”local”
+means that density, velocity and temperature in this expressions can be arbitrary functions of space and time. The local
+equilibrium annuls only the right hand side of the Boltzmann equation but not the left hand side, so it is not a solution
+of the Boltzmann equation. It, however becomes the solution when the density, flow velocity and temperature are
+constant. Then we speak of the global equilibrium, or just the equilibrium.
+The Boltzmann H-function is easily evaluated at the local (or global) equilibrium:
+Heq =
+�
+f eq ln f eqd3v = −n
+�3
+2 ln T − ln n
+�
+− 3
+2n (ln(2πR) + 1) .
+(71)
+Note that this expression does not depend on flow velocity as the consequence of Galilean invariance. Since the
+thermodynamic entropy concerns the equilibrium states, we consider the case of global equilibrium of N particles,
+and evaluate the total H-function difference between the two states. Integrating (71) over the volume, we find
+∆ ¯Heq = −NAν
+�3
+2 ln
+�T2
+T1
+�
++ ln
+�V2
+V1
+��
+,
+(72)
+where NA and ν are the Avogadro number and the number of moles of gas, respectively, N = NAν. On the other hand,
+the thermodynamic entropy difference between the two states of ν moles of ideal gas with the specific heat at constant
+volume cv = (3/2)RU is,
+∆S = ν
+�3
+2RU ln
+�T2
+T1
+�
++ RU ln
+�V2
+V1
+��
+.
+(73)
+Comparing (72) and (73), we see that the thermodynamic entropy difference and the H-function difference are related
+by a dimensional constant and the sign convention,
+∆S = −kB∆ ¯Heq,
+(74)
+where kB is the Boltzmann constant, or ”the universal gas constant per particle”,
+kB = RU
+NA
+.
+(75)
+Note that the matching of the specific heat through the thermodynamic entropy relation proves the assumption already
+made when choosing the parameterization of the energy (68). While identification of the thermodynamic entropy
+can be done only at the equilibrium, the function S ( f) = −kBH( f) can be considered as the non-equilibrium entropy
+density whenever the distribution function f differs from the global equilibrium. The Boltzmann H-theorem about
+the non-positive H-function production and non-increase of H can be considered as the specific realization of the
+thermodynamic concept of the entropy increase due to irreversible processes.
+3. From Boltzmann equation to hydrodynamics
+3.1. Fields and fluxes
+In this section, we use Cartesian coordinate notation, ∂α = ∂/∂xα, where α labels the three coordinate directions.
+We address in this section the thirteen fields of interest: the density ρ, momentum ρu, full pressure tensor P and
+14
+
+energy flux Z are defined as follows,
+ρ = m
+�
+fdv,
+(76)
+ρuα = m
+�
+vα fdv,
+(77)
+Pαβ = m
+�
+vαvβ fdv,
+(78)
+Zα = m
+2
+�
+vαv2 fdv.
+(79)
+Identifying pressure p as
+p = 1
+3
+�
+m(v − u)2 fdv,
+(80)
+the pressure tensor (78) and the energy flux (79) are decomposed as follows when measuring particle’s velocity relative
+to the flow velocity u,
+Pαβ = pδαβ + σαβ + ρuαuβ,
+(81)
+Zα =
+�5
+2 p + 1
+2ρu2
+�
+uα + σαβuβ + qα,
+(82)
+where nonequilibrium stress tensor σ and heat flux q are defined as
+σαβ = m
+� �
+(vα − uα)(vβ − uβ) − 1
+3δαβ(v − u)2
+�
+fdv,
+(83)
+qα = m
+2
+�
+(vα − uα)(v − u)2 fdv.
+(84)
+Rank two symmetric tensor σ is trace-free. Finally, temperature T is defined by the equation of state of ideal gas,
+p = ρRT.
+(85)
+Density ρ, flow velocity u, temperature T, nonequilibrium stress σ and heat flux q are the thirteen fields of Grad.
+3.2. Balance equations for thirteen moments
+Introducing the material derivative along streamline,
+Dt = ∂t + uα∂α,
+(86)
+we write kinetic equation in the co-moving reference frame,
+Dt f = −(vα − uα)∂α f + JB.
+(87)
+Here and below, summation convention is always understood. Multiplying (87) with 1, vα, vαvβ and vαv2 and integrat-
+ing over velocities, we come to the set of exact balance equations for the thirteen Grad’s fields. Balance equations for
+the locally conserved fields (mass-momentum-energy) imply
+Dtρ = −ρ(∂αuα),
+(88)
+Dtuα = −1
+ρ∂αp − 1
+ρ∂βσαβ,
+(89)
+DtT = −2
+3T(∂αuα) − 2
+3
+�T
+p
+�
+σαβ(∂βuα) − 2
+3
+�T
+p
+�
+(∂αqα).
+(90)
+15
+
+The nonequilibrium stress and heat flux are the only nonequilibrium fluxes engaged in the balance equations (89) and
+(90), and we continue with writing down the exact balance equations for σ and q:
+Dtσαβ = − p
+�
+∂αuβ + ∂βuα − 2
+3δαβ∂γuγ
+�
+−
+�
+σαγ∂γuβ + σβγ∂γuα − 2
+3δαβσµν∂νuµ
+�
+− σαβ
+�
+∂γuγ
+�
+− 2∂γ
+�
+Qαβγ − 1
+3δαβqγ
+�
++ Rσ
+αβ,
+(91)
+Dtqα = −qα∂βuβ − qβ∂βuα + 5
+2RT∂αp + 5
+2RT∂βσαβ + 1
+ρσαβ∂βp + 1
+ρσαβ∂γσγβ
+− ∂βTαβ − 2Qαβγ∂γuβ + Rq
+α.
+(92)
+Here, symmetric rank three tensor Q and symmetric rank two tensor T are,
+Qαβγ = m
+2
+�
+(vα − uα)(vβ − uβ)(vγ − uγ) fdv,
+(93)
+Tαβ = m
+2
+�
+(vα − uα)(vβ − uβ)(v − u)2 fdv.
+(94)
+For brevity, we refer to them as the Q-flux and the T-flux, respectively. The Q-flux is engaged as a divergence in the
+stress balance (91) and as a source term in the heat flux balance (92) while the T-flux contributes as a divergence in
+the heat flux balance only. The heat flux and the Q-flux are connected through,
+qα = Qαββ.
+(95)
+Furthermore, the relaxation terms are defined as rates over collisions,
+Rq
+α = m
+2
+�
+(vα − uα)(v − u)2JBdv,
+(96)
+Rσ
+αβ = m
+� �
+(vα − uα)(vβ − uβ) − 1
+3δαβ(v − u)2
+�
+JBdv.
+(97)
+Balance equations are identities and cannot be addressed unless a constitutive relation is provided for both the Q- and
+T-fluxes, as well as for the collision rates.
+3.3. Local equilibrium projection
+The balance equations for the locally conserved fields density (88), flow velocity (89) and temperature (90) become
+the equations of hydrodynamics once constitutive relations are supplied for the nonequilibrium pressure tensor (83)
+and heat flux (84). Evaluation of these fluxes on the local equilibrium (70) returns,
+σαβ[ f eq] = 0, qα[ f eq] = 0.
+(98)
+This implies the Euler’s equations of non-viscous, thermally non-conductive fluid,
+DE
+t ρ = −ρ(∂αuα),
+(99)
+DE
+t uα = −1
+ρ∂αp,
+(100)
+DE
+t T = −2
+3T(∂αuα).
+(101)
+The local equilibrium projection thus amounts to a neglect of any equilibration process, so that the distribution func-
+tion never leaves the submanifold of local Maxwellians while the parameters of the local Maxwellian evolve according
+to Euler’s equations. This can be viewed as an analogy to the ideal quasi-equilibrium reversible processes in thermo-
+dynamics. Addressing the equilibration processes towards the local equilibrium states is thus needed to obtain a more
+realistic picture.
+16
+
+3.4. Dynamic correction to the local equilibrium projection
+3.4.1. Estimates from the Maxwell-Boltzmann distribution
+We shall first do a few ”back-of-the-envelope” estimates concerning the Boltzmann equation and transport phe-
+nomena. We shall often use ∼ instead of = in these estimates, meaning that a more accurate computation shall bring
+numerical factors of order one but the estimates below will be valid ”on the order of magnitude”.
+The dimension of the distribution function f is
+f ∼
+1
+velocity3 ×
+1
+volume ∼
+1
+(cm/sec)3 ×
+1
+cm3 ,
+(102)
+which is consistent with the fact that dN = f(v, x, t)d3vd3x is the number of particles in the element of the phase-space
+volume d3vd3x ∼ (cm/sec)3 × cm3.
+We now need some characteristic values for the velocity and the volume to make things non-dimensional. Let us
+look at the Maxwell-Boltzmann distribution function (70). The factor in front the exponential is ∼ nv−3
+T , where
+vT =
+√
+RT,
+(103)
+has the dimension of the velocity, vT ∼ (cm/sec). We shall call it the thermal speed. Other characteristic velocities
+may be defined such as the r.m.s. of the velocity fluctuations about the mean velocity u is vr.m.s =
+√
+3RT or the speed
+of sound cs = √5RT/3, or the mean absolute value of the velocity fluctuation vm = √8RT/π. They all differ by a
+factor of order one from the thermal speed (103). Introducing the reduced peculiar velocity (this term is universally
+used, and means simply the deviation of the molecular velocity from the flow velocity u),
+C = v − u
+vT
+,
+(104)
+the Maxwell-Boltzmann distribution becomes,
+M =
+n
+(2π)3/2v3
+T
+e− C2
+2 .
+(105)
+We shall use vT to reduce all molecular velocities in the sequel. Of course, the temperature and the density (and the
+flow velocity) in the local Maxwell-Boltzmann distribution may vary in space and time, so we are talking about some
+characteristic number-density and temperature when using them for non-dimensionalization.
+3.4.2. Mean free path
+Mean free path is defined as the average distance traveled by a particel before it comes to a collision with some
+other particle. For the hard-sphere model of collision, the number density n and the diameter of the hart-spehere d can
+be combined to give the quantity with the dimension of the distance,
+lm.f.p. ∼
+1
+d2n.
+(106)
+The estimate of the mean free path (106) is intuitively clear, as we expect lm. f.p. to decrease with the increase of the
+scattering cross-section ∼ d2 and with the increase of the density of scattering centers n. More accurate definitions
+of lm.f.p. are available, in particular, upon the exact estimate of the number of binary collisions from the Bolztmann
+collision integral [11] but the above estimate is sufficient for our purpose here.
+3.4.3. Estimates from the Boltzmann collision integral
+We now reduce the Boltzmann collision integral for hard-spheres (46). We first make the distribution function
+dimensionless by reducing it with some typical thermal speed and number density, ¯f = v3
+Tn−1 f. Furthermore, we
+introduce the dimensionless scattering kernel, d2vT ¯B = B, so that ¯B depends only on the reduced relative velocity,
+| ¯v1 − ¯v| = v−1
+T |v1 − v|. Finally, reducing the element d3v1 = v3
+Td3¯v, we obtain
+JB = (d2n)vT(nv−3
+T ) ¯JB.
+(107)
+17
+
+where ¯
+JB is dimension-less,
+¯
+JB =
+�
+R3
+�
+S 2
+� ¯f ′ ¯f ′
+1 − ¯f ¯f1
+� ¯Kd2e′d3¯v1.
+(108)
+Using the definition of the mean free path (106), this is also
+JB =
+vT
+lm. f.p.
+(nv−3
+T ) ¯
+JB.
+(109)
+3.4.4. Reduced Boltzmann equation
+Now we turn to the left hand side of the Boltzmann equation and introduce the reduced time and space, t = T ¯t,
+x = L¯x, with some characteristic macroscopic length L and time T. Using the scaled collision integral (109), and also
+using the reduced flow velocity, u = (L/T)¯u, the Boltzmann equation is written in the reduced variables,
+� L
+TvT
+�
+¯Dt ¯f +
+�
+¯vα −
+� L
+TvT
+�
+¯uα
+�
+¯∂α ¯f =
+�
+L
+lm.f.p.
+�
+¯JB.
+(110)
+The dimensionless quantity, inverse of which multiplies the collision integral is called the Knudsen number,
+[Kn] = lm. f.p.
+L
+.
+(111)
+On the other hand, the dimensionless quantity which multiplies the time derivative is called the kinetic Strouhal
+number,
+[St] =
+L
+TvT
+.
+(112)
+With this, the reduced Boltzmann equation is written,
+[St] ¯Dt ¯f + (¯vα − [St]¯uα) ¯∂α ¯f =
+1
+[Kn]
+¯JB.
+(113)
+3.4.5. Hydrodynamic limit
+The hydrodynamic limit of the Boltzmann equation corresponds to a flows featuring a small Knudsen number,
+when the mean free path is small compared to a typical time-space variation of hydrodynamic fields (local density,
+flow velocity and temperature). A typical estimate of Knudsen number for our ”daily life” flows is of the order of
+[Kn] ∼ 10−5 − 10−6. In the classical case considered below, the Strouhal number is considered to be of the order one.
+A related quantity is the Mach number,
+[Ma] =
+L
+Tcs
+,
+(114)
+where cs = √γRT, γ = 5/3 is the adiabatic exponent of Boltzmann’s gas (monatomic particles without internal
+degrees of freedom). Since the speed of sound is of same order as thermal speed, we assume [Ma] ∼ [SM]. In
+summary, the standard hydrodynamic limit assumes the following scaling,
+[Kn] ≪ 1, [Ma] ∼ [St] ∼ O(1).
+(115)
+In that case, the hydrodynamic limit of the Boltzmann equation leads to a compressible flow. On the other hand,
+different other scaling can be also considered. In particular, if the Strouhal number, the Knudsen number but also the
+Mach number are small and of same order,
+[Kn] ∼ [St] ∼ [Ma] ≪ 1,
+(116)
+then the hydrodynamic limit of the Boltzmann equation corresponds to a nearly-incompressible flow. Notice, however
+that this latter scaling requires a really slow flow; in a typical situation, S t ∼ Ma ∼ 10−2 −10−1 are small, but still they
+are much larger than a typical Knudsen number by a few orders of magnitude). Before proceeding with the analysis of
+the hydrodynamic limit in a systematic fashion, we shall consider quantitatively on the example of viscous transport
+how the transport phenomena on a conventional macroscopic scale arises from kinetic considerations.
+18
+
+3.4.6. Elementary derivation of viscosity
+Using the above estimates for the thermal speed and the mean free path, we shall first derive the phenomenon
+of dissipative transport focusing on the viscosity. Since the mean free path is what is related to the collisions and
+bearing in mind that all the dissipation comes from the Boltzmann collision integral, we may guess that the viscosity
+is related to it. Let us therefore consider a gas flow parallel to the plane z = 0; the flow velocity is supposed to depend
+only on the vertical coordinate z, thus we have ux(z), uy = uz = 0. The latter particularly means that there is no net
+flow in the vertical direction. The vertical transport of the momentum is therefore effected by the z-component of
+the particle’s velocity, and since there is no net velocity in that direction, it can be estimated as being of the order of
+root-mean-square of the z-component of particle’s velocity vz, that is, proportional to the thermal speed vT.
+In order to estimate the net transport of the x-component of momentum through a plane parallel to (x, y)-plane
+(say, the plane z = 0), we need to consider two layers of gas distanced by the order of mean free path lm. f.p. on both
+sides of this plane. Considering the z = 0 plane, the transferred x-momentum at the location z = −lm. f.p. in the positive
+z-direction (towards the z = 0 plane) per unit of time is thus estimated as
+P+
+xz ∼ vT × ρux(z)|z=−lm.f.p..
+(117)
+Note that we could write here a prefactor 1/2 since it is the half of the of the particles on average which have the
+positive component of z-velocity. We shall omit all such factors in the present rough estimate.
+Similarly, the x-momentum transported in the negative direction from the layer above the z = 0 plane towards that
+plane is
+P−
+xz ∼ −vT × ρux(z)|z=lm.f.p..
+(118)
+The net transported momentum per unit of time from both the sides of the plane z = 0 becomes, assuming the mean
+free path is small on the scale of a variation of the net velocity,
+Pxz = P+
+xz + P−
+xz ∼ −(ρvTlm. f.p.)dux(z)
+dz
+�����z=0
+(119)
+This net transported momentum per unit of time is equivalent to the force (per unit area) exerted parallel to x. This
+force has the form of the usual viscous stress, where the coefficient of viscosity is found from our ”back-of-the-
+envelope” estimate as
+µ ∼ ρvTlm.f.p..
+(120)
+Note that the usual kinematic viscosity ν = µ/ρ is ν ∼ vTlm.f.p. ∼ cm2/sec. Using the above result for the mean free
+path, we obtain,
+µ = ¯bm
+√
+RT
+d2
+,
+(121)
+where the non-dimensional coefficient ¯b (pure number) is of the order one. A rigorous estimate from the Boltzmann
+equation gives ¯b ≈ 0.179, however the dependence of the viscosity coefficient on the temperature, particle’s mass and
+the diameter of the hard-sphere stays as in the estimate (121) obtained by simple argument. From the above elementary
+consideration we can already derive a classical result that the coefficient of the viscosity is not dependent on the
+number density n, which is a well-verified experimental fact. It is also interesting to note the inverse proportionality
+to the cross-section of the hard-sphere in the result (121), as it may seem counter-intuitive at a first glance. Indeed, it
+seems plausible that ”bigger” spheres should result in a ”higher” viscosity, contrary to what (121) suggests. However,
+the right interpretation is restored when one remembers that the mean free path becomes shorter if the cross-section
+is increased.
+3.4.7. Singularly perturbed Boltzmann equation
+In accord with the scaling (115), we write the Boltzmann equation in the co-moving frame, introducing a formal
+large parameter 1/ϵ in front of the collision integral,
+Dt f = −(cβ − uβ)∂β f + 1
+ϵ JB.
+(122)
+19
+
+Such a form is called a singularly perturbed system because a small parameter ϵ multiplies the derivative. For what
+will follow, it is useful to remember the balance equations for the number (or mass) density, flow momentum, and
+energy, already mentioned above. At this stage, you may already guess that if the distribution function used to close
+the balance equations is taken as the local Maxwell-Boltzmann distribution, then the non-equilibrium pressure tensor
+and heat flux vanish, and the balance equations become the Euler compressible equations where in the right hand side
+of the flow velocity equation we see the nonlinear advection term and the gradient of the pressure (ideal gas equation
+of state), while in the right hand side of the temperature equation there are the advection term and the compression
+work term. We shall obtain this in a more systematic way below when we shall consider a correction to the local
+Maxwell-Boltzmann distribution due to collisions.
+3.4.8. Normal solutions. The invariance principle
+Following the notion introduced by D. Hilbert (1913), a normal solution is a distribution function which depends
+on the space and the time only through its (yet unknown) dependence on the locally conserved fields.
+fnr(v, x, t) = fnr(v; ρ(x, t), u(x, t), T(x, t)).
+(123)
+Normal solutions satisfy two important conditions.
+Consistency conditions. Whatever the dependence on the local fields ρ(x, t), u(x, t), and T(x, t) may be found in fnr,
+it has to satisfy the following,
+�
+mfnr(v; ρ, u, T)d3v = ρ,
+(124)
+�
+vmfnr(v; ρ, u, T)d3v = ρu,
+(125)
+� mv2
+2
+fnr(v; ρ, u, T)d3v = 3
+2ρRT + ρu2
+2 .
+(126)
+Consistency condition means that if we evaluate density, momentum and energy on a given normal solution fnr, the
+result must be the same values, as the corresponding arguments of the normal solution.
+Invariance condition. So, if the normal solution depends only on the local conservations, at every point in space
+and at each instant of time, then so does also its time derivative. That means we have to express the time derivative
+of the distribution function through the time derivative of the locally conserved fields (density, flow velocity and
+temperature). So, the normal solution should satisfy the invariance condition: By chain rule of differentiation
+∂fnr
+∂ρ Dtρ + ∂fnr
+∂uα
+Dtuα + ∂fnr
+∂T DtT = −(vα − uα)∂α fnr + 1
+ϵ JB( fnr),
+(127)
+where the time derivative of the locally conserved fields are obtained with the same fnr (that is, the nonequilibrium
+pressure tensor and heat flux are evaluated on the same normal solution).
+∂fnr
+∂ρ (−ρ∂αuα) + ∂fnr
+∂uα
+·
+�
+−1
+ρ∂αp − 1
+ρ∂βσαβ[ fnr]
+�
++ ∂ fnr
+∂T
+�
+−2
+3T∂αuα − 2
+3
+�T
+p
+�
+σαβ[ fnr]∂βuα − 2
+3
+�T
+p
+�
+∂αqα[ fnr]
+�
+= −(vα − uα)∂α fnr + 1
+ϵ JB( fnr),
+(128)
+Note that because the dependence of the time derivatives in the left hand side on the distribution function is linear,
+the overall nonlinearity of the invariance condition in f is quadratic - because of the quadratic Boltzmann collision on
+the right but also because of the quadratic dependencies through the nonequilibrium pressure tensor σ[ fnr] and heat
+flux q[ fnr] in the balance equations for flow velocity and temperature on the left. The advantage of this ”increase of
+complexity” is that the ”real” time derivative is excluded in favor of space derivatives coming from the fluxes. This
+will immediately pay off below.
+20
+
+3.4.9. The Chapman–Enskog method
+Owing to the fact that there is a large parameter 1/ϵ, D. Enskog (1917) suggested to look for the normal solution in
+terms of a series for the distribution function. This method of solving the invariance equation of the previous section
+was in fact discovered by Enskog and was made widely known as the Chapman–Enskog method by S. Chapman. The
+normal solution is then expanded into a series,
+fnr = f (0) + ϵ f (1) + O(ϵ2).
+(129)
+Accordingly, the non-equilibrium pressure tensor and heat flux are expanded as
+σαβ[ fnr] = σαβ[ f (0)] + ϵσαβ[ f (1)] + O(ϵ2),
+(130)
+qβ[ fnr] = qβ[ f (0)] + ϵqβ[ f (1)] + O(ϵ2).
+(131)
+Substituting these two expansions into the left and right hand sides of the invariance equation, and equating terms of
+same order in ε, we obtain on the order ϵ0,
+JB( f (0)) = 0,
+(132)
+and on the order ϵ,
+∂ f (0)
+∂n D(0)
+t ρ + ∂ f (0)
+∂uα
+D(0)
+t uα + ∂f (0)
+∂T D(0)
+t T + (vα − uα)∂α f (0) = L f (1).
+(133)
+Here the material derivatives indicated as ”(0)” are understood in the sense that the zeroth-order distribution f (0) is
+used to evaluate the non-equilibrium pressure tensor and the heat flux,
+D(0)
+t ρ = −ρ∂αuα,
+(134)
+D(0)
+t uα = −1
+ρ∂α(ρRT) − 1
+ρ∂βσαβ[ f (0)],
+(135)
+D(0)
+t T = −2
+3T∂αuα −
+2
+3Rρ pαβ[f (0)]∂βuα −
+2
+3Rρ∂βqβ[ f (0)].
+(136)
+Furthermore, the derivative of the Boltzmann collision operator at the zeroth order distribution, L, is the linearized
+collision integral,
+L f (1) =
+�
+R3
+�
+S 2
+�
+f (0)′
+1
+f (1)′ + f (0)′ f (1)′
+1
+− f (0)
+1
+f (1) − f (0) f (1)
+1
+� ¯Bd2e′d3¯v1.
+(137)
+Since we shall deal with only these orders of the Chapman-Enskog expansion, we shall not write the next terms of
+higher-order in ε (although we shall discuss them briefly at the end).
+Finally, we need to expand also the consistency conditions:
+�
+{m, mv, mv2/2} f (0)d3v = {ρ, ρu, (3/2)ρRT + ρu2/2},
+(138)
+�
+{m, mv, mv2/2} f (k)d3v = 0, k ≥ 1.
+(139)
+3.4.10. Euler’s compressible flow equations
+On the zeroth order, we must have the velocity distribution which annuls the Boltzmann collision integral; That is
+it is a local Maxwell-Boltzmann distribution. Then, the nonequilibrium pressure tensor and the heat flux are vanishing
+on this approximation,
+σαβ[ f (0)] = 0, qα[ f (0)] = 0,
+(140)
+and the closed-form equations for the density, flow velocity and temperature become the Euler compressible flow
+equations, (99), (100) and (101),
+D(0)
+t ρ = DE
+t ρ,
+(141)
+D(0)
+t uα = DE
+t uα,
+(142)
+D(0)
+t T = DE
+t T.
+(143)
+But now we have the Euler equations as the lowest-order approximation to the hydrodynamic equations, while these
+time-derivatives generate the correction which we now discuss.
+21
+
+3.4.11. Navier-Stokes and Fourier compressible flow equations
+We shall now set up the equation for f (1). You may find it a bit tedious, even though these are just simple algebraic
+manipulations. So let us do it step-by-step.
+Evaluation of the derivatives. We first compute the derivatives of the local Maxwell-Boltzmann distribution with
+respect to the five hydrodynamic fields,
+∂ f eq
+∂ρ = 1
+ρ f eq,
+(144)
+∂ f eq
+∂uα
+= (cα − uα)
+RT
+f eq,
+(145)
+∂ f eq
+∂T
+= 1
+T
+�(v − u)2
+2RT
+− 3
+2
+�
+f eq.
+(146)
+Evaluation of the Boltzmann equation vector field on the local Maxwell-Boltzmann distribution. Using the above
+derivatives, we next compute the term (vα − uα)∂α f eq,
+(vα − uα)∂α f eq =
+∂f eq
+∂ρ (vα − uα)∂αρ + ∂f eq
+∂uβ
+(vα − uα)∂αuβ + ∂f eq
+∂T (vα − uα)∂αT =
+f eq
+�1
+ρ(vβ − uβ)∂βρ + 1
+RT (vα − uα)(vβ − uβ)∂βuα + 1
+T
+�(v − u)2
+2RT
+− 3
+2
+�
+(vα − uα)∂αT
+�
+.
+(147)
+Note that the combinations ∼ vαvβ and ∼ vαv2, related to nonequilibrium pressure tensor and heat flux, start popping
+out in this expression.
+Evaluation of the time derivative of the local Maxwell-Boltzmann distribution due to the Euler system. This is the
+last place we need to evaluate the derivatives due to the Euler equations;
+∂f eq
+∂ρ D(0)
+t ρ + ∂f eq
+∂uα
+D(0)
+t uα + ∂f eq
+∂T D(0)
+t T =
+∂f eq
+∂ρ DE
+t ρ + ∂ f eq
+∂uα
+DE
+t uα + ∂ f eq
+∂T DE
+t T =
+f eq 1
+ρ (−ρ∂αuα) + f eq (cα − uα)
+RT
+�
+−1
+ρ∂α(ρRT)
+�
++ f eq 1
+T
+�(v − u)2
+2RT
+− 3
+2
+� �
+−2
+3T∂αuα
+�
+.
+(148)
+Invariance defect of the local Maxwell-Boltzmann distribution. The sum of the two above expressions, (147) and
+(148), is so important that it deserves a name of its own. We call it the defect of invariance of the local Maxwell-
+Boltzmann distribution function with respect to the Boltzmann equation,
+∆M = ∂f eq
+∂ρ D(0)
+t ρ + ∂f eq
+∂uα
+D(0)
+t uα + ∂f eq
+∂T ∂(0)
+t T + (vβ − uβ)∂β f eq.
+(149)
+The first Chapman-Enskog equation (133) now reads,
+L f (1) = ∆M.
+(150)
+The defect of invariance tells us whether or not the local Maxwell-Boltzmann distribution solves the Boltzmann
+equation. If ∆M = 0, then the initial condition taken as f eq progresses in time due to the Boltzmann equation without
+changing its Gaussian shape, only the density, flow velocity and temperature alter in time and space due to the Euler
+system. In such case the manifold of the local Maxwell-Boltzmann distributions (all such distributions with different
+22
+
+macroscopic parameters) is said to be invariant of the Boltzmann equation, and the first (and higher) order Chapman–
+Enskog corrections (f (1), f (2) etc) are all vanishing. So let us compute the invariance defect. Adding the above two
+expressions, we have (after a lot of cancellations),
+∆M = f eq
+� 1
+RT
+�
+(cα − uα)(cβ − uβ) − 1
+3δαβ(v − u)2
+�
+(∂αuβ)
+�
++ f eq
+� 1
+T
+�(v − u)2
+2RT
+− 5
+2
+�
+(cβ − uβ)∂βT
+�
+.
+(151)
+Let’s briefly discuss this result. The invariance defect consists of two parts. The first part drives the distribution
+function away from the local Maxwellian due to the inhomogeneity of the flow velocity ∼ ∂αuβ, which results in the
+viscosity phenomena. The second part is due to the inhomogeneity of the temperature of the fluid ∼ ∂βT, which results
+in thermal conduction. Thus, the local Maxwell–Boltzmann distribution can be a solution to the Boltzmann equation
+only if the velocity of the flow and the temperature field are space-independent. Notice also that the invariance defect
+does not depend on a space derivative of the density. This reflects the fact that the non-equilibrium phenomena in
+the single-component gas do not give rise to any diffusion phenomena (in a mixture of several gases it does). The
+solution to the Boltzmann equation may exist in a form of a local Maxwell–Boltzmann distribution but only if the flow
+is moving with a uniform velocity and the temperature also stays uniform (the density then obeys ∂tρ = −uα∂αρ) but
+they are of no physical relevance. Further on, note that the invariance defect is Galilean invariant, that is, it depends
+only on the particles velocity in the reference frame of the flow. Finally, we immediately note that the defect is a truly
+non-equilibrium driver, as it does not change any value of neither density, nor flow velocity, nor the energy because,
+�
+∆Md3v =
+�
+v∆Md3v =
+�
+v2∆Md3v = 0.
+(152)
+What it does change are the fluxes of these quantities. We now need a final step in setting up the first Chapman–Enskog
+equation, a discussion of the linearized collision integral.
+Linearized collision integral. It is very convenient and customary to write the correction to the local Maxwell-
+Boltzmann distribution function in the form
+f (1) = f eqϕ.
+(153)
+Then the linearized Boltzmann collision integral is transformed by noting that the products of the equilibria factor out
+due to the detail balance, and we have,
+L f (1) = f eq
+�
+R3
+�
+S 2 f eq
+1
+�ϕ′
+1 + ϕ′ − ϕ1 − ϕ� Kd2e′d3v1.
+(154)
+Thus, we can define the linearized Boltzmann operator Λ,
+Λϕ =
+�
+R3
+�
+S 2 f eq
+1
+�ϕ′
+1 + ϕ′ − ϕ1 − ϕ� Kd2e′d3v1.
+(155)
+The integral operator Λ has the following important properties:
+• Null-space of Λ: The null-space ker Λ is the linear sub-space of summatorial invariants,
+Λϕ = 0 if and only if ϕ ∈ Lin{1, v, v2}.
+(156)
+• Let us define a scalar product of functions ϕ and ψ as
+⟨ψ|ϕ⟩ =
+�
+f eqϕψd3v.
+(157)
+Then operator Λ is symmetric with respect to this scalar product,
+⟨ψ|Λ|ϕ⟩ = ⟨ϕ|Λ|ψ⟩.
+(158)
+23
+
+• Operator Λ is non-positive,
+⟨ϕ|Λ|ϕ⟩ ≤ 0.
+(159)
+Proof:
+⟨ϕ|Λ|ϕ⟩ = −1
+4
+�
+R3×R3
+�
+S 2 f eq f eq
+1
+�ϕ′
+1 + ϕ′ − ϕ1 − ϕ�2 Kd2e′d3v1d3v ≤ 0.
+(160)
+Note that, the symmetry property of operator Λ (158) and its non-positivity (160) are the ”linearized” versions of the
+Boltzmann transport theorem and of the H-theorem, respectively.
+The Chapman–Enskog equation. Summarizing, the results of the previous sections, the Chapman-Enskog equation
+for the first correction can be written, using the reduced peculiar velocity (104),
+Λϕ = (∂βuα)
+�
+CαCβ − 1
+3δαβC2
+�
++
+√
+RT
+�∂αT
+T
+�
+Cα
+�C2
+2 − 5
+2
+�
+.
+(161)
+The linear non-homogeneous integral equation (161) is the first Chapman-Enskog equation, the study of which is
+exhaustively described in [11]. For the sake of completeness, we summarize here some major steps. By Fredholm
+alternative, the linear non-homogeneous integral equation of the form (161) has a solution if the right hand side is
+orthogonal to the null-space of the integral operator Λ. This solvability condition is satisfied since the defect of the
+invariance does not alter the density, momentum and energy (see above). The general solution is then a specific
+solution to the non-homogeneous integral equation plus a general solution to the homogeneous one, Λϕ = 0. The
+latter is the linear subspace of summatorial invariants, so we have
+ϕgen = ϕspec + ϕhom,
+(162)
+where ϕhom ∈ Lin{1, v, v2} while ϕspec is orthogonal to conservation laws,
+�
+ϕspec f eq{1, v, c2}d3v = 0. However, due to
+the consistency condition (139) mentioned at the very beginning of the analysis, we must have
+�
+f (1){1, v, c2}d3v = 0,
+therefore we must select ϕhom = 0 in the above general solution. The Chapman-Enskog solution is thus the special
+solution to the above integral equation (161).
+Now we look at the tensorial dimension of the right hand side of (161) and immediately realize that, since the
+function ϕ is a scalar, the solution can depend on the particle’s velocity in only one possible way,
+ϕ = A(C)Cα
+√
+RT
+�∂αT
+T
+�
++ B(C)
+�
+CαCβ − 1
+3δαβC2
+�
+(∂βuα),
+(163)
+where two scalar functions, A and B can depend only on the magnitude of reduced velocity, temperature and density
+while A satisfies the orthogonality condition,
+�
+e− C2
+2 A(C)C2d3C = 0.
+The Chapman-Enskog functions A and B are found from two integral equations,
+Λ (ACα) = Cα
+�C2
+2 − 5
+2
+�
+,
+(164)
+Λ
+�
+B
+�
+CαCβ − 1
+3δαβC2
+��
+=
+�
+CαCβ − 1
+3δαβC2
+�
+.
+(165)
+Apart from Maxwell’s molecules, for which A and B do not depend on C, appropriate technique of solving (164) and
+(165) is based on Sonine polynomial expansion [11]. Here we shall perform a merely dimensional analysis of (164)
+and (165) in order to understand the relation between transport coefficients and specific models of particles interaction.
+24
+
+Dimensional analysis of Chapman–Enskog equations. Since the Chapman–Enskog solution ϕ (161) is a non-dimensional
+quantity, the proper dimension of the Chapman–Enskog functions A and B is that of the time,
+[A] = [B] ∼ sec.
+(166)
+Furthermore, since the right hand side of the Chapman–Enskog equations (164) and (165) is also non-dimensional,
+we can introduce a relaxation time τ so that
+A = τ ¯A, B = τ ¯B,
+(167)
+where functions ¯A(C) and ¯B(C) are dimensionless.
+Evaluation of the relaxation time is based on the dimensional analysis of the linearized collision integral for each
+specific binary collision mode. For hard spheres, with the collision kernel (42), we write
+ΛHS =
+�
+nd2 √
+RT
+� ¯ΛHS ,
+(168)
+where ¯ΛHS is a non-dimensional linearized Boltzmann operator for hard spheres,
+¯ΛHS ϕ =
+1
+4(2π)3/2
+�
+R3
+�
+S 2 e−C2
+1/2 �ϕ′
+1 + ϕ′ − ϕ1 − ϕ� |C1 − C|d2e′d3C1.
+(169)
+Thus, for hard spheres, the relaxation time is defined as the inverse of the prefactor in (168),
+τHS =
+1
+nd2 √
+RT
+.
+(170)
+One can readily recognize the earlier estimate of the mean free path in this expression, and the relaxation time is
+interpreted as an average travel time between binary encounters, with a characteristic thermal speed. For Maxwell’s
+molecules, with the interaction potential U = κr−4, we notice that, since the collision kernel does not depend on the
+relative velocity (see Eq. (44) with n = 4) the only combination of the mass m and the strength of the potential κ that
+gives a proper dimension to the collision kernel is
+KMM ∼
+�
+κ
+m ∼ cm3
+sec .
+(171)
+Consequently, the dimensional analysis of the linearized collision operator for Maxwell’s molecules gives,
+ΛMM =
+�
+n
+�
+κ
+m
+�
+¯ΛMM,
+(172)
+where the non-dimensional linearized collision operator is,
+¯ΛMMϕ =
+1
+(2π)3/2
+�
+R3
+�
+S 2 e−C2
+1/2 �ϕ′
+1 + ϕ′ − ϕ1 − ϕ� ¯αd2e′d3C1,
+(173)
+where ¯α(θ) is a non-dimensional function of the deflection angle. From (172), we read off the relaxation time for
+Maxwell’s molecules,
+τMM =
+√m
+n √κ.
+(174)
+It is interesting to remark here that, the mean free path for Maxwell’s molecules is proportional to the square root
+of the temperature, lMM
+m. f.p ∼ τMMvT ∼ √kBT/(n √κ), while it is temperature-independent for hard spheres, lHS
+m.f.p. ∼
+1/(nd2). In other words, the average distance traveled freely by Maxwell’s molecules between collisions increases
+with the temperature of the gas. Thus, by the estimate (120), the viscosity of the Maxwell’s molecules is linear in the
+temperature,
+µMM ∼ ρlMM
+m. f.p.vT ∼ RT
+�
+m3
+κ .
+(175)
+25
+
+With the above dimensional analysis, we write the solution to the first Chapman–Enskog equation by introducing
+the relaxation time into (163),
+ϕ = ¯A(C)Cα
+�
+τ
+√
+RT
+�∂αT
+T
+��
++ ¯B(C)
+�
+CαCβ − 1
+3δαβC2
+� �
+τ∂βuα
+�
+,
+(176)
+where the non-dimensional functions ¯A(C) and ¯B(C) depend only on the magnitude of the reduced peculiar velocity
+and are special solutions to the reduced (non-dimensional) integral equations,
+2 ¯Λ
+��� ¯ACα
+�
+=
+����Cα
+�
+C2 − 5
+��
+,
+(177)
+¯Λ
+���� ¯B
+�
+3CαCβ − δαβC2��
+=
+���3CαCβ − δαβC2�
+.
+(178)
+We shall now proceed with the general form of the first Chapman-Enskog correction (176) to evaluate the non-
+equilibrium pressure tensor and the heat flux vector.
+Viscosity. We are now able to evaluate the nonequilibrium fluxes for a generic collision model. Let’s start with the
+nonequilibrium pressure tensor,
+σ(1)
+αβ = m
+�
+vαvβ f eqϕd3v.
+(179)
+With (176), we find
+σ(1)
+αβ = −µΠαβ,
+(180)
+where Παβ is the rate-of-shear tensor,
+Παβ = ∂αuβ + ∂αuβ − 2
+3δαβ∂γuγ,
+(181)
+while µ is the viscosity,
+µ = ¯bτp,
+(182)
+with the coefficient ¯b (pure number) expressed in terms of the Chapman–Enskog function ¯B as,
+¯b = −1
+5(2π)−3/2
+�
+e−C2/2 ¯B
+�
+CαCβ − 1
+3δαβC2
+� �
+CβCα − 1
+3δβαC2
+�
+d3C > 0.
+(183)
+The latter inequality follows immediately from the definition of the function ¯B (178) and the entropy production
+inequality (160): Indeed, the integral in (183) is proportional to the inner product,
+�
+¯B
+�
+CαCβ − 1
+3δαβC2� �����CβCα − 1
+3δβαC2
+�
+.
+Hence, from the definition (178), we have
+�
+¯B
+�
+CαCβ − 1
+3δαβC2� �����CβCα − 1
+3δβαC2
+�
+=
+�
+¯B
+�
+CαCβ − 1
+3δαβC2� ����� ¯Λ
+����� ¯B
+�
+CβCα − 1
+3δβαC2��
+< 0.
+Thermal conduction. Similarly, we evaluate the non-equilibrium heat flux,
+q(1)
+α = m
+2
+�
+(v − u)2(vα − uα) f eqϕd3v.
+(184)
+Substituting the solution ϕ (176), we get the nonequilibrium heat flux in the form of the Fourier law,
+q(1)
+α = −λ∂αT,
+(185)
+where λ is the coefficient of thermal conduction,
+λ = ¯aτRp,
+(186)
+and the coefficient ¯a (pure number) is given by a quadrature similar to (183),
+¯a = −1
+6(2π)−3/2
+�
+e−C2/2 ¯AC4d3C > 0.
+(187)
+26
+
+Transport coefficients. Evaluation of the function B for specific collision models is based on a Sonine polynomial
+expansion, and is exhaustively studied in the classical text by Chapman and Cowling [11]. For hard spheres, using the
+relaxation time (170), the lowest-order Sonine polynomial expansion results in
+µ0 = ¯b0
+m
+√
+RT
+d2
+,
+(188)
+where the ¯b0 (pure number) is
+¯b0 =
+5
+16 √π ≈ 0.176.
+(189)
+The dependence of the viscosity on the temperature and on the diameter of hard sphere has been already found by
+elementary considerations, cf. (121). The lowest-order Sonine polynomial approximation (188) is only insignificantly
+lower than the more accurate result ¯b ≈ 0.179 when more terms of the Sonine polynomial expansion are evaluated
+[11]. For Maxwell’s molecules, using the mean free path (174), the viscosity is obtained as
+µ = ¯bRT
+�
+m3
+κ ,
+(190)
+where the exact value of the constant ¯b is [11],
+¯b =
+√
+2
+3πA2(5) ≈ 0.344,
+(191)
+where A2(5) ≈ 0.436 [11]. Apart from the pure constant ¯b (191), the dependence of the viscosity on the temperature,
+particle’s mass and the strength of the interaction potential strength was already obtained by elementary considerations
+above, cf. Eq. (175). The thermal conduction coefficient (186) can be written in the following suggestive way,
+λ = cpPr−1µ,
+(192)
+where cp is the specific heat of ideal gas of monatomic molecules,
+cp = 5
+2R,
+(193)
+while Pr is the Prandtl number,
+Pr = cpµ
+λ
+=
+¯b
+¯a.
+(194)
+The first-order Sonine polynomial approximation results in the Prandtl number [11],
+Pr0 = 2
+3.
+(195)
+For Maxwell molecules, the Prantl number (195) is the exact result while for hard spheres Pr = 2/3 is only slightly
+lower than the exact value [11].
+Correction to the Euler system: The Navier-Stokes equations. Summarizing the above, the correction to the local
+equilibrium approximation results in the following balance equations for mass, momentum and energy,
+DNS
+t
+ρ = −ρ(∂αuα),
+(196)
+DNS
+t
+uα = −1
+ρ∂αp + 1
+ρ∂β
+�
+εµΠαβ
+�
+,
+(197)
+DNS
+t
+T = −2
+3T(∂αuα) + 2
+3
+�T
+p
+� �
+εµΠαβ
+�
+(∂βuα) + 2
+3
+�T
+p
+�
+∂α (ελ∂αT) .
+(198)
+Comments are in order:
+27
+
+• The correction to the local equilibrium approximation results in the Navier–Stokes–Fourier system for com-
+pressible ideal gas, with the caloric equation of state featured by the specific heat at constant volume cv = (3/2)R
+and Prantl number close to Pr = 2/3. The result of the derivation has led to the microscopic expressions for the
+coefficients of viscosity and thermal conductivity which can be computed from any given molecular interaction
+in the Boltzmann equation.
+• It is important to keep the smallness parameter ε in the above expressions for the non-equilibrium fluxes.
+Higher-order corrections, the Burnett (ϵ2) and the super-Burnett (ϵ3) systems remained controversial as they
+violate the stability of the equilibrium.
+• Hilbert’s 6th problem: Hilbert proposed to derive ”mathematically the limiting processes ... which lead from the
+atomistic view to the laws of motion of continua” (see, e. g. [13, 14] and references therein). The issue Hilbert
+was addressing, namely to use the atomistic theory of his day represented by Boltzmann’s kinetic theory of
+gases and a passage via a limiting process to the continuum theory of compressible Euler system as the Knudsen
+number approaches zero, or to the Navier-Stokes-Fourier system, if small corrections are allowed. The problem
+is however, that without a priori knowledge about solutions to Euler or Navier-Stokes-Fourier equations are, one
+cannot in general prove that Boltzmann’s kinetics converges to these continuum models [13]. The resolution
+likely requires addressing other continuum theories, one current candidate is Korteweg-like [14]. Interested
+reader is directed to [13, 14].
+3.5. Lifting the local equilibrium projection: BGK kinetic model
+The correction to the Euler system considered above explores more of the phase space than it was assumed by the
+local equilibrium projection. By measuring the defect of invariance of the local equilibrium we find in which direction
+the local equilibrium approximation should be corrected in order to take into account the fast motion towards it. There
+is another way to explore the fast motions: To lift the dynamics to the full phase space by means of a kinetic model.
+The lifting of the Euler dynamics which takes place on the local Maxwell manifold to a kinetics in the whole phase
+space is done by the very useful Bhatnagar–Gross–Krook model (BGK),
+∂t f + v · ∇ f = −1
+τ( f − f eq( f)),
+(199)
+where τ > 0 is the relaxation time, and f eq( f) is a map f → f eq established by local conservation laws,
+�
+{1, v, v2}( f − f eq( f))dv = 0.
+(200)
+The right hand side of Eq. (199),
+JBGK = −1
+τ( f − f eq(f)),
+(201)
+is called the BGK collision integral. Proof of the H-theorem for the BGK kinetic equation does not rely anymore
+on the microscopic reversibility as in the Boltzmann case, instead, it is a simple consequence of convexity of the
+H-function, and of the property of the map (200):
+σ = −1
+τ
+�
+ln f( f − f eq( f))d3v = −1
+τ
+�
+ln
+�
+f
+f eq( f)
+�
+( f − f eq( f))d3v ≤ 0.
+(202)
+When the BGK relaxation model is used instead of the Boltzmann collision operator in finding the correction to
+the local equilibrium projection, the Chapman–Enskog equation (150) becomes,
+− 1
+τ f (1) = ∆M.
+(203)
+Thus, the Chapman-Enskog solution is given by (176) with the Chapman–Enskog functions (177) and (178) as
+¯ABGK = −
+�C2
+2 − 5
+2
+�
+,
+(204)
+¯BBGK = −1.
+(205)
+28
+
+The resulting Navier–Stokes–Fourier equations feature the following coefficients of viscosity and thermal conduction,
+µBGK = τp,
+(206)
+λBGK = τcpp,
+(207)
+resulting in the BGK Prandtl number,
+PrBGK = 1.
+(208)
+The restriction to Prandtl number PrBGK = 1 arises from the fact that no intermediate states of relaxation towards the
+local equilibrium are addressed by the BGK kinetic model. This issue shall be considered below. Prior to that, we
+need to extend the notion of projection onto a wider class of specified states.
+3.6. Grad’s thirteen-moments projection
+3.6.1. Grad’s thirteen-moments distribution function
+Grad, in his seminal paper of 1949 [15], derived moment systems by projecting the Boltzmann equation onto
+an ansatz for the distribution function. Grad considered two sets of moments, and what will be referred to as G13
+and G20, with the number indicating how many fields are included. In G13, these are the locally conserved density,
+momentum and energy plus the nonequilibrium stress tensor and energy flux vector, while G20, a more symmetric
+system, includes the full third-order flux of the pressure tensor instead of the energy flux vector. Grad’s method
+was influential in many ways, far beyond applications to rarefied gas dynamics. It was the touchstone for numerous
+developments in nonequilibrium thermodynamics (see, e.g. [16, 17, 18] and references cited therein). However,
+the problem with almost any projection on a preselected (often simple) submanifold is that it is not invariant with
+respect to the the detailed dynamics. In Grad’s context, Grad’s distribution function (a polynomial around the local
+Maxwellian) is not invariant with respect to the Boltzmann equation. This is certainly not just the feature of Grad’s
+distribution per se. As we have seen above, the local Maxwellian is also not invariant of the Boltzmann equation, and
+the dynamic correction, well known through the Chapman-Enskog method, delivers the dissipative Navier–Stokes–
+Fourier terms, missing in the the projection on the local Maxwell manifold (compressible Euler equations). Both
+correction and lifting of Grad’s G13 system shall be considered below.
+Following Grad [15], the distribution function providing the closure for the balance equations (91) and (92) is
+written as,
+G = M + N,
+(209)
+N = MGσ + MGq,
+(210)
+where M is local Maxwellian (105), and N is the nonequilibrium part,
+Gσ = σαβ
+2p
+�
+CαCβ − 1
+3δαβC2
+�
+,
+(211)
+Gq = qαCα
+pvT
+�C2
+5 − 1
+�
+.
+(212)
+Without engaging a discussion of possible violation of positivity, we consider Grad’s function as a submanifold in the
+space of distribution functions, parameterized with the values of thirteen fields. Grad’s system is the natural projection
+of kinetic equation onto this submanifold.
+3.6.2. Grad’s thirteen-moments closure
+Grad’s projection amounts to evaluating everything that spoils the closure in the balance equations (91) and (92)
+with Grad’s distribution (209). For the Q-fluxes (93), we get, separating the local equilibrium and nonequilibrium
+contributions,
+QG
+αβγ = QM
+αβγ + QN
+αβγ,
+(213)
+QM
+αβγ = 0,
+(214)
+QN
+αβγ = 1
+5
+�
+qαδβγ + qβδαγ + qγδαβ
+�
+.
+(215)
+29
+
+In other words, Grad’s closure for the Q-flux amounts to reducing symmetric rank three tensor to its trace (215). For
+the T-flux (94), one finds
+T G
+αβ = T M
+αβ + T N
+αβ,
+(216)
+T M
+αβ = 5
+2 pRTδαβ,
+(217)
+T N
+αβ = 7
+2RTσαβ.
+(218)
+For the collision rates (97) and (96), there are several realizations depending on the choice of the collision or relaxation
+model which we list here in the order of increasing complexity.
+1. A ”poor man’s” approach is to use the BGK relaxation time approximation (201); then one simply gets
+RσG
+αβ = −m
+τ
+� �
+(vα − uα)(vβ − uβ) − 1
+3δαβ(v − u)2
+�
+MGσdv = −1
+τσαβ,
+(219)
+RqG
+α = − m
+2τ
+�
+(vα − uα)(v − u)2MGqdv = −1
+τqα.
+(220)
+Similar results are obtained when using most of the relaxation kinetic models available (with more that one
+relaxation time). While certainly far from realistic, relaxation time approximation is useful for analysis of
+complex situations in order to understand the structure of otherwise involved result.
+2. For the Boltzmann’s collision integral (40), substituting Grad’s distribution function, and taking into account
+the detail balance, JB(M) = 0, one gets
+JB(G) = LN + O(N2),
+(221)
+where L is the linearized Boltzmann collision integral (137). Computation of matrix elements of the opera-
+tor (137) greatly simplifies for Maxwell’s molecules because in that case functions M[CαCβ − 1
+3δαβC2] and
+M[Cα(C2 − 5/2)] are eigenfunctions,
+L
+�
+M
+�
+CαCβ − 1
+3δαβC2
+��
+= − p
+µM
+�
+CαCβ − 1
+3δαβC2
+�
+,
+(222)
+L
+�
+M
+�
+Cα
+�C2
+2 − 5
+2
+���
+= −2p
+3µM
+�
+Cα
+�C2
+2 − 5
+2
+��
+,
+(223)
+with µ the viscosity coefficient of Maxwell’s molecules (190). With (222) and (223), evaluation of matrix
+elements reduces to the same integrals as in the relaxation time approximation, and we get
+RσG
+αβ = m
+� �
+(vα − uα)(vβ − uβ) − 1
+3δαβ(v − u)2
+�
+L(MGσ)dv = − p
+µσαβ
+(224)
+RqG
+α = m
+2
+�
+(vα − uα)(v − u)2L(MGq)dv = −2p
+3µqα.
+(225)
+It should be noted that, for Maxwell’s molecules, evaluation of the relaxation rates for various moments can
+be done in closed form without specifying the distribution function, also for the nonlinear collision operator
+[19, 20], and relaxation rates (224,225) are valid for the full nonlinear case.
+3. For other particle’s collision models such as hard spheres or other power law potentials, functions M[CαCβ −
+1
+3δαβC2] and M[Cα(C2 − 5/2)] are not eigenfunctions of linearized collision integral any longer, and evaluation
+of matrix elements (224) and (225) gives instead
+RσG
+αβ = − p
+µ0
+σαβ,
+(226)
+RqG
+α = − 2p
+3µ0
+qα,
+(227)
+30
+
+where µ0 is not exact viscosity coefficient but rather the lowest-order Sonine polynomial approximation thereof,
+cf. Eq. (188). It is well known that first approximation µ0 is reasonably close to the exact value, in particular,
+for hard spheres [11]. This fact, however, does not imply that corresponding eigenfunctions of linearized
+Boltzmann collision integral are in any sense ”close” to those for Maxwell’s molecules, and it is therefore
+misleading to judge on the quality of Grad’s approximation for hard spheres on the basis of viscosity coefficient
+alone.
+3.6.3. Grad’s thirteen-moments system
+Substituting Grad’s closure relations for the Q- and T-fluxes (213) and (216) into balance equations (91) and (92),
+and also using any of the above realizations of the relaxation terms, one arrives at Grad’s equations. For later use, it
+proves convenient to partition Grad’s equations in four parts, three of which regards the non-local in space terms plus
+the relaxation term. For the stress, we write
+DG
+t σαβ = ˙σNSF
+αβ + ˙σlin
+αβ + ˙σnlin
+αβ + RσG
+αβ ,
+(228)
+˙σNSF
+αβ
+= −p
+�
+∂αuβ + ∂βuα − 2
+3δαβ∂γuγ
+�
+(229)
+˙σlin
+αβ = −2
+5
+�
+∂βqα + ∂αqβ − 2
+3δαβ∂γqγ
+�
+,
+(230)
+˙σnlin
+αβ = −σαβ
+�
+∂γuγ
+�
+−
+�
+σαγ∂γuβ + σβγ∂γuα − 2
+3δαβσµν∂νuµ
+�
+.
+(231)
+A comment on genesis of various terms in Grad’s equation (228) is in order. The first term, ˙σNSF
+αβ
+(229), is designated
+Navier-Stokes-Fourier (NSF) because it linearly depends on the strain tensor and gives rise to the Navier-Stokes stress
+in the first-order approximation to G13. This term appears as purely kinematic, that is, it shows up already in the
+balance equation for the stress before any closure assumption. The second term, ˙σlin
+αβ (230) is solely produced by the
+closure relation for the Q-flux (215). It is indicated as ”linear” since it depends linearly on the gradient of the heat
+flux but not on any gradient of locally conserved fields. Consequently, the term ˙σlin
+αβ survives linearization around a
+global equilibrium state. Finally, the nonlinear term ˙σnlin
+αβ (231) is again purely kinematic and independent of Grad’s
+closure assumption.
+Grad’s heat flux equation is decomposed in a similar fashion,
+DG
+t qα = ˙qNSF
+α
++ ˙qlin
+α + ˙qnlin
+α
++ RqG
+α ,
+(232)
+˙qNSF
+α
+= −5
+2Rp∂αT,
+(233)
+˙qlin
+α = −RT∂βσαβ,
+(234)
+˙qnlin
+α
+= −7
+5qα∂βuβ − 7
+5qβ∂βuα − 2
+5qβ∂αuβ − 5
+2Rσαβ∂βT + RT
+ρ σαβ∂βρ + 1
+ρσαβ∂γσγβ.
+(235)
+Here, the term (5/2)RT∂αp in the balance equation (92) conspired with the local equilibrium part of the closure (217)
+to produce the NSF contribution, ˙qNSF
+α
+(233). That one gives rise to the Fourier law in the first approximation, through
+balancing the relaxation term. The term ˙qlin
+α (234) appears with right sign thanks to Grad’s closure approximation of
+the nonequilibrium part of the T-flux (218). We term it ”linear” for the reason explained above, even though it is
+non-linear through multiplication with the temperature. Similarly to (230), contribution of ˙qlin
+α does not vanish under
+linearization. Finally, the nonlinear part of Grad’s heat flux equation, ˙qnlin
+α
+(235) contains a mixture of terms both
+present already in the balance equation (92) and those resulting from the closure assumption. Note that the ”most
+nonlinear” term, (1/ρ)σαβ∂γσγβ is purely kinematic and is not affected by Grad’s closure.
+Hydrodynamics from Grad’s equations. When the smallness parameter is re-introduced into Grad’s equations, the
+first-order correction to the Euler’s equations (σ(0) = 0, q(0) = 0) is found by balancing the first and the last terms in
+(228) and (232). Using the estimates for the relaxation rates (226) and (227), together with (229) and (233), we find
+31
+
+the nonequilibrium pressure tensor and heat flux as
+σ(1)
+αβ = −µ0
+�
+∂αuβ + ∂βuα − 2
+3δαβ∂γuγ
+�
+,
+(236)
+q(1)
+α = −15R
+4 µ0∂αT.
+(237)
+Thus, we once again derive the Navier–Stokes–Fourier system (196), (197) and (198), for the ideal gas with specific
+heat at constant pressure cp = (5/2)R and Prandtl number Pr = 2/3.
+Finally, we mention that, even when linearized, Grad’s equations (228) and (232) remain strongly coupled through
+their respective linear terms, (230) and (234). The linearized Grad’s equations can be used to study the hydrodynamic
+limit beyond the Navier–Stokes–Fourier approximation by summing up a rather involved Chapman-Enskog series
+expansion. Interested reader is directed to [21, 22].
+3.6.4. Quasi-equilibrium projection
+Grad’s method and its variants construct closed systems of equations for macroscopic variables when the latter
+are represented by moments of the distribution function f (hence their alternative name, the moment method). A
+different but closely related construction is the maximum entropy method or the quasi-equilibrium approximation. Let
+M = {M1, . . . , Mk} be a finite set of moments chosen to describe the macroscopic state,
+Mi(x, t) =
+�
+µi(v) f(v, x, t)d3v, i = 1, . . . , k,
+(238)
+where µ1(v), . . . , µk(v) are the corresponding microscopic densities of the moments. We assume that the microscopic
+densities are linearly independent and that locally conserved fields are included in the set M, that is, the linear envelope
+of {µ1(v), . . . , µk(v)} is included into the linear envelope of {µ1(v), . . . , µk(v)},
+Lin{1, v, v2} ⊂ Lin{µ1(v), . . . , µk(v)}.
+(239)
+The distribution function of the quasi-equilibrium state is defined as the minimizer of the H-function (62) under the
+constraint of fixed moments M,
+f ∗(v, M) = argmin
+�
+H( f)
+�����
+�
+µ1 fd3v = M1, . . . ,
+�
+µk fd3v = Mk
+�
+.
+(240)
+where The family of the quasi-equilibrium distribution functions f ∗(v, M) (240) parametrically depends on the mo-
+ments M and is a generalization of the local equilibrium distribution function. The latter corresponds to the choice
+of M as a set of the locally conserved moments and is a subset of the distribution functions (240) by the convention
+(239). The quasi-equilibrium projection is a closed system for the target moments M,
+∂tMi + ∇ ·
+�
+µi(v)vf ∗(v, M)d3v =
+�
+µi(v)JB( f ∗(v, M))d3v, i = 1, . . . , k.
+(241)
+Important feature of the quasi-equilibrium projection is that it retains the dissipative property of the Boltzmann
+equation: The quasi-equilibrium H-function,
+H∗(M) =
+�
+f ∗(v, M) ln f ∗(v, M)d3v,
+(242)
+is a non-increasing function due to the moment equations (241). This follows directly from the solution of the problem
+(240) using the method of Lagrange multipliers,
+f ∗ = exp
+k
+�
+i=1
+λiµi(v),
+(243)
+32
+
+where λi are Lagrange multipliers. Indeed, by noticing that λi = ∂H∗/∂Mi, the production of the quasi-equilibrium
+H-function (242) is obtained as,
+σ∗ =
+k
+�
+i=1
+∂H∗
+∂Mi
+�
+µi(v)JB( f ∗(v, M))d3v =
+�
+lnf ∗(v, M)JB( f ∗(v, M))d3v ≤ 0.
+(244)
+A rationale behind the maximum entropy method can be stated as follows: A state of the gas can be described by a
+finite set of moments M on a time scale θ only if all the other (“fast”) moments evolve on a shorter time scale time
+τ ≪ θ to their values determined by the chosen set of slow moments M, while the slow moments do not change
+appreciably over the time scale τ. In the process of the fast relaxation, the H-function decreases, and in the end of
+this fast relaxation process a quasi-equilibrium state sets in with the distribution function being the solution of the
+problem (240). After the fast processes reach their completion, the moments M evolve on the slow time scale by
+virtue of (241).
+Explicit solution to the minimization problem amounts to expressing the Lagrange multipliers in terms of the
+moments upon resolving the implicit system of equations,
+�
+µi(v) exp
+k
+�
+j=1
+λ jµ j(v)d3v = Mi, i = 1, . . . , k.
+(245)
+While the dissipation property (244) of the quasi-equilibrium projection (241) can be demonstrated without solving
+the equations for the Lagrange multipliers (245), operating equations (241) does require the knowledge of the quasi-
+equilibrium distribution function f ∗(v, M) explicitly. To that end, there is exactly one case known where the system
+(245) can be inverted in a closed form. This corresponds to the moments set M = {ρ, ρu, P} where P is the pressure
+tensor (78). Using the representation (81), we can write [23, 24],
+f ∗(n, u, Π) = n
+ρ
+3
+2
+(2π)
+3
+2 √
+det Π
+exp
+�
+−ρ
+2(v − u)† · Π−1 · (v − u)
+�
+,
+(246)
+where Π = P − ρuu is the pressure tensor in the co-moving reference frame, Παβ = pδαβ + σαβ, while the non-
+equilibrium part σαβ is the trace-free tensor (83). Vanishing of the latter returns the subset Meq = {ρ, ρu, tr[P]}, while
+(246) becomes the local Maxwell–Boltzmann distribution function (70). The quasi-equilibrium projection defined by
+the distribution function (246) results in the ten-moment Grad’s approximation for a compressible, viscous but heat
+non-conductive fluid (Pr → ∞), which is more conveniently written using the pressure rather than the temperature:
+D∗
+t ρ = −ρ∂αuα,
+(247)
+D∗
+t uα = −1
+ρ∂αp − 1
+ρ∂βσαβ,
+(248)
+D∗
+t p = −5
+3 p(∂αuα) − 2
+3σαβ(∂βuα).
+(249)
+D∗
+t σαβ = ˙σNSF
+αβ + ˙σnlin
+αβ + RσG
+αβ ,
+(250)
+where the right hand side of (250) is given by (229), (231) and (224).
+3.6.5. Triangle entropy method
+A remedy for the explicit construction of quasi-equilibrium approximations for general macroscopic variables
+has been proposed in [25, 26]. Let a set of macroscopic variables be specified as follows: First, a subset of linear
+functionals (moments) M is defined as before, see (238). Second, a subset of nonlinear functionals (in a general case)
+N is defined N( f) = {N1( f), . . . , Nl( f)}. Examples of nonlinear macroscopic variables are production rates (51), (96)
+or (97). The totality of the macroscopic variables is the set {M, N}.
+The triangle entropy method proceeds as follows: First, the quasi-equilibrium approximation is obtained for the
+subset M, as above in (240) to get the quasi-equilibrium distribution function f ∗(v, M). Second, we seek a correction
+to f ∗(v, M) in the form,
+f = f ∗(1 + ϕ),
+(251)
+33
+
+where ϕ is a deviation from the first quasi-equilibrium approximation due to the macroscopic variables N. In order to
+determine ϕ, the second quasi-equilibrium approximation is constructed. Let us denote ˜Hf ∗(ϕ) as the quadratic term
+in the expansion of the H-function into powers of ϕ in the neighborhood of the first quasi-equilibrium state f ∗,
+˜Hf ∗(ϕ) = H∗(M) +
+�
+f ∗(v, M) (ln f ∗(v, M) + 1) ϕ(v)d3v + 1
+2
+�
+f ∗(v, M)ϕ2(v)d3v,
+(252)
+where H∗(M) = H( f ∗) is the value of the H-function in the quasi-equilibrium state f ∗ (242). The distribution function
+of the second quasi-equilibrium approximation is the solution to the problem,
+˜Hf ∗(ϕ) → min,
+(253)
+�
+µi f ∗ϕd3v = 0, i = 1, . . . , k,
+(254)
+Df Nj
+��� f ∗ϕ = ∆Nj, j = 1, . . . , l,
+(255)
+where Df Nj
+���f ∗ are linear operators, i.e. the first differential of the operators Nj at the first quasi-equilibrium f ∗, while
+∆Nj are the deviations of the macroscopic variables from their values at the first quasi-equilibrium state,
+∆Nj = Nj − N∗
+j(M).
+(256)
+Note the importance of the homogeneous constraints (254) in the minimization problem (253). They reflect the
+condition that the variables ∆N are “slow” in the same sense as the variables M, at least in a small neighborhood of
+the first quasi-equilibrium f ∗.
+Because the optimization functional in the minimization problem (253) is quadratic in ϕ, and thanks to the linearity
+of the constraints (254) and (255), the solution is always available in closed form. The resulting distribution function
+shall be referred to as the second quasi-equilibrium,
+f ∗(v, M, N) = f ∗(v, M)(1 + ϕ∗(v, M, N − N∗(M))),
+(257)
+in order to make a distinction with the first quasi-equilibrium f ∗(v, M). By construction, the function ϕ∗ depends
+linearly on the macroscopic variables of the second quasi-equilibrium ∆Nj (256). Assuming that the first quasi-
+equilibrium can be also obtained in a closed form, the triangle entropy method makes it possible to extend the max-
+imum entropy construction to wider classes of macroscopic variables. Below, we shall consider a few pertinent
+realizations.
+3.6.6. Grad’s projections via triangle entropy method
+Let us consider the example of using the triangle entropy method, when all the macroscopic variables of the first
+and of the second quasi-equilibrium states are moments of the distribution function. In other words, the macroscopic
+variables M of the first quasi-equilibrium remain as in (238), (239), while the macroscopic variambes N of the second
+quasi-equilibrium state N are identified with the corresponding microscopic densities ν1(v), . . . , νl(v),
+Nj(x, t) =
+�
+ν j(v) f(v, x, t)d3v, j = 1, . . . , l.
+(258)
+Turning to the minimization problem (253), in order to take the homogeneous constraint (254) automatically into
+account, it is convenient to introduce the following structure of inner product:
+1. Define a scalar product,
+(ψ1, ψ2) =
+�
+f ∗(v, M)ψ1(v)ψ2(v)d3v.
+(259)
+2. Let Eµ be the linear hull of the set of moment densities µ1(v), . . . , µk(v).
+Let us construct a basis of Eµ
+{e1(v), . . . , er(v)} that is orthonormal in the sense of the scalar product (259):
+(ei, ej) = δi j, i, j = 1, . . . , r,
+(260)
+where δi j is the Kronecker delta.
+34
+
+3. Define a projector ˆP∗ on the first quasi-equilibrium state,
+ˆP∗ψ =
+r�
+i=1
+ei(ei, ψ).
+(261)
+The projector ˆP∗ is orthogonal: for any pair of functions ψ1, ψ2,
+( ˆP∗ψ1, (ˆ1 − ˆP∗)ψ2) = 0,
+(262)
+where ˆ1 is the unit operator.
+With this, the homogeneous condition (254) in the minimization problem (253) amounts to
+ˆP∗ϕ = 0,
+(263)
+and the expression for the quadratic part of the H-function (252) takes the form,
+˜Hf ∗(ϕ) = H∗(M) + (ln f ∗ + 1, ϕ) + 1
+2(ϕ, ϕ).
+(264)
+Now, let us note that the function ln f ∗ is invariant with respect to the action of the projector ˆP∗:
+ˆP∗(ln f ∗ + 1) = ln f ∗ + 1.
+(265)
+This follows directly from the solution of the first quasi-equilibrium problem using of the method of Lagrange multi-
+pliers (243) and also from the assumption that conservation laws are included into the set of moments M (239). Thus,
+if the condition (263) is satisfied, then from (262) and (265) it follows that
+(ln f ∗ + 1, ϕ) = ( ˆP∗(ln f ∗ + 1), (ˆ1 − ˆP∗)ϕ) = 0.
+Condition (263) is satisfied automatically, if the macroscopic variables ∆Ni (256) are defined as follows:
+∆Ni = ((ˆ1 − ˆP∗)νi, ϕ), i = 1, . . . , l.
+(266)
+Then the problem (253) of finding the second quasiequilibrium state reduces to
+(ϕ, ϕ) → min for ((ˆ1 − ˆP∗)νi, ϕ) = ∆Ni, i = 1, . . . , l.
+(267)
+In the remainder of this section we demonstrate how the triangle entropy method is related to Grad’s moment
+method. To that end, we take the five collision invariants as moment densities of the first quasi-equilibrium state,
+µ0 = 1, µα = vα, µ4 = mv2
+2 ,
+(268)
+Then the first quasi-equilibrium state is characterized with the local Maxwell–Boltzmann distribution function f eq
+(70). Orthogonalization of the set of moment densities (268) with the weight (70) delivers one of the possible or-
+thonormal basis as
+e0 =
+5
+(10n)1/2 −
+(v − u)2
+(10n)1/2RT ,
+(269)
+eα = (vα − uα)
+(nRT)1/2 ,
+(270)
+e4 =
+(v − u)2
+(15n)1/2RT .
+(271)
+We shall proceed with specific cases of the moments of the second quasi-equilibrium.
+35
+
+Ten-moments Grad’s approximation. For the moment densities of the second quasiequilibrium state, let us take,
+ναβ = mvαvβ.
+(272)
+Then
+�ˆ1 − ˆP∗�
+ναβ = m(vα − uα)(vβ − uβ) − 1
+3δαβm(v − u)2,
+(273)
+and, since ((ˆ1 − ˆP(0))ναβ, (ˆ1 − ˆP(0))νγκ) = (δαγδβκ + δακδβγ)pRT, where p = nkBT is the pressure, and σαβ = ( f, (ˆ1 −
+ˆP∗)ναβ) is the traceless part of the stress tensor, from (267) we obtain the distribution function of the second quasi-
+equilibrium state in the form,
+G10 = f eq
+�
+1 + σαβ
+2pRT
+�
+(vα − uα)(vβ − uβ) − 1
+3δαβ(v − u)2
+��
+.
+(274)
+This is the distribution function of the ten-moment Grad’s approximation, cf. Eq. (211). Note that the Grad’s distri-
+bution function (274) is the first-order expansion of the quasi-equilibrium distribution (246) in terms of the nonequi-
+librium pressure tensor σαβ. The Grad’s projection established by the ten-moment approximation (274) is identical to
+the quasi-equilibrium system (250).
+Thirteen-moments Grad approximation. In addition to (268), (272), let us extend the list of moment densities of the
+second quasiequilibrium state with the functions
+ξα = mvαv2
+2
+.
+(275)
+The corresponding orthogonal complements to the projection on the first quasi-equilibrium state are
+(ˆ1 − ˆP∗)ξα = m
+2 (vα − uα)
+�
+(v − u)2 − 5RT
+�
+.
+(276)
+The moments corresponding to the densities (ˆ1 − ˆP(0))ξα are the components of the heat flux vector qα,
+qα = (ϕ, (ˆ1 − ˆP∗)ξα).
+(277)
+Since ((ˆ1− ˆP∗)ξα, (ˆ1− ˆP∗)νβγ) = 0, the constraints ((ˆ1− ˆP∗)ναβ, ϕ) = σαβ and ((ˆ1− ˆP∗)ξγ, ϕ) = qγ in the problem (267)
+are independent, and Lagrange multipliers corresponding to ξα are (1/5n) (RT)2 qα. Thus, taking into account (268),
+(274), (276), we find the distribution function of the second quasi-equilibrium state,
+G13 = f eq
+�
+1 + σαβ
+2pRT
+�
+(vα − uα)(vβ − uβ) − 1
+3δαβ(v − u)2
+�
++ qα
+pRT (vα − uα)
+�(v − u)2
+5RT
+− 1
+��
+,
+(278)
+which coincides with the thirteen-moment Grad distribution function (209) [15].
+Eight- and fifteen-moments Grad’s approximations. We note two other quasi-equilibrium approximations of interest.
+If only the heat flux (277) is chosen as the slow variable then the second quasi-equilibrium approximation becomes
+G8 = f eq
+�
+1 + qα
+pRT (vα − uα)
+�(v − u)2
+5RT
+− 1
+��
+.
+(279)
+Distribution function (279) is used in the construction of the Shakhov’s S-model [27] to be discussed below. Grad’s
+projection established by the distribution function (279) corresponds to a non-viscous compressible, thermally con-
+ductive fluid (Pr → 0),
+D∗
+t ρ = −ρ∂αuα,
+(280)
+D∗
+t uα = −1
+ρ∂αp,
+(281)
+D∗
+t p = −5
+3 p(∂αuα) − 2
+3(∂αqα).
+(282)
+D∗
+t qα = −5
+2Rp∂αT − 7
+5qα∂βuβ − 7
+5qβ∂βuα − 2
+5qβ∂αuβ + RqG
+α .
+(283)
+36
+
+Projection
+Local conservation
+Target nonequilibrium moments
+G5
+ρ, ρu, tr[P]
+–
+G8
+ρ, ρu, tr[P]
+q
+G10
+ρ, ρu, tr[P]
+P − 1
+3tr[P]I
+G13
+ρ, ρu, tr[P]
+P − 1
+3tr[P]I, q
+G15
+ρ, ρu, tr[P]
+Q
+G20
+ρ, ρu, tr[P]
+P − 1
+3tr[P]I, Q
+Table 1: Grad’s projections mentioned in this contribution.
+It is interesting to note that, while the ten- and the eight-moments Grad’s projections have little practical usefulness
+by themselves, they nevertheless are helpful in constructing the kinetic models in order to overcome the restriction of
+the BGK model. Finally, if the full Q-flux (93) is used instead of the heat flux, the corresponding fifteen-moments
+second quasi-equilibrium distribution function is used in the construction of a family of lattice Boltzmann models
+with variable Prandtl number [28]. Various Grad’s projection mentioned above are collected in Table 1.
+3.7. Dynamic correction to Grad’s thirteen-moments projection: The R13 system
+3.7.1. Invariance defect of Grad’s thirteen-moments approximation
+Nothing tells us that Grad’s closure relations for both the Q- and T-fluxes, as well as the closure relation for
+the relaxation term, will stay invariant under kinetic equation (87). One thus needs, first, to quantify the discrepancy
+between the proposed projection and the real dynamics due to kinetic equation, to understand the physical mechanisms
+arising from this discrepancy and which were neglected by the projection, and, secondly, to correct the closure on the
+basis of the kinetic equation.
+Systematic method to derive dynamic correction to Grad’s G13 projection from kinetic equations was introduced in
+[29] (KGDN thereafter), and has been realized for near-equilibrium conditions. The dynamic correction [29] followed
+the path similar to that of the correction to the local equilibrium projection discussed above: first, one evaluates the
+defect of invariance of the projection, and second, one finds the first iteration of the invariance condition in order
+to compensate the defect in the lowest-order Knudsen number approximation. Later, taking a different route via a
+superset moment system with 26 moments, Struchtrup and Torrilhon [30] proposed a nonlinear extension thereof, and
+coined the name of regularized Grad’s system, or R13, which we here stick to.
+Evaluation of the invariance defect of Grad’s approximation is rather straightforward, and has been first reported
+by KGDN [29] in the linear approximation, and worked out in detail in [31] for the full nonlinear case. We begin
+with evaluating the derivatives of Grad’s distribution function with respect to all the thirteen fields, while separating
+the contributions of the Maxwellian already available from (144), (145) and (146) from that of the newly added
+nonequilibrium part:
+∂G
+∂ρ = ∂M
+∂ρ ,
+(284)
+∂G
+∂uα
+= ∂M
+∂uα
++ ∂N
+∂uα
+,
+(285)
+∂G
+∂T = ∂M
+∂T + ∂N
+∂T ,
+(286)
+where
+∂N
+∂uα
+= M (Gσ + Gq)
+�Cα
+vT
+�
+− M
+�����
+2qα
+5pv2
+T
+�C2
+2 − 5
+2
+�
++
+2
+5pv2
+T
+qβCβCα + σαβCβ
+pvT
+����� ,
+(287)
+∂N
+∂T = M
+�
+Gσ
+�C2 − 7
+2T
+�
++ Gq
+�C2 − 9
+2T
+��
+− M
+� qαCα
+pvTT
+�
+.
+(288)
+37
+
+Finally, derivatives with respect to the nonequilibrium fields are
+∂G
+∂σαβ
+= M
+� 1
+2p
+� �
+CαCβ − 1
+3δαβC2
+�
+,
+(289)
+∂G
+∂qα
+= M
+� Cα
+pvT
+� �C2
+5 − 1
+�
+.
+(290)
+Using these, we write down the invariance defect of Grad’s thirteen moment approximation separating contributions
+of propagation terms from those of the collisions. Following KGDN convention, the former are termed non-local and
+the latter local:
+∆G = ∆loc
+G + ∆nloc
+G .
+(291)
+The local piece reads,
+∆loc
+G =
+� ∂G
+∂σαβ
+RσG
+αβ + ∂G
+∂qα
+RqG
+α
+�
+− JB(G)
+=
+�
+M
+� 1
+2p
+� �
+CαCβ − 1
+3δαβC2
+�
+RσG
+αβ − L(MGσ)
+�
++
+�
+M
+� Cα
+pvT
+� �C2
+5 − 1
+�
+RqG
+α − L(MGq)
+�
+.
+(292)
+Neglect of quadratic terms here is consistent with their neglect already made in Grad’s closure of relaxation terms.
+First observation, already exposed in KGDN [29], is about vanishing of the local invariance defect in certain
+cases of collision models: Let functions M[CαCβ − 1
+3δαβC2] and M[Cα(C2/2 − 5/2)] be eigenfunctions of linearized
+collision integral,
+L
+�
+M
+�
+CαCβ − 1
+3δαβC2
+��
+= −λσM
+�
+CαCβ − 1
+3δαβC2
+�
+,
+(293)
+L
+�
+M
+�
+Cα
+�C2
+2 − 5
+2
+���
+= −λqM
+�
+Cα
+�C2
+2 − 5
+2
+��
+.
+(294)
+Then the local invariance defect of Grad’s approximation vanishes,
+∆loc
+G = 0.
+(295)
+Indeed, with the conditions (293) and (294), the relaxation terms in Grad’s approximation become RσG
+αβ = −λσσαβ and
+RqG
+αβ = −λqqα. Using these in (292), we prove (295).
+Non-vanishing of local invariance defect for Grad’s distribution function is the first apparent difference from the
+Maxwellian case. In Grad’s case, the relaxation has to be aligned with the direction dictated by the eigenfunction of
+the linearized collision integral in order to annihilate the local invariance defect. This is more demanding compared to
+the local Maxwellian which annuls the local terms in the invariance defect independently of the collision model used.
+Vanishing of the local invariance defect unifies the relaxation time approximation (and any similar kinetic model) with
+Maxwell’s molecules and is a consequence of the simple fact that all these have the same eigenfunctions of the form
+(293) and (294). Vanishing of local invariance defect has no relation to the values of transport coefficients, and is
+non-vanishing for any other model, such as hard spheres. Now we proceed with the analysis of the nonlocal part of
+the invariance defect which is independent of the choice of the collision model.
+The nonlocal part of the invariance defect shall be written as a sum of three pieces, where we distinguish the
+Navier-Stokes-Fourier, the linear and the nonlinear contributions,
+∆nloc
+G
+= ∆NSF
+G
++ ∆lin
+G + ∆nlin
+G .
+(296)
+38
+
+Each type of contributions is dictated by the partition of the Grad’s equations (228) and (232), and we have,
+∆NSF
+G
+=∂G
+∂ρ
+�
+Dtρ + vTCβ∂βρ
+�
++ ∂M
+∂uα
+�
+DM
+t uα + vTCβ∂βuα
+�
++ ∂M
+∂T
+�
+DM
+t T + vTCβ∂βT
+�
++ ∂G
+∂σαβ
+˙σNSF
+αβ + ∂G
+∂qα
+˙qNSF
+α
+,
+(297)
+∆lin
+G =∂M
+∂uα
+�
+−1
+ρ∂βσαβ
+�
++ ∂M
+∂T
+�
+−2T
+3p ∂αqα
+�
++ ∂G
+∂σαβ
+�
+˙σlin
+αβ + vTCγ∂γσαβ
+�
++ ∂G
+∂qα
+�
+˙qlin
+α + vTCβ∂βqα
+�
+,
+(298)
+∆nlin
+G
+=∂M
+∂T
+�
+−2T
+3p σαβ∂αuβ
+�
++ ∂N
+∂uα
+�
+Dtuα + vTCβ∂βuα
+�
++ ∂N
+∂T
+�
+DtT + vTCβ∂βT
+�
++ ∂G
+∂σαβ
+˙σnlin
+αβ + ∂G
+∂qα
+˙qnlin
+α .
+(299)
+3.7.2. The R13 distribution function
+The leading-order dynamic correction to Grad’s distribution function is written on the basis of the BGK model
+using a relaxation time τ as follows:
+R = G + K,
+(300)
+where G is Grad’s distribution and K is the correction,
+K = −τ∆nloc
+G .
+(301)
+First, we notice that the Navier-Stokes-Fourier part of the invariance defect of Grad’s approximation vanishes,
+∆NSF
+G
+= 0. Indeed, we notice that the first three terms in (297) assemble to the defect of invariance of the local
+Maxwellian already computed, see Eq. (151); evaluating the remaining two terms we get,
+∆NSF
+G
+= ∆M
++ M
+� 1
+2p
+� �
+CαCβ − 1
+3δαβC2
+� �
+−p
+�
+∂αuβ + ∂βuα − 2
+3δαβ∂γuγ
+��
++ M
+� 2Cα
+5pvT
+� �C2
+2 − 5
+2
+� �
+−5
+2 p∂α (RT)
+�
+= 0.
+(302)
+This observation was first made in KGDN [29], and it is not surprising. Indeed, since the Navier–Stokes–Fourier
+approximation is already fully contained in Grad’s equations, there is nothing to correct in Grad’s dynamics with
+respect to the Navier–Stokes–Fourier fluxes.
+The remaining therms in the nonlocal defect of invariance of the G13 projection were evaluated in [29] and [31].
+The result is written as a combination of eight modes:
+K = −τ
+8
+�
+i=1
+K(i).
+(303)
+Each mode has the form,
+K(i) = MP(i) • F(i),
+(304)
+39
+
+where M is the local Maxwellian (or mode’s amplitude), P(i) is velocity tensor (or mode’s direction), F(i) is the mode’s
+frequency, while • stands for convolution of tensors. Tensors P(i) are dimensionless and depend only on C, particle’s
+velocity relative to the flow u, reduced by thermal speed, C = (v − u)/vT, where vT =
+√
+RT. Dimension of the mode’s
+frequencies is inverse of time, [F(i)] ∼ 1/sec. Modes of R13 are collected in Tab. 2. In Tab. 2, we use shorthand
+notation for symmetric traceless velocity tensors of rank two, three and four,
+�
+CαCβ
+�
+= CαCβ − 1
+3δαβC2,
+(305)
+�
+CαCβCγ
+�
+= CαCβCγ − 1
+5C2 �
+Cαδβγ + Cβδαγ + Cγδαβ
+�
+,
+(306)
+�
+CαCβCγCλ
+�
+= CαCβCγCλ − C4
+15
+�
+δαβδγλ + δαλδβγ + δαγδβλ
+�
+.
+(307)
+The three primary modes K(1), K(2) and K(3) were already identified by KGDN [29]. Corresponding modes frequen-
+cies is the only part of the invariance defect that survives linearization around equilibrium [29], and thus contribute
+the conventional linear nonequilibrium thermodynamics dissipation to R13. The primary modes are accompanied by
+three nonlinear secondary modes K(4), K(5) and K(6). Finally, two modes K(7) and K(8) are ghost modes: while they
+contribute to the R13 distribution function, their projection onto R13 fluxes vanishes, and they are not visible in the
+R13 balance equations.
+K
+P
+F
+1
+⟨CCC⟩
+√
+RT
+2p ⟨∇σ⟩ +
+√
+RT
+2pT ⟨σ∇T⟩ +
+1
+2p
+√
+RT ⟨σDtu⟩
+2
+(C2 − 7) ⟨CC⟩
+1
+5p ⟨∇q⟩ +
+1
+5pRT ⟨qDtu⟩ +
+1
+4pT σDtT
+3
+C4 − 10C2 + 15
+1
+15p∇ · q +
+1
+15pσ : ∇u +
+1
+15pRT q · Dtu
+4
+(C2 − 7) ⟨CCC⟩
+1
+5p
+√
+RT ⟨q∇u⟩
+5
+⟨CCCC⟩ − sym(⟨CC⟩ U)
+1
+2pσ∇u
+6
+(C4 − 14C2 + 35)CC
+1
+10pT q∇T
+7
+(C2 − 9) ⟨CCC⟩
+√
+RT
+4pT ⟨σ∇T⟩
+8
+(C4 − 14C2 + 35)C
+2q·⟨∇q⟩
+25p
+√
+RT −
+1
+15T
+√
+RT q∇ · q −
+1
+15T
+√
+RT qσ : ∇u +
+√
+RT
+10pT σ · ∇T
+Table 2: Modes of R13. Angular brackets denote symmetrized traceless tensors of rank two, three and four. Dt = ∂t +u·∇ is the material derivative
+along streamline; u is flow velocity, p = ρRT is the pressure, R is gas constant, ρ is the density and T is the temperature.
+3.7.3. The R13 equations
+The R13 equations for the nonequilibrium stress tensor σ and the heat flux q are compactly written in vector
+notation as follows:
+DR
+t σ = DG
+t σ − ∇ · QK,
+(308)
+DR
+t q = DG
+t q − ∇ · TK − QK : ∇u,
+(309)
+where Dt is the material time derivative along streamline,
+Dt = ∂t + u · ∇,
+(310)
+40
+
+and DG
+t indicates Grad’s contribution. The rank three symmetric trace-free tensor QK and the rank two symmetric
+tensor TK are the R13 fluxes,
+QK = − ν
+�3
+2 ⟨∇σ⟩ + 3
+2T ⟨σ∇T⟩ +
+6
+5RT ⟨q∇u⟩
+�
+− τ
+�3
+2 ⟨σDtu⟩
+�
+,
+(311)
+TK =
+�
+TK�
++ 1
+3UT K,
+(312)
+�
+TK�
+= − ν
+�14
+5 ⟨∇q⟩ +28
+5 ⟨q∇ ln T⟩ + σ(∇ · u) + 2
+�
+σ · S + σ · S
+��
+− τ
+�14
+5 ⟨qDtu⟩ + 7
+2RσDtT
+�
+,
+(313)
+T K = − 4ν
+�
+∇ · q+7
+2 q · ∇ ln T + σ : ∇u
+�
+− 4τq · Dtu.
+(314)
+Here angular brackets indicate symmetrized traceless tensors of rank two and three, overline indicates transposition,
+U is unit tensor, S = (∇u + ∇u)/2 is the strain and ∇ ln T = T −1∇T.
+Brackets in (311) and (313) help to discern contributions of two different types. The first bracket in (313) and
+(311) is the dissipation flux. First part of dissipation is the linear thermodynamics dissipation flux (first term in (311)
+and (313)). The linear dissipation fluxes are the only contributions in (311) and (312) that survive linearization around
+equilibrium, as was already shown by KGDN. The rest of the terms in the first bracket form the nonlinear dissipation
+flux, driven by non-uniformity of the macroscopic velocity field and of the temperature. Both types of dissipative
+fluxes are associated with the kinematic viscosity ν = τRT, here in the relaxation time approximation.
+Second bracket in (311) and (313) is a remarkably distinct streamline convective flux, which we term this way
+because of the material time derivative (310) participating in their formation. Streamline convective fluxes are nonlin-
+ear and their contribution is non-dissipative in nature. They are characterized by the relaxation time τ rather than by
+the viscosity. From Tab. 2, it is visible that streamline convective flux is contributed by primary modes only. Finally,
+also the trace T K (314) reproduces the said structure. Together with the balance equations of density, momentum and
+energy,
+Dtρ = −ρ∇ · u,
+(315)
+Dtu = −1
+ρ∇p − 1
+ρ∇ · σ,
+(316)
+DtT = −2
+3T∇ · u − 2
+3
+�T
+p
+�
+σ : ∇u − 2
+3
+�T
+p
+�
+∇ · q,
+(317)
+and with Grad’s contribution,
+DG
+t σ = − 2p ⟨S⟩ − 4
+5 ⟨∇q⟩ − σ(∇ · u) − 2 ⟨σ · S⟩ − 1
+τσ,
+(318)
+DG
+t q = − 5
+2RΠ · ∇T − RT∇ · σ − σ · Dtu − 7
+5 q(∇ · u) − q · ∇u − 4
+5 q · S − 1
+τ q,
+(319)
+where Π = pU + σ is the pressure tensor, (308) and (309) build up the structure of the R13 system.
+The R13 theory was further refined and extensively studied by Struchtrup and Torrilhon, and their coauthors, in
+a number of contributions [32, 33, 34, 35, 36, 37, 38, 20, 39] that dissect the R13 equations carefully, and show that
+they can describe all relevant rarefaction phenomena, such as jump and slip at boundaries, Knudsen boundary layers,
+transpiration flow, thermal stresses, non-temperature-gradient heat flux induced by stresses, damping and dispersion
+of ultrasound waves and shock structures (for limited Mach numbers). A good summary of this work is referenced
+and discussed in a recent review [36].
+3.8. Lifting of Grad’s and quasi-equilibrium projections: Kinetic models for simple fluid
+3.8.1. Quasi-equilibrium and related kinetic models
+Lifting of the local equilibrium projection considered in sec. 3.5 results in the BGK model. A variety of kinetic
+models can be offered by a lifting the lifting of the Grad’s and related projections. We shall discuss now some main
+41
+
+classes of kinetic models from this perspective. Following [40], a kinetic model for a generic quasi-equilibrium
+approximation f ∗(M) (240) can be proposed as follows,
+∂t f + v · ∇ f = −1
+τ( f − f ∗(M)) + JB( f ∗(M)).
+(320)
+Here f ∗(M) ≡ f ∗(M( f)) is the natural map f → f ∗(M),
+�
+µi( f − f ∗(M)d3v = 0, i = 1, . . . , k,
+(321)
+and we omit displaying the dependence of the distribution function on the velocity, time and space to simplify notation.
+Thus, the first term in the right hand side of equation (320) is BGK-like, whereas the second term, the function
+JB(f ∗(M)), is the true (Boltzmann) collision integral evaluated on the quasi-equilibrium manifold. The latter is
+crucial: Unlike the true Boltzmann collision integral JB( f) which takes values in the entire phase space of distribution
+functions, the term JB( f ∗(M)) is evaluated only on a relatively ”thin” submanifold f ∗ known a priori, and can be thus
+pre-computed to the explicit function of the moments M and of the velocity v (see Ref. [40] for examples). If the
+quasi-equilibrium f ∗(M) consists only of the local Maxwellians, then JB( f ∗(M)) vanishes, and we get back the
+BGK-model. In all other cases, the second term in the kinetic model (320) is essential: If it is omitted in equation
+(320) then the null-space of the resulting collision integral is the entire quasi-equilibrium manifold f ∗(M), and not its
+local equilibrium submanifold, unlike the case of the Boltzmann collision integral.
+The H-theorem for kinetic models (320) has the following structure: Let us compute the entropy production σ:
+σ = σ1 + σ2,
+σ1 = −1
+τ
+�
+ln( f)( f − f ∗(M)d3v,
+σ2 =
+�
+ln( f)JB( f ∗(M))d3v.
+(322)
+Function σ1 is the contribution from the BGK-like relaation term in equation (320), and it is always non-positive,
+again due to the property of the map f → f ∗(M) (321). The second contribution, σ2 may be not sign-definite if
+f is far away from the quasi-equilibrium. However, there always exists a non-empty neighborhood of the quasi-
+equilibrium manifold, where σ2 ≤ 0 [40] (this is almost obvious: on the quasi-equilibrium manifold σ2( f ∗(M)) is the
+entropy production due to the Boltzmann collision integral). Thus, if the relaxation towards quasi-equilibrium states
+is fast enough (τ is sufficiently small), the net entropy production inequality holds, σ = σ1 + σ2 ≤ 0.
+Some further variants of the quasi-equilibrium models (320) are possible. Let us introduce the quasi-equilibrium
+projector P∗,
+P∗F =
+k
+�
+i=1
+∂ f ∗(M)
+∂Mi
+�
+µiFd3v.
+(323)
+Instead of the term JB(f ∗(M)) in (320), we can use its projection, P∗JB( f ∗(M)), so that the model (320) simplifies to
+∂t f + v · ∇ f = −1
+τ( f − f ∗(M)) +
+k
+�
+i=1
+∂ f ∗(M)
+∂Mi
+R∗
+i (M),
+(324)
+where R∗
+i (M) is the quasi-equilibrium production rate of the ith moment,
+R∗
+i (M) =
+�
+µiJB( f ∗(M))d3v.
+(325)
+The variant (324) is simpler than the original kinetic model(320) since the velocity dependence of the corresponding
+term arises in (324) only via the quasi-equilibrium distribution function rather than due to the function in the function
+JB( f ∗(M)). Moreover, a further simplification can be suggested in a ”multiple relaxation times” form,
+∂t f + v · ∇ f = − − 1
+τ( f − f ∗(M)) −
+k
+�
+i=1
+∂f ∗(M)
+∂Mi
+� 1
+τi
+� �
+Mi − Meq
+i
+�
+,
+(326)
+42
+
+where Meq
+i
+denotes the ith moment evaluated at the local equilibrium, while τ1, . . . , τk are corresponding relaxation
+times. Descending the path of simplification from the quasi-equilibrium kinetic model (320) through (324) to (326),
+the information about the ”true” Boltzmann collision integral, which is still manifest in (320), is gradually lost and is
+completely replaced by a relaxation-type form in (326). In the next section, we shall consider a special case of the
+two-relaxation time kinetic models which are mostly used in applications.
+3.8.2. Two relaxation times quasi-equilibrium models
+The two relaxation times quasi-equilibrium kinetic model is written,
+∂t f + v · ∇ f = − 1
+τfast
+( f − f ∗(M)) −
+1
+τslow
+( f ∗(M) − f eq),
+(327)
+and has the following interpretation: The relaxation to the local equilibrium f eq is decomposed into a ”fast” relaxation
+from the current state f to the intermediate quasi-equilibrium f ∗ followed by a ”slow” relaxation from the quasi-
+equilibrium f ∗ to the local equilibrium f eq. This is a special reduction of the quasi-equilibrium model (320), where
+the Boltzmann’s term JB( f ∗(M)) is replaced with the BGK relaxation [41]. Denoting Jfs the right hand side of (327),
+we can write,
+Jfs = −
+� 1
+τfast
+−
+1
+τslow
+�
+( f − f ∗(M)) −
+1
+τslow
+( f − f eq).
+(328)
+Now, in order to clarify the meaning of the fast-slow decomposition, we compute the entropy production induced by
+the relaxation term (328),
+σ = σfast + σslow,
+(329)
+σfast = −
+� 1
+τfast
+−
+1
+τslow
+� �
+ln
+�
+f
+f ∗(M)
+�
+( f − f ∗(M)) d3v,
+(330)
+σslow = − 1
+τslow
+�
+ln
+� f
+f eq
+� �f − f eq� d3v.
+(331)
+Clearly, the contribution of the slow relaxation into the entropy production, Eq. (331), is always non-positive, σslow ≤
+0. However, the contribution of the fast relaxation, Eq. (330), is non-positively definite, σfast ≤ 0, only if the fast
+relaxation time τfast is not greater than the slow relaxation time τslow:
+τfast ≤ τslow.
+(332)
+The equality τfast = τslow results in the BGK model. Thus, the compliance to the H-theorem for the quasi-equilibrium
+kinetic model (327) implies the fast-slow relaxation times hierarchy (332). It is convenient to introduce the ratio of
+the relaxations times,
+rfs = τfast
+τslow
+, rfs ∈ [0, 1].
+(333)
+Introducing also a convex linear combination of the quasi-equilibrium and the local equilibrium,
+˜ffs = (1 − rfs) f ∗(M) + rfs f eq.
+(334)
+the relaxation term can be written in a BGK-like form,
+Jfs = − 1
+τfast
+( f − ˜ffs).
+(335)
+Realizations of the two relaxation times kinetic model (327) depend on the availability of analytical expressions for
+the quasi-equilibrium distribution functions. In practice, the ”true” quasi-equilibrium can be substituted by Grad’s
+approximation, which is sufficient for many applications. However, the relaxation times hierarchy (332) must be
+respected also in such cases.
+43
+
+3.8.3. Lifting the eight-moments Grad’s projection: Shakhov’s S-model
+Using the eight-moments Grad’s distribution function (279), we obtain in (334) and (335),
+˜ffs = (1 − rfs) G8 + rfs f eq
+= f eq
+�
+1 + (1 − rfs)qα(vα − uα)
+pRT
+�(v − u)2
+5RT
+− 1
+��
+.
+(336)
+The corresponding two relaxation times kinetic model (327) is identified as the Shakhov’s S-model [27]. Hydrody-
+namic limit of the S-model results in the Navier–Stokes–Fourier system with the following viscosity and thermal
+conductivity,
+µ = τfastp,
+(337)
+λ = τslowcpp.
+(338)
+Thus, the Prandtl number of the S-model satisfies the inequality implied by the fast-slow relaxation hierarchy (332),
+Pr = rfs = τfast
+τslow
+≤ 1.
+(339)
+3.8.4. Lifting the ten-moments Grad’s projection.
+The ten-moments quasi-equilibrium is available in a closed form, Eq. (246), and hence can be straightforwardly
+used in the kinetic model (327). Here we shall instead consider lifting of the ten-moments Grad’s approximation
+(274). With (274), we obtain in (334) and (335),
+˜ffs = (1 − rfs) G10 + rfs f eq
+= f eq
+�
+1 + (1 − rfs) σαβ
+2pRT
+�
+(vα − uα)(vβ − uβ) − 1
+3δαβ(v − u)2
+��
+.
+(340)
+Hydrodynamic limit of the corresponding kinetic model results in the Navier–Stokes–Fourier system with the follow-
+ing viscosity and thermal conductivity,
+µ = τslowp,
+(341)
+λ = τfastcpp.
+(342)
+Note that, the dependence of the transport coefficients on the relaxation times in (341) and (342) is opposite to that
+of the S-model, Eqs. (337) and (338): the fast and slow relaxation times switch their places. Thus, in compliance
+with the relaxation times hierarchy (332), the Prandl number of the kinetic model based on the ten-moments Grad’s
+approximation satisfies the inequality,
+Pr = 1
+rfs
+= τslow
+τfast
+≥ 1.
+(343)
+Results (341), (342) remain valid when the full ten-moment quasi-equilibrium distribution function (246) is used in
+(327). We comment that, the S-model (336) and the model (340) are complementary to each other: The S-model
+covers the range of the Prandtl number 0 < Pr ≤ 1 while the model (340) corresponds to 1 ≤ Pr < ∞. This
+is consistent with the corresponding Grad’s projections: The ten-moments projection (274) provides a formal limit
+Pr → ∞, cf. Eq. (250), while the eight-moments projection (279) provides the limit of a vanishing Prandtl number
+Pr → 0, cf. Eq. (283). Both models are used in the thermal and compressible lattice Boltzmann models [42].
+3.8.5. Holway’s ellipsoidal-statistical kinetic model
+Finally, we mention another option of lifting the quasi-equilibrium projection. Starting with the BGK-like form
+(335), the attractor ˜f (334) can be replaced by another one, the quasi-equilibrium evaluated on a linear combination
+between the moments and their equilibrium values. In a general multi-parameter form, and a generic quasi-equilibrium
+distribution function f ∗(M, v), this is,
+˜f ∗ = f ∗((1 − α1)M1 + α1Meq
+1 , . . . , (1 − αk)Mk + αkMeq
+k , v),
+(344)
+44
+
+where α1, . . . , αk are free parameters. In other words, while the previous lifting operates with linear combinations
+between the quasi-equilibrium and the local equilibrium distribution functions (334), the present one uses the quasi-
+equilibrium distribution of linear combination of the corresponding moments. Whenever the Grad’s approximation is
+used instead of the true quasi-equilibrium, both approaches result in identical models.
+Because only one case of a genuine quasi-equilibrium distribution function is known in a closed-form, cf. Eq.
+(246), the unique model of the type (344) is the Holway’s ellipsoidal-statistical (ES) model [43]. Introducing in (246)
+a linear combination between the full pressure tensor Π = p1 + σ and its local equilibrium value p1, we obtain a
+one-parametric family of distribution functions,
+˜f ∗
+ES = n
+ρ
+3
+2
+(2π)
+3
+2 �
+det �(1 − α)Π + αp1� exp
+�
+−ρ
+2(v − u)† · �(1 − α)Π + αp1�−1 · (v − u)
+�
+.
+(345)
+With (345), the ES model is written in the BGK-like form,
+∂t f + v · ∇ f = −1
+τ
+�
+f − ˜f ∗
+ES
+�
+.
+(346)
+Hydrodynamic limit of the ES kinetic model (346) recovers the viscosity and thermal conductivity in the Navier–
+Stokes–Fourier system,
+µ = 1
+ατp,
+(347)
+λ = τcpp,
+(348)
+which allows to identify the parameter α as the inverse of the Prandtl number,
+α = 1
+Pr.
+(349)
+If the ES distribution function (345) is expanded to linear order in the nonequilibrium stress tensor σ, the result is
+identical to (340), and which makes it possible the matching of the parameters in both cases as rfs = α. Thus, the
+relation between the transport coefficients of the ES model, Eqs. (347) and (348), is the same as for the case (340),
+Eqs. (341) and (342). We note that, as was shown by [44], the H-theorem for the ES model can be proven for Prandtl
+number 2/3 ≤ Pr < ∞.
+3.9. Summary: Projections, corrections and lifting
+The review of some basic, classical aspects of the Boltzmann equation of this section are summarized in Tab. 3.
+With this, we emphasize a certain commonality among various approaches. The main building block is an approxi-
+mation provided by a distribution function, parameterized by a set of macroscopic fields of interest. The projection
+of the Boltzmann equation provides a starting point of the analysis. The projection can be corrected by improving its
+invariance property relative to the Boltzmann equation or lifted to a kinetic model. Both approaches are patterned in
+the lattice Boltzmann realizations to be discussed in the remainder of this contribution.
+Projection
+Equation
+Correction
+Lifting
+Local equilibrium
+Euler
+Navier–Stokes–Fourier
+BGK
+Grad 13
+Grad’s 13-moment system
+R13
+Grad 10
+Grad’s 10-moment system
+Quasi-equilibrium 10
+Grad’s 10-moment system
+ES model, model (340)
+Grad 8
+S-model
+Table 3: Summary of projections, their corrections and liftings.
+45
+
+4. Lattice Boltzmann for ideal fluid and related models
+In this section we discuss in detail the lattice Boltzmann method introduced in the early 90’s [45, 46, 47] as
+an improvement over the lattice gas automata [48]. In its modern form it is a discrete solver for the Boltzmann
+equation with the BGK approximation for the collision operator given in Eq. (199). After a detailed introduction of
+discretization strategies in both phase-space and space/time, we will discuss different approximations to external body
+forces, stability and applicability domain of the classical LBM and possible improvement strategies.
+4.1. Phase-space discretization
+The first step in deriving a discrete scheme from the Boltzmann-BGK equation, is to discretize the D-dimensional
+space of particles speed. Many different strategies have been adopted in the context of the kinetic theory of gases.
+Here we review quadrature-based approaches used mainly in the context of the LBM to reduce the continuous space
+of particles speed into a discrete set of velocities.
+4.1.1. Hermite expansion and Gauss-Hermite quadrature
+One approach to discretise phase-space and derive the corresponding discrete EDF consists in expanding it in
+terms of Hermite polynomials and operating a truncation using Gauss-Hermite quadratures [49, 50, 15].
+Before starting the derivation, let us review the basic concepts of multi-variate Hermite polynomials. More details on
+the Hermite polynomials can be found in Appendix A. They are defined as [50]:
+H n (v) = (−1)n
+w (v) ∇n
+vw (v) ,
+(350)
+where H n is a tensor of rank n and w (v) is the normalized weight function defined as:
+w (v) = (2π)−D/2 exp
+�
+−v2
+2
+�
+,
+(351)
+with D the dimension of v. A function f can then be expanded in terms of Hermite polynomials as:
+f = w (v)
+∞
+�
+n=0
+1
+n! an : H n (v) ,
+(352)
+where “:” is the Frobenius inner product and the coefficients tensor an are computed as:
+an =
+�
+H n (v) fdξ.
+(353)
+Note that Hermite polynomials are mutually orthogonal with respect to the weighted dot product defined as:
+�
+Hi(v)w(v)Hi′(v)dv =
+�������
+0
+if i � i′
+n!
+if i = i′,
+(354)
+where i and i′ are vectors of size n designating a component of the rank n Hermite polynomial tensor. The infinite set
+of Hermite polynomials forms a complete orthogonal basis of the weighted space Vw := L2(RD; R, wdv) only under
+the condition that any function f ∈ Vw satisfies:
+�
+f 2(v)w(v)dv < ∞,
+(355)
+meaning in practice that f(v) must decay faster than √w(v) which has implications on the choice of reference temper-
+ature in static reference frame-based methods like the LBM. Further discussion on that issue is out of the scope of the
+present review and will be presented in future publications.
+The first step in the expansion is the choice of the non-dimensionalization strategy, or reference state. While not
+46
+
+necessary in the expansion, this choice is one of the most important steps in the construction of a discrete kinetic
+scheme as it will play a key role in the final numerical scheme’s behavior, especially higher-order moments errors.
+The recent development of LB models relying on non-symmetrical stencils and adaptive non-dimensionalization is a
+clear proof of the previous assertion [51, 52, 53, 54, 55, 56]. For the sake of simplicity, let us re-write the EDF in
+non-dimensional form as:
+f eq (v, ρ, u, θ) = ρ(2πθ)−D/2 exp
+�
+−(v − u)2
+2θ
+�
+,
+(356)
+where for the remainder of this subsection u, and v are non-dimensionalized with a reference speed of sound cs,
+θ = kBT/m
+c2s
+and cs = kBT0
+m0 , and T0 and m0 are respectively defined as the reference temperature and molecular mass.
+This results in the following first few Hermite polynomials:
+H0 = 1,
+(357a)
+Hi1 = vi1,
+(357b)
+Hi1i2 = vi1vi2 − δi1i2,
+(357c)
+Hi1i2i3 = vi1vi2vi3 − �vi1δi2i3
+�
+cyc ,
+(357d)
+Hi1i2i3i4 = vi1vi2vi3vi4 + �δi1i2δi3i4
+�
+cyc − �vi3vi4δi1i2
+�
+cyc ,
+(357e)
+where []cyc designates cyclic permutations over the involved indexes, and corresponding isothermal (θ = 1) Hermite
+coefficients:
+aeq
+0 = ρ,
+(358a)
+aeq
+i1 = ρui1,
+(358b)
+aeq
+i1i2 = ρui1ui2,
+(358c)
+aeq
+i1i2i3 = ρui1ui2ui3,
+(358d)
+aeq
+i1i2i3i4 = ρui1ui2ui3ui4.
+(358e)
+In the context of the classical LBM, the flow is assumed isothermal. The continuous EDF is then expanded as:
+f eq (v, ρ, u) = w (v)
+∞
+�
+n=0
+1
+n! a(eq)
+n
+(ρ, u) : H n (v) .
+(359)
+As seen here, the expanded EDF still goes over the entire phase-space. Given the form of the EDF and the corre-
+sponding moments:
+Πx . . . x
+����
+×p
+y . . . y
+����
+×q
+z . . . z
+����
+×r
+=
+�
+vx
+pvy
+qvz
+r f eq (v, ρ, u) dv,
+(360)
+and using the Hermite expansion, it can be written as:
+Πx . . . x
+����
+×p
+y . . . y
+����
+×q
+z . . . z
+����
+×r
+=
+�
+P∞ (v, ρ, u) w (v) dv,
+(361)
+where:
+P∞ (v, ρ, u) = vxpvyqvzr f eq (v, ρ, u)
+w (v)
+,
+(362)
+and P∞ (v, ρ, u) as defined here is a polynomial function of the variable v with order ∞ as the Hermite expansion has
+not yet been truncated. Given that the aim of the LB method is to solve the Boltzmann equation in the hydrodynamic
+regime one only needs to correctly recover the moments of the EDF involved in the hydrodynamic equations. Further-
+more, Hermite polynomials are weighted orthogonal functions and as such higher-order polynomials have no effect
+on lower-order terms. Given the previously cited arguments, one can limit the Hermite expansion of the EDF:
+f eq,N (v, ρ, u) = w (v)
+N
+�
+n=0
+1
+n! aeq
+n (ρ, u, ) : Hn (v) ,
+(363)
+47
+
+where N corresponds to the highest-order moment involved in the targeted dynamics. For example, to correctly
+recover the NS equations for an isothermal flow one needs to correctly recover moments up to order three of the EDF.
+Now the polynomial P∞ can be replaced with a finite-order polynomial:
+PM (v, ρ, u) = vxpvyqvzr f eq,N (v, ρ, u)
+w (v)
+,
+(364)
+where M = 2N. The integral of Eq. (361) can be evaluated using a discrete sum through a Gauss-Hermite quadrature
+as:
+�
+PM (v, ρ, u) w (v) dv �
+Q
+�
+i=0
+wiPM (ci, ρ, u) ,
+(365)
+where ci are discrete non-dimensional abscissae used for the quadrature and wi are the corresponding weights.
+According to the fundamental theorem of Gaussian quadratures, choosing the abscissae to be the roots of the or-
+thogonal polynomial of the corresponding degree results in the maximum algebraic degree of precision, namely
+2Q − 1. To correctly recover the targeted moments one must have M ≤ 2Q − 1. The third-order quadrature (des-
+ignated by E3
+1,5 in 1-D) results in the following abscissae: ci ∈ {−
+√
+3, 0,
+√
+3} corresponding to the following values
+{− √3kBT0/m0, 0, √3kBT0/m0} in physical units. While being the most widely applied quadrature order, it is already
+clear that the third-order quadrature can not correctly recover all the moments appearing at the NS level. More on that
+issue in the next subsections. The corresponding weights are computed as:
+wi =
+n!
+(Hn−1 (ci))2 .
+(366)
+In the multi-variate case, the weights can be computed as the products of the weights in each dimension.
+4.1.2. Product form equilibria and moment matching
+As clearly stated by its name, in this approach one tries to construct a discrete equilibrium by matching the
+moments appearing in the targeted macroscopic balance equations.
+To identify the constraints, one first uses the CE analysis. For example, a simple CE analysis at order ϵ shows that
+to correctly recover the NS and continuity equations, one needs to exactly match moments up to order three [57, 58].
+For example let us consider a 1-D system with only translational degrees of freedom. The following moments need to
+be correctly recovered:
+Π0 =
+�
+vx
+ρ
+�
+m
+2πkBT exp
+�
+−m(vx − ux)2
+2kBT
+�
+dvx = ρ,
+(367a)
+Πx =
+�
+vx
+vxρ
+�
+m
+2πkBT exp
+�
+−m(vx − ux)2
+2kBT
+�
+dvx = ρux,
+(367b)
+Πxx =
+�
+vx
+v2
+xρ
+�
+m
+2πkBT exp
+�
+−m(vx − ux)2
+2kBT
+�
+dvx = ρ
+�
+u2
+x + kBT
+m
+�
+,
+(367c)
+Πxxx =
+�
+vx
+v3
+xρ
+�
+m
+2πkBT exp
+�
+−m(vx − ux)2
+2kBT
+�
+dvx = ρux
+�
+u2
+x + 3kBT
+m
+�
+.
+(367d)
+In the second step of the discrete equilibrium state construction, one chooses a symmetrical stencil (set of discrete
+velocities) with a number of degrees of freedom equal to the number of constraints [57, 59, 60]. For example, in the
+case of the isothermal NS solver, one can either use a four-velocity model or a five-velocity model with an additional
+constraint to have a unique solution. The discrete equilibrium is then found by solving the following system of
+equations:
+��������������
+1
+1
+1
+1
+c0
+c1
+c2
+c3
+c2
+0
+c2
+1
+c2
+2
+c2
+3
+c3
+0
+c3
+1
+c3
+2
+c3
+3
+��������������
+��������������
+f eq
+0
+f eq
+1
+f eq
+2
+f eq
+3
+��������������
+=
+����������������
+ρ
+ρux
+ρ
+�
+u2
+x + kBT
+m
+�
+ρux
+�
+u2
+x + 3 kBT
+m
+�
+����������������
+,
+(368)
+48
+
+where c0−3 are the discrete velocities in the stencil and f eq
+0−3 are the unknown discrete equilibria to be found by solving
+this system. The linear system formed using symmetrical stencils might not always be invertible. As such, for some
+models one might need to add non-symmetrical components to the system [61].
+The product form of the EDF is a special realization of the moments matching approach. Considering the standard
+discrete velocity set D3Q27, where D = 3 stands for three dimensions and Q = 27 is the number of discrete velocities,
+ci = (cix, ciy, ciz), ciα ∈ {−1, 0, 1},
+(369)
+one first defines a triplet of functions in two variables, ξα and ζαα,
+Ψ0(ξα, ζαα) = 1 − ζαα,
+(370)
+Ψ1(ξα, ζαα) = ξα + ζαα
+2
+,
+(371)
+Ψ−1(ξα, ζαα) = −ξα + ζαα
+2
+,
+(372)
+and considers a product-form associated with the discrete velocities ci (369),
+Ψi = Ψcix(ξx, ζxx)Ψciy(ξy, ζyy)Ψciz(ξz, ζzz).
+(373)
+All pertinent populations below are determined by specifying the parameters ξα and ζαα in the product-form (373). The
+two-dimensional version of the model on the D2Q9 lattice is obtained by omitting the z-component in all formulas.
+After matching moments with their continuous counter-parts the parameters are set as,
+ξα = uα,
+(374)
+ζαα = c2
+s + u2
+α,
+(375)
+and the local equilibrium populations are represented with the product-form (373),
+f eq
+i
+= ρ
+�
+α=x,y,z
+Ψciα
+�
+uα, c2
+s + u2
+α
+�
+.
+(376)
+This form of the discrete equilibrium populations, when c2
+s = kBT0/3m0 is equivalent to third-order quadrature-based
+scheme with a full expansion of the distribution function. As will be seen in the upcoming section this class of
+equilibrium populations allows to restore Galilean invariance of the Navier-Stokes level shear viscosity but fails to do
+so for the bulk component.
+4.1.3. Alternative to polynomial equilibria: Entropic equilibria
+In the context of the entropic lattice Boltzmann method as described in [62], the discrete equilibrium state is found
+as the minimizer of a convex discrete entropy functional under mass and momentum conservation constraints. It is this
+lower number of constraints on moments that allows the scheme to accomodate the entropy constraint. The derivation
+starts with the roots of the third-order Hermite polynomials as the discrete abscissae and considering the following
+conservation constraints:
+�
+α
+f eq
+i
+= ρ,
+(377)
+�
+i
+ci f eq
+i
+= ρu,
+(378)
+where notations follow those adopted in the previous subsection. The EDF is derived as the function extremizing the
+discrete entropy function:
+Hwi,ci =
+�
+i
+fi ln
+� fi
+wi
+�
+,
+(379)
+49
+
+under the previously set constraints. Given the Galilean invariance of the weights the expression for the entropy
+function is also Galilean invariant [54]. The EDF can be expressed as:
+f eq
+i
+= wi exp (λ0)
+D
+�
+α=1
+exp �ci,αλα
+� ,
+(380)
+where λ0 and λα are the Lagrange multipliers associated with constraints on the zeroth and first-order moments.
+Introducing the following changes of variables, X = exp (−λ0) and Zα = exp (λα) the EDF is re-written as:
+f eq
+i
+= wiX−1
+D
+�
+α=1
+Zci,α.
+(381)
+Writing down the conservation equations using the new variables for the D2Q9 stencil, the following algebraic system
+of equations is obtained:
+ρX =
+�
+i
+wi
+�
+α=x,y
+Zci,α,
+(382a)
+ρuxX =
+�
+i
+wici,x
+�
+α=x,y
+Zci,α,
+(382b)
+ρuyX =
+�
+i
+wici,y
+�
+α=x,y
+Zci,α.
+(382c)
+Solving this system of equation for Zx, Zy and X and keeping positive roots one gets:
+Zα = 2uα +
+�
+uα2/c2s + 1
+1 − uα
+,
+(383)
+X−1 = ρ
+�
+α=x,y
+�
+2 −
+�
+uα2/c2s + 1
+�
+,
+(384)
+and therefore can express the entropic discrete equilibrium as:
+f eq
+i
+= wiρ
+�
+α=x,y
+�
+2 −
+�
+uα2/c2s + 1
+� �������
+2uα +
+�
+uα2/c2s + 1
+1 − uα
+�������
+ci,α
+.
+(385)
+It will be shown in the next sections that this approach to constructing the discrete equilibrium populations satisfies a
+smaller number of constraint on moments, i.e. only of order zero and one, but guarantees unconditional positivity and
+linear stability of the scheme.
+4.1.4. Galilean invariance issues on standard lattices
+Errors in moments of the equilibrium distribution function. It is well-known that LB formulations based on standard
+first-neighbor stencils do not exactly recover the NS level dynamics, i.e. the stress tensor and, for the entropic equi-
+librium, the pressure tensor. The former comes from the fact that, due to a lack of symmetry, the third-order moments
+tensor does not correspond to its phase-space continuous counterpart. While including higher-order components of
+the Hermite expansion in the EDF or using the product-form can help correct the deviatoric components, consistency
+of the diagonal components can only be re-established through additional correction terms. Furthermore, use of the
+entropic approach which enforces smaller number of constraints on moments results in deviations in second-order
+moments too. To have a better measure of the applicability domain of the LB scheme, we will look at the deviations
+of these moments from their continuous counterparts for varying Mach numbers. Although readily extendable to
+other stencils, the D2Q9 stencil will be considered here. Moments of orders two and three of the EDF will be studied
+through their normalized deviations defined as:
+δ =
+�������������
+1 −
+�
+i cp
+i,xcq
+i,y f eq
+i
+ΠMB
+x . . . x
+����
+×p
+y . . . y
+����
+×q
+�������������
+,
+(386)
+50
+
+where ΠMB
+x . . . x
+����
+×p
+y . . . y
+����
+×q
+is the continuous moment and �
+i cp
+i,xcq
+i,y f eq
+i
+is the moment of the discrete EDF.
+First we consider the diagonal components of the second-order moments tensor in the co-moving reference frame. We
+consider the co-moving reference frame here to focus on the recovered thermodynamic pressure:
+�
+ΠMB
+xx + �
+ΠMB
+yy = 2ρc2
+s.
+(387)
+The deviations are illustrated in Fig. 1. While the entropic EDF does not exactly recover the correct trace of the
+-1.5
+-1
+-0.5
+0
+0.5
+1
+1.5
+ux/cs
+-1.5
+-1
+-0.5
+0
+0.5
+1
+1.5
+uy/cs
+102
+1
+10-2
+10-4
+-1
+-0.5
+0
+0.5
+1
+ux/cs
+10-8
+10-6
+10-4
+10-2
+100
+10-5
+10-4
+10-3
+10-2
+10-1
+Figure 1: Illustration of deviations in Πeq
+xx + Πeq
+yy moment for the entropic equilibrium. Left: Evolution of normalized error as a function of ux/cs
+and uy/cs. Right: Normalized error as a function of ux/cs with uy/cs = 0.
+diagonal components of the second-order moments tensor, the deviations are negligible for Mach numbers up to 0.4
+which goes above the validity of the weakly compressible flow assumption. Another point worth nothing is the nature
+of the deviations. The second order central equilibrium moment �
+Πeq
+αα for the entropic equilibrium is:
+�
+Πeq
+αα = −ρ(uα − 1)(6uα
+�
+3u2α + 1 + 12u2
+α − 2
+�
+3u2α + 1 + 4)
+6(2uα +
+�
+3u2α + 1)
+,
+(388)
+indicating that the thermodynamic pressure tensor loses Galilean-invariance and isotropy. In the limit of ux, uy → 0
+one recovers the correct pressure, i.e. ρc2
+s. The second-order Hermite-expanded and product form equilibria exactly
+recover the second-order moments tensor. Another point worth analyzing, is the behavior of sound speed in the
+entropic EDF. While sound speed is constant for polynomial equilibria it is a function of local speed in the entropic
+EDF. The behavior of sound speed as a function of local velocity is illustrated in Fig. 2. This behavior shows an
+interesting property of the entropic model pointing already to a (potentially) unconditional linear stability. Keeping
+in mind that the fastest eigen-modes in the system can not propagate faster than the lattice links and only considering
+three physical eigen-modes, i.e. ux, ux −cs and ux +cs, one arrives to the following strong condition on linear stability:
+max(ux, ux + cs, ux − cs) ≤ δr
+δt .
+(389)
+51
+
+Figure 2: (Left) Non-dimensional sound speed for entropic EDF as a function of velocity ux. (Right) Comparison of the speed of fastest propagating
+eigen-mode: (blue dotted line) polynomial EDF and (red line) entropic EDF.
+For the polynomial equilibria given that sound speed is constant one recovers the following maximum tolerable ve-
+locity:
+|umax
+x
+|= δr
+δt
+�������1 −
+�
+1
+3
+������� = 0.4226δr
+δt ,
+(390)
+which as will be shown in the next section through stability analyses, is indeed the maximum reachable velocity. For
+the entropic EDF on the other hand, it is observed that the sound speed self-adjusts as a function of local velocity to
+guarantee Eq. (389) is always satisfied. At the higher end of the velocity spectrum, i.e. ux → δr
+δt the speed of sound
+goes to cs → 0.
+For the NS level dynamics to be correctly recovered, the components of the third-order moments tensor must also
+match those of the continuous EDF. However, as observed in Fig. 3, none of the EDFs are able to recover the correct
+diagonal components for this tensor. This shortcoming is not related to the equilibrium state but, to the limited order of
+the Gauss-Hermite quadrature used for first-neighbor stencils. In Fig. 3, it is observed that all three EDFs considered
+there (second-order Hermite expansion, product-form and entropic) have the same moments, i.e. Πeq
+xxx = Πeq
+x = ρux.
+For the off-diagonal components of the third-order moments tensor however, as shown in Fig. 4, different EDFs result
+in different behaviors. While Hermite expansions of order higher than three, here the product form, exactly recover the
+correct moments, the second-order Hermite expansion and entropic EDFs show some deviations. Although not exactly
+recovering the correct moment the entropic EDF still closely follows its continuous counterpart even for large Mach
+numbers. This means that the entropic model exhibits less pronounced Galilean invariance in it effective viscosity as
+compared to the classical LBM with second-order EDF at moderate Mach numbers. In order to correctly recover the
+off-diagonal components of the third-order moments tensor in 2-D, the third-order terms of the Hermite expansion
+must be included. The diagonal components deviations on the other hand can only be accounted for via correction
+terms discussed in the next paragraph.
+Restoring Galilean-invarience of dissipation rate of shear/normal modes. Given that the EDF of the product-form
+is equivalent to the fourth-order Hermite-expanded EDF, only the Hermite expansion-based EDFs will be considered
+here. A simple CE analysis shows that at the NS level, to match the viscous (non-equilibrium) stress tensor for the
+continuous Boltzmann equation, moments of orders two and three of the EDF must be exactly recovered. Integrating
+in phase space, the following continuous second- and third-order moments are in fact recovered [49]:
+ΠMB
+αβ = ρuαuβ + ρc2
+sδαβθ,
+(391a)
+ΠMB
+αβγ = ρuαuβuγ + ρc2
+s
+�
+uαδβγθ
+�
+cyc ,
+(391b)
+52
+
+0.6
+1.4
+0.5
+1.2
+0.4
++
+0.3
+1
+0.2
+0.8
+0.1
+1
+U :
+3
+0.6
+0
+0
+0.5
+1
+0
+0.5
+1
+Wc-2
+-1
+0
+1
+2
+ux/cs
+-2
+-1
+0
+1
+2
+xxx
+-2
+-1
+0
+1
+2
+ux/cs
+10-4
+10-3
+10-2
+10-1
+100
+Figure 3: Deviations in the third order moment Πeq
+xxx. Left: Moments an Right: Normalized errors. Black solid line: Maxwellian distribution
+moment, blue dash-dotted line: second-order Hermite expansion, green dotted line: entropic equilibrium and red dashed line: product form
+equilibrium.
+-1.5
+-1
+-0.5
+0
+0.5
+1
+1.5
+ux/cs
+-1.5
+-1
+-0.5
+0
+0.5
+1
+1.5
+uy/cs
+-1.5
+-1
+-0.5
+0
+0.5
+1
+1.5
+ux/cs
+-1.5
+-1
+-0.5
+0
+0.5
+1
+1.5
+uy/cs
+102
+1
+10-2
+10-4
+Figure 4: Deviations in the third order moment Πeq
+xxy. Left: entropic equilibrium. Right: second-order Hermite expansion.
+while one gets the following moments with the second- and third-order discrete EDFs:
+Πeq,2
+αβ = ρuαuβ + ρc2
+sδαβθ,
+(392a)
+Πeq,2
+αβγ = ρc2
+s
+�
+uαδβγ
+�
+cyc ,
+(392b)
+53
+
+and :
+Πeq,2
+α
+= ρuαuα + ρc2
+sδαβθ,
+(393a)
+Πeq,3
+αβγ = ρc2
+sδαβγ
+�
+uαδβγ
+�
+cyc + ρ
+�
+1 − δαβγ
+�
+{uαuβuγ + c2
+s
+�
+uαδβγθ
+�
+cyc}.
+(393b)
+The product-form EDF recovers the same second- and third-order moments as the third-order Hermite expansion.
+To better put forward the shortcoming of the first-order stencil in recovering the NS level terms, let us perform now
+a brief CE analysis. Introducing the multi-scale expansion into the space and time-continuous system of equations
+and sorting terms of different orders in ϵ into separate equations and taking moments of orders zero and one to get
+mass and momentum balance, at order two in ε (NS level) the following momentum balance equations are recovered:
+∂(2)
+t ρuα + ∂βτ
+�
+∂(1)
+t Πeq
+αβ + ∂γΠeq
+αβγ
+�
++ ∂βτ
+�������
+�
+i
+ci,αci,βΨ(1)
+i
+������� = 0.
+(394)
+For the stress tensor to be correctly recovered at this scale one must have:
+Ψi = wi
+2c4s
+∂αHi,βγδΠeq
+αβγ,
+(395)
+where δΠeq
+αβγ designates the deviation of the discrete EDF moment from its continuous counterpart. An interesting
+point to note here is that this form of the correction term is only valid for the time and space continuous discrete
+Boltzmann system of equations. After discretization in space and time and operation of the change of variable specific
+to the LBM the correction term will be slightly modified.
+It is also worth noting that the treatment for third- and fourth-order EDFs differs from that at second-order. Regarding
+third- and fourth-order EDFs, in 2-D one obtains:
+Ψeq,N>2
+i
+= wi
+2c4s
+�
+Hi,xx∂xδΠeq
+xxx + Hi,yy∂yδΠeq
+yyy
+�
+.
+(396)
+Instead, for the second-order EDF, additional correction terms are required, or one fails to recover correctly deviatoric
+components of the third-order moments:
+Ψeq,2
+i
+= Ψeq,N>2
+i
++ wi
+c4s
+Hi,xy
+�
+∂x
+�
+δΠeq,2
+xxy + δΠeq,2
+xyy
+�
++ ∂y
+�
+δΠeq,2
+xxy + δΠeq,2
+xyy
+��
+.
+(397)
+This type of correction for the third-order equilibrium moments was introduced in [63] and later reprised in [64, 65,
+58].
+Different from the approach taken previously, one can also directly introduce the correction term at order ϵ2 as
+proposed in [66, 67]. In practice this means that the correction would involve a Laplacian and as such be expanded as:
+Ψ
+′
+i = ϵ2Ψ
+′
+i
+(2).
+(398)
+Re-writing the momentum balance equations at the NS level with this new correction term:
+∂(2)
+t ρuα + ∂βτ
+�
+∂(1)
+t Πeq
+αβ + ∂γΠeq
+αβγ
+�
+−
+�
+i
+ci,αΨ
+′
+i
+(2) = 0,
+(399)
+one gets the following restrictions on the correction term:
+�
+i
+Ψ
+′
+i
+(2) = 0,
+(400)
+and:
+�
+i
+ci,αΨ
+′
+i
+(2) = ∂β
+�µ
+p∂γδΠeq
+αβγ
+�
+.
+(401)
+54
+
+The correction term using the second approach can therefore be defined as:
+Ψ
+′
+i = wi
+c2s
+ci,α∂β
+�µ
+p∂γδΠeq
+αβγ
+�
+.
+(402)
+Both approaches effectively restore Galilean invariance at the NS level. However, the first approach allows for more
+flexibility in the treatment of the spatial derivative, and in practice allows for compressible flow simulations in the
+low supersonic regime. For a detailed comparative study of both approaches and different discretization strategies,
+interested readers are referred to [58].
+4.2. Space and time discretization: Integration along characteristics
+With the Discrete velocity Boltzmann system of non-homogeneous hyperbolic partial differential equations in
+hand, the next step is to operate discretization in physical space and time.
+4.2.1. Realization without force and correction term
+Starting from the phase-space discretized form of the Boltzmann equation (a set of Q equations):
+∂t fi + ci · ∇fi = Ωi,
+(403)
+where Ωi is the collision term, the idea of the Lagrangian approach consists of integrating them along their respective
+characteristics, which contrary to Lagrangian solvers for the NS equations (given that fluid particle path-lines are
+space- and time-dependent), results in an exact solution for the advection term. As such integrating the equations
+from a time t to t + δt along the stencil directions one obtains:
+fi (r + ciδt, t + δt) − fi (r, t) =
+� t+δt
+t
+Ωi
+�r(t′), t′� dt′.
+(404)
+Obviously within the context of the Lagrangian approach δr/δt is tied to the abscissae obtained from the Gauss-
+Hermite quadrature. In the case of the third-order quadrature for the streaming operation to results in space-filling
+lattices:
+||ci,α||=
+�
+3kBT0
+m0
+= δr
+δt .
+(405)
+Coming back to Eq. (404), it is observed that all the difficulty in this approach lies in the estimation of the collision
+contribution. A simple first-order explicite approximation would be:
+� t+δt
+t
+Ωi
+�
+r(t
+′), t
+′�
+dt
+′ = δt
+2 Ωi (r, t) + O
+�
+δt2�
+.
+(406)
+The classical LBM approach relies on a higher-order alternative; To get a second-order accurate scheme one can use
+the trapezoidal rule to evaluate the integral:
+� t+δt
+t
+Ωi
+�
+r(t
+′), t
+′�
+dt
+′ = δt
+2 Ωi (r, t) + δt
+2 Ωi (r + ciδt, t + δt) + O
+�
+δt3�
+,
+(407)
+which in turn results in an implicit scheme. To take out the implicitness of the resulting equation, the distribution
+function is re-defined via the following change of variables:
+¯fi = fi − δt
+2 Ωi,
+(408)
+¯f eq
+i
+= f eq
+i ,
+(409)
+Ωi =
+1
+τ + δt/2
+� ¯f eq
+i
+− ¯fi
+�
+.
+(410)
+55
+
+Using this change of variable and Eqs. (404) and (407) one gets:
+¯fi (r + ciδt, t + δt) − ¯fi (r, t) + δt
+2 Ωi (r + ciδt, t + δt) − δt
+2 Ωi (r, t) = δt
+2 Ωi (r + ciδt, t + δt) + δt
+2 Ωi (r, t) ,
+(411)
+which in turn using Eqs. (408)–(410) results in the classical collide-stream algorithm:
+¯fi (r + ciδt, t + δt) − ¯fi (r, t) = δt
+¯τ
+�
+f eq
+α (r, t) − ¯fi (r, t)
+�
+,
+(412)
+where ¯τ is defined as:
+¯τ = τ + δt/2.
+(413)
+It is also interesting to note that the new distribution functions have the following properties:
+�
+i
+¯fi =
+�
+i
+fi − δt
+2
+�
+i
+Ωi = ρ,
+(414)
+�
+i
+ci ¯fi =
+�
+i
+ci fi − δt
+2
+�
+i
+ciΩi = ρu,
+(415)
+where we have used the collision-invariance of the zeroth- and first-order moments. More generally for higher-order
+moments:
+�
+i
+Hn (ci) ¯fi =
+�
+i
+Hn (ci) fi − δt
+2
+�
+i
+Hn (ci) Ωi =
+�
+1 + δt
+2¯τ
+�
+an − δt
+2¯τ aeq
+n .
+(416)
+While to derive the previous scheme, particle streaming was restricted to be on-grid, it is not a necessary condition
+for a working LB scheme. For the so-called semi-Lagrangian methods the restriction of Eq. (405) is relaxed, resulting
+in off-lattice propagation. As such, in this formulation the time-evolution operator of Eq. (412) is supplemented with
+an interpolation step to reconstruct the populations at the discrete grid-points:
+¯fi (r, t + δt) =
+�
+rj
+A
+�
+r, r j
+� �
+¯fi
+�
+r j − ciδt, t
+�
++ δt
+¯τ
+� ¯f eq
+i
+�
+r j − ciδt, t
+�
+− ¯fi
+�
+r j − ciδt, t
+���
+,
+(417)
+where A
+�
+r, r j
+�
+are the coefficients involved in the interpolation process and r j are the interpolation stencil points. In
+practice, this approach has two main advantages: (a) it allows one to use quadratures of order four or five since those
+result in non-space-filling stencils, they are unusable with the on-lattice solvers [68], (b) freedom over the choice
+of the time-step as the streaming does not need to fall on-grid [69, 70]. On the other hand, the introduction of the
+interpolation operator strips the LBM from its strictly conservative property. The interpolation-supplemented LBM
+can only guarantee global mass conservation for uniform grids [68].
+4.2.2. Correction for the diagonal components of the equilibrium third-order moments tensor
+In LBM schemes taking account of the correction term the system of PDE’s changes into:
+∂t fi + ci · ∇ fi = Ωi + Ψi,
+(418)
+where Ψi denotes the correction term derived in Eqs. (395) and (402). The emergence of this additional term only
+affects the previously-detailed process of discretization in time and space through the change of variable:
+¯fi = fi − δt
+2 Ωi − δt
+2 Ψi,
+(419)
+¯f eq
+i
+= f eq
+i ,
+(420)
+Ωi =
+1
+τ + δt/2
+� ¯f eq
+i
+− ¯fi
+�
+−
+δt/2
+τ + δt/2Ψi,
+(421)
+which in turn leads to the following final algebraic system:
+¯fi (r + ciδt, t + δt) − ¯fi (r, t) = δt
+¯τ
+�
+f eq
+i
+(r, t) − ¯fi (r, t)
+�
++
+�
+1 − δt
+2¯τ
+�
+Ψi.
+(422)
+This consistent derivation of the extended LBM holds for any form of the correction term, whether it is introduced
+simply as a Hermite-expanded term [64] or the extended equilibrium approach [71].
+56
+
+4.3. Introduction of external body forces
+Introduction of body force contributions in the context of LBM boils down to finding suitable approximations to
+the body force term F
+ρ · ∇v f in the Boltzmann equation. A large number of approaches and approximations have been
+devised over the years; We will restrict our review to the most widely used schemes here. For a more in-depth study
+of different forcing schemes we invite interested readers to look into [72, 73, 74]. Given that all approximations can
+be recast into a generic form made up of a discrete source term Fi and a redefined real velocity ureal , they will all be
+presented in that form:
+fi(r + ciδt, t + δt) − fi(r, t) = δt
+¯τ
+�
+f eq
+i (ρ, u) − fi(r, t)
+�
++ Fi,
+(423)
+with:
+u = 1
+ρ
+�
+i
+ci fi.
+(424)
+The aim of the approximation here being recovery of correct hydrodynamic limit, i.e. Euler+NS level dynamic we
+will have a more detailed look at the moments of Fi appearing there. It is clear that zeroth- and first-order moments
+will appear at the Euler level:
+∂(1)
+t ρ + ∇ · ρu = 0,
+(425)
+∂(1)
+t ρu + ∇ · ρu ⊗ u + ∇ · ρc2
+sI +
+�
+i
+ciFi = 0,
+(426)
+At the NS level the CE analysis leads to:
+∂(2)
+t ρ + 1
+2∇ ·
+�
+i
+ciFi = 0,
+(427)
+∂(2)
+t ρu + 1
+2∂(1)
+t
+�
+i
+ciFi + 1
+2∇ ·
+�
+i
+ci ⊗ ciFi − ∇ ·
+�1
+2 − ¯τ
+δt
+� �
+i
+ci ⊗ ciFi + ∇ ·
+�1
+2 − ¯τ
+δt
+� �
+u ⊗ F + u ⊗ F†�
++∇ · ρc2
+s
+�1
+2 − ¯τ
+δt
+� �
+∇u + ∇u†�
+= 0.
+(428)
+For this system to match the targeted hydrodynamic limit it is obvious that one must have:
+�
+i
+ciFi = δtF,
+(429)
+ρu + 1
+2
+�
+i
+ciFi = ρureal,
+(430)
+�
+i
+ci ⊗ ciFi = δt2
+4ρ¯τ F ⊗ F + δt
+�
+u ⊗ F + u ⊗ F†�
+.
+(431)
+4.3.1. Shan and Chen’s forcing scheme
+This approach was initially proposed by Shan and Chen to model multi-phase fluid systems [12]. In Shan and
+Chen’s forcing scheme the velocity used in the computation of the discrete equilibrium is shifted by ∆u = ¯τF
+ρ . While
+in its original form, as presented in [12], the force contribution only appears in the EDF, the corresponding discrete
+time-evolution equations can be re-written as:
+fi(r + ciδt, t + δt) − fi(r, t) = δt
+¯τ
+�
+f eq
+i (ρ, u) − fi(r, t)
+�
++ δt
+¯τ
+�
+f eq
+i (ρ, u + ∆u) − f eq
+i (ρ, u)
+�
+������������������������������������������������������������������������
+Fi
+.
+(432)
+Additionally the real fluid velocity computation is also affected by the force as:
+ureal = 1
+ρ
+�
+i
+ci fi + δtF
+2ρ .
+(433)
+57
+
+The source term has the following zeroth- to second-order moments:
+�
+i
+Fi
+=
+0,
+(434)
+�
+i
+ciFi
+=
+Fδt,
+(435)
+�
+i
+ci ⊗ ciFi
+=
+δt
+�
+F ⊗ u + F ⊗ u†�
++ δt¯τ
+ρ F ⊗ F.
+(436)
+This means that this approach satisfies condition (429). However, given the definition of the real velocity,
+ρureal ⊗ ureal = ρu ⊗ u + δt
+2
+�
+u ⊗ F + u ⊗ F†�
++ δt2
+4ρ F ⊗ F,
+(437)
+it admits an error of the following form in the convective term of the NS level momentum balance equation:
+δconvection = ∇ · δt2
+ρ
+� ¯τ2
+δt2 − 1
+4
+�
+F ⊗ F.
+(438)
+It should be noted that, expanding the body force as a power series of the smallness parameter, this deviation in the
+second-order moment would scales with ε3 and therefor not appear formally in the momentum balance equation at the
+Navier-Stokes level. Nevertheless, for cases involving large force contributions higher-order dynamics can spoil Euler
+and NS level behavior. Later on, this scheme was improved upon via a Hermite expansion of the force term in the
+Boltzmann equation [75]. Using the Hermite expansion of the distribution function, the force term can be expanded
+as [75, 49]:
+F · ∇v f =
+�
+n=0
+(−1)n
+n!
+F ⊗ an−1 : ∇n+1
+v
+w(v) = −w(v)
+�
+n=0
+1
+(n − 1)! F ⊗ an−1 : Hn(v).
+(439)
+Absorbing the force in the Boltzmann equation into the equilibrium and using the above-presented Hermite expansion
+of the body force term a correction to the original Shan and Chen scheme was proposed as:
+Fi = δt
+¯τ
+�
+f eq
+i (ρ, u + ∆u) − f eq
+i (ρ, u)
+�
+− ρwi¯τ
+2
+�(ci · F)2
+c4sρ2
+− F2
+c2sρ2
+�
+,
+(440)
+which changes the second-order moment of the force term into:
+�
+i
+ci ⊗ ciFi = δt
+�
+u ⊗ F + u ⊗ F†�
+,
+(441)
+eventually leading to an error term that is still present but independent from the relaxation time:
+δconvection = −∇ · δt2
+4ρ F ⊗ F.
+(442)
+4.3.2. Luo’s scheme
+As an approximation to the body force term appearing in the Boltzmann expression, and assuming a near equilib-
+rium flow, Luo proposed an expansion similar to that used for the equilibrium [76], i.e.
+F
+ρ · ∇v f ≈ ρw(v) [a0 + a1 · v + a2 : v ⊗ v + . . . ] ,
+(443)
+where expansion coefficients ai are computed via the following constraints on the moments of the body force term:
+� F
+ρ · ∇v fdv
+=
+0,
+(444)
+�
+v F
+ρ · ∇v fdv
+=
+−F,
+(445)
+�
+v ⊗ v F
+ρ · ∇v fdv
+=
+−F ⊗ u − F ⊗ u†.
+(446)
+58
+
+Applying these constraints and limiting the expansion to order two the following space/time-continuous approxima-
+tion is obtained:
+F
+ρ · ∇v f = −w(v)
+� F · (v − u)
+c2s
++ (v · u)v · F
+c4s
+�
++ O
+�
+v3, u2�
+,
+(447)
+which after discretization in phase space results in:
+F
+ρ · ∇v f = −wi
+� F · (ci − u)
+c2s
++ (ci · u)ci · F
+c4s
+�
+.
+(448)
+One interesting point worth noting in Luo’s forcing scheme is that over the years a point of confusion seems to have
+been installed in the literature [72, 73, 74]; In the original article [76], the author has used a first-order approximation
+to the collision integral after integration along characteristics, i.e.
+� t+δt
+t
+1
+τ
+�
+f eq
+i (r + cit′, t′) − fi(r + cit′, t′)
+�
++ Fi(r + cit′, t′)dt′ ≈ δt
+τ
+�
+f eq
+i (r, t) − fi(r, t)
+�
++ δtFi(r, t),
+(449)
+naturaly leading to the following time-evolution equations:
+fi(r + ciδt, t + δt) − fi(r, t) = δt
+τ
+�
+f eq
+i
+− fi
+�
++ Fiδt,
+(450)
+where contrary to the second-order approach using the trapezoidal rule, the relaxation time and distribution functions
+have not been redefined. Most articles following this scheme apply this final expression in the context of the classical
+lattice Boltzmann model involving a re-definition of the relaxation coefficient and distribution function. Properly
+transposing Luo’s scheme to a second-order LBM would instead lead to:
+Fi = δt
+¯τ
+�
+f eq
+i (ρ, u + δtF
+2ρ ) − f eq
+i (ρ, u)
+�
++δt
+�
+1 − δt
+2¯τ
+�
+wi
+� F · (ci − u)
+c2s
++ (ci · u)ci · F
+c4s
+�
++
+�
+1 − δt
+2¯τ
+� wiδt2
+ρ
+�(ci · F)2
+c4s
+− F2
+c2s
+�
+,
+(451)
+with,
+ureal = 1
+ρ
+�������
+Fδt
+2
++
+�
+i
+ci fi
+������� .
+(452)
+This leads to an error in the convection term of the form:
+δconvection = ∇ · δt
+�
+¯τ − δt
+2
+� F ⊗ F
+ρ
+.
+(453)
+This approach is exactly equivalent to Guo’s forcing scheme [77]. A number of articles have reported better stability
+of this approach as compared to other forcing schemes [72], however this is clearly a consequence of the first-order
+nature of the model as (mis-)used there.
+4.3.3. He et al’s scheme
+The next scheme, proposed by He et al. relies on the following fundamental approximation when evaluating the
+body force contribution [78]:
+f(r, t, v) ≈ f eq(r, t, v),
+(454)
+leading to:
+F
+ρ · ∇v f ≈ F
+ρ · ∇v f eq = F
+ρ · v − u
+c2s
+f eq,
+(455)
+which after discretization in phase space, integration along characteristics and using the trapezoidal rule results in:
+Fi = δt
+¯τ
+�
+f eq
+i (ρ, u + δtF
+2ρ ) − f eq
+i (ρ, u)
+�
++ δt
+�
+1 − δt
+2¯τ
+� F
+ρ · ci − u
+c2s
+f eq(ρ, u + δtF
+2ρ ),
+(456)
+with
+ureal = 1
+ρ
+�������
+Fδt
+2
++
+�
+i
+ci fi
+������� .
+(457)
+59
+
+4.3.4. Guo’s scheme
+Guo proposed a modified forcing scheme taking into account so-called discrete effects in [77]. In essence Guo
+followed an approach quite similar to Luo to derive the new scheme, i.e. moment matching. Similar to Luo [76],
+Guo started with a polynomial approximation to the force contribution with coefficients to be fixed by moments
+constraints. However, at the difference of Luo, moments constraints were extracted from a Chapmann-Enskog analysis
+of the lattice Boltzmann equations, i.e. after discretization in space and time. Therefore, the remark made in the
+previous paragraphs about the exact correspondence between Luo’s scheme, once a second-order integration along
+characteristics has been applied, and Guo’s discrete forcing scheme is not surprising at all.
+4.3.5. Kupershtokh’s scheme
+This approach, also referred to as the exact difference method approximates the force contributions as [79, 80]:
+Fi =
+�
+f eq
+i (ρ, u + ∆u) − f eq
+i (ρ, u)
+�
+,
+(458)
+with, different from the Shan-Chen scheme, ∆u =
+Fδt
+ρ . Furthermore the velocity u is computed as the first-order
+moment of the distribution function with no additional terms and the real fluid velocity, ureal, is computed as ureal =
+u + Fδt
+2ρ . At the difference of the Shan-Chen scheme the second-order moment of the source term is:
+�
+i
+ci ⊗ ciFi = δt
+�
+F ⊗ u + F ⊗ u†�
++ δt2
+ρ F ⊗ F,
+(459)
+which does not show any dependence on the relaxation. As for previously-listed schemes, the exact difference method
+also admits a convective error of the form:
+δconvective = ∇δt
+�
+¯τ − δt
+4
+� F ⊗ F
+ρ
+.
+(460)
+This deviation can be eliminated by introducing an additional contribution in the source term as:
+Fi =
+�
+f eq
+i (ρ, u + ∆u) − f eq
+i (ρ, u)
+�
+−
+�
+1 − 1
+4¯τ
+�
+wiH2 : F ⊗ F
+ρ
+.
+(461)
+The different strategies to incorporate body forces into the LBM are listed in Table 4.
+Approach
+Fi
+ureal
+Leading-order error
+Improvement
+Shan and Chen [12]
+Eq. (432)
+Eq. (433)
+Eq. (438)
+Eq. (440)
+Luo [76]
+Eq. (451)
+Eq. (452)
+Eq. (453)
+None
+Guo [77]
+Eq. (451)
+Eq. (452)
+Eq. (453)
+None
+EDM [79]
+Eq. (458)
+Eq. (451)
+Eq. (460)
+Eq. (461)
+Table 4: Summary of body force methods in LBM.
+4.4. Stability of LB-BGK
+The applicability range of different closures for the discrete equilibrium distribution functions was characterized
+in previous sections by monitoring deviations of moments of order two and three. Here we discuss the issue of
+application range with more details via the linear stability and positivity domain of the discrete equilibrium distribution
+functions. Prior to that we also discuss a numerical artifact brought about by the isothermal assumption of the classical
+LBM responsible, in part, for the stability of the solver.
+60
+
+4.4.1. Isothermal closure: spurious bulk viscosity and stabilization of normal modes
+Although widely used for simulation in the incompressible regime, it is well known that the LBM relies instead
+on an isothermal closure leading to a fixed and finite speed of sound, cs. For a characteristic convective velocity
+U, in the limit U/cs → 0 it is expected to recover the incompressible flow behavior. This means that contrary to
+classical incompressible solvers with the Poisson equation as closure for the pressure field, here ∇ · u � 0 and cs � ∞,
+which in turn points to presence of so-called acoustic eigen-modes that are damped at a rate η, also referred to as the
+bulk viscosity. For low-dissipative central-in-space discretization methods like the LBM, one must therefor guarantee
+positivity of the dissipation rates of both shear and acoustic modes. However, it is well known that for a mono-atomic
+molecule η=0. Given that only translational degrees of freedom are accounted for, the LBM is based on a mono-
+atomic molecule and should lead to zero bulk viscosity. This is readily observed by looking at the non-equilibrium
+stress tensor of the Boltzmann equation at the NS level:
+Π(1)
+αβ = −τ
+�
+∂(1)
+t
+�
+vαvβ f eqdv + ∂γ
+�
+vγvαvβ f eqdv
+�
+,
+(462)
+where the first and second terms can be, after some algebra, re-written as:
+�
+vγvαvβ f eqdv = ρuαuβuγ + ρkBT
+m
+�
+uαδβ,γ
+�
+cyc ,
+(463)
+and
+∂(1)
+t
+�
+vαvβ f eqdv = δαβ∂(1)
+t ρkBT
+m + uα∂(1)
+t ρuβ + uβ∂(1)
+t ρuα − uαuβ∂(1)
+t ρ.
+(464)
+Using the mass, momentum and internal energy balance equations,
+∂(1)
+t ρkBT
+m + ∂αρkBT
+m uα = −2ρkBT
+Dm ∂αuα,
+(465)
+the non-equilibrium stress tensor can be re-written as:
+Π(1)
+αβ = −τρkBT
+m
+�
+∂αuβ + ∂βuα − 2
+D∂γuγ
+�
+,
+(466)
+confirming the absence of bulk viscosity. In the classical LBM, an isothermal closure is used for energy/temperature
+meaning the solvability condition for energy is replaced by kBT
+m = kBT0
+m0 leading to the following non-equilibrium stress
+tensor [81]:
+Π(1)
+αβ = −τρkBT
+m
+�
+∂αuβ + ∂βuα − 2
+D∂γuγ
+�
+− τρ2kBT
+Dm ∂γuγ,
+(467)
+meaning η = 2
+Dµ. After discretization in phase space, space and time this property is maintained and one recovers a
+non-zero bulk viscosity for the classical isothermal LBM:
+η = 2c2
+s
+D
+�
+¯τ − δt
+2
+�
++ O(Ma2),
+(468)
+where the Galilean-variant error comes from deviation in the diagonal components of the equilibrium third-order
+moments which can be eliminated via appropriate correction terms derived in previous sections.
+4.4.2. Positivity of the discrete equilibria
+Numerical instability in the LBM has been often tied to the absence of a positivity constraint on the discrete
+populations [82, 83, 84]. In the specific case of LBM for advection-diffusion equations the positivity region of the
+discrete EDF has been shown to coincide with the linear stability domain in the limit of vanishing diffusion coeffi-
+cient [85, 86, 87]. To that end, before conducting linear stability analyses we look at the positivity domains of different
+discrete EDFs. The positivity domains of the second-order polynomial, product-form and entropic EDFs are shown
+in Figs. 5, 6 and 7. While the polynomial forms of the EDF, both second-order and product form, do not guarantee
+positivity of the EDF for all velocities, the entropic EDF ensures that equilibrium populations remain positive for all
+velocities −1 ≤ uαδr/δt ≤ 1.
+However, as will be seen in the next chapter, different from the advection-diffusion
+LBM the positivity domain is not necessarily a reflection of linear stability.
+61
+
+Figure 5: Illustration of positivity of the second-order polynomial EDF. Left: Domain ensuring positivity of discrete equilibrium populations in
+red. Right: Values of three discrete populations as a function of ux/cs for uy/cs = 0.
+Figure 6: Illustration of positivity of the product-form EDF. Left: Domain ensuring positivity of discrete equilibrium populations in red. Right:
+Values of three discrete populations as a function of ux/cs for uy/cs = 0.
+4.4.3. Linear stability of discrete solver
+The von Neumann (VN) stability analysis aims at studying the time evolution of a perturbation ¯f
+′
+i that is injected
+into the linearized discrete time evolution equations. The perturbation is expanded as a combination of standing waves,
+whose propagation speed and attenuation rate will be obtained as a result of the VN analysis. A positive attenuation
+rate will result in a growth of the error at the corresponding wave-length and linear instability of the solver for the
+set of parameters considered (¯τ, Ma, etc). On the contrary, the scheme is linearly stable if it remains negative for all
+wave-numbers.
+Furthermore, the spectral behavior and accuracy can be readily analyzed by comparing the spectral dispersions and
+dissipations to the theoretical modes obtained from the linearized NS equations. The NS theoretical modes for an
+isothermal flow can be expressed as [88]:
+ωshear = u · k − iνk2,
+(469a)
+ωacoustic = (u ± cs) · k − i
+�D − 1
+D
+ν + η
+2ρ
+�
+νk2,
+(469b)
+where D is the physical dimension of the system and k the wave-number vector. As a consequence, the VN stability
+analysis can be used to evaluate the spectral behavior and linear stability domain of a LBM for a given set of param-
+62
+
+1
+1.5
+0.8
+1
+feq
+3
+feq
+0.5
+1
+0.6
+S
+req
+0
+0
+0.4
+-0.5
+-1
+0.2
+-1.5
+0
+-1
+0
+1
+-2
+-1
+0
+1
+2
+u /c
+u /c
+x
+s1.5
+0.8
+1
+0.5
+0.6
+c
+feq
+0
+IJ
+0
+0.4
+-0.5
+-1
+0.2
+-1.5
+0
+-1
+0
+1
+-2
+-1
+0
+1
+2
+u /c
+u. /c
+x
+S
+xFigure 7: Illustration of positivity of the entropic EDF. Left: Domain ensuring positivity of discrete equilibrium populations in red. Right: Values
+of three discrete populations as a function of ux/cs for uy/cs = 0.
+eters. As such it can be perceived as a tool to objectively evaluate the stabilization properties of different collision
+models, on the basis of necessary conditions. The latter comes from the fact that the analysis relies on a linearization
+step and as such gets the sufficient condition for stability only under the linear regime assumption (small amplitude
+perturbations). It has been widely used in the past to evaluate the stability properties of the LBM. Interested readers
+are referred to [89, 90, 91, 87, 92, 93, 94, 88], among other sources.
+As mentioned previously, the equilibrium state is one of the most important components of a kinetic scheme and
+controls, for the most part, the leading-order dynamics of the system (i.e. the macroscopic PDEs of interest), but
+also the behavior of higher-order (errors, ghost modes) terms. The effects of the EDF on leading-order terms were
+studied in previous sections. In this subsection, using the VN formalism we look at the effect of the EDF on the
+linear stability domain. To do so the eigenvalue problem of the VN equations is solved for different values of non-
+dimensional viscosities, over the entire wave-number space, i.e. kx and ky with a resolution of 100 points in each
+direction. The highest Mach number resulting in negative dissipation rates over all wave-numbers is retained as the
+linear stability limit. These limits are shown in Fig. 8. Looking at those results a number of points are worth noting:
+Figure 8: Linear stability domains of SRT collision operator with EDFs of orders (from left to right) two, three and four. The fourth-order expansion
+is equivalent to the product-form. Reproduced from [95].
+For all of these EDFs, regardless of the value of the non-dimensional viscosity (Fourier number), the maximum stable
+Mach number never goes beyond Ma =
+√
+3 − 1 ≈ 0.732. This confirm the observation in Eq. 390:
+Mamax
+α
+= |umax
+α
+|
+cs
+=
+√
+3 − 1.
+(470)
+63
+
+1.5
+0.8
+1
+feq
+3
+0.5
+0.6
+S
+feq
+0
+fi
+0
+0.4
+-0.5
+-1
+0.2
+-1.5
+0
+-1
+0
+1
+-2
+-1
+0
+1
+2
+u_ /c
+u_ /c
+xsgo-
+HO
+0.6
+0
+1
+1
+a
+0.4
+/
+9
+0.2
+Q
+0
+10-3
+10-1 100
+10-5
+10-3
+10-1 100
+10-5
+10-3
+10-1 100
+10-5
+vSt/ Sr2
+vSt/Sr2
+vSt/Sr2Furthermore while the addition of third-order components appears not to have a large effect on the stability domain,
+the fourth-order component (which does not affect the terms appearing at the NS level) extends it.
+Apart from extending the linear stability domain, the addition of the fourth-order component results in more isotropic
+behavior especially for small values of the non-dimensional viscosity. The directional stability domains obtained with
+different orders of the EDF are shown in Fig. 9. It is also worth noting that the entropic EDF, is found to come with
+Figure 9: Illustration of anisotropy of linear stability domains for EDFs of orders (from left to right) two, three and four, and for seven different non-
+dimensional kinematic viscosities, i.e. (
+)5 × 10−4, (
+)1 × 10−3, (
+)5 × 10−3, (
+)0.01, (
+)0.05, (
+)0.1, (
+)0.5. Reproduced
+from [95].
+unconditional linear stability for all values of the Mach number supported by the stencil, i.e. Ma =
+√
+3, even for
+vanishing viscosities. This unconditional stability can be readily explained by the observations in Fig. 2, i.e. self-
+adjusting sound speed guaranteeing fastest mode propagates at a speed smaller than or equal to δr/δt. The stability
+domain is shown in Fig. 10. This in turn confirms the effectiveness of the discrete EDF construction approach in
+guaranteeing linear stability (by enforcing a discrete H-theorem). Finally, one can readily confirm the assertion made
+Figure 10: Illustration of linear stability domain for the entropic EDF for seven different non-dimensional kinematic viscosities, i.e. (
+)5×10−4,
+(
+)1 × 10−3, (
+)5 × 10−3, (
+)0.01, (
+)0.05, (
+)0.1, (
+)0.5. Reproduced from [95] and [93].
+in the previous subsections concerning the effect of third-order Hermite terms on the deviatoric components of the
+third-order moments tensor by looking at the spectral dissipation of physical modes. The spectral dissipation of the
+shear modes of the third and second-order EDF for three different Mach numbers are shown in Fig. 11. It is clearly
+observed that for the third-order EDF, in the limit of vanishing wave-numbers kx/δr → 0, the obtained dissipations
+converge to the correct value regardless of the Mach number. However for the second-order EDF signs of Galilean
+invariance problems are clearly observed as the continuum limit of shear mode dissipation changes with the Mach
+64
+
+π/2
+π/3
+π/6
+0
+0
+1
+2
+Maπ/2
+π/2
+π/2
+π/3
+π/3
+元/3
+π/6
+π/6
+π/6
+0
+0
+0
+0.5
+0
+0.5
+0
+0.5
+Ma
+Ma
+MaFigure 11: Shear mode dissipation rate (normalized by its physical counterpart) for (left) third- and (right) second-order EDF for three different
+Mach numbers, i.e. (in red) 0.1, (in blue) 0.2 and (in green) 0.3. The continuum reference is shown with a plain black line. Reproduced from [95].
+number.
+The results obtained in this subsection also point to the fact that the SRT collision operator becomes practically unus-
+able below non-dimensional viscosities of 10−3 − 10−4. Different strategies have been developed to allow simulations
+at lower non-dimensional viscosities. We will discuss some of these approaches in the next section.
+4.5. Extension of stability domain
+4.5.1. Relaxation of discrete populations in alternate spaces
+A first attempt at extending the stability domain of the LB-BGK solver, introduced in the early 2000s’ is the so-
+called Multiple Relaxation Time (MRT) collision model [96, 97, 98]. The idea behind this approach is to relax the
+discrete populations in a space other than the discrete populations; In principle this introduces additional parameters
+independent from the kinematic viscosity, opening the door for a more flexible equilibration path [98, 97]. The added
+degrees of freedom can be useful both physically and numerically [81]. In this approach, the BGK collision operator
+is written as:
+ΩMRT
+i
+= M−1SM
+�
+f eq
+i
+− fi
+�
+,
+(471)
+where M is the transformation matrix from discrete population to the relaxation space such that:
+Πi =
+�
+j
+Mi j fj,
+(472)
+where Πi are the moments chosen for the application of the collision operation. As seen in Eq. 471, using the
+transformation matrix M the discrete populations are taken to momentum space. Then the relaxation matrix S is
+applied and relaxed moments are converted back to discrete populations through M−1. The relaxation rates tensor S
+is defined as:
+S = diag( 1
+¯τ0
+, . . . ,
+1
+¯τQ−1
+),
+(473)
+where the operator diag is defined as:
+diag(A) = (A ⊗ 1) ◦ I,
+(474)
+with A a given vector, 1 a vector with elements 1, I the unitary tensor and ◦ the Hadamard product. For a typical
+DdQq stencil, q moments are needed to span the phase-space. The choice of the relaxation space, is the other important
+ingredient in this class of models both differentiating between different approaches listed below and controlling the
+numerical properties of the solver. For instance Lallemand and Luo [91] proposed a set of mutually orthogonal
+moments for the D2Q9 stencil defined as:
+Πi ∈ {Π0, 3(Πxx + Πyy) − 4Π0, , Πx, 3(Πxxx + Πxxy) − 5Πx, Πy, 3(Πyyy + Πxyy) − 5Πy, Πxx − Πyy, Πxy}.
+(475)
+65
+
+1.8
+1.5
+1.6
+1.4
+1.2
+0.5
+0.8
+0
+元/4
+π/2
+3元/4
+0
+π/4
+π/2
+3元/4
+元
+T
+kaSr
+kaSrWith this choice of moments for the relaxation it is clear that the relaxation rates of the last two moments corresponds
+to shear viscosity and that of the second moment to the bulk viscosity while the rest can be freely tuned for stabil-
+ity [97], optimal dispersion [88], fixing the boundary position for the half-way bounce-back boundary condition [99]
+etc.. It is interesting to note that this specific choice of moments space along with the optimized set of ghost relaxation
+rates do not, as opposed to the conclusions of [91], actually extend the linear stability domain of the BGK collision
+operator as shown in Fig. 12. This might be explained by the fact that in [91], the authors assumed the wave-number
+Figure 12: Linear stability domain of the MRT collision operator of [91] with the corresponding set of optimized relaxation rates. Following the
+original publication the discrete equilibrium is taken to be a second-order polynomial expansion.
+vector k always parallel to the velocity vector u which is not a sufficient condition for linear stability. Here the full
+2-D space of wave-number vectors has been scanned for all considered velocities resulting in a smaller domain of
+stability. While the moments chosen as basis for the MRT realization of [91] are orthogonal, other alternatives based
+on weighted orthogonal moments have also been proposed. For instance the Hermite polynomials form a basis of
+moments that are mutually orthogonal with respect to the weighted dot-product and are defined as:
+Πi ∈ {Π0, Πx, Πy
+������
+a1
+,
+a2
+��������������������������������������������������
+Πxy, Πxx − c2
+s, Πyy − c2
+s, Πxxy − c2
+sΠy, Πxyy − c2
+sΠx
+��������������������������������������������������������
+a3
+,
+a4
+��������������������������������������������������������������
+Πxxyy − c2
+s
+�
+Πxx + Πyy
+�
++ c4
+s}.
+(476)
+Below we will look into two other classes of MRT collision models that present conceptual singularities with respect
+to other realizations, i.e. the two relaxation time model and central moments-based MRT.
+Two relaxation time model. As noted in [100], using the full set of moments leads to a number of free parameters, the
+ghost moments relaxation coefficients, for which no formal physical closures exist. As previously mentioned, apart
+from the entropic argument, only a posteriori closures based on numerical arguments can be devised for these free
+parameters. Another way around this issue is to adopt targeted, on specific moments of the distribution function, mini-
+malist MRT models. The TRT (Two Relaxation Time) collision operator developed and proposed by I. Ginzburg is an
+example of these minimalist models [101, 102, 103]. In this collision model the distribution function is decomposed
+into symmetrical, f +
+i , and non-symmetrical parts, f −
+i , defined as [103]:
+f +
+i = fi + f¯i
+2
+,
+(477a)
+f −
+i = fi − f¯i
+2
+,
+(477b)
+resulting in two relaxation times, ¯τ+ and ¯τ−, with the first one tied to the fluid viscosity. The collision operator is then
+expressed as [102]:
+ΩTRT
+i
+= 1
+¯τ+
+�
+f eq+
+i
+− f +
+i
+�
++ 1
+¯τ−
+�
+f eq−
+i
+− f −
+i
+�
+.
+(478)
+66
+
+0.5
+0.4
+Q
+101
+0.3
+a
+N
+@
+0.2
+0.1
+0
+10-3
+10-1
+100
+Vot/8r2As demonstrated in [104], judicious choices of the free parameter, the so-called “magic values”, can lead to, among
+other effects, the wall being placed exactly half-way when used with the half-way bounce-back boundary condition.
+Defining :
+Λ =
+� δt
+¯τ+ − 1
+2
+� � δt
+¯τ− − 1
+2
+�
+,
+(479)
+it can be shown that setting Λ = 3/16 places the wall half-way [105], while Λ = 1/6 and Λ = 1/12 cancel out,
+respectively, the third- and fourth-order spatial error terms [106, 107] and Λ = 1/4 results in optimal stability in that
+specific relaxation space [108].
+The lattice kinetic scheme. Another example of a minimalist MRT scheme is that of the so-called LKS (lattice kinetic
+scheme) [109, 110]. This collision model is a TRT scheme in the space of Hermite moments, where second-order
+moments are relaxed using the fluid viscosity while higher-order moments (three and four) are relaxed using a free
+parameter [92]. For the LKS the collision operator is written as [111, 109]:
+ΩLKS
+i
+= −1
+¯λ
+�
+fi − f eq,LKS
+i
+�
+.
+(480)
+The second relaxation coefficient ¯λ is related to the SRT relaxation coefficient through [110]:
+¯λ − A = ¯τ,
+(481)
+where A is a constant fixed by the choice of the free parameter. The EDF is then defined as [92]:
+f eq,LKS
+i
+= f eq
+i
+− A
+¯τ
+wi
+2 aneq
+2
+: H2,i.
+(482)
+The original regularized lattice Boltzmann method (RLBM), as will be shown in the next sections, is an LKS solver
+where the free relaxation coefficient is set to 1 [92]. This collision operator has been applied to a variety of configura-
+tions ranging from multi-phase [112] to non-Newtonian flows [113] and advection-diffusion equations with variable
+diffusion coefficients [114, 115].
+4.5.2. Central moments-based decomposition
+In the Central Moments Multiple Relaxation Time (from here on referred to as CM-MRT) model, while the
+paradigm is quite similar to the MRT, a different set of moments are used: the central moments, designated by
+�Πx . . . x
+����
+×p
+y . . . y
+����
+×q
+z . . . z
+����
+×r
+and defined as [116, 117]:
+�Πx . . . x
+����
+×p
+y . . . y
+����
+×q
+z . . . z
+����
+×r
+=
+�
+i
+�ci,x − ux
+�p�
+ci,y − uy
+�q�ci,z − uz
+�r fi.
+(483)
+Taking again the example of the D2Q9 stencil with the Hermite coefficients as the projection space and a fourth-order
+expansion of the EDF results in the following central equilibrium moments [118, 119, 120]:
+�Πeq = {ρ, 0, 0, 0, 0, 0, 0, 0, 0}.
+(484)
+The stability domain of this collision model is shown in Fig. 13. From the stability domain one can already see
+that setting ν′ = ν which is equivalent to the SRT operator is not the optimal choice in terms of linear stability. An
+optimal route can be observed at ν′δt
+δr2 ≈ 0.167 which, as will be seen in the next section, is equivalent to the recursive
+regularized collision operator. While the Hermite-based moments space does not allow for independent control over
+bulk viscosity this can readily be achieved by modifying the second-order moments resulting in the following system:
+Πi ∈ {�a0,�ax,�ay,�axy,�axx −�ayy,�axx +�ayy,�axxy,�axyy,�axxyy},
+(485)
+where �ai are central Hermite coefficients. Here the trace of the second-order moments is relaxed independently
+allowing for an independent bulk viscosity. It must be noted that when used in combination with the correction for
+diagonal components of the third-order equilibrium moments the coefficient in front of the correction term must be
+changed to 1 −
+δt
+¯τ+¯τη where ¯τη is the relaxation time tied to the bulk viscosity [121].
+67
+
+Figure 13: Linear stability domain of the central Hermite MRT collision operator. Here second-order moments relax with the viscosity while
+higher-order ghost moments relax with another pseudo-viscosity ν′. Reproduced from [95].
+4.5.3. Closures for the relaxation rates: entropic
+The single relaxation time entropic model. The original entropic LBM ensures stability of the solver by imposing a
+monotonous decrease of a discrete entropy function. While a number of different discrete entropy functionals have
+been proposed in the context of the ELBM [122, 123], the following form has gained the most attention [124, 125,
+126, 28, 127]:
+H =
+�
+i
+fi ln
+� fi
+wi
+�
+.
+(486)
+In practice, the monotonicity of the discrete entropy is enforced using a two-step linear reconstruction achieved
+through the following modified time-evolution equation [124, 125]:
+fi (r + ciδt, t + δt) − fi (r, t) = βγ
+�
+f eq
+i
+(r, t) − fi (r, t)
+�
+,
+(487)
+where β is tied to the fluid viscosity as:
+β =
+δt
+2τ + δt,
+(488)
+with τ = ν/c2
+s, while γ is obtained by solving the following system [128]:
+H ( f ∗) = H ( f) ,
+(489)
+with:
+f ∗
+i = fi + γ
+�
+f eq
+i
+− fi
+�
+.
+(490)
+This two-step reconstruction procedure is illustrated in Fig. 14. In the first step, the equal entropy mirror state relative
+to the equilibrium, f ∗, is found by solving the non-linear equation shown in Eq. 489. As observed there γ is the
+maximum path length not resulting in an increase in entropy [129]. It is interesting to note that at thermodynamic
+equilibrium Eq. 489 has the non-trivial root γ = 2 which corresponds to the SRT collision operator [129]. In the second
+step, dissipation is introduced via the parameter β. The solution to Eq. 489 can be obtained using a Newton-Raphson
+iterative solver as:
+γn+1 = γn − Gn
+∂γGn ,
+(491)
+with:
+Gn = H �f ∗n� − H ( f) ,
+(492)
+68
+
+0.8
+100
+10-1
+0.6
+VSt/ sr2
+Ma
+0.4
+10-3
+0.2
+10-5
+10-1 100
+10-5
+10-3
+VSt / Sr2Figure 14: Schematic representation of the relaxation process in the ELBM. Dashed lines represent entropy levels while the triangle illustrates the
+positivity polytope.
+and:
+∂Gn
+∂γ =
+�
+i
+�
+1 + ln
+� f ∗
+i
+n
+wi
+�� �
+f eq
+i
+− fi
+�
+,
+(493)
+where γn and γn+1 are solutions obtained in the previous and current iterations. The iterative root-finding algorithm
+being rather expensive (especially when the populations get away from equilibrium) alternative approaches have been
+developed in recent years [124, 129]. These approximate solutions are also useful in the vicinity of equilibrium as the
+Newton-Raphson solver might diverge there.
+Extension of the entropic closure to multiple relaxation rate formulations. The two-relaxation time entropic formula-
+tion is realized by writing discrete populations as [100]:
+fi = ki + si + hi.
+(494)
+where the kinematic part ki, represents contributions from conserved moments, si contributions from the stress and hi
+all higher-order moments contributions. Considering the discrete time evolution equation:
+fi (r + ciδt, t + δt) =
+�
+1 − δt
+2¯τ
+�
+fi (r, t) + δt
+2¯τ f mirr
+i
+(r, t) ,
+(495)
+Considering invariance of conserved moments and physical constraint on the relaxation rate of second-order moments
+defining si, the mirror state can be written:
+f mirr
+i
+= ki +
+�
+2seq
+i − si
+�
++ (1 − γ)hi + γheq,
+(496)
+where the free parameter γ here allows independent control over the relaxation rate of higher-order moments. This
+free parameter is found by minimizing the discrete entropy in the post-collision state, f ′
+i :
+dH( f ′)
+dγ
+= 0,
+(497)
+which upon expansion around equilibrium up to the first non-vanishing order results in [130]:
+γ
+2 = ¯τ
+δt −
+�
+1 − ¯τ
+δt
+� ⟨∆s|∆h⟩
+⟨∆h|∆h⟩,
+(498)
+where ∆si = seq
+i − si, ∆hi = heq
+i − hi, and the entropic scalar product ⟨|⟩ is defined as:
+⟨X|Y⟩ =
+Q
+�
+i=1
+XiYi
+f ∗
+i
+.
+(499)
+69
+
+It is interesting to note here that for a moments space where the moments are weighted-orthogonal in the co-moving
+reference frame, in the absence of body forces, the entropy minimizer free parameter γ → 2¯τ/δt setting all higher-
+order moments to the equilibrium state [131].
+4.5.4. The specific case of regularization
+The rational behind regularized collision operators is to filter out higher-order components of the distribution
+functions (in the sense of the Chapman-Enskog expansion). It can be shown that first-order terms appear at the NS
+level, while higher-order terms intervene at the Burnett, super Burnett etc. scales, not of interest in the context of
+the LBM. In the context of the regularized collision approach the non-equilibrium part of the distribution function
+is reconstructed using only first-order contributions, f neq
+i
+≈ f (1)
+i
+. The discrete time-evolution equation can be re-
+expressed as [132, 133]:
+fi (r + ciδt, t + δt) = f eq
+i
+(r, t) +
+�
+1 − δt
+¯τ
+�
+f neq
+i
+(r, t) .
+(500)
+Following the Hermite expansion used for the EDF, we can express the first-order component of the distribution
+function as:
+f (1)
+i
+= wi
+�
+n=2
+1
+n! a(1)
+n : Hn.
+(501)
+In the original regularized model [132] only the second-order Hermite polynomial was considered for the reconstruc-
+tion process:
+f (1)
+i
+= wi
+a(1)
+2 : H2
+2
+.
+(502)
+The only unknown in this equation is a(1)
+2 . In [132], this coefficient is computed as:
+a(1,PR)
+2
+≈ aneq
+2
+=
+�
+i
+H2 :
+�
+fi − f eq
+i
+�
+.
+(503)
+This approach to reconstructing the non-equilibrium part is commonly referred to as the projection regularization
+approach. In the context of the classical LB formulation with a second-order polynomial EDF, and given the orthogo-
+nality of the independent moments, this collision operator aimed at eliminating non-equilibrium effects of higher-order
+(kinetic) moments. It is interesting to note that this formulation has a number of shortcomings: (a) Errors in all com-
+ponents of the third-order moments tensor of the EDF (given the absence of higher-order terms in the EDF), and (b)
+presence of higher-order effects (tied to f (n)
+i
+with n ≥ 2) coming from the approximation used for a(1)
+2 . While initially
+believed to improve stability, the second-order projection-based regularized collision operator actually reduces the
+domain of stability as compared to the SRT collision operator as illusrtated in Fig. 15 via the linear stability domain.
+The latter can be, to some extent, cured using a CE-based closure for a(1)
+2 . Using this approach it can be shown that
+[134]:
+a(1,CE)
+2
+= −ρc2
+s
+¯τ
+δt
+�
+∇u + ∇uT�
+.
+(504)
+This expression can be computed using classical FD approximations [135], which has been shown to improve stabil-
+ity at the cost of non-negligible numerical dissipation considerably raising computational costs for direct numerical
+simulations. Recent publications have proposed to reduce dissipation by considering a weighted combination of the
+projection- and CE-based approaches [135, 65]:
+a(1)
+2 = σa(1,PR)
+2
++ (1 − σ) a(1,CE)
+2
+,
+(505)
+where σ is the weight.
+The first problem with the RLBM of [132], namely errors in the off-diagonal components of the third-order moments
+tensor can be accounted for by using third- (or fourth-)order terms in the EDF and using the recursive properties of
+the off-equilibrium Hermite coefficients [134], i.e.:
+a(1)
+α1α2...αm = a(1)
+α1,α2...αm−1uαn +
+�
+a(1)
+αnαn−1uα1uα2...uαn−2
+�
+cyc .
+(506)
+70
+
+Figure 15: Linear stability domain of the projection-based regularized collision model of [132] compared to the the SRT. Reproduced from [95].
+For the D2Q9 stencil, assuming a fourth-order isothermal polynomial EDF the different non-equilibrium Hermite
+coefficients are computed as:
+a(1)
+xyy = uxa(1)
+yy + 2uya(1)
+xy ,
+(507a)
+a(1)
+xxy = uya(1)
+xx + 2uxa(1)
+xy ,
+(507b)
+a(1)
+xxyy = uya(1)
+xxy + ux
+2a(1)
+yy + uxuya(1)
+xy .
+(507c)
+It can be shown, via simple algebra, that the projection-based recursive regularization approach is equivalent to a
+central Hermite collision operator with all ghost relaxation rates set to unity.
+71
+
+0.6
+@
+SRT
+/d
+0.2
+10-1100
+10°
+VSt / sr25. Extension to non-ideal fluids
+In this section we discuss introduction of non-ideal contributions to the LBM. Given that all models discussed in
+the present contribution recover some form of a second-gradient fluid, described first by van der Waals [6], we start
+by introducing fundamental aspects of this description of non-ideal fluids. The introduction of the target macroscopic
+system is followed by a brief overview of kinetic models for the dense fluid regime recovering the second-gradient
+fluid behavior in the hydrodynamic limit. Most widely used lattice Boltzmann models for isothermal non-ideal fluid
+flows are then reviewed and a comprehensive analysis of numerical and physical properties is provided.
+5.1. Second-gradient theory and non-ideal fluids thermodynamics
+5.1.1. Non-ideal equation of state: van der Waals
+At rather large pressures or in dense liquid phases the assumption used to derive the ideal gas equation of state, that
+molecules interact with each-other mostly via local elastic collisions does not hold anymore. The ideal gas law has
+two shortcomings in these regimes: it neglects the volume occupied by molecules via the local interaction assumption
+and it does not take into account long-range interactions. In doing so it fails to correctly model the behavior of so-
+called non-ideal fluids, e.g. co-existence of two phases at a given temperature and existence of a critical temperature
+Tc above which the fluid become single-phased. The first attempt at a model correctly describing non-ideal fluid
+thermodynamics was made by van der Waals [136] via a cubic equation of state:
+P =
+ρrT
+1 − bρ − aρ2,
+(508)
+where a and b are the long range interaction and volume exclusion constants. The thermodynamic behavior of the
+van der Waals equation of state is illustrated in Fig. 16 via the corresponding Clapeyron diagram. Looking at the
+Figure 16: Clapeyron diagram of van der Waals equation of state.
+isotherms of this equation of state, three categories can be identified: (a) T < Tc where
+∂P
+∂(1/ρ) = 0 has two roots and
+∂2P
+∂(1/ρ)2 = 0 one, (b) T = Tc where
+∂P
+∂(1/ρ) = 0 has a single root which is the same as and
+∂2P
+∂(1/ρ)2 = 0 and (c) T > Tc where
+the former equations do not admit any solutions. The transition isotherm, Tc, is known as the critical temperature and
+the combined root of
+∂P
+∂(1/ρ) = 0 and
+∂2P
+∂(1/ρ)2 = 0 on that isotherm identifies the critical state. The outer envelope shown
+in Fig. 16 is the saturation curve (also called binodal curve) corresponding to the liquid/vapor coexistence densities
+while the inner envelope is the spinodal curve. In the region within the spinodal envelope, referred to as the spinodal
+region, the thermodynamic states predicted by the van der Waals equation (more generally all cubic equations of
+state) are mechanically unstable,
+∂P
+∂(1/ρ) > 0. In the region between the spinodal and binodal envelops, referred to as
+the binodal region, the fluid is in a pseudo-stable state meaning that it is not mechanically unstable but at the same
+72
+
+2
+T>Tc
+1.5
+T=Tc
+Binodal curve
+P
+P
+>
+Spinodal curve
+0.5
+100
+101
+pc/ptime it is not a local minimzer of energy. As such when subjected to a small perturbation the fluid leaves the binodal
+region states towards the binodal curve which corresponds to local energy minima. In practice, a state in the bi- and
+spinodal regions corresponds to the coexistence of the liquid and vapor phases, i.e. both branches of the binodal curve,
+a distinctive feature for an interface. A point of cardinal importance is to identify the liquid and vapor coexistence
+states on given isotherms below the critical temperature.
+5.1.2. Co-existence densities: Common-tangent construction
+For the liquid and vapor states, ρl and ρv, in contact via an interface to coexist one can readily show that both states
+must have the same pressure, P, and chemical potential λ. A detailed derivation of these conditions will be given in
+5.1.5 for a flat interface. The interface equilibrium conditions can be re-cast in the following form:
+A(ρl) − A(ρv)
+ρl − ρv
+=
+∂A
+∂ρ
+�����ρv
+,
+(509)
+A(ρl) − A(ρv)
+ρl − ρv
+=
+∂A
+∂ρ
+�����ρl
+,
+(510)
+where we have introduced the free energy A, and λ = ∂A
+∂ρ . In simple words, the reformulated equilibrium conditions
+mean that in a plot of free energy versus density at a given temperature below critical the two minimizers of the bulk
+free energy, i.e. ρl and ρv, are characterized as two points that can be joined with a line of slope equal to the derivatives
+of the free energy at those points. This system of equations can be used to systematically find the two stable states of
+the fluid for a given temperature below critical and is known as the common tangent construction method. To further
+illustrate that consider the bulk free energy of the van der Waals fluid:
+A = ρrT ln
+�
+ρ
+1 − bρ
+�
+− aρ2.
+(511)
+Using this expression and conditions of Eqs.(509) and (510) one can find the coexistence densities at tany temperature.
+The free energy at T
+Tc = 0.9 along with the corresponding local minima and tangents are illustrated in Fig. 17. It is
+Figure 17: Illustration of the common tangent construction for the van der Waals equation of state at T/Tc = 0.9. In the y−axis W(ρ) =
+A(ρ) − ∂A
+∂ρ
+�����ρv
+(ρ − ρv) + A(ρv). The liquid/vapor coexsitence densities are found using Eqs.(509) and (510).
+readily observed that the derivatives at the two coexistence densities are the same and equal to the slope of the
+line joining them. The common tangent approach can therefor be used to systematically construct the liquid/vapor
+coexistence densities curve.
+73
+
+0.6
+0.4
+A
+0.2
+0
+p/pc
+1.6573
+0.4257
+-0.2
+0
+0.5
+1
+1.5
+2
+p/pc5.1.3. Co-existence densities: First-order transition and Maxwell construction
+As seen in the previous paragraph, below the critical point the free energy of non-ideal fluids admits two local
+minima separated by a local maxima indicating an energy barrier for transition. The concave nature of the free energy
+between those two stable states indicates that a homogeneous state is disadvantageous in-between them. In [137], dis-
+cussing an experiment where pressure variations are studied in a vessel containing a fixed amount of substance while
+gradually decreasing the volume Maxwell observes that ”We have hitherto supposed the experiment to be conducted
+in such a way that the density is the same in every part of the medium. This, however, is impossible in practice, as the
+only condition we can impose on the medium from without is that the whole of the medium shall be contained within
+a certain vessel. Hence, if it is possible for the medium to arrange itself so that part has one density and part another,
+we cannot prevent it from doing so. Now the points B and F represent two states of the medium in which the pressure is
+the same but the density very different. The whole of the medium may pass from the state B to the state F, not through
+the intermediate states C-D-E, but by small successive portions passing directly from the state B to the state F. In this
+way the successive states of the medium as a whole will be represented by points on the straight line B-F, the point B
+representing it when entirely in the rarefied state, and F representing it when entirely condensed. This is what takes
+place when a gas or vapour is liquefied. Under ordinary circumstances, therefore, the relation between pressure and
+volume at constant temperature is represented by the broken line A-B-F-G”. The original plot used by Maxwell to
+illustrate his purpose is shown in Fig. 18. In practice this means that in-between the liquid and vapor states, the fluid
+Figure 18: Plot used by Maxwell in [137] to illustrate phase transition. Vertical axis is pressure and horizontal axis is specific volume. The plot is
+reproduced from [137].
+is made up of a mixture of those two stable states which overcomes the concavity of free energy leading to instability.
+This is equivalent to replacing the free energy with its convex hull [138]. A simple way of determining the boundaries
+of this miscibility domain is the Maxwell construction. The thermodynamic argument leading to that approach is
+based on equality of Gibbs enthalpy, G = eint + Pv + T s where eint is internal energy, v the specific volume and s
+entropy, in the pure vapor and liquid states, i.e.
+Gv − Gl =
+� Pl
+Pv
+vdP −
+� Tl
+Tv
+sdT = 0,
+(512)
+which for an isothermal process, and using integration by parts leads to:
+� vv
+vl
+(P − Psat)dv = 0.
+(513)
+This can also be written as:
+� ρl
+ρv
+P − Psat
+ρ2
+dρ = 0.
+(514)
+In simple words, the Maxwell construction consists in finding the horizontal line P = Psat in the P − 1/ρ diagram
+intersecting a given isotherm below the critical temperature at three point that guarantees Eq. (514). The construction
+process is illustrated in Fig. 19. As shown in the left-hand plot of Fig. 19 for Psp1 < Psat < Psp2 where (ρsp1, Psp1)
+74
+
+Figure 19:
+Illustration of the Maxwell construction.
+(Left) Isotherms of of the van der Waals equation of state for T/Tc
+∈
+{0.5, 0.6, 0.7, 0.8, 0.9, 0.99}. Black markers are the liquid/vapor coexistence volumes. (right) Isotherm at T/Tc = 0.7 with (black square mark-
+ers) binodal and (blue circular markers) spinodal points. The binodal points guarantee that the red-colored and blue-colored domains have equal
+area.
+and (ρsp2, Psp2) are the two spinodal points P − Psat has systematically three non-degenerate roots 1/ρ1, 1/ρ2, 1/ρ3
+and an inflection point indicating the existence of two zones, S 1 =
+� 1/ρ2
+1/ρ1 (P − Psat)d(1/ρ) < 0, shown in red and
+S 2 =
+� 1/ρ3
+1/ρ2 (P − Psat)d(1/ρ) > 0, shown in blue in Fig. 19. The choice of pressure Psat that guarantees S 1 − S 2 = 0
+results in ρ1 = ρl and ρ2 = ρv. We have therefore introduced a second approach to determine the coexistence densities
+of non-ideal fluids completing our introductory discussion on the thermodynamics of uniform non-ideal fluids. The
+next step is to introduce the thermodynamic formalism describing non-uniform regions, i.e. interfaces.
+5.1.4. Free energy of non-uniform non-ideal fluid
+In the second-gradient theory as introduced in both [6] and [139], the presence of interfaces is conceptualized by
+endowing the fluid with capillary energy; In practice this means that free energy has both a classical bulk contribution
+function of local thermodynamic properties and a non-local contribution function of space-derivatives of, for single-
+component fluids, density:
+AvdW = AvdW(ρ, ∇ρ, ∇ ⊗ ∇ρ, . . . ).
+(515)
+Assuming that the non-homogeneities span over distances larger than the characteristic molecular interaction length,
+the free energy can be developed using a Taylor expansion around the homogeneous state as:
+AvdW = AvdW|0+∇ρ · ∂AvdW
+∂(∇ρ)
+�����0
++ ∇∇ρ : ∂AvdW
+∂(∇∇ρ)
+�����0
++ 1
+2∇ρ ⊗ ∇ρ : ∂AvdW
+∂(∇ρ)
+�����0
+⊗ ∂AvdW
+∂(∇ρ)
+�����0
++ . . .
+(516)
+where |0 refers to a function evaluated at the homogeneous state. Considering geometrical arguments such as symme-
+try and rotational-invariance the expression simplifies to the second-gradient free energy as introduced in [6]:
+AvdW = A + κ
+2|∇ρ|2,
+(517)
+with:
+κ = 2
+�
+2
+∂2A
+∂(|∇ρ|)2
+�����0
+−
+∂2A
+∂(∇2ρ)∂ρ
+�����0
+�
+.
+(518)
+where for the sake of readability we have replaced the bulk free energy AvdW|0 with A. The second term represents
+the interface energy while the bulk free energy is solely a function of the local density and temperature [139, 140].
+75
+
+2
+0
+P
+-1
+P
+-2 
+-3
+-4
+2
+100
+101
+100
+101
+pc/p5.1.5. Gibbs equilibrium conditions for a flat interface
+The equilibrium state of a 1-D infinite domain, in x-direction, made up of the vapor phase in one half and liquid
+phase in the other with an interface at the center is obtained as the minimizer of free energy under the constraint of
+constant total mass, i.e.
+δ
+� ∞
+−∞
+Ldx = 0,
+(519)
+with the Lagrange function L defined as
+L = A + κ
+2
+�����
+∂ρ
+∂x
+�����
+2
+− λρ,
+(520)
+where λ is the Lagrange multiplier for the mass constraint. Computing the variation term by term one gets
+�
+x
+δρ
+�∂A
+∂ρ − κ∂2ρ
+∂x2 − λ
+�
+dx,
+(521)
+which in turn leads to the equilibrium condition:
+∂A
+∂ρ − κ∂2ρ
+∂x2 − λ = 0,
+(522)
+subject to the boundary conditions: ρ(∞) = ρl, ρ(−∞) = ρv. As the gradient of density vanishes at infinity for both
+phases, we have
+∂A
+∂ρ
+�����ρl
+= ∂A
+∂ρ
+�����ρv
+= λ,
+(523)
+where we can readily identify λ as the bulk chemical potential, leading to the Gibbs equilibrium conditions, i.e.
+equality of chemical potentials
+λl = ∂A
+∂ρ
+�����ρl
+,
+λv = ∂A
+∂ρ
+�����ρv
+,
+(524)
+in both phases,
+λl = λv.
+(525)
+Multiplying (522) with dρ
+dx,
+d
+dx
+�������A − λρ − κ
+2
+�dρ
+dx
+�2������� = 0,
+(526)
+or
+P = −A + λρ + κ
+2
+�dρ
+dx
+�2
+= constant
+(527)
+Considering this expression at ±∞, and taking into account that the gradient of the density vanishes,
+� dρ
+dx
+�2 → 0 as
+x → ±∞, we get with the help of chemical potential equality (523):
+�
+ρ∂A
+∂ρ − A
+� �����ρl
+=
+�
+ρ∂A
+∂ρ − A
+� �����ρv
+(528)
+This enables to identify the pressure P (or equation of state, EoS),
+P = ρ∂A
+∂ρ − A,
+(529)
+and the result (528) is nothing but the remaining Gibbs equilibrium condition: The pressure is the same in both the
+phases,
+Pl = Pv.
+(530)
+76
+
+5.1.6. Korteweg stress tensor and second-gradient fluid balance equations
+The stress tensor of a non-ideal fluid in 3-D is obtained by extending the constrained minimization problem of
+(519) to 3-D leading to [8],
+TK = ∇ ⊗
+∂L
+∂(∇ρ) − LI,
+(531)
+where I is unit tensor and L is the Lagrange function in 3-D,
+L = A + 1
+2κ|∇ρ|2 − λρ,
+(532)
+and λ, corresponding to the chemical potential, is,
+λ = ∂A
+∂ρ − κ∇2ρ.
+(533)
+This in turn leads to the following Korteweg’s stress tensor [7]:
+TK =
+�
+P − κρ∇2ρ − 1
+2κ|∇ρ|2
+�
+I + κ∇ρ ⊗ ∇ρ,
+(534)
+where
+P = ρ∂A
+∂ρ − A,
+(535)
+is the thermodynamic pressure, or equation of state. From the local balance equations for mass and momentum one
+obtains the macroscopic governing laws for an isothermal capillary fluid:
+∂tρ + ∇ · ρu = 0,
+(536)
+∂tρu + ∇ · ρu ⊗ u + ∇ · T = 0,
+(537)
+where u is the fluid velocity and the stress tensor T is
+T = TK + TNS.
+(538)
+The Navier–Stokes viscous stress tensor reads,
+TNS = −µS − η(∇ · u)I,
+(539)
+where S is the trace-free rate-of-strain tensor,
+S = ∇u + ∇u† − 2
+3(∇ · u)I,
+(540)
+and µ and η are the dynamic and the bulk viscosity, respectively.
+The momentum balance equation (537) can be recast in the following form,
+∂tρu + ∇ · ρu ⊗ u + FK + ∇ · TNS = 0,
+(541)
+where Korteweg’s force FK is the divergence of the Korteweg pressure tensor,
+FK = ∇ · TK.
+(542)
+Eqs. (536) together with Eqs. (508), (534), (538), (539) and (540) describe the dynamics of the van der Waals fluid
+targeted by non-ideal lattice Boltzmann models in the hydrodynamic limit. One of the remarkable features of this
+description of non-ideal fluids and interfaces is that it can also be recovered from the kinetic theory of gases. In the
+next section we provide a brief description of simplified kinetic models leading to the second-gradient fluid model.
+77
+
+5.2. Kinetic models for non-ideal fluid
+To introduce a kinetic model for non-ideal fluids, one needs to begin with the first Bogolioubov–Born–Green–
+Kirkwood–Yvon (BBGKY) equation,
+∂t f + v · ∇ f = J =
+� �
+∇V (|r − r1|) · ∂
+∂v f2(r, v, r1, v1, t)dv1dr1,
+(543)
+where f(r, v, t) and f2(r, v, r1, v1, t) are the one- and the two-particle distribution functions, respectively, r, r1 and v,
+v1 are particles position and velocity, while V is a potential of pair interaction. The Boltzmann collision integral of
+Eq. (46) is not sufficient for the dense regime as it neglects the volume occupied by the molecules and long range
+interactions. The BBGKY equation on the other hand make no assumptions on the nature of the interaction as it
+involves a general non-local interaction potential and dependence on the two-particle distribution function. The main
+difficulty of the BBGKY is that to solve the one-particle equation one needs the two-particle distribution function
+which itself is governed by a non-homogeneous hyperbolic partial differential equation with a collision term involving
+the three-particle distribution function and so on. To operate a truncation at first-order proper approximations for the
+correlation function and the interaction potential are needed. In the next section we briefly present two of the most
+widely used models for short- and long-range interaction.
+5.2.1. Hard sphere potential: The Enskog model
+In Enskog’s approach, particles are assumed to be hard impenetrable spheres of diameter d. This fixes the form of
+the interaction potential effectively allowing to re-write the collision integral as [141, 142]:
+JE = d2
+� � �
+f2(r + d
+2 k, v′, r1, v′
+1, t) − f2(r − d
+2 k, v, r1, v1, t)
+�
+g · kdkdv1,
+(544)
+where k = (r1 − r)/|r1 − r|, g = v1 − v, v′ = v + k(g · k), v′
+1 = v1 − k(g · k). The second approximation in Enskog’s
+standard theory applies to the two-particle distribution function [9, 11]:
+f2(r + d
+2 k, v′, r1, v′
+1, t)
+=
+χ
+�
+r + d
+2 k
+�
+f �r, v′� f �r + dk, v′
+1
+� ,
+(545)
+f2(r − d
+2 k, v, r1, v1, t)
+=
+χ
+�
+r − d
+2 k
+�
+f (r, v) f (r − dk, v1) ,
+(546)
+where χ is the equilibrium pair correlation function, evaluated at local density taking into account the effect of volume
+of particles in the collision probability [11]. Using both these approximations one recovers Enskog’s hard-sphere
+collision integral [9, 11],
+JE = d2
+� � �
+χ
+�
+r + d
+2 k
+�
+f �r, v′� f �r + dk, v′
+1
+� − χ
+�
+r − d
+2 k
+�
+f (r, v) f (r − dk, v1)
+�
+g · kdkdv1.
+(547)
+The above integral can be approximated using a Taylor expansion around r as,
+χ
+�
+r ± d
+2 k
+�
+=
+χ (r) ± d
+2 k · ∇χ (r) + d2
+8 k ⊗ k : ∇∇χ (r) + O(d3),
+(548)
+f (r ± dk, w)
+=
+f (r, w) ± dk · ∇ f (r, w) + d2
+2 k ⊗ k : ∇∇f (r, w) + O(d3),
+(549)
+which leads to:
+JE = χJB + J(1)
+E + J(2)
+E ,
+(550)
+where we have neglected terms of order 3 and above, JB is the Boltzmann collision integral for hard-spheres,
+JB = d2
+� � � f �r, v′� f �r, v′
+1
+� − f (r, v) f (r, v1)� g · kdkdv1,
+(551)
+78
+
+and J(1)
+E and J(2)
+E are the first- and second-order non-local contributions defined as:
+J(1)
+E
+=d3χ (r)
+� �
+k · � f �r, v′� ∇f �r, v′
+1
+� + f (r, v) ∇f (r, v1)� g · kdkdv1
++ d3
+2
+� �
+k · ∇χ (r) � f �r, v′� f �r, v′
+1
+� + f (r, v) f (r, v1)� g · kdkdv1,
+(552)
+and [143]
+J(2)
+E
+=d4
+2 χ (r)
+� �
+k ⊗ k � f �r, v′� ∇∇ f �r, v′
+1
+� − f (r, v) ∇∇f (r, v1)� g · kdkdv1
++ d4
+2
+� �
+k ⊗ k : ∇χ (r) ⊗ � f �r, v′� ∇ f �r, v′
+1
+� − f (r, v) ∇ f (r, v1)� g · kdkdv1
++ d4
+8
+� �
+k ⊗ k : ∇∇χ (r) � f �r, v′� f �r, v′
+1
+� − f (r, v) f (r, v1)� g · kdkdv1.
+(553)
+Only keeping first-order contributions and evaluating J(1)
+E at the local equilibrium f eq (743) one gets [11],
+J(1)
+E
+= d3
+� �
+f eq (r, v) f eq (r, v1) k · ∇ ln �χ (r) f eq (r, v) f eq (r, v1)� g · kdkdv1,
+(554)
+which, after integration in v1 and k, for the isothermal flow results in,
+J(1)
+E
+= − bρχf eq �
+(v − u) · ∇ ln ρ2χT
+�
+− bρχ f eq
+� 2
+5RT (v − u)(v − u) : ∇u +
+� 1
+5RT |v − u|2 − 1
+�
+∇ · u
+�
+,
+(555)
+where b = 2πd3/3m. While the phenomenological Enskog’s collision integral [9] was used above, the lowest-order
+approximation Eq. (555) is identical in other versions of hard-sphere kinetic equations such as the revised Enskog
+theory (RET) [144] or kinetic variational theory [145].
+5.2.2. Long-range interactions: Vlasov model
+Enskog’s model only accounts for strong repulsive short-range interactions introducing the excluded volume into
+the equation of state. However it is not enough to account for long-range attractive interactions leading to spinodal
+decomposition. A widely used model for long-range attractive contributions of the collision intergal in Eq. (543)
+is Vlasov’s mean-field approximation. Here we briefly review this model. Assuming absence of correlations, the
+two-particle distribution function is approximated as
+f2(r, v, r1, v1) ≈ f(r, v) f(r1, v1),
+(556)
+while the long-range interaction integral can be simplified,
+JV = ∂f(r, v)
+∂v
+· ∇
+��
+|r1−r|>d
+ρ(r1)V(|r1 − r|)dr1
+�
+.
+(557)
+With a Taylor expansion around r,
+ρ(r1) = ρ(r) + (r1 − r) · ∇ρ(r) + 1
+2(r1 − r) ⊗ (r1 − r) : ∇ ⊗ ∇ρ(r) + O(∇3ρ),
+(558)
+and neglecting higher-order terms, with Eq. (557) one recovers the meanfield Valsov long-range molecular interaction,
+JV = −∇
+�
+2aρ(r) + κ∇2ρ(r)
+�
+· ∂
+∂v f(r, v),
+(559)
+79
+
+where parameters a and κ are, after integration over a unit sphere,
+a = −2π
+� ∞
+d
+r2V(r)dr,
+(560)
+κ = −2π
+3
+� ∞
+d
+r4V(r)dr.
+(561)
+Eq. (543) together with:
+J = χJB + J(1)
+E + JV,
+(562)
+and the short- and long-range interaction models of Eqs. (555) and (559) form the constitutive equations for mod-
+erately dense isothermal fluid Enskog-Vlasove model. This kinetic model, under some specific scaling assumptions
+detailed in Appendix C, is shown to recover the second-gradient fluid model at the Euler-Navier-Stokes level with,
+P = bρ2χrT − aρ2.
+(563)
+Motivated by our recently published work [146], before entering the discussion of lattice Boltzmann models for non-
+ideal fluids we introduce next a general kinetic framework for non-ideal fluids that can be easily transposed into the
+lattice Boltzmann framework.
+5.2.3. General Enkog-Vlasov-BGK kinetic framework for hydrodynamics
+In an attempt to provide a unified an numerically efficient kinetic framework for non-ideal fluids simulation in
+[146] the authors introduced a projector K onto a local equilibrium at constant temperature [147],
+KJ =
+�∂f eq
+∂ρ − 1
+ρu · ∂f eq
+∂u
+� �
+Jdv + 1
+ρ
+∂ f eq
+∂u ·
+�
+vJdv.
+(564)
+with the property, K2 = K, which can be verified by a direct computation. The equilibrium attractor is defined as:
+f eq =
+ρ
+(2πP0/ρ)D/2 exp
+�
+−(v − u)2
+2P0/ρ
+�
+,
+(565)
+where P0 is a freely tunable reference pressure. With the projector of Eq. (564), the interaction term in Eq. (543) is
+split into two parts by writing an identity,
+J = (1 − K) J + KJ.
+(566)
+The first term,
+Jloc = (1 − K) J,
+(567)
+satisfies the local conservation of both mass and momentum,
+KJloc = 0.
+(568)
+It is conventional to model the locally conserving part of the interaction with a single relaxation time Bhatnagar–
+Gross–Krook (BGK) approximation,
+Jloc → JBGK = −1
+τ (1 − K) f = −1
+τ
+�
+f − f eq(ρ, u, P0
+ρ )
+�
+,
+(569)
+where the relaxation time τ is a free parameter. The second term in the identity (566),
+Jnloc = KJ,
+(570)
+satisfies the local mass but not the local momentum conservation. After integration by part in the velocity v and
+neglecting boundary integrals, one arrives at
+Jnloc = −1
+ρ
+∂ f eq
+∂u · Fnloc,
+(571)
+80
+
+where the force Fnloc reads,
+Fnloc =
+� � �
+∇V (|r − r1|) f2(r, v, r1, v1, t)dv1dr1dv.
+(572)
+Collecting the BGK approximation together with the nonlocal contribution, a generic kinetic model may be written,
+∂t f + v · ∇f = −1
+τ
+� f − f eq� − 1
+ρ
+∂f eq
+∂u · Fnloc.
+(573)
+Evaluation of the force (572) requires us to specify the particles interaction. One can invoke the Enskog–Vlasov
+model [9, 10] where both hard-sphere collisions and a weak long-range attraction potential contribute to a non-local
+momentum transfer or any other type of closure. More generally Eq. (573) defines a family of kinetic models with
+P0 and Fnloc as tunable parameters to recover the hydrodynamics of interest. In the next section we review different
+lattice Boltzmann models for non-ideal fluids as closures for Fnloc and P0 within this general kinetic framework. For
+the sake of readability, in the remainder of the text we drop nloc and simply use F for the force. Before moving on to
+the LBM models we will discuss the hydrodynamic limit of non-ideal kinetic models under conventional scaling and
+alternative better suited to the recovery of the target macroscopic system.
+5.2.4. Scaling and hydrdynamic limit
+Considering the Enskog–Vlasov–BGK kinetic model introduced in the previous sections, let us introduce the
+following parameters:
+• characteristic flow velocity U,
+• characteristic flow scale L,
+• characteristic flow time T = L/U,
+• characteristic density ¯ρ,
+• isothermal speed of sound of ideal gas cs =
+√
+rT,
+• kinematic viscosity of the BGK model of ideal gas ν = τc2
+s.
+With the above, the variables are reduced as follows (primes denote non-dimensional variables):
+• time t = T t′,
+• space r = Lr′,
+• flow velocity u = Uu′,
+• particle velocity v = csv′,
+• density ρ=¯ρρ′,
+• distribution function f = ¯ρc−3
+s f ′.
+Furthermore, the following non-dimensional groups are introduced: Viscosity-based Knudsen number Kn = τcs/L,
+Mach number Ma = U/cs, Enskog number En = b¯ρKn/Ma and Vlasov number Vs = a/brT.
+With this, the Enskog–Vlasov–BGK kinetic model is written in non-dimensionla form as:
+Ma Kn ∂′
+t f ′ + v′ · Kn∇′ f ′ = − � f ′ − f eq′�
+− 1
+ρ′
+∂f eq′
+∂u′ · En
+�
+∇′ �
+χ �ρ′�2 − Vs �ρ′�2�
+−
+� δ
+L
+�2
+Vs
+�
+ρ′∇′∇
+′2ρ′��
+,
+(574)
+81
+
+where δ is the range of the attraction potential. Assuming d ≪ δ, we have a ∼ ¯Vδ3 and κ ∼ ¯Vδ5, where ¯V is a
+characteristic value of the potential, thus
+�
+κ/a ∼ δ.
+(575)
+The following scaling assumptions are applied: Acoustic scaling, Ma ∼ 1; Hydrodynamic scaling, Kn ∼ En ∼ δ/L ∼
+ϵ; Enskog–Vlasov parity, Vs ∼ 1. In other words, the conventional hydrodynamic limit treats all non-dimensional
+groups that are inversely proportional to the flow scale L (Kn, En and δ/L) as a small parameter while the Enskog–
+Vlasov parity ensures that both the short- and long-range contributions to the pressure are treated on equal footing.
+Returning to dimensional variables, we may write,
+ϵ∂t f + v · ϵ∇ f = − � f − f eq� − 1
+ρ
+∂f eq
+∂u ·
+�
+ϵF(1) + ϵ3F(3)�
+,
+(576)
+where,
+F(1) = ∇(P − P0).
+(577)
+F(3) = −κρ∇∇2ρ.
+(578)
+The analysis of the kinetic model under the above-detailed conventional scaling of a small deviation from a uniform
+state [11],
+∇ → ϵ∇, ∂t → ϵ∂t,
+(579)
+is detailed in Appendix C. To second order in space derivatives, the resulting momentum balance equation reads,
+∂tρu + ϵ∇ · ρu ⊗ u + ϵ∇P + ϵ∇ · ϵTNS + O(ϵ3) = 0,
+(580)
+where the dynamic viscosity µ and the bulk viscosity η in the Navier–Stokes stress tensor (539) are defined by the
+reference pressure (D = 3),
+µ = τP0,
+(581)
+η =
+�5
+3 − ∂ ln P0
+∂ ln ρ
+�
+τP0.
+(582)
+Thus, the momentum balance equation (580) is form-invariant with respect to the choice of reference pressure, pro-
+vided P0 satisfies a sub-isentropic condition,
+P0 ≤ Cρ5/3,
+(583)
+for some C > 0. With (583), the bulk viscosity (582) is positive and vanishes when the reference pressure follows an
+isentropic process for ideal monatomic gas, P0 = Cρ5/3. For example, any polytropic process, P0 = Aρn, 1 ≤ n ≤ 5/3
+satisfies the sub-isentropic condition and results in η = (5/3 − n)τP0. Special case of isothermal process n = 1 returns
+η = (2/3)τP0, and the viscous stress tensor becomes,
+TNS = −τP0
+�
+∇u + ∇u†�
+.
+(584)
+On the other hand, when compared to the two-phase momentum equation, the macroscopic limit recovers only the
+nonideal gas component thereof while missing Korteweg’s capillarity contribution. Indeed, the third-order term,
+∼ ϵ3ρ∇∇2ρ does not contribute to the momentum equation (580) under the scaling (579). This is consistent with the
+well-known results from kinetic theory [11] and is not surprising: The scaling (579) is essentially based on the Knud-
+sen number, which overrides the relative contribution of the capillarity term by two orders, cf. Appendix Appendix
+C. Thus, under weak non-uniformity assumption (579), the capillarity terms are seen as higher-order, Burnett-level
+contributions, and cannot appear in the main (first and second) orders in the momentum balance equation (580). In
+fact, condition (579) rules out situations at an interface between phases where gradients of density become large over
+a relatively short distance. Therefore, in order for the kinetic model to recover in-full the momentum balance (541), a
+different scaling needs to be applied.
+82
+
+To overcome that issue a rescaling of the kinetic model by a time step δt, here merely a characteristic time repre-
+senting the level of coarse-graining in time, was introduced in [146]. As a preliminary consideration, we evaluate the
+contribution of the force term over the time step. For a generic force F, the action of the force on the distribution
+function can be written as a full derivative in a frame that moves with the local fluid velocity,
+1
+ρ
+∂f eq
+∂u · F = d f eq
+dt .
+(585)
+Introducing the velocity increment,
+δu = F
+ρ δt,
+(586)
+and integrating in time, leads to the following contribution to the distribution from the force,
+F =
+� t+δt
+t
+1
+ρ
+∂ f eq
+∂u · Fdt.
+(587)
+With the characteristic values of the flow velocity U, the flow scale L, the density ρ, the force F and the velocity
+increment δu, the following smallness parameter is introduced:
+δu
+U ∼ δtF
+ρU ∼ ε,
+(588)
+δr
+L ∼ ε.
+(589)
+The first scaling condition (588) refers to a smallness of velocity increment, that is, to the smallness of the force action
+over time δt. The second scaling condition (589) is a resolution requirement. Both conditions are assumed to hold
+simultaneously. Details of the corresponding multi-scale analysis are provided in Appendix D. Unlike the previous
+results with the classical scaling, the momentum balance includes not only the nonideal gas pressure but also the
+capillarity term, and is thus consistent with Korteweg’s force in the momentum balance. It should be pointed out that
+the scaling (588) refers to smallness of the increment of the flow velocity rather that to smallness of either the time
+step or of the force. Thus, rescaling the kinetic model based on the smallness of flow velocity increments results in
+both the non-ideal gas equation of state and the capillarity revealed at the Euler level O(ε) of the momentum balance.
+This is in a contrast to the conventional scaling, which is tied to the non-uniformity and surface tension would appear
+only at a Burnett level O(ϵ3).
+5.3. Overview of lattice Boltzmann models for non-ideal fluids
+The general kinetic framework of Eq. (573), regardless of the choice of P0 and F can be readily discretized in
+phase-space, procedure detailed in section 4.1, and physical space and time, detailed in section 4.2, to yield a discrete
+time evolution equation of the form:
+¯fi(r + ciδt, t + δt) − ¯fi(r, t) = δt
+¯τ
+�
+f eq
+i (ρ, u) − ¯fi(r, t)
+�
++ Fi(F).
+(590)
+where Fi is the discrete form of the force contribution in the kinetic framework that can be treated using any of
+schemes detailed in section 4.3 and f eq
+i
+is the discrete equilibrium function that can be chosen among those discussed
+in section 4.1. For a correct recovery of the viscous stress tensor, the redefined relaxation time is tied to the reference
+pressure P0 as:
+¯τ = ρν
+P0
++ δt
+2 ,
+(591)
+and the bulk viscosity of the model, for the bare single relaxation time collision operator, is:
+η = P0
+�2 + D
+D
+− ∂ ln P0
+∂ ln ρ
+� �
+¯τ − δt
+2
+�
+.
+(592)
+Given that all models of interest in the present manuscript can be fitted within this discrete kinetic model, and that the
+only point of difference resides in the choice of F and P0 we will discuss the different lattice Boltzmann models from
+that specific perspective.
+83
+
+5.3.1. Shan and Chen’s pseudo-potential model
+In this extension of the classical lattice Boltzmann method for isothermal ideal gases to non-ideal fluids first
+proposed in [12], the authors introduced a source of non-local interaction through a potential defined as:
+V(r, r′) = G(r, r1)ψ(r)ψ(r1),
+(593)
+where G(r, r1) is a Green’s function and ψ is an effective number density. For the case of the discrete system, the
+authors proposed to only consider nearest-neighbour interactions to get the following discrete Green’s function:
+G(r − r1) =
+�������
+0, |r − r1|≤ 2,
+G, 0 < |r − r1|< 2,
+(594)
+which in turn leads to the discrete non-local momentum source:
+F = Gψ(r)
+Q−1
+�
+i=0
+w(|ci|)ψ(r + ciδt)ci,
+(595)
+where G is now a constant controlling the interaction strength. Furthermore, this model keeps the isothermal equilib-
+rium of the classical isothermal LBM, therefore effectively setting P0 = ρc2
+s. Computing the Euler-level momentum
+balance equation it is readily seen that the equation of state changes from the ideal isothermal pressure to:
+P = ρc2
+s + G
+2 ψ2,
+(596)
+potentially allowing for coexistence of a vapour and liquid phase at a given temperature. The only condition for the
+stable coexistence of these two phases at temperature T is the existence of two points ρ1 and ρ2, with ρ1 < ρv < ρl < ρ2,
+satisfying:
+∂2P
+∂ρ2 |ρ=ρ1,ρ2= ∂P
+∂ρ |ρ=ρ1,ρ2= 0.
+(597)
+For instance setting ψ ∝ ρ would lead to a quadratic equation of state and could not satisfy either of the above-listed
+conditions regardless of the choice of the coefficients. In [12], the authors propose an effective density number of the
+form:
+ψ = ρ0
+�
+1 − exp − ρ
+ρ0
+�
+,
+(598)
+where ρ0 is freely tunable parameter. This form of the effective density number systematically admits two roots to
+Eq. (597) for G < Gc, where Gc is the critical interaction strength above which the density degeneracy goes from two
+to one. Using the two conditions on derivatives of pressure at the critical state:
+c2
+s − 2Gcρ0 exp
+�
+−ρc
+ρ0
+� �
+exp
+�
+−ρc
+ρ0
+�
+− 1
+�
+=
+0,
+(599)
+−2Gc exp
+�
+−2ρc
+ρ0
+� �
+exp
+�ρc
+ρ0
+�
+− 2
+�
+=
+0,
+(600)
+the critical state is shown to be:
+ρc
+=
+ρ0 ln 2,
+(601)
+Gc
+=
+−2c2
+s
+ρ0
+.
+(602)
+While G is routinely assimilated to a pseudo-temperature as G = − 1
+T , see for instance [148], a dimensional analysis
+shows [G] =
+m5
+kgs2 , which indicates G ∝ rT
+ρ0 .
+From both kinetic theory and the van der Waals fluid theory one would expect two separate non-local contributions
+to allow for stable phase separation: A short-range repulsive and a long-range attractive interaction. As such the
+84
+
+single-term form of the pseudo-potential model should not produce long range interaction meanfield effects such as
+surface tension. This point can be clarified by writing a Taylor expansion of the discrete non-local momentum source
+term:
+F = Gψ(r)
+Q−1
+�
+i=0
+w(|ci|)ψ(r + ciδt)ci = Gψ∇ψ − Gδr2
+3
+ψ∇∆ψ + O(∇5).
+(603)
+It is observed that the discrete non-local interaction is akin to a second-order accurate finite-differences approximation
+to the the first-order derivative of ψ admitting a leading third-order error that takes on a form similar to surface tension.
+While naturally generating a non-zero surface tension via this leading-order error term it has the following short-
+comings: (a) the surface tension coefficient is fixed and (b) different from the Kortwewg stress tensor, van der Waals
+fluid and Enskog-Vlasov theory the interfacial excess energy is not a function of density but the effective number
+density, which in principle is not a conserved variable [149, 146].
+5.3.2. Free energy model and derivatives
+In its original form the free energy model was first introduced in [150]. Different from the pseudo-potential
+approach where the model was constructed based on a microscopic interaction argument, here it targets a specific
+macroscopic system: the van der Waals quasi-local thermodynamics, which results, after minimization of free energy
+in the Kortweweg pressure tensor:
+TK =
+�
+P − κρ∇2ρ − κ
+2|∇ρ|2�
+I + κ∇ρ ⊗ ∇ρ.
+(604)
+To extend the ideal gas LBM to recover the Korteweg stress tensor the authors derived a discrete equilibrium function
+by moment matching, considering moments up to order two. For a 1-D system with a three-velocity stencil:
+����������
+1
+1
+1
+c−1
+c0
+c1
+c2
+−1
+c0
+c1
+����������
+����������
+f eq
+−1
+f eq
+0
+f eq
+1
+���������� =
+����������
+ρ
+ρux
+ρu2
+x + P − κρ∂2
+xρ
+���������� .
+(605)
+This is equivalent to setting P0 = TK and F = 0. The 2-D version of the model with the standard D2Q9 velocity set can
+be found in [150]. We will refer to this type of approach, introducing non-ideal contribution directly into the second-
+order moment of the equilibrium as pressure-based model. Later multi-scale analyses showed that this approach is
+subject to Galilean-variant errors scaling with ∝ Ma [151, 152]. Via modification to the discrete equilibrium function,
+improved formulation with reduced Galilean-variant errors were proposed [151, 152]. Another way of introducing
+non-ideal contributions was discussed in [153]: Introducing a Vlasov-like forcing term given by the divergence of
+the pressure tensor. This approach, referred to as force-based, was first proposed in [154] and is equivalent to setting
+P0 = ρc2
+s and F = ∇ · (TK − P0I). While the force-based approach still had Galilean-variant errors, those affecting the
+viscous shear stress at the NS level could be easily eliminated using a third-order polynomial equilibrium function.
+The force-based approach was later extended to more complex and realistic configurations through the use of the
+entropic LBM [128, 155, 156].
+More recently the free energy method was reformulated using the chemical potential [157]; Using the definition of
+the chemical potential and pressure in the free energy model one can derive the following relationship between the
+divergence of the stress tensor and gradient of chemical potential:
+∇ · TK = ρ∇λ.
+(606)
+Using the ideal gas LBM, i.e. P0 = ρc2
+s, with a force-based approach to introduce non-ideal contribution the body
+force is derived as:
+F = −ρ∇λ + c2
+s∇ρ,
+(607)
+where, for instance, for the van de Waals equation of state, see Eq. (640):
+λ = rT
+�
+ln
+�
+ρ
+1 − bρ
+�
++
+1
+1 − bρ
+�
+− 2aρ − κ∇2ρ.
+(608)
+85
+
+Using this approach, in combination with a strategy to thicken the interface the authors were able to considerably
+extend the range of accessible density ratios.
+All lattice Boltzmann models discussed here, at the hydrodynamic scale, target a form of the Korteweg stress tensor
+with a non-ideal equation of state and surface tension term. However such models come with a limitation: the
+thickness of the interface which contrary to phase-field models relying on a double-well potential is dictated by
+physical properties of the considered fluid, i.e. the volume exclusion coefficient, the long-range interaction coefficient
+and the capillary coefficient. We discuss this limitation along with a solution allowing to go above that scale limitation
+which has long been overlooked in the literature.
+5.4. Bridging the scale gap: Principle of corresponding states
+As briefly mentioned in the previous sections, the non-ideal fluids models of interest here all come with inter-
+face thicknesses solely determined by thermodynamics and properties of considered fluids. This creates a scale gap
+between the characteristic size of the interface and target characteristic scales of interest for drops and bubble, e.g.
+≈ 10−2 − 10−3 m. We will clarify this size restriction here and discuss efficient solutions allowing to up-scale the
+solver.
+5.4.1. Dimensional form of equations and restriction by the interface thickness
+While discussions around second-gradient models for non-ideal fluids are expressed in non-dimensional units,
+we will show that such models come with characteristic sizes imposed by physics. Consider for that purpose a 1-D
+isothermal interface; The steady-state Navier-Stokes-Korteweg equation reduces to:
+∂P
+∂x = κρ∂3ρ
+∂x3 ,
+(609)
+with limx→−∞ ρ = ρl and limx→+∞ ρ = ρv. While we are considering the classical Korteweg stress tensor here, the
+same line of reasoning applies to the macroscopic equation recovered by the pseudo-potential method. Here for the
+sake of simplicity we use the van der Waals equation of state for the thermodynamic pressure. As a result the ordinary
+differential equation describing the interface has six degrees of freedom, i.e. a, b, r, κ, ρv and ρl. The former three
+along with with liquid and vapor phase densities are readily fixed via conditions on the critical state of the considered
+fluid and the temperature of the system. Consider for instance nitrogen N2; To recover proper critical density, pressure
+and temperature, i.e. ρc = 311 kg/m3, Pc = 33.5 Pa and Tc = 126 K [158], the excluded volume and attractive force
+coefficients and specific gas constant, i.e. b, a and r should be set to:
+aN2
+=
+105.28 m5
+kgs2 ,
+(610)
+bN2
+=
+0.00107 m3
+kg ,
+(611)
+rN2
+=
+230.99 m2
+s2K .
+(612)
+To recover the correct critical density, r is set to a value which is different from its ideal counterpart. This is justified
+by the fact that here to set the constants we have relied on properties of the fluid at the critical state where it does not
+behave as an ideal gas, see [159] for detailed discussion. The remaining degree of freedom, the capillary coefficient
+κ, is also a physical property of the considered fluid. A variety of expressions have been proposed for the capillary
+coefficient both in the context of the kinetic theory of gases, e.g. [160, 161, 162], or via semi-empirical correlations
+to match experimental measurements, see [163] for detailed review. Here for N2 we will set κ = 10−10
+m7
+kgs2 [164]. It
+is then clear that once the temperature of the system has been fixed, all parameters/variables in Eq. (609) are set by
+physical closures, also fixing the coexistence densities and density profile at the interface. The liquid/vapor interface
+at two different temperatures for the N2 system is illustrated in Fig. 20. The interfaces at both temperatures, resulting
+in density ratio of the order of 102 and 10, have sizes of the order of 200 − 400 nm. In practice, considering one
+needs to resolve the interfaces with at least 3-4 points, the maximum grid-size is limited to δr ≈ 100 nm meaning
+for configurations of practical interest involving drops, for instance of diameter 1 mm, one would need at least 1012
+86
+
+Figure 20: Density profile of N2 liquid/vapor interface at (black plain) T = 63 K and (red dashed) T = 94.5 K.
+grid-points in 3-D. This obviously makes the approach of little to no use for simulations of practical interest. The only
+workaround would be to rescale the interface thickness, here the limiting charactersitic size, to minimize the required
+number of grid-points for realistic simulations. In the next section we discuss the principle of corresponding states
+which provides the theoretical basis for such rescaling operations.
+5.4.2. Extension to realistic-sized systems: Rescaling interface thickness and the principle of corresponding states
+The principle of corresponding states, introduced for the first time by van der Waals in [136], quoting Guggenheim
+[158], may safely be regarded as the most useful by-product of van der Waals’ equation of state. The principle
+maintains that all properties that depend on inter-molecular forces are related to the critical properties of the substance
+in a universal way, regardless of the molecular compound of interest. This observation has had two main practical
+consequences: (a) prediction of unknown properties of many fluids from known properties of a few [165], (b) extension
+of the domain of applicability of second-gradient-based numerical solvers to large systems at acceptable cost. The
+possibility of the former was put forward first theoretically in [166] and confirmed experimentally in Guggenheim’s
+work, illustrated in Fig. 21, for a family of fluids called perfect liquids by Pitzer [166]. While the principle of
+Figure 21: Co-existence densities obtained from experiments as reported in [158] for three different fluids: (black squares) CH4, (red circles) N2
+and (blue diamonds) Xe.
+87
+
+800
+600
+p[kg/m3]
+400
+200
+0
+-300
+-200
+-100
+0
+100
+200
+300
+α[nm]0.9
+0.8
+0.7
+0.6
+0.5
+0
+2
+3
+p/pccorresponding states is an approximation for real fluids, it is an exact property of the van der Waals fluids. This is
+most notably demonstrated by the fact that the non-dimensional form of the equation of state, non-dimensionalized
+by critical state properties, does not have any fluid-dependent constant:
+Pr = 8ρrTr
+3 − ρr
+− 3ρ2
+r,
+(613)
+where we have introduced reduced variables, e.g. ρr =
+ρ
+ρc . The implication here is that regardless of the fluid
+considered, the coexistence densities plot in non-dimensional units are universal. To illustrate that four different fluids
+were considered and parameters a, b and r were chosen so as to fit the experimental critical state of each fluid. The
+corresponding data is summarized in Table 5. Plugged into the van der Waals equation of state, all fluids, as shown
+H2O
+Xe
+N2
+CH4
+Tc [K]
+647.14
+289.8
+126
+190.3
+ρc [kg/m3]
+322
+1155
+311
+162
+Pc [MPa]
+5.897
+3.394
+4.610
+a
+� m5
+kg·s2
+�
+1709
+13.2614
+105.272
+526.978
+b
+� m3
+kg
+�
+0.0017
+2.886 × 10−4
+0.0011
+0.0021
+r
+� m2
+s2K
+�
+196.79
+46.981
+230.967
+398.764
+Table 5: Critical state and corresponding van der Waals coefficients for different fluids; Experimental data from [158] and [167] (for water).
+in Fig. 21, result in exactly the same non-dimensional coexistence densities curve. Now that we have showed that the
+Figure 22: Co-existence densities obtained from the van der Waals equation of state for all fluids of Table 5. Given that all fluids led to exactly the
+same curve, only one is shown here.
+density ratio is independent of substance-specific variables let us go back to (609) and discuss simple strategies that
+would allow one to thicken the interface. To illustrate our purpose we will use the simple demonstration discussed
+in [168] by considering a 1-D interface of a fluid near the critical state. This consideration allows us to simplify the
+chemical potential of the van der Waals equation of state as a third-order polynomial [169]:
+λ − λsat = 4A(ρ − ρv)(ρ − ρl)
+�
+ρ − ρv + ρl
+2
+�
+,
+(614)
+88
+
+1
+0.9
+0.8
+H
+0.7
+0.6
+0.5
+0
+0.5
+1
+1.5
+2
+2.5
+p/pcwith
+A =
+1
+2ρl,v(ρl − ρv)2
+dP
+dρ ,
+(615)
+leading to the following analytical density profile:
+ρ(x) = ρv + ρl
+2
++ ρl − ρv
+2
+tanh
+�������
+ρl − ρv
+2
+�
+2A
+κ x
+������� .
+(616)
+Using this analytical profile the interface thickness, here defined as,
+W =
+ρl − ρv
+max(dρ/dx),
+(617)
+and surface tension, σ,
+σ = κ
+� ρl
+ρv
+dρ
+dxdρ,
+(618)
+are readily evaluated to be:
+W
+=
+4
+ρl − ρv
+�
+κ
+2A,
+(619)
+σ
+=
+(ρl − ρv)3
+6
+√
+2Aκ.
+(620)
+This means that the interface thickness and surface tension can be modified via different choices of the capillary
+coefficient and isothermal compressibility, through the coefficient A. Combined with the principle of corresponding
+states, this allows one to modify parameters κ, a and b at will to reach the desired interface thickness and surface
+tension at a fixed reduced temperature and maintain the density ratio unchanged. In addition a number of other
+considerations must be taken into account when using this strategy to thicken the interface:
+• Interface thickening via modification of A is akin to a rescaling of the isothermal speed of sound -tied to the
+isothermal compressibility. To remain within the low Mach approximation, assuming a characteristic convective
+speed U, one must ensure that U
+cs < 0.3.
+• Artificial thickening of the interface will correctly capture the dynamics of the considered interface in the limit
+of a sharp interface. By sharp interface we mean W ≪ L, where L is the characteristic hydrodynamic size
+and W the characteristic interface length. The characteristic interface length is W = max(W, δT) where δT is
+the Tolman length characterizing curvature-dependence of the surface tension detailed in section 5.8.4.
+It was shown here that the use of the principle of corresponding states in combination with restrictions on the Mach
+number and the ratio of characteristic interface to hydrodynamic sizes allows for a simple way to thicken the interface
+and remove the fundamental restriction on grid-size in second-gradient fluid simulations. While the analysis was
+restricted to the van der Waals equation near critical state it equally applies to other equations of state, the pseudo-
+potential model and temperatures much lower than the critical temperature. In the authors opinion this is one of the
+main components of modern lattice Boltzmann models for non-ideal fluids.
+5.5. Numerical artifacts and issues of non-ideal lattice Boltzmann models
+5.5.1. Deviations in normal stress at interface: The issue of thermodynamic consistency
+The issue of thermodynamic consistency as referred to in the lattice Boltzmann literature refers to the non-
+equivalence of the mechanical stability and Maxwell construction conditions when considering the discrete pressure
+tensor; To illustrate that purpose let us consider a force discretized with the first-neighbor D2Q9 stencil, i.e.
+F = 2
+�
+P − P0(r)
+Q−1
+�
+i=0
+w(|ci|)
+�
+P − P0(r + ciδt)ci.
+(621)
+89
+
+The discrete pressure tensor as introduced in the previous section is:
+P(r) = P0(r) +
+�
+P − P0(r)
+�
+i
+w(|ci|)
+�
+P − P0(r + ciδt)ci ⊗ ci,
+(622)
+which after Taylor expansion results in:
+P =
+�
+P + δr2
+6
+�
+P − P0∇2 �
+P − P0
+�
+I + δr2
+3
+�
+P − P0∇∇
+�
+P − P0.
+(623)
+Now considering a flat interface normal to the x-axis, the normal pressure can be written as:
+Pn = P + δr2
+2
+�
+P − P0
+d2
+dx2
+�
+P − P0,
+(624)
+and further developed into:
+Pn = P + δr2
+4
+�
+P − P0
+d
+d √P − P0
+�d √P − P0
+dx
+�2
+.
+(625)
+After some algebra one can recover the following equation:
+(Pn − P)
+4 d √P−P0
+dρ
+δr2 √P − P0
+= d
+dρ
+�������
+�d √P − P0
+dρ
+�2�dρ
+dx
+�2������� .
+(626)
+Integrating from the vapor phase to the liquid phase and noting that dρ/dx = 0 in both phases one arrives at the
+following mechanical stability condition:
+� ρl
+ρv
+(Pn − P) d ln(P − P0)
+dρ
+dρ = 0.
+(627)
+This form of the mechanical stability condition only matches the thermodynamic coexistence condition from Maxwell’s
+reconstruction only if:
+d ln(P − P0)
+dρ
+= 1
+ρ2 ,
+(628)
+which is the basis of the proposal formulated in [170] to define a pseudo-potential of the form:
+ψ =
+�
+P − P0 = ρ0 exp −ρ0
+ρ .
+(629)
+Note that other forms of the non-local contribution will lead to similar mistmatches; For instance consider the free
+energy form:
+F =
+Q−1
+�
+i=0
+w(|ci|)(P − P0)(r + ciδt)ci.
+(630)
+The stress normal to the interface will be:
+Pn = P + δr2
+4 (P − P0)
+d
+d(P − P0)
+�d(P − P0)
+dx
+�2
+,
+(631)
+which leads to exactly the same mechanical equilibrium condition as before. The mismatch between the Maxwell
+construction condition and discrete mechanical stability condition results in deviations in coexistence density in sim-
+ulations from those predicted by thermodynamics. This point is illustrated in Fig. 23. Fig. 23 shows that the lattice
+Boltzmann model correctly recovers the liquid/vapor coexistence densities closer to the critical temperature; As tem-
+perature goes further down, and density ratio increases, coexistence densities in simulations deviate significantly
+from the Maxwell construction predictions, and that regardless of the choice of the excluded volume and long range
+interaction coefficients.
+90
+
+10-5
+10-3
+10-1
+/ c
+0.4
+0.6
+0.8
+1
+T/Tc
+1.5
+2
+2.5
+Figure 23:
+Coexistence densities with van der Waals equation of state as obtained from (grey lines) Maxwell’s construction and (markers)
+simulations with different choices of a: (green x) a = 0.0102, (magenta +) a = 0.0051, (blue triangles) a = 0.0026, (red squares) a = 0.0013
+and (black circles) a = 0.00064. Simulations conducted using the first-neighbour pseudo-potential model with exact difference method to treat the
+force term. Plot is reproduced from [146].
+5.5.2. Fixed surface tension
+One point that was noted in Eq. (603) was the emergence of a surface tension-like leading error term in the
+single-neighbour pseudo-potential model. The leading-order error is the reason the original pseudo-potential method
+of [12] is able to recover a Korteweg-like surface tension. At the difference of the Korteweg stress tensor, which is
+a minimizer of the second-gradient free energy under global mass conservation constraint, and where surface tension
+explicitly appears in the macroscopic equations as an additional term, in the former it is strictly enslaved to the chosen
+stencil and form of the pseudo-potential and therefore not tunable, see Eq. (603):
+κ = Gδr2
+3
+.
+(632)
+Introduction of variable capillary coefficient and therefore surface tension has been the topic of a wide number of
+publications. We will discuss solutions provided in the literature in the next sections.
+5.5.3. The issue of spurious currents at interfaces
+Common to all multi-phase models, at curved interfaces between the liquid and vapor phases, spurious (often
+vortical) currents are observed. The magnitude of these spurious currents is often directly tied to the density ratio
+and interface thickness. The spurious currents are often associated to inbalance of forces at curved interfaces due to
+discretization errors, most notably the limited degree of isotropy. To illustrate the importance of isotropy consider
+a 2-D drop surrounded by a vapor phase. The density distribution, and therefore pressure, is only function of r in
+polar coordinate, i.e. ∂nρ/∂θn = ∂nP/∂θn = 0 for any n with n > 0 which results in driving forces of the form, if one
+considers the Korteweg stress tensor:
+∇P − κρ∇∆ρ = ∂P
+∂r er − κρ
+�∂3ρ
+∂r3 = 2
+r
+∂2ρ
+∂r2 − 2
+r2
+∂ρ
+∂r
+�
+er,
+(633)
+which clearly satisfy rotational invarience. In the absence of rotational forces one expects the velocity field to be
+rotational-invarient too. Furthermore, at steady state and assuming vanishing velocity far away from the drop the
+continuity equation
+1
+r
+∂ρur
+∂r
+= 0,
+(634)
+leads to:
+ur = 0.
+(635)
+91
+
+It can therefore be concluded that isotropy of the driving forces should guarantee the absence of any form of velocity
+in the case of the static 2-D droplet.
+Let us now consider the discretized form of the driving force on the D2Q9 stencil, i.e. Eq. (621). Operating a Taylor
+expansion on that stencil one finds:
+2
+�
+P − P0(r)
+�
+i
+w(|ciδt|)ciδt
+�
+P − P0(r + ci) = 2
+�
+P − P0∇
+�
+1 + 1
+6∇2 + 1
+72∇2∇2
+� � �
+P − P0
+�
++
+√P − P0
+90
+�∂5 √P − P0
+∂x5
+ex + ∂5 √P − P0
+∂y5
+ey
+�
+.
+(636)
+It is clear that the first term is isotropic. The last two terms however are not isotropic meaning this discrete approx-
+imation loses isotropy at order five in turn leading to force imbalance which is then countered by non-zero velocity
+components manifesting around the interface. A typical result from lattice Boltzmann simulations of a static 2-D drop
+is shown in Fig. 24. Note that while we have considered the specific form of the body force used in [171] to get
+Figure 24: Illustration of spurious currents near liquid/vapor interfaces: Time-evolution of maximum spurious currents along with the density and
+velocity fields at the converged state as obtained from simulations with SRT collision model and exact difference method, at νδt/δr2 = 0.03 and
+Tr = 0.59. Image reproduced from [131].
+Eq. (636), the classical form ∇(P − P0) would also lead to similar behavior, i.e.
+�
+i
+w(|ciδt|)ciδt(P − P0)(r + ci) = ∇
+�
+1 + 1
+6∇2 + 1
+72∇2∇2
+�
+(P − P0) +
+1
+180
+�∂5(P − P0)
+∂x5
+ex + ∂5(P − P0)
+∂y5
+ey
+�
+. (637)
+also generating non-isotropic terms forcing spurious currents at curved interfaces. The only difference is in the form
+of non-isotropic errors that appear at order 5. A more detailed discussion of the errors of different forms of the forcing
+term will be provided in later sections.
+5.5.4. Galilean invariance of viscous dissipation rates and stability
+For iso-thermal multi-phase flow simulations, even assuming the temperature in the discrete equilibrium is set
+to the lattice temperature, and that the Mach number is kept very low Galilean-variant errors in the viscous stress
+tensor, both deviatoric and diagonal components can be quite pronounced. For instance, consider the case of errors in
+deviatoric components of the third-order equilibrium moments tensor for a second-order equilibrium:
+δΠeq
+αβγ = ρuαuβuγ + (ρc2
+s − P0)[uαδβγ]cyc,
+(638)
+92
+
+Pu
+p1
+p
+0
+0.02
+udt/Sr
+ug /gxeun
+0.03
+0.02
+0.01
+100
+1050
+0.5
+1
+y/H
+0
+0.2
+0.4
+0.6
+0.8
+1
+u/umax
+0
+0.5
+1
+y/H
+0
+0.2
+0.4
+0.6
+0.8
+1
+u/umax
+Figure 25: Steady-state velocity profiles for the layered Poiseuille flow. Left: Configuration (a), Tr = 0.77, ρl/ρv = 10.1, µl/µv = 10.1 ; Right:
+Configuration (b), and (right) Tr = 0.36, ρl/ρv = 1030 and µl/µv = 11.3. Grey plain line: analytical solution; Black dashed line: Free energy LBM
+with product-form equilibrium; Red dashed line: Free energy LBM with conventional second-order equilibrium. Results are taken from [146].
+Assuming P0 = ρc2
+s is guaranteed everywhere the second term disappears leaving a term third-order in Mach num-
+ber. In the case of ideal fluid simulations given that density variation are small the third-order scaling of this term
+with Mach number allows one to neglect it for small Mach number simulations. However for non-ideal fluids, at liq-
+uid/vapor interface the density gradient can get quite large making this error term non-negligible even for small Mach
+numbers. In practice, the erroneous viscous stress tensor can lead to pronounced velocity jumps at the interface as it
+does not guarantee continuity of viscous momentum flux. For errors in the deviatoric components, i.e. viscous shear
+stress, this effect can be readily observed with a case as simple as the two-layer Poiseuille flow. This case consists of
+a rectangular domain filled with the liquid phase at the bottom and the vapor phase on top. The flow is driven by a
+body force. Top and bottom are subject to no-slip boundary conditions while the inlet and outlet are fixed by period-
+icity. Running this case with models relying on second-order polynomial equilibria one recovers results such as those
+shown in Fig. 25. Note that here the maximum non-dimensional velocities are quite small. As for ideal gas solvers, it
+is observed that including third-order terms in the discrete equilibrium eliminates this numerical artifact. This effect
+is common to all multi-phase LBM, regardless of the formulation and the collision model [172, 173]. For instance, it
+has been documented and studied for the color-gradient [172] and phase-field formulations [173, 174, 175, 176].
+While the effect of third-order moments error on Galilean-invariance of the viscous stress tensor is quite well-
+documented its effect on the continuity equation have never been discussed. The LBM is known to guarantee global
+conservation of mass to be exact. However locally one does not exactly recover the continuity equation. A third-order
+perturbation analysis shows that at order ε3 the zeroth-order moment satisfies [111]:
+∂(3)
+t ρ − 1
+12∇∇ :
+�
+∂(1)
+t Πeq
+2 + ∇ · Πeq
+3
+�
+= 0.
+(639)
+The second term in that equation shows that there is a third-order deviation in the continuity equation recovered by
+the LBM. However looking at the form of that deviation term one observes that it is nothing but the ε-level balance
+equation of the second-order moments restored to its correct form by the correction discussed in this section. We can
+therefore conclude that apart from restoring Galilean-invariance to the viscous stress the correction discussed here
+also removes third-order errors in the mass balance equation.
+All lattice Boltzmann models targeting non-ideal fluids, as all other classical discrete solvers, are subject to dis-
+cretization errors coming from both the lattice Boltzmann solver and the body force term. The specific form and
+properties of these higher-order error terms manifests in different forms, i.e.
+• Magnitude of discretization error normal to interface: As shown in Eq. (627) this affects the mechanical stability
+condition at the discrete level. The mismatch between the discrete-level mechanical stability condition with the
+Maxwell construction leads to errors in the coexistence densities even for flat interfaces as illustrated in Fig. 23.
+93
+
+• Spurious surface tension-like terms: As shown in Eqs. (636) and (637) a classical first-neighbour discretization
+is equivalent to a second-order central finite differences an leads to third-order errors with a surface tension-like
+structure. In the case of the pseudo-potential method this error is the reason one observes surface tension.
+However on the downside the capillary coefficient is fixed as shown in Eq. (632).
+• Non-isotropic terms: In 2- and 3-D a look at the form of the error terms recovered at orders three and above
+shows that non-isotropic terms appear; For instance for the first-neighbour discretization non-isotropic terms
+appear first at order five. This leads to the formation of spurious currents in the vicinity of curved interfaces.
+The magnitude of these spurious currents is directly proportional to density ratio and inversely proportional to
+interface thickness.
+• Errors affecting viscous stress tensor: The use of a second-order polynomial equilibrium leads to errors in the
+deviatoric components of the equilibrium third-order moments tensor in turn leading to errors in the effective
+shear viscosity. Even at very low velocities this error is quite pronounced around liquid/vapor interfaces.
+All these issues lead to practical limitation such as a maximum reachable density and/or viscosity ratio in simulations.
+A number of of improvements have been proposed over the year to relax constraints on density and viscosity ratio.
+We will review major improvements in the next section.
+5.6. Improvements and enhanced models for non-ideal fluids
+5.6.1. Equations of state
+One approach to reduce spurious currents and access larger coexistence densities that was proposed early on was
+the use of different equations of state starting with the work of [171]. The authors compared the maximum spurious
+currents as a function of density ratio for different equations of states. The effect of the choice of equation of state
+on maximum spurious currents as a function of density ratio is shown in Fig. 26 While initially such proposals were
+Figure 26: Maximum spurious currents as a function of density ratio for different equations of state: (plain line) Shan-Chen, (dashed line) van der
+Waals, (plain line with circular markers) Carnahan-Sterling, (plain line with square markers) Peng-Robinson, (plain line with diamond markers)
+Riedlich-Kwong and (plain line with triangle markers) Riedlich-Kwong-Soave. Simulation have been conducted with the realization of [171].
+Simulations have been conducted with the same choices of a and b as those reported in [171].
+limited to classical cubic equations of states, later many authors proposed tailored equations of state designed solely to
+allow phase separation at the target density ratio and minimize numerical artifacts. Here we provide a brief overview
+of these equations of state.
+Cubic equations of state. This family of equations of state are widely used in both thermodynamics and non-ideal
+fluid simulations. The most well-known equation of state in that family was proposed by van der Waals [136],
+P = ρRT
+1 − bρ − aρ2,
+(640)
+94
+
+4
+0.1
+0.08
+0.06
+0.04
+0.02
+0
+100
+101
+102
+103
+Pt/ puwhere parameters a and b are related to critical temperature Tc and pressure Pc as,
+a = 27
+64
+R2T 2
+c
+Pc
+, b = 1
+8
+RTc
+Pc
+.
+(641)
+The Peng–Robinson EoS [177],
+P = ρRT
+1 − bρ −
+aα(T)ρ2
+1 + 2ρb − b2ρ2 ,
+(642)
+with
+α(T) =
+�
+1 + (0.37464 + 1.54226ω′ − 0.26992ω′2)
+�
+1 −
+�
+T/Tc
+��2 ,
+(643)
+where ω′ the acentric factor (ω′ = 0.344 for water), and
+a = 0.45724R2T 2
+c
+Pc
+, b = 0.0778RTc
+Pc
+.
+(644)
+The Riedlich–Kwong–Soave EoS [178, 179],
+P = ρRT
+1 − bρ − aα(T)ρ2
+1 + ρb ,
+(645)
+with
+α(T) =
+�
+1 + (0.480 + 1.574ω′ − 0.176ω′2)
+�
+1 −
+�
+T/Tc
+��2 ,
+(646)
+and
+a = 0.42748R2T 2
+c
+Pc
+, b = 0.08664RTc
+Pc
+,
+(647)
+and the Carnahan–Starling EoS [180],
+P = ρRT 1 + bρ/4 + (bρ/4)2 − (bρ/4)3
+(1 − bρ/4)3
+− aρ2,
+(648)
+with
+a = 0.4963R2T 2
+c
+Pc
+, b = 0.18727RTc
+Pc
+.
+(649)
+The co-existence densities of these four EoS as obtained using the Maxwell reconstruction method and simulations
+reportes in [146] are shown in Fig. 27.
+Shan-Chen equations of state. In Shan-Chen-type equations of state the thermodynamic pressure is defined as:
+PSC = ρc2
+s + G
+2 ψ2,
+(650)
+where ψ is the non-local interaction potential. To derive an optimal form for the potential function a number of
+constraints have to be taken into account; First, using the mechanical equilibrium condition one should arrives at the
+following so-called thermodynamic consistency condition on the potential [181]:
+� ρv
+ρl
+�
+P − ρc2
+s − G
+2 ψ2� 1
+ρ2 dρ = 0,
+(651)
+which is only strictly satisfied with ψ ∝ ρ [149]. However, a potential interaction of that form would not allow for co-
+existence of two phases of different densities. Second, given that the original pseudo-potential has only an attractive
+non-local contribution term, as noted in [181, 182], to mimic the hard-core repulsive interaction of real molecules and
+prevent collapse of the liquid phase the potential must saturate at large densities, ψ → cst. Under these constraints
+95
+
+10-11
+10-7
+10-4
+10-1
+0
+0.2
+0.4
+0.6
+0.8
+1
+2
+3
+10-11
+10-7
+10-4
+10-1
+0
+0.2
+0.4
+0.6
+0.8
+1
+T/Tc
+1.5 2 2.5
+10-11
+10-7
+10-4
+10-1
+/ c
+0
+0.2
+0.4
+0.6
+0.8
+1
+2
+3
+10-11
+10-7
+10-4
+10-1
+/ c
+0
+0.2
+0.4
+0.6
+0.8
+1
+T/Tc
+2
+3
+4
+Figure 27: Liquid-vapor coexistence for various equations of state. Gray lines: Maxwell’s equal-area construction; Red symbol: Simulation. Top
+left: van der Waals (640) (a = 0.000159, b = 0.0952); Top right: Peng–Robinson (642) (a = 0.000159, b = 0.0952); Bottom left: Carnahan–
+Starling (648) (a = 0.000868, b = 4); Bottom right: Riedlich–Kwong–Soave (645) (a = 0.000159, b = 0.0952). For all simulation ˜κ = 0.02.
+Results reproduced from [146].
+96
+
+a family of potentials were proposed, to satisfy the previously-listed conditions as closely as possible. For instance
+in [12] the authors used a potential defined as:
+ψ = ρ0
+�
+1 − exp
+�
+− ρ
+ρ0
+��
+,
+(652)
+where ρ0 is a tunable constant. Another form was proposed in [183]:
+ψ = ρ0 exp
+�
+−ρ0
+ρ
+�
+.
+(653)
+The behavior of the pseudo-potential of Eq. 5.6.1 is illustrated in Fig. 28. A expected in the limit of ρ/ρ0 → 0 one
+Figure 28: Behavior of potential of Eq. 5.6.1 as a function of local density; Black line: ψ/ρ0 = ρ/ρ0, red dashed line: Eq. 5.6.1.
+recovers ψ ∝ ρ while on the other end of the spectrum, ρ/ρ0 → ∞ the potential saturates. This clearly shows that while
+the saturation allows for stable phases at large density ratios it deviates considerably from ∝ ρ making thermodynamic
+inconsistencies in the sense of Eq. (651) pronounced.
+Taylored equations of state for improved numerical properties. In [184] the authors proposed a new family of equa-
+tions of state to improve numerical properties of the pseudo-potential method, namely better compliance with thermo-
+mechanical consistency. The piece-wise linear equation of state proposed in [184] consists of defining the pressure
+as:
+P =
+�������������
+ρc2
+s,v
+ifρ ≤ ρ1
+ρ1c2
+s,v + (ρ − ρ1) c2
+s,m
+ifρ1 ≤ ρ ≤ ρ2
+ρ1c2
+s,v + (ρ2 − ρ1) c2
+s,m + (ρ − ρ2) c2
+s,l
+ifρ2 ≤ ρ
+(654)
+where in practice cs,v, cs,l and cs,m are chosen a priori. The choice of these three variables allows one to fix speed
+of sound in both the liquid and vapor phases and the interface thickness independently. Once they are fixed, the
+remaining free parameters, i.e. ρ1 and ρ2 are closed via two conditions, namely mechanical:
+� ρl
+ρv
+dP
+dρ dρ = 0,
+(655)
+and chemical potential balance:
+� ρl
+ρv
+1
+ρ
+dP
+dρ dρ = 0.
+(656)
+This equation of state is illustrated in Fig. 29. With this approach, the speed of sound in the liquid and vapor phase are
+97
+
+4
+3
+0
+2
+0
+0
+2
+3
+4
+Od jdFigure 29: P − ρ diagram for piece-wise linear equation of state, Eq. 654. The density ratio here is set to 10.
+tunable parameters and as such can be set to be as close to each-other as possible to minimize compressibility effects
+in the vapor phase and allow for larger CFL numbers. The piece-wise linear equation of state is now routinely used in
+combination with the pseudo-potential formulation to model multi-phase flows with density ratios of the order of 103,
+see for instance [185, 186].
+Another alternative proposed by [187], argues that the main issue of cubic equations of state is the van der Waal loop
+section of the P − V diagram. In this region cubic equations of state predict negative compressibility. To better deal
+with that region the authors proposed an apprioach that consists of using the classical cubic equations of state, e.g. van
+der Waal Peng-Robinson etc, in the liquid and vapor branch and replacing it with a tailored third-order polynomial in
+the van der Waals loop region ρv < ρ < ρl, i.e. both the binodal and spinodal regions:
+P =
+�������������
+PEoS(ρ)
+ifρ ≤ ρv
+P0(ρv) + θm(ρ − ρv)(ρ − ρl)(ρ − ρm)
+ifρv ≤ ρ ≤ ρl
+PEoS(ρ)
+ifρl ≤ ρ
+(657)
+The use of the cubic polynomial in the van der Waals loop comes with four free coefficients. Conditions on continuity
+of pressure and isothermal sound speed (or compressibility) at the vapor and liquid densities would in principle close
+all free parameters and lead to the original cubic equation of state selected in the vapor and liquid branches. As
+such, and as detailed in the article, this approach can only have potential to improve interface properties if one of the
+previously listed physical conditions are neglected. The removal of one of the conditions, sound speed in one of the
+bulk phases would in principle allow control over the shape in the van der Waals loop region.
+While the choice of the equation of state can be an efficient tool in reducing spurious currents and errors in coexistence
+densities, the way these non-ideal contributions are introduced into the kinetic model is not unique and can han
+dramatic effects on errors and stability.
+5.6.2. Partitioning of pressure contributions
+In previous sections we introduced a general kinetic framework for non-ideal fluids and discussed the invarience of
+the recovered macroscopic equations with respect to the choice of reference pressure P0 enforce by the BGK collision
+operator attractor. Here we discuss different possible choices of P0 and its repercussions on numerics.
+The classical route: equilibrium at stencil reference temperature. The most widely used partition approach in the
+litterateur consists of fixing P0 appearing in the equilibrium at a value optimizing numerical properties of the lattice
+Boltzmann solver. For instance for a model based on a third-order Gauss-Hermite quadrature the optimal value of P0
+is:
+P0 = ρ δr2
+3δt2 .
+(658)
+98
+
+0.08
+0.06
+P 0.04
+V
+0.02
+I
+I
+I
+P2
+II
+I
+11
+0
+0
+0.5
+1
+pSetting the reference pressure in that way has two main advantages; As discussed earlier the classical third-order
+quadrature admits a deviation in the diagonal components of the third-order equilibrium moment that has a third-
+order dependence on velocity and first-order dependence on P0/ρ:
+δΠeq
+ααα = ρuα
+�
+u2
+α + 3(P0/ρ − c2
+s)
+�
+.
+(659)
+Therefore small deviations of P0/ρ from the optimal temperature c2
+s can considerably increase the Galilean-variant
+errors in the dissipation rate of normal modes, as illustrated in Fig. 30. The second advantage of this choice of
+Figure 30: Error in the diagonal components of the third-order moments tensor as a function of the reference pressure.
+partition is stability domain. As illustrated in Fig. 31 via the linear stability domain best results in terms of maximum
+non-dimensional speed and minimum non-dimensional viscosity are achieved at P0/ρc2
+s = 1. Both above and below
+Figure 31: Linear stability domain of the SRT collision operator with a product-form equilibrium as a function of the reference pressure P0.
+P0/ρc2
+s = 1 the stability domain is considerably reduced making realistic simulations with acceptable CFL numbers
+practically impossible.
+The vast majority of publications treating of isothermal non-ideal fluids rely on this type of partition. For instance in
+the pseudo-potential model with the Shan-Chen equation of state:
+P0 = ρc2
+s,
+(660)
+99
+
+Po/pc=1
+cxx
+10-2
+0
+0.5
+1.02.2
+0.4
+1.9
+1.6
+0.3
+Po/pcs
+1.3
+IInl
+Sr/St
+1.0
+0.2
+0.7
+0.1
+0.4
+0.1
+0
+10-6
+10-2
+1
+VSt / Sr2and
+P − P0 = G
+2 ψ2.
+(661)
+In the free energy formulation, this is equivalent to the force-based approach with [128]:
+TK − P0I =
+�
+P − ρc2
+s − κρ∇2ρ − κ
+2|∇ρ|2�
+I + κ∇ρ ⊗ ∇ρ.
+(662)
+This specific partition of pressure is the most widely used approach in the literature, mainly because of the numerical
+properties enumerated above.
+Full pressure used in equilibrium attractor. As mentioned earlier, the idea of introducing the full thermodynamic
+pressure into the equilibrium function of a lattice Boltzmann solver started with the first free energy LBM [150, 188]
+where the non-ideal equation of state and surface tension were introduced into the discrete equilibrium via moments
+matching. A similar construction was also discussed in [189, 190]. The authors argued that this approach has the
+advantage of guaranteeing mass conservation locally. Furthermore, this approach has the additional advantage of
+reducing derivatives in the stress tensor by one order and therefore making the overall scheme more local. The first
+attempt presented in [150] was based on a second-order polynomial discrete equilibrium and subject to Galilean-
+variant errors in both the diagonal and deviatoric components of the viscous stress tensor. Consider a two-phase fluid
+in the incompressible regime with a density ratio of only 10: 10P0/ρl = P0/ρv. This means that inevitably at least
+one of the phases will have P0/ρ considerably larger or smaller than c2
+s resulting in diminished stability domain, see
+Fig. 31. Furthermore, without corrections the viscous stress tensor is subject to errors scaling with ∝ (P0/ρ − c2
+s), see
+Eq. (659). In effect this means that the application of such a model would be limited to very low density ratios. As a
+way to overcome this issue, and minimize errors related to deviation from the reference frame a realization based on
+the Particles-on-Demand was proposed and used in [191].
+5.6.3. Non-local thermodynamic pressure force contribution: Using mathematical identities to reduce discretization
+errors
+The first step in the realization of the force is the way it is treated. It can be introduced as is [192], i.e.
+F = ∇(P − P0),
+(663)
+or using an identity:
+∇(P − P0) = 2
+�
+P − P0∇
+�
+P − P0, forP ≥ P0
+(664)
+This approach, for general non-ideal equations of state was employed in [171] following the original form of the
+pseudo-potential model [12]. It should be noted that in the case of the original model this equality held unconditionally
+because the Shan-Chen equations of state were strictly positive. Positivity can become an issue especially near the
+liquid branch spinodal point where pressure is usually minimal.
+As a way to extend the domain of accessible density ratios by decreasing the magnitude of leading-order error terms
+and reduce spurious currents a weighed combination of these two approaches was also proposed [80, 193]:
+F = γ∇(P − P0) + 2(1 − γ)
+�
+P − P0∇
+�
+P − P0,
+(665)
+where the weight γ becomes a tuning parameter to better match co-existence densities or reduce spurious currents.
+Another possibility, not discussed in the literature, would be to rewrite the non-ideal pressure contribution as:
+∇(P − P0) = (P − P0)∇ ln(P − P0), forP ≥ P0.
+(666)
+To illustrate the effect of the way this term is introduced and provide a simple comparison of their performances let
+us consider a simple 1-D interface:
+P − P0 ∝ 1
+2
+�
+1 + tanh x − x0
+σ
+�
+,
+(667)
+100
+
+located at x0 of thickness σ. Assuming a second-order accurate finite difference discretization of the contribution,
+errors are governed by the third- and higher order derivatives. Denoting approaches of Eqs. (663), (664) and (666)
+respectively with F1, F2 and F3 and assuming zero surface tension, the leading order error of pressure normal to the
+interface would scale as:
+δF1
+=
+1
+3!∂3
+x(P − P0) + O(∂5
+x),
+(668)
+δF2
+=
+2 √P − P0
+3!
+∂3
+x
+�
+P − P0 + O(∂5
+x),
+(669)
+δF3
+=
+P − P0
+3!
+∂3
+x ln(P − P0) + O(∂5
+x).
+(670)
+The leading-order errors for the considered interface, for two different interface thicknesses illustrating the diffuse and
+near-sharp cases, are shown in Fig. 32. Comparing the different errors one can already observe that F1 leads to the
+Figure 32: Profiles of leading-order error terms for different realizations of the non-local pressure contributions for (left) σ = 8 and (right) σ = 1.
+Black line: F1, red line: F2 and blue line: F3.
+largest interfacial errors while F3 introduces the lowest amount of deviations both in the diffuse and sharp interface
+configurations.
+5.6.4. Higher order discretization: Leading order error and isotropy
+Once the form of the non-local pressure term has been determined it needs to be discretized; For the sake of
+readability we will only consider the form F2 here. The finite difference discretized form can be written in general as:
+F2 = 2
+�
+P − P0(r)
+Q
+�
+i=0
+w(|ci|)ci
+�
+P − P0(r + ciδt),
+(671)
+where ci defines the stencil used for the discretization and w(|ci|) are the associated weights. For instance, considering
+a simple second-order central difference approximation ci ∈ {(1, 0), (0, 1), (−1, 0), (0, −1)} and w = 1/2. From classical
+theory of finite differences method and Taylor expansion the order of accuracy of the approximation can be arbitrarily
+increased by relying on larger stencils. The weights w(|ci|) on such classical stencils for different order of accuracy are
+listed in Table 5.6.4. While the use of such higher order schemes reduces the errors in coexistence density stemming
+from the thermodynamic inconsistency issue it does necessarily improve the isotropy of the discrete approximation.
+101
+
+X10-4
+0.1
+2
+0.05
+0
+0
+-1
+-0.05
+-2
+-0.1
+-3
+-0.15
+-4
+-0.2
+50
+100
+150
+90
+95
+100
+105
+110
+X
+XOrder of accuracy
+w(1)
+w(2)
+w(3)
+w(4)
+2
+1/2
+4
+2/3
+−1/12
+6
+3/4
+−3/20
+1/60
+8
+4/5
+−1/5
+4/105
+−1/280
+Table 6: List of weights for classical stencils with different orders of accuracy. The notation w(k) refers to the weight of all stencil components of
+size k.
+w(1)
+w(
+√
+2)
+w(2)
+w(
+√
+5)
+w(2
+√
+2)
+w(3)
+w(
+√
+10)
+E(4)
+1/3
+1/12
+E(6)
+4/15
+1/15
+1/120
+E(8)
+4/21
+4/45
+1/60
+2/315
+1/5040
+E(10)
+262/1785
+93/1190
+7/340
+6/595
+9/9520
+2/5355
+1/7140
+Table 7: List of weights for stencils with different orders of isotropy. The notation E(2n) refers to a stencil with order of isotropy 2n. For weights
+the notation w(k) refers to the weight of all stencil components of size k. The corresponding stencils are illustrated in Fig. 33.
+Applying the Taylor expansion to the general form of the discretized force [182]:
+F2,α = 2
+�
+P − P0(r)E(2)
+α1 ∂α2
+�
+P − P0(r) + 1
+3!E(4)
+α1α2α3α4∂α1α2α3
+�
+P − P0(r) + . . .
+(672)
+where
+E(m)
+α1,...,αm =
+�
+i
+w(|ci|)ci,α1 . . . ci,αm,
+(673)
+with E2n+1 = 0. The even-order tensors can be re-written as:
+E(2n)
+α1...α2n = C(2n)∆(2n)
+α1...α2n,
+(674)
+where ∆(2n)
+α1...α2n can be computed using the following recursion relation:
+∆(2)
+α1α2
+=
+δα1α2,
+(675)
+∆(4)
+α1α2α3α4
+=
+δα1α2δα3α4 + δα4α1δα2α3 + δα2α3δα4α1,
+(676)
+∆(2n)
+α1...α2n
+=
+2n
+�
+j=2
+δα1α j∆α2...α j−1α j+1...α2n.
+(677)
+This general expansion of the discrete forcing term allows to analyze both the leading-order errors and the degree
+of isotropy of the discrete approximation. The latter is an important point to consider as the continuous form of the
+force is isotropic. Any non-isotropic errors in the discrete approximation would lead to force imbalance on curved
+interfaces and lead to spurious currents. The use of higher-order stencils can therefore help reduce the spurious
+currents stemming from these force imbalances. In [182] the authors have derived stencils of different order of
+isotropy with corresponding weights. These are listed in Table 5.6.4 for a 2-D system. The stencils corresponding
+to these weights are shown in Fig. 33. It was shown in this section that one can reduce discretization errors at
+interfaces, both magnitude and isotropy, via higher order approximations relying on larger discretization stencils.
+Larger discretization stencils also mean larger number of discrete operations per grid-point and larger degrees of non-
+locality of such operations which in turn translate into both computational and communication (for parallel simulations
+on clusters with distributed memory) overhead.
+102
+
+Figure 33: Illustration of different discrete stencils for different orders of isotropy. Weights are listed in Table 5.6.4. Figure partially reproduced
+from [182].
+5.6.5. Thickening interface
+Artificial thickening of the interface is another strategy to both reduce errors in coexistence densities and spuri-
+ous currents. This strategy is motivated by the invariance of the non-dimensional coexistence densities with respect
+substance-specific coefficients as demonstrated through the principle of corresponding states and and the fact that
+errors at interfaces are function of higher-order derivatives of the pressure field. In the context of cubic equations of
+state, the simple analysis leading to (619) showed that the interface thickness can in principle be controlled through
+the capillary coefficient and isothermal compressibility tied itself to the long range interaction coefficient a. Plugging
+the van der Waals equation of state into Eq. (619) one would expect the interface thickness to scale with ∝ 1/ √a. This
+scaling is readily demonstrated via simulations close to the critical point, shown in Fig. 34. Carrying out simulations
+Figure 34: Effect of the choice of a on the interface width. Diamond, square and circle: Simulation for Tr = 0.98, 0.99, 0.995, respectively.
+Simulation conducted using van der Waals equation of state. Plot reproduced from [146].
+with different values of a it can easily be shown that this increase in interface thickness allows for better resolution
+of interfaces and therefore reduced deviations in discrete stress tensor. The coexistence densities as obtained from
+simulations with different choices of a are shown in Fig. 35. It is observed that increasing the interface thickness one
+converges to the coexistence density prediction of the Maxwell construction even at very large density ratios.
+As discussed in previous section, another aspect of errors in the stress tensor that need attention are non-isotropic
+effects leading to spurious currents. As for errors for flat interfaces these deviations functions of higher-order deriva-
+tives of the pressure field and such should reduce with thicker interfaces. The effect of the choice of a controlling
+interface thickness on spurious currents for the discrete model of [146] is illustrated in Fig. 36. It is clearly observed
+that smaller values of a, which as seen before scale with interface thickness as W ∝ 1/ √a, lead to smaller spurious
+currents scaling as ∝ a1.3 for the discrete model of [146] meaning they scale with interface thickness as ∝ W−2.6. Such
+scaling relationships can also be obtained for other discrete stencils.
+While changing the isothermal compressibility in combination with capillary coefficient allows to thicken the inter-
+face independently from surface tension it comes with a limitation: It changes the isothermal speed of sound in both
+liquid and vapor phases. Lower values of a lead to smaller speeds of sound in both phases. This in turn means that for
+103
+
+4th
+6th
+8th
+10th3
+u/-M
+0.5
+10-2
+10-1
+aFigure 35: Coexistence densities as obtained from (grey lines) Maxwell’s construction and (markers) simulations with different choices of a: (green
+x) a = 0.0102, (magenta +) a = 0.0051, (blue triangles) a = 0.0026, (red squares) a = 0.0013 and (black circles) a = 0.00064 Simulation conducted
+using van der Waals equation of state. Plot reproduced from [146].
+Figure 36: Maximum spurious currents for different values of a at Tr = 0.59. Simulation conducted using Peng-Robinson equation of state. Plot
+reproduced from [131].
+the isothermal simulation to be close to the low Mach regime one would need to run simulation at lower convective
+CFL conditions leading to much smaller time-steps and additional computational costs.
+5.6.6. Independent control over surface tension
+A solution to the fixed nature of the surface tension recovered by the original pseudo-potential model was provided
+in [182, 194] where the authors introduced the concept of dual/multi-range pseudo-potential. In its simplest form a
+second layer of neighbours is added to the stencil considered for the discretization of the pressure term:
+F2 = 2
+�
+P − P0(r)
+�
+i
+w(|ci|)ci
+�
+G1
+�
+P − P0(r + ciδt) + G2
+�
+P − P0(r + 2ciδt)
+�
+,
+(678)
+where G1 and G2 are coefficients to be determined below. Taylor-expanding this term:
+F2 = 2(G1 + 2G2)
+�
+P − P0∇
+�
+P − P0 + 2
+�
+P − P0
+G1 + 8G2
+6
+∇∇2 �
+P − P0.
+(679)
+To correctly recover the thermodynamic pressure term one must satisfy G1 + 2G2 = 1. Using this condition the force
+can be re-written as:
+F2 = ∇|P − P0|+
+�
+P − P0
+1 + 6G2
+3
+∇∇2 �
+P − P0,
+(680)
+meaning the surface tension coefficient can now be tuned with G2, κ = 1+6G2
+3
+. Alternatives to the dual-range model
+have also been proposed in the past years to limit the effect of the choice of G2 on the mechanical stability conditions.
+104
+
+1
+0.8
+T/T
+0.6
+0.4
+0.2
+10-5
+10-3
+10-1
+1.5
+2
+2.5
+p/p10-2
+α a1.3
+10-3
+0.001
+0.005
+aFor instance in [195] the authors introduce an additional source term in the discrete equation:
+Qi =
+wi
+2c4s ¯τH2 : κ′ �
+P − P0(r + ci)δt
+Q
+�
+i′=0
+w(|ci′|)ci′ ⊗ ci′
+� �
+P − P0(r + ci′δt) −
+�
+P − P0(r)
+�
+,
+(681)
+where κ′ is the parameter that controls the surface tension. While allowing a variable coefficient in front of the surface
+tension-like term, the final stress tensor is still different from the Koerteweg tensor.
+An extension of the dual range approach to recover a consistent Korteweg stress tensor fourth-order accurate in space,
+guaranteeing the surface tension is not polluted by leading order errors from the discretization of the thermodynamic
+pressure term was proposed in [146]:
+F2 = 2
+�
+P − P0(r)
+�
+i
+w(|ci|)ci
+�
+G1
+�
+P − P0(r + ciδt) + G2
+�
+P − P0(r + 2ciδt)
+�
++ ρ(r)
+�
+i
+w(|ci|)ci
+�G3ρ(r + ciδt) + G4ρ(r + 2ciδt)� ,
+(682)
+where G1 + 2G2 = 1 and G1 + 8G2 = 0 guarantee correct recovery of the thermodynamic pressure term while
+G3 + 2G4 = 0 and G3 + 8G4 = 6κ recover the correct Korteweg surface tension.
+5.6.7. The discrete pressure tensor
+As shown through Taylor expansion in the previous section, the continuous and discrete pressure tensors are not
+exactly the same. In [194] proposed an approach to evaluate the discrete pressure tensor as momentum flux through a
+surface; Given an infinitesimal area dS and the force acting through that surface dF the pressure tensor is defined as:
+dF = P · dS.
+(683)
+Integrating over a closed control volume one arrives at the fact that the surface integral of the pressure has to match
+total force acting on the control volume:
+�
+P · dS =
+�
+FdV,
+(684)
+which in discrete form reduces to:
+�
+P · S =
+�
+F.
+(685)
+Considering for the sake of simplicity a specific discrete velocity direction, i.e. ciδt, it can be seen that the number of
+force vectors across a unit vertical surface element dS = ex is cixδt and that across a unit horizontal surface element
+is ciyδt. In simplest case where all pressure contributions from the force have a strength F the pressure contribution is
+then simply obtained as ci ⊗ ciδt2F. For a force field where each contribution has a different magnitude one uses the
+averaged force, where averaging is operated on all force contributions crossing the surface area. This results, for the
+simplest first neighbor stencil and the classical pseudo-potential interaction in:
+P = −G
+2 ψ(r)
+8
+�
+i=0
+w(|ci|)ci ⊗ ciψ(r + ciδt).
+(686)
+105
+
+Following that same construction logic write the contribution for a more complex force, like he one used in [146] as
+F = FA + FB + FC + FD,
+(687)
+FA = ±8
+3
+�
+P − P0(r)
+Q−1
+�
+i=0
+w(|ci|)ci
+�
+P − P0(r + ciδt),
+(688)
+FB = ∓1
+3
+�
+P − P0(r)
+Q−1
+�
+i=0
+w(|ci|)ci
+�
+P − P0(r + 2ciδt),
+(689)
+FC = 2˜κρ(r)
+Q−1
+�
+i=0
+w(|ci|)ciρ(r + ciδt),
+(690)
+FD = −˜κρ(r)
+Q−1
+�
+i=0
+w(|ci|)ciρ(r + 2ciδt).
+(691)
+The pressure tensor contributions from forces FA and FC can be readily written as:
+PA
+=
+∓8
+6
+�
+P − P0(r)
+Q−1
+�
+i=0
+w(|ci|)ci ⊗ ci
+�
+P − P0(r + ciδt),
+(692)
+PC
+=
+−˜κρ(r)
+Q−1
+�
+i=0
+w(|ci|)ci ⊗ ciρ(r + ciδt),
+(693)
+while FB and FD contribute to the pressure tensor as follows:
+PB = ± 1
+6
+��������
+�
+P − P0(r)
+Q−1
+�
+i=0
+w(|ci|)ci ⊗ ci
+�
+P − P0(r + 2ciδt) +
+Q−1
+�
+i=0
+w(|ci|)ci ⊗ ciψ(r − ciδt)
+�
+P − P0(r + ciδt)
+�������� ,
+(694)
+PD = ˜κ
+2
+��������ρ(r)
+Q−1
+�
+i=0
+w(|ci|)ci ⊗ ciρ(r + 2ciδt) +
+Q−1
+�
+i=0
+w(|ci|)ci ⊗ ciρ(r − ciδt)ρ(r + ciδt)
+�������� .
+(695)
+These expressions allow to compute the discrete pressure tensor with high accuracy. Fig. 37 shows the distribution
+of the normal pressure, Pxx, in a flat interface simulation as computed from both the discrete and continuous pressure
+tensors,
+Pcont
+xx
+= P + κ
+�
+∂2
+xρ − 1
+2|∂xρ|2
+�
+,
+(696)
+While the discrete evaluation method correctly results in a uniform pressure distribution throughout the domain, also
+across the interface, the continuous approximation evaluated using a finite differences approximation fails to do so,
+indicating errors due to higher-order terms. This points to the necessity of using the discrete pressure tensor for
+evaluation of sensitive quantities especially for sharper interfaces.
+5.6.8. Evaluating the effective surface tension
+Laplace’s law. In this approach, simulations of circular/spherical liquid drops of different radii surrounded with
+vapour are carried out. The corresponding surface tension coefficient is then evaluated using the Laplace law in a
+form,
+∆P = (D − 1)σ
+R
+,
+(697)
+where R is the drop radius. ∆P can readily be computed by extracting the pressure at the center of the drop Pin
+and a point in the vapor phase far away from the drop Pout as ∆P = Pin − Rout. For simulations carried out using
+diffuse interface formulations the notion of drop radius becomes ambiguous. To that end, for consistent analysis of
+106
+
+0
+50
+100
+150
+200
+-6
+-4
+-2
+0
+2
+4
+0
+1
+2
+3
+Figure 37: Pressure distribution from a simulation at Tr = 0.36, corresponding to Pr = 0.0022 and ρl/ρv = 103. Black line: Evaluation using the
+discrete pressure tensor; Red line: Evaluation using continuous pressure tensor. Dashed blue line: Density profile.
+results one has to introduce the notion of dividing surfaces, more specifically the equimolar surface here, proposed by
+Gibbs [196]. A brief reminder of Gibbs’ theory of dividing surfaces is in order. The total mass in both the diffuse and
+sharp interface pictures can be written as:
+�
+V
+ρdV = ρlVl + ρvVv + Γ,
+(698)
+where ρlVl and ρvVv are the masses in the bulk liquid and vapor phases in the sharp interface picture, while Γ is the
+excess mass on a dividing surface Σ, or mass adsorbance [196]. By requiring that no mass be stored on the dividing
+surface we get the definition of the equimolar surface:
+Γ = 0.
+(699)
+The family of dividing surfaces in the case of drop or bubble are concentric spheres (D = 3) or concentric circles
+(D = 2) parameterized by their radius R. In particular, for a two-dimensional drop, the mass adsorbance can be
+written as a function of the radius of the dividing circle,
+Γ(R) =
+� 2π
+0
+� ∞
+0
+(ρ(r) − ρv)rdrdϕ −
+� 2π
+0
+� R
+0
+(ρl − ρv)rdrdϕ,
+(700)
+while the zero-adsorbtion condition (699), Γ(Re) = 0, implies the equimolar radius Re,
+Re =
+�� ∞
+0 (ρ(r) − ρv)rdr
+(ρl − ρv)
+.
+(701)
+This definition can then be used to replace the radius in Eq. 718. Once both drop radii and pressure differences are
+known the surface tension can be extracted as the slope of ∆P = σ D−1
+Re . This is illustrated in Fig. 38.
+Kirkwood approach for flat interface. The surface tension coefficient of a flat interface can be evaluated using its
+mechanical definition [197] as,
+σ =
+� +∞
+−∞
+�
+Pxx − Pyy
+�
+dx,
+(702)
+where here the interface has been considered normal to the x-axis in a two-dimensional simulation setup. The nor-
+mal Pxx and the tangential Pyy components of the discrete pressure tensor can be computed from the continuous
+approximation or using the discrete pressure tensor introduced in the previous section.
+107
+
+0.01
+0.015
+0.02
+0.025
+0.03
+0
+0.2
+0.4
+0.6
+0.8
+1
+10-3
+Figure 38: Left: Circular D = 2 drop configurations; Right: Pressure difference scaling with drop radius for Tr = 0.99, 0.98, 0.97 and 0.96. The
+pressure difference is defined as ∆P = Pin − Pout. The slope of the straight line is the surface tension coefficient. Results are reproduced from [146].
+5.7. Fluid-solid interaction: wetting properties
+A first indication on the treatment of a solid boundary for second-gradient fluids, under the assumption of short
+range-only interaction, was given by Cahn (critical point wetting). Considering a control volume with a solid surface
+at the boundary the total free energy is defined as:
+A =
+�
+V
+�
+A0 + 1
+2κ|∇ρ|2
+�
+dV +
+�
+Aw(ρw)dS,
+(703)
+where V is the considered control volume, S the solid surface and Aw a surface free energy function which depends
+only on the fluid density at the solid surface ρw. The derivative of this functional is obtained as:
+δA =
+�
+V
+δρ
+�∂A0
+∂ρ − κ∇ · ∇ρ
+�
+dV +
+�
+δρw
+�
+κn · ∇ρ + ∂Aw
+∂ρw
+�
+dS,
+(704)
+where n is the unit vector normal to the solid surface. Minimzation of the total free energy with respect to ρw leads to:
+κn · ∇ρ = dAw
+dρw
+.
+(705)
+5.7.1. Static contact angle
+One of the first approaches to impose wetting boundary conditions for non-ideal fluids in the context of the pseudo-
+potential method was proposed in [198]. Following the structure of the non-local pseudo-potential interaction term
+they proposed an additional contribution modeling wall interaction of the form:
+Fwall = −ρ(r)Gwall
+�
+i
+wiciδts(r + ciδt),
+(706)
+where s is an indicator function equal to one in a solid cell and zero in a fluid cell and G)wall is the interaction
+strength parameter controlling the contact angle. Sukop and Thorn [199] proposed a slightly modified form of the
+wall interaction term as [200, 201]:
+Fwall = −ψ(r)Gwall
+�
+i
+wiciδts(r + ciδt).
+(707)
+108
+
+0
+0.5
+1
+0
+50
+100
+150
+200
+Figure 39: Static contact angles as (blue squares) obtained from the Young–Laplace equation and (red circles) measured directly from the simula-
+tions using the approach of [181, 203]. Image is taken from [146].
+Later on Kang et al. proposed a modified version of Martys and Chen’s approach to setting wetting boundary condi-
+tions as [202]:
+Fwall = −ρ(r)Gwall
+�
+i
+wiciδtρwall(r + ciδt).
+(708)
+The wall is modeled as a phase with a constant density ρwall. As with previous schemes Gwall is used to set the contact
+angle. Alternatively, Benzi et al proposed a slightly modified form, fully consistent with the bulk non-local interaction
+[181, 203]:
+Fwall = −ψ(r)G
+�
+i
+wiciδtψwall(r + ciδt),
+(709)
+where the only free parameter is ψwall which controls adhesion of the liquid/vapour phase to the solid boundary, i.e.
+for ψwall → ψl the contact angle goes to zeros while ψwall → ψv the contact angles goes to 180.
+Geometrical approach. In parallel with the previously-listed approaches, alternative geometrical approaches widely
+in use for phase-field based approaches have also been developed. Ding and Spelt proposed a geometrical approach
+to implement contact angles in phase-field methods as [204]:
+tan
+�π
+2 − θs
+�
+=
+−n · ∇ψ
+|∇ψ − (n · ∇)n|,
+(710)
+which once discretized leads to [204]:
+ψ(x, −δy) = ψ(x, δy) + tan
+�π
+2 − θs
+�
+|ψ(x + δx, 0) − ψ(x − δx, 0)|,
+(711)
+where assuming a flat solid interface perpendicular to the y-axis at y = 0, (x, −δy) designates a ghost layer within
+the solid. θs is the contact angle to be imposed. They showed that the geometrical approach can fix the slop of the
+liquid-gas interface to a value consistent with the imposed contact angle given that there are enough points within the
+interface, i.e. typically 4-8 grid-points [204]. The approach is illustrated in Fig. 40. The geometrical approach of
+Ding and Spelt was transposed into the pseudo-potential formulation in [205] for flat interfaces. Later on, in [206] it
+was extended to curved solid boundaries. While here we have used the pseudo-potential ψ as the order parameter in
+defining the contact angle, this approach can readily be extended to free energy methods by replacing ψ with the fluid
+density.
+109
+
+Figure 40: Illustration of contact line in geometrical approach to contact angle.
+5.7.2. Contact angle hysteresis
+To illustrate the meaning of contact angle angle hysteresis let us take the example detailed in [207]. Consider a
+small droplet resting on a solid surface. If the droplet is allowed to evaporate or if liquid is slowly withdrawn from
+the droplet with a syringe, over time both the volume and contact angle will decrease maintaining the same contact
+area, up until the onset of recession. The drop will then recede with a constant contact angle, θR, characteristic of
+both surface chemistry and topography. Now the opposite scenario: if the surface is cooled down below dew point
+leading to liquid condensing on the drop or if liquid is slowly added to the droplet the droplet both volume and contact
+angle will initially increase until the drop starts to advance. The drop will advance at a constant angle θA which is
+also determined by the characteristics of the solid surface. Both cases are illustrated in Fig. 41. A metastable droplet
+can form with any angle between these two angles. The interval between the two is referred to as the contact angle
+hysteresis. A simple realization of the contact angle hysteresis was proposed and used in [208] in the context of
+Figure 41: Illustration of (a) advancing and (b) receding drop on solid surface. In (c) a drop sliding on a surface exhibiting both receding and
+advancing contact angles in shown. Image is taken from [207].
+the geometrical approach to setting the contact angle. There the authors dynamically adjusted the contact angle as a
+function of the speed of the contact line, uCL:
+�������������
+θs = θA,
+∀uCL > 0,
+θs = θR,
+∀uCL < 0,
+θs = θs,
+uCL = 0.
+(712)
+In practice, the contact angle is evaluated at every time-steps. If the measure angle is within the hysteresis windows
+it is left unaltered. If it is outside the hysteresis windows it is set to either the advancing or receding contact angle,
+depending on the speed of the contact line. Similar approaches have been adopted in the contact of the LBM [209, 210,
+211]. For instance in [212] the authors used a similar feedback-based strategy without taking into account the contact
+line speed. The authors set θ = θA if the measured angle was larger than θA and θ = θR if its was smaller than θR. While
+this approach performed well for contact line motion on flat substrates and flow in tubes [213], as noted in [214], it
+110
+
+fluid 2
+interface thickness
+fluid 1
+n
+Solid wall6
+4.
+a
+b
+cresulted in un-physical behavior for isothermal drying of droplets. The correct behavior was restored by taking into
+account the contact line velocity [214]. One important point to note about contact angle hysteresis implementation is
+that to the authors knowledge all attempts at enforcing a hysteresis window have relied on the geometrical approach of
+Eq. 710. This is due to the fact that to dynamically set the contact angle to θR and θA there must be a way to estimate
+the corresponding boundary condition a priori. Other approaches to setting wetting conditions in the context of LBM
+do not establish a clear relationship between fluid/solid interaction force and contact angle.
+5.8. Assessment of thermo-physical properties of models
+5.8.1. Speed of sound and compressibility
+Different from hydrodynamic pressure-based formulation such as those employed in combination with Allen-Cahn
+interface tracking methods, all LBMs for weakly compressible non-ideal fluids recover the isothermal speed of sound
+of the implemented equation of state. The analytical isothermal sound speed can be obtained via the derivative of the
+pressure with respect to density at constant temperature, i.e. cs = �∂ρP|T. For instance for the van der Waals equation
+of state the isothermal sound speed is,
+cs =
+�
+∂P
+∂ρ
+�����T
+=
+�
+RT
+(bρ − 1)2 − 2aρ.
+(713)
+In simulations the sound speed can be measured by modeling the evolution of a pressure step-function and monitoring
+the position of the pressure front over time in a quasi-one-dimensional simulation at different temperatures. The sound
+speed for different cubic equations of state at different temperature in both liquid and vapor phases as obtained from
+simulations are compared to analytical data in Fig. 42. Similar to cubic equations of state, Shan-Chen-type equations
+Figure 42: Isothermal sound speed for various equations of state. Top row, from left to right: Peng–Robinson, Carnahan–Starling and Riedlich–
+Kwong–Soave; Bottom row: van der Waals. Grey plain lines: Theory; Symbol: Simulations. Plot reproduced from [146].
+also admit isothermal sound speeds that can be obtained both analytically and from simulations. The results for two
+different equations of state are shown in Fig. 43. There are two interesting points to note about the latter equations of
+state: (a) The difference in sound speed between the liquid and vapor branches is less pronounced than cubic equations
+of state making them interesting for simulations targeting the incompressible regime and (b) the sound speed in the
+111
+
+1.5
+1.5
+1.5
+L
+1
+liquid
+liquid
+liquid
+S
+0.5
+0.5
+0.5
+vapor
+vapor
+vapor
+0
+0
+0
+0.4
+0.6
+0.8
+I
+0.4
+0.6
+0.8
+1
+0.4
+0.6
+0.8
+T/Tc
+T/Tc
+T/Tc
+1
+0.8
+0.6
+0.4
+0.2
+0
+0.2
+0.4
+0.6
+0.8
+1
+T/TcFigure 43: Isothermal sound speed for two Shan-Chen equations of state. Grey plain lines: Theory; Symbol: Simulations. Plot reproduced from
+[146].
+vapor branch is always higher than that in the liquid branch which is not quite physical.
+In general it must be noted that simulations targeting non-ideal equations of state in the limit of the incompressible
+regime are more challenging than for ideal gases. In ideal gases to correctly recover the incompressible limit separation
+of scales between shear and normal mode speeds must be ensured, i.e. umax ≪ cs. Furthermore, given the explicit
+nature of the LBM solvers the time step size is limited by the fastest traveling eigen-mode, i.e. speed of sound:
+cs < δr/δt. In non-ideal systems, to ensure weak compressibility in both phases one must have umax ≪ min(cs,l, cs,v)
+and max(cs,l, cs,v) < δr/δt to ensure stability of the explicit solver. Given difference of scale of sound speed in the
+liquid and vapor phases, especially at larger density ratios, this can become extremely prohibitive. In most practical
+applications where only the behavior of the liquid phase is of interest the first condition is made weaker, i.e. umax ≪
+cs,l, allowing for larger time-steps and introducing more pronounced compressibility effects into the vapor phase.
+5.8.2. Meanfield scaling laws: Interface thickness
+Different from sharp interface methods, in diffuse interface approaches the liquid-vapor interface has a non-zero
+thickness. The thickness of the interface can be defined in many different ways; Here we use a definition for bearing
+numerical information as to how well the stiff gradients are resolved on a given mesh, making it directly related to the
+velocity increment per time-step:
+W = ρl − ρv
+max|∇ρ|,
+(714)
+where ρl and ρv are densities of saturated liquid and vapor, respectively. It is observed that in the limit of a sharp
+interface, i.e. resolved with δr, δr/W → 1. On the other end of the spectrum for δr/W → 0, akin to ε → 0, one
+expects to recover the hydrodynamic limit, i.e. meanfield behavior. In that limit, surface tension is known to vanish
+as the temperature approaches the critical, cf. Eq. (716), while the interface diverges as T → Tc. As noted by [215],
+the van der Waals theory predicts the temperature scaling of the interface width as,
+W(Tr) ∝ (1 − Tr)−1/2.
+(715)
+For a well-posed numerical solver for any of the non-ideal fluid models discusses here, e.g. Free energy, pseudo-
+potential etc, moving from δr/W ≈ 1 where numerical artefacts are known to dominate towards δr/W → 0 one
+expects to recover the behavior predicted by Eq. 715. Articles treating of that issues in the context of non-ideal
+fluid LBM are rather scarce. In [146] the authors studied the evolution of interface thickness for different reduced
+temperatures using the van der Waals equation of state to probe the consistency of the solver against the second-
+gradient fluid theory. To that end simulations of flat interfaces were carried out in a range of reduced temperatures
+Tr near the critical point, and corresponding interface widths W(Tr) (714) were measured. Results are shown in
+Fig. 44. Furthermore, to probe the W/δr → 1 and W/δr → 0 limits simulations were carried out for different values
+of a allowing to re-scale the interface thickness. This is equivalent to reducing the grid-size for a fixed substance
+or changing the substance for a fixed grid size. As noted by many authors in the literature [216], the parameter a
+112
+
+0.6
+vapor
+0.4
+0.5
+liquid
+vapor
+0.2
+liquid
+0
+0
+0.8
+0.9
+1
+0.85
+0.9
+0.95
+1
+Gc/G
+Gc/G0.001
+0.01 0.05 0.2
+1.5
+5
+15
+10-2
+10-1
+0.5
+1
+3
+Figure 44: (Left) Interface width as a function of temperature. Blue square: Simulation with a = 0.184; Red circle: Simulation with a = 0.02;
+Grey dashed line: Theoretical scaling (715). (Right) Effect of the choice of a on the interface width. Diamond, square and circle: Simulation for
+Tr = 0.98, 0.99, 0.995, respectively. Plot reproduced from [146].
+can be used to control the interface thickness, at a given density ratio, leaving the ratios and Maxwell construction
+unaffected. In agreement with the equivalent states theory, the right hand side plot in Fig. 44 points to the universality
+of the scaling of the interface width near the critical point regardless of the choice of a. In addition it is interesting
+to note that for a fixed grid-size δr, as (1 − Tr) → 1, δr/W → 1 (equivalent to the scaling parameter ε introduced
+in the multi-scale analysis) indicating deviation from the thermodymically converged state. This is illustrated by the
+deviation of the numerical interface thickness, starting at Tr ≈ 0.98 from the theoretical predictions. Lowering the
+value of a, i.e. rescaling the interface by a factor 1/ √a and therefor lowering ε, it is observed that interface is again
+well-resolved and the scaling (715) restored.
+5.8.3. Meanfield scaling laws: Surface tension
+Surface tension at liquid-vapour interface decreases with increasing temperature and vanishes at the critical point
+[158]. For the van der Waals equation of state, the surface tension coefficient σ follows a scaling law as Tr → 1
+[6, 217],
+σ = 16a
+27b2
+�
+κ
+a(1 − Tr)3/2.
+(716)
+A few publications have discussed the temperature scaling of the surface tension in the limit of a flat interface using
+the pseudo-potential method with a van der Waals equation of state [80] and the Shan-Chen equations of state [218]
+and the free energy approach with the van der Waals equation of state [146]. All have shown that these models are able
+to recover the correct scaling with temperature close to the critical temperature. As an example the results reported
+in [146] are shown in Fig. 45. It is clearly observed that the surface tensions agree very well with Eq. 716, provided
+that W ≪ Re. For larger interface thickness curvature-dependence come into play which will be discussed in the next
+section.
+5.8.4. Meanfield scaling laws: Tolman length
+In subsection 5.6.8, to measure surface tension using Laplace’s law we made use of the equimolar dividing surface
+of radius Re, Eq. 701. Further discussion on the non-uniqueness of the choice of dividing surface and curvature-
+dependence of surface tension is in order. Following [196], the free energy of a drop or bubble separated from the
+surrounding vapour or liquid by a dividing circle (D = 2) or sphere (D = 3) of length or area Σ is, A = U − TS + σΣ,
+where U and S are the internal energy and entropy of bulk phases while the last term is the adsorbance of free energy.
+The equilibrium condition requires vanishing of the variation δA; for the isothermal case we have,
+δA = −Pl,vδVl,v − Pv,lδVv,l + Σδσ + σδΣ = 0,
+(717)
+113
+
+0.001
+0.01
+0.050.1
+10-4
+10-3
+10-2
+10-1
+Figure 45: Temperature dependence of the surface tension coefficient near the critical point. Dashed grey line: Theory, Eq.
+716; Red circles:
+Simulation results using Laplace’s law; Blue squares: surface tension coefficient computed for a flat interface. Results are taken from [146].
+where Pl,v and Pv,l are the pressures inside and outside the liquid drop or vapour bubble. Using δVl,v = −δVv,l =
+2(D − 1)πRD−1δR and δΣ = 2(D − 1)2πRD−2δR leads to a generalized Laplace law,
+∆P = (D − 1)σ(R)
+R
++ dσ(R)
+dR .
+(718)
+The derivative of surface tension dσ/dR is termed a notional derivative by some authors [219] in order to stress that it
+refers to arbitrariness of the dividing surface. Apart from the equimolar surface (701), the surface of tension is another
+possible choice to lift the ambiguity of the dividing surface. The notional derivative vanishes at the surface of tension,
+dσ
+dR
+�����R=Rs
+= 0,
+(719)
+thereby reducing the generalized Laplace law (718) to a standard form,
+∆P = (D − 1)σ(Rs)
+Rs
+.
+(720)
+Integrating Eq. 718 from Rs to R, and eliminating ∆P using (720), one obtains analytic expression for the notional
+surface tension σ(R) relative to its minimum σs at the surface of tension Rs,
+σ(R)
+σs
+= 1
+D
+�Rs
+R
+�D−1
++ D − 1
+D
+� R
+Rs
+�
+.
+(721)
+While the notional derivative dσ(R)/dR vanishes at the surface of tension, the same does not hold for the surface
+tension at the surface of tension, dσs/dRs � 0. In other words, surface tension σs depends on the curvature of the
+surface of tension. In [220] the authors characterized the curvature-dependence of surface tension by the Tolman
+length: For sufficiently large Rs, the leading-order curvature-dependence of the surface tension may be written [220],
+σ(Rs) ≈ σ0
+�
+1 ∓ (D − 1)δT
+Rs
+�
+,
+(722)
+where δT is the Tolman length and σ0 is the flat interface surface tension coefficient. Here, the negative (positive) sign
+corresponds to drops (bubbles), respectively.
+While the leading-order Tolman correction Eq. 722 improves agreement with data at moderate Rs, it is not suffi-
+cient for smaller drops and bubbles. Higher-order terms in the inverse powers of Rs, important for droplets or bubbles
+of small radius, are neglected by Eq. 722 and were addressed by [221]:
+σ = σ0 ∓ σ0
+(D − 1)δT
+Rs
++ k(D − 1)2
+2R2s
++
+¯k(D − 2)
+R2s
++ . . . ,
+(723)
+114
+
+0
+0.01
+0.02
+0.03
+0.04
+0.05
+0.06
+0
+0.2
+0.4
+0.6
+0.8
+1
+10-3
+drops
+bubbles
+Figure 46: Pressure difference scaling with surface of tension radius Rs for liquid drops and vapour bubbles. Symbol: Simulation data for van der
+Waals equation of state with a = 0.18 and b = 0.095. Black line: Laplace law with σ = σ0; Blue lines: Best fit with Eq. 722 used to compute
+Tolman length δT ; Red lines: Best fit with the second-order Helfrich expansion Eq (723). Plot reproduced from [146].
+where k and ¯k are the bending and Gaussian rigidities; note that the latter vanishes for D = 2.
+The curvature-dependence of surface tension and Tolman length have also been discussed in a limited number of
+articles using the lattice Boltzmann method [218, 146]. The results of a systematic study of the Laplace law for
+droplets of different sizes as reported in [146] are shown in Fig. 46. Comparing the leading-order Tolman model
+Eq. 722 with the simulation. The values of Rs are plotted against the pressure difference for different drop and bubble
+sizes in Fig. 46. It is clear that, for smaller drops and bubbles, the pressure difference deviates from the Laplace law
+with constant σs = σ0, indicating a curvature-dependent surface tension. Fitting the data points with Eq. 722, the
+Tolman length can be extracted from the simulation. In Fig. 46 δT = 9δr for both drops and bubbles, at the reduced
+temperature Tr = 0.98. Taking the second-order term of Eq. 723 into account, the best fit in Fig. 46 results in bending
+rigidity k = 1.049 × 105σ0δr2.
+Another consequence of the second-gradient thermodynamics, as shown by [219], is that the Tolman length scales
+with the reduced temperature as,
+δT ∝ (1 − Tr)−1.
+(724)
+The scaling was also extracted in for the pseudo-potential and free energy models close to critical point [218, 146].
+There the Tolman length was extracted in the limit of a flat interface for different temperatures. The Tolman length in
+the limit of flat interface is the distance between the surface of tension and the equimolar surface [219, 217],
+δT = Xe − Xs.
+(725)
+An example from the simulation is presented in Fig. 48. In this case, location of the surface of tension Xs can be found
+as the normalized first-order moment of the normal stress difference [222],
+Xs =
+� ∞
+−∞ x(Pxx − Pyy)dx
+� ∞
+−∞(Pxx − Pyy)dx
+.
+(726)
+With the dividing surface as a vertical straight line at X in two dimensions, the mass adsorbance Γ(X) is defined as
+(see example in Fig. 47),
+Γ(X) =
+� ∞
+−∞
+�ρ(x) − ρv − (ρl − ρv)H(x − X)� dx.
+(727)
+Similar to the case of cylindrical symmetry considered in subsection 5.6.8 the equimolar surface is found by annihi-
+lating the mass adsorbance, Γ(Xe) = 0. The results as reported in [146] are shown in Fig. 48.
+After a detailed overview of different classes of models, shortcomings and numerical artifacts, solutions proposed
+in the literature and a comprehensive assessment of interface properties the next section will discuss some of the
+applications of non-ideal lattice Boltzmann models.
+115
+
+0
+50
+100
+150
+200
+0.6
+0.8
+1
+1.2
+1.4
+Figure 47: Example of mass adsorbance for a flat interface. Black continuous line: density profile at Tr = 0.98; Red dashed line: Sharp interface
+profile with the dividing surface at X/δr=70. Grey area represents the mass adsorbance Γ(X) (727). Plot reproduced from [146].
+30
+40
+50
+60
+0.8
+1
+1.2
+1.4
+10-3
+10-2
+10-1
+100
+101
+102
+Figure 48: (Left) Temperature dependence of Tolman length δT . Results from the flat interface simulation for van der Waals fluid are shown with
+blue squares while the grey dashed line represents theoretical scaling (724). (Right) Surface of tension, equimolar surface and Tolman length for
+flat interface. Continuous black line: Density profile at Tr = 0.98; Red dashed line: Sharp approximation with the equimolar surface as the dividing
+surface; Blue dotted line: Sharp approximation with the surface of tension as the dividing surface. Distance between the surface of tension and the
+equimolar surface: Tolman length. In all simulations a = 0.18 and b = 0.095. Plot reproduced from [146].
+116
+
+6. Illustration of applications
+Different from alternatives such as phase-field solvers or the color-gradient approach, non-ideal fluid LBMs have
+been mostly used for cases involving low or moderate Weber numbers. Below a few area where such solvers are
+widely in use are listed.
+6.1. Drop interaction with solid substrates
+One area of application where non-ideal fluid LBM has been widely and successfully applied is studies involving
+drop interaction with flat and complex solid substrates at low and moderate Weber numbers. We provide an overview
+of recent research in that area.
+6.1.1. Impact on non-wetting surfaces
+Dynamics of drops impacting flat non-wetting surfaces is a topic that has attracted a lot of attention in recent
+years. Extensive studies have shown that the contact time on such surfaces is independent of the Weber number,
+We = ρlD0U2
+0/σ, and only scales with the inertio-capillary time, τi =
+�
+ρlD3
+0/8σ, meaning for a given initial diam-
+eter D0 the contact time is unaffected by impact velocity [223, 224, 225, 226] prompting researchers to proposed a
+simplistic description of its dynamic via an analogy with a single harmonic oscillator of characteristic mass ρlD3
+0/8
+and spring constant σ [227]. Although different from the case of an oscillating drop studied by Rayleigh, in the sense
+of asymmetry of the drop dynamic due to the presence of the wall, the scaling of the contact time agrees with his
+predictions. The coefficient in front of the scaling law is however observed to be different; Rayleigh’s analysis led to a
+coefficient of π/
+√
+2 ≈ 2.2 while experimental studies of drops impacting non-wetting surfaces led to 2.5 ± 0.2 [226].
+A number of LBM-based studies have looked into the Weber-independence of contact time on non-wetting surfaces,
+see for instance [156, 146], and showed that non-ideal fluid LBMs correctly capture both the scaling and coefficient.
+An example in shown in Fig. 49.
+10
+20
+30
+We
+1
+1.5
+2
+2.5
+tc/ i
+Figure 49: Drop contact times on flat non-wetting surface (contact angle θ=165 for different Weber numbers as obtained from simulations and
+experiments. Simulations results are shown with red circular markers while experimental data reported by [223] are illustrated with blue square
+markers. The dashed grey line represents the average contact time as obtained from simulations, ¯tc/τi = 2.4. This plot is reproduced from [146].
+Another aspect of drops impact non-wetting surfaces, widely discussed in the literature is the diameter of the drop
+at the maximum spreading state and its dependence on the Weber and Reynolds numbers. A correlation widely used
+and accepted in the literature in the limit of vanishing Ohnesorge numbers, i.e. Oh =
+√
+We/Re, is the one proposed in
+[228]: Dmax
+D0
+∝ We1/4. Other correlations taking into account viscous dissipation for non-vanishing Oh numbers have
+also been proposed in the literature, for instance [229]:
+��Dmax
+D0
+�
+−
+�Dmax,0
+D0
+�
+Re−1/5 =
+We1/2
+A + We1/2 ,
+(728)
+where Dmax,0 is the maximum spreading diameter in the limit of zero impact velocity and A is constant. Both these
+correlations have been matched with LBM simulations. Results are shown in Fig. 50.
+117
+
+Figure 50: (Left) Reduced maximum diameter of drop as a function of the Weber number. Circles show LBM simulations and squares experimental
+data from [228]. The solid line corresponds to the scaling ∝ We1/4. This plot is reproduced from [230]. (Right) Rescaled maximum spreading ratio
+for viscous drops as a function of Weber number. Circles: LBM simulations. solid line: scaling of Eq. 728. This plot is reproduced from [231].
+D0
+Rb
+h
+RB
+w
+Figure 51: Illustration of the geometry of tapered posts. Image is reproduced from [146].
+6.1.2. Pancake bouncing
+To further reduce the drop contact times, a number of different strategies have been devised during the past
+decades. Recently, [232] proposed to use macroscopic structures, in the form of tapered posts shown in Fig. 51,
+to reduce the contact time. It has been shown that above a certain threshold Weber number these structures can
+decrease the contact time by approximately 75 percent. This mechanism is also known as pancake bouncing, due to
+the pancake-like shape of the drop at take off. The dynamics of drops impacting these tapered posts both below and
+above the said-threshold is illustrated in Fig. 52. The first numerical study of this phenomenon was conducted using
+the LBM free energy method in [233] in 2-D. Later a detailed numerical study of pancake bouncing using LBM was
+presented in [156], for density ratio of the order of 102. Similar studies were also conducted in [146] for larger density
+ratios, i.e. 103. All simulations were shown recover the drop contact time and capture the threshold Weber number
+were impact transitions in pancake mode. The results are illustrated in Fig. 53.
+6.1.3. Other approaches to reduce contact time via macro-structures
+As another simple approach to further reduce the contact time of drops on non-wetting surfaces via the introduction
+of a singular defect on the substrate in the form of small glass bead of a radius of 200 µm. For a drop impact the bead
+at its center and subsequently breaking at it center right after maximum spreading this approach was shown to reduce
+the contact time by a factor of two [234]. The breaking of the lamella at its center after maximum spreading causes
+retraction both from the edges and the center eventually leading to a ring-like shape at the time of take off. The
+reduced take-off time is therefor related to a reduction in retraction time which is a consequence of the reduction of
+the corresponding characteristic size. The formation of two so-called blobs and corresponding characteristic size are
+illustrated in Fig. 54. The effect of this characteristic size on contact time was extracted via systematic experimental
+runs and numerical simulations with a free energy LBM. As shown in Fig. 54 simulation results were in very good
+agreement with experimental observations. Non-ideal LBM solvers have been used for a wide variety of studies
+involving drop interaction with solids at low and moderate Weber numbers, such as impact on curved surfaces [235],
+118
+
+5
+口
+Clanet Experiment
+0
+ELBM
+4
+1
+-1/5
+0.8
+We1/2 / (7.6+We1/2)
+Re'
+3
+0.6
+EMRT-MPLBM
+>1/2
+0.4
+%
+max
+8
+D
+2
+xew
+0.2
+101
+102
+Webernumber
+10°
+10
+10
+We0 ms
+1.5 ms
+3 ms
+3.4 ms
+4.6 ms
+0 ms
+1.4 ms
+2.9 ms
+4.8 ms
+16.5 ms
+Figure 52: Drop impacting tapered posts at different Weber numbers (first and second rows) We=28.2 with pancake bouncing and (third and
+fourth rows) We=14.2. The first and third rows are experiments from [232] while the second and fourth rows are from simulations. This image is
+reproduced from [146].
+10
+20
+30
+40
+We
+0
+0.5
+1
+Q
+10
+20
+30
+40
+We
+0
+1
+2
+3
+tc/ i
+Figure 53: (left) Drop contact times and (right) pancake quality at rebound on tapered posts for different Weber numbers as obtained from simula-
+tions and experiments. Simulations results are shown with red circular markers while experimental data reported by [232] are illustrated with blue
+square markers. This plot is reproduced from [146].
+119
+
+一Figure 54: (a) Sketch of water droplet impacting a point-like defect at maximum spreading. (c) Water droplet (R = 1.3 mm) impacting at V = 1.3
+m/s a bead with diameter r = 200 µm, with off-centering x = 0.7 mm. (d) Contact time normalized by inertio-capillary time as a function of the
+normalized blob size. Dots are experimental data and red circles simulations. These plots are reproduced from [234].
+mesh arrays [236, 237] or perforated flat substrates [238].
+6.2. Flow in porous media
+Another area where non-ideal LBM solvers have been widely and successfully applied is flow in porous media.
+A wide variety of industrial processes and physics involve non-ideal fluids (or multi-phase flows) in porous media.
+The first attempt at modeling the flow of multiple phases in a realistic porous geometry was documented in [198]
+where the authors modeled both wetting and non-wetting liquid invasion of a porous geometry extracted from high
+resolution microtomography images of a Fontainebleau sandstone. Since then non-ideal LBM’s have been extended
+many more complexe configurations and physics. Here we briefly discuss two main areas, namely water transport in
+proton exchange membrane fuel cells and isothermal drying
+6.2.1. Water transport in proton exchange membrane fuel cells
+Proton-exchange membrane fuel cells are a promising class of fuel cells mainly developed for transport applica-
+tions and first introduced in the 60’s by General Electrics [239]. While most major manufacturers are close to the
+commercialization stage, water management remains one of the outstanding issues limiting efficiency and durability.
+Issues related to water are encountered in the gas diffusion layer and reactant channel [240]. A number of studies with
+LBM on liquid water transport mechanisms in both the gas diffusion layer and reactant channel have been conducted.
+In [241] the authors studied the effect of capillary pressure and contact angle on the water invasion dynamics into
+Toray-090 gas diffusion layers. The studied gas diffusion layers were made up of carbon fibers coated with Polyte-
+trafluoroethylene (PTFE) for enhanced hydrophobicity with different weight percentages of PTFE. In their studies the
+Figure 55: Snapshots of time evolution of liquid water transport inside GDL with 10 percent PTFE content. Image is reproduced from [241].
+authors observed that saturation levels within the gas diffusion layer slowly increased with capillary pressure until a
+threshold were it grows and reaches rapidly full saturation. The threshold level was shown to change as function of
+the apparent contact angle controlled by the weight percentage of PTFE. The evolution of liquid water front within
+the gas diffusion layer over time is illustrated in Fig. 55.
+Another aspect of water management studied in [242] is the transport dynamics of water droplets in the gas channel
+bound by the gas diffusion layer. Usually due to the roughness of the gas diffusion layer droplets moving in the gas
+120
+
+b
+d
+0.7
+0.6
+O.
+2R.
+...
+0.4
+0.3
+0.2
+0.5
+1.5channel can be subject to pining which can block the channel. The authors conducted systematic studies on the effect
+of inertia, considering both magnitude and direction. As expected it was observed that smaller contact angles reduced
+Figure 56: Image reproduced from [242].
+pining effects and penetration into the gas diffusion layer. Inertia effect with a non-zero component normal to the
+gas diffusion layer surface was also observe to increase chances of penetration into the gas diffusion layer and even
+break-up of the drop as illustrated in Fig. 56.
+6.2.2. Isothermal drying
+Drying in complex porous media is encountered in many set-ups of interest in science and engineering, such as
+food preservation, coating or volatile hydrocarbons recovery from reservoirs. Traditional description of the drying
+process at the continuum scale rely on phenomenological closures that come with many limitations. More detailed
+descriptions like the Pore Network models have, to some extent, helped to refine the continuum models however they
+have shortcomings in using the true geometry at the pore scale, and in considering capillary instabilities and film-
+effects. That is why in the past 30 years, pore-scale studies of drying in porous media have received more attention.
+On par with global trend, this topic has also been widely considered and studied with the LBM. For instance, in [243]
+and [214, 244] the authors investigated the effect of contact angle hysteresis on isothermal drying dynamics in porous
+media and proposed a hybrid solver coupling pore-scale lattice Boltzmann simulations to the pore network model.
+An illustration of the simulation conducted in [214] is given in Fig. 57. In [245] the authors coupled the free energy
+Figure 57: Sequential liquid configurations during drying of a bi-modal porous system obtained with LBM. Image reproduced from [214].
+model to a smoothed-profile LBM to model isothermal drying of colloidal suspensions and studied the aggregation of
+colloidal particles with different wetabilities under isothermal drying. The simulations are illustrated in Fig. 58. The
+121
+
+180
+(d)
+150
+Re=2.08
+120
+△t=0
+At=6000
+N 90
+60
+30
+0Figure 58: Snapshots of particle arrangement during the drying of a colloidal suspension containing 60 particles with contact angle 90. Image
+reproduced from [245].
+authors observed that particles with higher wettabilities aggregated more slowly, but more significantly. They justified
+the observations by capillary interactions such as capillary flotation and immersion forces between the particles.
+As shown in this section, the non-ideal LBMs have been used for a wide variety of applications covering drop
+interaction with different substrates, liquid invasion of porous media with a special interest for fuel cells and drying
+in porous geometries. The specific numerical properties of this class of model have made them quite efficient and at-
+tractive for flows involving interaction with complex solids, liquid-liquid interactions such as coalescence and binary
+collisions, all in the low and mid-Weber and Reynolds regimes. Considerable effort is still being put on extending
+such approaches to larger Weber number configurations such as droplet splashing or primary and secondary break-up
+in liquid jets. At this point in time, to the authors knowledge, no notable success has been reported in that area.
+Non-ideal fluid models in LBM are not limited to single component isothermal flow configurations. Considerable
+effort has been put in recent years to extend these models to thermal and multi-component flows. Some of these
+extensions will be briefly discussed in the next section
+122
+
+(bl) t*= 0
+(b2) t* = 0.6
+(b3) t* = 1.8
+(b4) t* = 6.07. Extension to more complex physics
+The non-ideal LBM, while initially developed for isothermal single-component fluids, have been extended to
+thermal and multi-component flows. Below we present a brief overview of some of the developements in that area.
+7.1. Thermal flows with evaporation
+Extension of non-ideal LBMs to non-isothermal flows can be categorized as pertaining to one of two main classes:
+(a) Hybrid and passive scalar-based approaches and (b) kinetic methods.
+7.1.1. The hybrid and passive scalar approaches
+The form of the energy balance equation. Two main routes have been taken to arrive at the final form of the en-
+ergy/temperature balance equation, namely from the entropy or the energy balance equations. In the hybrid approach
+the LBM solver for the density and momentum fields is coupled to classical, either finite differences or finite volumes,
+solvers for the following evolution equation for the temperature field [246]:
+∂tT + u · ∇T + T
+ρcv
+∂P
+∂T ∇ · u − 1
+ρcv
+∇ · λ∇T = 0.
+(729)
+Solver for the energy balance equation. Once the target form of the energy balance equation has been determined
+an additional solver has to be added/coupled to the flow solver. There are typically two possible routes: (a) LBM
+advection-diffusion type solvers or (b) classical finite differences or finite volumes solvers.
+In the first approach, one relies on an additional distribution function gi to solve an advection-diffusion type partial
+differential equation. In its simplest form the advection-diffusion LBM with [247]:
+�
+i
+gi = T,
+(730)
+as the conserved moment leads to a PDE of the following form:
+∂tT + ∇ · uT − ∇ · D∇T = 0.
+(731)
+This form of the balance equation poses a number of issues; The advection term u · ∇T is only valid in the limit of a
+divergence-free velocity field, i.e. T∇ · u, which given that the compressible fluid equations are targeted does not hold
+in general. Furthermore, the diffusion term ∇ · D∇T with D =
+λ
+ρcv only holds for ρ = const and cp = const. Finally
+the latent heat release term in Eq. () is missing here.
+To circumvent these shortcomings different authors have proposed corrections to be included as source terms in the
+LBM equation [248, 249, 250, 251]. For instance, noting:
+u · ∇T − ∇ · uT = −T∇ · u,
+(732)
+and,
+1
+ρcv
+∇ · λ∇T − ∇ · λ
+ρcv
+∇T = −λ∇T · ∇ 1
+ρcv
+,
+(733)
+a source term of the following form must be included:
+S = T
+�
+1 − 1
+ρcv
+∂P
+∂T
+�
+∇ · u + λ∇T · ∇ 1
+ρcv
+,
+(734)
+leading to the following LBM equation:
+¯gi(r + ciδt, t + δt) − ¯gi(r, t) = 1
+¯τ
+�
+geq
+i (r, t) − ¯gi(r, t)
+�
++
+�
+1 − 1
+2¯τ
+�
+wiS,
+(735)
+with:
+T =
+�
+i
+¯gi + δt
+2 S.
+(736)
+123
+
+An alternative to the above-described approach, discussed in [252] is to set:
+�
+i
+gi = ρcvT,
+(737)
+with
+geq
+i = cvT f eq
+i ,
+(738)
+which in combination with a correction term of the form:
+S = cvT
+c2s
+ci · F,
+(739)
+where F is the non-local force in the evolution equation of the distribution function fi results in the following conser-
+vative form of the energy balance equation:
+∂tρcvT + ∇ · ρcvTu − ∇ · λ∇T = 0.
+(740)
+Comparing this equation to the target balance law for non-ideal fluids one observes that the latent heat release due to
+phase change is missing here.
+Different variants of the passive scalar approach have been used in a wide number of publications targeting thermal
+non-ideal fluid flows [248, 249, 251].
+An alternative to this approach is to use classical discretization methods such as finite differences or finite volumes
+to solve the energy balance equation. One of the first documented attempts at modeling thermal non-ideal fluid flows
+using such a hybrid model was reported in [192]. In recent years most authors have opted for a second-order central
+isotropic finite differences discretization in space, see [253, 254, 255, 256] for more detail, and second-order Runge-
+Kutta scheme for time-stepping. The hybrid scheme is widely used in the literature for a variety of configurations and
+physics, see for instance [257, 258, 259, 260, 261].
+7.1.2. The kinetic route
+Introduction of generic framework. We will first introduce elements of a generic kinetic framework for non-ideal
+fluids. This model is introduced for the first time here and will be detailed in upcoming publications. The kinetic
+framework of Eq. 573 introduced for iso-thermal flows can be readily extended to compressible flows with energy
+balance by adding energy to the list of conserved variable in the definition of the projector onto the local equilibrium
+manifold:
+KJ = ∂f eq
+∂Πρ
+�
+JdvdI + ∂f eq
+∂Πu
+�
+vJdvdI + ∂f eq
+∂ΠE
+� �
+v2 + I2�
+JdvdI,
+(741)
+with
+Πρ = ρ, Πu = ρu, ΠE = ρ
+�
+u2 + (D + δ)RT
+�
+,
+(742)
+where to allow for variable specific heat ratios we have introduced the space of additional non-translational degrees
+of freedom I. The equilibrium distribution function is modified accordingly as:
+f eq =
+ρ
+(2πRT)(D+δ)/2 exp
+�
+−(v − u)2 + I2
+2RT
+�
+.
+(743)
+Here δ is the the number of non-translational degrees of freedom. Application of this projector to the collision term
+results in:
+Jnloc =
+�1
+ρ
+∂f eq
+∂u −
+2
+(D + δ)ρu∂f eq
+∂RT
+�
+· Fnloc +
+1
+ρ(D + δ)
+∂f eq
+∂RT Qnloc
+(744)
+where the force Fnloc reads,
+Fnloc = −
+� � �
+∇V (|r − r1|) f2(r, v, r1, v1, t)dv1dr1dv,
+(745)
+124
+
+where
+f2(r, v, r1, v1, t) =
+� �
+f2(r, v, I, r1, v1, I1, t)dI1dI,
+(746)
+and
+Qnloc = −2
+� � �
+∇V (|r − r1|) · v f2(r, v, r1, v1, t)dv1dr1dv.
+(747)
+Collecting the BGK approximation together with the nonlocal contribution, a generic model for the BBGKY equation
+may be written,
+∂t f + v · ∇ f = −1
+τ
+�f − f eq� + F + Q,
+(748)
+with:
+F =
+�1
+ρ
+∂f eq
+∂u −
+2
+ρ(D + δ)u∂f eq
+∂RT
+�
+· Fnloc
+(749)
+and:
+Q =
+1
+ρ(D + δ)
+∂f eq
+∂RT Qnloc.
+(750)
+The hard-sphere potential contribution is readily shown to lead to:
+Fnloc =
+�
+vJ(1)
+E dv = −∇bρ2χRT,
+(751)
+and
+Qnloc = −2∇bρ2χRT · u,
+(752)
+while the meanfield Vlasov long-range interaction leads to:
+JV = −∇
+�
+2aρ(r) + κ∇2ρ(r)
+�
+· ∂
+∂v f(r, v).
+(753)
+Upon application of the projector operator and addition of the Enskog contribution one gets:
+Fnloc = −∇bρ2χRT + ρ∇
+�
+2aρ + κ∇2ρ
+�
+,
+(754)
+and
+Qnloc = −2∇bρ2χRT · u + 2ρu · ∇
+�
+2aρ + κ∇2ρ
+�
+.
+(755)
+Upon application of a multi-scale perturbation analysis the generic model can be shown to recover the following
+system of equation up to NS level:
+∂tρ + ∇ · ρu + O(ϵ3) = 0,
+(756)
+∂tρu + ∇ · ρu ⊗ u + ∇ · ρRT
+�
+1 + bχρ − aρ
+RT
+�
+I − ρκ∇∇2ρ + ∇ · TNS + O(ϵ3) = 0
+(757)
+∂tE + ∇ · Eu + ∇ · ρRT(1 + bχρ)u − u · ∇aρ2 − κρu · ∇∇2ρ + ∇ · u · TNS − ∇ · λ∇T + O(ϵ3) = 0.
+(758)
+Defining the total energy Et as the sum of the internal energy E and potential energy from non-local interaction
+potentials Ev the following balance equation for total energy is obtained:
+∂tEt + ∇ · Etu + ∇ · ρRT
+�
+1 + bχρ − aρ
+RT −
+κ
+2RT ∇2ρ
+�
+u −
+�
+κρ∇∇ρ + κ
+2ρ∇2ρ
+�
+: ∇u
++ TNS : ∇u − ∇ · λ∇T + O(ϵ3) = 0.
+(759)
+In principle, as for the iso-thermal version introduced in [146], different equations of state, interactions beyond the
+meanfield approximation and choices of pressure partition can be realized with this generic framework. For instance,
+introducing the full thermodynamic pressure into the equilibrium distribution function one readily recovers the models
+in [189, 190, 191].
+125
+
+The Enkog-Vlasov-based model of He & Doolen. One of the first attempts at proposing a kinetically motivated LBM
+model for non-ideal fluids was documented in [149]. Following the original Enskog-Vlasov formalism the collision
+term is replaced with local and non-local contributions. Additionally the local contributions is replaced with a BGK-
+type approximation leading to the following discrete evolution equation:
+¯fi(r + ciδt, t + δt) − ¯fi(r, t) = −χ
+¯τ
+� ¯fi(r, t) − ¯f eq
+i (r, t)
+�
++ δt(1 − δt
+2¯τ)Fi ¯f eq
+i (r, t),
+(760)
+with,
+Fi = (ci − u) · (F − ∇V)
+RT
+− bρχ
+�
+(ci − u) ·
+�
+∇ ln ρ2χT + 3
+5
+�(ci − u)2
+2RT
+− 5
+2
+�
+∇ ln T
+�
++ 2
+5
+�(ci − u) ⊗ (ci − u)
+RT
+: ∇u +
+�(ci − u)2
+2RT
+− 5
+2
+�
+∇ · u
+��
+.
+(761)
+The discrete equilibrium distribution function was obtained as a second-order polynomial expansion. While in [149]
+the authors only reported the theory and derivation of the model, it was later reprised in [262] and used for 1-D and
+2-D simulations using a MRT realization.
+7.2. Multiple components
+Another area of active research to extend the range of application of non-ideal LBMs is the introduction of multiple
+components. While most of the application-oriented litterature in that area relies on the multi-component realization
+of the Shan-Chen model [263], a few different attempts at other models have also been reported. Here we will briefly
+discuss some of the multi-component models developed within that context.
+7.2.1. Ternary free energy model of W¨ohrwag et al.
+In an attempt to model ternary systems W¨ohrwag et al. [264] introduced a free energy functional allowing three
+distinct minima, corresponding to one gas and two liquid components. The thermodynamics of the system is governed
+by two order parameters, namely density, ρ, and a phase field, φ. As for the van der Waals fluid the total free energy
+density consists of two parts, bulk A and interfacial; The bulk free energy is defined as:
+A = λ1
+2 (AEoS(ρ) − A0) + λ2
+2 C2
+l1(1 − Cl1)2 + λ3
+2 C2
+l2(1 − Cl2)2,
+(762)
+where AEoS(ρ) can be derived from integrating the equation of state, P = ρ(∂AEoS/∂ρ) − AEoS, with coexisting
+liquid-gas densities at ρl and ρg. The two last terms in Eq.
+762 have the form of double well potentials with Cl1
+and Cl2 the relative concentrations of the two liquid components. Each term has two minima at C# = 0 (component
+absent) and C# = 1 (present). The relative concentration of the gas phase is defined as Cg = (ρ − ρl)/(ρg − ρl),
+which is 0 for ρ = ρl and 1 for ρ = ρg. The relative concentrations are related to the density and phase field through
+Cl1 = 1
+2
+�
+1 + φ/χ − (ρ − ρl)/(ρg − ρl)
+�
+and Cl2 = 1
+2
+�
+1 − φ/χ − (ρ − ρl)/(ρg − ρl)
+�
+, with χ a constant scaling parameter
+for φ. This form of the bulk free energy leads to three minima located at (ρg, 0), (ρl, +χ) and (ρl, −χ). The bulk free
+energy map is shown in Fig. 59. For the interfacial free energy density, the authors used
+AInter = κ1
+2 (∇ρ)2 + κ2
+2 (∇Cl1)2 + κ3
+2 (∇Cl2)2,
+(763)
+which ca be written as a function of the order parameters ρ and φ,
+AInter =
+�κ1
+2 +
+κ2 + κ3
+8(ρg − ρl)2
+�
+(∇ρ)2 + κ2 + κ3
+8χ2
+(∇φ)2 +
+κ3 − κ2
+4χ(ρg − ρl)(∇ρ · ∇φ),
+(764)
+which as expected includes three contributions, i.e. density gradient, phase field gradient and mixed density-phase
+field gradient. This new free energy functional only affects the NS equations through the total pressure tensor:
+∇ · Ptot = ρ∇µρ + φ∇µφ,
+(765)
+126
+
+Figure 59: Contour plot of the bulk free energy density of Eq. 762 as a function of two order parameters, ρ and φ. This plot is reproduced from
+[264].
+with the chemical potentials defined as:
+µk = δ
+δk
+�
+A + AInterdV|T,k′,
+(766)
+with k ∈ {ρ, φ} and k′ ∈ {φ, ρ}. The corresponding system of balance equations was solved using two distribution
+functions; One for the density and momentum fields and one for the balance of the phase field, i.e. Cahn-Hiliard
+equation. Using this model the authors successfully modeled collision of drops of immiscible liquids with density
+ratios of the order of 103. An example is shown in Fig. 60.
+Figure 60: Collision between two immiscible droplets (water and diesel oil). (a) experiments from [265]. (b),(c) simulation results. This figure is
+reproduced from [264].
+7.2.2. Mixtures with multi-component van der Waals equation of state
+In [266], Ridl & Wagner proposed a multi-component extension to the van der Waals second-gradient fluid. Start-
+ing with the single-component free energy:
+AvdW = ρRT ln
+�
+ρ
+1 − bρ
+�
+− aρ2 + κ
+2|∇ρ|2,
+(767)
+they proposed an N-component van der Waals free energy defined as [266]:
+AvdW−MC =
+N
+�
+k=1
+ρkRT ln
+������
+ρk
+1 − �N
+k′=1 bk′ρk′
+������ −
+N
+�
+k′=1
+�
+akk′ρkρk′ − κkk′
+2 ∇ρk · ∇ρk′
+�
+,
+(768)
+with the total bulk thermodynamic pressure obtained as:
+P =
+N
+�
+k=1
+ρkRT
+1 − �N
+k′=1 bk′ρk′ −
+N
+�
+k′=1
+akk′ρkρk′.
+(769)
+127
+
+d
+p
+-X
+X+a-i
+(a-i)
+(a-ii)
+(a-iv)
+a-v
+(b-i)
+(b-i)
+(b-ili)
+(b-iv)
+(b-v)
+(c-i)
+(c-ii)
+(c-ili)
+(c-iv)
+(c-V)To model the dynamics of the corresponding system they proposed a set of N discrete distribution functions, one for
+each component, evolving as [266, 267]:
+fik(r + ciδt, t + δt) − fik(r, t) = δt
+¯τ
+�
+f eq
+ik (r, t) − fik(r, t)
+�
+− Fik,
+(770)
+where the BGK collision operator accounts for the considered component’s ideal contributions while the term Fik
+takes into consideration non-ideal effects and interaction with other components. The densities and velocities of each
+individual component are obtained as zeroth- and first-order moments of the corresponding distribution functions
+while the mixture density and velocity are obtained as the sum of the density of all components and the mass-averaged
+velocities, respectively. The term Fik contributes at first order,
+�
+i
+ciFik = Fk,
+(771)
+where the force Fk has two contributions: one from the gradient of chemical potential Fµk and one friction between
+different components Ffk modeling cross-diffusion effects. The chemical potential gradient contribution is readily
+obtained as difference between the single-component ideal pressure and multi-component non-ideal one while Ffk is
+defined as
+Ffk = −
+N
+�
+k′=1
+λkk′ ρkρk′
+ρk + ρk′ (uk′ − uk) ,
+(772)
+where λkk′ are related to binary diffusion coefficients. It is readily demonstrated that under the assumption of symmetry
+of the diffusion coefficients tensor, i.e. λkk′ − λk′k the contribution of cross-diffusion to total momentum is zero:
+N
+�
+k=1
+Ffk = 0.
+(773)
+The authors showed that in the hydrodynamic limit under the assumption of λkk′ = λ, i.e. all components have the same
+Lewis number, one recovers the N-component Cahn-Hiliard equations. It should also be noted that similar models
+for two-component non-ideal mixture were also proposed in [268, 269] where the models were shown to recover
+non-ideal effects and the Fick diffusion, equivalent to the Maxwell-Stefan system for binary isothermal mixtures.
+7.2.3. The multi-component pseudo-potential method
+While initially developed for non-ideal fluids, extension of the model to multiple components were introduced in
+[263]. For a system with N components, the interaction force on component k is given by:
+Fk = −ψk(r)
+N
+�
+k′=1
+Gkk′ψk′(r + ciδt)ci,
+(774)
+where Gkk′ sets the interaction strength between components k and k′ and forms a symmetrical tensor, i.e. Gkk′ = Gk′k.
+Interestingly enough, upon application of a Taylor expansion the force is:
+Fk = −ψk
+N
+�
+k′=1
+Gkk′∇ψk′ + Gkk′
+3 ∇∆ψk′ + O(∇5).
+(775)
+As for the single-component non-ideal model, it leads to fixed surface tension coefficients and terms that are function
+of the pseudo-potential ψk instead of density ρk. Introduction of independent capillary coefficients can be readily intro-
+duced following the approaches used for the single-component version of the model, i.e. multiple-range interactions.
+128
+
+8. Conclusion
+Application of the LBM to non-ideal fluids, and multi-phase flows in general, has been the focus of intense work
+from the early days of that method with first publications appearing in the early 90s. This rapid extension and growth
+in popularity is, in part, due to the simple transition from ideal to non-ideal fluids with interfaces in the context of
+LBM, illustrated best by the simplicity of the original pseudo-potential model.
+Contrary to diffuse-interface models like the Allen-Cahn equation, the non-ideal LBM models come with interfacial
+properties, e.g. surface tension, interface thickness, Tolman length etc, linked to bulk physical properties of the
+considered fluid and follow the van der Waals thermodynamics of interfaces. The interface properties are therefore,
+in principle, dictated by the thermodynamics of the considered fluid. This was illustrated via the example of a N2
+liquid/vapor interface showing a thickness of the order of 10−7 m, see Fig. 20, limiting the grid-size and preventing
+simulations at larger realistic scales. As a result they can be perceived as models able to cover a wider range of
+parameters as compared to classical sharp and/or diffuse interface methods: In the limit of thick interfaces where its
+width is comparable to the flow characteristic size they recover the van der Waals fluid thermodynamics (or a modified
+form of it in the case of the pseudo-potential method) and the Korteweg stress tensor at the macroscopic level and can
+be derived from the Enskog-Vlasov approximation at the level of the kinetic theory. In the limit of thin interfaces, the
+extreme computational cost imposed by the physical thickness of the interface can be considerably reduced by relying
+on the principle of corresponding states.
+Non-ideal LBM-based solvers are also subject to a number of issues such as stability resulting in limited range of
+accessible non-dimensional viscosities, thermodynamic inconsistency leading mismatch in coexistences densities at
+smaller temperatures, spurious currents appearing at interfaces as a result of the non-isotropy of the discrete system etc.
+A wide variety of solution to eliminate or reduced the effect of these issues have been proposed allowing simulation
+with larger density ratios, Weber and Reynolds number to be conducted. With the most recent development around
+these approaches they have become quite competitive and accurate tools for simulations in the lower Weber number
+regimes in areas such as microfluidics, drop interaction with solid surfaces etc. For much larger Weber numbers and
+applications such as multiphase jets with primary and secondary break-up further improvement is needed, especially
+to extend the range of accessible surface tensions to lower values at given interface thicknesses and acceptable levels
+of spurious currents. Given the kinetic roots of some of the models in that class of solvers, extension of the models
+to higher order physics beyond the meanfield approximation would also be a possible area of developmenet in the
+feature.
+Acknowledgement
+This work was supported by European Research Council (ERC) Advanced Grant no. 834763-PonD (S.A.H and
+I.K.). Computational resources at the Swiss National Super Computing Center CSCS were provided under grant no.
+s1066.
+Declaration of interests
+The authors report no conflict of interest.
+Appendix A. Hermite expansion
+Single variable Hermite polynomials. The single variable Hermite polynomial Hn of order n of a variable x is
+defined as:
+Hn(x) = (−1)n
+w(x)
+dn
+dxn w(x),
+(A.1)
+where the normalized function w(x) is defined as:
+w(x) =
+1
+√
+2π
+e− x2
+2 .
+(A.2)
+129
+
+Based on this definition, the first few polynomials can be computed as:
+H0 = 1,
+(A.3a)
+H1 = x,
+(A.3b)
+H2 = x2 − 1,
+(A.3c)
+H3 = x3 − 3x,
+(A.3d)
+H4 = x4 − 6x2 + 3,
+(A.3e)
+H5 = x5 − 10x3 + 15x,
+(A.3f)
+H6 = x6 − 15x4 + 45x2 − 15.
+(A.3g)
+These polynomials are mutually orthogonal with respect to the weight function, w(x), i.e.:
+� +∞
+−∞
+Hm(x)w(x)Hn(x)dx = n!δmn,
+(A.4)
+where δmn is the Kronecker delta function. Furthermore, they form a complete orthogonal basis of the Hilbert space
+of functions f(x) satisfying:
+� +∞
+−∞
+| f(x)|2w(x)dx < ∞.
+(A.5)
+As such, one can express the function f(x) as:
+f(x) =
+∞
+�
+n=0
+1
+n! anHn(x),
+(A.6)
+where an is the order n Hermite coefficient. Multiplying both sides by Hm(x)w(x) and integrating over x:
+� +∞
+−∞
+Hm(x)w(x) f(x)dx =
+∞
+�
+n=0
+1
+n! an
+� +∞
+−∞
+Hm(x)w(x)Hndx,
+(A.7)
+and using the mutual orthogonality of Hermite polynomials, we get an expression for the Hermite coefficients as:
+am =
+� +∞
+−∞
+Hm(x)w(x)f(x)dx.
+(A.8)
+Alternatively, one can also expand the function f(x) as:
+f(x) = w(x)
+∞
+�
+n=0
+1
+n! anHn(x),
+(A.9)
+resulting in the following expression for the coefficient a(m):
+am =
+� +∞
+−∞
+Hm(x) f(x)dx.
+(A.10)
+To better illustrate this, let us consider the example of the following function:
+f(x) = ρ
+1
+√
+2πθ
+e− (x−u)2
+2θ .
+(A.11)
+This function can be shown to be square-integrable with respect to the previously-defined weight function. As such
+the corresponding Hermite coefficients can be computed through Eq. A.10:
+am =
+1
+√
+2πθ
+� +∞
+−∞
+Hm(x)e− (x−u)2
+2θ dx,
+(A.12)
+130
+
+n
+an
+Hn(x)
+0
+1
+1
+1
+u
+x
+2
+u2 + (θ − 1)
+x2 − 1
+3
+u3 + 3u(θ − 1)
+x3 − 3x
+4
+u4 + 6u2(θ − 1) + 3(θ − 1)2
+x4 − 6x2 + 3
+5
+u5 + 10u3(θ − 1) + 15u(θ − 1)2
+x5 − 10x3 + 15x
+6
+u6 + 15u4(θ − 1) + 45u2(θ − 1)2 + 15(θ − 1)3
+x6 − 15x4 + 45x2 − 15
+7
+u7 + 21u5(θ − 1) + 105u3(θ − 1)2 + 105u(θ − 1)3
+x7 − 21x5 + 105x3 − 105x
+8
+u8 + 28u6(θ − 1) + 210u4(θ − 1)2 + 420u2(θ − 1)3
++105(θ − 1)4
+x8 − 28x6 + 210x4 − 420x2
++105
+9
+u9 + 36u7(θ − 1) + 378u5(θ − 1)2 + 1260u3(θ − 1)3
++945u(θ − 1)4
+x9 − 36x7 + 378x5 − 1260x3
++945x
+Table A.8: Hermite polynomials and coefficients for the Gaussian distribution function
+which using the change of variable η = (x − u)/
+√
+θ can be re-written as:
+am =
+1
+√
+2π
+� +∞
+−∞
+Hm(
+√
+θη + u)e− η2
+2 dη.
+(A.13)
+The different order coefficients can be easily evaluated using the following integral:
+� +∞
+−∞
+xke−ax2dx =
+���������
+0
+k = 2k
+′ + 1
+(2k
+′−1)!
+(2a)k′
+� π
+a
+k = 2k
+′
+,
+(A.14)
+leading to the following expansion:
+f(x) =
+∞
+�
+n=0
+ρw(x)
+n!
+anHn(x).
+(A.15)
+The first few terms are given in Table A.8.
+Multivariate Hermite polynomials. In a D-dimensional space the Hermite polynomial of order n is defined as:
+H n (x) = (−1)n
+w (x) ∇nw (x) ,
+(A.16)
+where ∇n is the nth order derivative resulting in a tensor of rank n and w (x) is the weight function defined as:
+w (x) =
+1
+2πD/2 e− x2
+2 .
+(A.17)
+Orthogonality of the multivariate Hermite polynomials results in:
+� +∞
+−∞
+w (x) H i (x) : H j (x) dx =
+�������
+0
+i � j
+n!δi j
+i = j ,
+(A.18)
+131
+
+where i and j are abbreviations for the set of indices {i1, i2, . . . , in} and {j1, j2, . . . , jn} respectively, and δi j is equal to
+unity if i is a permutation of j and zero otherwise. In a 3-D space the first few Hermite polynomials are computed as:
+H0 = 1,
+(A.19a)
+Hi = xi,
+(A.19b)
+Hij = xix j − δij,
+(A.19c)
+Hijk = xix jxk −
+�
+δijxk + δikx j + δ jkxi
+�
+,
+(A.19d)
+Hijkl = xixjxkxl −
+�
+δijxkxl + δikxjxl + δilxjxk + δjkxixl + δ jlxixk + δklxix j
+�
++
+�
+δijδkl + δikδ jl + δilδjk
+�
+,
+(A.19e)
+Hijklm = xixjxkxlxm −
+�
+δlmxixjxk + δkmxix jxl + δklxixjxm + δ jmxixkxl
++δjlxixkxm + δklxixlxm + δimx jxkxl + δilxjxkxm + δikx jxlxm + δi jxkxlxm
+�
++ xm
+�
+δijδkl + δikδ jl + δilδjk
+�
++ xl
+�
+δi jδkm + δikδ jm + δimδ jk
+�
++ xk
+�
+δijδlm + δilδ jm + δimδ jl
+�
++ x j (δikδlm + δilδkm + δimδkl)
++ xi
+�
+δ jkδlm + δ jlδkm + δ jmδkl
+�
+,
+(A.19f)
+Hijklmn = xixjxkxlxmxn −
+�
+xixjxkxlδmn + xixjxkxmδln + xix jxkxnδlm
++xix jxlxmδkn + xixjxlxnδkm + xix jxmxnδlk + xixkxlxmδjn
+xixkxlxnδ jm + xixkxmxnδ jl + xixlxmxnδ jk + x jxkxlxmδin
++xjxkxlxnδim + x jxlxmxnδik + x jxkxlxnδim + xjxkxmxnδil + xkxlxmxnδi j
+�
++ xix j (δklδmn + δkmδln + δknδlm) + xixk
+�
+δ jlδmn + δ jmδln + δ jnδml
+�
++ xixl
+�
+δ jkδmn + δjmδkn + δ jnδmk
+�
++ xixm
+�
+δ jkδln + δ jlδkn + δjnδlk
+�
++ xixn
+�
+δjkδlm + δjlδkm + δjmδlk
+�
++ xjxk (δinδlm + δilδnm + δimδln)
++ xjxl (δinδkm + δikδnm + δimδkn) + x jxm (δinδkl + δikδnl + δilδkn)
++ xjxn (δilδkm + δikδlm + δimδkl) + xkxl
+�
+δmnδi j + δmiδn j + δm jδin
+�
++ xkxm
+�
+δijδln + δilδjn + δinδl j
+�
++ xkxn
+�
+δmlδi j + δmiδl j + δm jδil
+�
++ xlxm
+�
+δijδkn + δikδ jn + δinδk j
+�
++ xlxn
+�
+δmkδi j + δmiδk j + δm jδik
+�
++ xnxm
+�
+δijδkl + δikδ jl + δilδk j
+�
++ δi j (δklδmn + δkmδln + δknδml)
++ δik
+�
+δ jlδmn + δ jmδln + δ jnδml
+�
++ δil
+�
+δk jδmn + δkmδ jn + δknδm j
+�
++ δim
+�
+δ jlδln + δjkδln + δjnδkl
+�
++ δin
+�
+δk jδml + δkmδ jl + δklδm j
+�
+.
+(A.19g)
+As for the single variable case, for a square-integrable function f (x), it can be expressed as:
+f (x) = w (x)
+∞
+�
+n=0
+1
+n! an : Hn (x) ,
+(A.20)
+where the Hermite coefficients an are defined as:
+an =
+� +∞
+−∞
+f (x) Hn (x) dx,
+(A.21)
+132
+
+resulting in the following coefficients for the multi-variate version of the distribution function of Eq. A.11:
+a0 = ρ,
+(A.22a)
+ai = ρui,
+(A.22b)
+aij = ρuiu j + ρ (θ − 1) δij,
+(A.22c)
+aijk = ρuiujuk + ρ (θ − 1)
+�
+δijuk + δikuj + δ jkui
+�
+,
+(A.22d)
+aijkl = ρuiu jukul + ρ (θ − 1)
+�
+δi jukul + δiku jul + δilujuk + δ jkuiul + δ jluiuk + δkluiu j
+�
++ ρ(θ − 1)2 �
+δijδkl + δikδ jl + δilδ jk
+�
+,
+(A.22e)
+aijklm = ρuiu jukulum + ρ (θ − 1)
+�
+δlmuiu juk + δkmuiujul + δkluiujum + δjmuiukul
++δ jluiukum + δkluiulum + δimujukul + δilujukum + δiku julum + δi jukulum
+�
++ ρ(θ − 1)2 �
+um
+�
+δijδkl + δikδ jl + δilδjk
+�
++ ul
+�
+δi jδkm + δikδ jm + δimδjk
+�
++uk
+�
+δijδlm + δilδ jm + δimδ jl
+�
++ u j (δikδlm + δilδkm + δimδkl)
++ui
+�
+δjkδlm + δjlδkm + δ jmδkl
+��
+,
+(A.22f)
+aijklmn = ρuiujukulumun + ρ (θ − 1)
+�
+uiu jukulδmn + uiujukumδln + uiujukunδlm
++uiujulumδkn + uiu julunδkm + uiu jumunδlk + uiukulumδ jn
+uiukulunδ jm + uiukumunδjl + uiulumunδ jk + ujukulumδin
++ujukulunδim + u julumunδik + ujukulunδim + ujukumunδil + ukulumunδi j
+�
++ ρ(θ − 1)2 �
+uiuj (δklδmn + δkmδln + δknδlm) + uiuk
+�
+δjlδmn + δjmδln + δjnδml
+�
++uiul
+�
+δ jkδmn + δ jmδkn + δjnδmk
+�
++ uium
+�
+δ jkδln + δ jlδkn + δ jnδlk
+�
++uiun
+�
+δ jkδlm + δ jlδkm + δ jmδlk
+�
++ ujuk (δinδlm + δilδnm + δimδln)
++ujul (δinδkm + δikδnm + δimδkn) + ujum (δinδkl + δikδnl + δilδkn)
++ujun (δilδkm + δikδlm + δimδkl) + ukul
+�
+δmnδi j + δmiδn j + δm jδin
+�
++ukum
+�
+δijδln + δilδjn + δinδl j
+�
++ ukun
+�
+δmlδi j + δmiδl j + δm jδil
+�
++ulum
+�
+δijδkn + δikδjn + δinδk j
+�
++ ulun
+�
+δmkδi j + δmiδk j + δm jδik
+�
++unum
+�
+δijδkl + δikδjl + δilδk j
+��
++ ρ(θ − 1)3 �
+δi j (δklδmn + δkmδln + δknδml)
++δik
+�
+δ jlδmn + δ jmδln + δ jnδml
+�
++ δil
+�
+δk jδmn + δkmδ jn + δknδm j
+�
++δim
+�
+δ jlδln + δ jkδln + δjnδkl
+�
++ δin
+�
+δk jδml + δkmδjl + δklδm j
+��
+.
+(A.22g)
+Appendix B. Elements of the von Neumann formalism
+Starting with a given set of coupled continuous/discretized PDEs, bound by periodic boundary conditions, defined
+as:
+L ( fi, r, t) = 0,
+(B.1)
+where L is the time evolution operator, the equations have to be linearized in order to use the VN method. To achieve
+this for the LB system of equations one can expand (first-order Taylor-McLaurin expansion) the distribution function
+around a reference state fi (¯ρ, ¯u):
+fi ≈ ¯fi + f
+′
+i ,
+(B.2)
+δtΩi( fi) ≈ δtΩi| ¯fi + Ji j f
+′
+j,
+(B.3)
+133
+
+where Einstein’s notation (summation) over j is used, and for the sake of clarity, ¯fi = fi (¯ρ, ¯u). Obviously, relying on
+a first-order expansion around the distribution function this expansion is only valid in the linear regime (i.e. small
+perturbations around the reference state). In addition, Ji j is the Jacobian of the collision operator evaluated about ¯f j,
+i.e, Ji j = ∂ f jδtΩi| ¯f j. Placing back these expressions into the discrete LB time-evolution equation:
+f
+′
+i (r + ciδt, t + δt) − f
+′
+i (r, t) = Ji j f
+′
+i (r, t) −
+� ¯fi (r + ciδt, t + δt) − ¯fi (r, t) − δtΩi| ¯fi
+�
+��������������������������������������������������������������������������������������������
+=0
+,
+(B.4)
+and taking out the last terms on the RHS one gets:
+f
+′
+i (r + ciδt, t + δt) =
+�
+δi j + Ji j
+�
+f
+′
+j (r, t) ,
+(B.5)
+where δij is the Kronecker delta function. Using the SRT collision operator for instance, we can then re-write the
+linearized time-evolution equation as:
+f
+′
+i (r + ciδt, t + δt) =
+��
+1 − δt
+¯τ
+�
+δi j + δt
+¯τ Jeq
+i j
+�
+f
+′
+j (r, t) ,
+(B.6)
+with Jeq
+ij = ∂ j f eq
+α | ¯f j and ¯f j = f eq
+j (¯ρ, ¯u). To compute the Jacobian matrix of the EDF, knowing that ∂ f j fk = δ jk, the
+following expressions can be used:
+∂ f jaeq
+0 = ∂ f j(ρ) =
+�
+k
+δ jk = 1,
+(B.7)
+∂ f jaeq
+1 = ∂ fj(ρu) =
+�
+k
+ckδ jk = cj.
+(B.8)
+Once re-written as a function of the conserved Hermite coefficients, computing the Jacobians of higher-order compo-
+nents of the Hermite expansion is straightforward. Let us consider the second-order Hermite coefficient for example:
+∂ f jaeq
+2 = ∂ f j
+aeq
+1 ⊗ aeq
+1
+aeq
+0
+= − aeq
+1 ⊗ aeq
+1
+(aeq
+0 )2
++
+aeq
+1 ⊗ c j +
+�
+aeq
+1 ⊗ cj
+�†
+aeq
+0
+.
+(B.9)
+Eventually, for the second-order EDF the Jacobian reads:
+Jeq
+ij = wi
+�
+H0 + H1(ci) : ∂ f jaeq
+1 + H2(ci) :
+∂f j aeq
+2
+2
+�
+.
+(B.10)
+The last step of the VN analysis is to assume that perturbations f ′
+i are monochromatic plane waves :
+f ′
+i = Fi exp [
+√
+−1(k · r − ωit)],
+where Fi is the wave amplitude,
+√
+−1 is the imaginary unit, ||k|| = k is the wave-number, and ω is the complex time
+frequency of the wave. k is related to the wave-length of f ′
+i , whereas ℑ(ω) and ℜ(ω) are related to its attenuation and
+propagation speed. By injecting these perturbations into Eq. B.5 one obtains the following eigenvalue problem of size
+Q:
+MF = exp (−
+√
+−1ωi)F,
+(B.11)
+where F is the eigenvector composed of all amplitudes. It is related to the eigenvalue exp (−
+√
+−1ω). M is the matrix
+associated to Eq. B.5. Here this matrix can be expressed as :
+M = E [δ + J] ,
+(B.12)
+with
+Ei j = exp[−i(ci · k)]δi j.
+(B.13)
+It is important to notice that the matrix M and the eigenvalue problem B.11 depend on the mean flow (¯ρ, ¯u), the
+wave-number (kx and ky in 2-D) and the relaxation coefficient ¯τ, or equivalently the kinematic viscosity ν. This means
+that for each set of these parameters the eigenvalue problem needs to be solved to obtain the corresponding values of
+ℜ(ω) and ℑ(ω). Doing so, the spectral properties (dispersion and dissipation) can be obtained for any given collision
+model.
+134
+
+Appendix C. Hydrodynamic limit of the Enskog–Vlasov–BGK kinetic model
+Chapman–Enskog analysis Expanding the distribution function as:
+f = f (0) + ϵ f (1) + ϵ2 f (2) + O(ϵ3),
+(C.1)
+introducing it back into (576) and separating terms with different orders in ϵ, at order zero one recovers:
+f (0) = f eq.
+(C.2)
+This latter implies the solvability conditions,
+�
+f (k)dv = 0, ∀k � 0,
+(C.3)
+�
+v f (k)dv = 0, ∀k � 0.
+(C.4)
+At order ϵ:
+∂(1)
+t
+f (0) + v · ∇f (0) = −1
+τ f (1) − 1
+ρ
+∂f eq
+∂u · F(1),
+(C.5)
+which, upon integration in v, leads to
+∂(1)
+t ρ + ∇ · ρu = 0,
+(C.6)
+∂(1)
+t ρu + ∇ρu ⊗ u + ∇ · P0I + F(1) = 0.
+(C.7)
+At order ϵ2:
+∂(2)
+t
+f (0) + ∂(1)
+t
+f (1) + v · ∇ f (1) = −1
+τ f (2),
+(C.8)
+which leads to the following equation for mass conservation:
+∂(2)
+t ρ = 0,
+(C.9)
+while for momentum:
+∂(2)
+t ρu + ∇ ·
+��
+v ⊗ v f (1)dv
+�
+= 0.
+(C.10)
+The last term on the left hand side can be evaluated using the previous order in ϵ as:
+�
+v ⊗ v f (1)dv = −τ
+�
+∂(1)
+t
+�
+v ⊗ v f (0)dv + ∇ ·
+�
+v ⊗ v ⊗ v f (0)dv
++1
+ρ
+�
+v ⊗ v∂f eq
+∂u · F(1)dv
+�
+,
+(C.11)
+where:
+∂(1)
+t
+�
+v ⊗ v f (0)dv = −∇ · ρu ⊗ u ⊗ u −
+�
+u ⊗ (F(1) + ∇P0) + (F(1) + ∇P0) ⊗ u
+�
++ ∂(1)
+t P0I,
+(C.12)
+and:
+∇ ·
+�
+v ⊗ v ⊗ vf (1)dv = ∇ · ρu ⊗ u ⊗ u +
+�
+∇P0u + ∇P0u†�
++ I∇ · P0u,
+(C.13)
+1
+ρ
+�
+v ⊗ v∂f eq
+∂u · F(1)dv = u ⊗ F(1) + F(1) ⊗ u,
+(C.14)
+which leads to:
+�
+v ⊗ v f (1)dv = −τ
+�
+P0
+�
+∇u + ∇u†�
++
+�
+∂(1)
+t P0 + ∇ · P0u
+�
+I
+�
+,
+(C.15)
+135
+
+where the last two terms can be re-written as:
+∂(1)
+t P0 + ∇ · P0u =∂P0
+∂ρ (∂(1)
+t ρ + ∇ · ρu) +
+�
+P0 − ρ∂P0
+∂ρ
+�
+∇ · u
+=P0
+�
+1 − ∂ ln P0
+∂ ln ρ
+�
+∇ · u,
+(C.16)
+in turn recovering the Navier-Stokes-level momentum equation:
+∂(2)
+t ρu − ∇ · µ
+�
+∇u + ∇u† − 2
+3∇ · uI
+�
+− ∇ · (η∇ · uI) = 0,
+(C.17)
+where:
+µ = τP0,
+(C.18)
+η = τP0
+�5
+3 − ∂ ln P0
+∂ ln ρ
+�
+.
+(C.19)
+Appendix D. Chapman–Enskog analysis of the lattice Boltzmann method for non-ideal fluids
+Using a Taylor expansion around (r, t),
+fi (r + ciδt, t + δt) − fi (r, t) =
+�
+δtDt + δt2
+2 D2
+t
+�
+f (r, t) + O(δt3)
+(D.1)
+the discrete time-evolution equation is re-written as:
+δtDt fi + δt2
+2 Dt
+2 fi + O(δt3) = δt
+¯τ
+�
+f eq
+i
+− fi
+�
++
+�
+f ∗
+i − f eq
+i
+�
+,
+(D.2)
+where we have only retained terms up to order two. Then introducing characteristic flow size L and velocity U the
+equation is made non-dimensional as:
+�δr
+L
+�
+D′
+t fi + 1
+2
+�δr
+L
+�2
+D′
+t
+2 fi = δt
+¯τ
+�
+f eq
+i
+− fi
+�
++
+�
+f ∗
+i (u′ + δu
+U δu′) − f eq
+i (u′)
+�
+,
+(D.3)
+where primed variables denote non-dimensional form and
+D′
+t = U
+c
+�∂′
+t + c′
+i · ∇′� ,
+(D.4)
+where c = δr/δt. Assuming acoustic, i.e. U
+c ∼ 1 and hydrodynamic, i.e. δr
+L ∼ δu
+U ∼ ε, scaling and dropping the primes
+for the sake of readability:
+εDt fi + 1
+2ε2Dt
+2 fi + O(ε3) = δt
+¯τ
+�
+f eq
+i
+− fi
+�
++
+�
+f ∗
+i (u + εδu) − f eq
+i (u)
+�
+.
+(D.5)
+Then introducing multi-scale expansions:
+fi
+=
+f (0)
+i
++ ε f (1)
+i
++ ε2 f (2)
+i
++ O(ε3),
+(D.6)
+f ∗
+i
+=
+f ∗
+i
+(0) + ε f ∗
+i
+(1) + ε2 f ∗
+i
+(2) + O(ε3),
+(D.7)
+the following equations are recovered at scales ε and ε2:
+ε : D(1)
+t
+f (0)
+i
+= −δt
+¯τ f (1)
+i
++ f ∗(1)
+i ,
+(D.8a)
+ε2 : ∂(2)
+t
+f (0)
+i
++ D(1)
+t
+�
+1 − δt
+2¯τ
+�
+f (1)
+i
+= −δt
+¯τ f (2)
+i
++ f ∗(2)
+i
+− 1
+2D(1)
+t
+f ∗(1)
+i ,
+(D.8b)
+136
+
+with f (0)
+i
+= f ∗
+i
+(0) = f eq
+i . The moments of the non-local contributions (including both non-ideal contributions to the
+thermodynamic pressure, surface tension and the correction for the diagonals of the third-order moments tensor) are:
+�
+i
+f ∗(k)
+i
+= 0, ∀k > 0,
+(D.9a)
+�
+i
+ci f ∗
+i
+(1) = F,
+(D.9b)
+�
+i
+ci ⊗ ci f ∗
+i
+(1) = (u ⊗ F + F ⊗ u) + Φ
+(D.9c)
+�
+i
+ci ⊗ ci f ∗
+i
+(2) = 1
+ρ F ⊗ F.
+(D.9d)
+Taking the moments of the Chapman-Enskog-expanded equation at order ε:
+∂(1)
+t ρ + ∇ · ρu
+=
+0,
+(D.10)
+∂(1)
+t ρu + ∇ · ρu ⊗ u + ∇ · P0I + F
+=
+0,
+(D.11)
+while at order ε2 the continuity equation is:
+∂(2)
+t ρ + ∇ · F
+2 = 0.
+(D.12)
+Summing up Eqs. D.10 and D.12 we recover the continuity equation as:
+∂tρ + ∇ · ρU = 0,
+(D.13)
+where U = u + δt
+2ρ F. For the momentum equations we have:
+∂(2)
+t ρu + 1
+2∂(1)
+t F + 1
+2∇ · (u ⊗ F + F ⊗ u) + ∇ ·
+�1
+2 − ¯τ
+δt
+� �
+∂(1)
+t Π(0)
+2 + ∇ · Π(0)
+3
+�
+− ∇ ·
+�1
+2 − ¯τ
+δt
+�
+(u ⊗ F + F ⊗ u) + ∇ · ¯τ
+δtΦ = 0,
+(D.14)
+where Π(0)
+2 and Π(0)
+3 are the second- and third-order moments of f (0)
+i
+defined as:
+Π(0)
+2
+=
+ρu ⊗ u + P0I,
+(D.15)
+Π(0)
+3
+=
+ΠMB
+3
+− ρu ⊗ u ⊗ u ◦ J − 3(P0 − ρς2)J
+(D.16)
+where ΠMB
+αβγ = ρuαuβuγ +P0perm(uαδβγ) is the third-order moment of the Maxwell-Boltzmann distribution, and for the
+sake of simplicity we have introduced the diagonal rank three tensor J, with Jαβγ = δαβδαγδβγ and ◦ is the Hadamard
+product. The contributions in the fourth term on the left hand side can be expanded as:
+∂(1)
+t Π(0)
+2 =∂(1)
+t ρu ⊗ u + ∂(1)
+t P0I
+=u ⊗ ∂(1)
+t ρu + (∂(1)
+t ρu) ⊗ u − u ⊗ u∂(1)
+t ρ + ∂(1)
+t P0I
+= − ∇ · ρu ⊗ u ⊗ u − [u ⊗ (∇P0 − F) + (∇P0 − F) ⊗ u] + ∂(1)
+t P0I
+(D.17)
+and:
+∇ · Π(0)
+3 = ∇ · ρu ⊗ u ⊗ u +
+�
+∇P0u + ∇P0u†�
++ (∇ · P0u)I − ∇ ·
+�
+ρu ⊗ u ⊗ u ◦ J + 3(P0 − ρς2)J
+�
+,
+(D.18)
+resulting in:
+∂(1)
+t Π(0)
+2 + ∇ · Π(0)
+3 = P0
+�
+∇u + ∇u†�
++
+�
+u ⊗ F + u ⊗ F†�
++
+�
+∇ · P0u + ∂(1)
+t P0
+�
+I − ∇ ·
+�
+ρu ⊗ u ⊗ u ◦ J + 3(P0 − ρς2)J
+�
+.
+(D.19)
+137
+
+Plugging this last equation back into Eq. (D.14):
+∂(2)
+t ρu + ∂(1)
+t
+F
+2 + 1
+2∇ · (u ⊗ F + F ⊗ u) + ∇ ·
+�1
+2 − ¯τ
+δt
+�
+P0
+�
+∇u + ∇u†�
++ ∇
+�1
+2 − ¯τ
+δt
+� �
+∂(1)
+t P0 + ∇ · P0u
+�
++ ∇ ·
+��1
+2 − ¯τ
+δt
+�
+∇ ·
+�
+ρu ⊗ u ⊗ u ◦ J + 3(P0 − ρς2)J
+�
++ ¯τ
+δtΦ
+�
+= 0.
+(D.20)
+where the last term cancels out by setting:
+Φ =
+�
+1 − δt
+2¯τ
+�
+∇ ·
+�
+ρu ⊗ u ⊗ u ◦ J + 3(P0 − ρς2)J
+�
+,
+(D.21)
+and the fourth and fifth terms reduce to the viscous stress tensor by defining µ/P0 =
+� ¯τ
+δt − 1
+2
+�
+and:
+P0
+�2 + D
+D
+− ∂ ln P0
+∂ ln ρ
+� � ¯τ
+δt − 1
+2
+�
+= η.
+(D.22)
+Furthermore, using U = u + δt
+2ρ F and:
+ρU ⊗ U = ρu ⊗ u + δt
+2 (u ⊗ F + F ⊗ u) + δt2F ⊗ F
+4ρ
+,
+(D.23)
+in combination with the Euler-level equation, and keeping in mind that errors of the form ∇ · δt2F⊗F
+4ρ
+in the convective
+term and δt∇µ
+�
+∇ F
+ρ + ∇ F
+ρ
+†�
+in the viscous stress are of order ε3 one recovers:
+∂tρU + ∇ · ρU ⊗ U − ∇ · µ
+�
+∇U + ∇U† − 2
+D∇ · UI
+�
+− ∇ · (η∇ · U) + O(ε3) = 0.
+(D.24)
+References
+[1] J. A. Sethian, P. Smereka, Level set methods for fluid interfaces, Annual review of fluid mechanics 35 (1) (2003) 341–372, iSBN: 0066-4189
+Publisher: Annual Reviews 4139 El Camino Way, PO Box 10139, Palo Alto, CA 94303-0139, USA.
+[2] R. Scardovelli, S. Zaleski, Direct numerical simulation of free-surface and interfacial flow, Annual review of fluid mechanics 31 (1) (1999)
+567–603, iSBN: 0066-4189 Publisher: Annual Reviews 4139 El Camino Way, PO Box 10139, Palo Alto, CA 94303-0139, USA.
+[3] S. Popinet, Numerical models of surface tension, Annual Review of Fluid Mechanics 50 (2018) 49–75, iSBN: 0066-4189 Publisher: Annual
+Reviews.
+[4] A. Prosperetti, G. Tryggvason, Computational methods for multiphase flow, Cambridge university press, 2009.
+[5] P. G. Debenedetti, Metastable liquids, Princeton university press, 1997.
+[6] J. D. van der Waals, Thermodynamische Theorie der Kapillarit¨at unter Voraussetzung stetiger Dichte¨anderung, Zeitschrift f¨ur Physikalische
+Chemie 13U (1) (Jan. 1894). doi:10.1515/zpch-1894-1338.
+URL https://www.degruyter.com/document/doi/10.1515/zpch-1894-1338/html
+[7] D. J. Korteweg, Sur la forme que prennent les ´equations du mouvement des fluides si l’on tient compte des forces capillaires caus´ees par des
+variations de densit´e consid´erables mais continues et sur la th´eeorie de la capillarit´e dans l’hypothese d’une variation continue de la densit´e,
+Arch. N´eerl. Sci. Exactes Nat 6 (265) (1901).
+[8] D. M. Anderson, G. B. McFadden, A. A. Wheeler, Diffuse-interface methods in fluid mechanics, Annual review of fluid mechanics 30 (1)
+(1998) 139–165, iSBN: 0066-4189 Publisher: Annual Reviews 4139 El Camino Way, PO Box 10139, Palo Alto, CA 94303-0139, USA.
+[9] D. Enskog, Der warmeleitung, reibung und selbstdiffusion in gewissen verdichteten gasen und flussigkeiten, Kungl. Svenska Vetenskap-
+sakademiens Handlingar. 63 (4) (1921).
+[10] A. A. Vlasov, Many-particle theory and its application to plasma., New York (1961).
+[11] S. Chapman, T. G. Cowling, The mathematical theory of non-uniform gases: an account of the kinetic theory of viscosity, thermal conduction
+and diffusion in gases, Cambridge university press, 1939.
+[12] X. Shan, H. Chen, Lattice Boltzmann model for simulating flows with multiple phases and components, Physical Review E 47 (3) (1993)
+1815–1819. doi:10.1103/PhysRevE.47.1815.
+URL https://link.aps.org/doi/10.1103/PhysRevE.47.1815
+138
+
+[13] L. Saint-Raymond, A mathematical PDE perspective on the Chapman–Enskog expansion, Bulletin of the American Mathematical Society
+51 (2) (2013) 247–275. doi:10.1090/S0273-0979-2013-01440-X.
+URL http://www.ams.org/jourcgi/jour-getitem?pii=S0273-0979-2013-01440-X
+[14] A. N. Gorban, I. Karlin, Hilbert’s 6th Problem: exact and approximate hydrodynamic manifolds for kinetic equations, Bulletin of the
+American Mathematical Society 51 (2) (2013) 187–246. doi:10.1090/S0273-0979-2013-01439-3.
+URL http://www.ams.org/jourcgi/jour-getitem?pii=S0273-0979-2013-01439-3
+[15] H. Grad, On the kinetic theory of rarefied gases, Communications on Pure and Applied Mathematics 2 (4) (1949) 331–407. doi:10.1002/
+cpa.3160020403.
+URL https://onlinelibrary.wiley.com/doi/10.1002/cpa.3160020403
+[16] D. Jou, G. Lebon, Extended Irreversible Thermodynamics, Springer Netherlands, Dordrecht, 2010. doi:10.1007/978-90-481-3074-0.
+URL http://link.springer.com/10.1007/978-90-481-3074-0
+[17] M. Grmela, L. Hong, D. Jou, G. Lebon, M. Pavelka, Hamiltonian and Godunov structures of the Grad hierarchy, Physical Review E 95 (3)
+(2017) 033121. doi:10.1103/PhysRevE.95.033121.
+URL http://link.aps.org/doi/10.1103/PhysRevE.95.033121
+[18] M. Grmela, Externally Driven Macroscopic Systems: Dynamics Versus Thermodynamics, Journal of Statistical Physics 166 (2) (2017)
+282–316. doi:10.1007/s10955-016-1694-6.
+URL http://link.springer.com/10.1007/s10955-016-1694-6
+[19] C. Truesdell, R. G. Muncaster, Fundamentals of Maxwell’s kinetic theory of a simple monatomic gas, Academic Pres, New York, 1980.
+[20] H. Struchtrup, Macroscopic Transport Equations for Rarefied Gas Flows, Interaction of Mechanics and Mathematics, Springer Berlin Hei-
+delberg, Berlin, Heidelberg, 2005. doi:10.1007/3-540-32386-4.
+URL http://link.springer.com/10.1007/3-540-32386-4
+[21] A. N. Gorban, I. V. Karlin, Short-Wave Limit of Hydrodynamics: A Soluble Example, Physical Review Letters 77 (2) (1996) 282–285.
+doi:10.1103/PhysRevLett.77.282.
+URL https://link.aps.org/doi/10.1103/PhysRevLett.77.282
+[22] I. Karlin, A. Gorban, Hydrodynamics from Grad’s equations: What can we learn from exact solutions?, Annalen der Physik 514 (10-11)
+(2002) 783–833. doi:10.1002/andp.200251410-1103.
+URL https://onlinelibrary.wiley.com/doi/10.1002/andp.200251410-1103
+[23] A. Kogan, Derivation of Grad’s type equations and study of their relaxation properties by the method of maximization of entropy, Journal
+of Applied Mathematics and Mechanics 29 (1) (1965) 130–142. doi:10.1016/0021-8928(65)90157-7.
+URL https://linkinghub.elsevier.com/retrieve/pii/0021892865901577
+[24] R. M. Lewis, A Unifying Principle in Statistical Mechanics, Journal of Mathematical Physics 8 (7) (1967) 1448–1459. doi:10.1063/1.
+1705359.
+URL http://aip.scitation.org/doi/10.1063/1.1705359
+[25] I. V. Karlin, On the relaxation of the chemical reaction rate, in: Mathematical Problems of Chemical Kinetics, Novosibirsk, 1989, pp. 7–42.
+[26] A. N. Gorban, I. V. Karlin, Quasi–equilibrium approximation and nonstandard expansions in the theory of the Boltzmann kinetic equation,
+in: Mathematical Modelling in Biology and Chemistry. New Approaches, Novosibirsk, 1991, pp. 69–117.
+[27] E. M. Shakhov, Generalization of the Krook kinetic relaxation equation, Fluid Dynamics 3 (5) (1972) 95–96. doi:10.1007/BF01029546.
+URL http://link.springer.com/10.1007/BF01029546
+[28] N. Frapolli, S. S. Chikatamarla, I. V. Karlin, Multispeed entropic lattice Boltzmann model for thermal flows, Physical Review E 90 (4)
+(2014) 043306. doi:10.1103/PhysRevE.90.043306.
+URL https://link.aps.org/doi/10.1103/PhysRevE.90.043306
+[29] I. Karlin, A. Gorban, G. Dukek, T. Nonnenmacher, Dynamic correction to moment approximations, Physical Review E 57 (2) (1998) 1668–
+1672. doi:10.1103/PhysRevE.57.1668.
+URL https://link.aps.org/doi/10.1103/PhysRevE.57.1668
+[30] H. Struchtrup, M. Torrilhon, Regularization of Grad’s 13 moment equations: Derivation and linear analysis, Physics of Fluids 15 (9) (2003)
+2668–2680. doi:10.1063/1.1597472.
+URL http://aip.scitation.org/doi/10.1063/1.1597472
+[31] I. Karlin, Derivation of regularized Grad’s moment system from kinetic equations: modes, ghosts and non-Markov fluxes, Philosophical
+Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376 (2118) (2018) 20170230. doi:10.1098/
+rsta.2017.0230.
+URL https://royalsocietypublishing.org/doi/10.1098/rsta.2017.0230
+[32] A. Rana, M. Torrilhon, H. Struchtrup, A robust numerical method for the R13 equations of rarefied gas dynamics: Application to lid driven
+cavity, Journal of Computational Physics 236 (2013) 169–186. doi:10.1016/j.jcp.2012.11.023.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0021999112007036
+[33] H. Struchtrup, M. Torrilhon, Regularized 13 moment equations for hard sphere molecules: Linear bulk equations, Physics of Fluids 25 (5)
+(2013) 052001. doi:10.1063/1.4802041.
+URL http://aip.scitation.org/doi/10.1063/1.4802041
+[34] H. Struchtrup, Derivation of 13 Moment Equations for Rarefied Gas Flow to Second Order Accuracy for Arbitrary Interaction Potentials,
+Multiscale Modeling & Simulation 3 (1) (2005) 221–243. doi:10.1137/040603115.
+URL http://epubs.siam.org/doi/10.1137/040603115
+[35] H. Struchtrup, Stable transport equations for rarefied gases at high orders in the Knudsen number, Physics of Fluids 16 (11) (2004) 3921–
+3934. doi:10.1063/1.1782751.
+URL http://aip.scitation.org/doi/10.1063/1.1782751
+[36] M. Torrilhon, Modeling Nonequilibrium Gas Flow Based on Moment Equations, Annual Review of Fluid Mechanics 48 (1) (2016) 429–458.
+doi:10.1146/annurev-fluid-122414-034259.
+139
+
+URL https://www.annualreviews.org/doi/10.1146/annurev-fluid-122414-034259
+[37] M. Y. Timokhin, H. Struchtrup, A. A. Kokhanchik, Y. A. Bondar, Different variants of R13 moment equations applied to the shock-wave
+structure, Physics of Fluids 29 (3) (2017) 037105. doi:10.1063/1.4977978.
+URL http://aip.scitation.org/doi/10.1063/1.4977978
+[38] H. Struchtrup, M. Torrilhon, H Theorem, Regularization, and Boundary Conditions for Linearized 13 Moment Equations, Physical Review
+Letters 99 (1) (2007) 014502. doi:10.1103/PhysRevLett.99.014502.
+URL https://link.aps.org/doi/10.1103/PhysRevLett.99.014502
+[39] M. Torrilhon, H. Struchtrup, Regularized 13-moment equations: shock structure calculations and comparison to Burnett models, Journal of
+Fluid Mechanics 513 (2004) 171–198. doi:10.1017/S0022112004009917.
+URL http://www.journals.cambridge.org/abstract_S0022112004009917
+[40] A. N. Gorban, I. V. Karlin, General approach to constructing models of the Boltzmann equation, Physica A: Statistical Mechanics and its
+Applications 206 (3-4) (1994) 401–420. doi:10.1016/0378-4371(94)90314-X.
+URL https://linkinghub.elsevier.com/retrieve/pii/037843719490314X
+[41] C. D. Levermore, Moment closure hierarchies for kinetic theories, Journal of Statistical Physics 83 (5-6) (1996) 1021–1065. doi:10.1007/
+BF02179552.
+URL http://link.springer.com/10.1007/BF02179552
+[42] S. Ansumali, S. Arcidiacono, S. S. Chikatamarla, N. I. Prasianakis, A. N. Gorban, I. V. Karlin, Quasi-equilibrium lattice Boltzmann method,
+The European Physical Journal B 56 (2) (2007) 135–139. doi:10.1140/epjb/e2007-00100-1.
+URL http://link.springer.com/10.1140/epjb/e2007-00100-1
+[43] L. H. Holway, Kinetic Theory of Shock Structure Using an Ellipsoidal Distribution Function, in: Proceedings of the Fourth International
+Symposium on Rarefied Gas Dynamics, Vol. 1, Toronto, 1965.
+[44] P. Andries, P. Le Tallec, J.-P. Perlat, B. Perthame, The Gaussian-BGK model of Boltzmann equation with small Prandtl number, European
+Journal of Mechanics - B/Fluids 19 (6) (2000) 813–830. doi:10.1016/S0997-7546(00)01103-1.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0997754600011031
+[45] G. R. McNamara, G. Zanetti, Use of the Boltzmann equation to simulate lattice-gas automata, Physical review letters 61 (20) (1988) 2332,
+publisher: APS.
+[46] R. Benzi, S. Succi, M. Vergassola, The lattice Boltzmann equation: theory and applications, Physics Reports 222 (3) (1992) 145–197.
+doi:10.1016/0370-1573(92)90090-M.
+URL https://linkinghub.elsevier.com/retrieve/pii/037015739290090M
+[47] S. Succi, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Clarendon, 2002.
+URL http://physicstoday.scitation.org/doi/10.1063/1.1537916
+[48] U. Frisch, B. Hasslacher, Y. Pomeau, Lattice-Gas Automata for the Navier-Stokes Equation, Physical Review Letters 56 (14) (1986) 1505–
+1508. doi:10.1103/PhysRevLett.56.1505.
+URL https://link.aps.org/doi/10.1103/PhysRevLett.56.1505
+[49] X. Shan, X.-F. Yuan, H. Chen, Kinetic theory representation of hydrodynamics: a way beyond the Navier–Stokes equation, Journal of Fluid
+Mechanics 550 (2006) 413–441, iSBN: 1469-7645 Publisher: Cambridge University Press.
+[50] H. Grad, Note onN-dimensional hermite polynomials, Communications on Pure and Applied Mathematics 2 (4) (1949) 325–330. doi:
+10.1002/cpa.3160020402.
+URL https://onlinelibrary.wiley.com/doi/10.1002/cpa.3160020402
+[51] C. Sun, Lattice-Boltzmann models for high speed flows, Physical Review E 58 (6) (1998) 7283–7287. doi:10.1103/PhysRevE.58.7283.
+URL https://link.aps.org/doi/10.1103/PhysRevE.58.7283
+[52] C. Sun, Adaptive lattice Boltzmann model for compressible flows: Viscous and conductive properties, Physical Review E 61 (3) (2000)
+2645–2653. doi:10.1103/PhysRevE.61.2645.
+URL https://link.aps.org/doi/10.1103/PhysRevE.61.2645
+[53] C. Sun, A. T. Hsu, Three-dimensional lattice Boltzmann model for compressible flows, Physical Review E 68 (1) (2003) 016303. doi:
+10.1103/PhysRevE.68.016303.
+URL https://link.aps.org/doi/10.1103/PhysRevE.68.016303
+[54] N. Frapolli, S. Chikatamarla, I. Karlin, Lattice Kinetic Theory in a Comoving Galilean Reference Frame, Physical Review Letters 117 (1)
+(2016) 010604. doi:10.1103/PhysRevLett.117.010604.
+URL https://link.aps.org/doi/10.1103/PhysRevLett.117.010604
+[55] B. Dorschner, F. B¨osch, I. V. Karlin, Particles on demand for kinetic theory, Physical review letters 121 (13) (2018) 130602, publisher: APS.
+[56] M. H. Saadat, F. B¨osch, I. V. Karlin, Lattice Boltzmann model for compressible flows on standard lattices: Variable Prandtl number and
+adiabatic exponent, Physical Review E 99 (1) (2019) 013306. doi:10.1103/PhysRevE.99.013306.
+URL https://link.aps.org/doi/10.1103/PhysRevE.99.013306
+[57] C. Lin, A. Xu, G. Zhang, K. H. Luo, Y. Li, Discrete Boltzmann modeling of Rayleigh-Taylor instability in two-component compressible
+flows, Physical Review E 96 (5) (2017) 053305. doi:10.1103/PhysRevE.96.053305.
+URL https://link.aps.org/doi/10.1103/PhysRevE.96.053305
+[58] S. A. Hosseini, N. Darabiha, D. Th´evenin, Compressibility in lattice Boltzmann on standard stencils: effects of deviation from reference
+temperature, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378 (2175) (2020)
+20190399. doi:10.1098/rsta.2019.0399.
+URL https://royalsocietypublishing.org/doi/10.1098/rsta.2019.0399
+[59] Y. Gan, A. Xu, G. Zhang, H. Lai, Three-dimensional discrete Boltzmann models for compressible flows in and out of equilibrium,
+Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 232 (3) (2018) 477–490.
+doi:10.1177/0954406217742181.
+URL http://journals.sagepub.com/doi/10.1177/0954406217742181
+140
+
+[60] Y. Gan, A. Xu, G. Zhang, Y. Yang, Lattice BGK kinetic model for high-speed compressible flows: Hydrodynamic and nonequilibrium
+behaviors, EPL (Europhysics Letters) 103 (2) (2013) 24003. doi:10.1209/0295-5075/103/24003.
+URL https://iopscience.iop.org/article/10.1209/0295-5075/103/24003
+[61] Y. Gan, A. Xu, G. Zhang, Y. Zhang, S. Succi, Discrete Boltzmann trans-scale modeling of high-speed compressible flows, Physical Review
+E 97 (5) (2018) 053312. doi:10.1103/PhysRevE.97.053312.
+URL https://link.aps.org/doi/10.1103/PhysRevE.97.053312
+[62] S. Ansumali, I. V. Karlin, H. C. ¨Ottinger, Minimal entropic kinetic models for hydrodynamics, EPL (Europhysics Letters) 63 (6) (2003) 798,
+iSBN: 0295-5075 Publisher: IOP Publishing.
+[63] Q. Li, K. H. Luo, Y. L. He, Y. J. Gao, W. Q. Tao, Coupling lattice Boltzmann model for simulation of thermal flows on standard lattices,
+Physical Review E 85 (1) (2012) 016710. doi:10.1103/PhysRevE.85.016710.
+URL https://link.aps.org/doi/10.1103/PhysRevE.85.016710
+[64] Y. Feng, P. Sagaut, W. Tao, A three dimensional lattice model for thermal compressible flow on standard lattices, Journal of Computational
+Physics 303 (2015) 514–529, iSBN: 0021-9991 Publisher: Elsevier.
+[65] Y. Feng, P. Boivin, J. Jacob, P. Sagaut, Hybrid recursive regularized thermal lattice Boltzmann model for high subsonic compressible flows,
+Journal of Computational Physics 394 (2019) 82–99. doi:10.1016/j.jcp.2019.05.031.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0021999119303626
+[66] N. I. Prasianakis, I. V. Karlin, Lattice Boltzmann method for thermal flow simulation on standard lattices, Physical Review E 76 (1) (2007)
+016702. doi:10.1103/PhysRevE.76.016702.
+URL https://link.aps.org/doi/10.1103/PhysRevE.76.016702
+[67] N. I. Prasianakis, I. V. Karlin, Lattice Boltzmann method for simulation of compressible flows on standard lattices, Physical Review E 78 (1)
+(2008) 016704. doi:10.1103/PhysRevE.78.016704.
+URL https://link.aps.org/doi/10.1103/PhysRevE.78.016704
+[68] D. Wilde, A. Kr¨amer, D. Reith, H. Foysi, Semi-Lagrangian lattice Boltzmann method for compressible flows, Physical Review E 101 (5)
+(2020) 053306. doi:10.1103/PhysRevE.101.053306.
+URL https://link.aps.org/doi/10.1103/PhysRevE.101.053306
+[69] D. Wilde, A. Kr¨amer, K. K¨ullmer, H. Foysi, D. Reith, Multistep lattice Boltzmann methods: Theory and applications, International Journal
+for Numerical Methods in Fluids 90 (3) (2019) 156–169. doi:10.1002/fld.4716.
+URL https://onlinelibrary.wiley.com/doi/10.1002/fld.4716
+[70] A. Kr¨amer, K. K¨ullmer, D. Reith, W. Joppich, H. Foysi, Semi-Lagrangian off-lattice Boltzmann method for weakly compressible flows,
+Physical Review E 95 (2) (2017) 023305. doi:10.1103/PhysRevE.95.023305.
+URL https://link.aps.org/doi/10.1103/PhysRevE.95.023305
+[71] M. H. Saadat, S. A. Hosseini, B. Dorschner, I. V. Karlin, Extended lattice Boltzmann model for gas dynamics, Physics of Fluids 33 (4)
+(2021) 046104, iSBN: 1070-6631 Publisher: AIP Publishing LLC.
+[72] A. A. Mohamad, A. Kuzmin, A critical evaluation of force term in lattice Boltzmann method, natural convection problem, International
+Journal of Heat and Mass Transfer 53 (5-6) (2010) 990–996, iSBN: 0017-9310 Publisher: Elsevier.
+[73] H. Huang, M. Krafczyk, X. Lu, Forcing term in single-phase and Shan-Chen-type multiphase lattice Boltzmann models, Physical Review E
+84 (4) (2011) 046710. doi:10.1103/PhysRevE.84.046710.
+URL https://link.aps.org/doi/10.1103/PhysRevE.84.046710
+[74] S. A. Bawazeer, S. S. Baakeem, A. A. Mohamad, A Critical Review of Forcing Schemes in Lattice Boltzmann Method: 1993–2019, Archives
+of Computational Methods in Engineering 28 (7) (2021) 4405–4423. doi:10.1007/s11831-021-09535-4.
+URL https://link.springer.com/10.1007/s11831-021-09535-4
+[75] N. S. Martys, X. Shan, H. Chen, Evaluation of the external force term in the discrete Boltzmann equation, Physical Review E 58 (5) (1998)
+6855–6857. doi:10.1103/PhysRevE.58.6855.
+URL https://link.aps.org/doi/10.1103/PhysRevE.58.6855
+[76] L.-S. Luo, Unified Theory of Lattice Boltzmann Models for Nonideal Gases, Physical Review Letters 81 (8) (1998) 1618–1621. doi:
+10.1103/PhysRevLett.81.1618.
+URL https://link.aps.org/doi/10.1103/PhysRevLett.81.1618
+[77] Z. Guo, C. Zheng, B. Shi, Discrete lattice effects on the forcing term in the lattice Boltzmann method, Physical Review E 65 (4) (2002)
+046308. doi:10.1103/PhysRevE.65.046308.
+URL https://link.aps.org/doi/10.1103/PhysRevE.65.046308
+[78] X. He, X. Shan, G. D. Doolen, Discrete Boltzmann equation model for nonideal gases, Physical Review E 57 (1) (1998) R13–R16. doi:
+10.1103/PhysRevE.57.R13.
+URL https://link.aps.org/doi/10.1103/PhysRevE.57.R13
+[79] A. Kupershtokh, New method of incorporating a body force term into the lattice Boltzmann equation, 2004.
+[80] A. Kupershtokh, D. Medvedev, D. Karpov, On equations of state in a lattice Boltzmann method, Computers & Mathematics with Applica-
+tions 58 (5) (2009) 965–974. doi:10.1016/j.camwa.2009.02.024.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0898122109001011
+[81] P. J. Dellar, Bulk and shear viscosities in lattice Boltzmann equations, Physical Review E 64 (3) (2001) 031203, publisher: APS.
+[82] Y. Li, R. Shock, R. Zhang, H. Chen, Numerical study of flow past an impulsively started cylinder by the lattice-Boltzmann method, Journal
+of Fluid Mechanics 519 (2004) 273–300. doi:10.1017/S0022112004001272.
+URL http://www.journals.cambridge.org/abstract_S0022112004001272
+[83] F. Tosi, S. Ubertini, S. Succi, H. Chen, I. Karlin, Numerical stability of Entropic versus positivity-enforcing Lattice Boltzmann schemes,
+Mathematics and Computers in Simulation 72 (2-6) (2006) 227–231. doi:10.1016/j.matcom.2006.05.007.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0378475406001315
+[84] R. A. Brownlee, A. N. Gorban, J. Levesley, Stabilization of the lattice Boltzmann method using the Ehrenfests’ coarse-graining idea,
+141
+
+Physical Review E 74 (3) (2006) 037703. doi:10.1103/PhysRevE.74.037703.
+URL https://link.aps.org/doi/10.1103/PhysRevE.74.037703
+[85] B. Servan-Camas, F. T.-C. Tsai, Lattice Boltzmann method with two relaxation times for advection–diffusion equation: Third order analysis
+and stability analysis, Advances in Water Resources 31 (8) (2008) 1113–1126. doi:10.1016/j.advwatres.2008.05.001.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0309170808000833
+[86] B. Servan-Camas, F. T.-C. Tsai, Non-negativity and stability analyses of lattice Boltzmann method for advection–diffusion equation, Journal
+of Computational Physics 228 (1) (2009) 236–256. doi:10.1016/j.jcp.2008.09.005.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0021999108004749
+[87] S. A. Hosseini, N. Darabiha, D. Th´evenin, A. Eshghinejadfard, Stability limits of the single relaxation-time advection–diffusion lattice
+Boltzmann scheme, International Journal of Modern Physics C 28 (12) (2017) 1750141. doi:10.1142/S0129183117501418.
+URL https://www.worldscientific.com/doi/abs/10.1142/S0129183117501418
+[88] M. Ch´avez-Modena, E. Ferrer, G. Rubio, Improving the stability of multiple-relaxation lattice Boltzmann methods with central moments,
+Computers & Fluids 172 (2018) 397–409. doi:10.1016/j.compfluid.2018.03.084.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0045793018301889
+[89] J. D. Sterling, S. Chen, Stability Analysis of Lattice Boltzmann Methods, Journal of Computational Physics 123 (1) (1996) 196–206.
+doi:10.1006/jcph.1996.0016.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0021999196900169
+[90] R. A. Worthing, J. Mozer, G. Seeley, Stability of lattice Boltzmann methods in hydrodynamic regimes, Physical Review E 56 (2) (1997)
+2243–2253. doi:10.1103/PhysRevE.56.2243.
+URL https://link.aps.org/doi/10.1103/PhysRevE.56.2243
+[91] P. Lallemand, L.-S. Luo, Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, Galilean invariance, and stability,
+Physical Review E 61 (6) (2000) 6546–6562. doi:10.1103/PhysRevE.61.6546.
+URL https://link.aps.org/doi/10.1103/PhysRevE.61.6546
+[92] S. A. Hosseini, C. Coreixas, N. Darabiha, D. Th´evenin, Stability of the lattice kinetic scheme and choice of the free relaxation parameter,
+Physical Review E 99 (6) (2019) 063305. doi:10.1103/PhysRevE.99.063305.
+URL https://link.aps.org/doi/10.1103/PhysRevE.99.063305
+[93] S. A. Hosseini, C. Coreixas, N. Darabiha, D. Th´evenin, Extensive analysis of the lattice Boltzmann method on shifted stencils, Physical
+Review E 100 (6) (2019) 063301. doi:10.1103/PhysRevE.100.063301.
+URL https://link.aps.org/doi/10.1103/PhysRevE.100.063301
+[94] G. Wissocq, P. Sagaut, J.-F. Boussuge, An extended spectral analysis of the lattice Boltzmann method: modal interactions and stability
+issues, Journal of Computational Physics 380 (2019) 311–333. doi:10.1016/j.jcp.2018.12.015.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0021999118308118
+[95] S. A. Hosseini, Development of a lattice Boltzmann-based numerical method for the simulation od reacting flows, Ph.D. thesis, Universit{\’e}
+{P}aris-{S}aclay/{O}tto-von-{G}uericke-{U}niversit{\¨a}t {M}agdeburg, artwork Size: xxiv, 205 Seiten Publisher: Universit¨at Paris-Saclay
+(2020).
+URL https://opendata.uni-halle.de//handle/1981185920/33674
+[96] D. d’Humi`eres, Generalized lattice-Boltzmann equations, Rarefied gas dynamicsPublisher: AIAA (1992).
+[97] D. d’Humi`eres, Multiple–relaxation–time lattice Boltzmann models in three dimensions, Philosophical Transactions of the Royal Society of
+London. Series A: Mathematical, Physical and Engineering Sciences 360 (1792) (2002) 437–451. doi:10.1098/rsta.2001.0955.
+URL https://royalsocietypublishing.org/doi/10.1098/rsta.2001.0955
+[98] P. Lallemand, L.-S. Luo, Theory of the lattice Boltzmann method: Acoustic and thermal properties in two and three dimensions, Physical
+Review E 68 (3) (2003) 036706. doi:10.1103/PhysRevE.68.036706.
+URL https://link.aps.org/doi/10.1103/PhysRevE.68.036706
+[99] C. Pan, L.-S. Luo, C. T. Miller, An evaluation of lattice Boltzmann schemes for porous medium flow simulation, Computers & Fluids
+35 (8-9) (2006) 898–909. doi:10.1016/j.compfluid.2005.03.008.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0045793005001520
+[100] I. V. Karlin, F. B¨osch, S. Chikatamarla, Gibbs’ principle for the lattice-kinetic theory of fluid dynamics, Physical Review E 90 (3) (2014)
+031302, publisher: APS.
+[101] I. Ginzburg, Equilibrium-type and link-type lattice Boltzmann models for generic advection and anisotropic-dispersion equation, Advances
+in Water Resources 28 (11) (2005) 1171–1195. doi:10.1016/j.advwatres.2005.03.004.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0309170805000874
+[102] I. Ginzburg, Generic boundary conditions for lattice Boltzmann models and their application to advection and anisotropic dispersion equa-
+tions, Advances in Water Resources 28 (11) (2005) 1196–1216. doi:10.1016/j.advwatres.2005.03.009.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0309170805000886
+[103] I. Ginzburg, Lattice Boltzmann modeling with discontinuous collision components: Hydrodynamic and Advection-Diffusion Equations,
+Journal of Statistical Physics 126 (1) (2007) 157–206. doi:10.1007/s10955-006-9234-4.
+URL http://link.springer.com/10.1007/s10955-006-9234-4
+[104] D. d’Humi`eres, I. Ginzburg, Viscosity independent numerical errors for Lattice Boltzmann models: From recurrence equations to “magic”
+collision numbers, Computers & Mathematics with Applications 58 (5) (2009) 823–840. doi:10.1016/j.camwa.2009.02.008.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0898122109000893
+[105] I. Ginzburg, F. Verhaeghe, D. d’Humi`eres, Two-Relaxation-Time Lattice Boltzmann Scheme: About Parametrization, Velocity, Pressure
+and Mixed Boundary Conditions, Communications in Computational Physics 3 (2) (2008) 427–478.
+[106] I. Ginzburg, Consistent lattice Boltzmann schemes for the Brinkman model of porous flow and infinite Chapman-Enskog expansion, Physical
+Review E 77 (6) (2008) 066704. doi:10.1103/PhysRevE.77.066704.
+URL https://link.aps.org/doi/10.1103/PhysRevE.77.066704
+142
+
+[107] I. Ginzburg, Magic recipes for Lattice {B}oltzmann modeling of micro and macro flow, Habilitation thesis, Universit{\’e} {P}aris {VI} (2009).
+[108] A. Kuzmin, I. Ginzburg, A. Mohamad, The role of the kinetic parameter in the stability of two-relaxation-time advection–diffusion lattice
+Boltzmann schemes, Computers & Mathematics with Applications 61 (12) (2011) 3417–3442. doi:10.1016/j.camwa.2010.07.036.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0898122110005286
+[109] T. Inamuro, A lattice kinetic scheme for incompressible viscous flows with heat transfer, Philosophical Transactions of the Royal Society of
+London. Series A: Mathematical, Physical and Engineering Sciences 360 (1792) (2002) 477–484. doi:10.1098/rsta.2001.0942.
+URL https://royalsocietypublishing.org/doi/10.1098/rsta.2001.0942
+[110] L. Wang, J. Mi, X. Meng, Z. Guo, A Localized Mass-Conserving Lattice Boltzmann Approach for Non-Newtonian Fluid Flows, Communi-
+cations in Computational Physics 17 (4) (2015) 908–924. doi:10.4208/cicp.2014.m303.
+URL https://www.cambridge.org/core/product/identifier/S1815240615000249/type/journal_article
+[111] S. A. Hosseini, N. Darabiha, D. Th´evenin, Theoretical and numerical analysis of the lattice kinetic scheme for complex-flow simulations,
+Physical Review E 99 (2) (2019) 023305. doi:10.1103/PhysRevE.99.023305.
+URL https://link.aps.org/doi/10.1103/PhysRevE.99.023305
+[112] Y. Kataoka, T. Inamuro, Numerical simulations of the behaviour of a drop in a square pipe flow using the two-phase lattice Boltzmann
+method, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369 (1945) (2011) 2528–
+2536. doi:10.1098/rsta.2011.0041.
+URL https://royalsocietypublishing.org/doi/10.1098/rsta.2011.0041
+[113] M. Yoshino, Y. Hotta, T. Hirozane, M. Endo, A numerical method for incompressible non-Newtonian fluid flows based on the lattice
+Boltzmann method, Journal of Non-Newtonian Fluid Mechanics 147 (1-2) (2007) 69–78. doi:10.1016/j.jnnfm.2007.07.007.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0377025707001632
+[114] X. Meng, Z. Guo, Localized lattice Boltzmann equation model for simulating miscible viscous displacement in porous media, International
+Journal of Heat and Mass Transfer 100 (2016) 767–778. doi:10.1016/j.ijheatmasstransfer.2016.04.095.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0017931015312126
+[115] J. Perko, R. A. Patel, Single-relaxation-time lattice Boltzmann scheme for advection-diffusion problems with large diffusion-coefficient
+heterogeneities and high-advection transport, Physical Review E 89 (5) (2014) 053309. doi:10.1103/PhysRevE.89.053309.
+URL https://link.aps.org/doi/10.1103/PhysRevE.89.053309
+[116] M. Geier, A. Greiner, J. G. Korvink, Cascaded digital lattice Boltzmann automata for high Reynolds number flow, Physical Review E 73 (6)
+(2006) 066705, publisher: APS.
+[117] M. Geier, De-aliasing and stabilization formalism of the cascaded lattice Boltzmann automaton for under-resolved high Reynolds number
+flow, International Journal for Numerical Methods in Fluids 56 (8) (2008) 1249–1254. doi:10.1002/fld.1634.
+URL https://onlinelibrary.wiley.com/doi/10.1002/fld.1634
+[118] P. Asinari, Generalized local equilibrium in the cascaded lattice Boltzmann method, Physical Review E 78 (1) (2008) 016701.
+doi:
+10.1103/PhysRevE.78.016701.
+URL https://link.aps.org/doi/10.1103/PhysRevE.78.016701
+[119] S. A. Hosseini, P. Berg, F. Huang, C. Roloff, G. Janiga, D. Th´evenin, Central moments multiple relaxation time LBM for hemodynamic
+simulations in intracranial aneurysms: An in-vitro validation study using PIV and PC-MRI, Computers in Biology and Medicine 131 (2021)
+104251. doi:10.1016/j.compbiomed.2021.104251.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0010482521000457
+[120] F. Huang, R. No¨el, P. Berg, S. A. Hosseini, Simulation of the FDA nozzle benchmark: A lattice Boltzmann study, Computer Methods and
+Programs in Biomedicine 221 (2022) 106863. doi:10.1016/j.cmpb.2022.106863.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0169260722002450
+[121] S. A. Hosseini, F. Huang, D. Th´evenin, Lattice Boltzmann model for simulation of flow in intracranial aneurysms considering non-
+Newtonian effects, Physics of Fluids 34 (7) (2022) 073105. doi:10.1063/5.0098383.
+URL https://aip.scitation.org/doi/10.1063/5.0098383
+[122] I. V. Karlin, A. Ferrante, H. C. ¨Ottinger, Perfect entropy functions of the Lattice Boltzmann method, Europhysics Letters (EPL) 47 (2)
+(1999) 182–188. doi:10.1209/epl/i1999-00370-1.
+URL https://iopscience.iop.org/article/10.1209/epl/i1999-00370-1
+[123] I. V. Karlin, A. N. Gorban, S. Succi, V. Boffi, Maximum Entropy Principle for Lattice Kinetic Equations, Physical Review Letters 81 (1)
+(1998) 6–9. doi:10.1103/PhysRevLett.81.6.
+URL https://link.aps.org/doi/10.1103/PhysRevLett.81.6
+[124] S. S. Chikatamarla, S. Ansumali, I. V. Karlin, Entropic lattice Boltzmann models for hydrodynamics in three dimensions, Physical review
+letters 97 (1) (2006) 010201, publisher: APS.
+[125] S. Ansumali, S. S. Chikatamarla, C. E. Frouzakis, K. Boulouchos, ENTROPIC LATTICE BOLTZMANN SIMULATION OF THE FLOW
+PAST SQUARE CYLINDER, International Journal of Modern Physics C 15 (03) (2004) 435–445. doi:10.1142/S012918310400584X.
+URL https://www.worldscientific.com/doi/abs/10.1142/S012918310400584X
+[126] S. Ansumali, I. V. Karlin, Single relaxation time model for entropic lattice Boltzmann methods, Physical Review E 65 (5) (2002) 056312,
+publisher: APS.
+[127] B. M. Boghosian, P. J. Love, P. V. Coveney, I. V. Karlin, S. Succi, J. Yepez, Galilean-invariant lattice-Boltzmann models with H theorem,
+Physical Review E 68 (2) (2003) 025103. doi:10.1103/PhysRevE.68.025103.
+URL https://link.aps.org/doi/10.1103/PhysRevE.68.025103
+[128] A. Mazloomi, S. Chikatamarla, I. Karlin, Entropic Lattice Boltzmann Method for Multiphase Flows, Physical review Letters 114 (7) (2015)
+174502.
+[129] M. Atif, P. K. Kolluru, C. Thantanapally, S. Ansumali, Essentially Entropic Lattice Boltzmann Model, Physical Review Letters 119 (24)
+(2017) 240602. doi:10.1103/PhysRevLett.119.240602.
+URL https://link.aps.org/doi/10.1103/PhysRevLett.119.240602
+143
+
+[130] F. B¨osch, B. Dorschner, I. Karlin, Entropic multi-relaxation free-energy lattice Boltzmann model for two-phase flows, EPL (Europhysics
+Letters) 122 (1) (2018) 14002, iSBN: 0295-5075 Publisher: IOP Publishing.
+[131] S. A. Hosseini, B. Dorschner, I. V. Karlin, Entropic multi-relaxation-time lattice Boltzmann model for large density ratio two-phase flows,
+Communications in Computational PhysicsPublisher: arXiv Version Number: 2 (2022).
+URL https://arxiv.org/abs/2201.
+[132] J. Latt, B. Chopard, Lattice Boltzmann method with regularized pre-collision distribution functions, Mathematics and Computers in Simu-
+lation 72 (2-6) (2006) 165–168, iSBN: 0378-4754 Publisher: Elsevier.
+[133] J. Latt, Hydrodynamic limit of lattice Boltzmann equations, Ph.D. thesis, Universit{\’}e de Geneve, publisher: Universit´e de Gen`eve (2007).
+URL https://archive-ouverte.unige.ch/unige:464
+[134] O. Malaspinas, Increasing stability and accuracy of the lattice Boltzmann scheme: recursivity and regularization, arXivPublisher: arXiv
+(2015). doi:10.48550/ARXIV.1505.06900.
+URL https://arxiv.org/abs/1505.06900
+[135] J. Jacob, O. Malaspinas, P. Sagaut, A new hybrid recursive regularised Bhatnagar–Gross–Krook collision model for Lattice Boltzmann
+method-based large eddy simulation, Journal of Turbulence 19 (11-12) (2018) 1051–1076. doi:10.1080/14685248.2018.1540879.
+URL https://www.tandfonline.com/doi/full/10.1080/14685248.2018.1540879
+[136] J. D. van der Waals, Over de Continuiteit van den Gas- en Vloeistoftoestand, Ph.D. thesis, University of Leiden (1873).
+[137] J. Clerk-Maxwell, On the Dynamical Evidence of the Molecular Constitution of Bodies *, Nature 11 (279) (1875) 357–359. doi:10.1038/
+011357a0.
+URL https://www.nature.com/articles/011357a0
+[138] F. S. Sekerka, Thermal Physics, Elsevier, 2015. doi:10.1016/C2014-0-03233-9.
+URL https://linkinghub.elsevier.com/retrieve/pii/C20140032339
+[139] J. W. Cahn, J. E. Hilliard, Free Energy of a Nonuniform System. I. Interfacial Free Energy, The Journal of Chemical Physics 28 (2) (1958)
+258–267. doi:10.1063/1.1744102.
+URL http://aip.scitation.org/doi/10.1063/1.1744102
+[140] V. Giovangigli, Kinetic derivation of diffuse-interface fluid models, Physical Review E 102 (1) (2020) 012110, publisher: APS.
+[141] H. Struchtrup, A. Frezzotti, Grad’s 13 moments approximation for Enskog-Vlasov equation, in: AIP Conference Proceedings, Glasgow,
+UK, 2019, p. 120007. doi:10.1063/1.5119620.
+URL http://aip.scitation.org/doi/abs/10.1063/1.5119620
+[142] H. Struchtrup, A. Frezzotti, Twenty-six moment equations for the Enskog–Vlasov equation, Journal of Fluid Mechanics 940 (2022) A40.
+doi:doi:10.1017/jfm.2022.98.
+URL https://www.cambridge.org/core/product/identifier/S0022112022000982/type/journal_article
+[143] G. M. Kremer, An Introduction to the Boltzmann Equation and Transport Processes in Gases, Interaction of Mechanics and Mathematics,
+Springer Berlin Heidelberg, Berlin, Heidelberg, 2010. doi:10.1007/978-3-642-11696-4.
+URL http://link.springer.com/10.1007/978-3-642-11696-4
+[144] H. Van Beijeren, M. H. Ernst, The modified Enskog equation, Physica 68 (3) (1973) 437–456, iSBN: 0031-8914 Publisher: Elsevier.
+[145] J. Karkheck, G. Stell, Kinetic mean-field theories, The Journal of Chemical Physics 75 (3) (1981) 1475–1487. doi:10.1063/1.442154.
+URL http://aip.scitation.org/doi/10.1063/1.442154
+[146] S. A. Hosseini, B. Dorschner, I. V. Karlin, Towards a consistent lattice Boltzmann model for two-phase fluid, arXiv preprint
+arXiv:2112.01975 (2021).
+[147] A. N. Gorban, I. V. Karlin, Invariant manifolds for physical and chemical kinetics, no. 660 in Lecture notes in physics, Springer, Berlin ;
+New York, 2005, oCLC: ocm57729924.
+[148] L. Chen, Q. Kang, Y. Mu, Y.-L. He, W.-Q. Tao, A critical review of the pseudopotential multiphase lattice Boltzmann model: Methods and
+applications, International Journal of Heat and Mass Transfer 76 (2014) 210–236. doi:10.1016/j.ijheatmasstransfer.2014.04.
+032.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0017931014003378
+[149] X. He, G. D. Doolen, Thermodynamic foundations of kinetic theory and lattice Boltzmann models for multiphase flows, Journal of Statistical
+Physics 107 (1) (2002) 309–328, iSBN: 1572-9613 Publisher: Springer.
+[150] M. R. Swift, W. R. Osborn, J. M. Yeomans, Lattice Boltzmann Simulation of Nonideal Fluids, Physical Review Letters 75 (5) (1995) 830–
+833. doi:10.1103/PhysRevLett.75.830.
+URL https://link.aps.org/doi/10.1103/PhysRevLett.75.830
+[151] D. J. Holdych, D. Rovas, J. G. Georgiadis, R. O. Buckius, An Improved Hydrodynamics Formulation for Multiphase Flow Lattice-Boltzmann
+Models, International Journal of Modern Physics C 09 (08) (1998) 1393–1404. doi:10.1142/S0129183198001266.
+URL https://www.worldscientific.com/doi/abs/10.1142/S0129183198001266
+[152] T. Inamuro, N. Konishi, F. Ogino, A Galilean invariant model of the lattice Boltzmann method for multiphase fluid flows using free-energy
+approach, Computer Physics Communications 129 (1-3) (2000) 32–45. doi:10.1016/S0010-4655(00)00090-4.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0010465500000904
+[153] A. Wagner, Q. Li, Investigation of Galilean invariance of multi-phase lattice Boltzmann methods, Physica A: Statistical Mechanics and its
+Applications 362 (1) (2006) 105–110. doi:10.1016/j.physa.2005.09.030.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0378437105009647
+[154] L.-S. Luo, Theory of the lattice Boltzmann method: Lattice Boltzmann models for nonideal gases, Physical Review E 62 (4) (2000) 4982–
+4996. doi:10.1103/PhysRevE.62.4982.
+URL https://link.aps.org/doi/10.1103/PhysRevE.62.4982
+[155] A. Mazloomi Moqaddam, S. S. Chikatamarla, I. V. Karlin, Simulation of binary droplet collisions with the entropic lattice Boltzmann
+method, Physics of Fluids 28 (2) (2016) 022106. doi:10.1063/1.4942017.
+URL http://aip.scitation.org/doi/10.1063/1.4942017
+144
+
+[156] A. Mazloomi Moqaddam, S. S. Chikatamarla, I. V. Karlin, Drops bouncing off macro-textured superhydrophobic surfaces, Journal of Fluid
+Mechanics 824 (2017) 866–885. doi:10.1017/jfm.2017.306.
+URL https://www.cambridge.org/core/product/identifier/S0022112017003068/type/journal_article
+[157] B. Wen, L. Zhao, W. Qiu, Y. Ye, X. Shan, Chemical-potential multiphase lattice Boltzmann method with superlarge density ratios, Physical
+Review E 102 (1) (2020) 013303. doi:10.1103/PhysRevE.102.013303.
+URL https://link.aps.org/doi/10.1103/PhysRevE.102.013303
+[158] E. A. Guggenheim, The Principle of Corresponding States, The Journal of Chemical Physics 13 (7) (1945) 253–261. doi:10.1063/1.
+1724033.
+URL http://aip.scitation.org/doi/10.1063/1.1724033
+[159] D. E. Winterbone, Advanced Thermodynamics for Engineers, Elsevier, 1996. doi:10.1016/B978-0-340-67699-8.X5000-5.
+URL https://linkinghub.elsevier.com/retrieve/pii/B9780340676998X50005
+[160] A. J. M. Yang, P. D. Fleming, J. H. Gibbs, Molecular theory of surface tension, The Journal of Chemical Physics 64 (9) (1976) 3732–3747.
+doi:10.1063/1.432687.
+URL http://aip.scitation.org/doi/10.1063/1.432687
+[161] R. Lovett, P. W. DeHaven, J. J. Vieceli, F. P. Buff, Generalized van der Waals theories for surface tension and interfacial width, The Journal
+of Chemical Physics 58 (5) (1973) 1880–1885. doi:10.1063/1.1679447.
+URL http://aip.scitation.org/doi/10.1063/1.1679447
+[162] L. Ornstein, F. Zernik, Accidental deviations of density and opalescence at the critical point of a single substance, Proc. Akad. Sci. 17 (793)
+(1914).
+[163] H. Lin, Y.-Y. Duan, Q. Min, Gradient theory modeling of surface tension for pure fluids and binary mixtures, Fluid Phase Equilibria 254 (1-
+2) (2007) 75–90. doi:10.1016/j.fluid.2007.02.013.
+URL https://linkinghub.elsevier.com/retrieve/pii/S037838120700088X
+[164] D. Nayigizente, S. Ducruix, T. Schmitt, Development of an interface thickening method for the direct numerical simulation of compressible
+liquid–vapor flows in the framework of the second gradient theory, Physics of Fluids 33 (5) (2021) 052119. doi:10.1063/5.0048715.
+URL https://aip.scitation.org/doi/10.1063/5.0048715
+[165] T. W. Leland, P. S. Chappelear, The corresponding states principle—a review of current theory and practice, Industrial & Engineering
+Chemistry 60 (7) (1968) 15–43.
+[166] K. S. Pitzer, Corresponding States for Perfect Liquids, The Journal of Chemical Physics 7 (8) (1939) 583–590. doi:10.1063/1.1750496.
+URL http://aip.scitation.org/doi/10.1063/1.1750496
+[167] H. Sato, K. Watanabe, J. M. H. Levelt Sengers, J. S. Gallagher, P. G. Hill, J. Straub, W. Wagner, Sixteen Thousand Evaluated Experimental
+Thermodynamic Property Data for Water and Steam, Journal of Physical and Chemical Reference Data 20 (5) (1991) 1023–1044. doi:
+10.1063/1.555894.
+URL http://aip.scitation.org/doi/10.1063/1.555894
+[168] D. Jamet, ´Etude des potentialites de la theorie du second gradient pour la simulation numerique directe des ecoulements liquide-vapeur avec
+changement de phase, Ph.D. thesis, CEA Grenoble (1998).
+[169] C. Domb, The Critical Point: A Historical Introduction To The Modern Theory Of Critical Phenomena, 0th Edition, CRC Press, 1996.
+doi:10.1201/9781482295269.
+URL https://www.taylorfrancis.com/books/9781482295269
+[170] M. Sbragaglia, X. Shan, Consistent pseudopotential interactions in lattice Boltzmann models, Physical Review E 84 (3) (2011) 036703.
+doi:10.1103/PhysRevE.84.036703.
+URL https://link.aps.org/doi/10.1103/PhysRevE.84.036703
+[171] P. Yuan, L. Schaefer, Equations of state in a lattice Boltzmann model, Physics of Fluids 18 (4) (2006) 042101. doi:10.1063/1.2187070.
+URL http://aip.scitation.org/doi/10.1063/1.2187070
+[172] S. Leclaire, N. Pellerin, M. Reggio, J.-Y. Tr´epanier, Enhanced equilibrium distribution functions for simulating immiscible multiphase
+flows with variable density ratios in a class of lattice Boltzmann models, International Journal of Multiphase Flow 57 (2013) 159–168.
+doi:10.1016/j.ijmultiphaseflow.2013.07.001.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0301932213001043
+[173] A. Fakhari, M. Geier, T. Lee, A mass-conserving lattice Boltzmann method with dynamic grid refinement for immiscible two-phase flows,
+Journal of Computational Physics 315 (2016) 434–457. doi:10.1016/j.jcp.2016.03.058.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0021999116300237
+[174] Y. Q. Zu, S. He, Phase-field-based lattice Boltzmann model for incompressible binary fluid systems with density and viscosity contrasts,
+Physical Review E 87 (4) (2013) 043301. doi:10.1103/PhysRevE.87.043301.
+URL https://link.aps.org/doi/10.1103/PhysRevE.87.043301
+[175] A. Fakhari, T. Mitchell, C. Leonardi, D. Bolster, Improved locality of the phase-field lattice-Boltzmann model for immiscible fluids at high
+density ratios, Physical Review E 96 (5) (2017) 053301. doi:10.1103/PhysRevE.96.053301.
+URL https://link.aps.org/doi/10.1103/PhysRevE.96.053301
+[176] T. Mitchell, C. Leonardi, A. Fakhari, Development of a three-dimensional phase-field lattice Boltzmann method for the study of immiscible
+fluids at high density ratios, International Journal of Multiphase Flow 107 (2018) 1–15. doi:10.1016/j.ijmultiphaseflow.2018.05.
+004.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0301932217309369
+[177] D.-Y. Peng, D. B. Robinson, A new two-constant equation of state, Industrial & Engineering Chemistry Fundamentals 15 (1) (1976) 59–64,
+iSBN: 0196-4313 Publisher: ACS Publications.
+[178] O. Redlich, J. N. Kwong, On the thermodynamics of solutions. V. An equation of state. Fugacities of gaseous solutions., Chemical reviews
+44 (1) (1949) 233–244, iSBN: 0009-2665 Publisher: ACS Publications.
+[179] G. Soave, Equilibrium constants from a modified Redlich-Kwong equation of state, Chemical engineering science 27 (6) (1972) 1197–1203,
+145
+
+iSBN: 0009-2509 Publisher: Elsevier.
+[180] N. F. Carnahan, K. E. Starling, Equation of state for nonattracting rigid spheres, The Journal of chemical physics 51 (2) (1969) 635–636,
+iSBN: 0021-9606 Publisher: American Institute of Physics.
+[181] R. Benzi, L. Biferale, M. Sbragaglia, S. Succi, F. Toschi, Mesoscopic modeling of a two-phase flow in the presence of boundaries: The
+contact angle, Physical Review E 74 (2) (2006) 021509. doi:10.1103/PhysRevE.74.021509.
+URL https://link.aps.org/doi/10.1103/PhysRevE.74.021509
+[182] M. Sbragaglia, R. Benzi, L. Biferale, S. Succi, K. Sugiyama, F. Toschi, Generalized lattice Boltzmann method with multirange pseudopo-
+tential, Physical Review E 75 (2) (2007) 026702. doi:10.1103/PhysRevE.75.026702.
+URL https://link.aps.org/doi/10.1103/PhysRevE.75.026702
+[183] X. Shan, H. Chen, Simulation of nonideal gases and liquid-gas phase transitions by the lattice Boltzmann equation, Physical Review E 49 (4)
+(1994) 2941–2948. doi:10.1103/PhysRevE.49.2941.
+URL https://link.aps.org/doi/10.1103/PhysRevE.49.2941
+[184] C. E. Colosqui, G. Falcucci, S. Ubertini, S. Succi, Mesoscopic simulation of non-ideal fluids with self-tuning of the equation of state, Soft
+Matter 8 (14) (2012) 3798. doi:10.1039/c2sm06353k.
+URL http://xlink.rsc.org/?DOI=c2sm06353k
+[185] L. Fei, J. Du, K. H. Luo, S. Succi, M. Lauricella, A. Montessori, Q. Wang, Modeling realistic multiphase flows using a non-orthogonal
+multiple-relaxation-time lattice Boltzmann method, Physics of Fluids 31 (4) (2019) 042105. doi:10.1063/1.5087266.
+URL http://aip.scitation.org/doi/10.1063/1.5087266
+[186] Q. Li, K. H. Luo, X. J. Li, Lattice Boltzmann modeling of multiphase flows at large density ratio with an improved pseudopotential model,
+Physical Review E 87 (5) (2013) 053301. doi:10.1103/PhysRevE.87.053301.
+URL https://link.aps.org/doi/10.1103/PhysRevE.87.053301
+[187] C. Peng, L. F. Ayala, Z. Wang, O. M. Ayala, Attainment of rigorous thermodynamic consistency and surface tension in single-component
+pseudopotential lattice Boltzmann models via a customized equation of state, Physical Review E 101 (6) (2020) 063309. doi:10.1103/
+PhysRevE.101.063309.
+URL https://link.aps.org/doi/10.1103/PhysRevE.101.063309
+[188] M. R. Swift, E. Orlandini, W. R. Osborn, J. M. Yeomans, Lattice Boltzmann simulations of liquid-gas and binary fluid systems, Physical
+Review E 54 (5) (1996) 5041–5052. doi:10.1103/PhysRevE.54.5041.
+URL https://link.aps.org/doi/10.1103/PhysRevE.54.5041
+[189] N. S. Martys, Energy conserving discrete {B}oltzmann equation for nonideal systems, International Journal of Modern Physics C 10 (07)
+(1999) 1367–1382. doi:10.1142/S0129183199001121.
+URL https://www.worldscientific.com/doi/abs/10.1142/S0129183199001121
+[190] N. S. Martys, Aclassical kinetic theory approach to lattice {B}oltzmann simulation, International Journal of Modern Physics C 12 (08) (2001)
+1169–1178. doi:10.1142/S0129183101002474.
+URL https://www.worldscientific.com/doi/abs/10.1142/S0129183101002474
+[191] E. Reyhanian, B. Dorschner, I. V. Karlin, Thermokinetic lattice Boltzmann model of nonideal fluids, Physical Review E 102 (2) (2020)
+020103. doi:10.1103/PhysRevE.102.020103.
+URL https://link.aps.org/doi/10.1103/PhysRevE.102.020103
+[192] R. Zhang, H. Chen, Lattice Boltzmann method for simulations of liquid-vapor thermal flows, Physical Review E 67 (6) (2003) 066711.
+doi:10.1103/PhysRevE.67.066711.
+URL https://link.aps.org/doi/10.1103/PhysRevE.67.066711
+[193] S. Gong, P. Cheng, Numerical investigation of droplet motion and coalescence by an improved lattice Boltzmann model for phase transitions
+and multiphase flows, Computers & Fluids 53 (2012) 93–104. doi:10.1016/j.compfluid.2011.09.013.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0045793011002994
+[194] X. Shan, Pressure tensor calculation in a class of nonideal gas lattice Boltzmann models, Physical Review E 77 (6) (2008) 066702, publisher:
+APS.
+[195] Q. Li, K. H. Luo, Achieving tunable surface tension in the pseudopotential lattice Boltzmann modeling of multiphase flows, Physical Review
+E 88 (5) (2013) 053307. doi:10.1103/PhysRevE.88.053307.
+URL https://link.aps.org/doi/10.1103/PhysRevE.88.053307
+[196] J. Gibbs, On the equilibrium of heterogeneous substances, Transactions of the Connecticut Academy of Arts and Sciences III (1874) 108–
+248.
+[197] J. G. Kirkwood, F. P. Buff, The Statistical Mechanical Theory of Surface Tension, The Journal of Chemical Physics 17 (3) (1949) 338–343.
+doi:10.1063/1.1747248.
+URL http://aip.scitation.org/doi/10.1063/1.1747248
+[198] N. S. Martys, H. Chen, Simulation of multicomponent fluids in complex three-dimensional geometries by the lattice Boltzmann method,
+Physical Review E 53 (1) (1996) 743–750. doi:10.1103/PhysRevE.53.743.
+URL https://link.aps.org/doi/10.1103/PhysRevE.53.743
+[199] M. C. Sukop, D. T. Thorne, Lattice Boltzmann Modeling: An Introduction for Geoscientists and Engineers, Springer Berlin Heidelberg,
+Berlin, Heidelberg, 2006. doi:10.1007/978-3-540-27982-2.
+URL http://link.springer.com/10.1007/978-3-540-27982-2
+[200] P. Raiskinm¨aki, A. Koponen, J. Merikoski, J. Timonen, Spreading dynamics of three-dimensional droplets by the lattice-Boltzmann method,
+Computational Materials Science 18 (1) (2000) 7–12. doi:10.1016/S0927-0256(99)00095-6.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0927025699000956
+[201] P. Raiskinm¨aki, A. Shakib-Manesh, A. J¨asberg, A. Koponen, J. Merikoski, J. Timonen, Lattice-Boltzmann simulation of capillary rise
+dynamics, Journal of Statistical Physics 107 (1/2) (2002) 143–158. doi:10.1023/A:1014506503793.
+URL http://link.springer.com/10.1023/A:1014506503793
+146
+
+[202] Q. Kang, D. Zhang, S. Chen, Displacement of a two-dimensional immiscible droplet in a channel, Physics of Fluids 14 (9) (2002) 3203–
+3214. doi:10.1063/1.1499125.
+URL http://aip.scitation.org/doi/10.1063/1.1499125
+[203] M. Sbragaglia, R. Benzi, L. Biferale, S. Succi, F. Toschi, Surface Roughness-Hydrophobicity Coupling in Microchannel and Nanochannel
+Flows, Physical Review Letters 97 (20) (2006) 204503. doi:10.1103/PhysRevLett.97.204503.
+URL https://link.aps.org/doi/10.1103/PhysRevLett.97.204503
+[204] H. Ding, P. D. M. Spelt, Wetting condition in diffuse interface simulations of contact line motion, Physical Review E 75 (4) (2007) 046708.
+doi:10.1103/PhysRevE.75.046708.
+URL https://link.aps.org/doi/10.1103/PhysRevE.75.046708
+[205] A. Hu, L. Li, R. Uddin, D. Liu, Contact angle adjustment in equation-of-state-based pseudopotential model, Physical Review E 93 (5) (2016)
+053307. doi:10.1103/PhysRevE.93.053307.
+URL https://link.aps.org/doi/10.1103/PhysRevE.93.053307
+[206] Q. Li, Y. Yu, K. H. Luo, Implementation of contact angles in pseudopotential lattice Boltzmann simulations with curved boundaries, Physical
+Review E 100 (5) (2019) 053313. doi:10.1103/PhysRevE.100.053313.
+URL https://link.aps.org/doi/10.1103/PhysRevE.100.053313
+[207] L. Gao, T. J. McCarthy, Contact Angle Hysteresis Explained, Langmuir 22 (14) (2006) 6234–6237. doi:10.1021/la060254j.
+URL https://pubs.acs.org/doi/10.1021/la060254j
+[208] H. Ding, P. D. M. Spelt, Onset of motion of a three-dimensional droplet on a wall in shear flow at moderate Reynolds numbers, Journal of
+Fluid Mechanics 599 (2008) 341–362. doi:10.1017/S0022112008000190.
+URL https://www.cambridge.org/core/product/identifier/S0022112008000190/type/journal_article
+[209] Y. Ba, H. Liu, J. Sun, R. Zheng, Color-gradient lattice Boltzmann model for simulating droplet motion with contact-angle hysteresis,
+Physical Review E 88 (4) (2013) 043306. doi:10.1103/PhysRevE.88.043306.
+URL https://link.aps.org/doi/10.1103/PhysRevE.88.043306
+[210] C. Zhang, H. Zhang, X. Zhang, C. Yang, P. Cheng, Evaporation of a sessile droplet on flat surfaces: An axisymmetric lattice Boltzmann
+model with consideration of contact angle hysteresis, International Journal of Heat and Mass Transfer 178 (2021) 121577. doi:10.1016/
+j.ijheatmasstransfer.2021.121577.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0017931021006803
+[211] J. Yang, X. Ma, L. Fei, X. Zhang, K. H. Luo, S. Shuai, Effects of hysteresis window on contact angle hysteresis behaviour at large Bond
+number, Journal of Colloid and Interface Science 566 (2020) 327–337. doi:10.1016/j.jcis.2020.01.042.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0021979720300461
+[212] L. Wang, H.-b. Huang, X.-Y. Lu, Scheme for contact angle and its hysteresis in a multiphase lattice Boltzmann method, Physical Review E
+87 (1) (2013) 013301. doi:10.1103/PhysRevE.87.013301.
+URL https://link.aps.org/doi/10.1103/PhysRevE.87.013301
+[213] H. Liu, Y. Ju, N. Wang, G. Xi, Y. Zhang, Lattice Boltzmann modeling of contact angle and its hysteresis in two-phase flow with large
+viscosity difference, Physical Review E 92 (3) (2015) 033306. doi:10.1103/PhysRevE.92.033306.
+URL https://link.aps.org/doi/10.1103/PhysRevE.92.033306
+[214] F. Qin, J. Zhao, Q. Kang, D. Derome, J. Carmeliet, Lattice Boltzmann Modeling of Drying of Porous Media Considering Contact Angle
+Hysteresis, Transport in Porous Media 140 (1) (2021) 395–420. doi:10.1007/s11242-021-01644-9.
+URL https://link.springer.com/10.1007/s11242-021-01644-9
+[215] B. Widom, Surface Tension and Molecular Correlations near the Critical Point, The Journal of Chemical Physics 43 (11) (1965) 3892–3897.
+doi:10.1063/1.1696617.
+URL http://aip.scitation.org/doi/10.1063/1.1696617
+[216] D. Jamet, O. Lebaigue, N. Coutris, J. Delhaye, The Second Gradient Method for the Direct Numerical Simulation of Liquid–Vapor Flows
+with Phase Change, Journal of Computational Physics 169 (2) (2001) 624–651. doi:10.1006/jcph.2000.6692.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0021999100966920
+[217] E. M. Blokhuis, J. Kuipers, Thermodynamic expressions for the Tolman length, The Journal of Chemical Physics 124 (7) (2006) 074701.
+doi:10.1063/1.2167642.
+URL http://aip.scitation.org/doi/10.1063/1.2167642
+[218] M. Lulli, L. Biferale, G. Falcucci, M. Sbragaglia, X. Shan, Mesoscale perspective on the Tolman length, Physical Review E 105 (1) (2022)
+015301. doi:10.1103/PhysRevE.105.015301.
+URL https://link.aps.org/doi/10.1103/PhysRevE.105.015301
+[219] E. M. Blokhuis, D. Bedeaux, Pressure tensor of a spherical interface, The Journal of chemical physics 97 (5) (1992) 3576–3586, iSBN:
+0021-9606 Publisher: American Institute of Physics.
+[220] R. C. Tolman, The effect of droplet size on surface tension, The journal of chemical physics 17 (3) (1949) 333–337, iSBN: 0021-9606
+Publisher: American Institute of Physics.
+[221] W. Helfrich, Steric interaction of fluid membranes in multilayer systems, Zeitschrift f¨ur Naturforschung A 33 (3) (1978) 305–315, iSBN:
+1865-7109 Publisher: Verlag der Zeitschrift f¨ur Naturforschung.
+[222] M. Rao, B. J. Berne, On the location of surface of tension in the planar interface between liquid and vapour, Molecular Physics 37 (2) (1979)
+455–461, iSBN: 0026-8976 Publisher: Taylor & Francis.
+[223] A. Gauthier, S. Symon, C. Clanet, D. Qu´er´e, Water impacting on superhydrophobic macrotextures, Nature Communications 6 (1) (2015)
+8001. doi:10.1038/ncomms9001.
+URL http://www.nature.com/articles/ncomms9001
+[224] D. Richard, D. Qu´er´e, Bouncing water drops, Europhysics Letters (EPL) 50 (6) (2000) 769–775. doi:10.1209/epl/i2000-00547-6.
+URL https://iopscience.iop.org/article/10.1209/epl/i2000-00547-6
+[225] D. Qu´er´e, Non-sticking drops, Reports on Progress in Physics 68 (11) (2005) 2495–2532. doi:10.1088/0034-4885/68/11/R01.
+147
+
+URL https://iopscience.iop.org/article/10.1088/0034-4885/68/11/R01
+[226] D. Richard, C. Clanet, D. Qu´er´e, Contact time of a bouncing drop, Nature 417 (6891) (2002) 811–811. doi:10.1038/417811a.
+URL http://www.nature.com/articles/417811a
+[227] K. Okumura, F. Chevy, D. Richard, D. Qu´er´e, C. Clanet, Water spring: A model for bouncing drops, Europhysics Letters (EPL) 62 (2)
+(2003) 237–243. doi:10.1209/epl/i2003-00340-1.
+URL https://iopscience.iop.org/article/10.1209/epl/i2003-00340-1
+[228] C. Clanet, C. B´eguin, D. Richard, D. Qu´er´e, Maximal deformation of an impacting drop, Journal of Fluid Mechanics 517 (2004) 199–208.
+doi:10.1017/S0022112004000904.
+URL http://www.journals.cambridge.org/abstract_S0022112004000904
+[229] J. B. Lee, N. Laan, K. G. de Bruin, G. Skantzaris, N. Shahidzadeh, D. Derome, J. Carmeliet, D. Bonn, Universal rescaling of drop impact
+on smooth and rough surfaces, Journal of Fluid Mechanics 786 (2016) R4. doi:10.1017/jfm.2015.620.
+URL https://www.cambridge.org/core/product/identifier/S0022112015006205/type/journal_article
+[230] A. Mazloomi, S. Chikatamarla, I. Karlin, Entropic lattice Boltzmann method for multiphase flows: Fluid-solid interfaces, Physical Review
+E 92 (2) (2015) 023308. doi:10.1103/PhysRevE.92.023308.
+URL https://link.aps.org/doi/10.1103/PhysRevE.92.023308
+[231] F. Qin, A. Mazloomi Moqaddam, Q. Kang, D. Derome, J. Carmeliet, Entropic multiple-relaxation-time multirange pseudopotential lattice
+Boltzmann model for two-phase flow, Physics of Fluids 30 (3) (2018) 032104. doi:10.1063/1.5016965.
+URL http://aip.scitation.org/doi/10.1063/1.5016965
+[232] Y. Liu, L. Moevius, X. Xu, T. Qian, J. M. Yeomans, Z. Wang, Pancake bouncing on superhydrophobic surfaces, Nature Physics 10 (7) (2014)
+515–519. doi:10.1038/nphys2980.
+URL http://www.nature.com/articles/nphys2980
+[233] L. Moevius, Y. Liu, Z. Wang, J. M. Yeomans, Pancake Bouncing: Simulations and Theory and Experimental Verification, Langmuir 30 (43)
+(2014) 13021–13032. doi:10.1021/la5033916.
+URL https://pubs.acs.org/doi/10.1021/la5033916
+[234] P. Chantelot, A. Mazloomi Moqaddam, A. Gauthier, S. S. Chikatamarla, C. Clanet, I. V. Karlin, D. Qu´er´e, Water ring-bouncing on repellent
+singularities, Soft Matter 14 (12) (2018) 2227–2233. doi:10.1039/C7SM02004J.
+URL http://xlink.rsc.org/?DOI=C7SM02004J
+[235] Y. Liu, M. Andrew, J. Li, J. M. Yeomans, Z. Wang, Symmetry breaking in drop bouncing on curved surfaces, Nature Communications 6 (1)
+(2015) 10034. doi:10.1038/ncomms10034.
+URL http://www.nature.com/articles/ncomms10034
+[236] S. A. Kooij, A. M. Moqaddam, T. C. de Goede, D. Derome, J. Carmeliet, N. Shahidzadeh, D. Bonn, Sprays from droplets impacting a mesh,
+Journal of Fluid Mechanics 871 (2019) 489–509. doi:10.1017/jfm.2019.289.
+URL https://www.cambridge.org/core/product/identifier/S0022112019002891/type/journal_article
+[237] G. Wang, J. Gao, K. H. Luo, Droplet impacting a superhydrophobic mesh array: Effect of liquid properties, Physical Review Fluids 5 (12)
+(2020) 123605. doi:10.1103/PhysRevFluids.5.123605.
+URL https://link.aps.org/doi/10.1103/PhysRevFluids.5.123605
+[238] G. Wang, L. Fei, K. H. Luo, Lattice Boltzmann simulation of water droplet impacting a hydrophobic plate with a cylindrical pore, Physical
+Review Fluids 5 (8) (2020) 083602. doi:10.1103/PhysRevFluids.5.083602.
+URL https://link.aps.org/doi/10.1103/PhysRevFluids.5.083602
+[239] U. Uttamchandani, Wireless MEMS Networks and Applications, Elsevier, 2017. doi:10.1016/C2014-0-03941-X.
+URL https://linkinghub.elsevier.com/retrieve/pii/C2014003941X
+[240] S. G. Kandlikar, E. J. See, M. Koz, P. Gopalan, R. Banerjee, Two-phase flow in GDL and reactant channels of a proton exchange membrane
+fuel cell, International Journal of Hydrogen Energy 39 (12) (2014) 6620–6636. doi:10.1016/j.ijhydene.2014.02.045.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0360319914004054
+[241] J. Yang, L. Fei, X. Zhang, X. Ma, K. H. Luo, S. Shuai, Improved pseudopotential lattice Boltzmann model for liquid water transport inside
+gas diffusion layers, International Journal of Hydrogen Energy 46 (29) (2021) 15938–15950. doi:10.1016/j.ijhydene.2021.02.067.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0360319921005693
+[242] J. Yang, L. Fei, X. Zhang, X. Ma, K. H. Luo, S. Shuai, Dynamic behavior of droplet transport on realistic gas diffusion layer with inertial
+effect via a unified lattice Boltzmann method, International Journal of Hydrogen Energy 46 (66) (2021) 33260–33271. doi:10.1016/j.
+ijhydene.2021.07.124.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0360319921027890
+[243] J. Zhao, F. Qin, D. Derome, J. Carmeliet, Drying of porous materials at pore scale using lattice Boltzmann and pore network models, Journal
+of Physics: Conference Series 2069 (1) (2021) 012001. doi:10.1088/1742-6596/2069/1/012001.
+URL https://iopscience.iop.org/article/10.1088/1742-6596/2069/1/012001
+[244] J. Zhao, F. Qin, Q. Kang, D. Derome, J. Carmeliet, Pore-scale simulation of drying in porous media using a hybrid lattice Boltzmann: pore
+network model, Drying Technology 40 (4) (2022) 719–734. doi:10.1080/07373937.2021.1933017.
+URL https://www.tandfonline.com/doi/full/10.1080/07373937.2021.1933017
+[245] Y. Mino, C. Tanaka, H. Tanaka, K. Nakaso, K. Gotoh, Numerical simulation of a drying colloidal suspension on a wettable substrate using
+the lattice Boltzmann method, Chemical Engineering Science 263 (2022) 118050. doi:10.1016/j.ces.2022.118050.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0009250922006340
+[246] Q. Li, Q. Kang, M. Francois, Y. He, K. Luo, Lattice Boltzmann modeling of boiling heat transfer: The boiling curve and the effects of
+wettability, International Journal of Heat and Mass Transfer 85 (2015) 787–796. doi:10.1016/j.ijheatmasstransfer.2015.01.136.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0017931015001544
+[247] L. Biferale, P. Perlekar, M. Sbragaglia, F. Toschi, Convection in Multiphase Fluid Flows Using Lattice Boltzmann Methods, Physical Review
+Letters 108 (10) (2012) 104502. doi:10.1103/PhysRevLett.108.104502.
+148
+
+URL https://link.aps.org/doi/10.1103/PhysRevLett.108.104502
+[248] G. H´azi, A. M´arkus, Modeling heat transfer in supercritical fluid using the lattice Boltzmann method, Physical Review E 77 (2) (2008)
+026305. doi:10.1103/PhysRevE.77.026305.
+URL https://link.aps.org/doi/10.1103/PhysRevE.77.026305
+[249] G. Hazi, A. Markus, On the bubble departure diameter and release frequency based on numerical simulation results, International Journal of
+Heat and Mass Transfer 52 (5-6) (2009) 1472–1480. doi:10.1016/j.ijheatmasstransfer.2008.09.003.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0017931008005097
+[250] S. Gong, P. Cheng, A lattice Boltzmann method for simulation of liquid–vapor phase-change heat transfer, International Journal of Heat and
+Mass Transfer 55 (17-18) (2012) 4923–4927. doi:10.1016/j.ijheatmasstransfer.2012.04.037.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0017931012002888
+[251] L. Wang, J. Huang, K. He, Thermal lattice Boltzmann model for liquid-vapor phase change, Physical Review E 106 (5) (2022) 055308.
+doi:10.1103/PhysRevE.106.055308.
+URL https://link.aps.org/doi/10.1103/PhysRevE.106.055308
+[252] Q. Li, K. H. Luo, Effect of the forcing term in the pseudopotential lattice Boltzmann modeling of thermal flows, Physical Review E 89 (5)
+(2014) 053022. doi:10.1103/PhysRevE.89.053022.
+URL https://link.aps.org/doi/10.1103/PhysRevE.89.053022
+[253] A. Kumar, Isotropic finite-differences, Journal of Computational Physics 201 (1) (2004) 109–118. doi:10.1016/j.jcp.2004.05.005.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0021999104002037
+[254] S. P. Thampi, S. Ansumali, R. Adhikari, S. Succi, Isotropic discrete Laplacian operators from lattice hydrodynamics, Journal of Computa-
+tional Physics 234 (2013) 1–7. doi:10.1016/j.jcp.2012.07.037.
+URL https://linkinghub.elsevier.com/retrieve/pii/S0021999112004226
+[255] R. Ramadugu, S. P. Thampi, R. Adhikari, S. Succi, S. Ansumali, Lattice differential operators for computational physics, EPL (Europhysics
+Letters) 101 (5) (2013) 50006. doi:10.1209/0295-5075/101/50006.
+URL https://iopscience.iop.org/article/10.1209/0295-5075/101/50006
+[256] M. R. Banerjee, S. Succi, S. Ansumali, R. Adhikari, Isotropic finite-difference discretization of stochastic conservation laws preserving
+detailed balance, Journal of Statistical Mechanics: Theory and Experiment 2017 (10) (2017) 103202. doi:10.1088/1742-5468/aa8c35.
+URL https://iopscience.iop.org/article/10.1088/1742-5468/aa8c35
+[257] F. Qin, L. Del Carro, A. Mazloomi Moqaddam, Q. Kang, T. Brunschwiler, D. Derome, J. Carmeliet, Study of non-isothermal liq-
+uid evaporation in synthetic micro-pore structures with hybrid lattice Boltzmann model, Journal of Fluid Mechanics 866 (2019) 33–60.
+doi:10.1017/jfm.2019.69.
+URL https://www.cambridge.org/core/product/identifier/S0022112019000697/type/journal_article
+[258] G. Wang, L. Fei, T. Lei, Q. Wang, K. H. Luo, Droplet impact on a heated porous plate above the Leidenfrost temperature: A lattice
+Boltzmann study, Physics of Fluids 34 (9) (2022) 093319. doi:10.1063/5.0118079.
+URL https://aip.scitation.org/doi/10.1063/5.0118079
+[259] L. Fei, F. Qin, G. Wang, K. H. Luo, D. Derome, J. Carmeliet, Droplet evaporation in finite-size systems: Theoretical analysis and mesoscopic
+modeling, Physical Review E 105 (2) (2022) 025101. doi:10.1103/PhysRevE.105.025101.
+URL https://link.aps.org/doi/10.1103/PhysRevE.105.025101
+[260] L. Fei, J. Yang, Y. Chen, H. Mo, K. H. Luo, Mesoscopic simulation of three-dimensional pool boiling based on a phase-change cascaded
+lattice Boltzmann method, Physics of Fluids 32 (10) (2020) 103312. doi:10.1063/5.0023639.
+URL http://aip.scitation.org/doi/10.1063/5.0023639
+[261] S. Saito, A. De Rosis, L. Fei, K. H. Luo, K.-i. Ebihara, A. Kaneko, Y. Abe, Lattice Boltzmann modeling and simulation of forced-convection
+boiling on a cylinder, Physics of Fluids 33 (2) (2021) 023307. doi:10.1063/5.0032743.
+URL https://aip.scitation.org/doi/10.1063/5.0032743
+[262] R. Huang, H. Wu, N. A. Adams, Mesoscopic Lattice Boltzmann Modeling of the Liquid-Vapor Phase Transition, Physical Review Letters
+126 (24) (2021) 244501. doi:10.1103/PhysRevLett.126.244501.
+URL https://link.aps.org/doi/10.1103/PhysRevLett.126.244501
+[263] X. Shan, G. Doolen, Multicomponent lattice-Boltzmann model with interparticle interaction, Journal of Statistical Physics 81 (1-2) (1995)
+379–393. doi:10.1007/BF02179985.
+URL http://link.springer.com/10.1007/BF02179985
+[264] M. W¨ohrwag, C. Semprebon, A. Mazloomi Moqaddam, I. Karlin, H. Kusumaatmaja, Ternary Free-Energy Entropic Lattice Boltzmann
+Model with a High Density Ratio, Physical Review Letters 120 (23) (2018) 234501. doi:10.1103/PhysRevLett.120.234501.
+URL https://link.aps.org/doi/10.1103/PhysRevLett.120.234501
+[265] R.-H. Chen, C.-T. Chen, Collision between immiscible drops with large surface tension difference: diesel oil and water, Experiments in
+Fluids 41 (3) (2006) 453–461. doi:10.1007/s00348-006-0173-2.
+URL http://link.springer.com/10.1007/s00348-006-0173-2
+[266] K. S. Ridl, A. J. Wagner, Lattice Boltzmann simulation of mixtures with multicomponent van der Waals equation of state, Physical Review
+E 98 (4) (2018) 043305. doi:10.1103/PhysRevE.98.043305.
+URL https://link.aps.org/doi/10.1103/PhysRevE.98.043305
+[267] Q. Li, A. J. Wagner, Symmetric free-energy-based multicomponent lattice Boltzmann method, Physical Review E 76 (3) (2007) 036701.
+doi:10.1103/PhysRevE.76.036701.
+URL https://link.aps.org/doi/10.1103/PhysRevE.76.036701
+[268] Z. Guo, T. S. Zhao, Finite-difference-based lattice Boltzmann model for dense binary mixtures, Physical Review E 71 (2) (2005) 026701.
+doi:10.1103/PhysRevE.71.026701.
+URL https://link.aps.org/doi/10.1103/PhysRevE.71.026701
+[269] Z. Guo, T. S. Zhao, Discrete velocity and lattice Boltzmann models for binary mixtures of nonideal fluids, Physical Review E 68 (3) (2003)
+149
+
+035302. doi:10.1103/PhysRevE.68.035302.
+URL https://link.aps.org/doi/10.1103/PhysRevE.68.035302
+150
+
diff --git a/SdA0T4oBgHgl3EQfD_9b/content/tmp_files/load_file.txt b/SdA0T4oBgHgl3EQfD_9b/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..20f67fff75f6a937b21dd8102ee969549c6ea403
--- /dev/null
+++ b/SdA0T4oBgHgl3EQfD_9b/content/tmp_files/load_file.txt
@@ -0,0 +1,10338 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf,len=10337
+page_content='Lattice Boltzmann for non-ideal fluids: Fundamentals and Practice  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Hosseinia, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karlina,∗  aDepartment of Mechanical and Process Engineering, ETH Zurich, Zurich, 8092, Switzerland  Abstract  This contribution presents a comprehensive overview of of lattice Boltzmann models for non-ideal fluids, covering  both theoretical concepts at both kinetic and macroscopic levels and more practical discussion of numerical nature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  In that context, elements of kinetic theory of ideal gases are presented and discussed at length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Then a detailed dis-  cussion of the lattice Boltzmann method for ideal gases from discretization to Galilean invariance issues and different  collision models along with their effect on stability and consistency at the hydrodynamic level is presented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Exten-  sion to non-ideal fluids is then introduced in the context of the kinetic theory of gases along with the corresponding  thermodynamics at the macroscopic level, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' the van der Waals fluid, followed by an overview of different lattice  Boltzmann based models for non-ideal fluids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' After an in-depth discussion of different well-known issues and artifacts  and corresponding solutions, the article finishes with a brief discussion on most recent applications of such models  and extensions proposed in the literature towards non-isothermal and multi-component flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Keywords: non-ideal fluids, lattice Boltzmann method, kinetic theory,  PACS: 0000, 1111  2000 MSC: 0000, 1111  Contents  1  Introduction  5  2  Elements of kinetic theory  5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  The Boltzmann transport equation .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  Binary collision: Kinematics .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  6  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  Differential scattering cross-section .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  7  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3  Boltzmann’s collision integral .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  8  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  Transport equations for molecular properties .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  11  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  Boltzmann’s transport theorem .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  11  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  Invariants of collision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Conservation of mass, momentum and energy  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  12  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3  Boltzmann’s H-theorem .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  12  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  Equilibrium and local equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The Maxwell-Boltzmann distribution function .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  13  3  From Boltzmann equation to hydrodynamics  14  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  Fields and fluxes  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  14  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  Balance equations for thirteen moments .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  15  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3  Local equilibrium projection .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  16  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  Dynamic correction to the local equilibrium projection  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  17  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  Estimates from the Maxwell-Boltzmann distribution  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  17  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  Mean free path .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  17  ∗Corresponding author  Email address: ikarlin@ethz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='ch (I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karlin)  Preprint submitted to Physics reports  January 6, 2023  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='02011v1  [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='flu-dyn]  5 Jan 2023  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3  Estimates from the Boltzmann collision integral .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  17  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  Reduced Boltzmann equation  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  18  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  Hydrodynamic limit  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  18  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  Elementary derivation of viscosity .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  19  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='7  Singularly perturbed Boltzmann equation .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  19  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8  Normal solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The invariance principle  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  20  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='9  The Chapman–Enskog method .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  21  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='10 Euler’s compressible flow equations .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  21  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='11 Navier-Stokes and Fourier compressible flow equations .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  22  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  Lifting the local equilibrium projection: BGK kinetic model  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  28  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  Grad’s thirteen-moments projection  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  29  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  Grad’s thirteen-moments distribution function .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  29  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  Grad’s thirteen-moments closure .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  29  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3  Grad’s thirteen-moments system .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  31  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  Quasi-equilibrium projection .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  32  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  Triangle entropy method .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  33  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  Grad’s projections via triangle entropy method  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  34  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='7  Dynamic correction to Grad’s thirteen-moments projection: The R13 system .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  37  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  Invariance defect of Grad’s thirteen-moments approximation .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  37  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  The R13 distribution function  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  39  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3  The R13 equations .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  40  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8  Lifting of Grad’s and quasi-equilibrium projections: Kinetic models for simple fluid .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  41  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  Quasi-equilibrium and related kinetic models .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  41  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  Two relaxation times quasi-equilibrium models .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  43  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3  Lifting the eight-moments Grad’s projection: Shakhov’s S-model  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  44  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  Lifting the ten-moments Grad’s projection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  44  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  Holway’s ellipsoidal-statistical kinetic model .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  44  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='9  Summary: Projections, corrections and lifting .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  45  4  Lattice Boltzmann for ideal fluid and related models  46  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  Phase-space discretization  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  46  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  Hermite expansion and Gauss-Hermite quadrature  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  46  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  Product form equilibria and moment matching  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  48  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3  Alternative to polynomial equilibria: Entropic equilibria .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  49  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  Galilean invariance issues on standard lattices .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  50  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  Space and time discretization: Integration along characteristics .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  55  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  Realization without force and correction term .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  55  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  Correction for the diagonal components of the equilibrium third-order moments tensor .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  56  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3  Introduction of external body forces .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  57  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  Shan and Chen’s forcing scheme .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  57  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  Luo’s scheme .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  58  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3  He et al’s scheme .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  59  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  Guo’s scheme .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  60  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  Kupershtokh’s scheme .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  60  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  Stability of LB-BGK .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  60  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  Isothermal closure: spurious bulk viscosity and stabilization of normal modes .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  61  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  Positivity of the discrete equilibria .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  61  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3  Linear stability of discrete solver .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  62  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  Extension of stability domain .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  65  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  Relaxation of discrete populations in alternate spaces .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  65  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  Central moments-based decomposition  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  67  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3  Closures for the relaxation rates: entropic .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  68  2  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  The specific case of regularization .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  70  5  Extension to non-ideal fluids  72  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  Second-gradient theory and non-ideal fluids thermodynamics .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  72  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  Non-ideal equation of state: van der Waals  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  72  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  Co-existence densities: Common-tangent construction .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  73  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3  Co-existence densities: First-order transition and Maxwell construction .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  74  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  Free energy of non-uniform non-ideal fluid .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  75  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  Gibbs equilibrium conditions for a flat interface .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  76  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  Korteweg stress tensor and second-gradient fluid balance equations  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  77  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  Kinetic models for non-ideal fluid  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  78  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  Hard sphere potential: The Enskog model .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  78  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  Long-range interactions: Vlasov model .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  79  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3  General Enkog-Vlasov-BGK kinetic framework for hydrodynamics .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  80  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  Scaling and hydrdynamic limit .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  81  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3  Overview of lattice Boltzmann models for non-ideal fluids  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  83  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  Shan and Chen’s pseudo-potential model  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  84  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  Free energy model and derivatives .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  85  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  Bridging the scale gap: Principle of corresponding states .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  86  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  Dimensional form of equations and restriction by the interface thickness .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  86  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  Extension to realistic-sized systems: Rescaling interface thickness and the principle of corre-  sponding states .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  87  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  Numerical artifacts and issues of non-ideal lattice Boltzmann models .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  89  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  Deviations in normal stress at interface: The issue of thermodynamic consistency .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  89  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  Fixed surface tension .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  91  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3  The issue of spurious currents at interfaces  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  91  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  Galilean invariance of viscous dissipation rates and stability .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  92  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  Improvements and enhanced models for non-ideal fluids  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  94  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  Equations of state .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  94  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  Partitioning of pressure contributions  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  98  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3  Non-local thermodynamic pressure force contribution: Using mathematical identities to re-  duce discretization errors .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 100  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  Higher order discretization: Leading order error and isotropy .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 101  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  Thickening interface .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 103  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  Independent control over surface tension  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 104  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='7  The discrete pressure tensor  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 105  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8  Evaluating the effective surface tension  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 106  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='7  Fluid-solid interaction: wetting properties .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 108  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  Static contact angle .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 108  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  Contact angle hysteresis .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 110  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8  Assessment of thermo-physical properties of models  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 111  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  Speed of sound and compressibility .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 111  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  Meanfield scaling laws: Interface thickness .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 112  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3  Meanfield scaling laws: Surface tension .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 113  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  Meanfield scaling laws: Tolman length  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 113  6  Illustration of applications  117  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  Drop interaction with solid substrates  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 117  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  Impact on non-wetting surfaces  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 117  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  Pancake bouncing  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 118  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3  Other approaches to reduce contact time via macro-structures  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 118  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  Flow in porous media .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 120  3  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  Water transport in proton exchange membrane fuel cells  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 120  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  Isothermal drying .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 121  7  Extension to more complex physics  123  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  Thermal flows with evaporation  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 123  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  The hybrid and passive scalar approaches .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 123  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  The kinetic route .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 124  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  Multiple components .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 126  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  Ternary free energy model of W¨ohrwag et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 126  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  Mixtures with multi-component van der Waals equation of state .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 127  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3  The multi-component pseudo-potential method .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 128  8  Conclusion  129  Appendix A  Hermite expansion  129  Appendix B  Elements of the von Neumann formalism  133  Appendix C  Hydrodynamic limit of the Enskog–Vlasov–BGK kinetic model  135  Appendix D  Chapman–Enskog analysis of the lattice Boltzmann method for non-ideal fluids  136  4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Introduction  Non-ideal fluids are omnipresent in science and technology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' From micro-droplets coalescing in clouds, to so-  lidification or melting of alloys and diesel droplets evaporation and subsequent combustion, all involve multiple in-  teracting phases and moving interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This ubiquity fueled wide efforts focused on the development of predictive  mathematical models and numerical tools for multi-phase flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' While significant attention has been focused on sharp  interface methods requiring efficient tracking of the evolving and deforming interfaces, and imposing jump conditions  [1, 2, 3, 4], the ever-growing range of temperatures and pressures involved in typical systems of interest is making ther-  modynamic consistency of the computational models at interfaces essential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Dramatically different thermodynamic  regimes are encountered in diesel engines during the compression phase, in aeronautical engines during take-off while  most rocket engines operate in trans- and super-critical regimes, where the interface thickness becomes comparable  to the flow scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Nucleation and cavitation are yet another example, where the sharp interface limit does not hold  and modifications to the classical nucleation theory [5], related to curvature-dependence of the surface tension, are  required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In such cases, an accurate account of non-ideality of the fluid, including a finite interface thickness, is crucial  for predictive numerical simulations of the flow physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' At a macorscopic level, a primer example for thermodynam-  ics of non-ideal fluids is the second-gradient theory, first introduced by van der Waals for single-component fluids [6],  leading to the Navier-Stokes equations supplemented with the Korteweg stress tensor [7], and is a starting point for  numerical methods known as diffuse interface approach [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' On the other hand, extension of the Boltzmann equation  to dense gases within the Enskog hard-sphere collision model [9] and Vlasov mean-field approximation [10] provides  a kinetic-theory basis for dynamics of non-ideal fluid [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  The lattice Boltzmann method (LBM), a discrete solver for the discrete Boltzmann equation ( discrete in phase space)  is a numerical tool targeting the hydrodynamic balance equations (initially in the incompressible limit) that has expe-  rienced noticeable growth in both popularity and ability to incorporate complex physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Since the pioneering work  of [12], the LBM gained popularity as a viable numerical tool targeting the hydrodynamic regime of non-ideal fluids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Different models for non-ideal fluid dynamics have been developed since and used for a wide variety of applications  involving complex physics and geometries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The rapid growth, constant evolution of non-ideal fluid models within the  context of the LBM and very large number of yearly publications in that area point to the need for a comprehensive  document listing and discussing fundamentals, pitfalls, best practices and most recent developments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A couple of pub-  lications have previously taken upon this task in previous years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' While well-written and covering a number of topics  related to implementation and numerics they do not treat of fundamentals and do not provide in-depth discussions .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  In the present contribution we aim to provide a comprehensive overview of the LBM for non-ideal fluids simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Given the relatively wide area of topics covered in the present document and depth of discussions, sections have been  organised in a manner allowing readers to go directly to topics they are interested in without having to go through the  document in its entirety.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' As such readers interested in an introduction to the kinetic theory can read section 2 while  those looking for a more in-depth discussion can move on to section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Those with an interest only for the LBM can  directly go to section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' To give interested readers all necessary background to analyze and understand challenges  and shortcomings of different models we start with a detailed introductory discussion covering different aspects of the  kinetic theory of ideal gases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This is followed by a section covering all fundamental aspects of the lattice Boltzmann  method for ideal gases covering discretization in phase-space physical space and time, incorporation of body forces,  an overview of different collision operators and corresponding numerical and physical properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Extension of the  lattice Boltzmann method to non-ideal fluids is then discussed in details in section 5 where different models are re-  viewed and a comprehensive discussion covering most important challenges is provided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Some of the most interesting  and recent achievement in terms of application with LBMs for non-ideal fluids are then reviewed and discussed in  section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This is followed by a section discussing interesting extensions of the iso-thermal non-ideal fluid solvers to  compressible and multi-component fluids in section 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Elements of kinetic theory  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The Boltzmann transport equation  Following Boltzmann, we consider a gas consisting of a large number of identical particles of mass m = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The  state of the gas is described by the distribution function,  f(v, x, t),  (1)  5  with the interpretation that the number of particles dN1 in a differential volume of phase space centered at (x, v) at  time t is  dN = f(v, x, t)d3vd3x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (2)  We further assume that the gas is moderately dilute, that is, the particles mostly fly freely, and experience encounters  (collisions) from time to time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Collisions with a participation of more than two particles at a time can be neglected,  so we consider only binary collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' More specifically, think of hard spheres of a diameter d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Then if N is the  number of such spheres in a container of a volume V, we consider the case N → ∞ (”many particles”), V → ∞  (”big container”) and d → 0 (”interaction range is short”), so that with both these limits we have N/V ∼ const (the  average density of particles is finite).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Furthermore, Nd3/V → 0 (total volume occupied by the particles is negligible  to the volume of the container), but Nd2 ∼ const (total cross-section area is fixed, so that molecules will be able to  ”see” each other and collide).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This is called the Boltzmann–Grad limit and is used to rigorously justify the domain of  validity of the Boltzmann equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  With the above assumptions we can state that there will be two mechanisms which contribute to changing the  distribution function in time and space: the free flight (or a modification thereof if long-range forces are present), and  the binary collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Thus, we write,  ∂ f  ∂t + v · ∂f  ∂x + F  m · ∂ f  ∂v = JB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (3)  Here on the left we have the free flight operator (v · ∂/∂x) and we have also included an effect of action of large-scale  forces such as gravity, (F/m)·∂/∂v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' These two terms signify the net change of the number of particles in the element of  the phase space volume d3vd3x centered at (v, x) due to flying in and out of particles and the change of their velocities  through an acceleration caused by external forces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  The term on the right hand side is called the collision integral, and which takes into account the change of the  number of particles in the elementary volume d3vd3x through ”kicking out” a particle with the velocity about v when  it collides with some other particle and alters the velocity, and through ”kicking in” a particle with the velocity v  which is produced in a collision of two particles with some different velocities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Now we shall evaluate the effect of  the binary collisions according to Boltzmann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Binary collision: Kinematics  We need first to consider a purely mechanical part of the derivation, namely the collision of two particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In this  section, we shall neglect the long-range forces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Collision is vaguely understood as a relatively sharp change of the  trajectories of the particles approaching each other from a distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The range of the force which causes the sharp  change of their trajectories is assumed short so that the particles approach each other along straight trajectories (it is  best to think of hard spheres again);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' their encounter happens almost instantly, after which the molecules fly away from  each other along the changed straight trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  We shall consider two molecules labeled ”1” and ”2”, their velocities before the collision in the lab frame are v1  and v2, whereas after the collision they are denoted by primes, v′  1 and v′  2, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Furthermore, we introduce the  center-of-mass velocity G and the relative velocity g21, and similarly, after the collision, G′ and g′  21,  G = v1 + v2  2  ,  (4)  g21 = v2 − v1,  (5)  G′ = v′  1 + v′  2  2  ,  (6)  g′  21 = v′  2 − v′  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (7)  The unit vector in the direction of the relative velocity g21 will be denoted e;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' correspondingly, e′ for the post-collision  relative velocity g′  21,  e = v2 − v1  |v2 − v1| = g21  g21  ,  (8)  e′ = v′  2 − v′  1  |v′  2 − v′  1| = g′  21  g′  21  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (9)  6  Thus, before and after the collision, the velocities of the molecules in the lab frame are, respectively,  v1 = G − 1  2g21e,  (10)  v2 = G + 1  2g21e,  (11)  v′  1 = G′ − 1  2g′  21e′,  (12)  v2 = G′ + 1  2g′  21e′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (13)  Collision are further assumed to be elastic so that the momentum of the pair of molecules and their energy is conserved  as the result of the collision (particle’s mass m = 1),  v1 + v2 = v′  1 + v′  2,  (14)  |v1|2 + |v2|2 = |v′  1|2 + |v′  2|2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (15)  These are 3 + 1 = 4 equations (three components of momentum conservation and one energy conservation) for 6  unknowns (three components of v′ and three components of v′  1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' From the first equation, we infer that the center-of-  mass momentum is conserved in the collision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' From the second we get that the magnitude of the relative velocity does  not change in the collision,  G′ = G,  (16)  g′  21 = g21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (17)  The post-collision velocities in the lab frame are thus a two-parametric family is parameterized by a vector e′ belong-  ing to a unit sphere, |e′|2 = 1:  v′  1 = v1 + v2  2  − |v2 − v1|  2  e′,  (18)  v′  2 = v1 + v2  2  + |v2 − v1|  2  e′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (19)  From these relation we see that the vector |e′| is a rotation of the relative velocity as the result of the collision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Deflection angle θ is the angle between e and e′,  cos θ = e · e′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (20)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Differential scattering cross-section  We now shall move on, still in a pure mechanics mode, to considering a number of encounters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This is a scattering  problem, familiar from classical mechanics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' We shall further assume that molecules are interacting through a potential  which depends only on the absolute distance between them, U(r1, r2) = U(|r2 − r1|) (central forces).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In such a case  the trajectories of both molecules are confined to a plane, which is orthogonal to the angular momentum (the latter is  conserved for the central force interaction).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  The analysis is best done in the center-of-mass (CM) frame (co-moving with the center-of-mass velocity G).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The  problem then reduces to the scattering of a particle with a reduced mass m0 = m1m2/(m1 + m2) (m0 = m/2 in the case  of equal masses of particles), moving with the velocity g21 on a fixed center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Trajectories of such particles look most  simple: they are symmetric with respect to the line through the points of closest approach of the molecules and the  center of force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Now we need to specify the two parameters to characterize the initial data for the scattering particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For that we  use the azimuth angle ϵ which fixes the orientation of the plane containing the trajectory with respect to an arbitrary  fixed plane containing the center of force and parallel to g21, and the impact parameter b, defined as the distance  between the line drawn by g21 and the parallel to it line containing the center of force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  7  Let us consider the incident jet of particles through the area between the two concentric circles of radii b and  b + db, cut with the angle between ϵ and ϵ + dϵ,  dAin = bdbdϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (21)  The particles coming through the area dAin are scattered into the solid angle,  dAout = d2e′ = sin θdθdϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (22)  The differential scattering cross section α12 is defined as the ratio between these two areas,  α12 = dAin  dAout  =  bdbdϵ  sin θdθdϵ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (23)  Thus,  bdbdϵ = α12d2e′,  (24)  where  α21 =  b  ��� ∂b  ∂θ  ���  sin θ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (25)  Note that we have written the absolute value of the derivative of the impact parameter with respect to the deflection  angle because for repulsive force this function is negative (that is, with the decrease of the impact parameter the  particle is ”turned back” by the potential, the deflection angle is increased).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Differential scattering cross section thus represents intensity of the incoming flux of particles through the element  of the cross-section in terms of the flux of scattered particles into the solid angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Note that for the central forces,  the dependence on the azimuth angle is irrelevant, and the differential scattering cross section depends only on the  deflection angle θ and the magnitude of the relative velocity g21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For a specified central potential, the differential  cross-section is computed by classical mechanics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' We shall discuss a few relevant examples later, but for now we  shall keep it unspecified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Boltzmann’s collision integral  We shall now proceed with the evaluation of the rate of change of the distribution function,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' which we represent in  a ”gain-loss” form,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  JB = J+  B − J−  B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (26)  where  The loss,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  J−  B(v1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' x,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' t)d3v1d3xdt,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (27)  is the number of collisions of the type {v1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' v2} → {v′  1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' v′  2},' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' resulting in the loss of the particles of the type ”1”,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' in  the infinitesimal volume of phase space d3v1dx,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' during the time between t and t + dt,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' and  The gain,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  J+  B(v1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' x,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' t)d3v1d3xdt,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (28)  is the number of collisions of the type {v′  1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' v′  2} → {v1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' v2},' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' resulting in the gain of the particles of the type ”1”,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' in  the same infinitesimal phase space volume,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' for the same time duration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Note that when we say ”loss/gain”, we do not mean a particle is destroyed or created in the volume element dx;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' rather,  we mean that a particle, which was in d3v1 before the collision, has changed its velocity ”too much” after the collision,  so that is not within d3v1 any longer (loss), or that after a collision, the velocity of one of the particles changed in such  a way that it now belongs to d3v1 (gain).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' So it is about the loss and gain in the element of the phase space d3v1d3x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  For the evaluation of the rates J−  B and J+  B, Boltzmann assumed that any two particles which are about to collide,  ”do not know anything about each other”, neither with respect to their velocities, nor position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In other words, the  molecular chaos assumption means that velocities of any of the two particles entering an encounter are un-correlated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  With this assumption, we proceed as follows:  8  The loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The number of the type ”2” particles which will encounter the dN1 = f(v1, x, t)d3v1d3x particles of type  ”1” can be written as,  dN2 = f(v2, x, t)d3v2 (|v2 − v1|dt × bdbdϵ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (29)  Note the elementary collision volume in this expression, dVc = |v2 − v1|dt × bdbdϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The number of colliding pairs is  thus estimated as,  dN12 = dN1 × dN2 =  �  f(v1, x, t)d3v1d3x  � �  f(v2, x, t)|v2 − v1|bdbdϵd3v2dt  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (30)  Notice that the number of pairs of interacting particles is estimated in this expression as a product of two one-particle  distributions, dN12 ∼ f(v1, x, t) f(v2, x, t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This is implied by the molecular chaos assumption: if the colliding particles  were assumed to be correlated, then we would need a distribution function of pairs of particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' With the results of  the previous section, this expression can be written using the differential scattering cross section,  dN12 =  �  f(v1, x, t) f(v2, x, t)|v2 − v1|α12d2e′d3v2  �  d3v1d3xdt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (31)  Thus, the rate of loss of particles with velocities v1 is the sum (integral) of the above expression over all possible  velocities v2 and over all the directions of post-collision relative velocity e′ (the surface of the three-dimensional unit  sphere S 2):  J−  B(v1, x, t) = f(v1, x, t)  �  R3  �  S 2 f(v2, x, t)|v2 − v1|α12d2e′d3v2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (32)  The gain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' We now need to construct a similar expression for the rate with which the particles with the velocity v1 are  produced as the result of collisions of pairs of particles with other velocities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The counting process is greatly simplified  by the reversibility of mechanical motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Indeed, Newton’s equations are reversible in the time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Therefore, if in the  direct scattering the initial data for the velocities {v1, v2} was transformed into {v′  1, v′  2}, then we can take {v′  1, v′  2} as the  initial data in another (reverse) scattering experiment, and the result of scattering will be known, it is {v1, v2}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Precisely  this ability to interchange of the past and the future in a mechanical system (time-reversal) is what will be used to  count all the pairs of particles which produce the desired velocity v1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' We therefore do not need to start a counting  from the beginning, as we just need to repeat all of the above by changing non-primed variables into primed variables,  and vice versa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Note, however, that we still use the molecular chaos assumption when so doing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Thus, using the  reversibility, we can write the number of pair collisions of the type {v′  1, v′  2} → {v1, v2},  dN′  12 = f(v′  1, x, t) f(v′  2, x, t)|v′  2 − v′  1|α′  12d2ed3v′  1d3v′  2d3xdt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (33)  This expression is transformed in three steps: As the magnitude of the relative velocity does not change as the result  of collision, we have  dN′  12 = f(v′  1, x, t) f(v′  2, x, t)|v2 − v1|α′  12d2ed3v′  1d3v′  2d3xdt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (34)  Furthermore, the differential scattering cross section remains same under the inversion of the velocities,  dN′  12 = f(v′  1, x, t) f(v′  2, x, t)|v2 − v1|α12d2ed3v′  1d3v′  2d3xdt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (35)  Finally, the element of the 2 + 3 + 3-dimensional volume, d2ed3v′  1d3v′  2 is transformed to the elementary volume  d2e′d3v1d3v2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' First, we compute the Jacobian of the transformation {v1, v2} → {G, g21},  J = ∂(G, g21)  ∂(v1, v2) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (36)  Thus, by the definition of the transformation of the elementary volume which includes the determinant of the Jacobian,  we have d3Gd3 g21 = |J|d3v1d3v2 = d3v1d3v2, and similarly, d3Gd3 g′  21 = d3v′  1d3v′  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' On the other hand, d3g21 =  g2  21dg21d2e and d3 g′  21 = g2  21dg21d2e′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Combining these expressions, we have,  d2ed3v′  1d3v′  2 = d2e′d3v1d3v2,  (37)  9  and thus we obtain the final expression for dN′  12 in the form,  dN′  12 =  �  f(v′  1, x, t) f(v′  2, x, t)|v2 − v1|α12d2e′d3v2  �  d3v1d3xdt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (38)  As the result, we obtain the rate of gain after integration,  J+  B(v1, x, t) =  �  R3  �  S 2 f(v′  1, x, t) f(v′  2, x, t)|v2 − v1|α12d2e′d3v2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (39)  Combining the results of the above estimate for the gain (39) and loss (32), we obtain the rate of change of the  one-particle distribution function due to binary collisions,  JB =  �  R3  �  S 2  � f(v′  1, x, t) f(v′  2, x, t) − f(v1, x, t) f(v2, x, t)� K(|v2 − v1|, θ)e′d3v2,  (40)  where the post-collision velocities v′  1 and v′  2 are the functions of v1, v2 and e′, Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (18) and (19), and where the  function K is the collision kernel,  K = |v2 − v1|α12(|v2 − v1|, θ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (41)  This is the Boltzmann Stosszahlansatz or the Boltzmann collision integral.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  The collision kernel (41) depends on the magnitude of the relative velocity |v2 − v1| and on the deflection angle θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Computation of K is a matter of studying the mechanical scattering problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Here we mention two cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Hard spheres.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' These are ”billiard balls” of a diameter d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In this case the differential cross-section does not depend  on the relative velocity of colliding particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' By simple geometrical considerations we obtain  α12 = d2  4 , K = d2  4 |v2 − v1|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (42)  Inverse-power law potentials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For any interaction potential U(r), the dependence of the deflection angle on the impact  parameter and the relative velocity is given in terms of a quadrature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' We do not write it here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' However, if the potential  is inverse proportional to power of distance, U(r) ∼ r−n we can infer about the dependence of the differential scattering  cross-sections on the velocity even without integrating Newton’s equations explicitly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' It is sufficient to make use of  similarity: if the potential of a mechanical system is a homogeneous function of order k, that is U(αr) = αkU(r), then  the velocity and the geometric parameters of geometrically similar trajectories are related by  � v  V  �  =  � l  L  �k/2  ,  (43)  where v, V and l, L are the velocity and characteristic length on two geometrically similar trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This follows  immediately from the invariance of Newton’s equations under the transformation of space and time r → αr, t →  α(2−k)/2t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In our case k = −n, thus we have the following relation between the impact parameter and the relative  velocity: b ∼ |v2 − v1|−2/n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This implies for the Boltzmann collision kernel  K = a(θ)|v2 − v1|1−4/n,  (44)  where function a depends only on the deflection angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' We see that in the special case n = 4 (that is, for the molec-  ular potential inverse proportional to the fourth power of the separation distance in three dimensions), the collision  kernel depends only on the deflection angle but not on the relative velocity of particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This is known as Maxwell’s  molecules, and it was first shown by Maxwell that computations in that case greatly simplify.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Finally, we mention that  function a(θ) diverges as θ → 0 because of a large number of particles experiencing grazing collisions with almost no  deflection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In practice, one often uses a cutoff angle to regularize this divergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This works for most inverse-power  law potentials but not for the Coulomb potential n = −1 where grazing collisions have to be treated in a different  manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Summarizing, we can trace the assumptions behind the derivation of the Boltzmann equation by looking once  again at the structure of the Boltzmann collision integral (40):  10  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The gas is assumed to be dilute so that only binary collisions of molecules are considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This is reflected by  the quadratic nonlinearity of the collision integral.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Binary collisions are assumed to be local in time and space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' That is, the duration of the collision and the  effective range of interaction where the trajectories of the particles change appreciably are supposed to be much  smaller than any other characteristic time/distance scales of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This is reflected by the fact that x and t  are simply parameters in the collision integral, there is neither space or time derivative in there.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Collisions are supposed to be elastic, which is reflected by the specific post-collision velocities v′  1 and v′  2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' they  are the implication of the momentum and energy conservation in the elastic collision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Micro-reversibility of the Newton’s equation of mechanical interaction is reflected by the structure of the colli-  sion kernel;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' we have explicitly used it to count the pairs of colliding particles by tracing backward in time the  scattering trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The molecular chaos hypothesis is reflected by the specific structure of the gain and loss parts, quadratic in the  distribution function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Notation convention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' It is customary to use some abbreviation in writing the Boltzmann transport equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' First, we  change the notation for the velocity, v1 → v and v2 → v1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Second, one usually drops the space and time arguments,  and uses the abbreviations  f(v, x, t) = f, f(v1, x, t) = f1, f(v′, x, t) = f ′, f(v′  1, x, t) = f ′  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (45)  With this, the Boltzmann collision integral (40) is written as,  JB =  �  R3  �  S 2  � f ′ f ′  1 − f f1  � Bd2e′d3v1,  (46)  while the Boltzmann transport equation in the absence of long-range forces becomes,  ∂t f + v · ∇f = JB,  (47)  where ∂t = ∂/∂t and ∇ = ∂/∂x are shorthand notation for the derivatives in time and space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Transport equations for molecular properties  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Boltzmann’s transport theorem  A molecular (or microscopic) property can be thought as a generic function of the velocity ϕ(v), such as, for  example ϕ = m (particle’s mass), ϕ = mv (particle’s momentum), ϕ = mv2/2 (kinetic energy of the particle) and  so fort.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' With the help of the distribution function, we define the corresponding macroscopic densities (or fields) by  averaging over the entire range of the microscopic velocities according to their distribution function,  ρϕ(x, t) =  �  R3 ϕ(v) f(v, x, t)d3v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (48)  We can also define the microscopic flux of any microscopic property by multiplying it with v so that the macroscopic  flux jϕ is,  jϕ(x, t) =  �  R3 vϕ(v) f(v, x, t)d3v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (49)  When the distribution function evolves in time and space according to the Boltzmann equation, also all the macro-  scopic densities and fluxes evolve due to f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The transport equation for any macroscopic density is obtained by  multiplying the Boltzmann equation with the corresponding microscopic property and integrating over the velocities,  ∂tρϕ + ∇ · jϕ = Rϕ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (50)  The left hand side of this equation contains the divergence of the flux jϕ, while the right hand side is the production  rate due to collisions,  Rϕ =  �  R3  �  R3  �  S 2 ϕ � f ′ f ′  1 − f f1  � Kd2e′d3v1d3v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (51)  11  This expression can be written in a more symmetric and telling form by using the symmetries of the with respect to  renaming the particles,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' the time reversal and the combination thereof,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  d2e′d3v1d3v = d2e′d3vd3v1 = d2ed3v′  1d3v′ = d2ed3v′d3v′  1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  so that  Rϕ =  �  R3  �  R3  �  S 2 ϕ � f ′ f ′  1 − f f1  � Kd2e′d3v1d3v  =  �  R3  �  R3  �  S 2 ϕ1  � f ′ f ′  1 − f f1  � Kd2e′d3v1d3v,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  = −  �  R3  �  R3  �  S 2 ϕ′ � f ′ f ′  1 − f f1  � Kd2e′d3v1d3v,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  = −  �  R3  �  R3  �  S 2 ϕ′  1  � f ′ f ′  1 − f f1  � Kd2e′d3v1d3v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (52)  Thus, we arrive at Boltzmann’s transport theorem: The production rate of any molecular property is written in the  following symmetrized form,  Rϕ = 1  4  �  R3  �  R3  �  S 2(ϕ + ϕ1 − ϕ′ − ϕ′  1) � f ′ f ′  1 − f f1  � Kd2e′d3v1d3v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (53)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Invariants of collision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Conservation of mass, momentum and energy  Immediate implication of the Boltzmann’s transport theorem is vanishing of the rate whenever the molecular  property satisfies the condition,  ϕ + ϕ1 − ϕ′ − ϕ′  1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (54)  Because each binary collision conserves the number of particles, their momentum (14) and kinetic energy (15), the  most general solution to the collision invariants condition is a linear combination of five scalar quantities,  ϕ ∈ Lin  �  1, v, v2�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (55)  The conventional basis of the linear subspace (55) is built by five molecular properties m, mv and mv2/2, corresponding  to macroscopic densities ρ, ρu and ρE, respectively, interpreted as the mass density, the momentum flux and the energy  density,  ρ(x, t) = m  �  R3 f(v, x, t)d3v,  (56)  ρu(x, t) = m  �  R3 v f(v, x, t)d3v,  (57)  ρE(x, t) = (m/2)  �  R3 v2 f(v, x, t)d3v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (58)  Therefore, the corresponding terms Rϕ vanish, and the transport equations for these locally conserved fields become  conventional statements of the local conservation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Under suitable boundary conditions (vanishing at infinity, peri-  odic etc), this leads, after integration over the volume of the container, to the global mass, momentum and energy  conservation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Boltzmann’s H-theorem  Yet another implication of Boltzmann’s transport theorem is manifest when considering the following molecular  property,  ϕ = ln f(v, x, t) + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (59)  12  The corresponding production rate is,  σB = 1  4  �  R3  �  R3  �  S 2(ln f + ln f1 − ln f ′ − ln f ′  1) � f ′ f ′  1 − f f1  � Kd2e′d3v1d3v  = 1  4  �  R3  �  R3  �  S 2 ln  � f f1  f ′ f ′  1  � � f ′ f ′  1 − f f1  � Kd2e′d3v1d3v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (60)  Now we denote X = f f1, Y = f ′ f ′  1, and notice that the function under integration, F = ln X  Y (Y − X) ≤ 0 for any X > 0,  Y > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Thus, for any f, the rate σ is non-positive,  σB(x, t) ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (61)  Consider the following field, the Boltzmann H-function,  H(x, t) =  �  R3 f(v, x, t) ln f(v, x, t)d3v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (62)  The total H-function ¯H is obtained after integration of the density (62) over the volume V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Assuming suitable bound-  ary conditions under which the flux of the H-function vanishes at the boundaries, we find, based on the non-positivity  of the H-function production rate (60),  d ¯H  dt =  �  V  σB(x, t)d3x ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (63)  This is the H-theorem proven by Boltzmann: H-function never increases due to the Boltzmann equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This is the  spectacular implication of the Boltzmann equation, as it describes irreversible behavior, and the H-function has to be  related to the entropy of the system according to second law of thermodynamics (the non-decrease of the entropy with  the time).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Identification of the H-function with the entropy will be completed below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Equilibrium and local equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The Maxwell-Boltzmann distribution function  The structure of the Boltzmann collision integral (40) implies that its zero-point, JB( f) = 0, is achieved on the  family of local equilibrium distribution functions f eq(v, x, t), satisfying the detail balance condition,  f eq′ f eq′  1  = f eq f eq  1 ,  (64)  or, by taking the logarithm of this expression,  ln f eq′ + ln f eq′  1  − ln f eq − ln f eq  1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (65)  Comparison to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (54) shows that the logarithm of the local equilibrium distribution function is a linear combination  of collision invariants,  ln f eq ∈ {1, v, v2}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (66)  Thus, the generic local equilibrium can be written as a five-parametric subset,  f eq = A exp  �  −(v − λ)2  2σ  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (67)  We now turn to the definition of the density (56), the momentum (57) and the energy (58).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For the latter, we assume a  relation to the absolute temperature by the caloric equation of state of monatomic ideal gas,  ρE = 3  2ρRT + 1  2ρu2,  (68)  where R is gas constant,  R = RU  µ ,  (69)  13  with RU the universal gas constant and µ the molar mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Using (67) in (56), (57) and (58), the parameters {A, λ, σ} are  expressed in terms of the conventional parameters {ρ, u, T} upon evaluation of the Gauss integrals: A = (ρ/m) (2πRT)−3/2,  λ = u and σ = RT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' With this re-parameterization, the local equilibrium distribution function reads,  f eq = n (2πRT)−3/2 exp  �  −(v − u)2  2RT  �  ,  (70)  where n = ρ/m is the number density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This is the local Maxwell-Boltzmann distribution function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Specification ”local”  means that density, velocity and temperature in this expressions can be arbitrary functions of space and time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The local  equilibrium annuls only the right hand side of the Boltzmann equation but not the left hand side, so it is not a solution  of the Boltzmann equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' It, however becomes the solution when the density, flow velocity and temperature are  constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Then we speak of the global equilibrium, or just the equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  The Boltzmann H-function is easily evaluated at the local (or global) equilibrium:  Heq =  �  f eq ln f eqd3v = −n  �3  2 ln T − ln n  �  − 3  2n (ln(2πR) + 1) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (71)  Note that this expression does not depend on flow velocity as the consequence of Galilean invariance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Since the  thermodynamic entropy concerns the equilibrium states, we consider the case of global equilibrium of N particles,  and evaluate the total H-function difference between the two states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Integrating (71) over the volume, we find  ∆ ¯Heq = −NAν  �3  2 ln  �T2  T1  �  + ln  �V2  V1  ��  ,  (72)  where NA and ν are the Avogadro number and the number of moles of gas, respectively, N = NAν.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' On the other hand,  the thermodynamic entropy difference between the two states of ν moles of ideal gas with the specific heat at constant  volume cv = (3/2)RU is,  ∆S = ν  �3  2RU ln  �T2  T1  �  + RU ln  �V2  V1  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (73)  Comparing (72) and (73), we see that the thermodynamic entropy difference and the H-function difference are related  by a dimensional constant and the sign convention,  ∆S = −kB∆ ¯Heq,  (74)  where kB is the Boltzmann constant, or ”the universal gas constant per particle”,  kB = RU  NA  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (75)  Note that the matching of the specific heat through the thermodynamic entropy relation proves the assumption already  made when choosing the parameterization of the energy (68).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' While identification of the thermodynamic entropy  can be done only at the equilibrium, the function S ( f) = −kBH( f) can be considered as the non-equilibrium entropy  density whenever the distribution function f differs from the global equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The Boltzmann H-theorem about  the non-positive H-function production and non-increase of H can be considered as the specific realization of the  thermodynamic concept of the entropy increase due to irreversible processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' From Boltzmann equation to hydrodynamics  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Fields and fluxes  In this section, we use Cartesian coordinate notation, ∂α = ∂/∂xα, where α labels the three coordinate directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  We address in this section the thirteen fields of interest: the density ρ, momentum ρu, full pressure tensor P and  14  energy flux Z are defined as follows,  ρ = m  �  fdv,  (76)  ρuα = m  �  vα fdv,  (77)  Pαβ = m  �  vαvβ fdv,  (78)  Zα = m  2  �  vαv2 fdv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (79)  Identifying pressure p as  p = 1  3  �  m(v − u)2 fdv,  (80)  the pressure tensor (78) and the energy flux (79) are decomposed as follows when measuring particle’s velocity relative  to the flow velocity u,  Pαβ = pδαβ + σαβ + ρuαuβ,  (81)  Zα =  �5  2 p + 1  2ρu2  �  uα + σαβuβ + qα,  (82)  where nonequilibrium stress tensor σ and heat flux q are defined as  σαβ = m  � �  (vα − uα)(vβ − uβ) − 1  3δαβ(v − u)2  �  fdv,  (83)  qα = m  2  �  (vα − uα)(v − u)2 fdv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (84)  Rank two symmetric tensor σ is trace-free.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Finally, temperature T is defined by the equation of state of ideal gas,  p = ρRT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (85)  Density ρ, flow velocity u, temperature T, nonequilibrium stress σ and heat flux q are the thirteen fields of Grad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Balance equations for thirteen moments  Introducing the material derivative along streamline,  Dt = ∂t + uα∂α,  (86)  we write kinetic equation in the co-moving reference frame,  Dt f = −(vα − uα)∂α f + JB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (87)  Here and below, summation convention is always understood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Multiplying (87) with 1, vα, vαvβ and vαv2 and integrat-  ing over velocities, we come to the set of exact balance equations for the thirteen Grad’s fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Balance equations for  the locally conserved fields (mass-momentum-energy) imply  Dtρ = −ρ(∂αuα),  (88)  Dtuα = −1  ρ∂αp − 1  ρ∂βσαβ,  (89)  DtT = −2  3T(∂αuα) − 2  3  �T  p  �  σαβ(∂βuα) − 2  3  �T  p  �  (∂αqα).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (90)  15  The nonequilibrium stress and heat flux are the only nonequilibrium fluxes engaged in the balance equations (89) and  (90), and we continue with writing down the exact balance equations for σ and q:  Dtσαβ = − p  �  ∂αuβ + ∂βuα − 2  3δαβ∂γuγ  �  −  �  σαγ∂γuβ + σβγ∂γuα − 2  3δαβσµν∂νuµ  �  − σαβ  �  ∂γuγ  �  − 2∂γ  �  Qαβγ − 1  3δαβqγ  �  + Rσ  αβ,  (91)  Dtqα = −qα∂βuβ − qβ∂βuα + 5  2RT∂αp + 5  2RT∂βσαβ + 1  ρσαβ∂βp + 1  ρσαβ∂γσγβ  − ∂βTαβ − 2Qαβγ∂γuβ + Rq  α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (92)  Here, symmetric rank three tensor Q and symmetric rank two tensor T are,  Qαβγ = m  2  �  (vα − uα)(vβ − uβ)(vγ − uγ) fdv,  (93)  Tαβ = m  2  �  (vα − uα)(vβ − uβ)(v − u)2 fdv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (94)  For brevity, we refer to them as the Q-flux and the T-flux, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The Q-flux is engaged as a divergence in the  stress balance (91) and as a source term in the heat flux balance (92) while the T-flux contributes as a divergence in  the heat flux balance only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The heat flux and the Q-flux are connected through,  qα = Qαββ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (95)  Furthermore, the relaxation terms are defined as rates over collisions,  Rq  α = m  2  �  (vα − uα)(v − u)2JBdv,  (96)  Rσ  αβ = m  � �  (vα − uα)(vβ − uβ) − 1  3δαβ(v − u)2  �  JBdv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (97)  Balance equations are identities and cannot be addressed unless a constitutive relation is provided for both the Q- and  T-fluxes, as well as for the collision rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Local equilibrium projection  The balance equations for the locally conserved fields density (88), flow velocity (89) and temperature (90) become  the equations of hydrodynamics once constitutive relations are supplied for the nonequilibrium pressure tensor (83)  and heat flux (84).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Evaluation of these fluxes on the local equilibrium (70) returns,  σαβ[ f eq] = 0, qα[ f eq] = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (98)  This implies the Euler’s equations of non-viscous, thermally non-conductive fluid,  DE  t ρ = −ρ(∂αuα),  (99)  DE  t uα = −1  ρ∂αp,  (100)  DE  t T = −2  3T(∂αuα).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (101)  The local equilibrium projection thus amounts to a neglect of any equilibration process, so that the distribution func-  tion never leaves the submanifold of local Maxwellians while the parameters of the local Maxwellian evolve according  to Euler’s equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This can be viewed as an analogy to the ideal quasi-equilibrium reversible processes in thermo-  dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Addressing the equilibration processes towards the local equilibrium states is thus needed to obtain a more  realistic picture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  16  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Dynamic correction to the local equilibrium projection  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Estimates from the Maxwell-Boltzmann distribution  We shall first do a few ”back-of-the-envelope” estimates concerning the Boltzmann equation and transport phe-  nomena.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' We shall often use ∼ instead of = in these estimates, meaning that a more accurate computation shall bring  numerical factors of order one but the estimates below will be valid ”on the order of magnitude”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  The dimension of the distribution function f is  f ∼  1  velocity3 ×  1  volume ∼  1  (cm/sec)3 ×  1  cm3 ,  (102)  which is consistent with the fact that dN = f(v, x, t)d3vd3x is the number of particles in the element of the phase-space  volume d3vd3x ∼ (cm/sec)3 × cm3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  We now need some characteristic values for the velocity and the volume to make things non-dimensional.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Let us  look at the Maxwell-Boltzmann distribution function (70).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The factor in front the exponential is ∼ nv−3  T , where  vT =  √  RT,  (103)  has the dimension of the velocity, vT ∼ (cm/sec).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' We shall call it the thermal speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Other characteristic velocities  may be defined such as the r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' of the velocity fluctuations about the mean velocity u is vr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='s =  √  3RT or the speed  of sound cs = √5RT/3, or the mean absolute value of the velocity fluctuation vm = √8RT/π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' They all differ by a  factor of order one from the thermal speed (103).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Introducing the reduced peculiar velocity (this term is universally  used, and means simply the deviation of the molecular velocity from the flow velocity u),  C = v − u  vT  ,  (104)  the Maxwell-Boltzmann distribution becomes,  M =  n  (2π)3/2v3  T  e− C2  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (105)  We shall use vT to reduce all molecular velocities in the sequel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Of course, the temperature and the density (and the  flow velocity) in the local Maxwell-Boltzmann distribution may vary in space and time, so we are talking about some  characteristic number-density and temperature when using them for non-dimensionalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Mean free path  Mean free path is defined as the average distance traveled by a particel before it comes to a collision with some  other particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For the hard-sphere model of collision, the number density n and the diameter of the hart-spehere d can  be combined to give the quantity with the dimension of the distance,  lm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' ∼  1  d2n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (106)  The estimate of the mean free path (106) is intuitively clear, as we expect lm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' to decrease with the increase of the  scattering cross-section ∼ d2 and with the increase of the density of scattering centers n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' More accurate definitions  of lm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' are available, in particular, upon the exact estimate of the number of binary collisions from the Bolztmann  collision integral [11] but the above estimate is sufficient for our purpose here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Estimates from the Boltzmann collision integral  We now reduce the Boltzmann collision integral for hard-spheres (46).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' We first make the distribution function  dimensionless by reducing it with some typical thermal speed and number density, ¯f = v3  Tn−1 f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Furthermore, we  introduce the dimensionless scattering kernel, d2vT ¯B = B, so that ¯B depends only on the reduced relative velocity,  | ¯v1 − ¯v| = v−1  T |v1 − v|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Finally, reducing the element d3v1 = v3  Td3¯v, we obtain  JB = (d2n)vT(nv−3  T ) ¯JB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (107)  17  where ¯  JB is dimension-less,  ¯  JB =  �  R3  �  S 2  � ¯f ′ ¯f ′  1 − ¯f ¯f1  � ¯Kd2e′d3¯v1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (108)  Using the definition of the mean free path (106), this is also  JB =  vT  lm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (nv−3  T ) ¯  JB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (109)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Reduced Boltzmann equation  Now we turn to the left hand side of the Boltzmann equation and introduce the reduced time and space, t = T ¯t,  x = L¯x, with some characteristic macroscopic length L and time T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Using the scaled collision integral (109), and also  using the reduced flow velocity, u = (L/T)¯u, the Boltzmann equation is written in the reduced variables,  � L  TvT  �  ¯Dt ¯f +  �  ¯vα −  � L  TvT  �  ¯uα  �  ¯∂α ¯f =  �  L  lm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  �  ¯JB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (110)  The dimensionless quantity, inverse of which multiplies the collision integral is called the Knudsen number,  [Kn] = lm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  L  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (111)  On the other hand, the dimensionless quantity which multiplies the time derivative is called the kinetic Strouhal  number,  [St] =  L  TvT  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (112)  With this, the reduced Boltzmann equation is written,  [St] ¯Dt ¯f + (¯vα − [St]¯uα) ¯∂α ¯f =  1  [Kn]  ¯JB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (113)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Hydrodynamic limit  The hydrodynamic limit of the Boltzmann equation corresponds to a flows featuring a small Knudsen number,  when the mean free path is small compared to a typical time-space variation of hydrodynamic fields (local density,  flow velocity and temperature).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A typical estimate of Knudsen number for our ”daily life” flows is of the order of  [Kn] ∼ 10−5 − 10−6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In the classical case considered below, the Strouhal number is considered to be of the order one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  A related quantity is the Mach number,  [Ma] =  L  Tcs  ,  (114)  where cs = √γRT, γ = 5/3 is the adiabatic exponent of Boltzmann’s gas (monatomic particles without internal  degrees of freedom).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Since the speed of sound is of same order as thermal speed, we assume [Ma] ∼ [SM].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In  summary, the standard hydrodynamic limit assumes the following scaling,  [Kn] ≪ 1, [Ma] ∼ [St] ∼ O(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (115)  In that case, the hydrodynamic limit of the Boltzmann equation leads to a compressible flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' On the other hand,  different other scaling can be also considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In particular, if the Strouhal number, the Knudsen number but also the  Mach number are small and of same order,  [Kn] ∼ [St] ∼ [Ma] ≪ 1,  (116)  then the hydrodynamic limit of the Boltzmann equation corresponds to a nearly-incompressible flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Notice, however  that this latter scaling requires a really slow flow;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' in a typical situation, S t ∼ Ma ∼ 10−2 −10−1 are small, but still they  are much larger than a typical Knudsen number by a few orders of magnitude).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Before proceeding with the analysis of  the hydrodynamic limit in a systematic fashion, we shall consider quantitatively on the example of viscous transport  how the transport phenomena on a conventional macroscopic scale arises from kinetic considerations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  18  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Elementary derivation of viscosity  Using the above estimates for the thermal speed and the mean free path, we shall first derive the phenomenon  of dissipative transport focusing on the viscosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Since the mean free path is what is related to the collisions and  bearing in mind that all the dissipation comes from the Boltzmann collision integral, we may guess that the viscosity  is related to it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Let us therefore consider a gas flow parallel to the plane z = 0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' the flow velocity is supposed to depend  only on the vertical coordinate z, thus we have ux(z), uy = uz = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The latter particularly means that there is no net  flow in the vertical direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The vertical transport of the momentum is therefore effected by the z-component of  the particle’s velocity, and since there is no net velocity in that direction, it can be estimated as being of the order of  root-mean-square of the z-component of particle’s velocity vz, that is, proportional to the thermal speed vT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  In order to estimate the net transport of the x-component of momentum through a plane parallel to (x, y)-plane  (say, the plane z = 0), we need to consider two layers of gas distanced by the order of mean free path lm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' on both  sides of this plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Considering the z = 0 plane, the transferred x-momentum at the location z = −lm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' in the positive  z-direction (towards the z = 0 plane) per unit of time is thus estimated as  P+  xz ∼ vT × ρux(z)|z=−lm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='.  (117)  Note that we could write here a prefactor 1/2 since it is the half of the of the particles on average which have the  positive component of z-velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' We shall omit all such factors in the present rough estimate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Similarly, the x-momentum transported in the negative direction from the layer above the z = 0 plane towards that  plane is  P−  xz ∼ −vT × ρux(z)|z=lm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='.  (118)  The net transported momentum per unit of time from both the sides of the plane z = 0 becomes, assuming the mean  free path is small on the scale of a variation of the net velocity,  Pxz = P+  xz + P−  xz ∼ −(ρvTlm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' )dux(z)  dz  �����z=0  (119)  This net transported momentum per unit of time is equivalent to the force (per unit area) exerted parallel to x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This  force has the form of the usual viscous stress, where the coefficient of viscosity is found from our ”back-of-the-  envelope” estimate as  µ ∼ ρvTlm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='.  (120)  Note that the usual kinematic viscosity ν = µ/ρ is ν ∼ vTlm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' ∼ cm2/sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Using the above result for the mean free  path, we obtain,  µ = ¯bm  √  RT  d2  ,  (121)  where the non-dimensional coefficient ¯b (pure number) is of the order one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A rigorous estimate from the Boltzmann  equation gives ¯b ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='179, however the dependence of the viscosity coefficient on the temperature, particle’s mass and  the diameter of the hard-sphere stays as in the estimate (121) obtained by simple argument.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' From the above elementary  consideration we can already derive a classical result that the coefficient of the viscosity is not dependent on the  number density n, which is a well-verified experimental fact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' It is also interesting to note the inverse proportionality  to the cross-section of the hard-sphere in the result (121), as it may seem counter-intuitive at a first glance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Indeed, it  seems plausible that ”bigger” spheres should result in a ”higher” viscosity, contrary to what (121) suggests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' However,  the right interpretation is restored when one remembers that the mean free path becomes shorter if the cross-section  is increased.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Singularly perturbed Boltzmann equation  In accord with the scaling (115), we write the Boltzmann equation in the co-moving frame, introducing a formal  large parameter 1/ϵ in front of the collision integral,  Dt f = −(cβ − uβ)∂β f + 1  ϵ JB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (122)  19  Such a form is called a singularly perturbed system because a small parameter ϵ multiplies the derivative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For what  will follow, it is useful to remember the balance equations for the number (or mass) density, flow momentum, and  energy, already mentioned above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' At this stage,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' you may already guess that if the distribution function used to close  the balance equations is taken as the local Maxwell-Boltzmann distribution,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' then the non-equilibrium pressure tensor  and heat flux vanish,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' and the balance equations become the Euler compressible equations where in the right hand side  of the flow velocity equation we see the nonlinear advection term and the gradient of the pressure (ideal gas equation  of state),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' while in the right hand side of the temperature equation there are the advection term and the compression  work term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' We shall obtain this in a more systematic way below when we shall consider a correction to the local  Maxwell-Boltzmann distribution due to collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Normal solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The invariance principle  Following the notion introduced by D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Hilbert (1913), a normal solution is a distribution function which depends  on the space and the time only through its (yet unknown) dependence on the locally conserved fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  fnr(v, x, t) = fnr(v;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' ρ(x, t), u(x, t), T(x, t)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (123)  Normal solutions satisfy two important conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Consistency conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Whatever the dependence on the local fields ρ(x, t), u(x, t), and T(x, t) may be found in fnr,  it has to satisfy the following,  �  mfnr(v;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' ρ, u, T)d3v = ρ,  (124)  �  vmfnr(v;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' ρ, u, T)d3v = ρu,  (125)  � mv2  2  fnr(v;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' ρ, u, T)d3v = 3  2ρRT + ρu2  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (126)  Consistency condition means that if we evaluate density, momentum and energy on a given normal solution fnr, the  result must be the same values, as the corresponding arguments of the normal solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Invariance condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' So, if the normal solution depends only on the local conservations, at every point in space  and at each instant of time, then so does also its time derivative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' That means we have to express the time derivative  of the distribution function through the time derivative of the locally conserved fields (density, flow velocity and  temperature).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' So, the normal solution should satisfy the invariance condition: By chain rule of differentiation  ∂fnr  ∂ρ Dtρ + ∂fnr  ∂uα  Dtuα + ∂fnr  ∂T DtT = −(vα − uα)∂α fnr + 1  ϵ JB( fnr),  (127)  where the time derivative of the locally conserved fields are obtained with the same fnr (that is, the nonequilibrium  pressure tensor and heat flux are evaluated on the same normal solution).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  ∂fnr  ∂ρ (−ρ∂αuα) + ∂fnr  ∂uα �  −1  ρ∂αp − 1  ρ∂βσαβ[ fnr]  �  + ∂ fnr  ∂T  �  −2  3T∂αuα − 2  3  �T  p  �  σαβ[ fnr]∂βuα − 2  3  �T  p  �  ∂αqα[ fnr]  �  = −(vα − uα)∂α fnr + 1  ϵ JB( fnr),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (128)  Note that because the dependence of the time derivatives in the left hand side on the distribution function is linear,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  the overall nonlinearity of the invariance condition in f is quadratic - because of the quadratic Boltzmann collision on  the right but also because of the quadratic dependencies through the nonequilibrium pressure tensor σ[ fnr] and heat  flux q[ fnr] in the balance equations for flow velocity and temperature on the left.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The advantage of this ”increase of  complexity” is that the ”real” time derivative is excluded in favor of space derivatives coming from the fluxes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This  will immediately pay off below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  20  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The Chapman–Enskog method  Owing to the fact that there is a large parameter 1/ϵ, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Enskog (1917) suggested to look for the normal solution in  terms of a series for the distribution function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This method of solving the invariance equation of the previous section  was in fact discovered by Enskog and was made widely known as the Chapman–Enskog method by S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Chapman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The  normal solution is then expanded into a series,  fnr = f (0) + ϵ f (1) + O(ϵ2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (129)  Accordingly, the non-equilibrium pressure tensor and heat flux are expanded as  σαβ[ fnr] = σαβ[ f (0)] + ϵσαβ[ f (1)] + O(ϵ2),  (130)  qβ[ fnr] = qβ[ f (0)] + ϵqβ[ f (1)] + O(ϵ2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (131)  Substituting these two expansions into the left and right hand sides of the invariance equation, and equating terms of  same order in ε, we obtain on the order ϵ0,  JB( f (0)) = 0,  (132)  and on the order ϵ,  ∂ f (0)  ∂n D(0)  t ρ + ∂ f (0)  ∂uα  D(0)  t uα + ∂f (0)  ∂T D(0)  t T + (vα − uα)∂α f (0) = L f (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (133)  Here the material derivatives indicated as ”(0)” are understood in the sense that the zeroth-order distribution f (0) is  used to evaluate the non-equilibrium pressure tensor and the heat flux,  D(0)  t ρ = −ρ∂αuα,  (134)  D(0)  t uα = −1  ρ∂α(ρRT) − 1  ρ∂βσαβ[ f (0)],  (135)  D(0)  t T = −2  3T∂αuα −  2  3Rρ pαβ[f (0)]∂βuα −  2  3Rρ∂βqβ[ f (0)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (136)  Furthermore, the derivative of the Boltzmann collision operator at the zeroth order distribution, L, is the linearized  collision integral,  L f (1) =  �  R3  �  S 2  �  f (0)′  1  f (1)′ + f (0)′ f (1)′  1  − f (0)  1  f (1) − f (0) f (1)  1  � ¯Bd2e′d3¯v1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (137)  Since we shall deal with only these orders of the Chapman-Enskog expansion, we shall not write the next terms of  higher-order in ε (although we shall discuss them briefly at the end).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Finally, we need to expand also the consistency conditions:  �  {m, mv, mv2/2} f (0)d3v = {ρ, ρu, (3/2)ρRT + ρu2/2},  (138)  �  {m, mv, mv2/2} f (k)d3v = 0, k ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (139)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Euler’s compressible flow equations  On the zeroth order, we must have the velocity distribution which annuls the Boltzmann collision integral;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' That is  it is a local Maxwell-Boltzmann distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Then, the nonequilibrium pressure tensor and the heat flux are vanishing  on this approximation,  σαβ[ f (0)] = 0, qα[ f (0)] = 0,  (140)  and the closed-form equations for the density, flow velocity and temperature become the Euler compressible flow  equations, (99), (100) and (101),  D(0)  t ρ = DE  t ρ,  (141)  D(0)  t uα = DE  t uα,  (142)  D(0)  t T = DE  t T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (143)  But now we have the Euler equations as the lowest-order approximation to the hydrodynamic equations, while these  time-derivatives generate the correction which we now discuss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  21  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Navier-Stokes and Fourier compressible flow equations  We shall now set up the equation for f (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' You may find it a bit tedious, even though these are just simple algebraic  manipulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' So let us do it step-by-step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Evaluation of the derivatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' We first compute the derivatives of the local Maxwell-Boltzmann distribution with  respect to the five hydrodynamic fields,  ∂ f eq  ∂ρ = 1  ρ f eq,  (144)  ∂ f eq  ∂uα  = (cα − uα)  RT  f eq,  (145)  ∂ f eq  ∂T  = 1  T  �(v − u)2  2RT  − 3  2  �  f eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (146)  Evaluation of the Boltzmann equation vector field on the local Maxwell-Boltzmann distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Using the above  derivatives, we next compute the term (vα − uα)∂α f eq,  (vα − uα)∂α f eq =  ∂f eq  ∂ρ (vα − uα)∂αρ + ∂f eq  ∂uβ  (vα − uα)∂αuβ + ∂f eq  ∂T (vα − uα)∂αT =  f eq  �1  ρ(vβ − uβ)∂βρ + 1  RT (vα − uα)(vβ − uβ)∂βuα + 1  T  �(v − u)2  2RT  − 3  2  �  (vα − uα)∂αT  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (147)  Note that the combinations ∼ vαvβ and ∼ vαv2, related to nonequilibrium pressure tensor and heat flux, start popping  out in this expression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Evaluation of the time derivative of the local Maxwell-Boltzmann distribution due to the Euler system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This is the  last place we need to evaluate the derivatives due to the Euler equations;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  ∂f eq  ∂ρ D(0)  t ρ + ∂f eq  ∂uα  D(0)  t uα + ∂f eq  ∂T D(0)  t T =  ∂f eq  ∂ρ DE  t ρ + ∂ f eq  ∂uα  DE  t uα + ∂ f eq  ∂T DE  t T =  f eq 1  ρ (−ρ∂αuα) + f eq (cα − uα)  RT  �  −1  ρ∂α(ρRT)  �  + f eq 1  T  �(v − u)2  2RT  − 3  2  � �  −2  3T∂αuα  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (148)  Invariance defect of the local Maxwell-Boltzmann distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The sum of the two above expressions, (147) and  (148), is so important that it deserves a name of its own.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' We call it the defect of invariance of the local Maxwell-  Boltzmann distribution function with respect to the Boltzmann equation,  ∆M = ∂f eq  ∂ρ D(0)  t ρ + ∂f eq  ∂uα  D(0)  t uα + ∂f eq  ∂T ∂(0)  t T + (vβ − uβ)∂β f eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (149)  The first Chapman-Enskog equation (133) now reads,  L f (1) = ∆M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (150)  The defect of invariance tells us whether or not the local Maxwell-Boltzmann distribution solves the Boltzmann  equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' If ∆M = 0, then the initial condition taken as f eq progresses in time due to the Boltzmann equation without  changing its Gaussian shape, only the density, flow velocity and temperature alter in time and space due to the Euler  system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In such case the manifold of the local Maxwell-Boltzmann distributions (all such distributions with different  22  macroscopic parameters) is said to be invariant of the Boltzmann equation, and the first (and higher) order Chapman–  Enskog corrections (f (1), f (2) etc) are all vanishing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' So let us compute the invariance defect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Adding the above two  expressions, we have (after a lot of cancellations),  ∆M = f eq  � 1  RT  �  (cα − uα)(cβ − uβ) − 1  3δαβ(v − u)2  �  (∂αuβ)  �  + f eq  � 1  T  �(v − u)2  2RT  − 5  2  �  (cβ − uβ)∂βT  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (151)  Let’s briefly discuss this result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The invariance defect consists of two parts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The first part drives the distribution  function away from the local Maxwellian due to the inhomogeneity of the flow velocity ∼ ∂αuβ, which results in the  viscosity phenomena.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The second part is due to the inhomogeneity of the temperature of the fluid ∼ ∂βT, which results  in thermal conduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Thus, the local Maxwell–Boltzmann distribution can be a solution to the Boltzmann equation  only if the velocity of the flow and the temperature field are space-independent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Notice also that the invariance defect  does not depend on a space derivative of the density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This reflects the fact that the non-equilibrium phenomena in  the single-component gas do not give rise to any diffusion phenomena (in a mixture of several gases it does).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The  solution to the Boltzmann equation may exist in a form of a local Maxwell–Boltzmann distribution but only if the flow  is moving with a uniform velocity and the temperature also stays uniform (the density then obeys ∂tρ = −uα∂αρ) but  they are of no physical relevance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Further on, note that the invariance defect is Galilean invariant, that is, it depends  only on the particles velocity in the reference frame of the flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Finally, we immediately note that the defect is a truly  non-equilibrium driver, as it does not change any value of neither density, nor flow velocity, nor the energy because,  �  ∆Md3v =  �  v∆Md3v =  �  v2∆Md3v = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (152)  What it does change are the fluxes of these quantities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' We now need a final step in setting up the first Chapman–Enskog  equation, a discussion of the linearized collision integral.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Linearized collision integral.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' It is very convenient and customary to write the correction to the local Maxwell-  Boltzmann distribution function in the form  f (1) = f eqϕ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (153)  Then the linearized Boltzmann collision integral is transformed by noting that the products of the equilibria factor out  due to the detail balance, and we have,  L f (1) = f eq  �  R3  �  S 2 f eq  1  �ϕ′  1 + ϕ′ − ϕ1 − ϕ� Kd2e′d3v1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (154)  Thus, we can define the linearized Boltzmann operator Λ,  Λϕ =  �  R3  �  S 2 f eq  1  �ϕ′  1 + ϕ′ − ϕ1 − ϕ� Kd2e′d3v1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (155)  The integral operator Λ has the following important properties:  Null-space of Λ: The null-space ker Λ is the linear sub-space of summatorial invariants,  Λϕ = 0 if and only if ϕ ∈ Lin{1, v, v2}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (156)  Let us define a scalar product of functions ϕ and ψ as  ⟨ψ|ϕ⟩ =  �  f eqϕψd3v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (157)  Then operator Λ is symmetric with respect to this scalar product,  ⟨ψ|Λ|ϕ⟩ = ⟨ϕ|Λ|ψ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (158)  23  Operator Λ is non-positive,  ⟨ϕ|Λ|ϕ⟩ ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (159)  Proof:  ⟨ϕ|Λ|ϕ⟩ = −1  4  �  R3×R3  �  S 2 f eq f eq  1  �ϕ′  1 + ϕ′ − ϕ1 − ϕ�2 Kd2e′d3v1d3v ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (160)  Note that, the symmetry property of operator Λ (158) and its non-positivity (160) are the ”linearized” versions of the  Boltzmann transport theorem and of the H-theorem, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  The Chapman–Enskog equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Summarizing, the results of the previous sections, the Chapman-Enskog equation  for the first correction can be written, using the reduced peculiar velocity (104),  Λϕ = (∂βuα)  �  CαCβ − 1  3δαβC2  �  +  √  RT  �∂αT  T  �  Cα  �C2  2 − 5  2  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (161)  The linear non-homogeneous integral equation (161) is the first Chapman-Enskog equation, the study of which is  exhaustively described in [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For the sake of completeness, we summarize here some major steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' By Fredholm  alternative, the linear non-homogeneous integral equation of the form (161) has a solution if the right hand side is  orthogonal to the null-space of the integral operator Λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This solvability condition is satisfied since the defect of the  invariance does not alter the density, momentum and energy (see above).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The general solution is then a specific  solution to the non-homogeneous integral equation plus a general solution to the homogeneous one, Λϕ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The  latter is the linear subspace of summatorial invariants, so we have  ϕgen = ϕspec + ϕhom,  (162)  where ϕhom ∈ Lin{1, v, v2} while ϕspec is orthogonal to conservation laws,  �  ϕspec f eq{1, v, c2}d3v = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' However, due to  the consistency condition (139) mentioned at the very beginning of the analysis, we must have  �  f (1){1, v, c2}d3v = 0,  therefore we must select ϕhom = 0 in the above general solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The Chapman-Enskog solution is thus the special  solution to the above integral equation (161).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Now we look at the tensorial dimension of the right hand side of (161) and immediately realize that, since the  function ϕ is a scalar, the solution can depend on the particle’s velocity in only one possible way,  ϕ = A(C)Cα  √  RT  �∂αT  T  �  + B(C)  �  CαCβ − 1  3δαβC2  �  (∂βuα),  (163)  where two scalar functions, A and B can depend only on the magnitude of reduced velocity, temperature and density  while A satisfies the orthogonality condition,  �  e− C2  2 A(C)C2d3C = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  The Chapman-Enskog functions A and B are found from two integral equations,  Λ (ACα) = Cα  �C2  2 − 5  2  �  ,  (164)  Λ  �  B  �  CαCβ − 1  3δαβC2  ��  =  �  CαCβ − 1  3δαβC2  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (165)  Apart from Maxwell’s molecules, for which A and B do not depend on C, appropriate technique of solving (164) and  (165) is based on Sonine polynomial expansion [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Here we shall perform a merely dimensional analysis of (164)  and (165) in order to understand the relation between transport coefficients and specific models of particles interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  24  Dimensional analysis of Chapman–Enskog equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Since the Chapman–Enskog solution ϕ (161) is a non-dimensional  quantity, the proper dimension of the Chapman–Enskog functions A and B is that of the time,  [A] = [B] ∼ sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (166)  Furthermore, since the right hand side of the Chapman–Enskog equations (164) and (165) is also non-dimensional,  we can introduce a relaxation time τ so that  A = τ ¯A, B = τ ¯B,  (167)  where functions ¯A(C) and ¯B(C) are dimensionless.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Evaluation of the relaxation time is based on the dimensional analysis of the linearized collision integral for each  specific binary collision mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For hard spheres, with the collision kernel (42), we write  ΛHS =  �  nd2 √  RT  � ¯ΛHS ,  (168)  where ¯ΛHS is a non-dimensional linearized Boltzmann operator for hard spheres,  ¯ΛHS ϕ =  1  4(2π)3/2  �  R3  �  S 2 e−C2  1/2 �ϕ′  1 + ϕ′ − ϕ1 − ϕ� |C1 − C|d2e′d3C1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (169)  Thus, for hard spheres, the relaxation time is defined as the inverse of the prefactor in (168),  τHS =  1  nd2 √  RT  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (170)  One can readily recognize the earlier estimate of the mean free path in this expression, and the relaxation time is  interpreted as an average travel time between binary encounters, with a characteristic thermal speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For Maxwell’s  molecules, with the interaction potential U = κr−4, we notice that, since the collision kernel does not depend on the  relative velocity (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (44) with n = 4) the only combination of the mass m and the strength of the potential κ that  gives a proper dimension to the collision kernel is  KMM ∼  �  κ  m ∼ cm3  sec .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (171)  Consequently, the dimensional analysis of the linearized collision operator for Maxwell’s molecules gives,  ΛMM =  �  n  �  κ  m  �  ¯ΛMM,  (172)  where the non-dimensional linearized collision operator is,  ¯ΛMMϕ =  1  (2π)3/2  �  R3  �  S 2 e−C2  1/2 �ϕ′  1 + ϕ′ − ϕ1 − ϕ� ¯αd2e′d3C1,  (173)  where ¯α(θ) is a non-dimensional function of the deflection angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' From (172), we read off the relaxation time for  Maxwell’s molecules,  τMM =  √m  n √κ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (174)  It is interesting to remark here that, the mean free path for Maxwell’s molecules is proportional to the square root  of the temperature, lMM  m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='p ∼ τMMvT ∼ √kBT/(n √κ), while it is temperature-independent for hard spheres, lHS  m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' ∼  1/(nd2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In other words, the average distance traveled freely by Maxwell’s molecules between collisions increases  with the temperature of the gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Thus, by the estimate (120), the viscosity of the Maxwell’s molecules is linear in the  temperature,  µMM ∼ ρlMM  m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='vT ∼ RT  �  m3  κ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (175)  25  With the above dimensional analysis,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' we write the solution to the first Chapman–Enskog equation by introducing  the relaxation time into (163),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  ϕ = ¯A(C)Cα  �  τ  √  RT  �∂αT  T  ��  + ¯B(C)  �  CαCβ − 1  3δαβC2  � �  τ∂βuα  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (176)  where the non-dimensional functions ¯A(C) and ¯B(C) depend only on the magnitude of the reduced peculiar velocity  and are special solutions to the reduced (non-dimensional) integral equations,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  2 ¯Λ  ��� ¯ACα  �  =  ����Cα  �  C2 − 5  ��  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (177)  ¯Λ  ���� ¯B  �  3CαCβ − δαβC2��  =  ���3CαCβ − δαβC2�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (178)  We shall now proceed with the general form of the first Chapman-Enskog correction (176) to evaluate the non-  equilibrium pressure tensor and the heat flux vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Viscosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' We are now able to evaluate the nonequilibrium fluxes for a generic collision model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Let’s start with the  nonequilibrium pressure tensor,  σ(1)  αβ = m  �  vαvβ f eqϕd3v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (179)  With (176), we find  σ(1)  αβ = −µΠαβ,  (180)  where Παβ is the rate-of-shear tensor,  Παβ = ∂αuβ + ∂αuβ − 2  3δαβ∂γuγ,  (181)  while µ is the viscosity,  µ = ¯bτp,  (182)  with the coefficient ¯b (pure number) expressed in terms of the Chapman–Enskog function ¯B as,  ¯b = −1  5(2π)−3/2  �  e−C2/2 ¯B  �  CαCβ − 1  3δαβC2  � �  CβCα − 1  3δβαC2  �  d3C > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (183)  The latter inequality follows immediately from the definition of the function ¯B (178) and the entropy production  inequality (160): Indeed, the integral in (183) is proportional to the inner product,  �  ¯B  �  CαCβ − 1  3δαβC2� �����CβCα − 1  3δβαC2  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Hence, from the definition (178), we have  �  ¯B  �  CαCβ − 1  3δαβC2� �����CβCα − 1  3δβαC2  �  =  �  ¯B  �  CαCβ − 1  3δαβC2� ����� ¯Λ  ����� ¯B  �  CβCα − 1  3δβαC2��  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Thermal conduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Similarly, we evaluate the non-equilibrium heat flux,  q(1)  α = m  2  �  (v − u)2(vα − uα) f eqϕd3v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (184)  Substituting the solution ϕ (176), we get the nonequilibrium heat flux in the form of the Fourier law,  q(1)  α = −λ∂αT,  (185)  where λ is the coefficient of thermal conduction,  λ = ¯aτRp,  (186)  and the coefficient ¯a (pure number) is given by a quadrature similar to (183),  ¯a = −1  6(2π)−3/2  �  e−C2/2 ¯AC4d3C > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (187)  26  Transport coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Evaluation of the function B for specific collision models is based on a Sonine polynomial  expansion, and is exhaustively studied in the classical text by Chapman and Cowling [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For hard spheres, using the  relaxation time (170), the lowest-order Sonine polynomial expansion results in  µ0 = ¯b0  m  √  RT  d2  ,  (188)  where the ¯b0 (pure number) is  ¯b0 =  5  16 √π ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='176.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (189)  The dependence of the viscosity on the temperature and on the diameter of hard sphere has been already found by  elementary considerations, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (121).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The lowest-order Sonine polynomial approximation (188) is only insignificantly  lower than the more accurate result ¯b ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='179 when more terms of the Sonine polynomial expansion are evaluated  [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For Maxwell’s molecules, using the mean free path (174), the viscosity is obtained as  µ = ¯bRT  �  m3  κ ,  (190)  where the exact value of the constant ¯b is [11],  ¯b =  √  2  3πA2(5) ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='344,  (191)  where A2(5) ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='436 [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Apart from the pure constant ¯b (191), the dependence of the viscosity on the temperature,  particle’s mass and the strength of the interaction potential strength was already obtained by elementary considerations  above, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (175).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The thermal conduction coefficient (186) can be written in the following suggestive way,  λ = cpPr−1µ,  (192)  where cp is the specific heat of ideal gas of monatomic molecules,  cp = 5  2R,  (193)  while Pr is the Prandtl number,  Pr = cpµ  λ  =  ¯b  ¯a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (194)  The first-order Sonine polynomial approximation results in the Prandtl number [11],  Pr0 = 2  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (195)  For Maxwell molecules, the Prantl number (195) is the exact result while for hard spheres Pr = 2/3 is only slightly  lower than the exact value [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Correction to the Euler system: The Navier-Stokes equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Summarizing the above, the correction to the local  equilibrium approximation results in the following balance equations for mass, momentum and energy,  DNS  t  ρ = −ρ(∂αuα),  (196)  DNS  t  uα = −1  ρ∂αp + 1  ρ∂β  �  εµΠαβ  �  ,  (197)  DNS  t  T = −2  3T(∂αuα) + 2  3  �T  p  � �  εµΠαβ  �  (∂βuα) + 2  3  �T  p  �  ∂α (ελ∂αT) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (198)  Comments are in order:  27  The correction to the local equilibrium approximation results in the Navier–Stokes–Fourier system for com-  pressible ideal gas, with the caloric equation of state featured by the specific heat at constant volume cv = (3/2)R  and Prantl number close to Pr = 2/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The result of the derivation has led to the microscopic expressions for the  coefficients of viscosity and thermal conductivity which can be computed from any given molecular interaction  in the Boltzmann equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  It is important to keep the smallness parameter ε in the above expressions for the non-equilibrium fluxes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Higher-order corrections, the Burnett (ϵ2) and the super-Burnett (ϵ3) systems remained controversial as they  violate the stability of the equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Hilbert’s 6th problem: Hilbert proposed to derive ”mathematically the limiting processes .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' which lead from the  atomistic view to the laws of motion of continua” (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' [13, 14] and references therein).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The issue Hilbert  was addressing, namely to use the atomistic theory of his day represented by Boltzmann’s kinetic theory of  gases and a passage via a limiting process to the continuum theory of compressible Euler system as the Knudsen  number approaches zero, or to the Navier-Stokes-Fourier system, if small corrections are allowed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The problem  is however, that without a priori knowledge about solutions to Euler or Navier-Stokes-Fourier equations are, one  cannot in general prove that Boltzmann’s kinetics converges to these continuum models [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The resolution  likely requires addressing other continuum theories, one current candidate is Korteweg-like [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Interested  reader is directed to [13, 14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Lifting the local equilibrium projection: BGK kinetic model  The correction to the Euler system considered above explores more of the phase space than it was assumed by the  local equilibrium projection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' By measuring the defect of invariance of the local equilibrium we find in which direction  the local equilibrium approximation should be corrected in order to take into account the fast motion towards it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' There  is another way to explore the fast motions: To lift the dynamics to the full phase space by means of a kinetic model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  The lifting of the Euler dynamics which takes place on the local Maxwell manifold to a kinetics in the whole phase  space is done by the very useful Bhatnagar–Gross–Krook model (BGK),  ∂t f + v · ∇ f = −1  τ( f − f eq( f)),  (199)  where τ > 0 is the relaxation time, and f eq( f) is a map f → f eq established by local conservation laws,  �  {1, v, v2}( f − f eq( f))dv = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (200)  The right hand side of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (199),  JBGK = −1  τ( f − f eq(f)),  (201)  is called the BGK collision integral.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Proof of the H-theorem for the BGK kinetic equation does not rely anymore  on the microscopic reversibility as in the Boltzmann case, instead, it is a simple consequence of convexity of the  H-function, and of the property of the map (200):  σ = −1  τ  �  ln f( f − f eq( f))d3v = −1  τ  �  ln  �  f  f eq( f)  �  ( f − f eq( f))d3v ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (202)  When the BGK relaxation model is used instead of the Boltzmann collision operator in finding the correction to  the local equilibrium projection, the Chapman–Enskog equation (150) becomes,  − 1  τ f (1) = ∆M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (203)  Thus, the Chapman-Enskog solution is given by (176) with the Chapman–Enskog functions (177) and (178) as  ¯ABGK = −  �C2  2 − 5  2  �  ,  (204)  ¯BBGK = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (205)  28  The resulting Navier–Stokes–Fourier equations feature the following coefficients of viscosity and thermal conduction,  µBGK = τp,  (206)  λBGK = τcpp,  (207)  resulting in the BGK Prandtl number,  PrBGK = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (208)  The restriction to Prandtl number PrBGK = 1 arises from the fact that no intermediate states of relaxation towards the  local equilibrium are addressed by the BGK kinetic model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This issue shall be considered below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Prior to that, we  need to extend the notion of projection onto a wider class of specified states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Grad’s thirteen-moments projection  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Grad’s thirteen-moments distribution function  Grad, in his seminal paper of 1949 [15], derived moment systems by projecting the Boltzmann equation onto  an ansatz for the distribution function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Grad considered two sets of moments, and what will be referred to as G13  and G20, with the number indicating how many fields are included.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In G13, these are the locally conserved density,  momentum and energy plus the nonequilibrium stress tensor and energy flux vector, while G20, a more symmetric  system, includes the full third-order flux of the pressure tensor instead of the energy flux vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Grad’s method  was influential in many ways, far beyond applications to rarefied gas dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' It was the touchstone for numerous  developments in nonequilibrium thermodynamics (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' [16, 17, 18] and references cited therein).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' However,  the problem with almost any projection on a preselected (often simple) submanifold is that it is not invariant with  respect to the the detailed dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In Grad’s context, Grad’s distribution function (a polynomial around the local  Maxwellian) is not invariant with respect to the Boltzmann equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This is certainly not just the feature of Grad’s  distribution per se.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' As we have seen above, the local Maxwellian is also not invariant of the Boltzmann equation, and  the dynamic correction, well known through the Chapman-Enskog method, delivers the dissipative Navier–Stokes–  Fourier terms, missing in the the projection on the local Maxwell manifold (compressible Euler equations).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Both  correction and lifting of Grad’s G13 system shall be considered below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Following Grad [15], the distribution function providing the closure for the balance equations (91) and (92) is  written as,  G = M + N,  (209)  N = MGσ + MGq,  (210)  where M is local Maxwellian (105), and N is the nonequilibrium part,  Gσ = σαβ  2p  �  CαCβ − 1  3δαβC2  �  ,  (211)  Gq = qαCα  pvT  �C2  5 − 1  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (212)  Without engaging a discussion of possible violation of positivity, we consider Grad’s function as a submanifold in the  space of distribution functions, parameterized with the values of thirteen fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Grad’s system is the natural projection  of kinetic equation onto this submanifold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Grad’s thirteen-moments closure  Grad’s projection amounts to evaluating everything that spoils the closure in the balance equations (91) and (92)  with Grad’s distribution (209).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For the Q-fluxes (93), we get, separating the local equilibrium and nonequilibrium  contributions,  QG  αβγ = QM  αβγ + QN  αβγ,  (213)  QM  αβγ = 0,  (214)  QN  αβγ = 1  5  �  qαδβγ + qβδαγ + qγδαβ  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (215)  29  In other words, Grad’s closure for the Q-flux amounts to reducing symmetric rank three tensor to its trace (215).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For  the T-flux (94), one finds  T G  αβ = T M  αβ + T N  αβ,  (216)  T M  αβ = 5  2 pRTδαβ,  (217)  T N  αβ = 7  2RTσαβ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (218)  For the collision rates (97) and (96), there are several realizations depending on the choice of the collision or relaxation  model which we list here in the order of increasing complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A ”poor man’s” approach is to use the BGK relaxation time approximation (201);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' then one simply gets  RσG  αβ = −m  τ  � �  (vα − uα)(vβ − uβ) − 1  3δαβ(v − u)2  �  MGσdv = −1  τσαβ,  (219)  RqG  α = − m  2τ  �  (vα − uα)(v − u)2MGqdv = −1  τqα.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (220)  Similar results are obtained when using most of the relaxation kinetic models available (with more that one  relaxation time).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' While certainly far from realistic, relaxation time approximation is useful for analysis of  complex situations in order to understand the structure of otherwise involved result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For the Boltzmann’s collision integral (40), substituting Grad’s distribution function, and taking into account  the detail balance, JB(M) = 0, one gets  JB(G) = LN + O(N2),  (221)  where L is the linearized Boltzmann collision integral (137).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Computation of matrix elements of the opera-  tor (137) greatly simplifies for Maxwell’s molecules because in that case functions M[CαCβ − 1  3δαβC2] and  M[Cα(C2 − 5/2)] are eigenfunctions,  L  �  M  �  CαCβ − 1  3δαβC2  ��  = − p  µM  �  CαCβ − 1  3δαβC2  �  ,  (222)  L  �  M  �  Cα  �C2  2 − 5  2  ���  = −2p  3µM  �  Cα  �C2  2 − 5  2  ��  ,  (223)  with µ the viscosity coefficient of Maxwell’s molecules (190).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' With (222) and (223), evaluation of matrix  elements reduces to the same integrals as in the relaxation time approximation, and we get  RσG  αβ = m  � �  (vα − uα)(vβ − uβ) − 1  3δαβ(v − u)2  �  L(MGσ)dv = − p  µσαβ  (224)  RqG  α = m  2  �  (vα − uα)(v − u)2L(MGq)dv = −2p  3µqα.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (225)  It should be noted that, for Maxwell’s molecules, evaluation of the relaxation rates for various moments can  be done in closed form without specifying the distribution function, also for the nonlinear collision operator  [19, 20], and relaxation rates (224,225) are valid for the full nonlinear case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For other particle’s collision models such as hard spheres or other power law potentials, functions M[CαCβ −  1  3δαβC2] and M[Cα(C2 − 5/2)] are not eigenfunctions of linearized collision integral any longer, and evaluation  of matrix elements (224) and (225) gives instead  RσG  αβ = − p  µ0  σαβ,  (226)  RqG  α = − 2p  3µ0  qα,  (227)  30  where µ0 is not exact viscosity coefficient but rather the lowest-order Sonine polynomial approximation thereof,  cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (188).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' It is well known that first approximation µ0 is reasonably close to the exact value, in particular,  for hard spheres [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This fact, however, does not imply that corresponding eigenfunctions of linearized  Boltzmann collision integral are in any sense ”close” to those for Maxwell’s molecules, and it is therefore  misleading to judge on the quality of Grad’s approximation for hard spheres on the basis of viscosity coefficient  alone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Grad’s thirteen-moments system  Substituting Grad’s closure relations for the Q- and T-fluxes (213) and (216) into balance equations (91) and (92),  and also using any of the above realizations of the relaxation terms, one arrives at Grad’s equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For later use, it  proves convenient to partition Grad’s equations in four parts, three of which regards the non-local in space terms plus  the relaxation term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For the stress, we write  DG  t σαβ = ˙σNSF  αβ + ˙σlin  αβ + ˙σnlin  αβ + RσG  αβ ,  (228)  ˙σNSF  αβ  = −p  �  ∂αuβ + ∂βuα − 2  3δαβ∂γuγ  �  (229)  ˙σlin  αβ = −2  5  �  ∂βqα + ∂αqβ − 2  3δαβ∂γqγ  �  ,  (230)  ˙σnlin  αβ = −σαβ  �  ∂γuγ  �  −  �  σαγ∂γuβ + σβγ∂γuα − 2  3δαβσµν∂νuµ  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (231)  A comment on genesis of various terms in Grad’s equation (228) is in order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The first term, ˙σNSF  αβ  (229), is designated  Navier-Stokes-Fourier (NSF) because it linearly depends on the strain tensor and gives rise to the Navier-Stokes stress  in the first-order approximation to G13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This term appears as purely kinematic, that is, it shows up already in the  balance equation for the stress before any closure assumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The second term, ˙σlin  αβ (230) is solely produced by the  closure relation for the Q-flux (215).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' It is indicated as ”linear” since it depends linearly on the gradient of the heat  flux but not on any gradient of locally conserved fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Consequently, the term ˙σlin  αβ survives linearization around a  global equilibrium state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Finally, the nonlinear term ˙σnlin  αβ (231) is again purely kinematic and independent of Grad’s  closure assumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Grad’s heat flux equation is decomposed in a similar fashion,  DG  t qα = ˙qNSF  α  + ˙qlin  α + ˙qnlin  α  + RqG  α ,  (232)  ˙qNSF  α  = −5  2Rp∂αT,  (233)  ˙qlin  α = −RT∂βσαβ,  (234)  ˙qnlin  α  = −7  5qα∂βuβ − 7  5qβ∂βuα − 2  5qβ∂αuβ − 5  2Rσαβ∂βT + RT  ρ σαβ∂βρ + 1  ρσαβ∂γσγβ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (235)  Here, the term (5/2)RT∂αp in the balance equation (92) conspired with the local equilibrium part of the closure (217)  to produce the NSF contribution, ˙qNSF  α  (233).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' That one gives rise to the Fourier law in the first approximation, through  balancing the relaxation term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The term ˙qlin  α (234) appears with right sign thanks to Grad’s closure approximation of  the nonequilibrium part of the T-flux (218).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' We term it ”linear” for the reason explained above, even though it is  non-linear through multiplication with the temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Similarly to (230), contribution of ˙qlin  α does not vanish under  linearization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Finally, the nonlinear part of Grad’s heat flux equation, ˙qnlin  α  (235) contains a mixture of terms both  present already in the balance equation (92) and those resulting from the closure assumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Note that the ”most  nonlinear” term, (1/ρ)σαβ∂γσγβ is purely kinematic and is not affected by Grad’s closure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Hydrodynamics from Grad’s equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' When the smallness parameter is re-introduced into Grad’s equations, the  first-order correction to the Euler’s equations (σ(0) = 0, q(0) = 0) is found by balancing the first and the last terms in  (228) and (232).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Using the estimates for the relaxation rates (226) and (227), together with (229) and (233), we find  31  the nonequilibrium pressure tensor and heat flux as  σ(1)  αβ = −µ0  �  ∂αuβ + ∂βuα − 2  3δαβ∂γuγ  �  ,  (236)  q(1)  α = −15R  4 µ0∂αT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (237)  Thus, we once again derive the Navier–Stokes–Fourier system (196), (197) and (198), for the ideal gas with specific  heat at constant pressure cp = (5/2)R and Prandtl number Pr = 2/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Finally, we mention that, even when linearized, Grad’s equations (228) and (232) remain strongly coupled through  their respective linear terms, (230) and (234).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The linearized Grad’s equations can be used to study the hydrodynamic  limit beyond the Navier–Stokes–Fourier approximation by summing up a rather involved Chapman-Enskog series  expansion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Interested reader is directed to [21, 22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Quasi-equilibrium projection  Grad’s method and its variants construct closed systems of equations for macroscopic variables when the latter  are represented by moments of the distribution function f (hence their alternative name, the moment method).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A  different but closely related construction is the maximum entropy method or the quasi-equilibrium approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Let  M = {M1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' , Mk} be a finite set of moments chosen to describe the macroscopic state,  Mi(x, t) =  �  µi(v) f(v, x, t)d3v, i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' , k,  (238)  where µ1(v), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' , µk(v) are the corresponding microscopic densities of the moments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' We assume that the microscopic  densities are linearly independent and that locally conserved fields are included in the set M, that is, the linear envelope  of {µ1(v), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' , µk(v)} is included into the linear envelope of {µ1(v), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' , µk(v)},  Lin{1, v, v2} ⊂ Lin{µ1(v), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' , µk(v)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (239)  The distribution function of the quasi-equilibrium state is defined as the minimizer of the H-function (62) under the  constraint of fixed moments M,  f ∗(v, M) = argmin  �  H( f)  �����  �  µ1 fd3v = M1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' ,  �  µk fd3v = Mk  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (240)  where The family of the quasi-equilibrium distribution functions f ∗(v, M) (240) parametrically depends on the mo-  ments M and is a generalization of the local equilibrium distribution function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The latter corresponds to the choice  of M as a set of the locally conserved moments and is a subset of the distribution functions (240) by the convention  (239).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The quasi-equilibrium projection is a closed system for the target moments M,  ∂tMi + ∇ ·  �  µi(v)vf ∗(v, M)d3v =  �  µi(v)JB( f ∗(v, M))d3v, i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' , k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (241)  Important feature of the quasi-equilibrium projection is that it retains the dissipative property of the Boltzmann  equation: The quasi-equilibrium H-function,  H∗(M) =  �  f ∗(v, M) ln f ∗(v, M)d3v,  (242)  is a non-increasing function due to the moment equations (241).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This follows directly from the solution of the problem  (240) using the method of Lagrange multipliers,  f ∗ = exp  k  �  i=1  λiµi(v),  (243)  32  where λi are Lagrange multipliers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Indeed, by noticing that λi = ∂H∗/∂Mi, the production of the quasi-equilibrium  H-function (242) is obtained as,  σ∗ =  k  �  i=1  ∂H∗  ∂Mi  �  µi(v)JB( f ∗(v, M))d3v =  �  lnf ∗(v, M)JB( f ∗(v, M))d3v ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (244)  A rationale behind the maximum entropy method can be stated as follows: A state of the gas can be described by a  finite set of moments M on a time scale θ only if all the other (“fast”) moments evolve on a shorter time scale time  τ ≪ θ to their values determined by the chosen set of slow moments M, while the slow moments do not change  appreciably over the time scale τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In the process of the fast relaxation, the H-function decreases, and in the end of  this fast relaxation process a quasi-equilibrium state sets in with the distribution function being the solution of the  problem (240).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' After the fast processes reach their completion, the moments M evolve on the slow time scale by  virtue of (241).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Explicit solution to the minimization problem amounts to expressing the Lagrange multipliers in terms of the  moments upon resolving the implicit system of equations,  �  µi(v) exp  k  �  j=1  λ jµ j(v)d3v = Mi, i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' , k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (245)  While the dissipation property (244) of the quasi-equilibrium projection (241) can be demonstrated without solving  the equations for the Lagrange multipliers (245), operating equations (241) does require the knowledge of the quasi-  equilibrium distribution function f ∗(v, M) explicitly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' To that end, there is exactly one case known where the system  (245) can be inverted in a closed form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This corresponds to the moments set M = {ρ, ρu, P} where P is the pressure  tensor (78).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Using the representation (81), we can write [23, 24],  f ∗(n, u, Π) = n  ρ  3  2  (2π)  3  2 √  det Π  exp  �  −ρ  2(v − u)† · Π−1 · (v − u)  �  ,  (246)  where Π = P − ρuu is the pressure tensor in the co-moving reference frame, Παβ = pδαβ + σαβ, while the non-  equilibrium part σαβ is the trace-free tensor (83).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Vanishing of the latter returns the subset Meq = {ρ, ρu, tr[P]}, while  (246) becomes the local Maxwell–Boltzmann distribution function (70).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The quasi-equilibrium projection defined by  the distribution function (246) results in the ten-moment Grad’s approximation for a compressible, viscous but heat  non-conductive fluid (Pr → ∞), which is more conveniently written using the pressure rather than the temperature:  D∗  t ρ = −ρ∂αuα,  (247)  D∗  t uα = −1  ρ∂αp − 1  ρ∂βσαβ,  (248)  D∗  t p = −5  3 p(∂αuα) − 2  3σαβ(∂βuα).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (249)  D∗  t σαβ = ˙σNSF  αβ + ˙σnlin  αβ + RσG  αβ ,  (250)  where the right hand side of (250) is given by (229), (231) and (224).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Triangle entropy method  A remedy for the explicit construction of quasi-equilibrium approximations for general macroscopic variables  has been proposed in [25, 26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Let a set of macroscopic variables be specified as follows: First, a subset of linear  functionals (moments) M is defined as before, see (238).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Second, a subset of nonlinear functionals (in a general case)  N is defined N( f) = {N1( f), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' , Nl( f)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Examples of nonlinear macroscopic variables are production rates (51), (96)  or (97).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The totality of the macroscopic variables is the set {M, N}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  The triangle entropy method proceeds as follows: First, the quasi-equilibrium approximation is obtained for the  subset M, as above in (240) to get the quasi-equilibrium distribution function f ∗(v, M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Second, we seek a correction  to f ∗(v, M) in the form,  f = f ∗(1 + ϕ),  (251)  33  where ϕ is a deviation from the first quasi-equilibrium approximation due to the macroscopic variables N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In order to  determine ϕ, the second quasi-equilibrium approximation is constructed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Let us denote ˜Hf ∗(ϕ) as the quadratic term  in the expansion of the H-function into powers of ϕ in the neighborhood of the first quasi-equilibrium state f ∗,  ˜Hf ∗(ϕ) = H∗(M) +  �  f ∗(v, M) (ln f ∗(v, M) + 1) ϕ(v)d3v + 1  2  �  f ∗(v, M)ϕ2(v)d3v,  (252)  where H∗(M) = H( f ∗) is the value of the H-function in the quasi-equilibrium state f ∗ (242).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The distribution function  of the second quasi-equilibrium approximation is the solution to the problem,  ˜Hf ∗(ϕ) → min,  (253)  �  µi f ∗ϕd3v = 0, i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' , k,  (254)  Df Nj  ��� f ∗ϕ = ∆Nj, j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' , l,  (255)  where Df Nj  ���f ∗ are linear operators, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' the first differential of the operators Nj at the first quasi-equilibrium f ∗, while  ∆Nj are the deviations of the macroscopic variables from their values at the first quasi-equilibrium state,  ∆Nj = Nj − N∗  j(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (256)  Note the importance of the homogeneous constraints (254) in the minimization problem (253).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' They reflect the  condition that the variables ∆N are “slow” in the same sense as the variables M, at least in a small neighborhood of  the first quasi-equilibrium f ∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Because the optimization functional in the minimization problem (253) is quadratic in ϕ, and thanks to the linearity  of the constraints (254) and (255), the solution is always available in closed form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The resulting distribution function  shall be referred to as the second quasi-equilibrium,  f ∗(v, M, N) = f ∗(v, M)(1 + ϕ∗(v, M, N − N∗(M))),  (257)  in order to make a distinction with the first quasi-equilibrium f ∗(v, M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' By construction, the function ϕ∗ depends  linearly on the macroscopic variables of the second quasi-equilibrium ∆Nj (256).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Assuming that the first quasi-  equilibrium can be also obtained in a closed form, the triangle entropy method makes it possible to extend the max-  imum entropy construction to wider classes of macroscopic variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Below, we shall consider a few pertinent  realizations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Grad’s projections via triangle entropy method  Let us consider the example of using the triangle entropy method, when all the macroscopic variables of the first  and of the second quasi-equilibrium states are moments of the distribution function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In other words, the macroscopic  variables M of the first quasi-equilibrium remain as in (238), (239), while the macroscopic variambes N of the second  quasi-equilibrium state N are identified with the corresponding microscopic densities ν1(v), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' , νl(v),  Nj(x, t) =  �  ν j(v) f(v, x, t)d3v, j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' , l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (258)  Turning to the minimization problem (253), in order to take the homogeneous constraint (254) automatically into  account, it is convenient to introduce the following structure of inner product:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Define a scalar product,  (ψ1, ψ2) =  �  f ∗(v, M)ψ1(v)ψ2(v)d3v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (259)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Let Eµ be the linear hull of the set of moment densities µ1(v), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' , µk(v).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Let us construct a basis of Eµ  {e1(v), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' , er(v)} that is orthonormal in the sense of the scalar product (259):  (ei, ej) = δi j, i, j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' , r,  (260)  where δi j is the Kronecker delta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  34  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Define a projector ˆP∗ on the first quasi-equilibrium state,  ˆP∗ψ =  r�  i=1  ei(ei, ψ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (261)  The projector ˆP∗ is orthogonal: for any pair of functions ψ1, ψ2,  ( ˆP∗ψ1, (ˆ1 − ˆP∗)ψ2) = 0,  (262)  where ˆ1 is the unit operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  With this, the homogeneous condition (254) in the minimization problem (253) amounts to  ˆP∗ϕ = 0,  (263)  and the expression for the quadratic part of the H-function (252) takes the form,  ˜Hf ∗(ϕ) = H∗(M) + (ln f ∗ + 1, ϕ) + 1  2(ϕ, ϕ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (264)  Now, let us note that the function ln f ∗ is invariant with respect to the action of the projector ˆP∗:  ˆP∗(ln f ∗ + 1) = ln f ∗ + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (265)  This follows directly from the solution of the first quasi-equilibrium problem using of the method of Lagrange multi-  pliers (243) and also from the assumption that conservation laws are included into the set of moments M (239).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Thus,  if the condition (263) is satisfied, then from (262) and (265) it follows that  (ln f ∗ + 1, ϕ) = ( ˆP∗(ln f ∗ + 1), (ˆ1 − ˆP∗)ϕ) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Condition (263) is satisfied automatically, if the macroscopic variables ∆Ni (256) are defined as follows:  ∆Ni = ((ˆ1 − ˆP∗)νi, ϕ), i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' , l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (266)  Then the problem (253) of finding the second quasiequilibrium state reduces to  (ϕ, ϕ) → min for ((ˆ1 − ˆP∗)νi, ϕ) = ∆Ni, i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' , l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (267)  In the remainder of this section we demonstrate how the triangle entropy method is related to Grad’s moment  method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' To that end, we take the five collision invariants as moment densities of the first quasi-equilibrium state,  µ0 = 1, µα = vα, µ4 = mv2  2 ,  (268)  Then the first quasi-equilibrium state is characterized with the local Maxwell–Boltzmann distribution function f eq  (70).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Orthogonalization of the set of moment densities (268) with the weight (70) delivers one of the possible or-  thonormal basis as  e0 =  5  (10n)1/2 −  (v − u)2  (10n)1/2RT ,  (269)  eα = (vα − uα)  (nRT)1/2 ,  (270)  e4 =  (v − u)2  (15n)1/2RT .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (271)  We shall proceed with specific cases of the moments of the second quasi-equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  35  Ten-moments Grad’s approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For the moment densities of the second quasiequilibrium state, let us take,  ναβ = mvαvβ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (272)  Then  �ˆ1 − ˆP∗�  ναβ = m(vα − uα)(vβ − uβ) − 1  3δαβm(v − u)2,  (273)  and, since ((ˆ1 − ˆP(0))ναβ, (ˆ1 − ˆP(0))νγκ) = (δαγδβκ + δακδβγ)pRT, where p = nkBT is the pressure, and σαβ = ( f, (ˆ1 −  ˆP∗)ναβ) is the traceless part of the stress tensor, from (267) we obtain the distribution function of the second quasi-  equilibrium state in the form,  G10 = f eq  �  1 + σαβ  2pRT  �  (vα − uα)(vβ − uβ) − 1  3δαβ(v − u)2  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (274)  This is the distribution function of the ten-moment Grad’s approximation, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (211).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Note that the Grad’s distri-  bution function (274) is the first-order expansion of the quasi-equilibrium distribution (246) in terms of the nonequi-  librium pressure tensor σαβ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The Grad’s projection established by the ten-moment approximation (274) is identical to  the quasi-equilibrium system (250).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Thirteen-moments Grad approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In addition to (268), (272), let us extend the list of moment densities of the  second quasiequilibrium state with the functions  ξα = mvαv2  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (275)  The corresponding orthogonal complements to the projection on the first quasi-equilibrium state are  (ˆ1 − ˆP∗)ξα = m  2 (vα − uα)  �  (v − u)2 − 5RT  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (276)  The moments corresponding to the densities (ˆ1 − ˆP(0))ξα are the components of the heat flux vector qα,  qα = (ϕ, (ˆ1 − ˆP∗)ξα).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (277)  Since ((ˆ1− ˆP∗)ξα, (ˆ1− ˆP∗)νβγ) = 0, the constraints ((ˆ1− ˆP∗)ναβ, ϕ) = σαβ and ((ˆ1− ˆP∗)ξγ, ϕ) = qγ in the problem (267)  are independent, and Lagrange multipliers corresponding to ξα are (1/5n) (RT)2 qα.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Thus, taking into account (268),  (274), (276), we find the distribution function of the second quasi-equilibrium state,  G13 = f eq  �  1 + σαβ  2pRT  �  (vα − uα)(vβ − uβ) − 1  3δαβ(v − u)2  �  + qα  pRT (vα − uα)  �(v − u)2  5RT  − 1  ��  ,  (278)  which coincides with the thirteen-moment Grad distribution function (209) [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Eight- and fifteen-moments Grad’s approximations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' We note two other quasi-equilibrium approximations of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  If only the heat flux (277) is chosen as the slow variable then the second quasi-equilibrium approximation becomes  G8 = f eq  �  1 + qα  pRT (vα − uα)  �(v − u)2  5RT  − 1  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (279)  Distribution function (279) is used in the construction of the Shakhov’s S-model [27] to be discussed below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Grad’s  projection established by the distribution function (279) corresponds to a non-viscous compressible, thermally con-  ductive fluid (Pr → 0),  D∗  t ρ = −ρ∂αuα,  (280)  D∗  t uα = −1  ρ∂αp,  (281)  D∗  t p = −5  3 p(∂αuα) − 2  3(∂αqα).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (282)  D∗  t qα = −5  2Rp∂αT − 7  5qα∂βuβ − 7  5qβ∂βuα − 2  5qβ∂αuβ + RqG  α .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (283)  36  Projection  Local conservation  Target nonequilibrium moments  G5  ρ, ρu, tr[P]  –  G8  ρ, ρu, tr[P]  q  G10  ρ, ρu, tr[P]  P − 1  3tr[P]I  G13  ρ, ρu, tr[P]  P − 1  3tr[P]I, q  G15  ρ, ρu, tr[P]  Q  G20  ρ, ρu, tr[P]  P − 1  3tr[P]I, Q  Table 1: Grad’s projections mentioned in this contribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  It is interesting to note that, while the ten- and the eight-moments Grad’s projections have little practical usefulness  by themselves, they nevertheless are helpful in constructing the kinetic models in order to overcome the restriction of  the BGK model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Finally, if the full Q-flux (93) is used instead of the heat flux, the corresponding fifteen-moments  second quasi-equilibrium distribution function is used in the construction of a family of lattice Boltzmann models  with variable Prandtl number [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Various Grad’s projection mentioned above are collected in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Dynamic correction to Grad’s thirteen-moments projection: The R13 system  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Invariance defect of Grad’s thirteen-moments approximation  Nothing tells us that Grad’s closure relations for both the Q- and T-fluxes, as well as the closure relation for  the relaxation term, will stay invariant under kinetic equation (87).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' One thus needs, first, to quantify the discrepancy  between the proposed projection and the real dynamics due to kinetic equation, to understand the physical mechanisms  arising from this discrepancy and which were neglected by the projection, and, secondly, to correct the closure on the  basis of the kinetic equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Systematic method to derive dynamic correction to Grad’s G13 projection from kinetic equations was introduced in  [29] (KGDN thereafter), and has been realized for near-equilibrium conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The dynamic correction [29] followed  the path similar to that of the correction to the local equilibrium projection discussed above: first, one evaluates the  defect of invariance of the projection, and second, one finds the first iteration of the invariance condition in order  to compensate the defect in the lowest-order Knudsen number approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Later, taking a different route via a  superset moment system with 26 moments, Struchtrup and Torrilhon [30] proposed a nonlinear extension thereof, and  coined the name of regularized Grad’s system, or R13, which we here stick to.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Evaluation of the invariance defect of Grad’s approximation is rather straightforward, and has been first reported  by KGDN [29] in the linear approximation, and worked out in detail in [31] for the full nonlinear case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' We begin  with evaluating the derivatives of Grad’s distribution function with respect to all the thirteen fields,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' while separating  the contributions of the Maxwellian already available from (144),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (145) and (146) from that of the newly added  nonequilibrium part:  ∂G  ∂ρ = ∂M  ∂ρ ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (284)  ∂G  ∂uα  = ∂M  ∂uα  + ∂N  ∂uα  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (285)  ∂G  ∂T = ∂M  ∂T + ∂N  ∂T ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (286)  where  ∂N  ∂uα  = M (Gσ + Gq)  �Cα  vT  �  − M  �����  2qα  5pv2  T  �C2  2 − 5  2  �  +  2  5pv2  T  qβCβCα + σαβCβ  pvT  ����� ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (287)  ∂N  ∂T = M  �  Gσ  �C2 − 7  2T  �  + Gq  �C2 − 9  2T  ��  − M  � qαCα  pvTT  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (288)  37  Finally, derivatives with respect to the nonequilibrium fields are  ∂G  ∂σαβ  = M  � 1  2p  � �  CαCβ − 1  3δαβC2  �  ,  (289)  ∂G  ∂qα  = M  � Cα  pvT  � �C2  5 − 1  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (290)  Using these, we write down the invariance defect of Grad’s thirteen moment approximation separating contributions  of propagation terms from those of the collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Following KGDN convention, the former are termed non-local and  the latter local:  ∆G = ∆loc  G + ∆nloc  G .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (291)  The local piece reads,  ∆loc  G =  � ∂G  ∂σαβ  RσG  αβ + ∂G  ∂qα  RqG  α  �  − JB(G)  =  �  M  � 1  2p  � �  CαCβ − 1  3δαβC2  �  RσG  αβ − L(MGσ)  �  +  �  M  � Cα  pvT  � �C2  5 − 1  �  RqG  α − L(MGq)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (292)  Neglect of quadratic terms here is consistent with their neglect already made in Grad’s closure of relaxation terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  First observation, already exposed in KGDN [29], is about vanishing of the local invariance defect in certain  cases of collision models: Let functions M[CαCβ − 1  3δαβC2] and M[Cα(C2/2 − 5/2)] be eigenfunctions of linearized  collision integral,  L  �  M  �  CαCβ − 1  3δαβC2  ��  = −λσM  �  CαCβ − 1  3δαβC2  �  ,  (293)  L  �  M  �  Cα  �C2  2 − 5  2  ���  = −λqM  �  Cα  �C2  2 − 5  2  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (294)  Then the local invariance defect of Grad’s approximation vanishes,  ∆loc  G = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (295)  Indeed, with the conditions (293) and (294), the relaxation terms in Grad’s approximation become RσG  αβ = −λσσαβ and  RqG  αβ = −λqqα.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Using these in (292), we prove (295).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Non-vanishing of local invariance defect for Grad’s distribution function is the first apparent difference from the  Maxwellian case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In Grad’s case, the relaxation has to be aligned with the direction dictated by the eigenfunction of  the linearized collision integral in order to annihilate the local invariance defect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This is more demanding compared to  the local Maxwellian which annuls the local terms in the invariance defect independently of the collision model used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Vanishing of the local invariance defect unifies the relaxation time approximation (and any similar kinetic model) with  Maxwell’s molecules and is a consequence of the simple fact that all these have the same eigenfunctions of the form  (293) and (294).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Vanishing of local invariance defect has no relation to the values of transport coefficients, and is  non-vanishing for any other model, such as hard spheres.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Now we proceed with the analysis of the nonlocal part of  the invariance defect which is independent of the choice of the collision model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  The nonlocal part of the invariance defect shall be written as a sum of three pieces, where we distinguish the  Navier-Stokes-Fourier, the linear and the nonlinear contributions,  ∆nloc  G  = ∆NSF  G  + ∆lin  G + ∆nlin  G .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (296)  38  Each type of contributions is dictated by the partition of the Grad’s equations (228) and (232),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' and we have,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  ∆NSF  G  =∂G  ∂ρ  �  Dtρ + vTCβ∂βρ  �  + ∂M  ∂uα  �  DM  t uα + vTCβ∂βuα  �  + ∂M  ∂T  �  DM  t T + vTCβ∂βT  �  + ∂G  ∂σαβ  ˙σNSF  αβ + ∂G  ∂qα  ˙qNSF  α  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (297)  ∆lin  G =∂M  ∂uα  �  −1  ρ∂βσαβ  �  + ∂M  ∂T  �  −2T  3p ∂αqα  �  + ∂G  ∂σαβ  �  ˙σlin  αβ + vTCγ∂γσαβ  �  + ∂G  ∂qα  �  ˙qlin  α + vTCβ∂βqα  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (298)  ∆nlin  G  =∂M  ∂T  �  −2T  3p σαβ∂αuβ  �  + ∂N  ∂uα  �  Dtuα + vTCβ∂βuα  �  + ∂N  ∂T  �  DtT + vTCβ∂βT  �  + ∂G  ∂σαβ  ˙σnlin  αβ + ∂G  ∂qα  ˙qnlin  α .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (299)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The R13 distribution function  The leading-order dynamic correction to Grad’s distribution function is written on the basis of the BGK model  using a relaxation time τ as follows:  R = G + K,  (300)  where G is Grad’s distribution and K is the correction,  K = −τ∆nloc  G .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (301)  First, we notice that the Navier-Stokes-Fourier part of the invariance defect of Grad’s approximation vanishes,  ∆NSF  G  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Indeed, we notice that the first three terms in (297) assemble to the defect of invariance of the local  Maxwellian already computed, see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (151);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' evaluating the remaining two terms we get,  ∆NSF  G  = ∆M  + M  � 1  2p  � �  CαCβ − 1  3δαβC2  � �  −p  �  ∂αuβ + ∂βuα − 2  3δαβ∂γuγ  ��  + M  � 2Cα  5pvT  � �C2  2 − 5  2  � �  −5  2 p∂α (RT)  �  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (302)  This observation was first made in KGDN [29], and it is not surprising.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Indeed, since the Navier–Stokes–Fourier  approximation is already fully contained in Grad’s equations, there is nothing to correct in Grad’s dynamics with  respect to the Navier–Stokes–Fourier fluxes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  The remaining therms in the nonlocal defect of invariance of the G13 projection were evaluated in [29] and [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  The result is written as a combination of eight modes:  K = −τ  8  �  i=1  K(i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (303)  Each mode has the form,  K(i) = MP(i) • F(i),  (304)  39  where M is the local Maxwellian (or mode’s amplitude), P(i) is velocity tensor (or mode’s direction), F(i) is the mode’s  frequency, while • stands for convolution of tensors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Tensors P(i) are dimensionless and depend only on C, particle’s  velocity relative to the flow u, reduced by thermal speed, C = (v − u)/vT, where vT =  √  RT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Dimension of the mode’s  frequencies is inverse of time, [F(i)] ∼ 1/sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Modes of R13 are collected in Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 2, we use shorthand  notation for symmetric traceless velocity tensors of rank two, three and four,  �  CαCβ  �  = CαCβ − 1  3δαβC2,  (305)  �  CαCβCγ  �  = CαCβCγ − 1  5C2 �  Cαδβγ + Cβδαγ + Cγδαβ  �  ,  (306)  �  CαCβCγCλ  �  = CαCβCγCλ − C4  15  �  δαβδγλ + δαλδβγ + δαγδβλ  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (307)  The three primary modes K(1), K(2) and K(3) were already identified by KGDN [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Corresponding modes frequen-  cies is the only part of the invariance defect that survives linearization around equilibrium [29], and thus contribute  the conventional linear nonequilibrium thermodynamics dissipation to R13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The primary modes are accompanied by  three nonlinear secondary modes K(4), K(5) and K(6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Finally, two modes K(7) and K(8) are ghost modes: while they  contribute to the R13 distribution function, their projection onto R13 fluxes vanishes, and they are not visible in the  R13 balance equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  K  P  F  1  ⟨CCC⟩  √  RT  2p ⟨∇σ⟩ +  √  RT  2pT ⟨σ∇T⟩ +  1  2p  √  RT ⟨σDtu⟩  2  (C2 − 7) ⟨CC⟩  1  5p ⟨∇q⟩ +  1  5pRT ⟨qDtu⟩ +  1  4pT σDtT  3  C4 − 10C2 + 15  1  15p∇ · q +  1  15pσ : ∇u +  1  15pRT q · Dtu  4  (C2 − 7) ⟨CCC⟩  1  5p  √  RT ⟨q∇u⟩  5  ⟨CCCC⟩ − sym(⟨CC⟩ U)  1  2pσ∇u  6  (C4 − 14C2 + 35)CC  1  10pT q∇T  7  (C2 − 9) ⟨CCC⟩  √  RT  4pT ⟨σ∇T⟩  8  (C4 − 14C2 + 35)C  2q·⟨∇q⟩  25p  √  RT −  1  15T  √  RT q∇ · q −  1  15T  √  RT qσ : ∇u +  √  RT  10pT σ · ∇T  Table 2: Modes of R13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Angular brackets denote symmetrized traceless tensors of rank two, three and four.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Dt = ∂t +u·∇ is the material derivative  along streamline;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' u is flow velocity, p = ρRT is the pressure, R is gas constant, ρ is the density and T is the temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The R13 equations  The R13 equations for the nonequilibrium stress tensor σ and the heat flux q are compactly written in vector  notation as follows:  DR  t σ = DG  t σ − ∇ · QK,  (308)  DR  t q = DG  t q − ∇ · TK − QK : ∇u,  (309)  where Dt is the material time derivative along streamline,  Dt = ∂t + u · ∇,  (310)  40  and DG  t indicates Grad’s contribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The rank three symmetric trace-free tensor QK and the rank two symmetric  tensor TK are the R13 fluxes,  QK = − ν  �3  2 ⟨∇σ⟩ + 3  2T ⟨σ∇T⟩ +  6  5RT ⟨q∇u⟩  �  − τ  �3  2 ⟨σDtu⟩  �  ,  (311)  TK =  �  TK�  + 1  3UT K,  (312)  �  TK�  = − ν  �14  5 ⟨∇q⟩ +28  5 ⟨q∇ ln T⟩ + σ(∇ · u) + 2  �  σ · S + σ · S  ��  − τ  �14  5 ⟨qDtu⟩ + 7  2RσDtT  �  ,  (313)  T K = − 4ν  �  ∇ · q+7  2 q · ∇ ln T + σ : ∇u  �  − 4τq · Dtu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (314)  Here angular brackets indicate symmetrized traceless tensors of rank two and three, overline indicates transposition,  U is unit tensor, S = (∇u + ∇u)/2 is the strain and ∇ ln T = T −1∇T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Brackets in (311) and (313) help to discern contributions of two different types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The first bracket in (313) and  (311) is the dissipation flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' First part of dissipation is the linear thermodynamics dissipation flux (first term in (311)  and (313)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The linear dissipation fluxes are the only contributions in (311) and (312) that survive linearization around  equilibrium, as was already shown by KGDN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The rest of the terms in the first bracket form the nonlinear dissipation  flux, driven by non-uniformity of the macroscopic velocity field and of the temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Both types of dissipative  fluxes are associated with the kinematic viscosity ν = τRT, here in the relaxation time approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Second bracket in (311) and (313) is a remarkably distinct streamline convective flux, which we term this way  because of the material time derivative (310) participating in their formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Streamline convective fluxes are nonlin-  ear and their contribution is non-dissipative in nature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' They are characterized by the relaxation time τ rather than by  the viscosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' From Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 2, it is visible that streamline convective flux is contributed by primary modes only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Finally,  also the trace T K (314) reproduces the said structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Together with the balance equations of density,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' momentum and  energy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Dtρ = −ρ∇ · u,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (315)  Dtu = −1  ρ∇p − 1  ρ∇ · σ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (316)  DtT = −2  3T∇ · u − 2  3  �T  p  �  σ : ∇u − 2  3  �T  p  �  ∇ · q,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (317)  and with Grad’s contribution,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  DG  t σ = − 2p ⟨S⟩ − 4  5 ⟨∇q⟩ − σ(∇ · u) − 2 ⟨σ · S⟩ − 1  τσ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (318)  DG  t q = − 5  2RΠ · ∇T − RT∇ · σ − σ · Dtu − 7  5 q(∇ · u) − q · ∇u − 4  5 q · S − 1  τ q,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (319)  where Π = pU + σ is the pressure tensor,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (308) and (309) build up the structure of the R13 system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  The R13 theory was further refined and extensively studied by Struchtrup and Torrilhon,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' and their coauthors,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' in  a number of contributions [32,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 33,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 34,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 35,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 36,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 37,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 38,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 20,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 39] that dissect the R13 equations carefully,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' and show that  they can describe all relevant rarefaction phenomena,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' such as jump and slip at boundaries,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Knudsen boundary layers,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  transpiration flow,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' thermal stresses,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' non-temperature-gradient heat flux induced by stresses,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' damping and dispersion  of ultrasound waves and shock structures (for limited Mach numbers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A good summary of this work is referenced  and discussed in a recent review [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Lifting of Grad’s and quasi-equilibrium projections: Kinetic models for simple fluid  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Quasi-equilibrium and related kinetic models  Lifting of the local equilibrium projection considered in sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5 results in the BGK model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A variety of kinetic  models can be offered by a lifting the lifting of the Grad’s and related projections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' We shall discuss now some main  41  classes of kinetic models from this perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Following [40], a kinetic model for a generic quasi-equilibrium  approximation f ∗(M) (240) can be proposed as follows,  ∂t f + v · ∇ f = −1  τ( f − f ∗(M)) + JB( f ∗(M)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (320)  Here f ∗(M) ≡ f ∗(M( f)) is the natural map f → f ∗(M),  �  µi( f − f ∗(M)d3v = 0, i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' , k,  (321)  and we omit displaying the dependence of the distribution function on the velocity, time and space to simplify notation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Thus, the first term in the right hand side of equation (320) is BGK-like, whereas the second term, the function  JB(f ∗(M)), is the true (Boltzmann) collision integral evaluated on the quasi-equilibrium manifold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The latter is  crucial: Unlike the true Boltzmann collision integral JB( f) which takes values in the entire phase space of distribution  functions, the term JB( f ∗(M)) is evaluated only on a relatively ”thin” submanifold f ∗ known a priori, and can be thus  pre-computed to the explicit function of the moments M and of the velocity v (see Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' [40] for examples).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' If the  quasi-equilibrium f ∗(M) consists only of the local Maxwellians, then JB( f ∗(M)) vanishes, and we get back the  BGK-model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In all other cases, the second term in the kinetic model (320) is essential: If it is omitted in equation  (320) then the null-space of the resulting collision integral is the entire quasi-equilibrium manifold f ∗(M), and not its  local equilibrium submanifold, unlike the case of the Boltzmann collision integral.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  The H-theorem for kinetic models (320) has the following structure: Let us compute the entropy production σ:  σ = σ1 + σ2,  σ1 = −1  τ  �  ln( f)( f − f ∗(M)d3v,  σ2 =  �  ln( f)JB( f ∗(M))d3v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (322)  Function σ1 is the contribution from the BGK-like relaation term in equation (320), and it is always non-positive,  again due to the property of the map f → f ∗(M) (321).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The second contribution, σ2 may be not sign-definite if  f is far away from the quasi-equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' However, there always exists a non-empty neighborhood of the quasi-  equilibrium manifold, where σ2 ≤ 0 [40] (this is almost obvious: on the quasi-equilibrium manifold σ2( f ∗(M)) is the  entropy production due to the Boltzmann collision integral).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Thus, if the relaxation towards quasi-equilibrium states  is fast enough (τ is sufficiently small), the net entropy production inequality holds, σ = σ1 + σ2 ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Some further variants of the quasi-equilibrium models (320) are possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Let us introduce the quasi-equilibrium  projector P∗,  P∗F =  k  �  i=1  ∂ f ∗(M)  ∂Mi  �  µiFd3v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (323)  Instead of the term JB(f ∗(M)) in (320), we can use its projection, P∗JB( f ∗(M)), so that the model (320) simplifies to  ∂t f + v · ∇ f = −1  τ( f − f ∗(M)) +  k  �  i=1  ∂ f ∗(M)  ∂Mi  R∗  i (M),  (324)  where R∗  i (M) is the quasi-equilibrium production rate of the ith moment,  R∗  i (M) =  �  µiJB( f ∗(M))d3v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (325)  The variant (324) is simpler than the original kinetic model(320) since the velocity dependence of the corresponding  term arises in (324) only via the quasi-equilibrium distribution function rather than due to the function in the function  JB( f ∗(M)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Moreover, a further simplification can be suggested in a ”multiple relaxation times” form,  ∂t f + v · ∇ f = − − 1  τ( f − f ∗(M)) −  k  �  i=1  ∂f ∗(M)  ∂Mi  � 1  τi  � �  Mi − Meq  i  �  ,  (326)  42  where Meq  i  denotes the ith moment evaluated at the local equilibrium, while τ1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' , τk are corresponding relaxation  times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Descending the path of simplification from the quasi-equilibrium kinetic model (320) through (324) to (326),  the information about the ”true” Boltzmann collision integral, which is still manifest in (320), is gradually lost and is  completely replaced by a relaxation-type form in (326).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In the next section, we shall consider a special case of the  two-relaxation time kinetic models which are mostly used in applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Two relaxation times quasi-equilibrium models  The two relaxation times quasi-equilibrium kinetic model is written,  ∂t f + v · ∇ f = − 1  τfast  ( f − f ∗(M)) −  1  τslow  ( f ∗(M) − f eq),  (327)  and has the following interpretation: The relaxation to the local equilibrium f eq is decomposed into a ”fast” relaxation  from the current state f to the intermediate quasi-equilibrium f ∗ followed by a ”slow” relaxation from the quasi-  equilibrium f ∗ to the local equilibrium f eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This is a special reduction of the quasi-equilibrium model (320), where  the Boltzmann’s term JB( f ∗(M)) is replaced with the BGK relaxation [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Denoting Jfs the right hand side of (327),  we can write,  Jfs = −  � 1  τfast  −  1  τslow  �  ( f − f ∗(M)) −  1  τslow  ( f − f eq).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (328)  Now, in order to clarify the meaning of the fast-slow decomposition, we compute the entropy production induced by  the relaxation term (328),  σ = σfast + σslow,  (329)  σfast = −  � 1  τfast  −  1  τslow  � �  ln  �  f  f ∗(M)  �  ( f − f ∗(M)) d3v,  (330)  σslow = − 1  τslow  �  ln  � f  f eq  � �f − f eq� d3v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (331)  Clearly, the contribution of the slow relaxation into the entropy production, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (331), is always non-positive, σslow ≤  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' However, the contribution of the fast relaxation, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (330), is non-positively definite, σfast ≤ 0, only if the fast  relaxation time τfast is not greater than the slow relaxation time τslow:  τfast ≤ τslow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (332)  The equality τfast = τslow results in the BGK model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Thus, the compliance to the H-theorem for the quasi-equilibrium  kinetic model (327) implies the fast-slow relaxation times hierarchy (332).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' It is convenient to introduce the ratio of  the relaxations times,  rfs = τfast  τslow  , rfs ∈ [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (333)  Introducing also a convex linear combination of the quasi-equilibrium and the local equilibrium,  ˜ffs = (1 − rfs) f ∗(M) + rfs f eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (334)  the relaxation term can be written in a BGK-like form,  Jfs = − 1  τfast  ( f − ˜ffs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (335)  Realizations of the two relaxation times kinetic model (327) depend on the availability of analytical expressions for  the quasi-equilibrium distribution functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In practice, the ”true” quasi-equilibrium can be substituted by Grad’s  approximation, which is sufficient for many applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' However, the relaxation times hierarchy (332) must be  respected also in such cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  43  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Lifting the eight-moments Grad’s projection: Shakhov’s S-model  Using the eight-moments Grad’s distribution function (279), we obtain in (334) and (335),  ˜ffs = (1 − rfs) G8 + rfs f eq  = f eq  �  1 + (1 − rfs)qα(vα − uα)  pRT  �(v − u)2  5RT  − 1  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (336)  The corresponding two relaxation times kinetic model (327) is identified as the Shakhov’s S-model [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Hydrody-  namic limit of the S-model results in the Navier–Stokes–Fourier system with the following viscosity and thermal  conductivity,  µ = τfastp,  (337)  λ = τslowcpp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (338)  Thus, the Prandtl number of the S-model satisfies the inequality implied by the fast-slow relaxation hierarchy (332),  Pr = rfs = τfast  τslow  ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (339)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Lifting the ten-moments Grad’s projection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  The ten-moments quasi-equilibrium is available in a closed form, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (246), and hence can be straightforwardly  used in the kinetic model (327).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Here we shall instead consider lifting of the ten-moments Grad’s approximation  (274).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' With (274), we obtain in (334) and (335),  ˜ffs = (1 − rfs) G10 + rfs f eq  = f eq  �  1 + (1 − rfs) σαβ  2pRT  �  (vα − uα)(vβ − uβ) − 1  3δαβ(v − u)2  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (340)  Hydrodynamic limit of the corresponding kinetic model results in the Navier–Stokes–Fourier system with the follow-  ing viscosity and thermal conductivity,  µ = τslowp,  (341)  λ = τfastcpp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (342)  Note that, the dependence of the transport coefficients on the relaxation times in (341) and (342) is opposite to that  of the S-model, Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (337) and (338): the fast and slow relaxation times switch their places.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Thus, in compliance  with the relaxation times hierarchy (332), the Prandl number of the kinetic model based on the ten-moments Grad’s  approximation satisfies the inequality,  Pr = 1  rfs  = τslow  τfast  ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (343)  Results (341), (342) remain valid when the full ten-moment quasi-equilibrium distribution function (246) is used in  (327).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' We comment that, the S-model (336) and the model (340) are complementary to each other: The S-model  covers the range of the Prandtl number 0 < Pr ≤ 1 while the model (340) corresponds to 1 ≤ Pr < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This  is consistent with the corresponding Grad’s projections: The ten-moments projection (274) provides a formal limit  Pr → ∞, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (250), while the eight-moments projection (279) provides the limit of a vanishing Prandtl number  Pr → 0, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (283).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Both models are used in the thermal and compressible lattice Boltzmann models [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Holway’s ellipsoidal-statistical kinetic model  Finally, we mention another option of lifting the quasi-equilibrium projection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Starting with the BGK-like form  (335), the attractor ˜f (334) can be replaced by another one, the quasi-equilibrium evaluated on a linear combination  between the moments and their equilibrium values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In a general multi-parameter form, and a generic quasi-equilibrium  distribution function f ∗(M, v), this is,  ˜f ∗ = f ∗((1 − α1)M1 + α1Meq  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' , (1 − αk)Mk + αkMeq  k , v),  (344)  44  where α1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' , αk are free parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In other words, while the previous lifting operates with linear combinations  between the quasi-equilibrium and the local equilibrium distribution functions (334), the present one uses the quasi-  equilibrium distribution of linear combination of the corresponding moments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Whenever the Grad’s approximation is  used instead of the true quasi-equilibrium, both approaches result in identical models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Because only one case of a genuine quasi-equilibrium distribution function is known in a closed-form, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (246), the unique model of the type (344) is the Holway’s ellipsoidal-statistical (ES) model [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Introducing in (246)  a linear combination between the full pressure tensor Π = p1 + σ and its local equilibrium value p1, we obtain a  one-parametric family of distribution functions,  ˜f ∗  ES = n  ρ  3  2  (2π)  3  2 �  det �(1 − α)Π + αp1� exp  �  −ρ  2(v − u)† · �(1 − α)Π + αp1�−1 · (v − u)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (345)  With (345), the ES model is written in the BGK-like form,  ∂t f + v · ∇ f = −1  τ  �  f − ˜f ∗  ES  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (346)  Hydrodynamic limit of the ES kinetic model (346) recovers the viscosity and thermal conductivity in the Navier–  Stokes–Fourier system,  µ = 1  ατp,  (347)  λ = τcpp,  (348)  which allows to identify the parameter α as the inverse of the Prandtl number,  α = 1  Pr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (349)  If the ES distribution function (345) is expanded to linear order in the nonequilibrium stress tensor σ, the result is  identical to (340), and which makes it possible the matching of the parameters in both cases as rfs = α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Thus, the  relation between the transport coefficients of the ES model, Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (347) and (348), is the same as for the case (340),  Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (341) and (342).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' We note that, as was shown by [44], the H-theorem for the ES model can be proven for Prandtl  number 2/3 ≤ Pr < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Summary: Projections, corrections and lifting  The review of some basic, classical aspects of the Boltzmann equation of this section are summarized in Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  With this, we emphasize a certain commonality among various approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The main building block is an approxi-  mation provided by a distribution function, parameterized by a set of macroscopic fields of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The projection  of the Boltzmann equation provides a starting point of the analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The projection can be corrected by improving its  invariance property relative to the Boltzmann equation or lifted to a kinetic model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Both approaches are patterned in  the lattice Boltzmann realizations to be discussed in the remainder of this contribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Projection  Equation  Correction  Lifting  Local equilibrium  Euler  Navier–Stokes–Fourier  BGK  Grad 13  Grad’s 13-moment system  R13  Grad 10  Grad’s 10-moment system  Quasi-equilibrium 10  Grad’s 10-moment system  ES model, model (340)  Grad 8  S-model  Table 3: Summary of projections, their corrections and liftings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  45  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Lattice Boltzmann for ideal fluid and related models  In this section we discuss in detail the lattice Boltzmann method introduced in the early 90’s [45, 46, 47] as  an improvement over the lattice gas automata [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In its modern form it is a discrete solver for the Boltzmann  equation with the BGK approximation for the collision operator given in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (199).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' After a detailed introduction of  discretization strategies in both phase-space and space/time, we will discuss different approximations to external body  forces, stability and applicability domain of the classical LBM and possible improvement strategies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Phase-space discretization  The first step in deriving a discrete scheme from the Boltzmann-BGK equation, is to discretize the D-dimensional  space of particles speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Many different strategies have been adopted in the context of the kinetic theory of gases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Here we review quadrature-based approaches used mainly in the context of the LBM to reduce the continuous space  of particles speed into a discrete set of velocities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Hermite expansion and Gauss-Hermite quadrature  One approach to discretise phase-space and derive the corresponding discrete EDF consists in expanding it in  terms of Hermite polynomials and operating a truncation using Gauss-Hermite quadratures [49, 50, 15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Before starting the derivation, let us review the basic concepts of multi-variate Hermite polynomials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' More details on  the Hermite polynomials can be found in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' They are defined as [50]:  H n (v) = (−1)n  w (v) ∇n  vw (v) ,  (350)  where H n is a tensor of rank n and w (v) is the normalized weight function defined as:  w (v) = (2π)−D/2 exp  �  −v2  2  �  ,  (351)  with D the dimension of v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A function f can then be expanded in terms of Hermite polynomials as:  f = w (v)  ∞  �  n=0  1  n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' an : H n (v) ,  (352)  where “:” is the Frobenius inner product and the coefficients tensor an are computed as:  an =  �  H n (v) fdξ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (353)  Note that Hermite polynomials are mutually orthogonal with respect to the weighted dot product defined as:  �  Hi(v)w(v)Hi′(v)dv =  �������  0  if i � i′  n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  if i = i′,  (354)  where i and i′ are vectors of size n designating a component of the rank n Hermite polynomial tensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The infinite set  of Hermite polynomials forms a complete orthogonal basis of the weighted space Vw := L2(RD;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' R, wdv) only under  the condition that any function f ∈ Vw satisfies:  �  f 2(v)w(v)dv < ∞,  (355)  meaning in practice that f(v) must decay faster than √w(v) which has implications on the choice of reference temper-  ature in static reference frame-based methods like the LBM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Further discussion on that issue is out of the scope of the  present review and will be presented in future publications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  The first step in the expansion is the choice of the non-dimensionalization strategy, or reference state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' While not  46  necessary in the expansion, this choice is one of the most important steps in the construction of a discrete kinetic  scheme as it will play a key role in the final numerical scheme’s behavior, especially higher-order moments errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  The recent development of LB models relying on non-symmetrical stencils and adaptive non-dimensionalization is a  clear proof of the previous assertion [51, 52, 53, 54, 55, 56].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For the sake of simplicity, let us re-write the EDF in  non-dimensional form as:  f eq (v, ρ, u, θ) = ρ(2πθ)−D/2 exp  �  −(v − u)2  2θ  �  ,  (356)  where for the remainder of this subsection u, and v are non-dimensionalized with a reference speed of sound cs,  θ = kBT/m  c2s  and cs = kBT0  m0 , and T0 and m0 are respectively defined as the reference temperature and molecular mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  This results in the following first few Hermite polynomials:  H0 = 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (357a)  Hi1 = vi1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (357b)  Hi1i2 = vi1vi2 − δi1i2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (357c)  Hi1i2i3 = vi1vi2vi3 − �vi1δi2i3  �  cyc ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (357d)  Hi1i2i3i4 = vi1vi2vi3vi4 + �δi1i2δi3i4  �  cyc − �vi3vi4δi1i2  �  cyc ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (357e)  where []cyc designates cyclic permutations over the involved indexes,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' and corresponding isothermal (θ = 1) Hermite  coefficients:  aeq  0 = ρ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (358a)  aeq  i1 = ρui1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (358b)  aeq  i1i2 = ρui1ui2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (358c)  aeq  i1i2i3 = ρui1ui2ui3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (358d)  aeq  i1i2i3i4 = ρui1ui2ui3ui4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (358e)  In the context of the classical LBM, the flow is assumed isothermal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The continuous EDF is then expanded as:  f eq (v, ρ, u) = w (v)  ∞  �  n=0  1  n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' a(eq)  n  (ρ, u) : H n (v) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (359)  As seen here, the expanded EDF still goes over the entire phase-space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Given the form of the EDF and the corre-  sponding moments:  Πx .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' x  ����  ×p  y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' y  ����  ×q  z .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' z  ����  ×r  =  �  vx  pvy  qvz  r f eq (v, ρ, u) dv,  (360)  and using the Hermite expansion, it can be written as:  Πx .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' x  ����  ×p  y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' y  ����  ×q  z .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' z  ����  ×r  =  �  P∞ (v, ρ, u) w (v) dv,  (361)  where:  P∞ (v, ρ, u) = vxpvyqvzr f eq (v, ρ, u)  w (v)  ,  (362)  and P∞ (v, ρ, u) as defined here is a polynomial function of the variable v with order ∞ as the Hermite expansion has  not yet been truncated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Given that the aim of the LB method is to solve the Boltzmann equation in the hydrodynamic  regime one only needs to correctly recover the moments of the EDF involved in the hydrodynamic equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Further-  more, Hermite polynomials are weighted orthogonal functions and as such higher-order polynomials have no effect  on lower-order terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Given the previously cited arguments, one can limit the Hermite expansion of the EDF:  f eq,N (v, ρ, u) = w (v)  N  �  n=0  1  n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' aeq  n (ρ, u, ) : Hn (v) ,  (363)  47  where N corresponds to the highest-order moment involved in the targeted dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For example, to correctly  recover the NS equations for an isothermal flow one needs to correctly recover moments up to order three of the EDF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Now the polynomial P∞ can be replaced with a finite-order polynomial:  PM (v, ρ, u) = vxpvyqvzr f eq,N (v, ρ, u)  w (v)  ,  (364)  where M = 2N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The integral of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (361) can be evaluated using a discrete sum through a Gauss-Hermite quadrature  as:  �  PM (v, ρ, u) w (v) dv �  Q  �  i=0  wiPM (ci, ρ, u) ,  (365)  where ci are discrete non-dimensional abscissae used for the quadrature and wi are the corresponding weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  According to the fundamental theorem of Gaussian quadratures, choosing the abscissae to be the roots of the or-  thogonal polynomial of the corresponding degree results in the maximum algebraic degree of precision, namely  2Q − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' To correctly recover the targeted moments one must have M ≤ 2Q − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The third-order quadrature (des-  ignated by E3  1,5 in 1-D) results in the following abscissae: ci ∈ {−  √  3, 0,  √  3} corresponding to the following values  {− √3kBT0/m0, 0, √3kBT0/m0} in physical units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' While being the most widely applied quadrature order, it is already  clear that the third-order quadrature can not correctly recover all the moments appearing at the NS level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' More on that  issue in the next subsections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The corresponding weights are computed as:  wi =  n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (Hn−1 (ci))2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (366)  In the multi-variate case, the weights can be computed as the products of the weights in each dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Product form equilibria and moment matching  As clearly stated by its name, in this approach one tries to construct a discrete equilibrium by matching the  moments appearing in the targeted macroscopic balance equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  To identify the constraints, one first uses the CE analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For example, a simple CE analysis at order ϵ shows that  to correctly recover the NS and continuity equations, one needs to exactly match moments up to order three [57, 58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  For example let us consider a 1-D system with only translational degrees of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The following moments need to  be correctly recovered:  Π0 =  �  vx  ρ  �  m  2πkBT exp  �  −m(vx − ux)2  2kBT  �  dvx = ρ,  (367a)  Πx =  �  vx  vxρ  �  m  2πkBT exp  �  −m(vx − ux)2  2kBT  �  dvx = ρux,  (367b)  Πxx =  �  vx  v2  xρ  �  m  2πkBT exp  �  −m(vx − ux)2  2kBT  �  dvx = ρ  �  u2  x + kBT  m  �  ,  (367c)  Πxxx =  �  vx  v3  xρ  �  m  2πkBT exp  �  −m(vx − ux)2  2kBT  �  dvx = ρux  �  u2  x + 3kBT  m  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (367d)  In the second step of the discrete equilibrium state construction, one chooses a symmetrical stencil (set of discrete  velocities) with a number of degrees of freedom equal to the number of constraints [57, 59, 60].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For example, in the  case of the isothermal NS solver, one can either use a four-velocity model or a five-velocity model with an additional  constraint to have a unique solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The discrete equilibrium is then found by solving the following system of  equations:  ��������������  1  1  1  1  c0  c1  c2  c3  c2  0  c2  1  c2  2  c2  3  c3  0  c3  1  c3  2  c3  3  ��������������  ��������������  f eq  0  f eq  1  f eq  2  f eq  3  ��������������  =  ����������������  ρ  ρux  ρ  �  u2  x + kBT  m  �  ρux  �  u2  x + 3 kBT  m  �  ����������������  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (368)  48  where c0−3 are the discrete velocities in the stencil and f eq  0−3 are the unknown discrete equilibria to be found by solving  this system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The linear system formed using symmetrical stencils might not always be invertible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' As such, for some  models one might need to add non-symmetrical components to the system [61].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  The product form of the EDF is a special realization of the moments matching approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Considering the standard  discrete velocity set D3Q27, where D = 3 stands for three dimensions and Q = 27 is the number of discrete velocities,  ci = (cix, ciy, ciz), ciα ∈ {−1, 0, 1},  (369)  one first defines a triplet of functions in two variables, ξα and ζαα,  Ψ0(ξα, ζαα) = 1 − ζαα,  (370)  Ψ1(ξα, ζαα) = ξα + ζαα  2  ,  (371)  Ψ−1(ξα, ζαα) = −ξα + ζαα  2  ,  (372)  and considers a product-form associated with the discrete velocities ci (369),  Ψi = Ψcix(ξx, ζxx)Ψciy(ξy, ζyy)Ψciz(ξz, ζzz).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (373)  All pertinent populations below are determined by specifying the parameters ξα and ζαα in the product-form (373).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The  two-dimensional version of the model on the D2Q9 lattice is obtained by omitting the z-component in all formulas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  After matching moments with their continuous counter-parts the parameters are set as,  ξα = uα,  (374)  ζαα = c2  s + u2  α,  (375)  and the local equilibrium populations are represented with the product-form (373),  f eq  i  = ρ  �  α=x,y,z  Ψciα  �  uα, c2  s + u2  α  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (376)  This form of the discrete equilibrium populations, when c2  s = kBT0/3m0 is equivalent to third-order quadrature-based  scheme with a full expansion of the distribution function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' As will be seen in the upcoming section this class of  equilibrium populations allows to restore Galilean invariance of the Navier-Stokes level shear viscosity but fails to do  so for the bulk component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Alternative to polynomial equilibria: Entropic equilibria  In the context of the entropic lattice Boltzmann method as described in [62], the discrete equilibrium state is found  as the minimizer of a convex discrete entropy functional under mass and momentum conservation constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' It is this  lower number of constraints on moments that allows the scheme to accomodate the entropy constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The derivation  starts with the roots of the third-order Hermite polynomials as the discrete abscissae and considering the following  conservation constraints:  �  α  f eq  i  = ρ,  (377)  �  i  ci f eq  i  = ρu,  (378)  where notations follow those adopted in the previous subsection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The EDF is derived as the function extremizing the  discrete entropy function:  Hwi,ci =  �  i  fi ln  � fi  wi  �  ,  (379)  49  under the previously set constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Given the Galilean invariance of the weights the expression for the entropy  function is also Galilean invariant [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The EDF can be expressed as:  f eq  i  = wi exp (λ0)  D  �  α=1  exp �ci,αλα  � ,  (380)  where λ0 and λα are the Lagrange multipliers associated with constraints on the zeroth and first-order moments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Introducing the following changes of variables, X = exp (−λ0) and Zα = exp (λα) the EDF is re-written as:  f eq  i  = wiX−1  D  �  α=1  Zci,α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (381)  Writing down the conservation equations using the new variables for the D2Q9 stencil, the following algebraic system  of equations is obtained:  ρX =  �  i  wi  �  α=x,y  Zci,α,  (382a)  ρuxX =  �  i  wici,x  �  α=x,y  Zci,α,  (382b)  ρuyX =  �  i  wici,y  �  α=x,y  Zci,α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (382c)  Solving this system of equation for Zx, Zy and X and keeping positive roots one gets:  Zα = 2uα +  �  uα2/c2s + 1  1 − uα  ,  (383)  X−1 = ρ  �  α=x,y  �  2 −  �  uα2/c2s + 1  �  ,  (384)  and therefore can express the entropic discrete equilibrium as:  f eq  i  = wiρ  �  α=x,y  �  2 −  �  uα2/c2s + 1  � �������  2uα +  �  uα2/c2s + 1  1 − uα  �������  ci,α  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (385)  It will be shown in the next sections that this approach to constructing the discrete equilibrium populations satisfies a  smaller number of constraint on moments, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' only of order zero and one, but guarantees unconditional positivity and  linear stability of the scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Galilean invariance issues on standard lattices  Errors in moments of the equilibrium distribution function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' It is well-known that LB formulations based on standard  first-neighbor stencils do not exactly recover the NS level dynamics, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' the stress tensor and, for the entropic equi-  librium, the pressure tensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The former comes from the fact that, due to a lack of symmetry, the third-order moments  tensor does not correspond to its phase-space continuous counterpart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' While including higher-order components of  the Hermite expansion in the EDF or using the product-form can help correct the deviatoric components, consistency  of the diagonal components can only be re-established through additional correction terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Furthermore, use of the  entropic approach which enforces smaller number of constraints on moments results in deviations in second-order  moments too.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' To have a better measure of the applicability domain of the LB scheme, we will look at the deviations  of these moments from their continuous counterparts for varying Mach numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Although readily extendable to  other stencils, the D2Q9 stencil will be considered here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Moments of orders two and three of the EDF will be studied  through their normalized deviations defined as:  δ =  �������������  1 −  �  i cp  i,xcq  i,y f eq  i  ΠMB  x .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' x  ����  ×p  y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' y  ����  ×q  �������������  ,  (386)  50  where ΠMB  x .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' x  ����  ×p  y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' y  ����  ×q  is the continuous moment and �  i cp  i,xcq  i,y f eq  i  is the moment of the discrete EDF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  First we consider the diagonal components of the second-order moments tensor in the co-moving reference frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' We  consider the co-moving reference frame here to focus on the recovered thermodynamic pressure:  �  ΠMB  xx + �  ΠMB  yy = 2ρc2  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (387)  The deviations are illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' While the entropic EDF does not exactly recover the correct trace of the  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  ux/cs  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  uy/cs  102  1  10-2  10-4  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  1  ux/cs  10-8  10-6  10-4  10-2  100  10-5  10-4  10-3  10-2  10-1  Figure 1: Illustration of deviations in Πeq  xx + Πeq  yy moment for the entropic equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Left: Evolution of normalized error as a function of ux/cs  and uy/cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Right: Normalized error as a function of ux/cs with uy/cs = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  diagonal components of the second-order moments tensor, the deviations are negligible for Mach numbers up to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  which goes above the validity of the weakly compressible flow assumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Another point worth nothing is the nature  of the deviations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The second order central equilibrium moment �  Πeq  αα for the entropic equilibrium is:  �  Πeq  αα = −ρ(uα − 1)(6uα  �  3u2α + 1 + 12u2  α − 2  �  3u2α + 1 + 4)  6(2uα +  �  3u2α + 1)  ,  (388)  indicating that the thermodynamic pressure tensor loses Galilean-invariance and isotropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In the limit of ux, uy → 0  one recovers the correct pressure, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' ρc2  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The second-order Hermite-expanded and product form equilibria exactly  recover the second-order moments tensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Another point worth analyzing, is the behavior of sound speed in the  entropic EDF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' While sound speed is constant for polynomial equilibria it is a function of local speed in the entropic  EDF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The behavior of sound speed as a function of local velocity is illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This behavior shows an  interesting property of the entropic model pointing already to a (potentially) unconditional linear stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Keeping  in mind that the fastest eigen-modes in the system can not propagate faster than the lattice links and only considering  three physical eigen-modes, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' ux, ux −cs and ux +cs, one arrives to the following strong condition on linear stability:  max(ux, ux + cs, ux − cs) ≤ δr  δt .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (389)  51  Figure 2: (Left) Non-dimensional sound speed for entropic EDF as a function of velocity ux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (Right) Comparison of the speed of fastest propagating  eigen-mode: (blue dotted line) polynomial EDF and (red line) entropic EDF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  For the polynomial equilibria given that sound speed is constant one recovers the following maximum tolerable ve-  locity:  |umax  x  |= δr  δt  �������1 −  �  1  3  ������� = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4226δr  δt ,  (390)  which as will be shown in the next section through stability analyses, is indeed the maximum reachable velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For  the entropic EDF on the other hand, it is observed that the sound speed self-adjusts as a function of local velocity to  guarantee Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (389) is always satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' At the higher end of the velocity spectrum, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' ux → δr  δt the speed of sound  goes to cs → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  For the NS level dynamics to be correctly recovered, the components of the third-order moments tensor must also  match those of the continuous EDF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' However, as observed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 3, none of the EDFs are able to recover the correct  diagonal components for this tensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This shortcoming is not related to the equilibrium state but, to the limited order of  the Gauss-Hermite quadrature used for first-neighbor stencils.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 3, it is observed that all three EDFs considered  there (second-order Hermite expansion, product-form and entropic) have the same moments, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Πeq  xxx = Πeq  x = ρux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  For the off-diagonal components of the third-order moments tensor however, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 4, different EDFs result  in different behaviors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' While Hermite expansions of order higher than three, here the product form, exactly recover the  correct moments, the second-order Hermite expansion and entropic EDFs show some deviations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Although not exactly  recovering the correct moment the entropic EDF still closely follows its continuous counterpart even for large Mach  numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This means that the entropic model exhibits less pronounced Galilean invariance in it effective viscosity as  compared to the classical LBM with second-order EDF at moderate Mach numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In order to correctly recover the  off-diagonal components of the third-order moments tensor in 2-D, the third-order terms of the Hermite expansion  must be included.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The diagonal components deviations on the other hand can only be accounted for via correction  terms discussed in the next paragraph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Restoring Galilean-invarience of dissipation rate of shear/normal modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Given that the EDF of the product-form  is equivalent to the fourth-order Hermite-expanded EDF, only the Hermite expansion-based EDFs will be considered  here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A simple CE analysis shows that at the NS level, to match the viscous (non-equilibrium) stress tensor for the  continuous Boltzmann equation, moments of orders two and three of the EDF must be exactly recovered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Integrating  in phase space, the following continuous second- and third-order moments are in fact recovered [49]:  ΠMB  αβ = ρuαuβ + ρc2  sδαβθ,  (391a)  ΠMB  αβγ = ρuαuβuγ + ρc2  s  �  uαδβγθ  �  cyc ,  (391b)  52  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  +  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  1  U :  3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  0  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  1  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  1  Wc-2  1  0  1  2  ux/cs  2  1  0  1  2  xxx  2  1  0  1  2  ux/cs  10-4  10-3  10-2  10-1  100  Figure 3: Deviations in the third order moment Πeq  xxx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Left: Moments an Right: Normalized errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Black solid line: Maxwellian distribution  moment, blue dash-dotted line: second-order Hermite expansion, green dotted line: entropic equilibrium and red dashed line: product form  equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  ux/cs  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  uy/cs  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  ux/cs  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  uy/cs  102  1  10-2  10-4  Figure 4: Deviations in the third order moment Πeq  xxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Left: entropic equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Right: second-order Hermite expansion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  while one gets the following moments with the second- and third-order discrete EDFs:  Πeq,2  αβ = ρuαuβ + ρc2  sδαβθ,  (392a)  Πeq,2  αβγ = ρc2  s  �  uαδβγ  �  cyc ,  (392b)  53  and :  Πeq,2  α  = ρuαuα + ρc2  sδαβθ,  (393a)  Πeq,3  αβγ = ρc2  sδαβγ  �  uαδβγ  �  cyc + ρ  �  1 − δαβγ  �  {uαuβuγ + c2  s  �  uαδβγθ  �  cyc}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (393b)  The product-form EDF recovers the same second- and third-order moments as the third-order Hermite expansion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  To better put forward the shortcoming of the first-order stencil in recovering the NS level terms, let us perform now  a brief CE analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Introducing the multi-scale expansion into the space and time-continuous system of equations  and sorting terms of different orders in ϵ into separate equations and taking moments of orders zero and one to get  mass and momentum balance, at order two in ε (NS level) the following momentum balance equations are recovered:  ∂(2)  t ρuα + ∂βτ  �  ∂(1)  t Πeq  αβ + ∂γΠeq  αβγ  �  + ∂βτ  �������  �  i  ci,αci,βΨ(1)  i  ������� = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (394)  For the stress tensor to be correctly recovered at this scale one must have:  Ψi = wi  2c4s  ∂αHi,βγδΠeq  αβγ,  (395)  where δΠeq  αβγ designates the deviation of the discrete EDF moment from its continuous counterpart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' An interesting  point to note here is that this form of the correction term is only valid for the time and space continuous discrete  Boltzmann system of equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' After discretization in space and time and operation of the change of variable specific  to the LBM the correction term will be slightly modified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  It is also worth noting that the treatment for third- and fourth-order EDFs differs from that at second-order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Regarding  third- and fourth-order EDFs, in 2-D one obtains:  Ψeq,N>2  i  = wi  2c4s  �  Hi,xx∂xδΠeq  xxx + Hi,yy∂yδΠeq  yyy  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (396)  Instead, for the second-order EDF, additional correction terms are required, or one fails to recover correctly deviatoric  components of the third-order moments:  Ψeq,2  i  = Ψeq,N>2  i  + wi  c4s  Hi,xy  �  ∂x  �  δΠeq,2  xxy + δΠeq,2  xyy  �  + ∂y  �  δΠeq,2  xxy + δΠeq,2  xyy  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (397)  This type of correction for the third-order equilibrium moments was introduced in [63] and later reprised in [64, 65,  58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Different from the approach taken previously, one can also directly introduce the correction term at order ϵ2 as  proposed in [66, 67].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In practice this means that the correction would involve a Laplacian and as such be expanded as:  Ψ  ′  i = ϵ2Ψ  ′  i  (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (398)  Re-writing the momentum balance equations at the NS level with this new correction term:  ∂(2)  t ρuα + ∂βτ  �  ∂(1)  t Πeq  αβ + ∂γΠeq  αβγ  �  −  �  i  ci,αΨ  ′  i  (2) = 0,  (399)  one gets the following restrictions on the correction term:  �  i  Ψ  ′  i  (2) = 0,  (400)  and:  �  i  ci,αΨ  ′  i  (2) = ∂β  �µ  p∂γδΠeq  αβγ  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (401)  54  The correction term using the second approach can therefore be defined as:  Ψ  ′  i = wi  c2s  ci,α∂β  �µ  p∂γδΠeq  αβγ  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (402)  Both approaches effectively restore Galilean invariance at the NS level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' However, the first approach allows for more  flexibility in the treatment of the spatial derivative, and in practice allows for compressible flow simulations in the  low supersonic regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For a detailed comparative study of both approaches and different discretization strategies,  interested readers are referred to [58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Space and time discretization: Integration along characteristics  With the Discrete velocity Boltzmann system of non-homogeneous hyperbolic partial differential equations in  hand, the next step is to operate discretization in physical space and time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Realization without force and correction term  Starting from the phase-space discretized form of the Boltzmann equation (a set of Q equations):  ∂t fi + ci · ∇fi = Ωi,  (403)  where Ωi is the collision term, the idea of the Lagrangian approach consists of integrating them along their respective  characteristics, which contrary to Lagrangian solvers for the NS equations (given that fluid particle path-lines are  space- and time-dependent), results in an exact solution for the advection term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' As such integrating the equations  from a time t to t + δt along the stencil directions one obtains:  fi (r + ciδt, t + δt) − fi (r, t) =  � t+δt  t  Ωi  �r(t′), t′� dt′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (404)  Obviously within the context of the Lagrangian approach δr/δt is tied to the abscissae obtained from the Gauss-  Hermite quadrature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In the case of the third-order quadrature for the streaming operation to results in space-filling  lattices:  ||ci,α||=  �  3kBT0  m0  = δr  δt .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (405)  Coming back to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (404), it is observed that all the difficulty in this approach lies in the estimation of the collision  contribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A simple first-order explicite approximation would be:  � t+δt  t  Ωi  �  r(t  ′), t  ′�  dt  ′ = δt  2 Ωi (r, t) + O  �  δt2�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (406)  The classical LBM approach relies on a higher-order alternative;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' To get a second-order accurate scheme one can use  the trapezoidal rule to evaluate the integral:  � t+δt  t  Ωi  �  r(t  ′), t  ′�  dt  ′ = δt  2 Ωi (r, t) + δt  2 Ωi (r + ciδt, t + δt) + O  �  δt3�  ,  (407)  which in turn results in an implicit scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' To take out the implicitness of the resulting equation, the distribution  function is re-defined via the following change of variables:  ¯fi = fi − δt  2 Ωi,  (408)  ¯f eq  i  = f eq  i ,  (409)  Ωi =  1  τ + δt/2  � ¯f eq  i  − ¯fi  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (410)  55  Using this change of variable and Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (404) and (407) one gets:  ¯fi (r + ciδt, t + δt) − ¯fi (r, t) + δt  2 Ωi (r + ciδt, t + δt) − δt  2 Ωi (r, t) = δt  2 Ωi (r + ciδt, t + δt) + δt  2 Ωi (r, t) ,  (411)  which in turn using Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (408)–(410) results in the classical collide-stream algorithm:  ¯fi (r + ciδt, t + δt) − ¯fi (r, t) = δt  ¯τ  �  f eq  α (r, t) − ¯fi (r, t)  �  ,  (412)  where ¯τ is defined as:  ¯τ = τ + δt/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (413)  It is also interesting to note that the new distribution functions have the following properties:  �  i  ¯fi =  �  i  fi − δt  2  �  i  Ωi = ρ,  (414)  �  i  ci ¯fi =  �  i  ci fi − δt  2  �  i  ciΩi = ρu,  (415)  where we have used the collision-invariance of the zeroth- and first-order moments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' More generally for higher-order  moments:  �  i  Hn (ci) ¯fi =  �  i  Hn (ci) fi − δt  2  �  i  Hn (ci) Ωi =  �  1 + δt  2¯τ  �  an − δt  2¯τ aeq  n .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (416)  While to derive the previous scheme, particle streaming was restricted to be on-grid, it is not a necessary condition  for a working LB scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For the so-called semi-Lagrangian methods the restriction of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (405) is relaxed, resulting  in off-lattice propagation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' As such, in this formulation the time-evolution operator of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (412) is supplemented with  an interpolation step to reconstruct the populations at the discrete grid-points:  ¯fi (r, t + δt) =  �  rj  A  �  r, r j  � �  ¯fi  �  r j − ciδt, t  �  + δt  ¯τ  � ¯f eq  i  �  r j − ciδt, t  �  − ¯fi  �  r j − ciδt, t  ���  ,  (417)  where A  �  r, r j  �  are the coefficients involved in the interpolation process and r j are the interpolation stencil points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In  practice, this approach has two main advantages: (a) it allows one to use quadratures of order four or five since those  result in non-space-filling stencils, they are unusable with the on-lattice solvers [68], (b) freedom over the choice  of the time-step as the streaming does not need to fall on-grid [69, 70].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' On the other hand, the introduction of the  interpolation operator strips the LBM from its strictly conservative property.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The interpolation-supplemented LBM  can only guarantee global mass conservation for uniform grids [68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Correction for the diagonal components of the equilibrium third-order moments tensor  In LBM schemes taking account of the correction term the system of PDE’s changes into:  ∂t fi + ci · ∇ fi = Ωi + Ψi,  (418)  where Ψi denotes the correction term derived in Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (395) and (402).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The emergence of this additional term only  affects the previously-detailed process of discretization in time and space through the change of variable:  ¯fi = fi − δt  2 Ωi − δt  2 Ψi,  (419)  ¯f eq  i  = f eq  i ,  (420)  Ωi =  1  τ + δt/2  � ¯f eq  i  − ¯fi  �  −  δt/2  τ + δt/2Ψi,  (421)  which in turn leads to the following final algebraic system:  ¯fi (r + ciδt, t + δt) − ¯fi (r, t) = δt  ¯τ  �  f eq  i  (r, t) − ¯fi (r, t)  �  +  �  1 − δt  2¯τ  �  Ψi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (422)  This consistent derivation of the extended LBM holds for any form of the correction term, whether it is introduced  simply as a Hermite-expanded term [64] or the extended equilibrium approach [71].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  56  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Introduction of external body forces  Introduction of body force contributions in the context of LBM boils down to finding suitable approximations to  the body force term F  ρ · ∇v f in the Boltzmann equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A large number of approaches and approximations have been  devised over the years;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' We will restrict our review to the most widely used schemes here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For a more in-depth study  of different forcing schemes we invite interested readers to look into [72, 73, 74].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Given that all approximations can  be recast into a generic form made up of a discrete source term Fi and a redefined real velocity ureal , they will all be  presented in that form:  fi(r + ciδt, t + δt) − fi(r, t) = δt  ¯τ  �  f eq  i (ρ, u) − fi(r, t)  �  + Fi,  (423)  with:  u = 1  ρ  �  i  ci fi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (424)  The aim of the approximation here being recovery of correct hydrodynamic limit, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Euler+NS level dynamic we  will have a more detailed look at the moments of Fi appearing there.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' It is clear that zeroth- and first-order moments  will appear at the Euler level:  ∂(1)  t ρ + ∇ · ρu = 0,  (425)  ∂(1)  t ρu + ∇ · ρu ⊗ u + ∇ · ρc2  sI +  �  i  ciFi = 0,  (426)  At the NS level the CE analysis leads to:  ∂(2)  t ρ + 1  2∇ ·  �  i  ciFi = 0,  (427)  ∂(2)  t ρu + 1  2∂(1)  t  �  i  ciFi + 1  2∇ ·  �  i  ci ⊗ ciFi − ∇ ·  �1  2 − ¯τ  δt  � �  i  ci ⊗ ciFi + ∇ ·  �1  2 − ¯τ  δt  � �  u ⊗ F + u ⊗ F†�  +∇ · ρc2  s  �1  2 − ¯τ  δt  � �  ∇u + ∇u†�  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (428)  For this system to match the targeted hydrodynamic limit it is obvious that one must have:  �  i  ciFi = δtF,  (429)  ρu + 1  2  �  i  ciFi = ρureal,  (430)  �  i  ci ⊗ ciFi = δt2  4ρ¯τ F ⊗ F + δt  �  u ⊗ F + u ⊗ F†�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (431)  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Shan and Chen’s forcing scheme  This approach was initially proposed by Shan and Chen to model multi-phase fluid systems [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In Shan and  Chen’s forcing scheme the velocity used in the computation of the discrete equilibrium is shifted by ∆u = ¯τF  ρ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' While  in its original form, as presented in [12], the force contribution only appears in the EDF, the corresponding discrete  time-evolution equations can be re-written as:  fi(r + ciδt, t + δt) − fi(r, t) = δt  ¯τ  �  f eq  i (ρ, u) − fi(r, t)  �  + δt  ¯τ  �  f eq  i (ρ, u + ∆u) − f eq  i (ρ, u)  �  ������������������������������������������������������������������������  Fi  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (432)  Additionally the real fluid velocity computation is also affected by the force as:  ureal = 1  ρ  �  i  ci fi + δtF  2ρ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (433)  57  The source term has the following zeroth- to second-order moments:  �  i  Fi  =  0,  (434)  �  i  ciFi  =  Fδt,  (435)  �  i  ci ⊗ ciFi  =  δt  �  F ⊗ u + F ⊗ u†�  + δt¯τ  ρ F ⊗ F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (436)  This means that this approach satisfies condition (429).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' However, given the definition of the real velocity,  ρureal ⊗ ureal = ρu ⊗ u + δt  2  �  u ⊗ F + u ⊗ F†�  + δt2  4ρ F ⊗ F,  (437)  it admits an error of the following form in the convective term of the NS level momentum balance equation:  δconvection = ∇ · δt2  ρ  � ¯τ2  δt2 − 1  4  �  F ⊗ F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (438)  It should be noted that, expanding the body force as a power series of the smallness parameter, this deviation in the  second-order moment would scales with ε3 and therefor not appear formally in the momentum balance equation at the  Navier-Stokes level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Nevertheless, for cases involving large force contributions higher-order dynamics can spoil Euler  and NS level behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Later on, this scheme was improved upon via a Hermite expansion of the force term in the  Boltzmann equation [75].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Using the Hermite expansion of the distribution function, the force term can be expanded  as [75, 49]:  F · ∇v f =  �  n=0  (−1)n  n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  F ⊗ an−1 : ∇n+1  v  w(v) = −w(v)  �  n=0  1  (n − 1)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' F ⊗ an−1 : Hn(v).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (439)  Absorbing the force in the Boltzmann equation into the equilibrium and using the above-presented Hermite expansion  of the body force term a correction to the original Shan and Chen scheme was proposed as:  Fi = δt  ¯τ  �  f eq  i (ρ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' u + ∆u) − f eq  i (ρ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' u)  �  − ρwi¯τ  2  �(ci · F)2  c4sρ2  − F2  c2sρ2  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (440)  which changes the second-order moment of the force term into:  �  i  ci ⊗ ciFi = δt  �  u ⊗ F + u ⊗ F†�  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (441)  eventually leading to an error term that is still present but independent from the relaxation time:  δconvection = −∇ · δt2  4ρ F ⊗ F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (442)  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Luo’s scheme  As an approximation to the body force term appearing in the Boltzmann expression, and assuming a near equilib-  rium flow, Luo proposed an expansion similar to that used for the equilibrium [76], i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  F  ρ · ∇v f ≈ ρw(v) [a0 + a1 · v + a2 : v ⊗ v + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' ] ,  (443)  where expansion coefficients ai are computed via the following constraints on the moments of the body force term:  � F  ρ · ∇v fdv  =  0,  (444)  �  v F  ρ · ∇v fdv  =  −F,  (445)  �  v ⊗ v F  ρ · ∇v fdv  =  −F ⊗ u − F ⊗ u†.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (446)  58  Applying these constraints and limiting the expansion to order two the following space/time-continuous approxima-  tion is obtained:  F  ρ · ∇v f = −w(v)  � F · (v − u)  c2s  + (v · u)v · F  c4s  �  + O  �  v3, u2�  ,  (447)  which after discretization in phase space results in:  F  ρ · ∇v f = −wi  � F · (ci − u)  c2s  + (ci · u)ci · F  c4s  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (448)  One interesting point worth noting in Luo’s forcing scheme is that over the years a point of confusion seems to have  been installed in the literature [72, 73, 74];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In the original article [76], the author has used a first-order approximation  to the collision integral after integration along characteristics, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  � t+δt  t  1  τ  �  f eq  i (r + cit′, t′) − fi(r + cit′, t′)  �  + Fi(r + cit′, t′)dt′ ≈ δt  τ  �  f eq  i (r, t) − fi(r, t)  �  + δtFi(r, t),  (449)  naturaly leading to the following time-evolution equations:  fi(r + ciδt, t + δt) − fi(r, t) = δt  τ  �  f eq  i  − fi  �  + Fiδt,  (450)  where contrary to the second-order approach using the trapezoidal rule, the relaxation time and distribution functions  have not been redefined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Most articles following this scheme apply this final expression in the context of the classical  lattice Boltzmann model involving a re-definition of the relaxation coefficient and distribution function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Properly  transposing Luo’s scheme to a second-order LBM would instead lead to:  Fi = δt  ¯τ  �  f eq  i (ρ, u + δtF  2ρ ) − f eq  i (ρ, u)  �  +δt  �  1 − δt  2¯τ  �  wi  � F · (ci − u)  c2s  + (ci · u)ci · F  c4s  �  +  �  1 − δt  2¯τ  � wiδt2  ρ  �(ci · F)2  c4s  − F2  c2s  �  ,  (451)  with,  ureal = 1  ρ  �������  Fδt  2  +  �  i  ci fi  ������� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (452)  This leads to an error in the convection term of the form:  δconvection = ∇ · δt  �  ¯τ − δt  2  � F ⊗ F  ρ  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (453)  This approach is exactly equivalent to Guo’s forcing scheme [77].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A number of articles have reported better stability  of this approach as compared to other forcing schemes [72], however this is clearly a consequence of the first-order  nature of the model as (mis-)used there.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' He et al’s scheme  The next scheme, proposed by He et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' relies on the following fundamental approximation when evaluating the  body force contribution [78]:  f(r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' t,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' v) ≈ f eq(r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' t,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' v),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (454)  leading to:  F  ρ · ∇v f ≈ F  ρ · ∇v f eq = F  ρ · v − u  c2s  f eq,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (455)  which after discretization in phase space,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' integration along characteristics and using the trapezoidal rule results in:  Fi = δt  ¯τ  �  f eq  i (ρ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' u + δtF  2ρ ) − f eq  i (ρ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' u)  �  + δt  �  1 − δt  2¯τ  � F  ρ · ci − u  c2s  f eq(ρ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' u + δtF  2ρ ),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (456)  with  ureal = 1  ρ  �������  Fδt  2  +  �  i  ci fi  ������� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (457)  59  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Guo’s scheme  Guo proposed a modified forcing scheme taking into account so-called discrete effects in [77].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In essence Guo  followed an approach quite similar to Luo to derive the new scheme, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' moment matching.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Similar to Luo [76],  Guo started with a polynomial approximation to the force contribution with coefficients to be fixed by moments  constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' However, at the difference of Luo, moments constraints were extracted from a Chapmann-Enskog analysis  of the lattice Boltzmann equations, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' after discretization in space and time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Therefore, the remark made in the  previous paragraphs about the exact correspondence between Luo’s scheme, once a second-order integration along  characteristics has been applied, and Guo’s discrete forcing scheme is not surprising at all.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Kupershtokh’s scheme  This approach, also referred to as the exact difference method approximates the force contributions as [79, 80]:  Fi =  �  f eq  i (ρ, u + ∆u) − f eq  i (ρ, u)  �  ,  (458)  with, different from the Shan-Chen scheme, ∆u =  Fδt  ρ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Furthermore the velocity u is computed as the first-order  moment of the distribution function with no additional terms and the real fluid velocity, ureal, is computed as ureal =  u + Fδt  2ρ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' At the difference of the Shan-Chen scheme the second-order moment of the source term is:  �  i  ci ⊗ ciFi = δt  �  F ⊗ u + F ⊗ u†�  + δt2  ρ F ⊗ F,  (459)  which does not show any dependence on the relaxation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' As for previously-listed schemes, the exact difference method  also admits a convective error of the form:  δconvective = ∇δt  �  ¯τ − δt  4  � F ⊗ F  ρ  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (460)  This deviation can be eliminated by introducing an additional contribution in the source term as:  Fi =  �  f eq  i (ρ, u + ∆u) − f eq  i (ρ, u)  �  −  �  1 − 1  4¯τ  �  wiH2 : F ⊗ F  ρ  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (461)  The different strategies to incorporate body forces into the LBM are listed in Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Approach  Fi  ureal  Leading-order error  Improvement  Shan and Chen [12]  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (432)  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (433)  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (438)  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (440)  Luo [76]  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (451)  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (452)  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (453)  None  Guo [77]  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (451)  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (452)  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (453)  None  EDM [79]  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (458)  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (451)  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (460)  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (461)  Table 4: Summary of body force methods in LBM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Stability of LB-BGK  The applicability range of different closures for the discrete equilibrium distribution functions was characterized  in previous sections by monitoring deviations of moments of order two and three.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Here we discuss the issue of  application range with more details via the linear stability and positivity domain of the discrete equilibrium distribution  functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Prior to that we also discuss a numerical artifact brought about by the isothermal assumption of the classical  LBM responsible, in part, for the stability of the solver.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  60  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Isothermal closure: spurious bulk viscosity and stabilization of normal modes  Although widely used for simulation in the incompressible regime, it is well known that the LBM relies instead  on an isothermal closure leading to a fixed and finite speed of sound, cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For a characteristic convective velocity  U, in the limit U/cs → 0 it is expected to recover the incompressible flow behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This means that contrary to  classical incompressible solvers with the Poisson equation as closure for the pressure field, here ∇ · u � 0 and cs � ∞,  which in turn points to presence of so-called acoustic eigen-modes that are damped at a rate η, also referred to as the  bulk viscosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For low-dissipative central-in-space discretization methods like the LBM, one must therefor guarantee  positivity of the dissipation rates of both shear and acoustic modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' However, it is well known that for a mono-atomic  molecule η=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Given that only translational degrees of freedom are accounted for, the LBM is based on a mono-  atomic molecule and should lead to zero bulk viscosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This is readily observed by looking at the non-equilibrium  stress tensor of the Boltzmann equation at the NS level:  Π(1)  αβ = −τ  �  ∂(1)  t  �  vαvβ f eqdv + ∂γ  �  vγvαvβ f eqdv  �  ,  (462)  where the first and second terms can be, after some algebra, re-written as:  �  vγvαvβ f eqdv = ρuαuβuγ + ρkBT  m  �  uαδβ,γ  �  cyc ,  (463)  and  ∂(1)  t  �  vαvβ f eqdv = δαβ∂(1)  t ρkBT  m + uα∂(1)  t ρuβ + uβ∂(1)  t ρuα − uαuβ∂(1)  t ρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (464)  Using the mass, momentum and internal energy balance equations,  ∂(1)  t ρkBT  m + ∂αρkBT  m uα = −2ρkBT  Dm ∂αuα,  (465)  the non-equilibrium stress tensor can be re-written as:  Π(1)  αβ = −τρkBT  m  �  ∂αuβ + ∂βuα − 2  D∂γuγ  �  ,  (466)  confirming the absence of bulk viscosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In the classical LBM, an isothermal closure is used for energy/temperature  meaning the solvability condition for energy is replaced by kBT  m = kBT0  m0 leading to the following non-equilibrium stress  tensor [81]:  Π(1)  αβ = −τρkBT  m  �  ∂αuβ + ∂βuα − 2  D∂γuγ  �  − τρ2kBT  Dm ∂γuγ,  (467)  meaning η = 2  Dµ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' After discretization in phase space, space and time this property is maintained and one recovers a  non-zero bulk viscosity for the classical isothermal LBM:  η = 2c2  s  D  �  ¯τ − δt  2  �  + O(Ma2),  (468)  where the Galilean-variant error comes from deviation in the diagonal components of the equilibrium third-order  moments which can be eliminated via appropriate correction terms derived in previous sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Positivity of the discrete equilibria  Numerical instability in the LBM has been often tied to the absence of a positivity constraint on the discrete  populations [82, 83, 84].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In the specific case of LBM for advection-diffusion equations the positivity region of the  discrete EDF has been shown to coincide with the linear stability domain in the limit of vanishing diffusion coeffi-  cient [85, 86, 87].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' To that end, before conducting linear stability analyses we look at the positivity domains of different  discrete EDFs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The positivity domains of the second-order polynomial, product-form and entropic EDFs are shown  in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 5, 6 and 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' While the polynomial forms of the EDF, both second-order and product form, do not guarantee  positivity of the EDF for all velocities, the entropic EDF ensures that equilibrium populations remain positive for all  velocities −1 ≤ uαδr/δt ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  However, as will be seen in the next chapter, different from the advection-diffusion  LBM the positivity domain is not necessarily a reflection of linear stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  61  Figure 5: Illustration of positivity of the second-order polynomial EDF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Left: Domain ensuring positivity of discrete equilibrium populations in  red.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Right: Values of three discrete populations as a function of ux/cs for uy/cs = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Figure 6: Illustration of positivity of the product-form EDF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Left: Domain ensuring positivity of discrete equilibrium populations in red.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Right:  Values of three discrete populations as a function of ux/cs for uy/cs = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Linear stability of discrete solver  The von Neumann (VN) stability analysis aims at studying the time evolution of a perturbation ¯f  ′  i that is injected  into the linearized discrete time evolution equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The perturbation is expanded as a combination of standing waves,  whose propagation speed and attenuation rate will be obtained as a result of the VN analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A positive attenuation  rate will result in a growth of the error at the corresponding wave-length and linear instability of the solver for the  set of parameters considered (¯τ, Ma, etc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' On the contrary, the scheme is linearly stable if it remains negative for all  wave-numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Furthermore, the spectral behavior and accuracy can be readily analyzed by comparing the spectral dispersions and  dissipations to the theoretical modes obtained from the linearized NS equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The NS theoretical modes for an  isothermal flow can be expressed as [88]:  ωshear = u · k − iνk2,  (469a)  ωacoustic = (u ± cs) · k − i  �D − 1  D  ν + η  2ρ  �  νk2,  (469b)  where D is the physical dimension of the system and k the wave-number vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' As a consequence, the VN stability  analysis can be used to evaluate the spectral behavior and linear stability domain of a LBM for a given set of param-  62  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8  1  feq  3  feq  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  S  req  0  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  0  1  0  1  2  1  0  1  2  u /c  u /c  x  s1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  c  feq  0  IJ  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  0  1  0  1  2  1  0  1  2  u /c  u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' /c  x  S  xFigure 7: Illustration of positivity of the entropic EDF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Left: Domain ensuring positivity of discrete equilibrium populations in red.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Right: Values  of three discrete populations as a function of ux/cs for uy/cs = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  eters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' As such it can be perceived as a tool to objectively evaluate the stabilization properties of different collision  models, on the basis of necessary conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The latter comes from the fact that the analysis relies on a linearization  step and as such gets the sufficient condition for stability only under the linear regime assumption (small amplitude  perturbations).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' It has been widely used in the past to evaluate the stability properties of the LBM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Interested readers  are referred to [89, 90, 91, 87, 92, 93, 94, 88], among other sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  As mentioned previously, the equilibrium state is one of the most important components of a kinetic scheme and  controls, for the most part, the leading-order dynamics of the system (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' the macroscopic PDEs of interest), but  also the behavior of higher-order (errors, ghost modes) terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The effects of the EDF on leading-order terms were  studied in previous sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In this subsection, using the VN formalism we look at the effect of the EDF on the  linear stability domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' To do so the eigenvalue problem of the VN equations is solved for different values of non-  dimensional viscosities, over the entire wave-number space, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' kx and ky with a resolution of 100 points in each  direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The highest Mach number resulting in negative dissipation rates over all wave-numbers is retained as the  linear stability limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' These limits are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Looking at those results a number of points are worth noting:  Figure 8: Linear stability domains of SRT collision operator with EDFs of orders (from left to right) two, three and four.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The fourth-order expansion  is equivalent to the product-form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Reproduced from [95].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  For all of these EDFs, regardless of the value of the non-dimensional viscosity (Fourier number), the maximum stable  Mach number never goes beyond Ma =  √  3 − 1 ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='732.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This confirm the observation in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 390:  Mamax  α  = |umax  α  |  cs  =  √  3 − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (470)  63  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8  1  feq  3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  S  feq  0  fi  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  0  1  0  1  2  1  0  1  2  u_ /c  u_ /c  xsgo-  HO  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  0  1  1  a  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  /  9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  Q  0  10-3  10-1 100  10-5  10-3  10-1 100  10-5  10-3  10-1 100  10-5  vSt/ Sr2  vSt/Sr2  vSt/Sr2Furthermore while the addition of third-order components appears not to have a large effect on the stability domain,  the fourth-order component (which does not affect the terms appearing at the NS level) extends it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Apart from extending the linear stability domain, the addition of the fourth-order component results in more isotropic  behavior especially for small values of the non-dimensional viscosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The directional stability domains obtained with  different orders of the EDF are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' It is also worth noting that the entropic EDF, is found to come with  Figure 9: Illustration of anisotropy of linear stability domains for EDFs of orders (from left to right) two, three and four, and for seven different non-  dimensional kinematic viscosities, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (  )5 × 10−4, (  )1 × 10−3, (  )5 × 10−3, (  )0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='01, (  )0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='05, (  )0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1, (  )0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Reproduced  from [95].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  unconditional linear stability for all values of the Mach number supported by the stencil, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ma =  √  3, even for  vanishing viscosities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This unconditional stability can be readily explained by the observations in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 2, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' self-  adjusting sound speed guaranteeing fastest mode propagates at a speed smaller than or equal to δr/δt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The stability  domain is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This in turn confirms the effectiveness of the discrete EDF construction approach in  guaranteeing linear stability (by enforcing a discrete H-theorem).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Finally, one can readily confirm the assertion made  Figure 10: Illustration of linear stability domain for the entropic EDF for seven different non-dimensional kinematic viscosities, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (  )5×10−4,  (  )1 × 10−3, (  )5 × 10−3, (  )0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='01, (  )0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='05, (  )0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1, (  )0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Reproduced from [95] and [93].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  in the previous subsections concerning the effect of third-order Hermite terms on the deviatoric components of the  third-order moments tensor by looking at the spectral dissipation of physical modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The spectral dissipation of the  shear modes of the third and second-order EDF for three different Mach numbers are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' It is clearly  observed that for the third-order EDF, in the limit of vanishing wave-numbers kx/δr → 0, the obtained dissipations  converge to the correct value regardless of the Mach number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' However for the second-order EDF signs of Galilean  invariance problems are clearly observed as the continuum limit of shear mode dissipation changes with the Mach  64  π/2  π/3  π/6  0  0  1  2  Maπ/2  π/2  π/2  π/3  π/3  元/3  π/6  π/6  π/6  0  0  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  Ma  Ma  MaFigure 11: Shear mode dissipation rate (normalized by its physical counterpart) for (left) third- and (right) second-order EDF for three different  Mach numbers, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (in red) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1, (in blue) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2 and (in green) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The continuum reference is shown with a plain black line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Reproduced from [95].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  The results obtained in this subsection also point to the fact that the SRT collision operator becomes practically unus-  able below non-dimensional viscosities of 10−3 − 10−4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Different strategies have been developed to allow simulations  at lower non-dimensional viscosities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' We will discuss some of these approaches in the next section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Extension of stability domain  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Relaxation of discrete populations in alternate spaces  A first attempt at extending the stability domain of the LB-BGK solver, introduced in the early 2000s’ is the so-  called Multiple Relaxation Time (MRT) collision model [96, 97, 98].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The idea behind this approach is to relax the  discrete populations in a space other than the discrete populations;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In principle this introduces additional parameters  independent from the kinematic viscosity, opening the door for a more flexible equilibration path [98, 97].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The added  degrees of freedom can be useful both physically and numerically [81].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In this approach, the BGK collision operator  is written as:  ΩMRT  i  = M−1SM  �  f eq  i  − fi  �  ,  (471)  where M is the transformation matrix from discrete population to the relaxation space such that:  Πi =  �  j  Mi j fj,  (472)  where Πi are the moments chosen for the application of the collision operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' As seen in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 471, using the  transformation matrix M the discrete populations are taken to momentum space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Then the relaxation matrix S is  applied and relaxed moments are converted back to discrete populations through M−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The relaxation rates tensor S  is defined as:  S = diag( 1  ¯τ0  , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' ,  1  ¯τQ−1  ),  (473)  where the operator diag is defined as:  diag(A) = (A ⊗ 1) ◦ I,  (474)  with A a given vector, 1 a vector with elements 1, I the unitary tensor and ◦ the Hadamard product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For a typical  DdQq stencil, q moments are needed to span the phase-space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The choice of the relaxation space, is the other important  ingredient in this class of models both differentiating between different approaches listed below and controlling the  numerical properties of the solver.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For instance Lallemand and Luo [91] proposed a set of mutually orthogonal  moments for the D2Q9 stencil defined as:  Πi ∈ {Π0, 3(Πxx + Πyy) − 4Π0, , Πx, 3(Πxxx + Πxxy) − 5Πx, Πy, 3(Πyyy + Πxyy) − 5Πy, Πxx − Πyy, Πxy}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (475)  65  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8  0  元/4  π/2  3元/4  0  π/4  π/2  3元/4  元  T  kaSr  kaSrWith this choice of moments for the relaxation it is clear that the relaxation rates of the last two moments corresponds  to shear viscosity and that of the second moment to the bulk viscosity while the rest can be freely tuned for stabil-  ity [97], optimal dispersion [88], fixing the boundary position for the half-way bounce-back boundary condition [99]  etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='. It is interesting to note that this specific choice of moments space along with the optimized set of ghost relaxation  rates do not, as opposed to the conclusions of [91], actually extend the linear stability domain of the BGK collision  operator as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This might be explained by the fact that in [91], the authors assumed the wave-number  Figure 12: Linear stability domain of the MRT collision operator of [91] with the corresponding set of optimized relaxation rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Following the  original publication the discrete equilibrium is taken to be a second-order polynomial expansion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  vector k always parallel to the velocity vector u which is not a sufficient condition for linear stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Here the full  2-D space of wave-number vectors has been scanned for all considered velocities resulting in a smaller domain of  stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' While the moments chosen as basis for the MRT realization of [91] are orthogonal, other alternatives based  on weighted orthogonal moments have also been proposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For instance the Hermite polynomials form a basis of  moments that are mutually orthogonal with respect to the weighted dot-product and are defined as:  Πi ∈ {Π0, Πx, Πy  ������  a1  ,  a2  ��������������������������������������������������  Πxy, Πxx − c2  s, Πyy − c2  s, Πxxy − c2  sΠy, Πxyy − c2  sΠx  ��������������������������������������������������������  a3  ,  a4  ��������������������������������������������������������������  Πxxyy − c2  s  �  Πxx + Πyy  �  + c4  s}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (476)  Below we will look into two other classes of MRT collision models that present conceptual singularities with respect  to other realizations, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' the two relaxation time model and central moments-based MRT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Two relaxation time model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' As noted in [100], using the full set of moments leads to a number of free parameters, the  ghost moments relaxation coefficients, for which no formal physical closures exist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' As previously mentioned, apart  from the entropic argument, only a posteriori closures based on numerical arguments can be devised for these free  parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Another way around this issue is to adopt targeted, on specific moments of the distribution function, mini-  malist MRT models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The TRT (Two Relaxation Time) collision operator developed and proposed by I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ginzburg is an  example of these minimalist models [101, 102, 103].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In this collision model the distribution function is decomposed  into symmetrical, f +  i , and non-symmetrical parts, f −  i , defined as [103]:  f +  i = fi + f¯i  2  ,  (477a)  f −  i = fi − f¯i  2  ,  (477b)  resulting in two relaxation times, ¯τ+ and ¯τ−, with the first one tied to the fluid viscosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The collision operator is then  expressed as [102]:  ΩTRT  i  = 1  ¯τ+  �  f eq+  i  − f +  i  �  + 1  ¯τ−  �  f eq−  i  − f −  i  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (478)  66  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  Q  101  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3  a  N  @  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  0  10-3  10-1  100  Vot/8r2As demonstrated in [104], judicious choices of the free parameter, the so-called “magic values”, can lead to, among  other effects, the wall being placed exactly half-way when used with the half-way bounce-back boundary condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Defining :  Λ =  � δt  ¯τ+ − 1  2  � � δt  ¯τ− − 1  2  �  ,  (479)  it can be shown that setting Λ = 3/16 places the wall half-way [105], while Λ = 1/6 and Λ = 1/12 cancel out,  respectively, the third- and fourth-order spatial error terms [106, 107] and Λ = 1/4 results in optimal stability in that  specific relaxation space [108].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  The lattice kinetic scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Another example of a minimalist MRT scheme is that of the so-called LKS (lattice kinetic  scheme) [109, 110].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This collision model is a TRT scheme in the space of Hermite moments, where second-order  moments are relaxed using the fluid viscosity while higher-order moments (three and four) are relaxed using a free  parameter [92].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For the LKS the collision operator is written as [111, 109]:  ΩLKS  i  = −1  ¯λ  �  fi − f eq,LKS  i  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (480)  The second relaxation coefficient ¯λ is related to the SRT relaxation coefficient through [110]:  ¯λ − A = ¯τ,  (481)  where A is a constant fixed by the choice of the free parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The EDF is then defined as [92]:  f eq,LKS  i  = f eq  i  − A  ¯τ  wi  2 aneq  2  : H2,i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (482)  The original regularized lattice Boltzmann method (RLBM), as will be shown in the next sections, is an LKS solver  where the free relaxation coefficient is set to 1 [92].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This collision operator has been applied to a variety of configura-  tions ranging from multi-phase [112] to non-Newtonian flows [113] and advection-diffusion equations with variable  diffusion coefficients [114, 115].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Central moments-based decomposition  In the Central Moments Multiple Relaxation Time (from here on referred to as CM-MRT) model, while the  paradigm is quite similar to the MRT, a different set of moments are used: the central moments, designated by  �Πx .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' x  ����  ×p  y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' y  ����  ×q  z .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' z  ����  ×r  and defined as [116, 117]:  �Πx .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' x  ����  ×p  y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' y  ����  ×q  z .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' z  ����  ×r  =  �  i  �ci,x − ux  �p�  ci,y − uy  �q�ci,z − uz  �r fi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (483)  Taking again the example of the D2Q9 stencil with the Hermite coefficients as the projection space and a fourth-order  expansion of the EDF results in the following central equilibrium moments [118, 119, 120]:  �Πeq = {ρ, 0, 0, 0, 0, 0, 0, 0, 0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (484)  The stability domain of this collision model is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' From the stability domain one can already see  that setting ν′ = ν which is equivalent to the SRT operator is not the optimal choice in terms of linear stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' An  optimal route can be observed at ν′δt  δr2 ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='167 which, as will be seen in the next section, is equivalent to the recursive  regularized collision operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' While the Hermite-based moments space does not allow for independent control over  bulk viscosity this can readily be achieved by modifying the second-order moments resulting in the following system:  Πi ∈ {�a0,�ax,�ay,�axy,�axx −�ayy,�axx +�ayy,�axxy,�axyy,�axxyy},  (485)  where �ai are central Hermite coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Here the trace of the second-order moments is relaxed independently  allowing for an independent bulk viscosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' It must be noted that when used in combination with the correction for  diagonal components of the third-order equilibrium moments the coefficient in front of the correction term must be  changed to 1 −  δt  ¯τ+¯τη where ¯τη is the relaxation time tied to the bulk viscosity [121].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  67  Figure 13: Linear stability domain of the central Hermite MRT collision operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Here second-order moments relax with the viscosity while  higher-order ghost moments relax with another pseudo-viscosity ν′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Reproduced from [95].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Closures for the relaxation rates: entropic  The single relaxation time entropic model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The original entropic LBM ensures stability of the solver by imposing a  monotonous decrease of a discrete entropy function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' While a number of different discrete entropy functionals have  been proposed in the context of the ELBM [122, 123], the following form has gained the most attention [124, 125,  126, 28, 127]:  H =  �  i  fi ln  � fi  wi  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (486)  In practice, the monotonicity of the discrete entropy is enforced using a two-step linear reconstruction achieved  through the following modified time-evolution equation [124, 125]:  fi (r + ciδt, t + δt) − fi (r, t) = βγ  �  f eq  i  (r, t) − fi (r, t)  �  ,  (487)  where β is tied to the fluid viscosity as:  β =  δt  2τ + δt,  (488)  with τ = ν/c2  s, while γ is obtained by solving the following system [128]:  H ( f ∗) = H ( f) ,  (489)  with:  f ∗  i = fi + γ  �  f eq  i  − fi  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (490)  This two-step reconstruction procedure is illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In the first step, the equal entropy mirror state relative  to the equilibrium, f ∗, is found by solving the non-linear equation shown in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 489.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' As observed there γ is the  maximum path length not resulting in an increase in entropy [129].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' It is interesting to note that at thermodynamic  equilibrium Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 489 has the non-trivial root γ = 2 which corresponds to the SRT collision operator [129].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In the second  step, dissipation is introduced via the parameter β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The solution to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 489 can be obtained using a Newton-Raphson  iterative solver as:  γn+1 = γn − Gn  ∂γGn ,  (491)  with:  Gn = H �f ∗n� − H ( f) ,  (492)  68  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8  100  10-1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  VSt/ sr2  Ma  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  10-3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  10-5  10-1 100  10-5  10-3  VSt / Sr2Figure 14: Schematic representation of the relaxation process in the ELBM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Dashed lines represent entropy levels while the triangle illustrates the  positivity polytope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  and:  ∂Gn  ∂γ =  �  i  �  1 + ln  � f ∗  i  n  wi  �� �  f eq  i  − fi  �  ,  (493)  where γn and γn+1 are solutions obtained in the previous and current iterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The iterative root-finding algorithm  being rather expensive (especially when the populations get away from equilibrium) alternative approaches have been  developed in recent years [124, 129].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' These approximate solutions are also useful in the vicinity of equilibrium as the  Newton-Raphson solver might diverge there.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Extension of the entropic closure to multiple relaxation rate formulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The two-relaxation time entropic formula-  tion is realized by writing discrete populations as [100]:  fi = ki + si + hi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (494)  where the kinematic part ki, represents contributions from conserved moments, si contributions from the stress and hi  all higher-order moments contributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Considering the discrete time evolution equation:  fi (r + ciδt, t + δt) =  �  1 − δt  2¯τ  �  fi (r, t) + δt  2¯τ f mirr  i  (r, t) ,  (495)  Considering invariance of conserved moments and physical constraint on the relaxation rate of second-order moments  defining si, the mirror state can be written:  f mirr  i  = ki +  �  2seq  i − si  �  + (1 − γ)hi + γheq,  (496)  where the free parameter γ here allows independent control over the relaxation rate of higher-order moments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This  free parameter is found by minimizing the discrete entropy in the post-collision state, f ′  i :  dH( f ′)  dγ  = 0,  (497)  which upon expansion around equilibrium up to the first non-vanishing order results in [130]:  γ  2 = ¯τ  δt −  �  1 − ¯τ  δt  � ⟨∆s|∆h⟩  ⟨∆h|∆h⟩,  (498)  where ∆si = seq  i − si, ∆hi = heq  i − hi, and the entropic scalar product ⟨|⟩ is defined as:  ⟨X|Y⟩ =  Q  �  i=1  XiYi  f ∗  i  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (499)  69  It is interesting to note here that for a moments space where the moments are weighted-orthogonal in the co-moving  reference frame, in the absence of body forces, the entropy minimizer free parameter γ → 2¯τ/δt setting all higher-  order moments to the equilibrium state [131].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The specific case of regularization  The rational behind regularized collision operators is to filter out higher-order components of the distribution  functions (in the sense of the Chapman-Enskog expansion).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' It can be shown that first-order terms appear at the NS  level, while higher-order terms intervene at the Burnett, super Burnett etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' scales, not of interest in the context of  the LBM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In the context of the regularized collision approach the non-equilibrium part of the distribution function  is reconstructed using only first-order contributions, f neq  i  ≈ f (1)  i  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The discrete time-evolution equation can be re-  expressed as [132, 133]:  fi (r + ciδt, t + δt) = f eq  i  (r, t) +  �  1 − δt  ¯τ  �  f neq  i  (r, t) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (500)  Following the Hermite expansion used for the EDF, we can express the first-order component of the distribution  function as:  f (1)  i  = wi  �  n=2  1  n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' a(1)  n : Hn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (501)  In the original regularized model [132] only the second-order Hermite polynomial was considered for the reconstruc-  tion process:  f (1)  i  = wi  a(1)  2 : H2  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (502)  The only unknown in this equation is a(1)  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In [132], this coefficient is computed as:  a(1,PR)  2  ≈ aneq  2  =  �  i  H2 :  �  fi − f eq  i  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (503)  This approach to reconstructing the non-equilibrium part is commonly referred to as the projection regularization  approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In the context of the classical LB formulation with a second-order polynomial EDF, and given the orthogo-  nality of the independent moments, this collision operator aimed at eliminating non-equilibrium effects of higher-order  (kinetic) moments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' It is interesting to note that this formulation has a number of shortcomings: (a) Errors in all com-  ponents of the third-order moments tensor of the EDF (given the absence of higher-order terms in the EDF), and (b)  presence of higher-order effects (tied to f (n)  i  with n ≥ 2) coming from the approximation used for a(1)  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' While initially  believed to improve stability, the second-order projection-based regularized collision operator actually reduces the  domain of stability as compared to the SRT collision operator as illusrtated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 15 via the linear stability domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  The latter can be, to some extent, cured using a CE-based closure for a(1)  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Using this approach it can be shown that  [134]:  a(1,CE)  2  = −ρc2  s  ¯τ  δt  �  ∇u + ∇uT�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (504)  This expression can be computed using classical FD approximations [135], which has been shown to improve stabil-  ity at the cost of non-negligible numerical dissipation considerably raising computational costs for direct numerical  simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Recent publications have proposed to reduce dissipation by considering a weighted combination of the  projection- and CE-based approaches [135, 65]:  a(1)  2 = σa(1,PR)  2  + (1 − σ) a(1,CE)  2  ,  (505)  where σ is the weight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  The first problem with the RLBM of [132], namely errors in the off-diagonal components of the third-order moments  tensor can be accounted for by using third- (or fourth-)order terms in the EDF and using the recursive properties of  the off-equilibrium Hermite coefficients [134], i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' :  a(1)  α1α2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='αm = a(1)  α1,α2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='αm−1uαn +  �  a(1)  αnαn−1uα1uα2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='uαn−2  �  cyc .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (506)  70  Figure 15: Linear stability domain of the projection-based regularized collision model of [132] compared to the the SRT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Reproduced from [95].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  For the D2Q9 stencil, assuming a fourth-order isothermal polynomial EDF the different non-equilibrium Hermite  coefficients are computed as:  a(1)  xyy = uxa(1)  yy + 2uya(1)  xy ,  (507a)  a(1)  xxy = uya(1)  xx + 2uxa(1)  xy ,  (507b)  a(1)  xxyy = uya(1)  xxy + ux  2a(1)  yy + uxuya(1)  xy .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (507c)  It can be shown, via simple algebra, that the projection-based recursive regularization approach is equivalent to a  central Hermite collision operator with all ghost relaxation rates set to unity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  71  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  @  SRT  /d  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  10-1100  10°  VSt / sr25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Extension to non-ideal fluids  In this section we discuss introduction of non-ideal contributions to the LBM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Given that all models discussed in  the present contribution recover some form of a second-gradient fluid, described first by van der Waals [6], we start  by introducing fundamental aspects of this description of non-ideal fluids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The introduction of the target macroscopic  system is followed by a brief overview of kinetic models for the dense fluid regime recovering the second-gradient  fluid behavior in the hydrodynamic limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Most widely used lattice Boltzmann models for isothermal non-ideal fluid  flows are then reviewed and a comprehensive analysis of numerical and physical properties is provided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Second-gradient theory and non-ideal fluids thermodynamics  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Non-ideal equation of state: van der Waals  At rather large pressures or in dense liquid phases the assumption used to derive the ideal gas equation of state, that  molecules interact with each-other mostly via local elastic collisions does not hold anymore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The ideal gas law has  two shortcomings in these regimes: it neglects the volume occupied by molecules via the local interaction assumption  and it does not take into account long-range interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In doing so it fails to correctly model the behavior of so-  called non-ideal fluids, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' co-existence of two phases at a given temperature and existence of a critical temperature  Tc above which the fluid become single-phased.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The first attempt at a model correctly describing non-ideal fluid  thermodynamics was made by van der Waals [136] via a cubic equation of state:  P =  ρrT  1 − bρ − aρ2,  (508)  where a and b are the long range interaction and volume exclusion constants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The thermodynamic behavior of the  van der Waals equation of state is illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 16 via the corresponding Clapeyron diagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Looking at the  Figure 16: Clapeyron diagram of van der Waals equation of state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  isotherms of this equation of state, three categories can be identified: (a) T < Tc where  ∂P  ∂(1/ρ) = 0 has two roots and  ∂2P  ∂(1/ρ)2 = 0 one, (b) T = Tc where  ∂P  ∂(1/ρ) = 0 has a single root which is the same as and  ∂2P  ∂(1/ρ)2 = 0 and (c) T > Tc where  the former equations do not admit any solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The transition isotherm, Tc, is known as the critical temperature and  the combined root of  ∂P  ∂(1/ρ) = 0 and  ∂2P  ∂(1/ρ)2 = 0 on that isotherm identifies the critical state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The outer envelope shown  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 16 is the saturation curve (also called binodal curve) corresponding to the liquid/vapor coexistence densities  while the inner envelope is the spinodal curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In the region within the spinodal envelope, referred to as the spinodal  region, the thermodynamic states predicted by the van der Waals equation (more generally all cubic equations of  state) are mechanically unstable,  ∂P  ∂(1/ρ) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In the region between the spinodal and binodal envelops, referred to as  the binodal region, the fluid is in a pseudo-stable state meaning that it is not mechanically unstable but at the same  72  2  T>Tc  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  T=Tc  Binodal curve  P  P  >  Spinodal curve  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  100  101  pc/ptime it is not a local minimzer of energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' As such when subjected to a small perturbation the fluid leaves the binodal  region states towards the binodal curve which corresponds to local energy minima.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In practice, a state in the bi- and  spinodal regions corresponds to the coexistence of the liquid and vapor phases, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' both branches of the binodal curve,  a distinctive feature for an interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A point of cardinal importance is to identify the liquid and vapor coexistence  states on given isotherms below the critical temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Co-existence densities: Common-tangent construction  For the liquid and vapor states, ρl and ρv, in contact via an interface to coexist one can readily show that both states  must have the same pressure, P, and chemical potential λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A detailed derivation of these conditions will be given in  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5 for a flat interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The interface equilibrium conditions can be re-cast in the following form:  A(ρl) − A(ρv)  ρl − ρv  =  ∂A  ∂ρ  �����ρv  ,  (509)  A(ρl) − A(ρv)  ρl − ρv  =  ∂A  ∂ρ  �����ρl  ,  (510)  where we have introduced the free energy A, and λ = ∂A  ∂ρ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In simple words, the reformulated equilibrium conditions  mean that in a plot of free energy versus density at a given temperature below critical the two minimizers of the bulk  free energy, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' ρl and ρv, are characterized as two points that can be joined with a line of slope equal to the derivatives  of the free energy at those points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This system of equations can be used to systematically find the two stable states of  the fluid for a given temperature below critical and is known as the common tangent construction method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' To further  illustrate that consider the bulk free energy of the van der Waals fluid:  A = ρrT ln  �  ρ  1 − bρ  �  − aρ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (511)  Using this expression and conditions of Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (509) and (510) one can find the coexistence densities at tany temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  The free energy at T  Tc = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='9 along with the corresponding local minima and tangents are illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' It is  Figure 17: Illustration of the common tangent construction for the van der Waals equation of state at T/Tc = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In the y−axis W(ρ) =  A(ρ) − ∂A  ∂ρ  �����ρv  (ρ − ρv) + A(ρv).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The liquid/vapor coexsitence densities are found using Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (509) and (510).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  readily observed that the derivatives at the two coexistence densities are the same and equal to the slope of the  line joining them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The common tangent approach can therefor be used to systematically construct the liquid/vapor  coexistence densities curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  73  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  A  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  0  p/pc  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6573  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4257  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  2  p/pc5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Co-existence densities: First-order transition and Maxwell construction  As seen in the previous paragraph, below the critical point the free energy of non-ideal fluids admits two local  minima separated by a local maxima indicating an energy barrier for transition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The concave nature of the free energy  between those two stable states indicates that a homogeneous state is disadvantageous in-between them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In [137], dis-  cussing an experiment where pressure variations are studied in a vessel containing a fixed amount of substance while  gradually decreasing the volume Maxwell observes that ”We have hitherto supposed the experiment to be conducted  in such a way that the density is the same in every part of the medium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This, however, is impossible in practice, as the  only condition we can impose on the medium from without is that the whole of the medium shall be contained within  a certain vessel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Hence, if it is possible for the medium to arrange itself so that part has one density and part another,  we cannot prevent it from doing so.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Now the points B and F represent two states of the medium in which the pressure is  the same but the density very different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The whole of the medium may pass from the state B to the state F, not through  the intermediate states C-D-E, but by small successive portions passing directly from the state B to the state F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In this  way the successive states of the medium as a whole will be represented by points on the straight line B-F, the point B  representing it when entirely in the rarefied state, and F representing it when entirely condensed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This is what takes  place when a gas or vapour is liquefied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Under ordinary circumstances, therefore, the relation between pressure and  volume at constant temperature is represented by the broken line A-B-F-G”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The original plot used by Maxwell to  illustrate his purpose is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In practice this means that in-between the liquid and vapor states, the fluid  Figure 18: Plot used by Maxwell in [137] to illustrate phase transition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Vertical axis is pressure and horizontal axis is specific volume.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The plot is  reproduced from [137].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  is made up of a mixture of those two stable states which overcomes the concavity of free energy leading to instability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  This is equivalent to replacing the free energy with its convex hull [138].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A simple way of determining the boundaries  of this miscibility domain is the Maxwell construction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The thermodynamic argument leading to that approach is  based on equality of Gibbs enthalpy, G = eint + Pv + T s where eint is internal energy, v the specific volume and s  entropy, in the pure vapor and liquid states, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Gv − Gl =  � Pl  Pv  vdP −  � Tl  Tv  sdT = 0,  (512)  which for an isothermal process, and using integration by parts leads to:  � vv  vl  (P − Psat)dv = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (513)  This can also be written as:  � ρl  ρv  P − Psat  ρ2  dρ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (514)  In simple words, the Maxwell construction consists in finding the horizontal line P = Psat in the P − 1/ρ diagram  intersecting a given isotherm below the critical temperature at three point that guarantees Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (514).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The construction  process is illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' As shown in the left-hand plot of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 19 for Psp1 < Psat < Psp2 where (ρsp1, Psp1)  74  Figure 19:  Illustration of the Maxwell construction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (Left) Isotherms of of the van der Waals equation of state for T/Tc  ∈  {0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='7, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='9, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='99}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Black markers are the liquid/vapor coexistence volumes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (right) Isotherm at T/Tc = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='7 with (black square mark-  ers) binodal and (blue circular markers) spinodal points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The binodal points guarantee that the red-colored and blue-colored domains have equal  area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  and (ρsp2, Psp2) are the two spinodal points P − Psat has systematically three non-degenerate roots 1/ρ1, 1/ρ2, 1/ρ3  and an inflection point indicating the existence of two zones, S 1 =  � 1/ρ2  1/ρ1 (P − Psat)d(1/ρ) < 0, shown in red and  S 2 =  � 1/ρ3  1/ρ2 (P − Psat)d(1/ρ) > 0, shown in blue in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The choice of pressure Psat that guarantees S 1 − S 2 = 0  results in ρ1 = ρl and ρ2 = ρv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' We have therefore introduced a second approach to determine the coexistence densities  of non-ideal fluids completing our introductory discussion on the thermodynamics of uniform non-ideal fluids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The  next step is to introduce the thermodynamic formalism describing non-uniform regions, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Free energy of non-uniform non-ideal fluid  In the second-gradient theory as introduced in both [6] and [139], the presence of interfaces is conceptualized by  endowing the fluid with capillary energy;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In practice this means that free energy has both a classical bulk contribution  function of local thermodynamic properties and a non-local contribution function of space-derivatives of, for single-  component fluids, density:  AvdW = AvdW(ρ, ∇ρ, ∇ ⊗ ∇ρ, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (515)  Assuming that the non-homogeneities span over distances larger than the characteristic molecular interaction length,  the free energy can be developed using a Taylor expansion around the homogeneous state as:  AvdW = AvdW|0+∇ρ · ∂AvdW  ∂(∇ρ)  �����0  + ∇∇ρ : ∂AvdW  ∂(∇∇ρ)  �����0  + 1  2∇ρ ⊗ ∇ρ : ∂AvdW  ∂(∇ρ)  �����0  ⊗ ∂AvdW  ∂(∇ρ)  �����0  + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (516)  where |0 refers to a function evaluated at the homogeneous state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Considering geometrical arguments such as symme-  try and rotational-invariance the expression simplifies to the second-gradient free energy as introduced in [6]:  AvdW = A + κ  2|∇ρ|2,  (517)  with:  κ = 2  �  2  ∂2A  ∂(|∇ρ|)2  �����0  −  ∂2A  ∂(∇2ρ)∂ρ  �����0  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (518)  where for the sake of readability we have replaced the bulk free energy AvdW|0 with A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The second term represents  the interface energy while the bulk free energy is solely a function of the local density and temperature [139, 140].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  75  2  0  P  1  P  2  3  4  2  100  101  100  101  pc/p5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Gibbs equilibrium conditions for a flat interface  The equilibrium state of a 1-D infinite domain, in x-direction, made up of the vapor phase in one half and liquid  phase in the other with an interface at the center is obtained as the minimizer of free energy under the constraint of  constant total mass, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  δ  � ∞  −∞  Ldx = 0,  (519)  with the Lagrange function L defined as  L = A + κ  2  �����  ∂ρ  ∂x  �����  2  − λρ,  (520)  where λ is the Lagrange multiplier for the mass constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Computing the variation term by term one gets  �  x  δρ  �∂A  ∂ρ − κ∂2ρ  ∂x2 − λ  �  dx,  (521)  which in turn leads to the equilibrium condition:  ∂A  ∂ρ − κ∂2ρ  ∂x2 − λ = 0,  (522)  subject to the boundary conditions: ρ(∞) = ρl, ρ(−∞) = ρv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' As the gradient of density vanishes at infinity for both  phases, we have  ∂A  ∂ρ  �����ρl  = ∂A  ∂ρ  �����ρv  = λ,  (523)  where we can readily identify λ as the bulk chemical potential, leading to the Gibbs equilibrium conditions, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  equality of chemical potentials  λl = ∂A  ∂ρ  �����ρl  ,  λv = ∂A  ∂ρ  �����ρv  ,  (524)  in both phases,  λl = λv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (525)  Multiplying (522) with dρ  dx,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  d  dx  �������A − λρ − κ  2  �dρ  dx  �2������� = 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (526)  or  P = −A + λρ + κ  2  �dρ  dx  �2  = constant  (527)  Considering this expression at ±∞,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' and taking into account that the gradient of the density vanishes,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  � dρ  dx  �2 → 0 as  x → ±∞,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' we get with the help of chemical potential equality (523):  �  ρ∂A  ∂ρ − A  � �����ρl  =  �  ρ∂A  ∂ρ − A  � �����ρv  (528)  This enables to identify the pressure P (or equation of state,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' EoS),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  P = ρ∂A  ∂ρ − A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (529)  and the result (528) is nothing but the remaining Gibbs equilibrium condition: The pressure is the same in both the  phases,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Pl = Pv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (530)  76  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Korteweg stress tensor and second-gradient fluid balance equations  The stress tensor of a non-ideal fluid in 3-D is obtained by extending the constrained minimization problem of  (519) to 3-D leading to [8],  TK = ∇ ⊗  ∂L  ∂(∇ρ) − LI,  (531)  where I is unit tensor and L is the Lagrange function in 3-D,  L = A + 1  2κ|∇ρ|2 − λρ,  (532)  and λ, corresponding to the chemical potential, is,  λ = ∂A  ∂ρ − κ∇2ρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (533)  This in turn leads to the following Korteweg’s stress tensor [7]:  TK =  �  P − κρ∇2ρ − 1  2κ|∇ρ|2  �  I + κ∇ρ ⊗ ∇ρ,  (534)  where  P = ρ∂A  ∂ρ − A,  (535)  is the thermodynamic pressure, or equation of state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' From the local balance equations for mass and momentum one  obtains the macroscopic governing laws for an isothermal capillary fluid:  ∂tρ + ∇ · ρu = 0,  (536)  ∂tρu + ∇ · ρu ⊗ u + ∇ · T = 0,  (537)  where u is the fluid velocity and the stress tensor T is  T = TK + TNS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (538)  The Navier–Stokes viscous stress tensor reads,  TNS = −µS − η(∇ · u)I,  (539)  where S is the trace-free rate-of-strain tensor,  S = ∇u + ∇u† − 2  3(∇ · u)I,  (540)  and µ and η are the dynamic and the bulk viscosity, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  The momentum balance equation (537) can be recast in the following form,  ∂tρu + ∇ · ρu ⊗ u + FK + ∇ · TNS = 0,  (541)  where Korteweg’s force FK is the divergence of the Korteweg pressure tensor,  FK = ∇ · TK.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (542)  Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (536) together with Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (508), (534), (538), (539) and (540) describe the dynamics of the van der Waals fluid  targeted by non-ideal lattice Boltzmann models in the hydrodynamic limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' One of the remarkable features of this  description of non-ideal fluids and interfaces is that it can also be recovered from the kinetic theory of gases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In the  next section we provide a brief description of simplified kinetic models leading to the second-gradient fluid model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  77  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Kinetic models for non-ideal fluid  To introduce a kinetic model for non-ideal fluids, one needs to begin with the first Bogolioubov–Born–Green–  Kirkwood–Yvon (BBGKY) equation,  ∂t f + v · ∇ f = J =  � �  ∇V (|r − r1|) · ∂  ∂v f2(r, v, r1, v1, t)dv1dr1,  (543)  where f(r, v, t) and f2(r, v, r1, v1, t) are the one- and the two-particle distribution functions, respectively, r, r1 and v,  v1 are particles position and velocity, while V is a potential of pair interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The Boltzmann collision integral of  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (46) is not sufficient for the dense regime as it neglects the volume occupied by the molecules and long range  interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The BBGKY equation on the other hand make no assumptions on the nature of the interaction as it  involves a general non-local interaction potential and dependence on the two-particle distribution function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The main  difficulty of the BBGKY is that to solve the one-particle equation one needs the two-particle distribution function  which itself is governed by a non-homogeneous hyperbolic partial differential equation with a collision term involving  the three-particle distribution function and so on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' To operate a truncation at first-order proper approximations for the  correlation function and the interaction potential are needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In the next section we briefly present two of the most  widely used models for short- and long-range interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Hard sphere potential: The Enskog model  In Enskog’s approach, particles are assumed to be hard impenetrable spheres of diameter d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This fixes the form of  the interaction potential effectively allowing to re-write the collision integral as [141, 142]:  JE = d2  � � �  f2(r + d  2 k, v′, r1, v′  1, t) − f2(r − d  2 k, v, r1, v1, t)  �  g · kdkdv1,  (544)  where k = (r1 − r)/|r1 − r|, g = v1 − v, v′ = v + k(g · k), v′  1 = v1 − k(g · k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The second approximation in Enskog’s  standard theory applies to the two-particle distribution function [9, 11]:  f2(r + d  2 k, v′, r1, v′  1, t)  =  χ  �  r + d  2 k  �  f �r, v′� f �r + dk, v′  1  � ,  (545)  f2(r − d  2 k, v, r1, v1, t)  =  χ  �  r − d  2 k  �  f (r, v) f (r − dk, v1) ,  (546)  where χ is the equilibrium pair correlation function, evaluated at local density taking into account the effect of volume  of particles in the collision probability [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Using both these approximations one recovers Enskog’s hard-sphere  collision integral [9, 11],  JE = d2  � � �  χ  �  r + d  2 k  �  f �r, v′� f �r + dk, v′  1  � − χ  �  r − d  2 k  �  f (r, v) f (r − dk, v1)  �  g · kdkdv1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (547)  The above integral can be approximated using a Taylor expansion around r as,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  χ  �  r ± d  2 k  �  =  χ (r) ± d  2 k · ∇χ (r) + d2  8 k ⊗ k : ∇∇χ (r) + O(d3),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (548)  f (r ± dk,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' w)  =  f (r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' w) ± dk · ∇ f (r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' w) + d2  2 k ⊗ k : ∇∇f (r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' w) + O(d3),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (549)  which leads to:  JE = χJB + J(1)  E + J(2)  E ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (550)  where we have neglected terms of order 3 and above,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' JB is the Boltzmann collision integral for hard-spheres,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  JB = d2  � � � f �r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' v′� f �r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' v′  1  � − f (r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' v) f (r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' v1)� g · kdkdv1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (551)  78  and J(1)  E and J(2)  E are the first- and second-order non-local contributions defined as:  J(1)  E  =d3χ (r)  � �  k · � f �r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' v′� ∇f �r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' v′  1  � + f (r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' v) ∇f (r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' v1)� g · kdkdv1  + d3  2  � �  k · ∇χ (r) � f �r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' v′� f �r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' v′  1  � + f (r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' v) f (r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' v1)� g · kdkdv1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (552)  and [143]  J(2)  E  =d4  2 χ (r)  � �  k ⊗ k � f �r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' v′� ∇∇ f �r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' v′  1  � − f (r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' v) ∇∇f (r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' v1)� g · kdkdv1  + d4  2  � �  k ⊗ k : ∇χ (r) ⊗ � f �r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' v′� ∇ f �r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' v′  1  � − f (r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' v) ∇ f (r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' v1)� g · kdkdv1  + d4  8  � �  k ⊗ k : ∇∇χ (r) � f �r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' v′� f �r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' v′  1  � − f (r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' v) f (r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' v1)� g · kdkdv1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (553)  Only keeping first-order contributions and evaluating J(1)  E at the local equilibrium f eq (743) one gets [11],  J(1)  E  = d3  � �  f eq (r, v) f eq (r, v1) k · ∇ ln �χ (r) f eq (r, v) f eq (r, v1)� g · kdkdv1,  (554)  which, after integration in v1 and k, for the isothermal flow results in,  J(1)  E  = − bρχf eq �  (v − u) · ∇ ln ρ2χT  �  − bρχ f eq  � 2  5RT (v − u)(v − u) : ∇u +  � 1  5RT |v − u|2 − 1  �  ∇ · u  �  ,  (555)  where b = 2πd3/3m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' While the phenomenological Enskog’s collision integral [9] was used above, the lowest-order  approximation Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (555) is identical in other versions of hard-sphere kinetic equations such as the revised Enskog  theory (RET) [144] or kinetic variational theory [145].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Long-range interactions: Vlasov model  Enskog’s model only accounts for strong repulsive short-range interactions introducing the excluded volume into  the equation of state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' However it is not enough to account for long-range attractive interactions leading to spinodal  decomposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A widely used model for long-range attractive contributions of the collision intergal in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (543)  is Vlasov’s mean-field approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Here we briefly review this model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Assuming absence of correlations, the  two-particle distribution function is approximated as  f2(r, v, r1, v1) ≈ f(r, v) f(r1, v1),  (556)  while the long-range interaction integral can be simplified,  JV = ∂f(r, v)  ∂v  ∇  ��  |r1−r|>d  ρ(r1)V(|r1 − r|)dr1  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (557)  With a Taylor expansion around r,  ρ(r1) = ρ(r) + (r1 − r) · ∇ρ(r) + 1  2(r1 − r) ⊗ (r1 − r) : ∇ ⊗ ∇ρ(r) + O(∇3ρ),  (558)  and neglecting higher-order terms, with Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (557) one recovers the meanfield Valsov long-range molecular interaction,  JV = −∇  �  2aρ(r) + κ∇2ρ(r)  �  ∂  ∂v f(r, v),  (559)  79  where parameters a and κ are, after integration over a unit sphere,  a = −2π  � ∞  d  r2V(r)dr,  (560)  κ = −2π  3  � ∞  d  r4V(r)dr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (561)  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (543) together with:  J = χJB + J(1)  E + JV,  (562)  and the short- and long-range interaction models of Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (555) and (559) form the constitutive equations for mod-  erately dense isothermal fluid Enskog-Vlasove model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This kinetic model, under some specific scaling assumptions  detailed in Appendix C, is shown to recover the second-gradient fluid model at the Euler-Navier-Stokes level with,  P = bρ2χrT − aρ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (563)  Motivated by our recently published work [146], before entering the discussion of lattice Boltzmann models for non-  ideal fluids we introduce next a general kinetic framework for non-ideal fluids that can be easily transposed into the  lattice Boltzmann framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' General Enkog-Vlasov-BGK kinetic framework for hydrodynamics  In an attempt to provide a unified an numerically efficient kinetic framework for non-ideal fluids simulation in  [146] the authors introduced a projector K onto a local equilibrium at constant temperature [147],  KJ =  �∂f eq  ∂ρ − 1  ρu · ∂f eq  ∂u  � �  Jdv + 1  ρ  ∂ f eq  ∂u ·  �  vJdv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (564)  with the property, K2 = K, which can be verified by a direct computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The equilibrium attractor is defined as:  f eq =  ρ  (2πP0/ρ)D/2 exp  �  −(v − u)2  2P0/ρ  �  ,  (565)  where P0 is a freely tunable reference pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' With the projector of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (564), the interaction term in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (543) is  split into two parts by writing an identity,  J = (1 − K) J + KJ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (566)  The first term,  Jloc = (1 − K) J,  (567)  satisfies the local conservation of both mass and momentum,  KJloc = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (568)  It is conventional to model the locally conserving part of the interaction with a single relaxation time Bhatnagar–  Gross–Krook (BGK) approximation,  Jloc → JBGK = −1  τ (1 − K) f = −1  τ  �  f − f eq(ρ, u, P0  ρ )  �  ,  (569)  where the relaxation time τ is a free parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The second term in the identity (566),  Jnloc = KJ,  (570)  satisfies the local mass but not the local momentum conservation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' After integration by part in the velocity v and  neglecting boundary integrals, one arrives at  Jnloc = −1  ρ  ∂ f eq  ∂u · Fnloc,  (571)  80  where the force Fnloc reads,  Fnloc =  � � �  ∇V (|r − r1|) f2(r, v, r1, v1, t)dv1dr1dv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (572)  Collecting the BGK approximation together with the nonlocal contribution, a generic kinetic model may be written,  ∂t f + v · ∇f = −1  τ  � f − f eq� − 1  ρ  ∂f eq  ∂u · Fnloc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (573)  Evaluation of the force (572) requires us to specify the particles interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' One can invoke the Enskog–Vlasov  model [9, 10] where both hard-sphere collisions and a weak long-range attraction potential contribute to a non-local  momentum transfer or any other type of closure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' More generally Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (573) defines a family of kinetic models with  P0 and Fnloc as tunable parameters to recover the hydrodynamics of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In the next section we review different  lattice Boltzmann models for non-ideal fluids as closures for Fnloc and P0 within this general kinetic framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For  the sake of readability, in the remainder of the text we drop nloc and simply use F for the force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Before moving on to  the LBM models we will discuss the hydrodynamic limit of non-ideal kinetic models under conventional scaling and  alternative better suited to the recovery of the target macroscopic system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Scaling and hydrdynamic limit  Considering the Enskog–Vlasov–BGK kinetic model introduced in the previous sections, let us introduce the  following parameters:  characteristic flow velocity U,  characteristic flow scale L,  characteristic flow time T = L/U,  characteristic density ¯ρ,  isothermal speed of sound of ideal gas cs =  √  rT,  kinematic viscosity of the BGK model of ideal gas ν = τc2  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  With the above, the variables are reduced as follows (primes denote non-dimensional variables):  time t = T t′,  space r = Lr′,  flow velocity u = Uu′,  particle velocity v = csv′,  density ρ=¯ρρ′,  distribution function f = ¯ρc−3  s f ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Furthermore, the following non-dimensional groups are introduced: Viscosity-based Knudsen number Kn = τcs/L,  Mach number Ma = U/cs, Enskog number En = b¯ρKn/Ma and Vlasov number Vs = a/brT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  With this, the Enskog–Vlasov–BGK kinetic model is written in non-dimensionla form as:  Ma Kn ∂′  t f ′ + v′ · Kn∇′ f ′ = − � f ′ − f eq′�  − 1  ρ′  ∂f eq′  ∂u′ · En  �  ∇′ �  χ �ρ′�2 − Vs �ρ′�2�  −  � δ  L  �2  Vs  �  ρ′∇′∇  ′2ρ′��  ,  (574)  81  where δ is the range of the attraction potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Assuming d ≪ δ, we have a ∼ ¯Vδ3 and κ ∼ ¯Vδ5, where ¯V is a  characteristic value of the potential, thus  �  κ/a ∼ δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (575)  The following scaling assumptions are applied: Acoustic scaling, Ma ∼ 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Hydrodynamic scaling, Kn ∼ En ∼ δ/L ∼  ϵ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Enskog–Vlasov parity, Vs ∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In other words, the conventional hydrodynamic limit treats all non-dimensional  groups that are inversely proportional to the flow scale L (Kn, En and δ/L) as a small parameter while the Enskog–  Vlasov parity ensures that both the short- and long-range contributions to the pressure are treated on equal footing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Returning to dimensional variables, we may write,  ϵ∂t f + v · ϵ∇ f = − � f − f eq� − 1  ρ  ∂f eq  ∂u ·  �  ϵF(1) + ϵ3F(3)�  ,  (576)  where,  F(1) = ∇(P − P0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (577)  F(3) = −κρ∇∇2ρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (578)  The analysis of the kinetic model under the above-detailed conventional scaling of a small deviation from a uniform  state [11],  ∇ → ϵ∇, ∂t → ϵ∂t,  (579)  is detailed in Appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' To second order in space derivatives, the resulting momentum balance equation reads,  ∂tρu + ϵ∇ · ρu ⊗ u + ϵ∇P + ϵ∇ · ϵTNS + O(ϵ3) = 0,  (580)  where the dynamic viscosity µ and the bulk viscosity η in the Navier–Stokes stress tensor (539) are defined by the  reference pressure (D = 3),  µ = τP0,  (581)  η =  �5  3 − ∂ ln P0  ∂ ln ρ  �  τP0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (582)  Thus, the momentum balance equation (580) is form-invariant with respect to the choice of reference pressure, pro-  vided P0 satisfies a sub-isentropic condition,  P0 ≤ Cρ5/3,  (583)  for some C > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' With (583), the bulk viscosity (582) is positive and vanishes when the reference pressure follows an  isentropic process for ideal monatomic gas, P0 = Cρ5/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For example, any polytropic process, P0 = Aρn, 1 ≤ n ≤ 5/3  satisfies the sub-isentropic condition and results in η = (5/3 − n)τP0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Special case of isothermal process n = 1 returns  η = (2/3)τP0, and the viscous stress tensor becomes,  TNS = −τP0  �  ∇u + ∇u†�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (584)  On the other hand, when compared to the two-phase momentum equation, the macroscopic limit recovers only the  nonideal gas component thereof while missing Korteweg’s capillarity contribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Indeed, the third-order term,  ∼ ϵ3ρ∇∇2ρ does not contribute to the momentum equation (580) under the scaling (579).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This is consistent with the  well-known results from kinetic theory [11] and is not surprising: The scaling (579) is essentially based on the Knud-  sen number, which overrides the relative contribution of the capillarity term by two orders, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Appendix Appendix  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Thus, under weak non-uniformity assumption (579), the capillarity terms are seen as higher-order, Burnett-level  contributions, and cannot appear in the main (first and second) orders in the momentum balance equation (580).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In  fact, condition (579) rules out situations at an interface between phases where gradients of density become large over  a relatively short distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Therefore, in order for the kinetic model to recover in-full the momentum balance (541), a  different scaling needs to be applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  82  To overcome that issue a rescaling of the kinetic model by a time step δt, here merely a characteristic time repre-  senting the level of coarse-graining in time, was introduced in [146].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' As a preliminary consideration, we evaluate the  contribution of the force term over the time step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For a generic force F, the action of the force on the distribution  function can be written as a full derivative in a frame that moves with the local fluid velocity,  1  ρ  ∂f eq  ∂u · F = d f eq  dt .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (585)  Introducing the velocity increment,  δu = F  ρ δt,  (586)  and integrating in time, leads to the following contribution to the distribution from the force,  F =  � t+δt  t  1  ρ  ∂ f eq  ∂u · Fdt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (587)  With the characteristic values of the flow velocity U, the flow scale L, the density ρ, the force F and the velocity  increment δu, the following smallness parameter is introduced:  δu  U ∼ δtF  ρU ∼ ε,  (588)  δr  L ∼ ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (589)  The first scaling condition (588) refers to a smallness of velocity increment, that is, to the smallness of the force action  over time δt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The second scaling condition (589) is a resolution requirement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Both conditions are assumed to hold  simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Details of the corresponding multi-scale analysis are provided in Appendix D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Unlike the previous  results with the classical scaling, the momentum balance includes not only the nonideal gas pressure but also the  capillarity term, and is thus consistent with Korteweg’s force in the momentum balance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' It should be pointed out that  the scaling (588) refers to smallness of the increment of the flow velocity rather that to smallness of either the time  step or of the force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Thus, rescaling the kinetic model based on the smallness of flow velocity increments results in  both the non-ideal gas equation of state and the capillarity revealed at the Euler level O(ε) of the momentum balance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  This is in a contrast to the conventional scaling, which is tied to the non-uniformity and surface tension would appear  only at a Burnett level O(ϵ3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Overview of lattice Boltzmann models for non-ideal fluids  The general kinetic framework of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (573), regardless of the choice of P0 and F can be readily discretized in  phase-space, procedure detailed in section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1, and physical space and time, detailed in section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2, to yield a discrete  time evolution equation of the form:  ¯fi(r + ciδt, t + δt) − ¯fi(r, t) = δt  ¯τ  �  f eq  i (ρ, u) − ¯fi(r, t)  �  + Fi(F).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (590)  where Fi is the discrete form of the force contribution in the kinetic framework that can be treated using any of  schemes detailed in section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3 and f eq  i  is the discrete equilibrium function that can be chosen among those discussed  in section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For a correct recovery of the viscous stress tensor, the redefined relaxation time is tied to the reference  pressure P0 as:  ¯τ = ρν  P0  + δt  2 ,  (591)  and the bulk viscosity of the model, for the bare single relaxation time collision operator, is:  η = P0  �2 + D  D  − ∂ ln P0  ∂ ln ρ  � �  ¯τ − δt  2  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (592)  Given that all models of interest in the present manuscript can be fitted within this discrete kinetic model, and that the  only point of difference resides in the choice of F and P0 we will discuss the different lattice Boltzmann models from  that specific perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  83  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Shan and Chen’s pseudo-potential model  In this extension of the classical lattice Boltzmann method for isothermal ideal gases to non-ideal fluids first  proposed in [12], the authors introduced a source of non-local interaction through a potential defined as:  V(r, r′) = G(r, r1)ψ(r)ψ(r1),  (593)  where G(r, r1) is a Green’s function and ψ is an effective number density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For the case of the discrete system, the  authors proposed to only consider nearest-neighbour interactions to get the following discrete Green’s function:  G(r − r1) =  �������  0, |r − r1|≤ 2,  G, 0 < |r − r1|< 2,  (594)  which in turn leads to the discrete non-local momentum source:  F = Gψ(r)  Q−1  �  i=0  w(|ci|)ψ(r + ciδt)ci,  (595)  where G is now a constant controlling the interaction strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Furthermore, this model keeps the isothermal equilib-  rium of the classical isothermal LBM, therefore effectively setting P0 = ρc2  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Computing the Euler-level momentum  balance equation it is readily seen that the equation of state changes from the ideal isothermal pressure to:  P = ρc2  s + G  2 ψ2,  (596)  potentially allowing for coexistence of a vapour and liquid phase at a given temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The only condition for the  stable coexistence of these two phases at temperature T is the existence of two points ρ1 and ρ2, with ρ1 < ρv < ρl < ρ2,  satisfying:  ∂2P  ∂ρ2 |ρ=ρ1,ρ2= ∂P  ∂ρ |ρ=ρ1,ρ2= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (597)  For instance setting ψ ∝ ρ would lead to a quadratic equation of state and could not satisfy either of the above-listed  conditions regardless of the choice of the coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In [12], the authors propose an effective density number of the  form:  ψ = ρ0  �  1 − exp − ρ  ρ0  �  ,  (598)  where ρ0 is freely tunable parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This form of the effective density number systematically admits two roots to  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (597) for G < Gc, where Gc is the critical interaction strength above which the density degeneracy goes from two  to one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Using the two conditions on derivatives of pressure at the critical state:  c2  s − 2Gcρ0 exp  �  −ρc  ρ0  � �  exp  �  −ρc  ρ0  �  − 1  �  =  0,  (599)  −2Gc exp  �  −2ρc  ρ0  � �  exp  �ρc  ρ0  �  − 2  �  =  0,  (600)  the critical state is shown to be:  ρc  =  ρ0 ln 2,  (601)  Gc  =  −2c2  s  ρ0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (602)  While G is routinely assimilated to a pseudo-temperature as G = − 1  T , see for instance [148], a dimensional analysis  shows [G] =  m5  kgs2 , which indicates G ∝ rT  ρ0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  From both kinetic theory and the van der Waals fluid theory one would expect two separate non-local contributions  to allow for stable phase separation: A short-range repulsive and a long-range attractive interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' As such the  84  single-term form of the pseudo-potential model should not produce long range interaction meanfield effects such as  surface tension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This point can be clarified by writing a Taylor expansion of the discrete non-local momentum source  term:  F = Gψ(r)  Q−1  �  i=0  w(|ci|)ψ(r + ciδt)ci = Gψ∇ψ − Gδr2  3  ψ∇∆ψ + O(∇5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (603)  It is observed that the discrete non-local interaction is akin to a second-order accurate finite-differences approximation  to the the first-order derivative of ψ admitting a leading third-order error that takes on a form similar to surface tension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  While naturally generating a non-zero surface tension via this leading-order error term it has the following short-  comings: (a) the surface tension coefficient is fixed and (b) different from the Kortwewg stress tensor, van der Waals  fluid and Enskog-Vlasov theory the interfacial excess energy is not a function of density but the effective number  density, which in principle is not a conserved variable [149, 146].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Free energy model and derivatives  In its original form the free energy model was first introduced in [150].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Different from the pseudo-potential  approach where the model was constructed based on a microscopic interaction argument, here it targets a specific  macroscopic system: the van der Waals quasi-local thermodynamics, which results, after minimization of free energy  in the Kortweweg pressure tensor:  TK =  �  P − κρ∇2ρ − κ  2|∇ρ|2�  I + κ∇ρ ⊗ ∇ρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (604)  To extend the ideal gas LBM to recover the Korteweg stress tensor the authors derived a discrete equilibrium function  by moment matching, considering moments up to order two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For a 1-D system with a three-velocity stencil:  ����������  1  1  1  c−1  c0  c1  c2  −1  c0  c1  ����������  ����������  f eq  −1  f eq  0  f eq  1  ���������� =  ����������  ρ  ρux  ρu2  x + P − κρ∂2  xρ  ���������� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (605)  This is equivalent to setting P0 = TK and F = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The 2-D version of the model with the standard D2Q9 velocity set can  be found in [150].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' We will refer to this type of approach, introducing non-ideal contribution directly into the second-  order moment of the equilibrium as pressure-based model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Later multi-scale analyses showed that this approach is  subject to Galilean-variant errors scaling with ∝ Ma [151, 152].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Via modification to the discrete equilibrium function,  improved formulation with reduced Galilean-variant errors were proposed [151, 152].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Another way of introducing  non-ideal contributions was discussed in [153]: Introducing a Vlasov-like forcing term given by the divergence of  the pressure tensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This approach, referred to as force-based, was first proposed in [154] and is equivalent to setting  P0 = ρc2  s and F = ∇ · (TK − P0I).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' While the force-based approach still had Galilean-variant errors, those affecting the  viscous shear stress at the NS level could be easily eliminated using a third-order polynomial equilibrium function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  The force-based approach was later extended to more complex and realistic configurations through the use of the  entropic LBM [128, 155, 156].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  More recently the free energy method was reformulated using the chemical potential [157];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Using the definition of  the chemical potential and pressure in the free energy model one can derive the following relationship between the  divergence of the stress tensor and gradient of chemical potential:  ∇ · TK = ρ∇λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (606)  Using the ideal gas LBM, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' P0 = ρc2  s, with a force-based approach to introduce non-ideal contribution the body  force is derived as:  F = −ρ∇λ + c2  s∇ρ,  (607)  where, for instance, for the van de Waals equation of state, see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (640):  λ = rT  �  ln  �  ρ  1 − bρ  �  +  1  1 − bρ  �  − 2aρ − κ∇2ρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (608)  85  Using this approach, in combination with a strategy to thicken the interface the authors were able to considerably  extend the range of accessible density ratios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  All lattice Boltzmann models discussed here, at the hydrodynamic scale, target a form of the Korteweg stress tensor  with a non-ideal equation of state and surface tension term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' However such models come with a limitation: the  thickness of the interface which contrary to phase-field models relying on a double-well potential is dictated by  physical properties of the considered fluid, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' the volume exclusion coefficient, the long-range interaction coefficient  and the capillary coefficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' We discuss this limitation along with a solution allowing to go above that scale limitation  which has long been overlooked in the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Bridging the scale gap: Principle of corresponding states  As briefly mentioned in the previous sections, the non-ideal fluids models of interest here all come with inter-  face thicknesses solely determined by thermodynamics and properties of considered fluids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This creates a scale gap  between the characteristic size of the interface and target characteristic scales of interest for drops and bubble, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  ≈ 10−2 − 10−3 m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' We will clarify this size restriction here and discuss efficient solutions allowing to up-scale the  solver.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Dimensional form of equations and restriction by the interface thickness  While discussions around second-gradient models for non-ideal fluids are expressed in non-dimensional units,  we will show that such models come with characteristic sizes imposed by physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Consider for that purpose a 1-D  isothermal interface;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The steady-state Navier-Stokes-Korteweg equation reduces to:  ∂P  ∂x = κρ∂3ρ  ∂x3 ,  (609)  with limx→−∞ ρ = ρl and limx→+∞ ρ = ρv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' While we are considering the classical Korteweg stress tensor here, the  same line of reasoning applies to the macroscopic equation recovered by the pseudo-potential method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Here for the  sake of simplicity we use the van der Waals equation of state for the thermodynamic pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' As a result the ordinary  differential equation describing the interface has six degrees of freedom, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' a, b, r, κ, ρv and ρl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The former three  along with with liquid and vapor phase densities are readily fixed via conditions on the critical state of the considered  fluid and the temperature of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Consider for instance nitrogen N2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' To recover proper critical density, pressure  and temperature, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' ρc = 311 kg/m3, Pc = 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5 Pa and Tc = 126 K [158], the excluded volume and attractive force  coefficients and specific gas constant, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' b, a and r should be set to:  aN2  =  105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='28 m5  kgs2 ,  (610)  bN2  =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='00107 m3  kg ,  (611)  rN2  =  230.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='99 m2  s2K .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (612)  To recover the correct critical density, r is set to a value which is different from its ideal counterpart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This is justified  by the fact that here to set the constants we have relied on properties of the fluid at the critical state where it does not  behave as an ideal gas, see [159] for detailed discussion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The remaining degree of freedom, the capillary coefficient  κ, is also a physical property of the considered fluid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A variety of expressions have been proposed for the capillary  coefficient both in the context of the kinetic theory of gases, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' [160, 161, 162], or via semi-empirical correlations  to match experimental measurements, see [163] for detailed review.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Here for N2 we will set κ = 10−10  m7  kgs2 [164].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' It  is then clear that once the temperature of the system has been fixed, all parameters/variables in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (609) are set by  physical closures, also fixing the coexistence densities and density profile at the interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The liquid/vapor interface  at two different temperatures for the N2 system is illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The interfaces at both temperatures, resulting  in density ratio of the order of 102 and 10, have sizes of the order of 200 − 400 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In practice, considering one  needs to resolve the interfaces with at least 3-4 points, the maximum grid-size is limited to δr ≈ 100 nm meaning  for configurations of practical interest involving drops, for instance of diameter 1 mm, one would need at least 1012  86  Figure 20: Density profile of N2 liquid/vapor interface at (black plain) T = 63 K and (red dashed) T = 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  grid-points in 3-D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This obviously makes the approach of little to no use for simulations of practical interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The only  workaround would be to rescale the interface thickness, here the limiting charactersitic size, to minimize the required  number of grid-points for realistic simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In the next section we discuss the principle of corresponding states  which provides the theoretical basis for such rescaling operations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Extension to realistic-sized systems: Rescaling interface thickness and the principle of corresponding states  The principle of corresponding states, introduced for the first time by van der Waals in [136], quoting Guggenheim  [158], may safely be regarded as the most useful by-product of van der Waals’ equation of state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The principle  maintains that all properties that depend on inter-molecular forces are related to the critical properties of the substance  in a universal way, regardless of the molecular compound of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This observation has had two main practical  consequences: (a) prediction of unknown properties of many fluids from known properties of a few [165], (b) extension  of the domain of applicability of second-gradient-based numerical solvers to large systems at acceptable cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The  possibility of the former was put forward first theoretically in [166] and confirmed experimentally in Guggenheim’s  work, illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 21, for a family of fluids called perfect liquids by Pitzer [166].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' While the principle of  Figure 21: Co-existence densities obtained from experiments as reported in [158] for three different fluids: (black squares) CH4, (red circles) N2  and (blue diamonds) Xe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  87  800  600  p[kg/m3]  400  200  0  300  200  100  0  100  200  300  α[nm]0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  0  2  3  p/pccorresponding states is an approximation for real fluids, it is an exact property of the van der Waals fluids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This is  most notably demonstrated by the fact that the non-dimensional form of the equation of state, non-dimensionalized  by critical state properties, does not have any fluid-dependent constant:  Pr = 8ρrTr  3 − ρr  − 3ρ2  r,  (613)  where we have introduced reduced variables, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' ρr =  ρ  ρc .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The implication here is that regardless of the fluid  considered, the coexistence densities plot in non-dimensional units are universal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' To illustrate that four different fluids  were considered and parameters a, b and r were chosen so as to fit the experimental critical state of each fluid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The  corresponding data is summarized in Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Plugged into the van der Waals equation of state, all fluids, as shown  H2O  Xe  N2  CH4  Tc [K]  647.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='14  289.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8  126  190.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3  ρc [kg/m3]  322  1155  311  162  Pc [MPa]  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='897  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='394  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='610  a  � m5  kg·s2  �  1709  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2614  105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='272  526.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='978  b  � m3  kg  �  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0017  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='886 × 10−4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0011  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0021  r  � m2  s2K  �  196.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='79  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='981  230.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='967  398.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='764  Table 5: Critical state and corresponding van der Waals coefficients for different fluids;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Experimental data from [158] and [167] (for water).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 21, result in exactly the same non-dimensional coexistence densities curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Now that we have showed that the  Figure 22: Co-existence densities obtained from the van der Waals equation of state for all fluids of Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Given that all fluids led to exactly the  same curve, only one is shown here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  density ratio is independent of substance-specific variables let us go back to (609) and discuss simple strategies that  would allow one to thicken the interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' To illustrate our purpose we will use the simple demonstration discussed  in [168] by considering a 1-D interface of a fluid near the critical state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This consideration allows us to simplify the  chemical potential of the van der Waals equation of state as a third-order polynomial [169]:  λ − λsat = 4A(ρ − ρv)(ρ − ρl)  �  ρ − ρv + ρl  2  �  ,  (614)  88  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8  H  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  p/pcwith  A =  1  2ρl,v(ρl − ρv)2  dP  dρ ,  (615)  leading to the following analytical density profile:  ρ(x) = ρv + ρl  2  + ρl − ρv  2  tanh  �������  ρl − ρv  2  �  2A  κ x  ������� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (616)  Using this analytical profile the interface thickness, here defined as,  W =  ρl − ρv  max(dρ/dx),  (617)  and surface tension, σ,  σ = κ  � ρl  ρv  dρ  dxdρ,  (618)  are readily evaluated to be:  W  =  4  ρl − ρv  �  κ  2A,  (619)  σ  =  (ρl − ρv)3  6  √  2Aκ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (620)  This means that the interface thickness and surface tension can be modified via different choices of the capillary  coefficient and isothermal compressibility, through the coefficient A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Combined with the principle of corresponding  states, this allows one to modify parameters κ, a and b at will to reach the desired interface thickness and surface  tension at a fixed reduced temperature and maintain the density ratio unchanged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In addition a number of other  considerations must be taken into account when using this strategy to thicken the interface:  Interface thickening via modification of A is akin to a rescaling of the isothermal speed of sound -tied to the  isothermal compressibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' To remain within the low Mach approximation, assuming a characteristic convective  speed U, one must ensure that U  cs < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Artificial thickening of the interface will correctly capture the dynamics of the considered interface in the limit  of a sharp interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' By sharp interface we mean W ≪ L, where L is the characteristic hydrodynamic size  and W the characteristic interface length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The characteristic interface length is W = max(W, δT) where δT is  the Tolman length characterizing curvature-dependence of the surface tension detailed in section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  It was shown here that the use of the principle of corresponding states in combination with restrictions on the Mach  number and the ratio of characteristic interface to hydrodynamic sizes allows for a simple way to thicken the interface  and remove the fundamental restriction on grid-size in second-gradient fluid simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' While the analysis was  restricted to the van der Waals equation near critical state it equally applies to other equations of state, the pseudo-  potential model and temperatures much lower than the critical temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In the authors opinion this is one of the  main components of modern lattice Boltzmann models for non-ideal fluids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Numerical artifacts and issues of non-ideal lattice Boltzmann models  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Deviations in normal stress at interface: The issue of thermodynamic consistency  The issue of thermodynamic consistency as referred to in the lattice Boltzmann literature refers to the non-  equivalence of the mechanical stability and Maxwell construction conditions when considering the discrete pressure  tensor;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' To illustrate that purpose let us consider a force discretized with the first-neighbor D2Q9 stencil, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  F = 2  �  P − P0(r)  Q−1  �  i=0  w(|ci|)  �  P − P0(r + ciδt)ci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (621)  89  The discrete pressure tensor as introduced in the previous section is:  P(r) = P0(r) +  �  P − P0(r)  �  i  w(|ci|)  �  P − P0(r + ciδt)ci ⊗ ci,  (622)  which after Taylor expansion results in:  P =  �  P + δr2  6  �  P − P0∇2 �  P − P0  �  I + δr2  3  �  P − P0∇∇  �  P − P0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (623)  Now considering a flat interface normal to the x-axis, the normal pressure can be written as:  Pn = P + δr2  2  �  P − P0  d2  dx2  �  P − P0,  (624)  and further developed into:  Pn = P + δr2  4  �  P − P0  d  d √P − P0  �d √P − P0  dx  �2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (625)  After some algebra one can recover the following equation:  (Pn − P)  4 d √P−P0  dρ  δr2 √P − P0  = d  dρ  �������  �d √P − P0  dρ  �2�dρ  dx  �2������� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (626)  Integrating from the vapor phase to the liquid phase and noting that dρ/dx = 0 in both phases one arrives at the  following mechanical stability condition:  � ρl  ρv  (Pn − P) d ln(P − P0)  dρ  dρ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (627)  This form of the mechanical stability condition only matches the thermodynamic coexistence condition from Maxwell’s  reconstruction only if:  d ln(P − P0)  dρ  = 1  ρ2 ,  (628)  which is the basis of the proposal formulated in [170] to define a pseudo-potential of the form:  ψ =  �  P − P0 = ρ0 exp −ρ0  ρ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (629)  Note that other forms of the non-local contribution will lead to similar mistmatches;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For instance consider the free  energy form:  F =  Q−1  �  i=0  w(|ci|)(P − P0)(r + ciδt)ci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (630)  The stress normal to the interface will be:  Pn = P + δr2  4 (P − P0)  d  d(P − P0)  �d(P − P0)  dx  �2  ,  (631)  which leads to exactly the same mechanical equilibrium condition as before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The mismatch between the Maxwell  construction condition and discrete mechanical stability condition results in deviations in coexistence density in sim-  ulations from those predicted by thermodynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This point is illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 23 shows that the lattice  Boltzmann model correctly recovers the liquid/vapor coexistence densities closer to the critical temperature;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' As tem-  perature goes further down, and density ratio increases, coexistence densities in simulations deviate significantly  from the Maxwell construction predictions, and that regardless of the choice of the excluded volume and long range  interaction coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  90  10-5  10-3  10-1  / c  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8  1  T/Tc  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  Figure 23:  Coexistence densities with van der Waals equation of state as obtained from (grey lines) Maxwell’s construction and (markers)  simulations with different choices of a: (green x) a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0102, (magenta +) a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0051, (blue triangles) a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0026, (red squares) a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0013  and (black circles) a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='00064.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Simulations conducted using the first-neighbour pseudo-potential model with exact difference method to treat the  force term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Plot is reproduced from [146].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Fixed surface tension  One point that was noted in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (603) was the emergence of a surface tension-like leading error term in the  single-neighbour pseudo-potential model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The leading-order error is the reason the original pseudo-potential method  of [12] is able to recover a Korteweg-like surface tension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' At the difference of the Korteweg stress tensor, which is  a minimizer of the second-gradient free energy under global mass conservation constraint, and where surface tension  explicitly appears in the macroscopic equations as an additional term, in the former it is strictly enslaved to the chosen  stencil and form of the pseudo-potential and therefore not tunable, see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (603):  κ = Gδr2  3  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (632)  Introduction of variable capillary coefficient and therefore surface tension has been the topic of a wide number of  publications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' We will discuss solutions provided in the literature in the next sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The issue of spurious currents at interfaces  Common to all multi-phase models, at curved interfaces between the liquid and vapor phases, spurious (often  vortical) currents are observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The magnitude of these spurious currents is often directly tied to the density ratio  and interface thickness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The spurious currents are often associated to inbalance of forces at curved interfaces due to  discretization errors, most notably the limited degree of isotropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' To illustrate the importance of isotropy consider  a 2-D drop surrounded by a vapor phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The density distribution, and therefore pressure, is only function of r in  polar coordinate, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' ∂nρ/∂θn = ∂nP/∂θn = 0 for any n with n > 0 which results in driving forces of the form, if one  considers the Korteweg stress tensor:  ∇P − κρ∇∆ρ = ∂P  ∂r er − κρ  �∂3ρ  ∂r3 = 2  r  ∂2ρ  ∂r2 − 2  r2  ∂ρ  ∂r  �  er,  (633)  which clearly satisfy rotational invarience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In the absence of rotational forces one expects the velocity field to be  rotational-invarient too.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Furthermore, at steady state and assuming vanishing velocity far away from the drop the  continuity equation  1  r  ∂ρur  ∂r  = 0,  (634)  leads to:  ur = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (635)  91  It can therefore be concluded that isotropy of the driving forces should guarantee the absence of any form of velocity  in the case of the static 2-D droplet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Let us now consider the discretized form of the driving force on the D2Q9 stencil, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (621).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Operating a Taylor  expansion on that stencil one finds:  2  �  P − P0(r)  �  i  w(|ciδt|)ciδt  �  P − P0(r + ci) = 2  �  P − P0∇  �  1 + 1  6∇2 + 1  72∇2∇2  � � �  P − P0  �  +  √P − P0  90  �∂5 √P − P0  ∂x5  ex + ∂5 √P − P0  ∂y5  ey  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (636)  It is clear that the first term is isotropic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The last two terms however are not isotropic meaning this discrete approx-  imation loses isotropy at order five in turn leading to force imbalance which is then countered by non-zero velocity  components manifesting around the interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A typical result from lattice Boltzmann simulations of a static 2-D drop  is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Note that while we have considered the specific form of the body force used in [171] to get  Figure 24: Illustration of spurious currents near liquid/vapor interfaces: Time-evolution of maximum spurious currents along with the density and  velocity fields at the converged state as obtained from simulations with SRT collision model and exact difference method, at νδt/δr2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='03 and  Tr = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Image reproduced from [131].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (636), the classical form ∇(P − P0) would also lead to similar behavior, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  �  i  w(|ciδt|)ciδt(P − P0)(r + ci) = ∇  �  1 + 1  6∇2 + 1  72∇2∇2  �  (P − P0) +  1  180  �∂5(P − P0)  ∂x5  ex + ∂5(P − P0)  ∂y5  ey  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (637)  also generating non-isotropic terms forcing spurious currents at curved interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The only difference is in the form  of non-isotropic errors that appear at order 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A more detailed discussion of the errors of different forms of the forcing  term will be provided in later sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Galilean invariance of viscous dissipation rates and stability  For iso-thermal multi-phase flow simulations, even assuming the temperature in the discrete equilibrium is set  to the lattice temperature, and that the Mach number is kept very low Galilean-variant errors in the viscous stress  tensor, both deviatoric and diagonal components can be quite pronounced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For instance, consider the case of errors in  deviatoric components of the third-order equilibrium moments tensor for a second-order equilibrium:  δΠeq  αβγ = ρuαuβuγ + (ρc2  s − P0)[uαδβγ]cyc,  (638)  92  Pu  p1  p  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='02  udt/Sr  ug /gxeun  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='01  100  1050  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  1  y/H  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8  1  u/umax  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  1  y/H  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8  1  u/umax  Figure 25: Steady-state velocity profiles for the layered Poiseuille flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Left: Configuration (a), Tr = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='77, ρl/ρv = 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1, µl/µv = 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Right:  Configuration (b), and (right) Tr = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='36, ρl/ρv = 1030 and µl/µv = 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Grey plain line: analytical solution;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Black dashed line: Free energy LBM  with product-form equilibrium;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Red dashed line: Free energy LBM with conventional second-order equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Results are taken from [146].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Assuming P0 = ρc2  s is guaranteed everywhere the second term disappears leaving a term third-order in Mach num-  ber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In the case of ideal fluid simulations given that density variation are small the third-order scaling of this term  with Mach number allows one to neglect it for small Mach number simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' However for non-ideal fluids, at liq-  uid/vapor interface the density gradient can get quite large making this error term non-negligible even for small Mach  numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In practice, the erroneous viscous stress tensor can lead to pronounced velocity jumps at the interface as it  does not guarantee continuity of viscous momentum flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For errors in the deviatoric components, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' viscous shear  stress, this effect can be readily observed with a case as simple as the two-layer Poiseuille flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This case consists of  a rectangular domain filled with the liquid phase at the bottom and the vapor phase on top.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The flow is driven by a  body force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Top and bottom are subject to no-slip boundary conditions while the inlet and outlet are fixed by period-  icity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Running this case with models relying on second-order polynomial equilibria one recovers results such as those  shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Note that here the maximum non-dimensional velocities are quite small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' As for ideal gas solvers, it  is observed that including third-order terms in the discrete equilibrium eliminates this numerical artifact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This effect  is common to all multi-phase LBM, regardless of the formulation and the collision model [172, 173].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For instance, it  has been documented and studied for the color-gradient [172] and phase-field formulations [173, 174, 175, 176].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  While the effect of third-order moments error on Galilean-invariance of the viscous stress tensor is quite well-  documented its effect on the continuity equation have never been discussed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The LBM is known to guarantee global  conservation of mass to be exact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' However locally one does not exactly recover the continuity equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A third-order  perturbation analysis shows that at order ε3 the zeroth-order moment satisfies [111]:  ∂(3)  t ρ − 1  12∇∇ :  �  ∂(1)  t Πeq  2 + ∇ · Πeq  3  �  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (639)  The second term in that equation shows that there is a third-order deviation in the continuity equation recovered by  the LBM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' However looking at the form of that deviation term one observes that it is nothing but the ε-level balance  equation of the second-order moments restored to its correct form by the correction discussed in this section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' We can  therefore conclude that apart from restoring Galilean-invariance to the viscous stress the correction discussed here  also removes third-order errors in the mass balance equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  All lattice Boltzmann models targeting non-ideal fluids, as all other classical discrete solvers, are subject to dis-  cretization errors coming from both the lattice Boltzmann solver and the body force term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The specific form and  properties of these higher-order error terms manifests in different forms, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Magnitude of discretization error normal to interface: As shown in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (627) this affects the mechanical stability  condition at the discrete level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The mismatch between the discrete-level mechanical stability condition with the  Maxwell construction leads to errors in the coexistence densities even for flat interfaces as illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  93  Spurious surface tension-like terms: As shown in Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (636) and (637) a classical first-neighbour discretization  is equivalent to a second-order central finite differences an leads to third-order errors with a surface tension-like  structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In the case of the pseudo-potential method this error is the reason one observes surface tension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  However on the downside the capillary coefficient is fixed as shown in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (632).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Non-isotropic terms: In 2- and 3-D a look at the form of the error terms recovered at orders three and above  shows that non-isotropic terms appear;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For instance for the first-neighbour discretization non-isotropic terms  appear first at order five.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This leads to the formation of spurious currents in the vicinity of curved interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  The magnitude of these spurious currents is directly proportional to density ratio and inversely proportional to  interface thickness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Errors affecting viscous stress tensor: The use of a second-order polynomial equilibrium leads to errors in the  deviatoric components of the equilibrium third-order moments tensor in turn leading to errors in the effective  shear viscosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Even at very low velocities this error is quite pronounced around liquid/vapor interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  All these issues lead to practical limitation such as a maximum reachable density and/or viscosity ratio in simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  A number of of improvements have been proposed over the year to relax constraints on density and viscosity ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  We will review major improvements in the next section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Improvements and enhanced models for non-ideal fluids  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Equations of state  One approach to reduce spurious currents and access larger coexistence densities that was proposed early on was  the use of different equations of state starting with the work of [171].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The authors compared the maximum spurious  currents as a function of density ratio for different equations of states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The effect of the choice of equation of state  on maximum spurious currents as a function of density ratio is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 26 While initially such proposals were  Figure 26: Maximum spurious currents as a function of density ratio for different equations of state: (plain line) Shan-Chen, (dashed line) van der  Waals, (plain line with circular markers) Carnahan-Sterling, (plain line with square markers) Peng-Robinson, (plain line with diamond markers)  Riedlich-Kwong and (plain line with triangle markers) Riedlich-Kwong-Soave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Simulation have been conducted with the realization of [171].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Simulations have been conducted with the same choices of a and b as those reported in [171].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  limited to classical cubic equations of states, later many authors proposed tailored equations of state designed solely to  allow phase separation at the target density ratio and minimize numerical artifacts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Here we provide a brief overview  of these equations of state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Cubic equations of state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This family of equations of state are widely used in both thermodynamics and non-ideal  fluid simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The most well-known equation of state in that family was proposed by van der Waals [136],  P = ρRT  1 − bρ − aρ2,  (640)  94  4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='02  0  100  101  102  103  Pt/ puwhere parameters a and b are related to critical temperature Tc and pressure Pc as,  a = 27  64  R2T 2  c  Pc  , b = 1  8  RTc  Pc  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (641)  The Peng–Robinson EoS [177],  P = ρRT  1 − bρ −  aα(T)ρ2  1 + 2ρb − b2ρ2 ,  (642)  with  α(T) =  �  1 + (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='37464 + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='54226ω′ − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='26992ω′2)  �  1 −  �  T/Tc  ��2 ,  (643)  where ω′ the acentric factor (ω′ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='344 for water), and  a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='45724R2T 2  c  Pc  , b = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0778RTc  Pc  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (644)  The Riedlich–Kwong–Soave EoS [178, 179],  P = ρRT  1 − bρ − aα(T)ρ2  1 + ρb ,  (645)  with  α(T) =  �  1 + (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='480 + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='574ω′ − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='176ω′2)  �  1 −  �  T/Tc  ��2 ,  (646)  and  a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='42748R2T 2  c  Pc  , b = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='08664RTc  Pc  ,  (647)  and the Carnahan–Starling EoS [180],  P = ρRT 1 + bρ/4 + (bρ/4)2 − (bρ/4)3  (1 − bρ/4)3  − aρ2,  (648)  with  a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4963R2T 2  c  Pc  , b = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='18727RTc  Pc  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (649)  The co-existence densities of these four EoS as obtained using the Maxwell reconstruction method and simulations  reportes in [146] are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Shan-Chen equations of state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In Shan-Chen-type equations of state the thermodynamic pressure is defined as:  PSC = ρc2  s + G  2 ψ2,  (650)  where ψ is the non-local interaction potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' To derive an optimal form for the potential function a number of  constraints have to be taken into account;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' First, using the mechanical equilibrium condition one should arrives at the  following so-called thermodynamic consistency condition on the potential [181]:  � ρv  ρl  �  P − ρc2  s − G  2 ψ2� 1  ρ2 dρ = 0,  (651)  which is only strictly satisfied with ψ ∝ ρ [149].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' However, a potential interaction of that form would not allow for co-  existence of two phases of different densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Second, given that the original pseudo-potential has only an attractive  non-local contribution term, as noted in [181, 182], to mimic the hard-core repulsive interaction of real molecules and  prevent collapse of the liquid phase the potential must saturate at large densities, ψ → cst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Under these constraints  95  10-11  10-7  10-4  10-1  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8  1  2  3  10-11  10-7  10-4  10-1  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8  1  T/Tc  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5 2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  10-11  10-7  10-4  10-1  / c  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8  1  2  3  10-11  10-7  10-4  10-1  / c  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8  1  T/Tc  2  3  4  Figure 27: Liquid-vapor coexistence for various equations of state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Gray lines: Maxwell’s equal-area construction;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Red symbol: Simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Top  left: van der Waals (640) (a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='000159, b = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0952);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Top right: Peng–Robinson (642) (a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='000159, b = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0952);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Bottom left: Carnahan–  Starling (648) (a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='000868, b = 4);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Bottom right: Riedlich–Kwong–Soave (645) (a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='000159, b = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0952).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For all simulation ˜κ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='02.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Results reproduced from [146].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  96  a family of potentials were proposed, to satisfy the previously-listed conditions as closely as possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For instance  in [12] the authors used a potential defined as:  ψ = ρ0  �  1 − exp  �  − ρ  ρ0  ��  ,  (652)  where ρ0 is a tunable constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Another form was proposed in [183]:  ψ = ρ0 exp  �  −ρ0  ρ  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (653)  The behavior of the pseudo-potential of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1 is illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A expected in the limit of ρ/ρ0 → 0 one  Figure 28: Behavior of potential of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1 as a function of local density;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Black line: ψ/ρ0 = ρ/ρ0, red dashed line: Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  recovers ψ ∝ ρ while on the other end of the spectrum, ρ/ρ0 → ∞ the potential saturates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This clearly shows that while  the saturation allows for stable phases at large density ratios it deviates considerably from ∝ ρ making thermodynamic  inconsistencies in the sense of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (651) pronounced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Taylored equations of state for improved numerical properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In [184] the authors proposed a new family of equa-  tions of state to improve numerical properties of the pseudo-potential method, namely better compliance with thermo-  mechanical consistency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The piece-wise linear equation of state proposed in [184] consists of defining the pressure  as:  P =  �������������  ρc2  s,v  ifρ ≤ ρ1  ρ1c2  s,v + (ρ − ρ1) c2  s,m  ifρ1 ≤ ρ ≤ ρ2  ρ1c2  s,v + (ρ2 − ρ1) c2  s,m + (ρ − ρ2) c2  s,l  ifρ2 ≤ ρ  (654)  where in practice cs,v, cs,l and cs,m are chosen a priori.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The choice of these three variables allows one to fix speed  of sound in both the liquid and vapor phases and the interface thickness independently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Once they are fixed, the  remaining free parameters, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' ρ1 and ρ2 are closed via two conditions, namely mechanical:  � ρl  ρv  dP  dρ dρ = 0,  (655)  and chemical potential balance:  � ρl  ρv  1  ρ  dP  dρ dρ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (656)  This equation of state is illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' With this approach, the speed of sound in the liquid and vapor phase are  97  4  3  0  2  0  0  2  3  4  Od jdFigure 29: P − ρ diagram for piece-wise linear equation of state, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 654.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The density ratio here is set to 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  tunable parameters and as such can be set to be as close to each-other as possible to minimize compressibility effects  in the vapor phase and allow for larger CFL numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The piece-wise linear equation of state is now routinely used in  combination with the pseudo-potential formulation to model multi-phase flows with density ratios of the order of 103,  see for instance [185, 186].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Another alternative proposed by [187], argues that the main issue of cubic equations of state is the van der Waal loop  section of the P − V diagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In this region cubic equations of state predict negative compressibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' To better deal  with that region the authors proposed an apprioach that consists of using the classical cubic equations of state, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' van  der Waal Peng-Robinson etc, in the liquid and vapor branch and replacing it with a tailored third-order polynomial in  the van der Waals loop region ρv < ρ < ρl, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' both the binodal and spinodal regions:  P =  �������������  PEoS(ρ)  ifρ ≤ ρv  P0(ρv) + θm(ρ − ρv)(ρ − ρl)(ρ − ρm)  ifρv ≤ ρ ≤ ρl  PEoS(ρ)  ifρl ≤ ρ  (657)  The use of the cubic polynomial in the van der Waals loop comes with four free coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Conditions on continuity  of pressure and isothermal sound speed (or compressibility) at the vapor and liquid densities would in principle close  all free parameters and lead to the original cubic equation of state selected in the vapor and liquid branches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' As  such, and as detailed in the article, this approach can only have potential to improve interface properties if one of the  previously listed physical conditions are neglected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The removal of one of the conditions, sound speed in one of the  bulk phases would in principle allow control over the shape in the van der Waals loop region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  While the choice of the equation of state can be an efficient tool in reducing spurious currents and errors in coexistence  densities, the way these non-ideal contributions are introduced into the kinetic model is not unique and can han  dramatic effects on errors and stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Partitioning of pressure contributions  In previous sections we introduced a general kinetic framework for non-ideal fluids and discussed the invarience of  the recovered macroscopic equations with respect to the choice of reference pressure P0 enforce by the BGK collision  operator attractor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Here we discuss different possible choices of P0 and its repercussions on numerics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  The classical route: equilibrium at stencil reference temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The most widely used partition approach in the  litterateur consists of fixing P0 appearing in the equilibrium at a value optimizing numerical properties of the lattice  Boltzmann solver.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For instance for a model based on a third-order Gauss-Hermite quadrature the optimal value of P0  is:  P0 = ρ δr2  3δt2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (658)  98  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='06  P 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='04  V  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='02  I  I  I  P2  II  I  11  0  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  1  pSetting the reference pressure in that way has two main advantages;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' As discussed earlier the classical third-order  quadrature admits a deviation in the diagonal components of the third-order equilibrium moment that has a third-  order dependence on velocity and first-order dependence on P0/ρ:  δΠeq  ααα = ρuα  �  u2  α + 3(P0/ρ − c2  s)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (659)  Therefore small deviations of P0/ρ from the optimal temperature c2  s can considerably increase the Galilean-variant  errors in the dissipation rate of normal modes, as illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The second advantage of this choice of  Figure 30: Error in the diagonal components of the third-order moments tensor as a function of the reference pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  partition is stability domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' As illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 31 via the linear stability domain best results in terms of maximum  non-dimensional speed and minimum non-dimensional viscosity are achieved at P0/ρc2  s = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Both above and below  Figure 31: Linear stability domain of the SRT collision operator with a product-form equilibrium as a function of the reference pressure P0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  P0/ρc2  s = 1 the stability domain is considerably reduced making realistic simulations with acceptable CFL numbers  practically impossible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  The vast majority of publications treating of isothermal non-ideal fluids rely on this type of partition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For instance in  the pseudo-potential model with the Shan-Chen equation of state:  P0 = ρc2  s,  (660)  99  Po/pc=1  cxx  10-2  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='02.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3  Po/pcs  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3  IInl  Sr/St  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  0  10-6  10-2  1  VSt / Sr2and  P − P0 = G  2 ψ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (661)  In the free energy formulation, this is equivalent to the force-based approach with [128]:  TK − P0I =  �  P − ρc2  s − κρ∇2ρ − κ  2|∇ρ|2�  I + κ∇ρ ⊗ ∇ρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (662)  This specific partition of pressure is the most widely used approach in the literature, mainly because of the numerical  properties enumerated above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Full pressure used in equilibrium attractor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' As mentioned earlier, the idea of introducing the full thermodynamic  pressure into the equilibrium function of a lattice Boltzmann solver started with the first free energy LBM [150, 188]  where the non-ideal equation of state and surface tension were introduced into the discrete equilibrium via moments  matching.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A similar construction was also discussed in [189, 190].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The authors argued that this approach has the  advantage of guaranteeing mass conservation locally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Furthermore, this approach has the additional advantage of  reducing derivatives in the stress tensor by one order and therefore making the overall scheme more local.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The first  attempt presented in [150] was based on a second-order polynomial discrete equilibrium and subject to Galilean-  variant errors in both the diagonal and deviatoric components of the viscous stress tensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Consider a two-phase fluid  in the incompressible regime with a density ratio of only 10: 10P0/ρl = P0/ρv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This means that inevitably at least  one of the phases will have P0/ρ considerably larger or smaller than c2  s resulting in diminished stability domain, see  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Furthermore, without corrections the viscous stress tensor is subject to errors scaling with ∝ (P0/ρ − c2  s), see  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (659).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In effect this means that the application of such a model would be limited to very low density ratios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' As a  way to overcome this issue, and minimize errors related to deviation from the reference frame a realization based on  the Particles-on-Demand was proposed and used in [191].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Non-local thermodynamic pressure force contribution: Using mathematical identities to reduce discretization  errors  The first step in the realization of the force is the way it is treated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' It can be introduced as is [192], i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  F = ∇(P − P0),  (663)  or using an identity:  ∇(P − P0) = 2  �  P − P0∇  �  P − P0, forP ≥ P0  (664)  This approach, for general non-ideal equations of state was employed in [171] following the original form of the  pseudo-potential model [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' It should be noted that in the case of the original model this equality held unconditionally  because the Shan-Chen equations of state were strictly positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Positivity can become an issue especially near the  liquid branch spinodal point where pressure is usually minimal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  As a way to extend the domain of accessible density ratios by decreasing the magnitude of leading-order error terms  and reduce spurious currents a weighed combination of these two approaches was also proposed [80, 193]:  F = γ∇(P − P0) + 2(1 − γ)  �  P − P0∇  �  P − P0,  (665)  where the weight γ becomes a tuning parameter to better match co-existence densities or reduce spurious currents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Another possibility, not discussed in the literature, would be to rewrite the non-ideal pressure contribution as:  ∇(P − P0) = (P − P0)∇ ln(P − P0), forP ≥ P0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (666)  To illustrate the effect of the way this term is introduced and provide a simple comparison of their performances let  us consider a simple 1-D interface:  P − P0 ∝ 1  2  �  1 + tanh x − x0  σ  �  ,  (667)  100  located at x0 of thickness σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Assuming a second-order accurate finite difference discretization of the contribution,  errors are governed by the third- and higher order derivatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Denoting approaches of Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (663), (664) and (666)  respectively with F1, F2 and F3 and assuming zero surface tension, the leading order error of pressure normal to the  interface would scale as:  δF1  =  1  3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='∂3  x(P − P0) + O(∂5  x),  (668)  δF2  =  2 √P − P0  3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  ∂3  x  �  P − P0 + O(∂5  x),  (669)  δF3  =  P − P0  3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  ∂3  x ln(P − P0) + O(∂5  x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (670)  The leading-order errors for the considered interface, for two different interface thicknesses illustrating the diffuse and  near-sharp cases, are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Comparing the different errors one can already observe that F1 leads to the  Figure 32: Profiles of leading-order error terms for different realizations of the non-local pressure contributions for (left) σ = 8 and (right) σ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Black line: F1, red line: F2 and blue line: F3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  largest interfacial errors while F3 introduces the lowest amount of deviations both in the diffuse and sharp interface  configurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Higher order discretization: Leading order error and isotropy  Once the form of the non-local pressure term has been determined it needs to be discretized;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For the sake of  readability we will only consider the form F2 here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The finite difference discretized form can be written in general as:  F2 = 2  �  P − P0(r)  Q  �  i=0  w(|ci|)ci  �  P − P0(r + ciδt),  (671)  where ci defines the stencil used for the discretization and w(|ci|) are the associated weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For instance, considering  a simple second-order central difference approximation ci ∈ {(1, 0), (0, 1), (−1, 0), (0, −1)} and w = 1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' From classical  theory of finite differences method and Taylor expansion the order of accuracy of the approximation can be arbitrarily  increased by relying on larger stencils.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The weights w(|ci|) on such classical stencils for different order of accuracy are  listed in Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' While the use of such higher order schemes reduces the errors in coexistence density stemming  from the thermodynamic inconsistency issue it does necessarily improve the isotropy of the discrete approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  101  X10-4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='05  0  0  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='05  2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='15  4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  50  100  150  90  95  100  105  110  X  XOrder of accuracy  w(1)  w(2)  w(3)  w(4)  2  1/2  4  2/3  −1/12  6  3/4  −3/20  1/60  8  4/5  −1/5  4/105  −1/280  Table 6: List of weights for classical stencils with different orders of accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The notation w(k) refers to the weight of all stencil components of  size k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  w(1)  w(  √  2)  w(2)  w(  √  5)  w(2  √  2)  w(3)  w(  √  10)  E(4)  1/3  1/12  E(6)  4/15  1/15  1/120  E(8)  4/21  4/45  1/60  2/315  1/5040  E(10)  262/1785  93/1190  7/340  6/595  9/9520  2/5355  1/7140  Table 7: List of weights for stencils with different orders of isotropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The notation E(2n) refers to a stencil with order of isotropy 2n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For weights  the notation w(k) refers to the weight of all stencil components of size k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The corresponding stencils are illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Applying the Taylor expansion to the general form of the discretized force [182]:  F2,α = 2  �  P − P0(r)E(2)  α1 ∂α2  �  P − P0(r) + 1  3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='E(4)  α1α2α3α4∂α1α2α3  �  P − P0(r) + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (672)  where  E(m)  α1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=',αm =  �  i  w(|ci|)ci,α1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' ci,αm,  (673)  with E2n+1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The even-order tensors can be re-written as:  E(2n)  α1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='α2n = C(2n)∆(2n)  α1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='α2n,  (674)  where ∆(2n)  α1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='α2n can be computed using the following recursion relation:  ∆(2)  α1α2  =  δα1α2,  (675)  ∆(4)  α1α2α3α4  =  δα1α2δα3α4 + δα4α1δα2α3 + δα2α3δα4α1,  (676)  ∆(2n)  α1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='α2n  =  2n  �  j=2  δα1α j∆α2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='α j−1α j+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='α2n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (677)  This general expansion of the discrete forcing term allows to analyze both the leading-order errors and the degree  of isotropy of the discrete approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The latter is an important point to consider as the continuous form of the  force is isotropic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Any non-isotropic errors in the discrete approximation would lead to force imbalance on curved  interfaces and lead to spurious currents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The use of higher-order stencils can therefore help reduce the spurious  currents stemming from these force imbalances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In [182] the authors have derived stencils of different order of  isotropy with corresponding weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' These are listed in Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4 for a 2-D system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The stencils corresponding  to these weights are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' It was shown in this section that one can reduce discretization errors at  interfaces, both magnitude and isotropy, via higher order approximations relying on larger discretization stencils.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Larger discretization stencils also mean larger number of discrete operations per grid-point and larger degrees of non-  locality of such operations which in turn translate into both computational and communication (for parallel simulations  on clusters with distributed memory) overhead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  102  Figure 33: Illustration of different discrete stencils for different orders of isotropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Weights are listed in Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Figure partially reproduced  from [182].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Thickening interface  Artificial thickening of the interface is another strategy to both reduce errors in coexistence densities and spuri-  ous currents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This strategy is motivated by the invariance of the non-dimensional coexistence densities with respect  substance-specific coefficients as demonstrated through the principle of corresponding states and and the fact that  errors at interfaces are function of higher-order derivatives of the pressure field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In the context of cubic equations of  state, the simple analysis leading to (619) showed that the interface thickness can in principle be controlled through  the capillary coefficient and isothermal compressibility tied itself to the long range interaction coefficient a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Plugging  the van der Waals equation of state into Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (619) one would expect the interface thickness to scale with ∝ 1/ √a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This  scaling is readily demonstrated via simulations close to the critical point, shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Carrying out simulations  Figure 34: Effect of the choice of a on the interface width.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Diamond, square and circle: Simulation for Tr = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='98, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='99, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='995, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Simulation conducted using van der Waals equation of state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Plot reproduced from [146].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  with different values of a it can easily be shown that this increase in interface thickness allows for better resolution  of interfaces and therefore reduced deviations in discrete stress tensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The coexistence densities as obtained from  simulations with different choices of a are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' It is observed that increasing the interface thickness one  converges to the coexistence density prediction of the Maxwell construction even at very large density ratios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  As discussed in previous section, another aspect of errors in the stress tensor that need attention are non-isotropic  effects leading to spurious currents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' As for errors for flat interfaces these deviations functions of higher-order deriva-  tives of the pressure field and such should reduce with thicker interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The effect of the choice of a controlling  interface thickness on spurious currents for the discrete model of [146] is illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' It is clearly observed  that smaller values of a, which as seen before scale with interface thickness as W ∝ 1/ √a, lead to smaller spurious  currents scaling as ∝ a1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3 for the discrete model of [146] meaning they scale with interface thickness as ∝ W−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Such  scaling relationships can also be obtained for other discrete stencils.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  While changing the isothermal compressibility in combination with capillary coefficient allows to thicken the inter-  face independently from surface tension it comes with a limitation: It changes the isothermal speed of sound in both  liquid and vapor phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Lower values of a lead to smaller speeds of sound in both phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This in turn means that for  103  4th  6th  8th  10th3  u/-M  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  10-2  10-1  aFigure 35: Coexistence densities as obtained from (grey lines) Maxwell’s construction and (markers) simulations with different choices of a: (green  x) a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0102, (magenta +) a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0051, (blue triangles) a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0026, (red squares) a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0013 and (black circles) a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='00064 Simulation conducted  using van der Waals equation of state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Plot reproduced from [146].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Figure 36: Maximum spurious currents for different values of a at Tr = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Simulation conducted using Peng-Robinson equation of state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Plot  reproduced from [131].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  the isothermal simulation to be close to the low Mach regime one would need to run simulation at lower convective  CFL conditions leading to much smaller time-steps and additional computational costs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Independent control over surface tension  A solution to the fixed nature of the surface tension recovered by the original pseudo-potential model was provided  in [182, 194] where the authors introduced the concept of dual/multi-range pseudo-potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In its simplest form a  second layer of neighbours is added to the stencil considered for the discretization of the pressure term:  F2 = 2  �  P − P0(r)  �  i  w(|ci|)ci  �  G1  �  P − P0(r + ciδt) + G2  �  P − P0(r + 2ciδt)  �  ,  (678)  where G1 and G2 are coefficients to be determined below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Taylor-expanding this term:  F2 = 2(G1 + 2G2)  �  P − P0∇  �  P − P0 + 2  �  P − P0  G1 + 8G2  6  ∇∇2 �  P − P0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (679)  To correctly recover the thermodynamic pressure term one must satisfy G1 + 2G2 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Using this condition the force  can be re-written as:  F2 = ∇|P − P0|+  �  P − P0  1 + 6G2  3  ∇∇2 �  P − P0,  (680)  meaning the surface tension coefficient can now be tuned with G2, κ = 1+6G2  3  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Alternatives to the dual-range model  have also been proposed in the past years to limit the effect of the choice of G2 on the mechanical stability conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  104  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8  T/T  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  10-5  10-3  10-1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  p/p10-2  α a1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3  10-3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='001  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='005  aFor instance in [195] the authors introduce an additional source term in the discrete equation:  Qi =  wi  2c4s ¯τH2 : κ′ �  P − P0(r + ci)δt  Q  �  i′=0  w(|ci′|)ci′ ⊗ ci′  � �  P − P0(r + ci′δt) −  �  P − P0(r)  �  ,  (681)  where κ′ is the parameter that controls the surface tension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' While allowing a variable coefficient in front of the surface  tension-like term, the final stress tensor is still different from the Koerteweg tensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  An extension of the dual range approach to recover a consistent Korteweg stress tensor fourth-order accurate in space,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  guaranteeing the surface tension is not polluted by leading order errors from the discretization of the thermodynamic  pressure term was proposed in [146]:  F2 = 2  �  P − P0(r)  �  i  w(|ci|)ci  �  G1  �  P − P0(r + ciδt) + G2  �  P − P0(r + 2ciδt)  �  + ρ(r)  �  i  w(|ci|)ci  �G3ρ(r + ciδt) + G4ρ(r + 2ciδt)� ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (682)  where G1 + 2G2 = 1 and G1 + 8G2 = 0 guarantee correct recovery of the thermodynamic pressure term while  G3 + 2G4 = 0 and G3 + 8G4 = 6κ recover the correct Korteweg surface tension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The discrete pressure tensor  As shown through Taylor expansion in the previous section, the continuous and discrete pressure tensors are not  exactly the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In [194] proposed an approach to evaluate the discrete pressure tensor as momentum flux through a  surface;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Given an infinitesimal area dS and the force acting through that surface dF the pressure tensor is defined as:  dF = P · dS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (683)  Integrating over a closed control volume one arrives at the fact that the surface integral of the pressure has to match  total force acting on the control volume:  �  P · dS =  �  FdV,  (684)  which in discrete form reduces to:  �  P · S =  �  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (685)  Considering for the sake of simplicity a specific discrete velocity direction, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' ciδt, it can be seen that the number of  force vectors across a unit vertical surface element dS = ex is cixδt and that across a unit horizontal surface element  is ciyδt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In simplest case where all pressure contributions from the force have a strength F the pressure contribution is  then simply obtained as ci ⊗ ciδt2F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For a force field where each contribution has a different magnitude one uses the  averaged force, where averaging is operated on all force contributions crossing the surface area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This results, for the  simplest first neighbor stencil and the classical pseudo-potential interaction in:  P = −G  2 ψ(r)  8  �  i=0  w(|ci|)ci ⊗ ciψ(r + ciδt).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (686)  105  Following that same construction logic write the contribution for a more complex force, like he one used in [146] as  F = FA + FB + FC + FD,  (687)  FA = ±8  3  �  P − P0(r)  Q−1  �  i=0  w(|ci|)ci  �  P − P0(r + ciδt),  (688)  FB = ∓1  3  �  P − P0(r)  Q−1  �  i=0  w(|ci|)ci  �  P − P0(r + 2ciδt),  (689)  FC = 2˜κρ(r)  Q−1  �  i=0  w(|ci|)ciρ(r + ciδt),  (690)  FD = −˜κρ(r)  Q−1  �  i=0  w(|ci|)ciρ(r + 2ciδt).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (691)  The pressure tensor contributions from forces FA and FC can be readily written as:  PA  =  ∓8  6  �  P − P0(r)  Q−1  �  i=0  w(|ci|)ci ⊗ ci  �  P − P0(r + ciδt),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (692)  PC  =  −˜κρ(r)  Q−1  �  i=0  w(|ci|)ci ⊗ ciρ(r + ciδt),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (693)  while FB and FD contribute to the pressure tensor as follows:  PB = ± 1  6  ��������  �  P − P0(r)  Q−1  �  i=0  w(|ci|)ci ⊗ ci  �  P − P0(r + 2ciδt) +  Q−1  �  i=0  w(|ci|)ci ⊗ ciψ(r − ciδt)  �  P − P0(r + ciδt)  �������� ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (694)  PD = ˜κ  2  ��������ρ(r)  Q−1  �  i=0  w(|ci|)ci ⊗ ciρ(r + 2ciδt) +  Q−1  �  i=0  w(|ci|)ci ⊗ ciρ(r − ciδt)ρ(r + ciδt)  �������� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (695)  These expressions allow to compute the discrete pressure tensor with high accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 37 shows the distribution  of the normal pressure, Pxx, in a flat interface simulation as computed from both the discrete and continuous pressure  tensors,  Pcont  xx  = P + κ  �  ∂2  xρ − 1  2|∂xρ|2  �  ,  (696)  While the discrete evaluation method correctly results in a uniform pressure distribution throughout the domain, also  across the interface, the continuous approximation evaluated using a finite differences approximation fails to do so,  indicating errors due to higher-order terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This points to the necessity of using the discrete pressure tensor for  evaluation of sensitive quantities especially for sharper interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Evaluating the effective surface tension  Laplace’s law.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In this approach, simulations of circular/spherical liquid drops of different radii surrounded with  vapour are carried out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The corresponding surface tension coefficient is then evaluated using the Laplace law in a  form,  ∆P = (D − 1)σ  R  ,  (697)  where R is the drop radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' ∆P can readily be computed by extracting the pressure at the center of the drop Pin  and a point in the vapor phase far away from the drop Pout as ∆P = Pin − Rout.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For simulations carried out using  diffuse interface formulations the notion of drop radius becomes ambiguous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' To that end, for consistent analysis of  106  0  50  100  150  200  6  4  2  0  2  4  0  1  2  3  Figure 37: Pressure distribution from a simulation at Tr = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='36, corresponding to Pr = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0022 and ρl/ρv = 103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Black line: Evaluation using the  discrete pressure tensor;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Red line: Evaluation using continuous pressure tensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Dashed blue line: Density profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  results one has to introduce the notion of dividing surfaces, more specifically the equimolar surface here, proposed by  Gibbs [196].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A brief reminder of Gibbs’ theory of dividing surfaces is in order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The total mass in both the diffuse and  sharp interface pictures can be written as:  �  V  ρdV = ρlVl + ρvVv + Γ,  (698)  where ρlVl and ρvVv are the masses in the bulk liquid and vapor phases in the sharp interface picture, while Γ is the  excess mass on a dividing surface Σ, or mass adsorbance [196].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' By requiring that no mass be stored on the dividing  surface we get the definition of the equimolar surface:  Γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (699)  The family of dividing surfaces in the case of drop or bubble are concentric spheres (D = 3) or concentric circles  (D = 2) parameterized by their radius R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In particular, for a two-dimensional drop, the mass adsorbance can be  written as a function of the radius of the dividing circle,  Γ(R) =  � 2π  0  � ∞  0  (ρ(r) − ρv)rdrdϕ −  � 2π  0  � R  0  (ρl − ρv)rdrdϕ,  (700)  while the zero-adsorbtion condition (699), Γ(Re) = 0, implies the equimolar radius Re,  Re =  �� ∞  0 (ρ(r) − ρv)rdr  (ρl − ρv)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (701)  This definition can then be used to replace the radius in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 718.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Once both drop radii and pressure differences are  known the surface tension can be extracted as the slope of ∆P = σ D−1  Re .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This is illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Kirkwood approach for flat interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The surface tension coefficient of a flat interface can be evaluated using its  mechanical definition [197] as,  σ =  � +∞  −∞  �  Pxx − Pyy  �  dx,  (702)  where here the interface has been considered normal to the x-axis in a two-dimensional simulation setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The nor-  mal Pxx and the tangential Pyy components of the discrete pressure tensor can be computed from the continuous  approximation or using the discrete pressure tensor introduced in the previous section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  107  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='015  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='025  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='03  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8  1  10-3  Figure 38: Left: Circular D = 2 drop configurations;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Right: Pressure difference scaling with drop radius for Tr = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='99, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='98, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='97 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The  pressure difference is defined as ∆P = Pin − Pout.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The slope of the straight line is the surface tension coefficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Results are reproduced from [146].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Fluid-solid interaction: wetting properties  A first indication on the treatment of a solid boundary for second-gradient fluids, under the assumption of short  range-only interaction, was given by Cahn (critical point wetting).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Considering a control volume with a solid surface  at the boundary the total free energy is defined as:  A =  �  V  �  A0 + 1  2κ|∇ρ|2  �  dV +  �  Aw(ρw)dS,  (703)  where V is the considered control volume, S the solid surface and Aw a surface free energy function which depends  only on the fluid density at the solid surface ρw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The derivative of this functional is obtained as:  δA =  �  V  δρ  �∂A0  ∂ρ − κ∇ · ∇ρ  �  dV +  �  δρw  �  κn · ∇ρ + ∂Aw  ∂ρw  �  dS,  (704)  where n is the unit vector normal to the solid surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Minimzation of the total free energy with respect to ρw leads to:  κn · ∇ρ = dAw  dρw  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (705)  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Static contact angle  One of the first approaches to impose wetting boundary conditions for non-ideal fluids in the context of the pseudo-  potential method was proposed in [198].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Following the structure of the non-local pseudo-potential interaction term  they proposed an additional contribution modeling wall interaction of the form:  Fwall = −ρ(r)Gwall  �  i  wiciδts(r + ciδt),  (706)  where s is an indicator function equal to one in a solid cell and zero in a fluid cell and G)wall is the interaction  strength parameter controlling the contact angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Sukop and Thorn [199] proposed a slightly modified form of the  wall interaction term as [200, 201]:  Fwall = −ψ(r)Gwall  �  i  wiciδts(r + ciδt).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (707)  108  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  1  0  50  100  150  200  Figure 39: Static contact angles as (blue squares) obtained from the Young–Laplace equation and (red circles) measured directly from the simula-  tions using the approach of [181, 203].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Image is taken from [146].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Later on Kang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' proposed a modified version of Martys and Chen’s approach to setting wetting boundary condi-  tions as [202]:  Fwall = −ρ(r)Gwall  �  i  wiciδtρwall(r + ciδt).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (708)  The wall is modeled as a phase with a constant density ρwall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' As with previous schemes Gwall is used to set the contact  angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Alternatively, Benzi et al proposed a slightly modified form, fully consistent with the bulk non-local interaction  [181, 203]:  Fwall = −ψ(r)G  �  i  wiciδtψwall(r + ciδt),  (709)  where the only free parameter is ψwall which controls adhesion of the liquid/vapour phase to the solid boundary, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  for ψwall → ψl the contact angle goes to zeros while ψwall → ψv the contact angles goes to 180.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Geometrical approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In parallel with the previously-listed approaches, alternative geometrical approaches widely  in use for phase-field based approaches have also been developed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ding and Spelt proposed a geometrical approach  to implement contact angles in phase-field methods as [204]:  tan  �π  2 − θs  �  =  −n · ∇ψ  |∇ψ − (n · ∇)n|,  (710)  which once discretized leads to [204]:  ψ(x, −δy) = ψ(x, δy) + tan  �π  2 − θs  �  |ψ(x + δx, 0) − ψ(x − δx, 0)|,  (711)  where assuming a flat solid interface perpendicular to the y-axis at y = 0, (x, −δy) designates a ghost layer within  the solid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' θs is the contact angle to be imposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' They showed that the geometrical approach can fix the slop of the  liquid-gas interface to a value consistent with the imposed contact angle given that there are enough points within the  interface, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' typically 4-8 grid-points [204].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The approach is illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The geometrical approach of  Ding and Spelt was transposed into the pseudo-potential formulation in [205] for flat interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Later on, in [206] it  was extended to curved solid boundaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' While here we have used the pseudo-potential ψ as the order parameter in  defining the contact angle, this approach can readily be extended to free energy methods by replacing ψ with the fluid  density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  109  Figure 40: Illustration of contact line in geometrical approach to contact angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Contact angle hysteresis  To illustrate the meaning of contact angle angle hysteresis let us take the example detailed in [207].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Consider a  small droplet resting on a solid surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' If the droplet is allowed to evaporate or if liquid is slowly withdrawn from  the droplet with a syringe, over time both the volume and contact angle will decrease maintaining the same contact  area, up until the onset of recession.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The drop will then recede with a constant contact angle, θR, characteristic of  both surface chemistry and topography.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Now the opposite scenario: if the surface is cooled down below dew point  leading to liquid condensing on the drop or if liquid is slowly added to the droplet the droplet both volume and contact  angle will initially increase until the drop starts to advance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The drop will advance at a constant angle θA which is  also determined by the characteristics of the solid surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Both cases are illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A metastable droplet  can form with any angle between these two angles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The interval between the two is referred to as the contact angle  hysteresis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A simple realization of the contact angle hysteresis was proposed and used in [208] in the context of  Figure 41: Illustration of (a) advancing and (b) receding drop on solid surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In (c) a drop sliding on a surface exhibiting both receding and  advancing contact angles in shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Image is taken from [207].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  the geometrical approach to setting the contact angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' There the authors dynamically adjusted the contact angle as a  function of the speed of the contact line, uCL:  �������������  θs = θA,  ∀uCL > 0,  θs = θR,  ∀uCL < 0,  θs = θs,  uCL = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (712)  In practice, the contact angle is evaluated at every time-steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' If the measure angle is within the hysteresis windows  it is left unaltered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' If it is outside the hysteresis windows it is set to either the advancing or receding contact angle,  depending on the speed of the contact line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Similar approaches have been adopted in the contact of the LBM [209, 210,  211].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For instance in [212] the authors used a similar feedback-based strategy without taking into account the contact  line speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The authors set θ = θA if the measured angle was larger than θA and θ = θR if its was smaller than θR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' While  this approach performed well for contact line motion on flat substrates and flow in tubes [213], as noted in [214], it  110  fluid 2  interface thickness  fluid 1  n  Solid wall6  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  a  b  cresulted in un-physical behavior for isothermal drying of droplets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The correct behavior was restored by taking into  account the contact line velocity [214].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' One important point to note about contact angle hysteresis implementation is  that to the authors knowledge all attempts at enforcing a hysteresis window have relied on the geometrical approach of  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 710.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This is due to the fact that to dynamically set the contact angle to θR and θA there must be a way to estimate  the corresponding boundary condition a priori.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Other approaches to setting wetting conditions in the context of LBM  do not establish a clear relationship between fluid/solid interaction force and contact angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Assessment of thermo-physical properties of models  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Speed of sound and compressibility  Different from hydrodynamic pressure-based formulation such as those employed in combination with Allen-Cahn  interface tracking methods, all LBMs for weakly compressible non-ideal fluids recover the isothermal speed of sound  of the implemented equation of state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The analytical isothermal sound speed can be obtained via the derivative of the  pressure with respect to density at constant temperature, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' cs = �∂ρP|T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For instance for the van der Waals equation  of state the isothermal sound speed is,  cs =  �  ∂P  ∂ρ  �����T  =  �  RT  (bρ − 1)2 − 2aρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (713)  In simulations the sound speed can be measured by modeling the evolution of a pressure step-function and monitoring  the position of the pressure front over time in a quasi-one-dimensional simulation at different temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The sound  speed for different cubic equations of state at different temperature in both liquid and vapor phases as obtained from  simulations are compared to analytical data in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Similar to cubic equations of state, Shan-Chen-type equations  Figure 42: Isothermal sound speed for various equations of state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Top row, from left to right: Peng–Robinson, Carnahan–Starling and Riedlich–  Kwong–Soave;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Bottom row: van der Waals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Grey plain lines: Theory;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Symbol: Simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Plot reproduced from [146].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  also admit isothermal sound speeds that can be obtained both analytically and from simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The results for two  different equations of state are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' There are two interesting points to note about the latter equations of  state: (a) The difference in sound speed between the liquid and vapor branches is less pronounced than cubic equations  of state making them interesting for simulations targeting the incompressible regime and (b) the sound speed in the  111  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  L  1  liquid  liquid  liquid  S  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  vapor  vapor  vapor  0  0  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8  I  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8  T/Tc  T/Tc  T/Tc  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8  1  T/TcFigure 43: Isothermal sound speed for two Shan-Chen equations of state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Grey plain lines: Theory;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Symbol: Simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Plot reproduced from  [146].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  vapor branch is always higher than that in the liquid branch which is not quite physical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  In general it must be noted that simulations targeting non-ideal equations of state in the limit of the incompressible  regime are more challenging than for ideal gases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In ideal gases to correctly recover the incompressible limit separation  of scales between shear and normal mode speeds must be ensured, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' umax ≪ cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Furthermore, given the explicit  nature of the LBM solvers the time step size is limited by the fastest traveling eigen-mode, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' speed of sound:  cs < δr/δt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In non-ideal systems, to ensure weak compressibility in both phases one must have umax ≪ min(cs,l, cs,v)  and max(cs,l, cs,v) < δr/δt to ensure stability of the explicit solver.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Given difference of scale of sound speed in the  liquid and vapor phases, especially at larger density ratios, this can become extremely prohibitive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In most practical  applications where only the behavior of the liquid phase is of interest the first condition is made weaker, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' umax ≪  cs,l, allowing for larger time-steps and introducing more pronounced compressibility effects into the vapor phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Meanfield scaling laws: Interface thickness  Different from sharp interface methods, in diffuse interface approaches the liquid-vapor interface has a non-zero  thickness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The thickness of the interface can be defined in many different ways;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Here we use a definition for bearing  numerical information as to how well the stiff gradients are resolved on a given mesh, making it directly related to the  velocity increment per time-step:  W = ρl − ρv  max|∇ρ|,  (714)  where ρl and ρv are densities of saturated liquid and vapor, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' It is observed that in the limit of a sharp  interface, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' resolved with δr, δr/W → 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' On the other end of the spectrum for δr/W → 0, akin to ε → 0, one  expects to recover the hydrodynamic limit, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' meanfield behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In that limit, surface tension is known to vanish  as the temperature approaches the critical, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (716), while the interface diverges as T → Tc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' As noted by [215],  the van der Waals theory predicts the temperature scaling of the interface width as,  W(Tr) ∝ (1 − Tr)−1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (715)  For a well-posed numerical solver for any of the non-ideal fluid models discusses here, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Free energy, pseudo-  potential etc, moving from δr/W ≈ 1 where numerical artefacts are known to dominate towards δr/W → 0 one  expects to recover the behavior predicted by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 715.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Articles treating of that issues in the context of non-ideal  fluid LBM are rather scarce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In [146] the authors studied the evolution of interface thickness for different reduced  temperatures using the van der Waals equation of state to probe the consistency of the solver against the second-  gradient fluid theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' To that end simulations of flat interfaces were carried out in a range of reduced temperatures  Tr near the critical point, and corresponding interface widths W(Tr) (714) were measured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Results are shown in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Furthermore, to probe the W/δr → 1 and W/δr → 0 limits simulations were carried out for different values  of a allowing to re-scale the interface thickness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This is equivalent to reducing the grid-size for a fixed substance  or changing the substance for a fixed grid size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' As noted by many authors in the literature [216], the parameter a  112  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  vapor  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  liquid  vapor  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  liquid  0  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='9  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='85  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='95  1  Gc/G  Gc/G0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='001  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  5  15  10-2  10-1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  1  3  Figure 44: (Left) Interface width as a function of temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Blue square: Simulation with a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='184;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Red circle: Simulation with a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='02;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Grey dashed line: Theoretical scaling (715).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (Right) Effect of the choice of a on the interface width.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Diamond, square and circle: Simulation for  Tr = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='98, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='99, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='995, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Plot reproduced from [146].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  can be used to control the interface thickness, at a given density ratio, leaving the ratios and Maxwell construction  unaffected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In agreement with the equivalent states theory, the right hand side plot in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 44 points to the universality  of the scaling of the interface width near the critical point regardless of the choice of a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In addition it is interesting  to note that for a fixed grid-size δr, as (1 − Tr) → 1, δr/W → 1 (equivalent to the scaling parameter ε introduced  in the multi-scale analysis) indicating deviation from the thermodymically converged state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This is illustrated by the  deviation of the numerical interface thickness, starting at Tr ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='98 from the theoretical predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Lowering the  value of a, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' rescaling the interface by a factor 1/ √a and therefor lowering ε, it is observed that interface is again  well-resolved and the scaling (715) restored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Meanfield scaling laws: Surface tension  Surface tension at liquid-vapour interface decreases with increasing temperature and vanishes at the critical point  [158].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For the van der Waals equation of state, the surface tension coefficient σ follows a scaling law as Tr → 1  [6, 217],  σ = 16a  27b2  �  κ  a(1 − Tr)3/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (716)  A few publications have discussed the temperature scaling of the surface tension in the limit of a flat interface using  the pseudo-potential method with a van der Waals equation of state [80] and the Shan-Chen equations of state [218]  and the free energy approach with the van der Waals equation of state [146].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' All have shown that these models are able  to recover the correct scaling with temperature close to the critical temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' As an example the results reported  in [146] are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' It is clearly observed that the surface tensions agree very well with Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 716, provided  that W ≪ Re.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For larger interface thickness curvature-dependence come into play which will be discussed in the next  section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Meanfield scaling laws: Tolman length  In subsection 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8, to measure surface tension using Laplace’s law we made use of the equimolar dividing surface  of radius Re, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 701.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Further discussion on the non-uniqueness of the choice of dividing surface and curvature-  dependence of surface tension is in order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Following [196], the free energy of a drop or bubble separated from the  surrounding vapour or liquid by a dividing circle (D = 2) or sphere (D = 3) of length or area Σ is, A = U − TS + σΣ,  where U and S are the internal energy and entropy of bulk phases while the last term is the adsorbance of free energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  The equilibrium condition requires vanishing of the variation δA;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' for the isothermal case we have,  δA = −Pl,vδVl,v − Pv,lδVv,l + Σδσ + σδΣ = 0,  (717)  113  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='001  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='050.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  10-4  10-3  10-2  10-1  Figure 45: Temperature dependence of the surface tension coefficient near the critical point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Dashed grey line: Theory, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  716;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Red circles:  Simulation results using Laplace’s law;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Blue squares: surface tension coefficient computed for a flat interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Results are taken from [146].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  where Pl,v and Pv,l are the pressures inside and outside the liquid drop or vapour bubble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Using δVl,v = −δVv,l =  2(D − 1)πRD−1δR and δΣ = 2(D − 1)2πRD−2δR leads to a generalized Laplace law,  ∆P = (D − 1)σ(R)  R  + dσ(R)  dR .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (718)  The derivative of surface tension dσ/dR is termed a notional derivative by some authors [219] in order to stress that it  refers to arbitrariness of the dividing surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Apart from the equimolar surface (701), the surface of tension is another  possible choice to lift the ambiguity of the dividing surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The notional derivative vanishes at the surface of tension,  dσ  dR  �����R=Rs  = 0,  (719)  thereby reducing the generalized Laplace law (718) to a standard form,  ∆P = (D − 1)σ(Rs)  Rs  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (720)  Integrating Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 718 from Rs to R, and eliminating ∆P using (720), one obtains analytic expression for the notional  surface tension σ(R) relative to its minimum σs at the surface of tension Rs,  σ(R)  σs  = 1  D  �Rs  R  �D−1  + D − 1  D  � R  Rs  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (721)  While the notional derivative dσ(R)/dR vanishes at the surface of tension, the same does not hold for the surface  tension at the surface of tension, dσs/dRs � 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In other words, surface tension σs depends on the curvature of the  surface of tension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In [220] the authors characterized the curvature-dependence of surface tension by the Tolman  length: For sufficiently large Rs, the leading-order curvature-dependence of the surface tension may be written [220],  σ(Rs) ≈ σ0  �  1 ∓ (D − 1)δT  Rs  �  ,  (722)  where δT is the Tolman length and σ0 is the flat interface surface tension coefficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Here, the negative (positive) sign  corresponds to drops (bubbles), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  While the leading-order Tolman correction Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 722 improves agreement with data at moderate Rs, it is not suffi-  cient for smaller drops and bubbles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Higher-order terms in the inverse powers of Rs, important for droplets or bubbles  of small radius, are neglected by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 722 and were addressed by [221]:  σ = σ0 ∓ σ0  (D − 1)δT  Rs  + k(D − 1)2  2R2s  +  ¯k(D − 2)  R2s  + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' ,  (723)  114  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='06  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8  1  10-3  drops  bubbles  Figure 46: Pressure difference scaling with surface of tension radius Rs for liquid drops and vapour bubbles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Symbol: Simulation data for van der  Waals equation of state with a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='18 and b = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='095.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Black line: Laplace law with σ = σ0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Blue lines: Best fit with Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 722 used to compute  Tolman length δT ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Red lines: Best fit with the second-order Helfrich expansion Eq (723).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Plot reproduced from [146].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  where k and ¯k are the bending and Gaussian rigidities;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' note that the latter vanishes for D = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  The curvature-dependence of surface tension and Tolman length have also been discussed in a limited number of  articles using the lattice Boltzmann method [218, 146].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The results of a systematic study of the Laplace law for  droplets of different sizes as reported in [146] are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Comparing the leading-order Tolman model  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 722 with the simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The values of Rs are plotted against the pressure difference for different drop and bubble  sizes in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' It is clear that, for smaller drops and bubbles, the pressure difference deviates from the Laplace law  with constant σs = σ0, indicating a curvature-dependent surface tension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Fitting the data points with Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 722, the  Tolman length can be extracted from the simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 46 δT = 9δr for both drops and bubbles, at the reduced  temperature Tr = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Taking the second-order term of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 723 into account, the best fit in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 46 results in bending  rigidity k = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='049 × 105σ0δr2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Another consequence of the second-gradient thermodynamics, as shown by [219], is that the Tolman length scales  with the reduced temperature as,  δT ∝ (1 − Tr)−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (724)  The scaling was also extracted in for the pseudo-potential and free energy models close to critical point [218, 146].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  There the Tolman length was extracted in the limit of a flat interface for different temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The Tolman length in  the limit of flat interface is the distance between the surface of tension and the equimolar surface [219, 217],  δT = Xe − Xs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (725)  An example from the simulation is presented in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In this case, location of the surface of tension Xs can be found  as the normalized first-order moment of the normal stress difference [222],  Xs =  � ∞  −∞ x(Pxx − Pyy)dx  � ∞  −∞(Pxx − Pyy)dx  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (726)  With the dividing surface as a vertical straight line at X in two dimensions, the mass adsorbance Γ(X) is defined as  (see example in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 47),  Γ(X) =  � ∞  −∞  �ρ(x) − ρv − (ρl − ρv)H(x − X)� dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (727)  Similar to the case of cylindrical symmetry considered in subsection 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8 the equimolar surface is found by annihi-  lating the mass adsorbance, Γ(Xe) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The results as reported in [146] are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  After a detailed overview of different classes of models, shortcomings and numerical artifacts, solutions proposed  in the literature and a comprehensive assessment of interface properties the next section will discuss some of the  applications of non-ideal lattice Boltzmann models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  115  0  50  100  150  200  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  Figure 47: Example of mass adsorbance for a flat interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Black continuous line: density profile at Tr = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='98;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Red dashed line: Sharp interface  profile with the dividing surface at X/δr=70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Grey area represents the mass adsorbance Γ(X) (727).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Plot reproduced from [146].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  30  40  50  60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  10-3  10-2  10-1  100  101  102  Figure 48: (Left) Temperature dependence of Tolman length δT .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Results from the flat interface simulation for van der Waals fluid are shown with  blue squares while the grey dashed line represents theoretical scaling (724).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (Right) Surface of tension, equimolar surface and Tolman length for  flat interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Continuous black line: Density profile at Tr = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='98;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Red dashed line: Sharp approximation with the equimolar surface as the dividing  surface;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Blue dotted line: Sharp approximation with the surface of tension as the dividing surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Distance between the surface of tension and the  equimolar surface: Tolman length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In all simulations a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='18 and b = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='095.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Plot reproduced from [146].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  116  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Illustration of applications  Different from alternatives such as phase-field solvers or the color-gradient approach, non-ideal fluid LBMs have  been mostly used for cases involving low or moderate Weber numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Below a few area where such solvers are  widely in use are listed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Drop interaction with solid substrates  One area of application where non-ideal fluid LBM has been widely and successfully applied is studies involving  drop interaction with flat and complex solid substrates at low and moderate Weber numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' We provide an overview  of recent research in that area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Impact on non-wetting surfaces  Dynamics of drops impacting flat non-wetting surfaces is a topic that has attracted a lot of attention in recent  years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Extensive studies have shown that the contact time on such surfaces is independent of the Weber number,  We = ρlD0U2  0/σ, and only scales with the inertio-capillary time, τi =  �  ρlD3  0/8σ, meaning for a given initial diam-  eter D0 the contact time is unaffected by impact velocity [223, 224, 225, 226] prompting researchers to proposed a  simplistic description of its dynamic via an analogy with a single harmonic oscillator of characteristic mass ρlD3  0/8  and spring constant σ [227].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Although different from the case of an oscillating drop studied by Rayleigh, in the sense  of asymmetry of the drop dynamic due to the presence of the wall, the scaling of the contact time agrees with his  predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The coefficient in front of the scaling law is however observed to be different;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Rayleigh’s analysis led to a  coefficient of π/  √  2 ≈ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2 while experimental studies of drops impacting non-wetting surfaces led to 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2 [226].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  A number of LBM-based studies have looked into the Weber-independence of contact time on non-wetting surfaces,  see for instance [156, 146], and showed that non-ideal fluid LBMs correctly capture both the scaling and coefficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  An example in shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  10  20  30  We  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  tc/ i  Figure 49: Drop contact times on flat non-wetting surface (contact angle θ=165 for different Weber numbers as obtained from simulations and  experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Simulations results are shown with red circular markers while experimental data reported by [223] are illustrated with blue square  markers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The dashed grey line represents the average contact time as obtained from simulations, ¯tc/τi = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This plot is reproduced from [146].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Another aspect of drops impact non-wetting surfaces, widely discussed in the literature is the diameter of the drop  at the maximum spreading state and its dependence on the Weber and Reynolds numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A correlation widely used  and accepted in the literature in the limit of vanishing Ohnesorge numbers, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Oh =  √  We/Re, is the one proposed in  [228]: Dmax  D0  ∝ We1/4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Other correlations taking into account viscous dissipation for non-vanishing Oh numbers have  also been proposed in the literature, for instance [229]:  ��Dmax  D0  �  −  �Dmax,0  D0  �  Re−1/5 =  We1/2  A + We1/2 ,  (728)  where Dmax,0 is the maximum spreading diameter in the limit of zero impact velocity and A is constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Both these  correlations have been matched with LBM simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Results are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  117  Figure 50: (Left) Reduced maximum diameter of drop as a function of the Weber number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Circles show LBM simulations and squares experimental  data from [228].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The solid line corresponds to the scaling ∝ We1/4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This plot is reproduced from [230].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (Right) Rescaled maximum spreading ratio  for viscous drops as a function of Weber number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Circles: LBM simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' solid line: scaling of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 728.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This plot is reproduced from [231].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  D0  Rb  h  RB  w  Figure 51: Illustration of the geometry of tapered posts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Image is reproduced from [146].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Pancake bouncing  To further reduce the drop contact times, a number of different strategies have been devised during the past  decades.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Recently, [232] proposed to use macroscopic structures, in the form of tapered posts shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 51,  to reduce the contact time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' It has been shown that above a certain threshold Weber number these structures can  decrease the contact time by approximately 75 percent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This mechanism is also known as pancake bouncing, due to  the pancake-like shape of the drop at take off.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The dynamics of drops impacting these tapered posts both below and  above the said-threshold is illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The first numerical study of this phenomenon was conducted using  the LBM free energy method in [233] in 2-D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Later a detailed numerical study of pancake bouncing using LBM was  presented in [156], for density ratio of the order of 102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Similar studies were also conducted in [146] for larger density  ratios, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' All simulations were shown recover the drop contact time and capture the threshold Weber number  were impact transitions in pancake mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The results are illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Other approaches to reduce contact time via macro-structures  As another simple approach to further reduce the contact time of drops on non-wetting surfaces via the introduction  of a singular defect on the substrate in the form of small glass bead of a radius of 200 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For a drop impact the bead  at its center and subsequently breaking at it center right after maximum spreading this approach was shown to reduce  the contact time by a factor of two [234].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The breaking of the lamella at its center after maximum spreading causes  retraction both from the edges and the center eventually leading to a ring-like shape at the time of take off.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The  reduced take-off time is therefor related to a reduction in retraction time which is a consequence of the reduction of  the corresponding characteristic size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The formation of two so-called blobs and corresponding characteristic size are  illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The effect of this characteristic size on contact time was extracted via systematic experimental  runs and numerical simulations with a free energy LBM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 54 simulation results were in very good  agreement with experimental observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Non-ideal LBM solvers have been used for a wide variety of studies  involving drop interaction with solids at low and moderate Weber numbers, such as impact on curved surfaces [235],  118  5  口  Clanet Experiment  0  ELBM  4  1  1/5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8  We1/2 / (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content="6+We1/2)  Re'  3  0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  EMRT-MPLBM  >1/2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  %  max  8  D  2  xew  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  101  102  Webernumber  10°  10  10  We0 ms  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5 ms  3 ms  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4 ms  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6 ms  0 ms  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4 ms  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='9 ms  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8 ms  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5 ms  Figure 52: Drop impacting tapered posts at different Weber numbers (first and second rows) We=28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2 with pancake bouncing and (third and  fourth rows) We=14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The first and third rows are experiments from [232] while the second and fourth rows are from simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This image is  reproduced from [146].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  10  20  30  40  We  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  1  Q  10  20  30  40  We  0  1  2  3  tc/ i  Figure 53: (left) Drop contact times and (right) pancake quality at rebound on tapered posts for different Weber numbers as obtained from simula-  tions and experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Simulations results are shown with red circular markers while experimental data reported by [232] are illustrated with blue  square markers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This plot is reproduced from [146].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  119  一Figure 54: (a) Sketch of water droplet impacting a point-like defect at maximum spreading.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (c) Water droplet (R = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3 mm) impacting at V = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3  m/s a bead with diameter r = 200 µm, with off-centering x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='7 mm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (d) Contact time normalized by inertio-capillary time as a function of the  normalized blob size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Dots are experimental data and red circles simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' These plots are reproduced from [234].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  mesh arrays [236, 237] or perforated flat substrates [238].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Flow in porous media  Another area where non-ideal LBM solvers have been widely and successfully applied is flow in porous media.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  A wide variety of industrial processes and physics involve non-ideal fluids (or multi-phase flows) in porous media.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  The first attempt at modeling the flow of multiple phases in a realistic porous geometry was documented in [198]  where the authors modeled both wetting and non-wetting liquid invasion of a porous geometry extracted from high  resolution microtomography images of a Fontainebleau sandstone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Since then non-ideal LBM’s have been extended  many more complexe configurations and physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Here we briefly discuss two main areas, namely water transport in  proton exchange membrane fuel cells and isothermal drying  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Water transport in proton exchange membrane fuel cells  Proton-exchange membrane fuel cells are a promising class of fuel cells mainly developed for transport applica-  tions and first introduced in the 60’s by General Electrics [239].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' While most major manufacturers are close to the  commercialization stage, water management remains one of the outstanding issues limiting efficiency and durability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Issues related to water are encountered in the gas diffusion layer and reactant channel [240].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A number of studies with  LBM on liquid water transport mechanisms in both the gas diffusion layer and reactant channel have been conducted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  In [241] the authors studied the effect of capillary pressure and contact angle on the water invasion dynamics into  Toray-090 gas diffusion layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The studied gas diffusion layers were made up of carbon fibers coated with Polyte-  trafluoroethylene (PTFE) for enhanced hydrophobicity with different weight percentages of PTFE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In their studies the  Figure 55: Snapshots of time evolution of liquid water transport inside GDL with 10 percent PTFE content.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Image is reproduced from [241].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  authors observed that saturation levels within the gas diffusion layer slowly increased with capillary pressure until a  threshold were it grows and reaches rapidly full saturation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The threshold level was shown to change as function of  the apparent contact angle controlled by the weight percentage of PTFE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The evolution of liquid water front within  the gas diffusion layer over time is illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Another aspect of water management studied in [242] is the transport dynamics of water droplets in the gas channel  bound by the gas diffusion layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Usually due to the roughness of the gas diffusion layer droplets moving in the gas  120  b  d  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  2R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5channel can be subject to pining which can block the channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The authors conducted systematic studies on the effect  of inertia, considering both magnitude and direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' As expected it was observed that smaller contact angles reduced  Figure 56: Image reproduced from [242].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  pining effects and penetration into the gas diffusion layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Inertia effect with a non-zero component normal to the  gas diffusion layer surface was also observe to increase chances of penetration into the gas diffusion layer and even  break-up of the drop as illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Isothermal drying  Drying in complex porous media is encountered in many set-ups of interest in science and engineering, such as  food preservation, coating or volatile hydrocarbons recovery from reservoirs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Traditional description of the drying  process at the continuum scale rely on phenomenological closures that come with many limitations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' More detailed  descriptions like the Pore Network models have, to some extent, helped to refine the continuum models however they  have shortcomings in using the true geometry at the pore scale, and in considering capillary instabilities and film-  effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' That is why in the past 30 years, pore-scale studies of drying in porous media have received more attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  On par with global trend, this topic has also been widely considered and studied with the LBM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For instance, in [243]  and [214, 244] the authors investigated the effect of contact angle hysteresis on isothermal drying dynamics in porous  media and proposed a hybrid solver coupling pore-scale lattice Boltzmann simulations to the pore network model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  An illustration of the simulation conducted in [214] is given in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In [245] the authors coupled the free energy  Figure 57: Sequential liquid configurations during drying of a bi-modal porous system obtained with LBM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Image reproduced from [214].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  model to a smoothed-profile LBM to model isothermal drying of colloidal suspensions and studied the aggregation of  colloidal particles with different wetabilities under isothermal drying.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The simulations are illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The  121  180  (d)  150  Re=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='08  120  △t=0  At=6000  N 90  60  30  0Figure 58: Snapshots of particle arrangement during the drying of a colloidal suspension containing 60 particles with contact angle 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Image  reproduced from [245].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  authors observed that particles with higher wettabilities aggregated more slowly, but more significantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' They justified  the observations by capillary interactions such as capillary flotation and immersion forces between the particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  As shown in this section, the non-ideal LBMs have been used for a wide variety of applications covering drop  interaction with different substrates, liquid invasion of porous media with a special interest for fuel cells and drying  in porous geometries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The specific numerical properties of this class of model have made them quite efficient and at-  tractive for flows involving interaction with complex solids, liquid-liquid interactions such as coalescence and binary  collisions, all in the low and mid-Weber and Reynolds regimes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Considerable effort is still being put on extending  such approaches to larger Weber number configurations such as droplet splashing or primary and secondary break-up  in liquid jets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' At this point in time, to the authors knowledge, no notable success has been reported in that area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Non-ideal fluid models in LBM are not limited to single component isothermal flow configurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Considerable  effort has been put in recent years to extend these models to thermal and multi-component flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Some of these  extensions will be briefly discussed in the next section  122  (bl) t*= 0  (b2) t* = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  (b3) t* = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8  (b4) t* = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Extension to more complex physics  The non-ideal LBM, while initially developed for isothermal single-component fluids, have been extended to  thermal and multi-component flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Below we present a brief overview of some of the developements in that area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Thermal flows with evaporation  Extension of non-ideal LBMs to non-isothermal flows can be categorized as pertaining to one of two main classes:  (a) Hybrid and passive scalar-based approaches and (b) kinetic methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The hybrid and passive scalar approaches  The form of the energy balance equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Two main routes have been taken to arrive at the final form of the en-  ergy/temperature balance equation, namely from the entropy or the energy balance equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In the hybrid approach  the LBM solver for the density and momentum fields is coupled to classical, either finite differences or finite volumes,  solvers for the following evolution equation for the temperature field [246]:  ∂tT + u · ∇T + T  ρcv  ∂P  ∂T ∇ · u − 1  ρcv  ∇ · λ∇T = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (729)  Solver for the energy balance equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Once the target form of the energy balance equation has been determined  an additional solver has to be added/coupled to the flow solver.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' There are typically two possible routes: (a) LBM  advection-diffusion type solvers or (b) classical finite differences or finite volumes solvers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  In the first approach, one relies on an additional distribution function gi to solve an advection-diffusion type partial  differential equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In its simplest form the advection-diffusion LBM with [247]:  �  i  gi = T,  (730)  as the conserved moment leads to a PDE of the following form:  ∂tT + ∇ · uT − ∇ · D∇T = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (731)  This form of the balance equation poses a number of issues;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The advection term u · ∇T is only valid in the limit of a  divergence-free velocity field, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' T∇ · u, which given that the compressible fluid equations are targeted does not hold  in general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Furthermore, the diffusion term ∇ · D∇T with D =  λ  ρcv only holds for ρ = const and cp = const.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Finally  the latent heat release term in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' () is missing here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  To circumvent these shortcomings different authors have proposed corrections to be included as source terms in the  LBM equation [248, 249, 250, 251].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For instance, noting:  u · ∇T − ∇ · uT = −T∇ · u,  (732)  and,  1  ρcv  ∇ · λ∇T − ∇ · λ  ρcv  ∇T = −λ∇T · ∇ 1  ρcv  ,  (733)  a source term of the following form must be included:  S = T  �  1 − 1  ρcv  ∂P  ∂T  �  ∇ · u + λ∇T · ∇ 1  ρcv  ,  (734)  leading to the following LBM equation:  ¯gi(r + ciδt, t + δt) − ¯gi(r, t) = 1  ¯τ  �  geq  i (r, t) − ¯gi(r, t)  �  +  �  1 − 1  2¯τ  �  wiS,  (735)  with:  T =  �  i  ¯gi + δt  2 S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (736)  123  An alternative to the above-described approach, discussed in [252] is to set:  �  i  gi = ρcvT,  (737)  with  geq  i = cvT f eq  i ,  (738)  which in combination with a correction term of the form:  S = cvT  c2s  ci · F,  (739)  where F is the non-local force in the evolution equation of the distribution function fi results in the following conser-  vative form of the energy balance equation:  ∂tρcvT + ∇ · ρcvTu − ∇ · λ∇T = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (740)  Comparing this equation to the target balance law for non-ideal fluids one observes that the latent heat release due to  phase change is missing here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Different variants of the passive scalar approach have been used in a wide number of publications targeting thermal  non-ideal fluid flows [248, 249, 251].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  An alternative to this approach is to use classical discretization methods such as finite differences or finite volumes  to solve the energy balance equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' One of the first documented attempts at modeling thermal non-ideal fluid flows  using such a hybrid model was reported in [192].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In recent years most authors have opted for a second-order central  isotropic finite differences discretization in space, see [253, 254, 255, 256] for more detail, and second-order Runge-  Kutta scheme for time-stepping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The hybrid scheme is widely used in the literature for a variety of configurations and  physics, see for instance [257, 258, 259, 260, 261].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The kinetic route  Introduction of generic framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' We will first introduce elements of a generic kinetic framework for non-ideal  fluids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This model is introduced for the first time here and will be detailed in upcoming publications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The kinetic  framework of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 573 introduced for iso-thermal flows can be readily extended to compressible flows with energy  balance by adding energy to the list of conserved variable in the definition of the projector onto the local equilibrium  manifold:  KJ = ∂f eq  ∂Πρ  �  JdvdI + ∂f eq  ∂Πu  �  vJdvdI + ∂f eq  ∂ΠE  � �  v2 + I2�  JdvdI,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (741)  with  Πρ = ρ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Πu = ρu,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' ΠE = ρ  �  u2 + (D + δ)RT  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (742)  where to allow for variable specific heat ratios we have introduced the space of additional non-translational degrees  of freedom I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The equilibrium distribution function is modified accordingly as:  f eq =  ρ  (2πRT)(D+δ)/2 exp  �  −(v − u)2 + I2  2RT  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (743)  Here δ is the the number of non-translational degrees of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Application of this projector to the collision term  results in:  Jnloc =  �1  ρ  ∂f eq  ∂u −  2  (D + δ)ρu∂f eq  ∂RT  �  Fnloc +  1  ρ(D + δ)  ∂f eq  ∂RT Qnloc  (744)  where the force Fnloc reads,  Fnloc = −  � � �  ∇V (|r − r1|) f2(r, v, r1, v1, t)dv1dr1dv,  (745)  124  where  f2(r, v, r1, v1, t) =  � �  f2(r, v, I, r1, v1, I1, t)dI1dI,  (746)  and  Qnloc = −2  � � �  ∇V (|r − r1|) · v f2(r, v, r1, v1, t)dv1dr1dv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (747)  Collecting the BGK approximation together with the nonlocal contribution, a generic model for the BBGKY equation  may be written,  ∂t f + v · ∇ f = −1  τ  �f − f eq� + F + Q,  (748)  with:  F =  �1  ρ  ∂f eq  ∂u −  2  ρ(D + δ)u∂f eq  ∂RT  �  Fnloc  (749)  and:  Q =  1  ρ(D + δ)  ∂f eq  ∂RT Qnloc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (750)  The hard-sphere potential contribution is readily shown to lead to:  Fnloc =  �  vJ(1)  E dv = −∇bρ2χRT,  (751)  and  Qnloc = −2∇bρ2χRT · u,  (752)  while the meanfield Vlasov long-range interaction leads to:  JV = −∇  �  2aρ(r) + κ∇2ρ(r)  �  ∂  ∂v f(r, v).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (753)  Upon application of the projector operator and addition of the Enskog contribution one gets:  Fnloc = −∇bρ2χRT + ρ∇  �  2aρ + κ∇2ρ  �  ,  (754)  and  Qnloc = −2∇bρ2χRT · u + 2ρu · ∇  �  2aρ + κ∇2ρ  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (755)  Upon application of a multi-scale perturbation analysis the generic model can be shown to recover the following  system of equation up to NS level:  ∂tρ + ∇ · ρu + O(ϵ3) = 0,  (756)  ∂tρu + ∇ · ρu ⊗ u + ∇ · ρRT  �  1 + bχρ − aρ  RT  �  I − ρκ∇∇2ρ + ∇ · TNS + O(ϵ3) = 0  (757)  ∂tE + ∇ · Eu + ∇ · ρRT(1 + bχρ)u − u · ∇aρ2 − κρu · ∇∇2ρ + ∇ · u · TNS − ∇ · λ∇T + O(ϵ3) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (758)  Defining the total energy Et as the sum of the internal energy E and potential energy from non-local interaction  potentials Ev the following balance equation for total energy is obtained:  ∂tEt + ∇ · Etu + ∇ · ρRT  �  1 + bχρ − aρ  RT −  κ  2RT ∇2ρ  �  u −  �  κρ∇∇ρ + κ  2ρ∇2ρ  �  : ∇u  + TNS : ∇u − ∇ · λ∇T + O(ϵ3) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (759)  In principle, as for the iso-thermal version introduced in [146], different equations of state, interactions beyond the  meanfield approximation and choices of pressure partition can be realized with this generic framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For instance,  introducing the full thermodynamic pressure into the equilibrium distribution function one readily recovers the models  in [189, 190, 191].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  125  The Enkog-Vlasov-based model of He & Doolen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' One of the first attempts at proposing a kinetically motivated LBM  model for non-ideal fluids was documented in [149].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Following the original Enskog-Vlasov formalism the collision  term is replaced with local and non-local contributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Additionally the local contributions is replaced with a BGK-  type approximation leading to the following discrete evolution equation:  ¯fi(r + ciδt, t + δt) − ¯fi(r, t) = −χ  ¯τ  � ¯fi(r, t) − ¯f eq  i (r, t)  �  + δt(1 − δt  2¯τ)Fi ¯f eq  i (r, t),  (760)  with,  Fi = (ci − u) · (F − ∇V)  RT  − bρχ  �  (ci − u) ·  �  ∇ ln ρ2χT + 3  5  �(ci − u)2  2RT  − 5  2  �  ∇ ln T  �  + 2  5  �(ci − u) ⊗ (ci − u)  RT  : ∇u +  �(ci − u)2  2RT  − 5  2  �  ∇ · u  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (761)  The discrete equilibrium distribution function was obtained as a second-order polynomial expansion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' While in [149]  the authors only reported the theory and derivation of the model, it was later reprised in [262] and used for 1-D and  2-D simulations using a MRT realization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Multiple components  Another area of active research to extend the range of application of non-ideal LBMs is the introduction of multiple  components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' While most of the application-oriented litterature in that area relies on the multi-component realization  of the Shan-Chen model [263], a few different attempts at other models have also been reported.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Here we will briefly  discuss some of the multi-component models developed within that context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ternary free energy model of W¨ohrwag et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  In an attempt to model ternary systems W¨ohrwag et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' [264] introduced a free energy functional allowing three  distinct minima, corresponding to one gas and two liquid components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The thermodynamics of the system is governed  by two order parameters, namely density, ρ, and a phase field, φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' As for the van der Waals fluid the total free energy  density consists of two parts, bulk A and interfacial;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The bulk free energy is defined as:  A = λ1  2 (AEoS(ρ) − A0) + λ2  2 C2  l1(1 − Cl1)2 + λ3  2 C2  l2(1 − Cl2)2,  (762)  where AEoS(ρ) can be derived from integrating the equation of state, P = ρ(∂AEoS/∂ρ) − AEoS, with coexisting  liquid-gas densities at ρl and ρg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The two last terms in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  762 have the form of double well potentials with Cl1  and Cl2 the relative concentrations of the two liquid components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Each term has two minima at C# = 0 (component  absent) and C# = 1 (present).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The relative concentration of the gas phase is defined as Cg = (ρ − ρl)/(ρg − ρl),  which is 0 for ρ = ρl and 1 for ρ = ρg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The relative concentrations are related to the density and phase field through  Cl1 = 1  2  �  1 + φ/χ − (ρ − ρl)/(ρg − ρl)  �  and Cl2 = 1  2  �  1 − φ/χ − (ρ − ρl)/(ρg − ρl)  �  , with χ a constant scaling parameter  for φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This form of the bulk free energy leads to three minima located at (ρg, 0), (ρl, +χ) and (ρl, −χ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The bulk free  energy map is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For the interfacial free energy density, the authors used  AInter = κ1  2 (∇ρ)2 + κ2  2 (∇Cl1)2 + κ3  2 (∇Cl2)2,  (763)  which ca be written as a function of the order parameters ρ and φ,  AInter =  �κ1  2 +  κ2 + κ3  8(ρg − ρl)2  �  (∇ρ)2 + κ2 + κ3  8χ2  (∇φ)2 +  κ3 − κ2  4χ(ρg − ρl)(∇ρ · ∇φ),  (764)  which as expected includes three contributions, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' density gradient, phase field gradient and mixed density-phase  field gradient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This new free energy functional only affects the NS equations through the total pressure tensor:  ∇ · Ptot = ρ∇µρ + φ∇µφ,  (765)  126  Figure 59: Contour plot of the bulk free energy density of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 762 as a function of two order parameters, ρ and φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This plot is reproduced from  [264].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  with the chemical potentials defined as:  µk = δ  δk  �  A + AInterdV|T,k′,  (766)  with k ∈ {ρ, φ} and k′ ∈ {φ, ρ}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The corresponding system of balance equations was solved using two distribution  functions;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' One for the density and momentum fields and one for the balance of the phase field, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Cahn-Hiliard  equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Using this model the authors successfully modeled collision of drops of immiscible liquids with density  ratios of the order of 103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' An example is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Figure 60: Collision between two immiscible droplets (water and diesel oil).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (a) experiments from [265].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (b),(c) simulation results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This figure is  reproduced from [264].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Mixtures with multi-component van der Waals equation of state  In [266], Ridl & Wagner proposed a multi-component extension to the van der Waals second-gradient fluid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Start-  ing with the single-component free energy:  AvdW = ρRT ln  �  ρ  1 − bρ  �  − aρ2 + κ  2|∇ρ|2,  (767)  they proposed an N-component van der Waals free energy defined as [266]:  AvdW−MC =  N  �  k=1  ρkRT ln  ������  ρk  1 − �N  k′=1 bk′ρk′  ������ −  N  �  k′=1  �  akk′ρkρk′ − κkk′  2 ∇ρk · ∇ρk′  �  ,  (768)  with the total bulk thermodynamic pressure obtained as:  P =  N  �  k=1  ρkRT  1 − �N  k′=1 bk′ρk′ −  N  �  k′=1  akk′ρkρk′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (769)  127  d  p  X  X+a-i  (a-i)  (a-ii)  (a-iv)  a-v  (b-i)  (b-i)  (b-ili)  (b-iv)  (b-v)  (c-i)  (c-ii)  (c-ili)  (c-iv)  (c-V)To model the dynamics of the corresponding system they proposed a set of N discrete distribution functions,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' one for  each component,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' evolving as [266,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 267]:  fik(r + ciδt,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' t + δt) − fik(r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' t) = δt  ¯τ  �  f eq  ik (r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' t) − fik(r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' t)  �  − Fik,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (770)  where the BGK collision operator accounts for the considered component’s ideal contributions while the term Fik  takes into consideration non-ideal effects and interaction with other components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The densities and velocities of each  individual component are obtained as zeroth- and first-order moments of the corresponding distribution functions  while the mixture density and velocity are obtained as the sum of the density of all components and the mass-averaged  velocities, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The term Fik contributes at first order,  �  i  ciFik = Fk,  (771)  where the force Fk has two contributions: one from the gradient of chemical potential Fµk and one friction between  different components Ffk modeling cross-diffusion effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The chemical potential gradient contribution is readily  obtained as difference between the single-component ideal pressure and multi-component non-ideal one while Ffk is  defined as  Ffk = −  N  �  k′=1  λkk′ ρkρk′  ρk + ρk′ (uk′ − uk) ,  (772)  where λkk′ are related to binary diffusion coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' It is readily demonstrated that under the assumption of symmetry  of the diffusion coefficients tensor, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' λkk′ − λk′k the contribution of cross-diffusion to total momentum is zero:  N  �  k=1  Ffk = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (773)  The authors showed that in the hydrodynamic limit under the assumption of λkk′ = λ, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' all components have the same  Lewis number, one recovers the N-component Cahn-Hiliard equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' It should also be noted that similar models  for two-component non-ideal mixture were also proposed in [268, 269] where the models were shown to recover  non-ideal effects and the Fick diffusion, equivalent to the Maxwell-Stefan system for binary isothermal mixtures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The multi-component pseudo-potential method  While initially developed for non-ideal fluids, extension of the model to multiple components were introduced in  [263].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For a system with N components, the interaction force on component k is given by:  Fk = −ψk(r)  N  �  k′=1  Gkk′ψk′(r + ciδt)ci,  (774)  where Gkk′ sets the interaction strength between components k and k′ and forms a symmetrical tensor, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Gkk′ = Gk′k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Interestingly enough, upon application of a Taylor expansion the force is:  Fk = −ψk  N  �  k′=1  Gkk′∇ψk′ + Gkk′  3 ∇∆ψk′ + O(∇5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (775)  As for the single-component non-ideal model, it leads to fixed surface tension coefficients and terms that are function  of the pseudo-potential ψk instead of density ρk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Introduction of independent capillary coefficients can be readily intro-  duced following the approaches used for the single-component version of the model, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' multiple-range interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  128  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Conclusion  Application of the LBM to non-ideal fluids, and multi-phase flows in general, has been the focus of intense work  from the early days of that method with first publications appearing in the early 90s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This rapid extension and growth  in popularity is, in part, due to the simple transition from ideal to non-ideal fluids with interfaces in the context of  LBM, illustrated best by the simplicity of the original pseudo-potential model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Contrary to diffuse-interface models like the Allen-Cahn equation, the non-ideal LBM models come with interfacial  properties, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' surface tension, interface thickness, Tolman length etc, linked to bulk physical properties of the  considered fluid and follow the van der Waals thermodynamics of interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The interface properties are therefore,  in principle, dictated by the thermodynamics of the considered fluid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This was illustrated via the example of a N2  liquid/vapor interface showing a thickness of the order of 10−7 m, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 20, limiting the grid-size and preventing  simulations at larger realistic scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' As a result they can be perceived as models able to cover a wider range of  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='parameters as compared to classical sharp and/or diffuse interface methods: In the limit of thick interfaces where its  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='width is comparable to the flow characteristic size they recover the van der Waals fluid thermodynamics (or a modified  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='form of it in the case of the pseudo-potential method) and the Korteweg stress tensor at the macroscopic level and can  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='be derived from the Enskog-Vlasov approximation at the level of the kinetic theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In the limit of thin interfaces, the  extreme computational cost imposed by the physical thickness of the interface can be considerably reduced by relying  on the principle of corresponding states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Non-ideal LBM-based solvers are also subject to a number of issues such as stability resulting in limited range of  accessible non-dimensional viscosities, thermodynamic inconsistency leading mismatch in coexistences densities at  smaller temperatures, spurious currents appearing at interfaces as a result of the non-isotropy of the discrete system etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  A wide variety of solution to eliminate or reduced the effect of these issues have been proposed allowing simulation  with larger density ratios, Weber and Reynolds number to be conducted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' With the most recent development around  these approaches they have become quite competitive and accurate tools for simulations in the lower Weber number  regimes in areas such as microfluidics, drop interaction with solid surfaces etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For much larger Weber numbers and  applications such as multiphase jets with primary and secondary break-up further improvement is needed, especially  to extend the range of accessible surface tensions to lower values at given interface thicknesses and acceptable levels  of spurious currents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Given the kinetic roots of some of the models in that class of solvers, extension of the models  to higher order physics beyond the meanfield approximation would also be a possible area of developmenet in the  feature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Acknowledgement  This work was supported by European Research Council (ERC) Advanced Grant no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 834763-PonD (S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='H and  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Computational resources at the Swiss National Super Computing Center CSCS were provided under grant no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  s1066.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Declaration of interests  The authors report no conflict of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Hermite expansion  Single variable Hermite polynomials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The single variable Hermite polynomial Hn of order n of a variable x is  defined as:  Hn(x) = (−1)n  w(x)  dn  dxn w(x),  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1)  where the normalized function w(x) is defined as:  w(x) =  1  √  2π  e− x2  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2)  129  Based on this definition, the first few polynomials can be computed as:  H0 = 1,  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3a)  H1 = x,  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3b)  H2 = x2 − 1,  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3c)  H3 = x3 − 3x,  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3d)  H4 = x4 − 6x2 + 3,  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3e)  H5 = x5 − 10x3 + 15x,  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3f)  H6 = x6 − 15x4 + 45x2 − 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3g)  These polynomials are mutually orthogonal with respect to the weight function, w(x), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' :  � +∞  −∞  Hm(x)w(x)Hn(x)dx = n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='δmn,  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4)  where δmn is the Kronecker delta function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Furthermore, they form a complete orthogonal basis of the Hilbert space  of functions f(x) satisfying:  � +∞  −∞  | f(x)|2w(x)dx < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5)  As such, one can express the function f(x) as:  f(x) =  ∞  �  n=0  1  n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' anHn(x),  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6)  where an is the order n Hermite coefficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Multiplying both sides by Hm(x)w(x) and integrating over x:  � +∞  −∞  Hm(x)w(x) f(x)dx =  ∞  �  n=0  1  n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' an  � +∞  −∞  Hm(x)w(x)Hndx,  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='7)  and using the mutual orthogonality of Hermite polynomials, we get an expression for the Hermite coefficients as:  am =  � +∞  −∞  Hm(x)w(x)f(x)dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8)  Alternatively, one can also expand the function f(x) as:  f(x) = w(x)  ∞  �  n=0  1  n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' anHn(x),  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='9)  resulting in the following expression for the coefficient a(m):  am =  � +∞  −∞  Hm(x) f(x)dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='10)  To better illustrate this, let us consider the example of the following function:  f(x) = ρ  1  √  2πθ  e− (x−u)2  2θ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='11)  This function can be shown to be square-integrable with respect to the previously-defined weight function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' As such  the corresponding Hermite coefficients can be computed through Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='10:  am =  1  √  2πθ  � +∞  −∞  Hm(x)e− (x−u)2  2θ dx,  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='12)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='130  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='n  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='an  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='Hn(x)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='u  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='x  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='u2 + (θ − 1)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='x2 − 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='u3 + 3u(θ − 1)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='x3 − 3x  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='u4 + 6u2(θ − 1) + 3(θ − 1)2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='x4 − 6x2 + 3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='u5 + 10u3(θ − 1) + 15u(θ − 1)2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='x5 − 10x3 + 15x  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='u6 + 15u4(θ − 1) + 45u2(θ − 1)2 + 15(θ − 1)3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='x6 − 15x4 + 45x2 − 15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='u7 + 21u5(θ − 1) + 105u3(θ − 1)2 + 105u(θ − 1)3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='x7 − 21x5 + 105x3 − 105x  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='u8 + 28u6(θ − 1) + 210u4(θ − 1)2 + 420u2(θ − 1)3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+105(θ − 1)4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='x8 − 28x6 + 210x4 − 420x2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+105  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='u9 + 36u7(θ − 1) + 378u5(θ − 1)2 + 1260u3(θ − 1)3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+945u(θ − 1)4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='x9 − 36x7 + 378x5 − 1260x3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+945x  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='Table A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8: Hermite polynomials and coefficients for the Gaussian distribution function  which using the change of variable η = (x − u)/  √  θ can be re-written as:  am =  1  √  2π  � +∞  −∞  Hm(  √  θη + u)e− η2  2 dη.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='13)  The different order coefficients can be easily evaluated using the following integral:  � +∞  −∞  xke−ax2dx =  ���������  0  k = 2k  ′ + 1  (2k  ′−1)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (2a)k′  � π  a  k = 2k  ′  ,  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='14)  leading to the following expansion:  f(x) =  ∞  �  n=0  ρw(x)  n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  anHn(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='15)  The first few terms are given in Table A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  Multivariate Hermite polynomials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In a D-dimensional space the Hermite polynomial of order n is defined as:  H n (x) = (−1)n  w (x) ∇nw (x) ,  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='16)  where ∇n is the nth order derivative resulting in a tensor of rank n and w (x) is the weight function defined as:  w (x) =  1  2πD/2 e− x2  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='17)  Orthogonality of the multivariate Hermite polynomials results in:  � +∞  −∞  w (x) H i (x) : H j (x) dx =  �������  0  i � j  n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='δi j  i = j ,  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='18)  131  where i and j are abbreviations for the set of indices {i1, i2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' , in} and {j1, j2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' , jn} respectively, and δi j is equal to  unity if i is a permutation of j and zero otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In a 3-D space the first few Hermite polynomials are computed as:  H0 = 1,  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='19a)  Hi = xi,  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='19b)  Hij = xix j − δij,  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='19c)  Hijk = xix jxk −  �  δijxk + δikx j + δ jkxi  �  ,  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='19d)  Hijkl = xixjxkxl −  �  δijxkxl + δikxjxl + δilxjxk + δjkxixl + δ jlxixk + δklxix j  �  +  �  δijδkl + δikδ jl + δilδjk  �  ,  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='19e)  Hijklm = xixjxkxlxm −  �  δlmxixjxk + δkmxix jxl + δklxixjxm + δ jmxixkxl  +δjlxixkxm + δklxixlxm + δimx jxkxl + δilxjxkxm + δikx jxlxm + δi jxkxlxm  �  + xm  �  δijδkl + δikδ jl + δilδjk  �  + xl  �  δi jδkm + δikδ jm + δimδ jk  �  + xk  �  δijδlm + δilδ jm + δimδ jl  �  + x j (δikδlm + δilδkm + δimδkl)  + xi  �  δ jkδlm + δ jlδkm + δ jmδkl  �  ,  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='19f)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='Hijklmn = xixjxkxlxmxn −  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='xixjxkxlδmn + xixjxkxmδln + xix jxkxnδlm  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+xix jxlxmδkn + xixjxlxnδkm + xix jxmxnδlk + xixkxlxmδjn  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='xixkxlxnδ jm + xixkxmxnδ jl + xixlxmxnδ jk + x jxkxlxmδin  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+xjxkxlxnδim + x jxlxmxnδik + x jxkxlxnδim + xjxkxmxnδil + xkxlxmxnδi j  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+ xix j (δklδmn + δkmδln + δknδlm) + xixk  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='δ jlδmn + δ jmδln + δ jnδml  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+ xixl  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='δ jkδmn + δjmδkn + δ jnδmk  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+ xixm  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='δ jkδln + δ jlδkn + δjnδlk  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+ xixn  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='δjkδlm + δjlδkm + δjmδlk  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+ xjxk (δinδlm + δilδnm + δimδln)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+ xjxl (δinδkm + δikδnm + δimδkn) + x jxm (δinδkl + δikδnl + δilδkn)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+ xjxn (δilδkm + δikδlm + δimδkl) + xkxl  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='δmnδi j + δmiδn j + δm jδin  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+ xkxm  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='δijδln + δilδjn + δinδl j  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+ xkxn  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='δmlδi j + δmiδl j + δm jδil  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+ xlxm  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='δijδkn + δikδ jn + δinδk j  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+ xlxn  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='δmkδi j + δmiδk j + δm jδik  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+ xnxm  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='δijδkl + δikδ jl + δilδk j  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+ δi j (δklδmn + δkmδln + δknδml)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+ δik  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='δ jlδmn + δ jmδln + δ jnδml  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+ δil  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='δk jδmn + δkmδ jn + δknδm j  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+ δim  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='δ jlδln + δjkδln + δjnδkl  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+ δin  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='δk jδml + δkmδ jl + δklδm j  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='19g)  As for the single variable case, for a square-integrable function f (x), it can be expressed as:  f (x) = w (x)  ∞  �  n=0  1  n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' an : Hn (x) ,  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='20)  where the Hermite coefficients an are defined as:  an =  � +∞  −∞  f (x) Hn (x) dx,  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='21)  132  resulting in the following coefficients for the multi-variate version of the distribution function of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='11:  a0 = ρ,  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='22a)  ai = ρui,  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='22b)  aij = ρuiu j + ρ (θ − 1) δij,  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='22c)  aijk = ρuiujuk + ρ (θ − 1)  �  δijuk + δikuj + δ jkui  �  ,  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='22d)  aijkl = ρuiu jukul + ρ (θ − 1)  �  δi jukul + δiku jul + δilujuk + δ jkuiul + δ jluiuk + δkluiu j  �  + ρ(θ − 1)2 �  δijδkl + δikδ jl + δilδ jk  �  ,  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='22e)  aijklm = ρuiu jukulum + ρ (θ − 1)  �  δlmuiu juk + δkmuiujul + δkluiujum + δjmuiukul  +δ jluiukum + δkluiulum + δimujukul + δilujukum + δiku julum + δi jukulum  �  + ρ(θ − 1)2 �  um  �  δijδkl + δikδ jl + δilδjk  �  + ul  �  δi jδkm + δikδ jm + δimδjk  �  +uk  �  δijδlm + δilδ jm + δimδ jl  �  + u j (δikδlm + δilδkm + δimδkl)  +ui  �  δjkδlm + δjlδkm + δ jmδkl  ��  ,  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='22f)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aijklmn = ρuiujukulumun + ρ (θ − 1)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='uiu jukulδmn + uiujukumδln + uiujukunδlm  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+uiujulumδkn + uiu julunδkm + uiu jumunδlk + uiukulumδ jn  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='uiukulunδ jm + uiukumunδjl + uiulumunδ jk + ujukulumδin  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+ujukulunδim + u julumunδik + ujukulunδim + ujukumunδil + ukulumunδi j  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+ ρ(θ − 1)2 �  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='uiuj (δklδmn + δkmδln + δknδlm) + uiuk  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='δjlδmn + δjmδln + δjnδml  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+uiul  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='δ jkδmn + δ jmδkn + δjnδmk  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+ uium  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='δ jkδln + δ jlδkn + δ jnδlk  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+uiun  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='δ jkδlm + δ jlδkm + δ jmδlk  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+ ujuk (δinδlm + δilδnm + δimδln)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+ujul (δinδkm + δikδnm + δimδkn) + ujum (δinδkl + δikδnl + δilδkn)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+ujun (δilδkm + δikδlm + δimδkl) + ukul  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='δmnδi j + δmiδn j + δm jδin  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+ukum  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='δijδln + δilδjn + δinδl j  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+ ukun  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='δmlδi j + δmiδl j + δm jδil  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+ulum  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='δijδkn + δikδjn + δinδk j  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+ ulun  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='δmkδi j + δmiδk j + δm jδik  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+unum  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='δijδkl + δikδjl + δilδk j  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='��  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+ ρ(θ − 1)3 �  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='δi j (δklδmn + δkmδln + δknδml)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+δik  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='δ jlδmn + δ jmδln + δ jnδml  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+ δil  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='δk jδmn + δkmδ jn + δknδm j  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+δim  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='δ jlδln + δ jkδln + δjnδkl  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='+ δin  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='δk jδml + δkmδjl + δklδm j  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='��  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='22g)  Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Elements of the von Neumann formalism  Starting with a given set of coupled continuous/discretized PDEs, bound by periodic boundary conditions, defined  as:  L ( fi, r, t) = 0,  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1)  where L is the time evolution operator, the equations have to be linearized in order to use the VN method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' To achieve  this for the LB system of equations one can expand (first-order Taylor-McLaurin expansion) the distribution function  around a reference state fi (¯ρ, ¯u):  fi ≈ ¯fi + f  ′  i ,  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2)  δtΩi( fi) ≈ δtΩi| ¯fi + Ji j f  ′  j,  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3)  133  where Einstein’s notation (summation) over j is used, and for the sake of clarity, ¯fi = fi (¯ρ, ¯u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Obviously, relying on  a first-order expansion around the distribution function this expansion is only valid in the linear regime (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' small  perturbations around the reference state).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' In addition, Ji j is the Jacobian of the collision operator evaluated about ¯f j,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e, Ji j = ∂ f jδtΩi| ¯f j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Placing back these expressions into the discrete LB time-evolution equation:  f  ′  i (r + ciδt, t + δt) − f  ′  i (r, t) = Ji j f  ′  i (r, t) −  � ¯fi (r + ciδt, t + δt) − ¯fi (r, t) − δtΩi| ¯fi  �  ��������������������������������������������������������������������������������������������  =0  ,  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4)  and taking out the last terms on the RHS one gets:  f  ′  i (r + ciδt, t + δt) =  �  δi j + Ji j  �  f  ′  j (r, t) ,  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5)  where δij is the Kronecker delta function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Using the SRT collision operator for instance, we can then re-write the  linearized time-evolution equation as:  f  ′  i (r + ciδt, t + δt) =  ��  1 − δt  ¯τ  �  δi j + δt  ¯τ Jeq  i j  �  f  ′  j (r, t) ,  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6)  with Jeq  ij = ∂ j f eq  α | ¯f j and ¯f j = f eq  j (¯ρ, ¯u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' To compute the Jacobian matrix of the EDF, knowing that ∂ f j fk = δ jk, the  following expressions can be used:  ∂ f jaeq  0 = ∂ f j(ρ) =  �  k  δ jk = 1,  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='7)  ∂ f jaeq  1 = ∂ fj(ρu) =  �  k  ckδ jk = cj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8)  Once re-written as a function of the conserved Hermite coefficients, computing the Jacobians of higher-order compo-  nents of the Hermite expansion is straightforward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Let us consider the second-order Hermite coefficient for example:  ∂ f jaeq  2 = ∂ f j  aeq  1 ⊗ aeq  1  aeq  0  = − aeq  1 ⊗ aeq  1  (aeq  0 )2  +  aeq  1 ⊗ c j +  �  aeq  1 ⊗ cj  �†  aeq  0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='9)  Eventually, for the second-order EDF the Jacobian reads:  Jeq  ij = wi  �  H0 + H1(ci) : ∂ f jaeq  1 + H2(ci) :  ∂f j aeq  2  2  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='10)  The last step of the VN analysis is to assume that perturbations f ′  i are monochromatic plane waves :  f ′  i = Fi exp [  √  −1(k · r − ωit)],  where Fi is the wave amplitude,  √  −1 is the imaginary unit, ||k|| = k is the wave-number, and ω is the complex time  frequency of the wave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' k is related to the wave-length of f ′  i , whereas ℑ(ω) and ℜ(ω) are related to its attenuation and  propagation speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' By injecting these perturbations into Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5 one obtains the following eigenvalue problem of size  Q:  MF = exp (−  √  −1ωi)F,  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='11)  where F is the eigenvector composed of all amplitudes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' It is related to the eigenvalue exp (−  √  −1ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' M is the matrix  associated to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Here this matrix can be expressed as :  M = E [δ + J] ,  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='12)  with  Ei j = exp[−i(ci · k)]δi j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='13)  It is important to notice that the matrix M and the eigenvalue problem B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='11 depend on the mean flow (¯ρ, ¯u), the  wave-number (kx and ky in 2-D) and the relaxation coefficient ¯τ, or equivalently the kinematic viscosity ν.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' This means  that for each set of these parameters the eigenvalue problem needs to be solved to obtain the corresponding values of  ℜ(ω) and ℑ(ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Doing so, the spectral properties (dispersion and dissipation) can be obtained for any given collision  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  134  Appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Hydrodynamic limit of the Enskog–Vlasov–BGK kinetic model  Chapman–Enskog analysis Expanding the distribution function as:  f = f (0) + ϵ f (1) + ϵ2 f (2) + O(ϵ3),  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1)  introducing it back into (576) and separating terms with different orders in ϵ, at order zero one recovers:  f (0) = f eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2)  This latter implies the solvability conditions,  �  f (k)dv = 0, ∀k � 0,  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3)  �  v f (k)dv = 0, ∀k � 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4)  At order ϵ:  ∂(1)  t  f (0) + v · ∇f (0) = −1  τ f (1) − 1  ρ  ∂f eq  ∂u · F(1),  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5)  which, upon integration in v, leads to  ∂(1)  t ρ + ∇ · ρu = 0,  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6)  ∂(1)  t ρu + ∇ρu ⊗ u + ∇ · P0I + F(1) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='7)  At order ϵ2:  ∂(2)  t  f (0) + ∂(1)  t  f (1) + v · ∇ f (1) = −1  τ f (2),  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8)  which leads to the following equation for mass conservation:  ∂(2)  t ρ = 0,  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='9)  while for momentum:  ∂(2)  t ρu + ∇ ·  ��  v ⊗ v f (1)dv  �  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='10)  The last term on the left hand side can be evaluated using the previous order in ϵ as:  �  v ⊗ v f (1)dv = −τ  �  ∂(1)  t  �  v ⊗ v f (0)dv + ∇ ·  �  v ⊗ v ⊗ v f (0)dv  +1  ρ  �  v ⊗ v∂f eq  ∂u · F(1)dv  �  ,  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='11)  where:  ∂(1)  t  �  v ⊗ v f (0)dv = −∇ · ρu ⊗ u ⊗ u −  �  u ⊗ (F(1) + ∇P0) + (F(1) + ∇P0) ⊗ u  �  + ∂(1)  t P0I,  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='12)  and:  ∇ ·  �  v ⊗ v ⊗ vf (1)dv = ∇ · ρu ⊗ u ⊗ u +  �  ∇P0u + ∇P0u†�  + I∇ · P0u,  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='13)  1  ρ  �  v ⊗ v∂f eq  ∂u · F(1)dv = u ⊗ F(1) + F(1) ⊗ u,  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='14)  which leads to:  �  v ⊗ v f (1)dv = −τ  �  P0  �  ∇u + ∇u†�  +  �  ∂(1)  t P0 + ∇ · P0u  �  I  �  ,  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='15)  135  where the last two terms can be re-written as:  ∂(1)  t P0 + ∇ · P0u =∂P0  ∂ρ (∂(1)  t ρ + ∇ · ρu) +  �  P0 − ρ∂P0  ∂ρ  �  ∇ · u  =P0  �  1 − ∂ ln P0  ∂ ln ρ  �  ∇ · u,  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='16)  in turn recovering the Navier-Stokes-level momentum equation:  ∂(2)  t ρu − ∇ · µ  �  ∇u + ∇u† − 2  3∇ · uI  �  − ∇ · (η∇ · uI) = 0,  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='17)  where:  µ = τP0,  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='18)  η = τP0  �5  3 − ∂ ln P0  ∂ ln ρ  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='19)  Appendix D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Chapman–Enskog analysis of the lattice Boltzmann method for non-ideal fluids  Using a Taylor expansion around (r, t),  fi (r + ciδt, t + δt) − fi (r, t) =  �  δtDt + δt2  2 D2  t  �  f (r, t) + O(δt3)  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1)  the discrete time-evolution equation is re-written as:  δtDt fi + δt2  2 Dt  2 fi + O(δt3) = δt  ¯τ  �  f eq  i  − fi  �  +  �  f ∗  i − f eq  i  �  ,  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2)  where we have only retained terms up to order two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Then introducing characteristic flow size L and velocity U the  equation is made non-dimensional as:  �δr  L  �  D′  t fi + 1  2  �δr  L  �2  D′  t  2 fi = δt  ¯τ  �  f eq  i  − fi  �  +  �  f ∗  i (u′ + δu  U δu′) − f eq  i (u′)  �  ,  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3)  where primed variables denote non-dimensional form and  D′  t = U  c  �∂′  t + c′  i · ∇′� ,  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4)  where c = δr/δt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Assuming acoustic, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' U  c ∼ 1 and hydrodynamic, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' δr  L ∼ δu  U ∼ ε, scaling and dropping the primes  for the sake of readability:  εDt fi + 1  2ε2Dt  2 fi + O(ε3) = δt  ¯τ  �  f eq  i  − fi  �  +  �  f ∗  i (u + εδu) − f eq  i (u)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5)  Then introducing multi-scale expansions:  fi  =  f (0)  i  + ε f (1)  i  + ε2 f (2)  i  + O(ε3),  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6)  f ∗  i  =  f ∗  i  (0) + ε f ∗  i  (1) + ε2 f ∗  i  (2) + O(ε3),  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='7)  the following equations are recovered at scales ε and ε2:  ε : D(1)  t  f (0)  i  = −δt  ¯τ f (1)  i  + f ∗(1)  i ,  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8a)  ε2 : ∂(2)  t  f (0)  i  + D(1)  t  �  1 − δt  2¯τ  �  f (1)  i  = −δt  ¯τ f (2)  i  + f ∗(2)  i  − 1  2D(1)  t  f ∗(1)  i ,  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='8b)  136  with f (0)  i  = f ∗  i  (0) = f eq  i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The moments of the non-local contributions (including both non-ideal contributions to the  thermodynamic pressure, surface tension and the correction for the diagonals of the third-order moments tensor) are:  �  i  f ∗(k)  i  = 0, ∀k > 0,  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='9a)  �  i  ci f ∗  i  (1) = F,  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='9b)  �  i  ci ⊗ ci f ∗  i  (1) = (u ⊗ F + F ⊗ u) + Φ  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='9c)  �  i  ci ⊗ ci f ∗  i  (2) = 1  ρ F ⊗ F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='9d)  Taking the moments of the Chapman-Enskog-expanded equation at order ε:  ∂(1)  t ρ + ∇ · ρu  =  0,  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='10)  ∂(1)  t ρu + ∇ · ρu ⊗ u + ∇ · P0I + F  =  0,  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='11)  while at order ε2 the continuity equation is:  ∂(2)  t ρ + ∇ · F  2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='12)  Summing up Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='10 and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='12 we recover the continuity equation as:  ∂tρ + ∇ · ρU = 0,  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='13)  where U = u + δt  2ρ F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' For the momentum equations we have:  ∂(2)  t ρu + 1  2∂(1)  t F + 1  2∇ · (u ⊗ F + F ⊗ u) + ∇ ·  �1  2 − ¯τ  δt  � �  ∂(1)  t Π(0)  2 + ∇ · Π(0)  3  �  − ∇ ·  �1  2 − ¯τ  δt  �  (u ⊗ F + F ⊗ u) + ∇ · ¯τ  δtΦ = 0,  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='14)  where Π(0)  2 and Π(0)  3 are the second- and third-order moments of f (0)  i  defined as:  Π(0)  2  =  ρu ⊗ u + P0I,  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='15)  Π(0)  3  =  ΠMB  3  − ρu ⊗ u ⊗ u ◦ J − 3(P0 − ρς2)J  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='16)  where ΠMB  αβγ = ρuαuβuγ +P0perm(uαδβγ) is the third-order moment of the Maxwell-Boltzmann distribution, and for the  sake of simplicity we have introduced the diagonal rank three tensor J, with Jαβγ = δαβδαγδβγ and ◦ is the Hadamard  product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' The contributions in the fourth term on the left hand side can be expanded as:  ∂(1)  t Π(0)  2 =∂(1)  t ρu ⊗ u + ∂(1)  t P0I  =u ⊗ ∂(1)  t ρu + (∂(1)  t ρu) ⊗ u − u ⊗ u∂(1)  t ρ + ∂(1)  t P0I  = − ∇ · ρu ⊗ u ⊗ u − [u ⊗ (∇P0 − F) + (∇P0 − F) ⊗ u] + ∂(1)  t P0I  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='17)  and:  ∇ · Π(0)  3 = ∇ · ρu ⊗ u ⊗ u +  �  ∇P0u + ∇P0u†�  + (∇ · P0u)I − ∇ ·  �  ρu ⊗ u ⊗ u ◦ J + 3(P0 − ρς2)J  �  ,  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='18)  resulting in:  ∂(1)  t Π(0)  2 + ∇ · Π(0)  3 = P0  �  ∇u + ∇u†�  +  �  u ⊗ F + u ⊗ F†�  +  �  ∇ · P0u + ∂(1)  t P0  �  I − ∇ ·  �  ρu ⊗ u ⊗ u ◦ J + 3(P0 − ρς2)J  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='19)  137  Plugging this last equation back into Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='14):  ∂(2)  t ρu + ∂(1)  t  F  2 + 1  2∇ · (u ⊗ F + F ⊗ u) + ∇ ·  �1  2 − ¯τ  δt  �  P0  �  ∇u + ∇u†�  + ∇  �1  2 − ¯τ  δt  � �  ∂(1)  t P0 + ∇ · P0u  �  + ∇ ·  ��1  2 − ¯τ  δt  �  ∇ ·  �  ρu ⊗ u ⊗ u ◦ J + 3(P0 − ρς2)J  �  + ¯τ  δtΦ  �  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='20)  where the last term cancels out by setting:  Φ =  �  1 − δt  2¯τ  �  ∇ ·  �  ρu ⊗ u ⊗ u ◦ J + 3(P0 − ρς2)J  �  ,  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='21)  and the fourth and fifth terms reduce to the viscous stress tensor by defining µ/P0 =  � ¯τ  δt − 1  2  �  and:  P0  �2 + D  D  − ∂ ln P0  ∂ ln ρ  � � ¯τ  δt − 1  2  �  = η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='22)  Furthermore, using U = u + δt  2ρ F and:  ρU ⊗ U = ρu ⊗ u + δt  2 (u ⊗ F + F ⊗ u) + δt2F ⊗ F  4ρ  ,  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='23)  in combination with the Euler-level equation, and keeping in mind that errors of the form ∇ · δt2F⊗F  4ρ  in the convective  term and δt∇µ  �  ∇ F  ρ + ∇ F  ρ  †�  in the viscous stress are of order ε3 one recovers:  ∂tρU + ∇ · ρU ⊗ U − ∇ · µ  �  ∇U + ∇U† − 2  D∇ · UI  �  − ∇ · (η∇ · U) + O(ε3) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='24)  References  [1] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Sethian, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Smereka, Level set methods for fluid interfaces, Annual review of fluid mechanics 35 (1) (2003) 341–372, iSBN: 0066-4189  Publisher: Annual Reviews 4139 El Camino Way, PO Box 10139, Palo Alto, CA 94303-0139, USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [2] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Scardovelli, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Zaleski, Direct numerical simulation of free-surface and interfacial flow, Annual review of fluid mechanics 31 (1) (1999)  567–603, iSBN: 0066-4189 Publisher: Annual Reviews 4139 El Camino Way, PO Box 10139, Palo Alto, CA 94303-0139, USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [3] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Popinet, Numerical models of surface tension, Annual Review of Fluid Mechanics 50 (2018) 49–75, iSBN: 0066-4189 Publisher: Annual  Reviews.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [4] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Prosperetti, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Tryggvason, Computational methods for multiphase flow, Cambridge university press, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [5] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Debenedetti, Metastable liquids, Princeton university press, 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [6] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' van der Waals, Thermodynamische Theorie der Kapillarit¨at unter Voraussetzung stetiger Dichte¨anderung, Zeitschrift f¨ur Physikalische  Chemie 13U (1) (Jan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 1894).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1515/zpch-1894-1338.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='degruyter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/document/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1515/zpch-1894-1338/html  [7] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Korteweg, Sur la forme que prennent les ´equations du mouvement des fluides si l’on tient compte des forces capillaires caus´ees par des  variations de densit´e consid´erables mais continues et sur la th´eeorie de la capillarit´e dans l’hypothese d’une variation continue de la densit´e,  Arch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' N´eerl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Exactes Nat 6 (265) (1901).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [8] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Anderson, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' McFadden, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Wheeler, Diffuse-interface methods in fluid mechanics, Annual review of fluid mechanics 30 (1)  (1998) 139–165, iSBN: 0066-4189 Publisher: Annual Reviews 4139 El Camino Way, PO Box 10139, Palo Alto, CA 94303-0139, USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [9] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Enskog, Der warmeleitung, reibung und selbstdiffusion in gewissen verdichteten gasen und flussigkeiten, Kungl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Svenska Vetenskap-  sakademiens Handlingar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 63 (4) (1921).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [10] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Vlasov, Many-particle theory and its application to plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=', New York (1961).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [11] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Chapman, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Cowling, The mathematical theory of non-uniform gases: an account of the kinetic theory of viscosity, thermal conduction  and diffusion in gases, Cambridge university press, 1939.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [12] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Shan, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Chen, Lattice Boltzmann model for simulating flows with multiple phases and components, Physical Review E 47 (3) (1993)  1815–1819.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1815.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1815  138  [13] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Saint-Raymond, A mathematical PDE perspective on the Chapman–Enskog expansion, Bulletin of the American Mathematical Society  51 (2) (2013) 247–275.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1090/S0273-0979-2013-01440-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='ams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/jourcgi/jour-getitem?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='pii=S0273-0979-2013-01440-X  [14] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Gorban, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karlin, Hilbert’s 6th Problem: exact and approximate hydrodynamic manifolds for kinetic equations, Bulletin of the  American Mathematical Society 51 (2) (2013) 187–246.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1090/S0273-0979-2013-01439-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='ams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/jourcgi/jour-getitem?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='pii=S0273-0979-2013-01439-3  [15] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Grad, On the kinetic theory of rarefied gases, Communications on Pure and Applied Mathematics 2 (4) (1949) 331–407.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1002/  cpa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3160020403.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://onlinelibrary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='wiley.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1002/cpa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3160020403  [16] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Jou, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Lebon, Extended Irreversible Thermodynamics, Springer Netherlands, Dordrecht, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1007/978-90-481-3074-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='springer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1007/978-90-481-3074-0  [17] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Grmela, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Hong, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Jou, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Lebon, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Pavelka, Hamiltonian and Godunov structures of the Grad hierarchy, Physical Review E 95 (3)  (2017) 033121.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='033121.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='033121  [18] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Grmela, Externally Driven Macroscopic Systems: Dynamics Versus Thermodynamics, Journal of Statistical Physics 166 (2) (2017)  282–316.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1007/s10955-016-1694-6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='springer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1007/s10955-016-1694-6  [19] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Truesdell, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Muncaster, Fundamentals of Maxwell’s kinetic theory of a simple monatomic gas, Academic Pres, New York, 1980.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [20] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Struchtrup, Macroscopic Transport Equations for Rarefied Gas Flows, Interaction of Mechanics and Mathematics, Springer Berlin Hei-  delberg, Berlin, Heidelberg, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1007/3-540-32386-4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='springer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1007/3-540-32386-4  [21] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Gorban, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karlin, Short-Wave Limit of Hydrodynamics: A Soluble Example, Physical Review Letters 77 (2) (1996) 282–285.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='282.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='282  [22] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karlin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Gorban, Hydrodynamics from Grad’s equations: What can we learn from exact solutions?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=', Annalen der Physik 514 (10-11)  (2002) 783–833.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1002/andp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='200251410-1103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://onlinelibrary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='wiley.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1002/andp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='200251410-1103  [23] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Kogan, Derivation of Grad’s type equations and study of their relaxation properties by the method of maximization of entropy, Journal  of Applied Mathematics and Mechanics 29 (1) (1965) 130–142.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/0021-8928(65)90157-7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/0021892865901577  [24] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Lewis, A Unifying Principle in Statistical Mechanics, Journal of Mathematical Physics 8 (7) (1967) 1448–1459.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  1705359.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://aip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='scitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1705359  [25] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karlin, On the relaxation of the chemical reaction rate, in: Mathematical Problems of Chemical Kinetics, Novosibirsk, 1989, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 7–42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [26] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Gorban, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karlin, Quasi–equilibrium approximation and nonstandard expansions in the theory of the Boltzmann kinetic equation,  in: Mathematical Modelling in Biology and Chemistry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' New Approaches, Novosibirsk, 1991, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 69–117.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [27] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Shakhov, Generalization of the Krook kinetic relaxation equation, Fluid Dynamics 3 (5) (1972) 95–96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1007/BF01029546.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='springer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1007/BF01029546  [28] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Frapolli, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Chikatamarla, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karlin, Multispeed entropic lattice Boltzmann model for thermal flows, Physical Review E 90 (4)  (2014) 043306.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='043306.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='043306  [29] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karlin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Gorban, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Dukek, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Nonnenmacher, Dynamic correction to moment approximations, Physical Review E 57 (2) (1998) 1668–  1672.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1668.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1668  [30] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Struchtrup, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Torrilhon, Regularization of Grad’s 13 moment equations: Derivation and linear analysis, Physics of Fluids 15 (9) (2003)  2668–2680.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1597472.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://aip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='scitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1597472  [31] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karlin, Derivation of regularized Grad’s moment system from kinetic equations: modes, ghosts and non-Markov fluxes, Philosophical  Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376 (2118) (2018) 20170230.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1098/  rsta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0230.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://royalsocietypublishing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1098/rsta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0230  [32] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Rana, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Torrilhon, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Struchtrup, A robust numerical method for the R13 equations of rarefied gas dynamics: Application to lid driven  cavity, Journal of Computational Physics 236 (2013) 169–186.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='jcp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0021999112007036  [33] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Struchtrup, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Torrilhon, Regularized 13 moment equations for hard sphere molecules: Linear bulk equations, Physics of Fluids 25 (5)  (2013) 052001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4802041.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://aip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='scitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4802041  [34] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Struchtrup, Derivation of 13 Moment Equations for Rarefied Gas Flow to Second Order Accuracy for Arbitrary Interaction Potentials,  Multiscale Modeling & Simulation 3 (1) (2005) 221–243.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1137/040603115.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://epubs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='siam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1137/040603115  [35] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Struchtrup, Stable transport equations for rarefied gases at high orders in the Knudsen number, Physics of Fluids 16 (11) (2004) 3921–  3934.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1782751.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://aip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='scitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1782751  [36] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Torrilhon, Modeling Nonequilibrium Gas Flow Based on Moment Equations, Annual Review of Fluid Mechanics 48 (1) (2016) 429–458.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1146/annurev-fluid-122414-034259.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  139  URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='annualreviews.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1146/annurev-fluid-122414-034259  [37] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Timokhin, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Struchtrup, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Kokhanchik, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Bondar, Different variants of R13 moment equations applied to the shock-wave  structure, Physics of Fluids 29 (3) (2017) 037105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4977978.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://aip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='scitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4977978  [38] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Struchtrup, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Torrilhon, H Theorem, Regularization, and Boundary Conditions for Linearized 13 Moment Equations, Physical Review  Letters 99 (1) (2007) 014502.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='014502.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='014502  [39] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Torrilhon, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Struchtrup, Regularized 13-moment equations: shock structure calculations and comparison to Burnett models, Journal of  Fluid Mechanics 513 (2004) 171–198.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1017/S0022112004009917.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='journals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='cambridge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/abstract_S0022112004009917  [40] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Gorban, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karlin, General approach to constructing models of the Boltzmann equation, Physica A: Statistical Mechanics and its  Applications 206 (3-4) (1994) 401–420.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/0378-4371(94)90314-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/037843719490314X  [41] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Levermore, Moment closure hierarchies for kinetic theories, Journal of Statistical Physics 83 (5-6) (1996) 1021–1065.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1007/  BF02179552.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='springer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1007/BF02179552  [42] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ansumali, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Arcidiacono, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Chikatamarla, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Prasianakis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Gorban, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karlin, Quasi-equilibrium lattice Boltzmann method,  The European Physical Journal B 56 (2) (2007) 135–139.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1140/epjb/e2007-00100-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='springer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1140/epjb/e2007-00100-1  [43] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Holway, Kinetic Theory of Shock Structure Using an Ellipsoidal Distribution Function, in: Proceedings of the Fourth International  Symposium on Rarefied Gas Dynamics, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 1, Toronto, 1965.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [44] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Andries, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Le Tallec, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Perlat, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Perthame, The Gaussian-BGK model of Boltzmann equation with small Prandtl number, European  Journal of Mechanics - B/Fluids 19 (6) (2000) 813–830.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/S0997-7546(00)01103-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0997754600011031  [45] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' McNamara, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Zanetti, Use of the Boltzmann equation to simulate lattice-gas automata, Physical review letters 61 (20) (1988) 2332,  publisher: APS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [46] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Benzi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Succi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Vergassola, The lattice Boltzmann equation: theory and applications, Physics Reports 222 (3) (1992) 145–197.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/0370-1573(92)90090-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/037015739290090M  [47] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Succi, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Clarendon, 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://physicstoday.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='scitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1537916  [48] U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Frisch, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Hasslacher, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Pomeau, Lattice-Gas Automata for the Navier-Stokes Equation, Physical Review Letters 56 (14) (1986) 1505–  1508.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1505.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1505  [49] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Shan, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Yuan, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Chen, Kinetic theory representation of hydrodynamics: a way beyond the Navier–Stokes equation, Journal of Fluid  Mechanics 550 (2006) 413–441, iSBN: 1469-7645 Publisher: Cambridge University Press.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [50] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Grad, Note onN-dimensional hermite polynomials, Communications on Pure and Applied Mathematics 2 (4) (1949) 325–330.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1002/cpa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3160020402.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://onlinelibrary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='wiley.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1002/cpa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='3160020402  [51] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Sun, Lattice-Boltzmann models for high speed flows, Physical Review E 58 (6) (1998) 7283–7287.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='7283.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='7283  [52] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Sun, Adaptive lattice Boltzmann model for compressible flows: Viscous and conductive properties, Physical Review E 61 (3) (2000)  2645–2653.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2645.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2645  [53] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Sun, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Hsu, Three-dimensional lattice Boltzmann model for compressible flows, Physical Review E 68 (1) (2003) 016303.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='016303.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='016303  [54] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Frapolli, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Chikatamarla, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karlin, Lattice Kinetic Theory in a Comoving Galilean Reference Frame, Physical Review Letters 117 (1)  (2016) 010604.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='117.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='010604.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='117.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='010604  [55] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Dorschner, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' B¨osch, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karlin, Particles on demand for kinetic theory, Physical review letters 121 (13) (2018) 130602, publisher: APS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [56] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Saadat, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' B¨osch, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karlin, Lattice Boltzmann model for compressible flows on standard lattices: Variable Prandtl number and  adiabatic exponent, Physical Review E 99 (1) (2019) 013306.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='013306.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='013306  [57] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Lin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Xu, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Zhang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Luo, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Li, Discrete Boltzmann modeling of Rayleigh-Taylor instability in two-component compressible  flows, Physical Review E 96 (5) (2017) 053305.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='053305.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='053305  [58] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Hosseini, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Darabiha, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Th´evenin, Compressibility in lattice Boltzmann on standard stencils: effects of deviation from reference  temperature, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378 (2175) (2020)  20190399.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1098/rsta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0399.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://royalsocietypublishing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1098/rsta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0399  [59] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Gan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Xu, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Zhang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Lai, Three-dimensional discrete Boltzmann models for compressible flows in and out of equilibrium,  Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 232 (3) (2018) 477–490.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1177/0954406217742181.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://journals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='sagepub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1177/0954406217742181  140  [60] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Gan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Xu, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Yang, Lattice BGK kinetic model for high-speed compressible flows: Hydrodynamic and nonequilibrium  behaviors, EPL (Europhysics Letters) 103 (2) (2013) 24003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1209/0295-5075/103/24003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://iopscience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='iop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/article/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1209/0295-5075/103/24003  [61] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Gan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Xu, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Zhang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Succi, Discrete Boltzmann trans-scale modeling of high-speed compressible flows, Physical Review  E 97 (5) (2018) 053312.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='053312.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='053312  [62] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ansumali, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karlin, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' ¨Ottinger, Minimal entropic kinetic models for hydrodynamics, EPL (Europhysics Letters) 63 (6) (2003) 798,  iSBN: 0295-5075 Publisher: IOP Publishing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [63] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Li, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Luo, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' He, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Gao, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Tao, Coupling lattice Boltzmann model for simulation of thermal flows on standard lattices,  Physical Review E 85 (1) (2012) 016710.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='016710.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='016710  [64] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Feng, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Sagaut, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Tao, A three dimensional lattice model for thermal compressible flow on standard lattices, Journal of Computational  Physics 303 (2015) 514–529, iSBN: 0021-9991 Publisher: Elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [65] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Feng, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Boivin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Jacob, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Sagaut, Hybrid recursive regularized thermal lattice Boltzmann model for high subsonic compressible flows,  Journal of Computational Physics 394 (2019) 82–99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='jcp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='031.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0021999119303626  [66] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Prasianakis, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karlin, Lattice Boltzmann method for thermal flow simulation on standard lattices, Physical Review E 76 (1) (2007)  016702.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='016702.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='016702  [67] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Prasianakis, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karlin, Lattice Boltzmann method for simulation of compressible flows on standard lattices, Physical Review E 78 (1)  (2008) 016704.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='016704.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='016704  [68] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Wilde, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Kr¨amer, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Reith, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Foysi, Semi-Lagrangian lattice Boltzmann method for compressible flows, Physical Review E 101 (5)  (2020) 053306.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='053306.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='053306  [69] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Wilde, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Kr¨amer, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' K¨ullmer, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Foysi, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Reith, Multistep lattice Boltzmann methods: Theory and applications, International Journal  for Numerical Methods in Fluids 90 (3) (2019) 156–169.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1002/fld.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4716.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://onlinelibrary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='wiley.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1002/fld.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4716  [70] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Kr¨amer, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' K¨ullmer, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Reith, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Joppich, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Foysi, Semi-Lagrangian off-lattice Boltzmann method for weakly compressible flows,  Physical Review E 95 (2) (2017) 023305.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='023305.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='023305  [71] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Saadat, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Hosseini, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Dorschner, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karlin, Extended lattice Boltzmann model for gas dynamics, Physics of Fluids 33 (4)  (2021) 046104, iSBN: 1070-6631 Publisher: AIP Publishing LLC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [72] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Mohamad, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Kuzmin, A critical evaluation of force term in lattice Boltzmann method, natural convection problem, International  Journal of Heat and Mass Transfer 53 (5-6) (2010) 990–996, iSBN: 0017-9310 Publisher: Elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [73] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Huang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Krafczyk, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Lu, Forcing term in single-phase and Shan-Chen-type multiphase lattice Boltzmann models, Physical Review E  84 (4) (2011) 046710.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='046710.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='046710  [74] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Bawazeer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Baakeem, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Mohamad, A Critical Review of Forcing Schemes in Lattice Boltzmann Method: 1993–2019, Archives  of Computational Methods in Engineering 28 (7) (2021) 4405–4423.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1007/s11831-021-09535-4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='springer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1007/s11831-021-09535-4  [75] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Martys, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Shan, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Chen, Evaluation of the external force term in the discrete Boltzmann equation, Physical Review E 58 (5) (1998)  6855–6857.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6855.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6855  [76] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Luo, Unified Theory of Lattice Boltzmann Models for Nonideal Gases, Physical Review Letters 81 (8) (1998) 1618–1621.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1618.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1618  [77] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Guo, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Zheng, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Shi, Discrete lattice effects on the forcing term in the lattice Boltzmann method, Physical Review E 65 (4) (2002)  046308.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='046308.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='046308  [78] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' He, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Shan, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Doolen, Discrete Boltzmann equation model for nonideal gases, Physical Review E 57 (1) (1998) R13–R16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='R13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='R13  [79] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Kupershtokh, New method of incorporating a body force term into the lattice Boltzmann equation, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [80] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Kupershtokh, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Medvedev, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karpov, On equations of state in a lattice Boltzmann method, Computers & Mathematics with Applica-  tions 58 (5) (2009) 965–974.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='camwa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='02.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='024.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0898122109001011  [81] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Dellar, Bulk and shear viscosities in lattice Boltzmann equations, Physical Review E 64 (3) (2001) 031203, publisher: APS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [82] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Li, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Shock, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Zhang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Chen, Numerical study of flow past an impulsively started cylinder by the lattice-Boltzmann method, Journal  of Fluid Mechanics 519 (2004) 273–300.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1017/S0022112004001272.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='journals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='cambridge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/abstract_S0022112004001272  [83] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Tosi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ubertini, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Succi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Chen, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karlin, Numerical stability of Entropic versus positivity-enforcing Lattice Boltzmann schemes,  Mathematics and Computers in Simulation 72 (2-6) (2006) 227–231.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='matcom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0378475406001315  [84] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Brownlee, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Gorban, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Levesley, Stabilization of the lattice Boltzmann method using the Ehrenfests’ coarse-graining idea,  141  Physical Review E 74 (3) (2006) 037703.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='037703.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='037703  [85] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Servan-Camas, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Tsai, Lattice Boltzmann method with two relaxation times for advection–diffusion equation: Third order analysis  and stability analysis, Advances in Water Resources 31 (8) (2008) 1113–1126.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='advwatres.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0309170808000833  [86] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Servan-Camas, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Tsai, Non-negativity and stability analyses of lattice Boltzmann method for advection–diffusion equation, Journal  of Computational Physics 228 (1) (2009) 236–256.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='jcp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='09.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0021999108004749  [87] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Hosseini, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Darabiha, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Th´evenin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Eshghinejadfard, Stability limits of the single relaxation-time advection–diffusion lattice  Boltzmann scheme, International Journal of Modern Physics C 28 (12) (2017) 1750141.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1142/S0129183117501418.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='worldscientific.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/doi/abs/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1142/S0129183117501418  [88] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ch´avez-Modena, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ferrer, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Rubio, Improving the stability of multiple-relaxation lattice Boltzmann methods with central moments,  Computers & Fluids 172 (2018) 397–409.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='compfluid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='03.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='084.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0045793018301889  [89] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Sterling, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Chen, Stability Analysis of Lattice Boltzmann Methods, Journal of Computational Physics 123 (1) (1996) 196–206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1006/jcph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0021999196900169  [90] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Worthing, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Mozer, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Seeley, Stability of lattice Boltzmann methods in hydrodynamic regimes, Physical Review E 56 (2) (1997)  2243–2253.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2243.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2243  [91] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Lallemand, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Luo, Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, Galilean invariance, and stability,  Physical Review E 61 (6) (2000) 6546–6562.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6546.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6546  [92] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Hosseini, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Coreixas, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Darabiha, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Th´evenin, Stability of the lattice kinetic scheme and choice of the free relaxation parameter,  Physical Review E 99 (6) (2019) 063305.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='063305.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='063305  [93] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Hosseini, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Coreixas, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Darabiha, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Th´evenin, Extensive analysis of the lattice Boltzmann method on shifted stencils, Physical  Review E 100 (6) (2019) 063301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='063301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='063301  [94] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Wissocq, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Sagaut, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Boussuge, An extended spectral analysis of the lattice Boltzmann method: modal interactions and stability  issues, Journal of Computational Physics 380 (2019) 311–333.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='jcp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0021999118308118  [95] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Hosseini, Development of a lattice Boltzmann-based numerical method for the simulation od reacting flows, Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' thesis, Universit{\\’e}  {P}aris-{S}aclay/{O}tto-von-{G}uericke-{U}niversit{\\¨a}t {M}agdeburg, artwork Size: xxiv, 205 Seiten Publisher: Universit¨at Paris-Saclay  (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://opendata.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='uni-halle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='de//handle/1981185920/33674  [96] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' d’Humi`eres, Generalized lattice-Boltzmann equations, Rarefied gas dynamicsPublisher: AIAA (1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [97] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' d’Humi`eres, Multiple–relaxation–time lattice Boltzmann models in three dimensions, Philosophical Transactions of the Royal Society of  London.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Series A: Mathematical, Physical and Engineering Sciences 360 (1792) (2002) 437–451.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1098/rsta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0955.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://royalsocietypublishing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1098/rsta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0955  [98] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Lallemand, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Luo, Theory of the lattice Boltzmann method: Acoustic and thermal properties in two and three dimensions, Physical  Review E 68 (3) (2003) 036706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='036706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='036706  [99] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Pan, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Luo, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Miller, An evaluation of lattice Boltzmann schemes for porous medium flow simulation, Computers & Fluids  35 (8-9) (2006) 898–909.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='compfluid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='03.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0045793005001520  [100] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karlin, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' B¨osch, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Chikatamarla, Gibbs’ principle for the lattice-kinetic theory of fluid dynamics, Physical Review E 90 (3) (2014)  031302, publisher: APS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [101] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ginzburg, Equilibrium-type and link-type lattice Boltzmann models for generic advection and anisotropic-dispersion equation, Advances  in Water Resources 28 (11) (2005) 1171–1195.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='advwatres.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='03.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0309170805000874  [102] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ginzburg, Generic boundary conditions for lattice Boltzmann models and their application to advection and anisotropic dispersion equa-  tions, Advances in Water Resources 28 (11) (2005) 1196–1216.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='advwatres.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='03.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0309170805000886  [103] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ginzburg, Lattice Boltzmann modeling with discontinuous collision components: Hydrodynamic and Advection-Diffusion Equations,  Journal of Statistical Physics 126 (1) (2007) 157–206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1007/s10955-006-9234-4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='springer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1007/s10955-006-9234-4  [104] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' d’Humi`eres, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ginzburg, Viscosity independent numerical errors for Lattice Boltzmann models: From recurrence equations to “magic”  collision numbers, Computers & Mathematics with Applications 58 (5) (2009) 823–840.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='camwa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='02.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0898122109000893  [105] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ginzburg, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Verhaeghe, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' d’Humi`eres, Two-Relaxation-Time Lattice Boltzmann Scheme: About Parametrization, Velocity, Pressure  and Mixed Boundary Conditions, Communications in Computational Physics 3 (2) (2008) 427–478.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [106] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ginzburg, Consistent lattice Boltzmann schemes for the Brinkman model of porous flow and infinite Chapman-Enskog expansion, Physical  Review E 77 (6) (2008) 066704.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='066704.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='066704  142  [107] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ginzburg, Magic recipes for Lattice {B}oltzmann modeling of micro and macro flow, Habilitation thesis, Universit{\\’e} {P}aris {VI} (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [108] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Kuzmin, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ginzburg, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Mohamad, The role of the kinetic parameter in the stability of two-relaxation-time advection–diffusion lattice  Boltzmann schemes, Computers & Mathematics with Applications 61 (12) (2011) 3417–3442.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='camwa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='036.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0898122110005286  [109] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Inamuro, A lattice kinetic scheme for incompressible viscous flows with heat transfer, Philosophical Transactions of the Royal Society of  London.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Series A: Mathematical, Physical and Engineering Sciences 360 (1792) (2002) 477–484.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1098/rsta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0942.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://royalsocietypublishing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1098/rsta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0942  [110] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Mi, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Meng, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Guo, A Localized Mass-Conserving Lattice Boltzmann Approach for Non-Newtonian Fluid Flows, Communi-  cations in Computational Physics 17 (4) (2015) 908–924.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4208/cicp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='m303.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='cambridge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/core/product/identifier/S1815240615000249/type/journal_article  [111] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Hosseini, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Darabiha, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Th´evenin, Theoretical and numerical analysis of the lattice kinetic scheme for complex-flow simulations,  Physical Review E 99 (2) (2019) 023305.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='023305.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='023305  [112] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Kataoka, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Inamuro, Numerical simulations of the behaviour of a drop in a square pipe flow using the two-phase lattice Boltzmann  method, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369 (1945) (2011) 2528–  2536.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1098/rsta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0041.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://royalsocietypublishing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1098/rsta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0041  [113] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Yoshino, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Hotta, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Hirozane, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Endo, A numerical method for incompressible non-Newtonian fluid flows based on the lattice  Boltzmann method, Journal of Non-Newtonian Fluid Mechanics 147 (1-2) (2007) 69–78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='jnnfm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0377025707001632  [114] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Meng, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Guo, Localized lattice Boltzmann equation model for simulating miscible viscous displacement in porous media, International  Journal of Heat and Mass Transfer 100 (2016) 767–778.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='ijheatmasstransfer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='095.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0017931015312126  [115] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Perko, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Patel, Single-relaxation-time lattice Boltzmann scheme for advection-diffusion problems with large diffusion-coefficient  heterogeneities and high-advection transport, Physical Review E 89 (5) (2014) 053309.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='053309.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='053309  [116] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Geier, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Greiner, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Korvink, Cascaded digital lattice Boltzmann automata for high Reynolds number flow, Physical Review E 73 (6)  (2006) 066705, publisher: APS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [117] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Geier, De-aliasing and stabilization formalism of the cascaded lattice Boltzmann automaton for under-resolved high Reynolds number  flow, International Journal for Numerical Methods in Fluids 56 (8) (2008) 1249–1254.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1002/fld.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1634.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://onlinelibrary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='wiley.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1002/fld.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1634  [118] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Asinari, Generalized local equilibrium in the cascaded lattice Boltzmann method, Physical Review E 78 (1) (2008) 016701.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  doi:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='016701.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='016701  [119] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Hosseini, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Berg, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Huang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Roloff, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Janiga, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Th´evenin, Central moments multiple relaxation time LBM for hemodynamic  simulations in intracranial aneurysms: An in-vitro validation study using PIV and PC-MRI, Computers in Biology and Medicine 131 (2021)  104251.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='compbiomed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='104251.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0010482521000457  [120] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Huang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' No¨el, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Berg, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Hosseini, Simulation of the FDA nozzle benchmark: A lattice Boltzmann study, Computer Methods and  Programs in Biomedicine 221 (2022) 106863.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='cmpb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='106863.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0169260722002450  [121] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Hosseini, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Huang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Th´evenin, Lattice Boltzmann model for simulation of flow in intracranial aneurysms considering non-  Newtonian effects, Physics of Fluids 34 (7) (2022) 073105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0098383.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://aip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='scitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0098383  [122] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karlin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ferrante, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' ¨Ottinger, Perfect entropy functions of the Lattice Boltzmann method, Europhysics Letters (EPL) 47 (2)  (1999) 182–188.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1209/epl/i1999-00370-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://iopscience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='iop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/article/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1209/epl/i1999-00370-1  [123] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karlin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Gorban, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Succi, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Boffi, Maximum Entropy Principle for Lattice Kinetic Equations, Physical Review Letters 81 (1)  (1998) 6–9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6  [124] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Chikatamarla, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ansumali, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karlin, Entropic lattice Boltzmann models for hydrodynamics in three dimensions, Physical review  letters 97 (1) (2006) 010201, publisher: APS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [125] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ansumali, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Chikatamarla, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Frouzakis, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Boulouchos, ENTROPIC LATTICE BOLTZMANN SIMULATION OF THE FLOW  PAST SQUARE CYLINDER, International Journal of Modern Physics C 15 (03) (2004) 435–445.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1142/S012918310400584X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='worldscientific.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/doi/abs/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1142/S012918310400584X  [126] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ansumali, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karlin, Single relaxation time model for entropic lattice Boltzmann methods, Physical Review E 65 (5) (2002) 056312,  publisher: APS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [127] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Boghosian, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Love, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Coveney, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karlin, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Succi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Yepez, Galilean-invariant lattice-Boltzmann models with H theorem,  Physical Review E 68 (2) (2003) 025103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='025103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='025103  [128] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Mazloomi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Chikatamarla, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karlin, Entropic Lattice Boltzmann Method for Multiphase Flows, Physical review Letters 114 (7) (2015)  174502.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [129] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Atif, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Kolluru, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Thantanapally, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ansumali, Essentially Entropic Lattice Boltzmann Model, Physical Review Letters 119 (24)  (2017) 240602.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='119.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='240602.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='119.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='240602  143  [130] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' B¨osch, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Dorschner, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karlin, Entropic multi-relaxation free-energy lattice Boltzmann model for two-phase flows, EPL (Europhysics  Letters) 122 (1) (2018) 14002, iSBN: 0295-5075 Publisher: IOP Publishing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [131] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Hosseini, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Dorschner, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karlin, Entropic multi-relaxation-time lattice Boltzmann model for large density ratio two-phase flows,  Communications in Computational PhysicsPublisher: arXiv Version Number: 2 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/abs/2201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [132] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Latt, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Chopard, Lattice Boltzmann method with regularized pre-collision distribution functions, Mathematics and Computers in Simu-  lation 72 (2-6) (2006) 165–168, iSBN: 0378-4754 Publisher: Elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [133] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Latt, Hydrodynamic limit of lattice Boltzmann equations, Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' thesis, Universit{\\’}e de Geneve, publisher: Universit´e de Gen`eve (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://archive-ouverte.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='unige.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='ch/unige:464  [134] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Malaspinas, Increasing stability and accuracy of the lattice Boltzmann scheme: recursivity and regularization, arXivPublisher: arXiv  (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='48550/ARXIV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1505.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='06900.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/abs/1505.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='06900  [135] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Jacob, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Malaspinas, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Sagaut, A new hybrid recursive regularised Bhatnagar–Gross–Krook collision model for Lattice Boltzmann  method-based large eddy simulation, Journal of Turbulence 19 (11-12) (2018) 1051–1076.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1080/14685248.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1540879.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='tandfonline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/doi/full/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1080/14685248.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1540879  [136] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' van der Waals, Over de Continuiteit van den Gas- en Vloeistoftoestand, Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' thesis, University of Leiden (1873).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [137] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Clerk-Maxwell, On the Dynamical Evidence of the Molecular Constitution of Bodies *, Nature 11 (279) (1875) 357–359.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1038/  011357a0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='nature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/articles/011357a0  [138] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Sekerka, Thermal Physics, Elsevier, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/C2014-0-03233-9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/C20140032339  [139] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Cahn, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Hilliard, Free Energy of a Nonuniform System.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Interfacial Free Energy, The Journal of Chemical Physics 28 (2) (1958)  258–267.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1744102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://aip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='scitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1744102  [140] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Giovangigli, Kinetic derivation of diffuse-interface fluid models, Physical Review E 102 (1) (2020) 012110, publisher: APS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [141] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Struchtrup, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Frezzotti, Grad’s 13 moments approximation for Enskog-Vlasov equation, in: AIP Conference Proceedings, Glasgow,  UK, 2019, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 120007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5119620.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://aip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='scitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/abs/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5119620  [142] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Struchtrup, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Frezzotti, Twenty-six moment equations for the Enskog–Vlasov equation, Journal of Fluid Mechanics 940 (2022) A40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  doi:doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1017/jfm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='cambridge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/core/product/identifier/S0022112022000982/type/journal_article  [143] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Kremer, An Introduction to the Boltzmann Equation and Transport Processes in Gases, Interaction of Mechanics and Mathematics,  Springer Berlin Heidelberg, Berlin, Heidelberg, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1007/978-3-642-11696-4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='springer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1007/978-3-642-11696-4  [144] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Van Beijeren, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ernst, The modified Enskog equation, Physica 68 (3) (1973) 437–456, iSBN: 0031-8914 Publisher: Elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [145] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karkheck, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Stell, Kinetic mean-field theories, The Journal of Chemical Physics 75 (3) (1981) 1475–1487.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='442154.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://aip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='scitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='442154  [146] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Hosseini, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Dorschner, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karlin, Towards a consistent lattice Boltzmann model for two-phase fluid, arXiv preprint  arXiv:2112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='01975 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [147] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Gorban, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karlin, Invariant manifolds for physical and chemical kinetics, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 660 in Lecture notes in physics, Springer, Berlin ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  New York, 2005, oCLC: ocm57729924.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [148] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Chen, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Kang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Mu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' He, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='-Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Tao, A critical review of the pseudopotential multiphase lattice Boltzmann model: Methods and  applications, International Journal of Heat and Mass Transfer 76 (2014) 210–236.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='ijheatmasstransfer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  032.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0017931014003378  [149] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' He, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Doolen, Thermodynamic foundations of kinetic theory and lattice Boltzmann models for multiphase flows, Journal of Statistical  Physics 107 (1) (2002) 309–328, iSBN: 1572-9613 Publisher: Springer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [150] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Swift, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Osborn, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Yeomans, Lattice Boltzmann Simulation of Nonideal Fluids, Physical Review Letters 75 (5) (1995) 830–  833.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='830.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='830  [151] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Holdych, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Rovas, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Georgiadis, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Buckius, An Improved Hydrodynamics Formulation for Multiphase Flow Lattice-Boltzmann  Models, International Journal of Modern Physics C 09 (08) (1998) 1393–1404.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1142/S0129183198001266.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='worldscientific.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/doi/abs/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1142/S0129183198001266  [152] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Inamuro, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Konishi, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ogino, A Galilean invariant model of the lattice Boltzmann method for multiphase fluid flows using free-energy  approach, Computer Physics Communications 129 (1-3) (2000) 32–45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/S0010-4655(00)00090-4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0010465500000904  [153] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Wagner, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Li, Investigation of Galilean invariance of multi-phase lattice Boltzmann methods, Physica A: Statistical Mechanics and its  Applications 362 (1) (2006) 105–110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='physa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='09.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='030.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0378437105009647  [154] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Luo, Theory of the lattice Boltzmann method: Lattice Boltzmann models for nonideal gases, Physical Review E 62 (4) (2000) 4982–  4996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4982.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4982  [155] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Mazloomi Moqaddam, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Chikatamarla, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karlin, Simulation of binary droplet collisions with the entropic lattice Boltzmann  method, Physics of Fluids 28 (2) (2016) 022106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4942017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://aip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='scitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='4942017  144  [156] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Mazloomi Moqaddam, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Chikatamarla, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karlin, Drops bouncing off macro-textured superhydrophobic surfaces, Journal of Fluid  Mechanics 824 (2017) 866–885.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1017/jfm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='306.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='cambridge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/core/product/identifier/S0022112017003068/type/journal_article  [157] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Wen, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Zhao, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Qiu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ye, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Shan, Chemical-potential multiphase lattice Boltzmann method with superlarge density ratios, Physical  Review E 102 (1) (2020) 013303.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='013303.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='013303  [158] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Guggenheim, The Principle of Corresponding States, The Journal of Chemical Physics 13 (7) (1945) 253–261.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  1724033.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://aip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='scitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1724033  [159] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Winterbone, Advanced Thermodynamics for Engineers, Elsevier, 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/B978-0-340-67699-8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='X5000-5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/B9780340676998X50005  [160] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Yang, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Fleming, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Gibbs, Molecular theory of surface tension, The Journal of Chemical Physics 64 (9) (1976) 3732–3747.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='432687.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://aip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='scitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='432687  [161] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Lovett, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' DeHaven, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Vieceli, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Buff, Generalized van der Waals theories for surface tension and interfacial width, The Journal  of Chemical Physics 58 (5) (1973) 1880–1885.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1679447.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://aip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='scitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1679447  [162] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ornstein, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Zernik, Accidental deviations of density and opalescence at the critical point of a single substance, Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Akad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' 17 (793)  (1914).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [163] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Lin, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Duan, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Min, Gradient theory modeling of surface tension for pure fluids and binary mixtures, Fluid Phase Equilibria 254 (1-  2) (2007) 75–90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='fluid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='02.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S037838120700088X  [164] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Nayigizente, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ducruix, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Schmitt, Development of an interface thickening method for the direct numerical simulation of compressible  liquid–vapor flows in the framework of the second gradient theory, Physics of Fluids 33 (5) (2021) 052119.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0048715.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://aip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='scitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0048715  [165] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Leland, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Chappelear, The corresponding states principle—a review of current theory and practice, Industrial & Engineering  Chemistry 60 (7) (1968) 15–43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [166] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Pitzer, Corresponding States for Perfect Liquids, The Journal of Chemical Physics 7 (8) (1939) 583–590.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1750496.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://aip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='scitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1750496  [167] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Sato, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Watanabe, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Levelt Sengers, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Gallagher, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Hill, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Straub, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Wagner, Sixteen Thousand Evaluated Experimental  Thermodynamic Property Data for Water and Steam, Journal of Physical and Chemical Reference Data 20 (5) (1991) 1023–1044.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='555894.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://aip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='scitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='555894  [168] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Jamet, ´Etude des potentialites de la theorie du second gradient pour la simulation numerique directe des ecoulements liquide-vapeur avec  changement de phase, Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' thesis, CEA Grenoble (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [169] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Domb, The Critical Point: A Historical Introduction To The Modern Theory Of Critical Phenomena, 0th Edition, CRC Press, 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1201/9781482295269.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='taylorfrancis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/books/9781482295269  [170] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Sbragaglia, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Shan, Consistent pseudopotential interactions in lattice Boltzmann models, Physical Review E 84 (3) (2011) 036703.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='036703.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='036703  [171] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Yuan, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Schaefer, Equations of state in a lattice Boltzmann model, Physics of Fluids 18 (4) (2006) 042101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2187070.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://aip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='scitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2187070  [172] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Leclaire, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Pellerin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Reggio, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Tr´epanier, Enhanced equilibrium distribution functions for simulating immiscible multiphase  flows with variable density ratios in a class of lattice Boltzmann models, International Journal of Multiphase Flow 57 (2013) 159–168.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='ijmultiphaseflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0301932213001043  [173] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Fakhari, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Geier, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Lee, A mass-conserving lattice Boltzmann method with dynamic grid refinement for immiscible two-phase flows,  Journal of Computational Physics 315 (2016) 434–457.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='jcp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='03.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='058.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0021999116300237  [174] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Zu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' He, Phase-field-based lattice Boltzmann model for incompressible binary fluid systems with density and viscosity contrasts,  Physical Review E 87 (4) (2013) 043301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='043301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='043301  [175] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Fakhari, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Mitchell, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Leonardi, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Bolster, Improved locality of the phase-field lattice-Boltzmann model for immiscible fluids at high  density ratios, Physical Review E 96 (5) (2017) 053301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='053301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='053301  [176] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Mitchell, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Leonardi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Fakhari, Development of a three-dimensional phase-field lattice Boltzmann method for the study of immiscible  fluids at high density ratios, International Journal of Multiphase Flow 107 (2018) 1–15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='ijmultiphaseflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0301932217309369  [177] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Peng, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Robinson, A new two-constant equation of state, Industrial & Engineering Chemistry Fundamentals 15 (1) (1976) 59–64,  iSBN: 0196-4313 Publisher: ACS Publications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [178] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Redlich, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Kwong, On the thermodynamics of solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' An equation of state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Fugacities of gaseous solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=', Chemical reviews  44 (1) (1949) 233–244, iSBN: 0009-2665 Publisher: ACS Publications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [179] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Soave, Equilibrium constants from a modified Redlich-Kwong equation of state, Chemical engineering science 27 (6) (1972) 1197–1203,  145  iSBN: 0009-2509 Publisher: Elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [180] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Carnahan, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Starling, Equation of state for nonattracting rigid spheres, The Journal of chemical physics 51 (2) (1969) 635–636,  iSBN: 0021-9606 Publisher: American Institute of Physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [181] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Benzi, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Biferale, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Sbragaglia, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Succi, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Toschi, Mesoscopic modeling of a two-phase flow in the presence of boundaries: The  contact angle, Physical Review E 74 (2) (2006) 021509.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='021509.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='021509  [182] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Sbragaglia, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Benzi, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Biferale, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Succi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Sugiyama, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Toschi, Generalized lattice Boltzmann method with multirange pseudopo-  tential, Physical Review E 75 (2) (2007) 026702.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='026702.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='026702  [183] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Shan, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Chen, Simulation of nonideal gases and liquid-gas phase transitions by the lattice Boltzmann equation, Physical Review E 49 (4)  (1994) 2941–2948.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2941.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2941  [184] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Colosqui, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Falcucci, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ubertini, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Succi, Mesoscopic simulation of non-ideal fluids with self-tuning of the equation of state, Soft  Matter 8 (14) (2012) 3798.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1039/c2sm06353k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://xlink.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='rsc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='DOI=c2sm06353k  [185] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Fei, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Du, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Luo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Succi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Lauricella, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Montessori, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Wang, Modeling realistic multiphase flows using a non-orthogonal  multiple-relaxation-time lattice Boltzmann method, Physics of Fluids 31 (4) (2019) 042105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5087266.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://aip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='scitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5087266  [186] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Li, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Luo, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Li, Lattice Boltzmann modeling of multiphase flows at large density ratio with an improved pseudopotential model,  Physical Review E 87 (5) (2013) 053301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='053301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='053301  [187] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Peng, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ayala, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Wang, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ayala, Attainment of rigorous thermodynamic consistency and surface tension in single-component  pseudopotential lattice Boltzmann models via a customized equation of state, Physical Review E 101 (6) (2020) 063309.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/  PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='063309.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='063309  [188] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Swift, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Orlandini, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Osborn, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Yeomans, Lattice Boltzmann simulations of liquid-gas and binary fluid systems, Physical  Review E 54 (5) (1996) 5041–5052.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5041.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5041  [189] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Martys, Energy conserving discrete {B}oltzmann equation for nonideal systems, International Journal of Modern Physics C 10 (07)  (1999) 1367–1382.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1142/S0129183199001121.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='worldscientific.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/doi/abs/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1142/S0129183199001121  [190] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Martys, Aclassical kinetic theory approach to lattice {B}oltzmann simulation, International Journal of Modern Physics C 12 (08) (2001)  1169–1178.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1142/S0129183101002474.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='worldscientific.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/doi/abs/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1142/S0129183101002474  [191] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Reyhanian, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Dorschner, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karlin, Thermokinetic lattice Boltzmann model of nonideal fluids, Physical Review E 102 (2) (2020)  020103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='020103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='020103  [192] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Zhang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Chen, Lattice Boltzmann method for simulations of liquid-vapor thermal flows, Physical Review E 67 (6) (2003) 066711.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='066711.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='066711  [193] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Gong, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Cheng, Numerical investigation of droplet motion and coalescence by an improved lattice Boltzmann model for phase transitions  and multiphase flows, Computers & Fluids 53 (2012) 93–104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='compfluid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='09.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0045793011002994  [194] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Shan, Pressure tensor calculation in a class of nonideal gas lattice Boltzmann models, Physical Review E 77 (6) (2008) 066702, publisher:  APS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [195] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Li, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Luo, Achieving tunable surface tension in the pseudopotential lattice Boltzmann modeling of multiphase flows, Physical Review  E 88 (5) (2013) 053307.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='053307.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='053307  [196] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Gibbs, On the equilibrium of heterogeneous substances, Transactions of the Connecticut Academy of Arts and Sciences III (1874) 108–  248.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [197] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Kirkwood, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Buff, The Statistical Mechanical Theory of Surface Tension, The Journal of Chemical Physics 17 (3) (1949) 338–343.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1747248.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://aip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='scitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1747248  [198] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Martys, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Chen, Simulation of multicomponent fluids in complex three-dimensional geometries by the lattice Boltzmann method,  Physical Review E 53 (1) (1996) 743–750.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='743.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='743  [199] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Sukop, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Thorne, Lattice Boltzmann Modeling: An Introduction for Geoscientists and Engineers, Springer Berlin Heidelberg,  Berlin, Heidelberg, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1007/978-3-540-27982-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='springer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1007/978-3-540-27982-2  [200] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Raiskinm¨aki, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Koponen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Merikoski, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Timonen, Spreading dynamics of three-dimensional droplets by the lattice-Boltzmann method,  Computational Materials Science 18 (1) (2000) 7–12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/S0927-0256(99)00095-6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0927025699000956  [201] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Raiskinm¨aki, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Shakib-Manesh, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' J¨asberg, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Koponen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Merikoski, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Timonen, Lattice-Boltzmann simulation of capillary rise  dynamics, Journal of Statistical Physics 107 (1/2) (2002) 143–158.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1023/A:1014506503793.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='springer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1023/A:1014506503793  146  [202] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Kang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Zhang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Chen, Displacement of a two-dimensional immiscible droplet in a channel, Physics of Fluids 14 (9) (2002) 3203–  3214.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1499125.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://aip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='scitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1499125  [203] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Sbragaglia, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Benzi, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Biferale, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Succi, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Toschi, Surface Roughness-Hydrophobicity Coupling in Microchannel and Nanochannel  Flows, Physical Review Letters 97 (20) (2006) 204503.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='204503.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='204503  [204] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ding, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Spelt, Wetting condition in diffuse interface simulations of contact line motion, Physical Review E 75 (4) (2007) 046708.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='046708.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='046708  [205] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Hu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Li, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Uddin, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Liu, Contact angle adjustment in equation-of-state-based pseudopotential model, Physical Review E 93 (5) (2016)  053307.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='053307.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='053307  [206] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Yu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Luo, Implementation of contact angles in pseudopotential lattice Boltzmann simulations with curved boundaries, Physical  Review E 100 (5) (2019) 053313.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='053313.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='053313  [207] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Gao, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' McCarthy, Contact Angle Hysteresis Explained, Langmuir 22 (14) (2006) 6234–6237.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1021/la060254j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://pubs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='acs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1021/la060254j  [208] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ding, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Spelt, Onset of motion of a three-dimensional droplet on a wall in shear flow at moderate Reynolds numbers, Journal of  Fluid Mechanics 599 (2008) 341–362.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1017/S0022112008000190.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='cambridge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/core/product/identifier/S0022112008000190/type/journal_article  [209] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ba, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Liu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Sun, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Zheng, Color-gradient lattice Boltzmann model for simulating droplet motion with contact-angle hysteresis,  Physical Review E 88 (4) (2013) 043306.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='043306.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='043306  [210] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Zhang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Zhang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Zhang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Yang, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Cheng, Evaporation of a sessile droplet on flat surfaces: An axisymmetric lattice Boltzmann  model with consideration of contact angle hysteresis, International Journal of Heat and Mass Transfer 178 (2021) 121577.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/  j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='ijheatmasstransfer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='121577.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0017931021006803  [211] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Yang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ma, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Fei, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Zhang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Luo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Shuai, Effects of hysteresis window on contact angle hysteresis behaviour at large Bond  number, Journal of Colloid and Interface Science 566 (2020) 327–337.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='jcis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='042.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0021979720300461  [212] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='-b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Huang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Lu, Scheme for contact angle and its hysteresis in a multiphase lattice Boltzmann method, Physical Review E  87 (1) (2013) 013301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='013301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='013301  [213] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ju, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Wang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Xi, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Zhang, Lattice Boltzmann modeling of contact angle and its hysteresis in two-phase flow with large  viscosity difference, Physical Review E 92 (3) (2015) 033306.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='033306.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='033306  [214] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Qin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Zhao, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Kang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Derome, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Carmeliet, Lattice Boltzmann Modeling of Drying of Porous Media Considering Contact Angle  Hysteresis, Transport in Porous Media 140 (1) (2021) 395–420.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1007/s11242-021-01644-9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='springer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1007/s11242-021-01644-9  [215] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Widom, Surface Tension and Molecular Correlations near the Critical Point, The Journal of Chemical Physics 43 (11) (1965) 3892–3897.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1696617.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://aip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='scitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1696617  [216] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Jamet, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Lebaigue, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Coutris, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Delhaye, The Second Gradient Method for the Direct Numerical Simulation of Liquid–Vapor Flows  with Phase Change, Journal of Computational Physics 169 (2) (2001) 624–651.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1006/jcph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='6692.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0021999100966920  [217] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Blokhuis, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Kuipers, Thermodynamic expressions for the Tolman length, The Journal of Chemical Physics 124 (7) (2006) 074701.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2167642.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://aip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='scitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2167642  [218] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Lulli, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Biferale, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Falcucci, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Sbragaglia, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Shan, Mesoscale perspective on the Tolman length, Physical Review E 105 (1) (2022)  015301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='015301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='015301  [219] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Blokhuis, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Bedeaux, Pressure tensor of a spherical interface, The Journal of chemical physics 97 (5) (1992) 3576–3586, iSBN:  0021-9606 Publisher: American Institute of Physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [220] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Tolman, The effect of droplet size on surface tension, The journal of chemical physics 17 (3) (1949) 333–337, iSBN: 0021-9606  Publisher: American Institute of Physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [221] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Helfrich, Steric interaction of fluid membranes in multilayer systems, Zeitschrift f¨ur Naturforschung A 33 (3) (1978) 305–315, iSBN:  1865-7109 Publisher: Verlag der Zeitschrift f¨ur Naturforschung.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [222] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Rao, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Berne, On the location of surface of tension in the planar interface between liquid and vapour, Molecular Physics 37 (2) (1979)  455–461, iSBN: 0026-8976 Publisher: Taylor & Francis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  [223] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Gauthier, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Symon, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Clanet, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Qu´er´e, Water impacting on superhydrophobic macrotextures, Nature Communications 6 (1) (2015)  8001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1038/ncomms9001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='nature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/articles/ncomms9001  [224] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Richard, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Qu´er´e, Bouncing water drops, Europhysics Letters (EPL) 50 (6) (2000) 769–775.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1209/epl/i2000-00547-6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://iopscience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='iop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/article/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1209/epl/i2000-00547-6  [225] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Qu´er´e, Non-sticking drops, Reports on Progress in Physics 68 (11) (2005) 2495–2532.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1088/0034-4885/68/11/R01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  147  URL https://iopscience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='iop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/article/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1088/0034-4885/68/11/R01  [226] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Richard, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Clanet, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Qu´er´e, Contact time of a bouncing drop, Nature 417 (6891) (2002) 811–811.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1038/417811a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='nature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/articles/417811a  [227] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Okumura, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Chevy, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Richard, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Qu´er´e, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Clanet, Water spring: A model for bouncing drops, Europhysics Letters (EPL) 62 (2)  (2003) 237–243.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1209/epl/i2003-00340-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://iopscience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='iop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/article/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1209/epl/i2003-00340-1  [228] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Clanet, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' B´eguin, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Richard, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Qu´er´e, Maximal deformation of an impacting drop, Journal of Fluid Mechanics 517 (2004) 199–208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1017/S0022112004000904.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='journals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='cambridge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/abstract_S0022112004000904  [229] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Lee, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Laan, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' de Bruin, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Skantzaris, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Shahidzadeh, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Derome, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Carmeliet, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Bonn, Universal rescaling of drop impact  on smooth and rough surfaces, Journal of Fluid Mechanics 786 (2016) R4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1017/jfm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='620.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='cambridge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/core/product/identifier/S0022112015006205/type/journal_article  [230] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Mazloomi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Chikatamarla, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karlin, Entropic lattice Boltzmann method for multiphase flows: Fluid-solid interfaces, Physical Review  E 92 (2) (2015) 023308.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='023308.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='023308  [231] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Qin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Mazloomi Moqaddam, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Kang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Derome, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Carmeliet, Entropic multiple-relaxation-time multirange pseudopotential lattice  Boltzmann model for two-phase flow, Physics of Fluids 30 (3) (2018) 032104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5016965.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://aip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='scitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5016965  [232] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Liu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Moevius, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Xu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Qian, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Yeomans, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Wang, Pancake bouncing on superhydrophobic surfaces, Nature Physics 10 (7) (2014)  515–519.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1038/nphys2980.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='nature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/articles/nphys2980  [233] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Moevius, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Liu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Yeomans, Pancake Bouncing: Simulations and Theory and Experimental Verification, Langmuir 30 (43)  (2014) 13021–13032.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1021/la5033916.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://pubs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='acs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1021/la5033916  [234] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Chantelot, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Mazloomi Moqaddam, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Gauthier, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Chikatamarla, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Clanet, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karlin, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Qu´er´e, Water ring-bouncing on repellent  singularities, Soft Matter 14 (12) (2018) 2227–2233.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1039/C7SM02004J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://xlink.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='rsc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='DOI=C7SM02004J  [235] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Liu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Andrew, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Yeomans, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Wang, Symmetry breaking in drop bouncing on curved surfaces, Nature Communications 6 (1)  (2015) 10034.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1038/ncomms10034.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='nature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/articles/ncomms10034  [236] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Kooij, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Moqaddam, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' de Goede, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Derome, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Carmeliet, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Shahidzadeh, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Bonn, Sprays from droplets impacting a mesh,  Journal of Fluid Mechanics 871 (2019) 489–509.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1017/jfm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='289.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='cambridge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/core/product/identifier/S0022112019002891/type/journal_article  [237] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Gao, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Luo, Droplet impacting a superhydrophobic mesh array: Effect of liquid properties, Physical Review Fluids 5 (12)  (2020) 123605.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevFluids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='123605.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevFluids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='123605  [238] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Wang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Fei, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Luo, Lattice Boltzmann simulation of water droplet impacting a hydrophobic plate with a cylindrical pore, Physical  Review Fluids 5 (8) (2020) 083602.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevFluids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='083602.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevFluids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='083602  [239] U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Uttamchandani, Wireless MEMS Networks and Applications, Elsevier, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/C2014-0-03941-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/C2014003941X  [240] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Kandlikar, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' See, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Koz, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Gopalan, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Banerjee, Two-phase flow in GDL and reactant channels of a proton exchange membrane  fuel cell, International Journal of Hydrogen Energy 39 (12) (2014) 6620–6636.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='ijhydene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='02.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='045.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0360319914004054  [241] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Yang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Fei, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Zhang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ma, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Luo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Shuai, Improved pseudopotential lattice Boltzmann model for liquid water transport inside  gas diffusion layers, International Journal of Hydrogen Energy 46 (29) (2021) 15938–15950.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='ijhydene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='02.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='067.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0360319921005693  [242] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Yang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Fei, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Zhang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ma, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Luo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Shuai, Dynamic behavior of droplet transport on realistic gas diffusion layer with inertial  effect via a unified lattice Boltzmann method, International Journal of Hydrogen Energy 46 (66) (2021) 33260–33271.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  ijhydene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='124.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0360319921027890  [243] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Zhao, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Qin, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Derome, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Carmeliet, Drying of porous materials at pore scale using lattice Boltzmann and pore network models, Journal  of Physics: Conference Series 2069 (1) (2021) 012001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1088/1742-6596/2069/1/012001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://iopscience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='iop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/article/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1088/1742-6596/2069/1/012001  [244] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Zhao, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Qin, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Kang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Derome, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Carmeliet, Pore-scale simulation of drying in porous media using a hybrid lattice Boltzmann: pore  network model, Drying Technology 40 (4) (2022) 719–734.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1080/07373937.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1933017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='tandfonline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/doi/full/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1080/07373937.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1933017  [245] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Mino, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Tanaka, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Tanaka, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Nakaso, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Gotoh, Numerical simulation of a drying colloidal suspension on a wettable substrate using  the lattice Boltzmann method, Chemical Engineering Science 263 (2022) 118050.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='ces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='118050.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0009250922006340  [246] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Li, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Kang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Francois, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' He, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Luo, Lattice Boltzmann modeling of boiling heat transfer: The boiling curve and the effects of  wettability, International Journal of Heat and Mass Transfer 85 (2015) 787–796.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='ijheatmasstransfer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='136.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0017931015001544  [247] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Biferale, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Perlekar, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Sbragaglia, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Toschi, Convection in Multiphase Fluid Flows Using Lattice Boltzmann Methods, Physical Review  Letters 108 (10) (2012) 104502.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='104502.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  148  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='104502  [248] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' H´azi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' M´arkus, Modeling heat transfer in supercritical fluid using the lattice Boltzmann method, Physical Review E 77 (2) (2008)  026305.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='026305.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='026305  [249] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Hazi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Markus, On the bubble departure diameter and release frequency based on numerical simulation results, International Journal of  Heat and Mass Transfer 52 (5-6) (2009) 1472–1480.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='ijheatmasstransfer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='09.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0017931008005097  [250] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Gong, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Cheng, A lattice Boltzmann method for simulation of liquid–vapor phase-change heat transfer, International Journal of Heat and  Mass Transfer 55 (17-18) (2012) 4923–4927.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='ijheatmasstransfer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='037.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0017931012002888  [251] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Huang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' He, Thermal lattice Boltzmann model for liquid-vapor phase change, Physical Review E 106 (5) (2022) 055308.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='055308.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='055308  [252] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Li, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Luo, Effect of the forcing term in the pseudopotential lattice Boltzmann modeling of thermal flows, Physical Review E 89 (5)  (2014) 053022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='053022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='053022  [253] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Kumar, Isotropic finite-differences, Journal of Computational Physics 201 (1) (2004) 109–118.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='jcp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0021999104002037  [254] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Thampi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ansumali, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Adhikari, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Succi, Isotropic discrete Laplacian operators from lattice hydrodynamics, Journal of Computa-  tional Physics 234 (2013) 1–7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='jcp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='037.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://linkinghub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/retrieve/pii/S0021999112004226  [255] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ramadugu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Thampi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Adhikari, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Succi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ansumali, Lattice differential operators for computational physics, EPL (Europhysics  Letters) 101 (5) (2013) 50006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1209/0295-5075/101/50006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://iopscience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='iop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/article/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1209/0295-5075/101/50006  [256] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Banerjee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Succi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ansumali, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Adhikari, Isotropic finite-difference discretization of stochastic conservation laws preserving  detailed balance, Journal of Statistical Mechanics: Theory and Experiment 2017 (10) (2017) 103202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1088/1742-5468/aa8c35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://iopscience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='iop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/article/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1088/1742-5468/aa8c35  [257] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Qin, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Del Carro, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Mazloomi Moqaddam, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Kang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Brunschwiler, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Derome, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Carmeliet, Study of non-isothermal liq-  uid evaporation in synthetic micro-pore structures with hybrid lattice Boltzmann model, Journal of Fluid Mechanics 866 (2019) 33–60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1017/jfm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='cambridge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/core/product/identifier/S0022112019000697/type/journal_article  [258] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Wang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Fei, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Lei, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Wang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Luo, Droplet impact on a heated porous plate above the Leidenfrost temperature: A lattice  Boltzmann study, Physics of Fluids 34 (9) (2022) 093319.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0118079.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://aip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='scitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0118079  [259] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Fei, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Qin, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Wang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Luo, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Derome, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Carmeliet, Droplet evaporation in finite-size systems: Theoretical analysis and mesoscopic  modeling, Physical Review E 105 (2) (2022) 025101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='025101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='025101  [260] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Fei, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Yang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Chen, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Mo, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Luo, Mesoscopic simulation of three-dimensional pool boiling based on a phase-change cascaded  lattice Boltzmann method, Physics of Fluids 32 (10) (2020) 103312.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0023639.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://aip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='scitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0023639  [261] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Saito, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' De Rosis, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Fei, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Luo, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='-i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ebihara, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Kaneko, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Abe, Lattice Boltzmann modeling and simulation of forced-convection  boiling on a cylinder, Physics of Fluids 33 (2) (2021) 023307.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0032743.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://aip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='scitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1063/5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='0032743  [262] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Huang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Wu, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Adams, Mesoscopic Lattice Boltzmann Modeling of the Liquid-Vapor Phase Transition, Physical Review Letters  126 (24) (2021) 244501.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='126.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='244501.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='126.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='244501  [263] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Shan, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Doolen, Multicomponent lattice-Boltzmann model with interparticle interaction, Journal of Statistical Physics 81 (1-2) (1995)  379–393.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1007/BF02179985.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='springer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1007/BF02179985  [264] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' W¨ohrwag, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Semprebon, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Mazloomi Moqaddam, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Karlin, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Kusumaatmaja, Ternary Free-Energy Entropic Lattice Boltzmann  Model with a High Density Ratio, Physical Review Letters 120 (23) (2018) 234501.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='120.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='234501.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='120.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='234501  [265] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Chen, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='-T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Chen, Collision between immiscible drops with large surface tension difference: diesel oil and water, Experiments in  Fluids 41 (3) (2006) 453–461.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1007/s00348-006-0173-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL http://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='springer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='com/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1007/s00348-006-0173-2  [266] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Ridl, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Wagner, Lattice Boltzmann simulation of mixtures with multicomponent van der Waals equation of state, Physical Review  E 98 (4) (2018) 043305.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='043305.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='043305  [267] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Li, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Wagner, Symmetric free-energy-based multicomponent lattice Boltzmann method, Physical Review E 76 (3) (2007) 036701.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='036701.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='036701  [268] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Guo, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Zhao, Finite-difference-based lattice Boltzmann model for dense binary mixtures, Physical Review E 71 (2) (2005) 026701.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='026701.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='026701  [269] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Guo, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' Zhao, Discrete velocity and lattice Boltzmann models for binary mixtures of nonideal fluids, Physical Review E 68 (3) (2003)  149  035302.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='035302.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='1103/PhysRevE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
+page_content='035302  150' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdA0T4oBgHgl3EQfD_9b/content/2301.02011v1.pdf'}
diff --git a/T9E3T4oBgHgl3EQfaQqr/content/2301.04505v1.pdf b/T9E3T4oBgHgl3EQfaQqr/content/2301.04505v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..c292d97251cfe933a96e4dd7c9706b85f0865e8a
--- /dev/null
+++ b/T9E3T4oBgHgl3EQfaQqr/content/2301.04505v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:240c75531624ca41b75aba7edbd55988ef7236996440ac16d44d99b6f45fdfa5
+size 3276056
diff --git a/T9E3T4oBgHgl3EQfaQqr/vector_store/index.faiss b/T9E3T4oBgHgl3EQfaQqr/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..7e7ec29d37fee44c1b0167780995920d7972bac8
--- /dev/null
+++ b/T9E3T4oBgHgl3EQfaQqr/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2ff71c705890aef71c72eee67525c001b9119ed3b684a666ca94e4234b3ea965
+size 6094893
diff --git a/T9E3T4oBgHgl3EQfaQqr/vector_store/index.pkl b/T9E3T4oBgHgl3EQfaQqr/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..cc689463b4833d9f5175e057765a1b66bc0cc1d2
--- /dev/null
+++ b/T9E3T4oBgHgl3EQfaQqr/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:076da8500d75be85f875dcbbe2e5f4949f31f3f192665b9bbab9e56d12fb2fd2
+size 215664
diff --git a/UdE0T4oBgHgl3EQflgEz/vector_store/index.faiss b/UdE0T4oBgHgl3EQflgEz/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..b6d17fc306b8a30387baaf1cae00092f0ab66b72
--- /dev/null
+++ b/UdE0T4oBgHgl3EQflgEz/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1b48416add5e4bce4eb363e0474ca85c1ec751f9674c85dcbd6a6d12e2ba6f79
+size 4784173
diff --git a/UtAzT4oBgHgl3EQflv2x/content/tmp_files/2301.01553v1.pdf.txt b/UtAzT4oBgHgl3EQflv2x/content/tmp_files/2301.01553v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9c040df524a359b4b0691cd12f8cef8931e69897
--- /dev/null
+++ b/UtAzT4oBgHgl3EQflv2x/content/tmp_files/2301.01553v1.pdf.txt
@@ -0,0 +1,711 @@
+arXiv:2301.01553v1  [math.GT]  4 Jan 2023
+NON-DENSITY OF C0-STABLE MAPPINGS
+ON NON-COMPACT MANIFOLDS
+SHUNSUKE ICHIKI
+Abstract. In 1973, Mather showed that the set of proper C0-stable mappings
+is dense in the set of all proper mappings, which implies that the set of C0-
+stable mappings is dense in the set of all mappings if the source manifold is
+compact. In this paper, we show that the set of C0-stable mappings is never
+dense in the set of all mappings if the source manifold is non-compact. To
+prove it, we provide a more essential result by using the notion of topologically
+critical points.
+1. Introduction
+Let N and P be C∞-manifolds. Two C∞-mappings f and g from N into P are
+said to be C∞-equivalent (resp. C0-equivalent) if there exist C∞-diffeomorphisms
+(resp. homeomorphisms) Φ : N → N and Ψ : P → P such that g = Ψ ◦ f ◦ Φ−1.
+We denote the space of all C∞-mappings of N into P (resp. the space of all proper
+C∞-mappings of N into P) endowed with the Whitney C∞-topology by C∞(N, P)
+(resp. C∞
+pr(N, P)). We say that f is C∞-stable (resp. C0-stable) if there exists an
+open neighborhood U of f such that any mapping in U is C∞-equivalent (resp.
+C0-equivalent) to f. In what follows, unless otherwise stated, all manifolds and
+mappings are of class C∞.
+On the C∞-stability, in a celebrated series around 1970 [5, 6, 7, 8, 9, 10], Mather
+established a significant theory and he gave a characterization of the density of
+proper C∞-stable mappings in C∞
+pr(N, P) as follows:
+Theorem 1.1 ([10]). Let N and P be manifolds of dimensions n and p, respectively.
+Then, the set of all proper C∞-stable mappings is dense in C∞
+pr(N, P) if and only
+if the pair (n, p) satisfies one of the following conditions.
+(1) n < 6
+7p + 8
+7 and p − n ≥ 4
+(2) n < 6
+7p + 9
+7 and 3 ≥ p − n ≥ 0
+(3) p < 8 and p − n = −1
+(4) p < 6 and p − n = −2
+(5) p < 7 and p − n ≤ −3
+A dimension pair (n, p) is called nice if it satisfies one of the conditions (1)–(5)
+in Theorem 1.1. Since C∞
+pr(N, P) = C∞(N, P) in the case where N is compact,
+Theorem 1.1 yields a characterization of the density of C∞-stable mappings in
+C∞(N, P) in the case.
+2020 Mathematics Subject Classification. 57R45, 58K30.
+Key words and phrases. C0-stable mapping, Whitney C∞-topology, topologically critical
+point.
+1
+
+2
+SHUNSUKE ICHIKI
+After that, the case where a source manifold is non-compact was considered by
+Dimca, and in 1979, he gave the following result.
+Proposition 1.2 ([1]). Let N be a non-compact manifold. Then, the set of all
+C∞-stable mappings is not dense in C∞(N, R).
+Then, in [4], for a non-compact source manifold N and an arbitrary target man-
+ifold P, the following has been shown rigorously:
+Theorem 1.3 ([4]). Let N be a non-compact manifold, and P a manifold. Then,
+the set of all C∞-stable mappings is never dense in C∞(N, P).
+By combining Mather’s theorem (Theorem 1.1) and Theorem 1.3, we obtain the
+following characterization of the density of C∞-stable mappings in C∞(N, P) in
+the case where N is not necessarily compact.
+Corollary 1.4 ([10, 4]). Let N and P be manifolds of dimensions n and p, respec-
+tively. Then, the set of all C∞-stable mappings is dense in C∞(N, P) if and only
+if N is compact and (n, p) is nice.
+On the C0-stability, Mather established the following theorem in 1973, which is
+so significant as well as Theorem 1.1, and the bibles [2, 3, 12] have been published.
+Theorem 1.5 ([11]). Let N and P be manifolds. Then, the set of all proper C0-
+stable mappings is dense in C∞
+pr(N, P).
+Theorem 1.5 implies that the set of all C0-stable mappings is always dense in
+C∞(N, P) if N is compact. In this paper, we give the following result in the case
+where N is non-compact.
+Theorem 1.6. Let N be a non-compact manifold, and P a manifold. Then, the
+set of all C0-stable mappings is never dense in C∞(N, P).
+In Section 2, we state a more essential result (see Theorem 2.2) than Theorem 1.6
+by using the notion of topologically critical points, which is the main theorem of
+this paper, and Theorem 1.6 follows from the result as a corollary. We note that
+Theorem 1.6 implies Theorem 1.3 since any C∞-stable mapping is C0-stable. By
+combining Mather’s theorem on C0-stability (Theorem 1.5) and Theorem 1.6, we
+also obtain a characterization of the density of C0-stable mappings in C∞(N, P) in
+the case where N is not necessarily compact as follows:
+Corollary 1.7. Let N and P be manifolds. Then, the set of all C0-stable mappings
+is dense in C∞(N, P) if and only if N is compact.
+The remainder of this paper is organized as follows. In Section 2, we state the
+main theorem, which is a more essential result than Theorem 1.6, and preparations
+for the proof. In Section 3, we show the main theorem.
+2. Main theorem and preparations for the proof
+Let N and P be manifolds, and f : N → P a mapping. A point q ∈ N is called
+a topologically critical point (resp. critical point) of f if f|U: U → P is not an open
+mapping for any open neighborhood U of q (resp. rank dfq < dim P). We give the
+following remark on topologically critical points.
+
+NON-DENSITY OF C0-STABLE MAPPINGS ON NON-COMPACT MANIFOLDS
+3
+Remark 2.1.
+(1) If q ∈ N is a topologically critical point of f : N → P, then
+q is a critical point as follows: Suppose that q ∈ N is not a critical point.
+Then, since rank dfq ≥ dim P, there exists an open neighborhood U such
+that f|U: U → P is an open mapping by the implicit function theorem,
+which contradicts the hypothesis that q is a topologically critical point.
+(2) A critical point is not necessarily a topologically critical point. For example,
+let f : R → R be the function defined by f(x) = x3. Then, x = 0 is a critical
+point of f, however the point is not a topologically critical point.
+(3) Suppose that f, g ∈ C∞(N, P) are C0-equivalent, that is, g = Ψ ◦ f ◦ Φ−1,
+where Φ : N → N and Ψ : P → P are homeomorphisms. If q ∈ N is a topo-
+logically critical point of f, then Φ(q) is a topologically critical point of g.
+Namely, topologically critical points can be preserved by homeomorphisms
+although usual critical points are not necessarily preserved by them.
+The following is the main theorem, and Theorem 1.6 is an easy consequence of
+this theorem.
+Theorem 2.2. Let N be a non-compact manifold, and P a manifold. Then, there
+exists a non-empty open subset U of C∞(N, P) such that for any positive integer
+d satisfying d ≥ 2,
+Ud = { f ∈ U | f has d topologically critical points with the same image }
+is dense in U . In particular, any mapping in U is not C0-stable.
+In Theorem 2.2, when we show that any mapping in U is not C0-stable, we use
+the simple fact that topologically critical points are preserved by homeomorphisms
+as mentioned in Remark 2.1(3), which is an advantage of topologically critical points
+compared to usual critical points.
+In what follows, for a given positive integer m, we denote the origin (0, . . . , 0) of
+Rm by 0, the Euclidean norm of x ∈ Rm by ∥x∥, and the m-dimensional open ball
+with center x ∈ Rm and radius r > 0 by Bm(x, r), that is,
+Bm(x, r) = { x′ ∈ Rm | ∥x − x′∥< r } .
+For a set (resp.
+a topological space) X and a subset A of X, we denote the
+complement of A (resp. the closure of A) by Ac (resp. A).
+The former assertion on a usual critical point of the following lemma is the same
+as [4, Lemma 2.1], and we update the lemma by adding the latter assertion on
+topologically critical points as follows:
+Lemma 2.3. Let f = (f1, . . . , fp) : Bn(0, r) → Rp (r > 0) be a mapping such that
+fp(x) = 1
+2
+n
+�
+i=1
+x2
+i + a,
+where a is a real number and x = (x1, . . . , xn). If g = (g1, . . . , gp) : Bn(0, r) → Rp
+satisfies
+�
+�
+�
+�
+n
+�
+i=1
+�∂fp
+∂xi
+(x) − ∂gp
+∂xi
+(x)
+�2
+< r
+2
+(2.1)
+for any x ∈ Bn(0, r), then there exists a critical point x0 of g in Bn(0, r). Moreover,
+if Hess(gp)x0 is positive definite, then x0 is a topologically critical point of g, where
+Hess(gp)x0 is the Hessian matrix of gp at x0.
+
+4
+SHUNSUKE ICHIKI
+Proof of Lemma 2.3. By the same proof as [4, Lemma 2.1], it follows that there ex-
+ists a critical point x0 of g in Bn(0, r) such that ∂gp
+∂xi (x0) = 0 for any i ∈ { 1, . . ., n }.
+Suppose that Hess(gp)x0 is positive definite. Since x0 is also a critical point of gp,
+there exists a coordinate neighborhood (U, ϕ) of Bn(0, r) containing x0 (ϕ(x0) =
+0 ∈ Rn) such that gp ◦ ϕ−1 : ϕ(U) → R has the following form:
+(gp ◦ ϕ−1)(t1, . . . , tn) = gp(x0) + t2
+1 + · · · + t2
+n,
+which implies that x0 is a topologically critical point of g.
+□
+3. Proof of the main theorem
+The proof is divided into the following three steps: In STEP 1, we construct
+the C∞ mapping f : N → P defined by (3.1). In STEP 2, we construct the open
+neighborhood U of f in C∞(N, P) given by (3.3), and we provide a lemma on
+properties of a mapping in U (see Lemma 3.1). Finally, in STEP 3, after preparing
+two lemmas (Lemmas 3.2 and 3.3), we show that Ud is dense in U , and by using
+this assertion and the simple fact that topologically critical points are preserved by
+homeomorphisms, we prove that any mapping in U is not C0-stable.
+The method of the proof is almost the same as that of Theorem 1.3, but the
+most important difference is the addition of condition (c) in the definition of Oα in
+(3.2) of STEP 2 to deal with topological critical points instead of ordinary critical
+points (more precisely, to use Lemma 2.3). In fact, in the proof of Theorem 1.3,
+there are only conditions (a) and (b) in the definition of Oα, and the open set U in
+(3.3) is defined by using an open subset of the 1-jet space J1(N, P). On the other
+hand, in this proof, since we add condition (c), we define U in (3.3) using an open
+set in the 2-jet space J2(N, P).
+STEP 1 is the same as that in Theorem 1.3, but is also described in this paper for
+the sake of readers’ convenience since in this first step we introduce some symbols
+that will be subsequently used.
+STEP 1. Set n = dim N, p = dim P and ℓ = 2n + 1. By Whitney’s embedding
+theorem, there exist an embedding F : N → Rℓ such that F(N) is a closed subset
+of Rℓ. Then, there exists a point z0 ∈ Rℓ \ F(N). Since N is non-compact, F(N)
+is also non-compact. Thus, F(N) is not bounded, which implies that there exists a
+sequence { Rα }α∈N of positive real numbers and a sequence { zα }α∈N of points in
+Rℓ such that
+• Rα < Rα+1 for any α ∈ N and lim
+α→∞ Rα = ∞,
+• zα ∈ F(N) ∩ (Bℓ(z0, Rα+1) \ Bℓ(z0, Rα)) for any α ∈ N.
+Let α be a positive integer. Set qα = F −1(zα). Here, note that
+F −1(Bℓ(z0, Rα+1) \ Bℓ(z0, Rα))
+is an open neighborhood of qα.
+Then, there exists a coordinate neighborhood
+(Uα, ϕα) of N with the following properties:
+• Uα is compact,
+• qα ∈ Uα ⊂ F −1(Bℓ(z0, Rα+1) \ Bℓ(z0, Rα)),
+• ϕα(qα) = 0 ∈ Rn.
+Moreover, there exist an open neighborhood U ′
+α of qα and ρα : N → R (0 ≤ ρα(q) ≤
+1) such that
+• U ′α ⊂ Uα,
+
+NON-DENSITY OF C0-STABLE MAPPINGS ON NON-COMPACT MANIFOLDS
+5
+• ρα(q) = 1 for any q ∈ U ′α,
+• supp ρα ⊂ Uα,
+where supp ρα = { q ∈ N | ρα(q) ̸= 0 }. Notice that supp ρα is compact since Uα is
+compact. By choosing U ′
+α smaller for each α ∈ N we can assume that
+• ϕα(U ′
+α) = Bn(0, rα),
+•
+lim
+α→∞ rα = 0,
+where each rα is a positive real number.
+Let γ = (γ1, . . . , γp) : N → Qp be a bijection, and let ηα : ϕα(Uα) → Rp be the
+mapping defined by
+ηα(x) =
+�
+γ1(α), . . . , γp−1(α), 1
+2
+n
+�
+i=1
+x2
+i + γp(α)
+�
+for each α ∈ N, where x = (x1, . . . , xn). Let (V, ψ) be a coordinate neighborhood of
+P that satisfies ψ(V ) = Rp. Since Uα ∩ Uβ = ∅ if α ̸= β, we can define f : N → P
+as follows:
+f(q) =
+
+
+
+ψ−1(ρα(q)(ηα ◦ ϕα)(q))
+if q ∈ Uα,
+ψ−1(0)
+if q ̸∈ �
+α∈N Uα.
+(3.1)
+We show that f is of class C∞. Let q ∈ N be any point. If q ∈ �
+α∈N Uα, then
+by the definition of f it is clear that f is of class C∞ at q. Thus, we consider
+the case q ∈ (�
+α∈N Uα)c.
+Since
+lim
+α→∞ Rα = ∞, there exists β ∈ N such that
+q ∈ F −1(Bℓ(z0, Rβ)). For simplicity, set
+A = F −1(Bℓ(z0, Rβ)) ∩
+� �
+α∈N
+supp ρα
+�c
+.
+Note that q ∈ A. Since Rα < Rα+1 for any α ∈ N, we have
+F −1(Bℓ(z0, Rβ)) ⊂ (supp ρα)c
+for each α ∈ N satisfying α > β. Thus, we obtain
+A = F −1(Bℓ(z0, Rβ)) ∩
+� �
+α∈N
+(supp ρα)c
+�
+= F −1(Bℓ(z0, Rβ)) ∩
+
+ �
+α≤β
+(supp ρα)c
+
+ ,
+which implies that A is an open subset of N. Since ρα|A is a constant function with
+a constant value 0 for each α ∈ N, the mapping f|A is also constant. Thus, f is of
+class C∞ at q.
+STEP 2. In this step, we construct the open neighborhood U of f in C∞(N, P)
+given by (3.3), and we provide a lemma on properties of a mapping in U . Since
+z0 ∈ Rℓ \ F(N), we can define the following continuous function δ : N → R:
+δ(q) =
+1
+∥F(q) − z0∥.
+Let π : J2(N, P) → N×P be the natural projection defined by π(j2g(q)) = (q, g(q)).
+Then, for each α ∈ N, set
+
+6
+SHUNSUKE ICHIKI
+Oα = { j2g(q) ∈ π−1(Uα × V ) | j2g(q) satisfies (a), (b) and (c) } ,
+(3.2)
+where
+(a) ∥(ψ ◦ f)(q) − (ψ ◦ g)(q)∥ < δ(q),
+(b)
+�
+�
+�
+�
+n
+�
+i=1
+�∂(ψp ◦ f ◦ ϕ−1
+α )
+∂xi
+(ϕα(q)) − ∂(ψp ◦ g ◦ ϕ−1
+α )
+∂xi
+(ϕα(q))
+�2
+< rα
+2 ,
+(c) Hess(ψp ◦ g ◦ ϕ−1
+α )ϕα(q) is positive definite,
+where ψp is the p-th component of ψ. From (a), (b) and (c), it is not hard to see
+that Oα is an open subset of J2(N, P).
+We prove that �
+α∈N(U ′α)c is an open subset of N. Let q ∈ �
+α∈N(U ′α)c be any
+point. Since lim
+α→∞ Rα = ∞, there exists β ∈ N such that q ∈ F −1(Bℓ(z0, Rβ)).
+Since Rα < Rα+1 for each α ∈ N, we obtain F −1(Bℓ(z0, Rβ)) ⊂ (U ′α)c for any
+α ∈ N satisfying α > β, which implies that
+F −1(Bℓ(z0, Rβ)) ∩
+
+ �
+α≤β
+(U ′α)c
+
+ ⊂
+�
+α∈N
+(U ′α)c.
+Since the left-hand side of the above expression is an open neighborhood of q, it
+follows that �
+α∈N(U ′α)c is open. Thus, since π is continuous,
+O :=
+� �
+α∈N
+Oα
+�
+∪ π−1
+�� �
+α∈N
+�
+U ′α
+�c
+�
+× V
+�
+is open in J2(N, P).
+Therefore, we can construct the following open subset of
+C∞(N, P):
+U := { g ∈ C∞(N, P) | j2g(N) ⊂ O } .
+(3.3)
+By showing that j2f(N) ⊂ O, we will prove that U ̸= ∅. Let j2f(q) (q ∈ N) be any
+element of j2f(N). If there exists α ∈ N such that q ∈ Uα, then j2f(q) ∈ Oα (⊂ O)
+since f(q) ∈ V and j2f(q) clearly satisfies (a), (b) and (c). When q ̸∈ �
+α∈N Uα,
+since
+N =
+� �
+α∈N
+Uα
+�
+∪
+� �
+α∈N
+�
+U ′α
+�c
+�
+,
+(3.4)
+it must follow that q ∈ �
+α∈N
+�
+U ′α
+�c. Therefore, since f(q) ∈ V , we obtain
+j2f(q) ∈ π−1
+�� �
+α∈N
+(U ′α)c
+�
+× V
+�
+(⊂ O),
+which implies that U ̸= ∅.
+The following lemma describes properties of a mapping in U and it is an upgrade
+of [4, Lemma 3.1] to a claim about a topological critical point instead of a usual
+critical point.
+Lemma 3.1. For any mapping g ∈ U , we have g(N) ⊂ V and there exists a
+sequence { q′
+α }α∈N of points in N with the following properties.
+(1) For each α ∈ N, q′
+α is a topologically critical point of g in U ′
+α.
+
+NON-DENSITY OF C0-STABLE MAPPINGS ON NON-COMPACT MANIFOLDS
+7
+(2) The set { g(q′
+α) | α ∈ N } is dense in V .
+Proof of Lemma 3.1. From the definition of U , we have g(N) ⊂ V .
+Let α be any positive integer. Then, we have
+(ψp ◦ f ◦ ϕ−1
+α )(x) = 1
+2
+n
+�
+i=1
+x2
+i + γp(α)
+for any x = (x1, . . . , xn) ∈ ϕα(U ′
+α) (= Bn(0, rα)).
+For any q ∈ U ′
+α, we obtain
+j2g(q) ∈ Oα since we have (3.4) and U ′
+α is contained in Uα which does not intersect
+with Uβ (β ̸= α). Hence, (ψp ◦ g ◦ ϕ−1
+α )|Bn(0,rα) satisfies (b) and (c), which implies
+that there exists a topologically critical point of (ψp ◦ g ◦ ϕ−1
+α )|Bn(0,rα) in Bn(0, rα)
+by Lemma 2.3. Namely, there exists a topologically critical point of g in U ′
+α. We
+denote this point by q′
+α.
+Since { q′
+α }α∈N satisfies (1), it is sufficient to prove that the sequence of points
+also satisfies (2). Let V ′ be any open subset of V . We show that { g(q′
+α) | α ∈ N }∩
+V ′ ̸= ∅. Then, by choosing V ′ smaller, we can assume that ψ(V ′) = Bp(y0, ε),
+where y0 is a point of Rp and ε is a positive real number. Note that for each α ∈ N,
+we have
+∥(ψ ◦ g)(q′
+α) − y0∥ ≤ ∥(ψ ◦ g)(q′
+α) − (ψ ◦ f)(q′
+α)∥ +
+∥(ψ ◦ f)(q′
+α) − (ψ ◦ f)(qα)∥ + ∥(ψ ◦ f)(qα) − y0∥ .
+(3.5)
+Since
+δ(q′
+α) =
+1
+∥F(q′α) − z0∥ <
+1
+Rα
+for any α ∈ N and lim
+α→∞ Rα = ∞, there exists α1 ∈ N such that δ(q′
+α) < ε
+3 for any
+α ∈ N satisfying α ≥ α1. Here, note that for each α ∈ N, we get
+∥(ψ ◦ g)(q′
+α) − (ψ ◦ f)(q′
+α)∥ < δ(q′
+α)
+by (a) since j2g(q′
+α) ∈ Oα. Thus, it follows that for any α ∈ N,
+α ≥ α1 =⇒ ∥(ψ ◦ g)(q′
+α) − (ψ ◦ f)(q′
+α)∥ < ε
+3.
+(3.6)
+For each α ∈ N, since qα, q′
+α ∈ U ′
+α, we have
+∥(ψ ◦ f)(q′
+α) − (ψ ◦ f)(qα)∥ = ∥ηα(ϕα(q′
+α)) − γ(α)∥ = ∥ϕα(q′
+α)∥2
+2
+< r2
+α
+2 .
+Since lim
+α→∞ rα = 0, there exists α2 ∈ N such that for any α ∈ N,
+α ≥ α2 =⇒ ∥(ψ ◦ f)(q′
+α) − (ψ ◦ f)(qα)∥ < ε
+3.
+(3.7)
+Since (ψ ◦ f)(qα) = γ(α) for each α ∈ N, we have
+{ (ψ ◦ f)(qα) | α ∈ N } = Qp.
+Hence, there exists α3 ∈ N such that α3 > max { α1, α2 } and
+∥(ψ ◦ f)(qα3) − y0∥ < ε
+3.
+(3.8)
+Thus, we get
+��(ψ ◦ g)(q′
+α3) − y0
+�� < ε by (3.5) to (3.8), which implies that g(q′
+α3) ∈
+V ′.
+□
+
+8
+SHUNSUKE ICHIKI
+STEP 3. The purpose of this step is to show that Ud is dense in U , where d ≥ 2
+is a given integer. Let g ∈ U be an arbitrary mapping, and let Ug be any open
+neighborhood of g. Then, there exist a non-negative integer k and an open set O′
+of Jk(N, P) such that
+g ∈ { h ∈ C∞(N, P) | jkh(N) ⊂ O′ } ⊂ Ug.
+For the proof, it is sufficient to show that there exists a mapping h ∈ Ud such that
+jkh(N) ⊂ O′.
+For any α ∈ N and c ∈ Rp, let Gα,c : N → P be the mapping defined by
+Gα,c = ψ−1 ◦ (ψ ◦ g + ραc).
+Lemma 3.2 ([4, Lemma 3.2]). Let α be any positive integer. Then, there exists a
+positive real number r′
+α such that jkGα,c(N) ⊂ O′ for any c ∈ Bp(0, r′
+α).
+Since g ∈ U , note that there exists a sequence { q′
+α }α∈N of points in N satisfying
+(1) and (2) of Lemma 3.1. The following lemma can be also shown by the same
+method as [4, Lemma 3.3].
+Lemma 3.3. Let m be any positive integer. Then, there exist (m + 1) distinct
+positive integers α1, . . . , αm+1 and m positive real numbers r′
+α1, . . . , r′
+αm (r′
+α1 >
+· · · > r′
+αm) such that for any j ∈ { 1, . . ., m },
+(1) jkGαj,c(N) ⊂ O′ for any c ∈ Bp(0, r′
+αj),
+(2)
+���(ψ ◦ g)(q′
+αj+1) − (ψ ◦ g)(q′
+αj)
+��� <
+r′
+αj
+d − 1, where d ≥ 2 is given in Theorem 2.2.
+Proof of Lemma 3.3. We will prove this lemma by induction on m.
+Let α1 be a positive integer. By Lemma 3.2, there exists a positive real number
+r′
+α1 such that jkGα1,c(N) ⊂ O′ for any c ∈ Bp(0, r′
+α1). From Lemma 3.1 (2), there
+exists α2 ∈ N \ { α1 } satisfying
+��(ψ ◦ g)(q′
+α2) − (ψ ◦ g)(q′
+α1)
+�� <
+r′
+α1
+d − 1.
+Thus, the case m = 1 holds.
+We assume that the lemma holds for m = i, where i is a positive integer. By
+Lemma 3.2, there exists a positive real number r′
+αi+1 (r′
+αi > r′
+αi+1) such that
+jkGαi+1,c(N) ⊂ O′ for any c ∈ Bp(0, r′
+αi+1).
+From Lemma 3.1 (2), there ex-
+ists αi+2 ∈ N \ { α1, . . . , αi+1 } satisfying
+���(ψ ◦ g)(q′
+αi+2) − (ψ ◦ g)(q′
+αi+1)
+��� <
+r′
+αi+1
+d−1 .
+Therefore, the case m = i + 1 holds.
+□
+For simplicity, set I = { 1, . . . , d − 1 }. By Lemma 3.3 in the case m = d − 1,
+there exist d distinct positive integers α1, . . . , αd and d − 1 positive real numbers
+r′
+α1, . . . , r′
+αd−1 (r′
+α1 > · · · > r′
+αd−1) such that for any j ∈ I,
+(d) jkGαj,c(N) ⊂ O′ for any c ∈ Bp(0, r′
+αj),
+(e)
+���(ψ ◦ g)(q′
+αj+1) − (ψ ◦ g)(q′
+αj)
+��� <
+r′
+αj
+d − 1.
+Let h : N → P be the mapping defined by
+h = ψ−1 ◦
+�
+ψ ◦ g +
+d−1
+�
+i=1
+ραici
+�
+,
+
+NON-DENSITY OF C0-STABLE MAPPINGS ON NON-COMPACT MANIFOLDS
+9
+where ci = (ψ ◦ g)(q′
+αd) − (ψ ◦ g)(q′
+αi) ∈ Rp.
+First, we show that jkh(N) ⊂ O′. Let q ∈ N be an arbitrary point. In the case
+where q is an element of (�d−1
+j=1 supp ραj)c, since h = g on the open neighborhood
+(�d−1
+j=1 supp ραj)c of q, we have jkh(q) = jkg(q) ∈ O′. We consider the case where
+there exists j ∈ I satisfying q ∈ supp ραj. Since supp ραj ⊂ �
+i∈I\{ j }(supp ραi)c
+and h = Gαj,cj on the open neighborhood �
+i∈I\{ j }(supp ραi)c of q, we obtain
+jkh(q) = jkGαj,cj(q). Moreover, since
+∥cj∥ =
+���(ψ ◦ g)(q′
+αd) − (ψ ◦ g)(q′
+αj)
+���
+≤
+d−1
+�
+i=j
+���(ψ ◦ g)(q′
+αi+1) − (ψ ◦ g)(q′
+αi)
+���
+<
+d−1
+�
+i=j
+r′
+αi
+d − 1
+≤ r′
+αj,
+(3.9)
+we have cj ∈ Bp(0, r′
+αj). The last two inequalities in (3.9) follow from (e) and
+r′
+αj > · · · > r′
+αd−1, respectively. Thus, we obtain jkGαj,cj(q) ∈ O′ by (d), which
+implies that jkh(q) ∈ O′.
+Now, we show that h ∈ Ud. For any i, j ∈ I, since ραi(q′
+αj) = δij and ραi(q′
+αd) =
+0, we obtain
+�
+ψ ◦ g +
+d−1
+�
+i=1
+ραici
+�
+(q′
+αj) = (ψ ◦ g)(q′
+αj) + cj = (ψ ◦ g)(q′
+αd) = (ψ ◦ h)(q′
+αd),
+where δij is the Kronecker delta. Thus, we have h(q′
+α1) = · · · = h(q′
+αd). Moreover,
+for any j ∈ I, the point q′
+αj (resp. q′
+αd) is a topologically critical point of h since
+h = ψ−1 ◦ (ψ ◦ g + cj) on an open neighborhood of q′
+αj (resp. h = g on an open
+neighborhood of q′
+αd). Therefore, we obtain h ∈ Ud.
+Finally, we will show that any mapping in U is not C0-stable. Suppose that there
+exists a C0-stable mapping ˜g in U . Then, there exists an open neighborhood U˜g of ˜g
+such that any mapping in U˜g is C0-equivalent to ˜g. Since we have shown that Up+1
+is dense in U , and topologically critical points are preserved by homeomorphisms
+as mentioned in Remark 2.1(3), any mapping in U˜g has (p+1) topologically critical
+points with the same image. This contradicts the fact that the set of all mappings
+with normal crossings is dense in C∞(N, P).
+✷
+Acknowledgements
+The author would like to thank Toru Ohmoto for his kind comments. This work
+was supported by JSPS KAKENHI Grant Number JP21K13786.
+References
+[1] Alexandru Dimca. Morse functions and stable mappings. Rev. Roumaine Math. Pures Appl.,
+24(9):1293–1297, 1979.
+[2] Andrew du Plessis and Terry Wall. The geometry of topological stability, volume 9 of London
+Mathematical Society Monographs. New Series. Oxford Science Publications. The Clarendon
+Press, Oxford University Press, New York, 1995.
+
+10
+SHUNSUKE ICHIKI
+[3] Christopher G. Gibson, Klaus Wirthm¨uller, Andrew A. du Plessis, and Eduard J. N. Looi-
+jenga. Topological stability of smooth mappings, volume 552 of Lecture Notes in Mathematics.
+Springer-Verlag, Berlin-New York, 1976.
+[4] Shunsuke Ichiki. Non-density of stable mappings on non-compact manifolds. to appear in
+Pure Appl. Math. Q., https://arxiv.org/abs/2109.08760
+[5] John Norman Mather. Stability of C∞ mappings. I. The division theorem. Ann. of Math.
+(2), 87:89–104, 1968.
+[6] John Norman Mather. Stability of C∞ mappings. III. Finitely determined mapgerms. Inst.
+Hautes ´Etudes Sci. Publ. Math., 35:279–308, 1968.
+[7] John Norman Mather. Stability of C∞ mappings. II. Infinitesimal stability implies stability.
+Ann. of Math. (2), 89:254–291, 1969.
+[8] John Norman Mather. Stability of C∞ mappings. IV. Classification of stable germs by R-
+algebras. Inst. Hautes ´Etudes Sci. Publ. Math., (2) 37:223–248, 1969.
+[9] John Norman Mather. Stability of C∞ mappings. V. Transversality. Advances in Math.,
+4:301–336, 1970.
+[10] John Norman Mather. Stability of C∞ mappings. VI. The nice dimensions. Proceedings of
+Liverpool Singularities-Symposium, I. Lecture Notes in Math., 192:207–253, 1971.
+[11] John Norman Mather. Stratifications and mappings. Dynamical systems (Proc. Sympos.,
+Univ. Bahia, Salvador, 1971), 195–232, 1973.
+[12] Maria Aparecida Soares Ruas. Old and new results on density of stable mappings, volume
+552 of Handbook of geometry and topology of singularities III. Springer, Cham, 2022.
+Department of Mathematical and Computing Science, School of Computing, Tokyo
+Institute of Technology, Tokyo 152-8552, Japan
+Email address: ichiki@c.titech.ac.jp
+
diff --git a/UtAzT4oBgHgl3EQflv2x/content/tmp_files/load_file.txt b/UtAzT4oBgHgl3EQflv2x/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c4f76df5a7bd68d70801c6237e703eb4a1fd3b2e
--- /dev/null
+++ b/UtAzT4oBgHgl3EQflv2x/content/tmp_files/load_file.txt
@@ -0,0 +1,426 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf,len=425
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='01553v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='GT]  4 Jan 2023  NON-DENSITY OF C0-STABLE MAPPINGS  ON NON-COMPACT MANIFOLDS  SHUNSUKE ICHIKI  Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' In 1973, Mather showed that the set of proper C0-stable mappings  is dense in the set of all proper mappings, which implies that the set of C0-  stable mappings is dense in the set of all mappings if the source manifold is  compact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' In this paper, we show that the set of C0-stable mappings is never  dense in the set of all mappings if the source manifold is non-compact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' To  prove it, we provide a more essential result by using the notion of topologically  critical points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Introduction  Let N and P be C∞-manifolds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Two C∞-mappings f and g from N into P are  said to be C∞-equivalent (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' C0-equivalent) if there exist C∞-diffeomorphisms  (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' homeomorphisms) Φ : N → N and Ψ : P → P such that g = Ψ ◦ f ◦ Φ−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  We denote the space of all C∞-mappings of N into P (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' the space of all proper  C∞-mappings of N into P) endowed with the Whitney C∞-topology by C∞(N, P)  (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' C∞  pr(N, P)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' We say that f is C∞-stable (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' C0-stable) if there exists an  open neighborhood U of f such that any mapping in U is C∞-equivalent (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  C0-equivalent) to f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' In what follows, unless otherwise stated, all manifolds and  mappings are of class C∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  On the C∞-stability, in a celebrated series around 1970 [5, 6, 7, 8, 9, 10], Mather  established a significant theory and he gave a characterization of the density of  proper C∞-stable mappings in C∞  pr(N, P) as follows:  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='1 ([10]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Let N and P be manifolds of dimensions n and p, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Then, the set of all proper C∞-stable mappings is dense in C∞  pr(N, P) if and only  if the pair (n, p) satisfies one of the following conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  (1) n < 6  7p + 8  7 and p − n ≥ 4  (2) n < 6  7p + 9  7 and 3 ≥ p − n ≥ 0  (3) p < 8 and p − n = −1  (4) p < 6 and p − n = −2  (5) p < 7 and p − n ≤ −3  A dimension pair (n, p) is called nice if it satisfies one of the conditions (1)–(5)  in Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Since C∞  pr(N, P) = C∞(N, P) in the case where N is compact,  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='1 yields a characterization of the density of C∞-stable mappings in  C∞(N, P) in the case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  2020 Mathematics Subject Classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' 57R45, 58K30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Key words and phrases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' C0-stable mapping, Whitney C∞-topology, topologically critical  point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  1  2  SHUNSUKE ICHIKI  After that, the case where a source manifold is non-compact was considered by  Dimca, and in 1979, he gave the following result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='2 ([1]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Let N be a non-compact manifold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Then, the set of all  C∞-stable mappings is not dense in C∞(N, R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Then, in [4], for a non-compact source manifold N and an arbitrary target man-  ifold P, the following has been shown rigorously:  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='3 ([4]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Let N be a non-compact manifold, and P a manifold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Then,  the set of all C∞-stable mappings is never dense in C∞(N, P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  By combining Mather’s theorem (Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='1) and Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='3, we obtain the  following characterization of the density of C∞-stable mappings in C∞(N, P) in  the case where N is not necessarily compact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Corollary 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='4 ([10, 4]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Let N and P be manifolds of dimensions n and p, respec-  tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Then, the set of all C∞-stable mappings is dense in C∞(N, P) if and only  if N is compact and (n, p) is nice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  On the C0-stability, Mather established the following theorem in 1973, which is  so significant as well as Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='1, and the bibles [2, 3, 12] have been published.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='5 ([11]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Let N and P be manifolds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Then, the set of all proper C0-  stable mappings is dense in C∞  pr(N, P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='5 implies that the set of all C0-stable mappings is always dense in  C∞(N, P) if N is compact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' In this paper, we give the following result in the case  where N is non-compact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Let N be a non-compact manifold, and P a manifold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Then, the  set of all C0-stable mappings is never dense in C∞(N, P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  In Section 2, we state a more essential result (see Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='2) than Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='6  by using the notion of topologically critical points, which is the main theorem of  this paper, and Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='6 follows from the result as a corollary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' We note that  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='6 implies Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='3 since any C∞-stable mapping is C0-stable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' By  combining Mather’s theorem on C0-stability (Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='5) and Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='6, we  also obtain a characterization of the density of C0-stable mappings in C∞(N, P) in  the case where N is not necessarily compact as follows:  Corollary 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Let N and P be manifolds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Then, the set of all C0-stable mappings  is dense in C∞(N, P) if and only if N is compact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  The remainder of this paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' In Section 2, we state the  main theorem, which is a more essential result than Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='6, and preparations  for the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' In Section 3, we show the main theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Main theorem and preparations for the proof  Let N and P be manifolds, and f : N → P a mapping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' A point q ∈ N is called  a topologically critical point (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' critical point) of f if f|U: U → P is not an open  mapping for any open neighborhood U of q (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' rank dfq < dim P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' We give the  following remark on topologically critical points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  NON-DENSITY OF C0-STABLE MAPPINGS ON NON-COMPACT MANIFOLDS  3  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  (1) If q ∈ N is a topologically critical point of f : N → P, then  q is a critical point as follows: Suppose that q ∈ N is not a critical point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Then, since rank dfq ≥ dim P, there exists an open neighborhood U such  that f|U: U → P is an open mapping by the implicit function theorem,  which contradicts the hypothesis that q is a topologically critical point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  (2) A critical point is not necessarily a topologically critical point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' For example,  let f : R → R be the function defined by f(x) = x3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Then, x = 0 is a critical  point of f, however the point is not a topologically critical point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  (3) Suppose that f, g ∈ C∞(N, P) are C0-equivalent, that is, g = Ψ ◦ f ◦ Φ−1,  where Φ : N → N and Ψ : P → P are homeomorphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' If q ∈ N is a topo-  logically critical point of f, then Φ(q) is a topologically critical point of g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Namely, topologically critical points can be preserved by homeomorphisms  although usual critical points are not necessarily preserved by them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  The following is the main theorem, and Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='6 is an easy consequence of  this theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Let N be a non-compact manifold, and P a manifold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Then, there  exists a non-empty open subset U of C∞(N, P) such that for any positive integer  d satisfying d ≥ 2,  Ud = { f ∈ U | f has d topologically critical points with the same image }  is dense in U .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' In particular, any mapping in U is not C0-stable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  In Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='2, when we show that any mapping in U is not C0-stable, we use  the simple fact that topologically critical points are preserved by homeomorphisms  as mentioned in Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='1(3), which is an advantage of topologically critical points  compared to usual critical points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  In what follows, for a given positive integer m, we denote the origin (0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' , 0) of  Rm by 0, the Euclidean norm of x ∈ Rm by ∥x∥, and the m-dimensional open ball  with center x ∈ Rm and radius r > 0 by Bm(x, r), that is,  Bm(x, r) = { x′ ∈ Rm | ∥x − x′∥< r } .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  For a set (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  a topological space) X and a subset A of X, we denote the  complement of A (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' the closure of A) by Ac (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  The former assertion on a usual critical point of the following lemma is the same  as [4, Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='1], and we update the lemma by adding the latter assertion on  topologically critical points as follows:  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Let f = (f1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' , fp) : Bn(0, r) → Rp (r > 0) be a mapping such that  fp(x) = 1  2  n  �  i=1  x2  i + a,  where a is a real number and x = (x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' , xn).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' If g = (g1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' , gp) : Bn(0, r) → Rp  satisfies  �  �  �  �  n  �  i=1  �∂fp  ∂xi  (x) − ∂gp  ∂xi  (x)  �2  < r  2  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='1)  for any x ∈ Bn(0, r), then there exists a critical point x0 of g in Bn(0, r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Moreover,  if Hess(gp)x0 is positive definite, then x0 is a topologically critical point of g, where  Hess(gp)x0 is the Hessian matrix of gp at x0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  4  SHUNSUKE ICHIKI  Proof of Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' By the same proof as [4, Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='1], it follows that there ex-  ists a critical point x0 of g in Bn(0, r) such that ∂gp  ∂xi (x0) = 0 for any i ∈ { 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=', n }.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Suppose that Hess(gp)x0 is positive definite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Since x0 is also a critical point of gp,  there exists a coordinate neighborhood (U, ϕ) of Bn(0, r) containing x0 (ϕ(x0) =  0 ∈ Rn) such that gp ◦ ϕ−1 : ϕ(U) → R has the following form:  (gp ◦ ϕ−1)(t1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' , tn) = gp(x0) + t2  1 + · · · + t2  n,  which implies that x0 is a topologically critical point of g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  □  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Proof of the main theorem  The proof is divided into the following three steps: In STEP 1, we construct  the C∞ mapping f : N → P defined by (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' In STEP 2, we construct the open  neighborhood U of f in C∞(N, P) given by (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='3), and we provide a lemma on  properties of a mapping in U (see Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Finally, in STEP 3, after preparing  two lemmas (Lemmas 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='2 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='3), we show that Ud is dense in U , and by using  this assertion and the simple fact that topologically critical points are preserved by  homeomorphisms, we prove that any mapping in U is not C0-stable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  The method of the proof is almost the same as that of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='3, but the  most important difference is the addition of condition (c) in the definition of Oα in  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='2) of STEP 2 to deal with topological critical points instead of ordinary critical  points (more precisely, to use Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' In fact, in the proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='3,  there are only conditions (a) and (b) in the definition of Oα, and the open set U in  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='3) is defined by using an open subset of the 1-jet space J1(N, P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' On the other  hand, in this proof, since we add condition (c), we define U in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='3) using an open  set in the 2-jet space J2(N, P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  STEP 1 is the same as that in Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='3, but is also described in this paper for  the sake of readers’ convenience since in this first step we introduce some symbols  that will be subsequently used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  STEP 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Set n = dim N, p = dim P and ℓ = 2n + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' By Whitney’s embedding  theorem, there exist an embedding F : N → Rℓ such that F(N) is a closed subset  of Rℓ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Then, there exists a point z0 ∈ Rℓ \\ F(N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Since N is non-compact, F(N)  is also non-compact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Thus, F(N) is not bounded, which implies that there exists a  sequence { Rα }α∈N of positive real numbers and a sequence { zα }α∈N of points in  Rℓ such that  Rα < Rα+1 for any α ∈ N and lim  α→∞ Rα = ∞,  zα ∈ F(N) ∩ (Bℓ(z0, Rα+1) \\ Bℓ(z0, Rα)) for any α ∈ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Let α be a positive integer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Set qα = F −1(zα).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Here, note that  F −1(Bℓ(z0, Rα+1) \\ Bℓ(z0, Rα))  is an open neighborhood of qα.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Then, there exists a coordinate neighborhood  (Uα, ϕα) of N with the following properties:  Uα is compact,  qα ∈ Uα ⊂ F −1(Bℓ(z0, Rα+1) \\ Bℓ(z0, Rα)),  ϕα(qα) = 0 ∈ Rn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Moreover, there exist an open neighborhood U ′  α of qα and ρα : N → R (0 ≤ ρα(q) ≤  1) such that  U ′α ⊂ Uα,  NON-DENSITY OF C0-STABLE MAPPINGS ON NON-COMPACT MANIFOLDS  5  ρα(q) = 1 for any q ∈ U ′α,  supp ρα ⊂ Uα,  where supp ρα = { q ∈ N | ρα(q) ̸= 0 }.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Notice that supp ρα is compact since Uα is  compact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' By choosing U ′  α smaller for each α ∈ N we can assume that  ϕα(U ′  α) = Bn(0, rα), lim  α→∞ rα = 0,  where each rα is a positive real number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Let γ = (γ1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' , γp) : N → Qp be a bijection, and let ηα : ϕα(Uα) → Rp be the  mapping defined by  ηα(x) =  �  γ1(α), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' , γp−1(α), 1  2  n  �  i=1  x2  i + γp(α)  �  for each α ∈ N, where x = (x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' , xn).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Let (V, ψ) be a coordinate neighborhood of  P that satisfies ψ(V ) = Rp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Since Uα ∩ Uβ = ∅ if α ̸= β, we can define f : N → P  as follows:  f(q) =  \uf8f1  \uf8f2  \uf8f3  ψ−1(ρα(q)(ηα ◦ ϕα)(q))  if q ∈ Uα,  ψ−1(0)  if q ̸∈ �  α∈N Uα.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='1)  We show that f is of class C∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Let q ∈ N be any point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' If q ∈ �  α∈N Uα, then  by the definition of f it is clear that f is of class C∞ at q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Thus, we consider  the case q ∈ (�  α∈N Uα)c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Since  lim  α→∞ Rα = ∞, there exists β ∈ N such that  q ∈ F −1(Bℓ(z0, Rβ)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' For simplicity, set  A = F −1(Bℓ(z0, Rβ)) ∩  � �  α∈N  supp ρα  �c  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Note that q ∈ A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Since Rα < Rα+1 for any α ∈ N, we have  F −1(Bℓ(z0, Rβ)) ⊂ (supp ρα)c  for each α ∈ N satisfying α > β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Thus, we obtain  A = F −1(Bℓ(z0, Rβ)) ∩  � �  α∈N  (supp ρα)c  �  = F −1(Bℓ(z0, Rβ)) ∩  \uf8eb  \uf8ed �  α≤β  (supp ρα)c  \uf8f6  \uf8f8 ,  which implies that A is an open subset of N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Since ρα|A is a constant function with  a constant value 0 for each α ∈ N, the mapping f|A is also constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Thus, f is of  class C∞ at q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  STEP 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' In this step, we construct the open neighborhood U of f in C∞(N, P)  given by (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='3), and we provide a lemma on properties of a mapping in U .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Since  z0 ∈ Rℓ \\ F(N), we can define the following continuous function δ : N → R:  δ(q) =  1  ∥F(q) − z0∥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Let π : J2(N, P) → N×P be the natural projection defined by π(j2g(q)) = (q, g(q)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Then, for each α ∈ N, set  6  SHUNSUKE ICHIKI  Oα = { j2g(q) ∈ π−1(Uα × V ) | j2g(q) satisfies (a), (b) and (c) } ,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='2)  where  (a) ∥(ψ ◦ f)(q) − (ψ ◦ g)(q)∥ < δ(q),  (b)  �  �  �  �  n  �  i=1  �∂(ψp ◦ f ◦ ϕ−1  α )  ∂xi  (ϕα(q)) − ∂(ψp ◦ g ◦ ϕ−1  α )  ∂xi  (ϕα(q))  �2  < rα  2 ,  (c) Hess(ψp ◦ g ◦ ϕ−1  α )ϕα(q) is positive definite,  where ψp is the p-th component of ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' From (a), (b) and (c), it is not hard to see  that Oα is an open subset of J2(N, P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  We prove that �  α∈N(U ′α)c is an open subset of N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Let q ∈ �  α∈N(U ′α)c be any  point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Since lim  α→∞ Rα = ∞, there exists β ∈ N such that q ∈ F −1(Bℓ(z0, Rβ)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Since Rα < Rα+1 for each α ∈ N, we obtain F −1(Bℓ(z0, Rβ)) ⊂ (U ′α)c for any  α ∈ N satisfying α > β, which implies that  F −1(Bℓ(z0, Rβ)) ∩  \uf8eb  \uf8ed �  α≤β  (U ′α)c  \uf8f6  \uf8f8 ⊂  �  α∈N  (U ′α)c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Since the left-hand side of the above expression is an open neighborhood of q, it  follows that �  α∈N(U ′α)c is open.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Thus, since π is continuous,  O :=  � �  α∈N  Oα  �  ∪ π−1  �� �  α∈N  �  U ′α  �c  �  × V  �  is open in J2(N, P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Therefore, we can construct the following open subset of  C∞(N, P):  U := { g ∈ C∞(N, P) | j2g(N) ⊂ O } .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='3)  By showing that j2f(N) ⊂ O, we will prove that U ̸= ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Let j2f(q) (q ∈ N) be any  element of j2f(N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' If there exists α ∈ N such that q ∈ Uα, then j2f(q) ∈ Oα (⊂ O)  since f(q) ∈ V and j2f(q) clearly satisfies (a), (b) and (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' When q ̸∈ �  α∈N Uα,  since  N =  � �  α∈N  Uα  �  ∪  � �  α∈N  �  U ′α  �c  �  ,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='4)  it must follow that q ∈ �  α∈N  �  U ′α  �c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Therefore, since f(q) ∈ V , we obtain  j2f(q) ∈ π−1  �� �  α∈N  (U ′α)c  �  × V  �  (⊂ O),  which implies that U ̸= ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  The following lemma describes properties of a mapping in U and it is an upgrade  of [4, Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='1] to a claim about a topological critical point instead of a usual  critical point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' For any mapping g ∈ U , we have g(N) ⊂ V and there exists a  sequence { q′  α }α∈N of points in N with the following properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  (1) For each α ∈ N, q′  α is a topologically critical point of g in U ′  α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  NON-DENSITY OF C0-STABLE MAPPINGS ON NON-COMPACT MANIFOLDS  7  (2) The set { g(q′  α) | α ∈ N } is dense in V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Proof of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' From the definition of U , we have g(N) ⊂ V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Let α be any positive integer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Then, we have  (ψp ◦ f ◦ ϕ−1  α )(x) = 1  2  n  �  i=1  x2  i + γp(α)  for any x = (x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' , xn) ∈ ϕα(U ′  α) (= Bn(0, rα)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  For any q ∈ U ′  α, we obtain  j2g(q) ∈ Oα since we have (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='4) and U ′  α is contained in Uα which does not intersect  with Uβ (β ̸= α).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Hence, (ψp ◦ g ◦ ϕ−1  α )|Bn(0,rα) satisfies (b) and (c), which implies  that there exists a topologically critical point of (ψp ◦ g ◦ ϕ−1  α )|Bn(0,rα) in Bn(0, rα)  by Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Namely, there exists a topologically critical point of g in U ′  α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' We  denote this point by q′  α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Since { q′  α }α∈N satisfies (1), it is sufficient to prove that the sequence of points  also satisfies (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Let V ′ be any open subset of V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' We show that { g(q′  α) | α ∈ N }∩  V ′ ̸= ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Then, by choosing V ′ smaller, we can assume that ψ(V ′) = Bp(y0, ε),  where y0 is a point of Rp and ε is a positive real number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Note that for each α ∈ N,  we have  ∥(ψ ◦ g)(q′  α) − y0∥ ≤ ∥(ψ ◦ g)(q′  α) − (ψ ◦ f)(q′  α)∥ +  ∥(ψ ◦ f)(q′  α) − (ψ ◦ f)(qα)∥ + ∥(ψ ◦ f)(qα) − y0∥ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='5)  Since  δ(q′  α) =  1  ∥F(q′α) − z0∥ <  1  Rα  for any α ∈ N and lim  α→∞ Rα = ∞, there exists α1 ∈ N such that δ(q′  α) < ε  3 for any  α ∈ N satisfying α ≥ α1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Here, note that for each α ∈ N, we get  ∥(ψ ◦ g)(q′  α) − (ψ ◦ f)(q′  α)∥ < δ(q′  α)  by (a) since j2g(q′  α) ∈ Oα.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Thus, it follows that for any α ∈ N,  α ≥ α1 =⇒ ∥(ψ ◦ g)(q′  α) − (ψ ◦ f)(q′  α)∥ < ε  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='6)  For each α ∈ N, since qα, q′  α ∈ U ′  α, we have  ∥(ψ ◦ f)(q′  α) − (ψ ◦ f)(qα)∥ = ∥ηα(ϕα(q′  α)) − γ(α)∥ = ∥ϕα(q′  α)∥2  2  < r2  α  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Since lim  α→∞ rα = 0, there exists α2 ∈ N such that for any α ∈ N,  α ≥ α2 =⇒ ∥(ψ ◦ f)(q′  α) − (ψ ◦ f)(qα)∥ < ε  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='7)  Since (ψ ◦ f)(qα) = γ(α) for each α ∈ N, we have  { (ψ ◦ f)(qα) | α ∈ N } = Qp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Hence, there exists α3 ∈ N such that α3 > max { α1, α2 } and  ∥(ψ ◦ f)(qα3) − y0∥ < ε  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='8)  Thus, we get  ��(ψ ◦ g)(q′  α3) − y0  �� < ε by (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='5) to (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='8), which implies that g(q′  α3) ∈  V ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  □  8  SHUNSUKE ICHIKI  STEP 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' The purpose of this step is to show that Ud is dense in U , where d ≥ 2  is a given integer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Let g ∈ U be an arbitrary mapping, and let Ug be any open  neighborhood of g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Then, there exist a non-negative integer k and an open set O′  of Jk(N, P) such that  g ∈ { h ∈ C∞(N, P) | jkh(N) ⊂ O′ } ⊂ Ug.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  For the proof, it is sufficient to show that there exists a mapping h ∈ Ud such that  jkh(N) ⊂ O′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  For any α ∈ N and c ∈ Rp, let Gα,c : N → P be the mapping defined by  Gα,c = ψ−1 ◦ (ψ ◦ g + ραc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='2 ([4, Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='2]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Let α be any positive integer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Then, there exists a  positive real number r′  α such that jkGα,c(N) ⊂ O′ for any c ∈ Bp(0, r′  α).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Since g ∈ U , note that there exists a sequence { q′  α }α∈N of points in N satisfying  (1) and (2) of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' The following lemma can be also shown by the same  method as [4, Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Let m be any positive integer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Then, there exist (m + 1) distinct  positive integers α1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' , αm+1 and m positive real numbers r′  α1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' , r′  αm (r′  α1 >  · · > r′  αm) such that for any j ∈ { 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=', m },  (1) jkGαj,c(N) ⊂ O′ for any c ∈ Bp(0, r′  αj),  (2)  ���(ψ ◦ g)(q′  αj+1) − (ψ ◦ g)(q′  αj)  ��� <  r′  αj  d − 1, where d ≥ 2 is given in Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Proof of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' We will prove this lemma by induction on m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Let α1 be a positive integer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' By Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='2, there exists a positive real number  r′  α1 such that jkGα1,c(N) ⊂ O′ for any c ∈ Bp(0, r′  α1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' From Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='1 (2), there  exists α2 ∈ N \\ { α1 } satisfying  ��(ψ ◦ g)(q′  α2) − (ψ ◦ g)(q′  α1)  �� <  r′  α1  d − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Thus, the case m = 1 holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  We assume that the lemma holds for m = i, where i is a positive integer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' By  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='2, there exists a positive real number r′  αi+1 (r′  αi > r′  αi+1) such that  jkGαi+1,c(N) ⊂ O′ for any c ∈ Bp(0, r′  αi+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  From Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='1 (2), there ex-  ists αi+2 ∈ N \\ { α1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' , αi+1 } satisfying  ���(ψ ◦ g)(q′  αi+2) − (ψ ◦ g)(q′  αi+1)  ��� <  r′  αi+1  d−1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Therefore, the case m = i + 1 holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  □  For simplicity, set I = { 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' , d − 1 }.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' By Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='3 in the case m = d − 1,  there exist d distinct positive integers α1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' , αd and d − 1 positive real numbers  r′  α1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' , r′  αd−1 (r′  α1 > · · · > r′  αd−1) such that for any j ∈ I,  (d) jkGαj,c(N) ⊂ O′ for any c ∈ Bp(0, r′  αj),  (e)  ���(ψ ◦ g)(q′  αj+1) − (ψ ◦ g)(q′  αj)  ��� <  r′  αj  d − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Let h : N → P be the mapping defined by  h = ψ−1 ◦  �  ψ ◦ g +  d−1  �  i=1  ραici  �  ,  NON-DENSITY OF C0-STABLE MAPPINGS ON NON-COMPACT MANIFOLDS  9  where ci = (ψ ◦ g)(q′  αd) − (ψ ◦ g)(q′  αi) ∈ Rp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  First, we show that jkh(N) ⊂ O′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Let q ∈ N be an arbitrary point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' In the case  where q is an element of (�d−1  j=1 supp ραj)c, since h = g on the open neighborhood  (�d−1  j=1 supp ραj)c of q, we have jkh(q) = jkg(q) ∈ O′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' We consider the case where  there exists j ∈ I satisfying q ∈ supp ραj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Since supp ραj ⊂ �  i∈I\\{ j }(supp ραi)c  and h = Gαj,cj on the open neighborhood �  i∈I\\{ j }(supp ραi)c of q, we obtain  jkh(q) = jkGαj,cj(q).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Moreover, since  ∥cj∥ =  ���(ψ ◦ g)(q′  αd) − (ψ ◦ g)(q′  αj)  ���  ≤  d−1  �  i=j  ���(ψ ◦ g)(q′  αi+1) − (ψ ◦ g)(q′  αi)  ���  <  d−1  �  i=j  r′  αi  d − 1  ≤ r′  αj,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='9)  we have cj ∈ Bp(0, r′  αj).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' The last two inequalities in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='9) follow from (e) and  r′  αj > · · · > r′  αd−1, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Thus, we obtain jkGαj,cj(q) ∈ O′ by (d), which  implies that jkh(q) ∈ O′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Now, we show that h ∈ Ud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' For any i, j ∈ I, since ραi(q′  αj) = δij and ραi(q′  αd) =  0, we obtain  �  ψ ◦ g +  d−1  �  i=1  ραici  �  (q′  αj) = (ψ ◦ g)(q′  αj) + cj = (ψ ◦ g)(q′  αd) = (ψ ◦ h)(q′  αd),  where δij is the Kronecker delta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Thus, we have h(q′  α1) = · · · = h(q′  αd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Moreover,  for any j ∈ I, the point q′  αj (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' q′  αd) is a topologically critical point of h since  h = ψ−1 ◦ (ψ ◦ g + cj) on an open neighborhood of q′  αj (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' h = g on an open  neighborhood of q′  αd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Therefore, we obtain h ∈ Ud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Finally, we will show that any mapping in U is not C0-stable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Suppose that there  exists a C0-stable mapping ˜g in U .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Then, there exists an open neighborhood U˜g of ˜g  such that any mapping in U˜g is C0-equivalent to ˜g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Since we have shown that Up+1  is dense in U , and topologically critical points are preserved by homeomorphisms  as mentioned in Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='1(3), any mapping in U˜g has (p+1) topologically critical  points with the same image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' This contradicts the fact that the set of all mappings  with normal crossings is dense in C∞(N, P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  ✷  Acknowledgements  The author would like to thank Toru Ohmoto for his kind comments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' This work  was supported by JSPS KAKENHI Grant Number JP21K13786.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  References  [1] Alexandru Dimca.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Morse functions and stable mappings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Roumaine Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Pures Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=',  24(9):1293–1297, 1979.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  [2] Andrew du Plessis and Terry Wall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' The geometry of topological stability, volume 9 of London  Mathematical Society Monographs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' New Series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Oxford Science Publications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' The Clarendon  Press, Oxford University Press, New York, 1995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  10  SHUNSUKE ICHIKI  [3] Christopher G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Gibson, Klaus Wirthm¨uller, Andrew A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' du Plessis, and Eduard J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Looi-  jenga.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Topological stability of smooth mappings, volume 552 of Lecture Notes in Mathematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Springer-Verlag, Berlin-New York, 1976.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  [4] Shunsuke Ichiki.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Non-density of stable mappings on non-compact manifolds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' to appear in  Pure Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=', https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='org/abs/2109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='08760  [5] John Norman Mather.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Stability of C∞ mappings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' The division theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' of Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  (2), 87:89–104, 1968.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  [6] John Norman Mather.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Stability of C∞ mappings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Finitely determined mapgerms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Inst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Hautes ´Etudes Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Publ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=', 35:279–308, 1968.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  [7] John Norman Mather.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Stability of C∞ mappings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Infinitesimal stability implies stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' of Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' (2), 89:254–291, 1969.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  [8] John Norman Mather.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Stability of C∞ mappings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Classification of stable germs by R-  algebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Inst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Hautes ´Etudes Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Publ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=', (2) 37:223–248, 1969.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  [9] John Norman Mather.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Stability of C∞ mappings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Transversality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Advances in Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=',  4:301–336, 1970.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  [10] John Norman Mather.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Stability of C∞ mappings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' The nice dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Proceedings of  Liverpool Singularities-Symposium, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Lecture Notes in Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=', 192:207–253, 1971.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  [11] John Norman Mather.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Stratifications and mappings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Dynamical systems (Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Sympos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=',  Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Bahia, Salvador, 1971), 195–232, 1973.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  [12] Maria Aparecida Soares Ruas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Old and new results on density of stable mappings, volume  552 of Handbook of geometry and topology of singularities III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content=' Springer, Cham, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='  Department of Mathematical and Computing Science, School of Computing, Tokyo  Institute of Technology, Tokyo 152-8552, Japan  Email address: ichiki@c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='titech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
+page_content='jp' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UtAzT4oBgHgl3EQflv2x/content/2301.01553v1.pdf'}
diff --git a/UtE1T4oBgHgl3EQfawTU/content/2301.03166v1.pdf b/UtE1T4oBgHgl3EQfawTU/content/2301.03166v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..098dbabb1147eba275f152086c22df64554853d4
--- /dev/null
+++ b/UtE1T4oBgHgl3EQfawTU/content/2301.03166v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:cb3653ff6fc4bde4d46b1a3c4def978f918b46dd55293ee9b3fa708e66fda305
+size 1451931
diff --git a/UtE1T4oBgHgl3EQfawTU/vector_store/index.faiss b/UtE1T4oBgHgl3EQfawTU/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..6a79e57b2c03162231a5a26b5e15fdadd74fc7be
--- /dev/null
+++ b/UtE1T4oBgHgl3EQfawTU/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e5776c7dd03dc0c264b10ed5d5be9aa9d37dfbecbd2ef332ddc633232a4aa78f
+size 3997741
diff --git a/UtE1T4oBgHgl3EQfawTU/vector_store/index.pkl b/UtE1T4oBgHgl3EQfawTU/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..aac716a999219b8f9ce2e77db23b6f8e8c79a90c
--- /dev/null
+++ b/UtE1T4oBgHgl3EQfawTU/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:978ea49d3c0ef4b94c75594410c6ce61c2c54c3e7a56ac10e93d6b1e51a71819
+size 168126
diff --git a/V9AzT4oBgHgl3EQfYPyg/content/tmp_files/2301.01332v1.pdf.txt b/V9AzT4oBgHgl3EQfYPyg/content/tmp_files/2301.01332v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b1c0c4836b4b777b16f897eb23ddc0249a1e5919
--- /dev/null
+++ b/V9AzT4oBgHgl3EQfYPyg/content/tmp_files/2301.01332v1.pdf.txt
@@ -0,0 +1,860 @@
+All-optical control of topological valley transport in graphene metasurfaces
+Yupei Wang,∗ Jian Wei You,† and Nicolae C. Panoiu
+Department of Electronic and Electrical Engineering,
+University College London, London WC1E 7JE, U.K.
+(Dated: January 5, 2023)
+We demonstrate that the influence of Kerr effect on valley-Hall topological transport in graphene
+metasurfaces can be used to implement an all-optical switch. In particular, by taking advantage of
+the large Kerr coefficient of graphene, the index of refraction of a topologically-protected graphene
+metasurface can be tuned via a pump beam, which results in an optically controllable frequency shift
+of the photonic bands of the metasurface. This spectral variation can in turn be readily employed to
+control and switch the propagation of an optical signal in certain waveguide modes of the graphene
+metasurface. Importantly, our theoretical and computational analysis reveals that the threshold
+pump power needed to optically switch ON/OFF the signal is strongly dependent on the group
+velocity of the pump mode, especially when the device is operated in the slow-light regime. This
+study could open up new routes towards active photonic nanodevices whose underlying functionality
+stems from their topological characteristics.
+I.
+INTRODUCTION
+Topological plasmonic edge states have recently at-
+tracted a great deal of attention, particularly due to
+their unique and robust optical properties, including
+unidirectional propagation and backscattering-free opti-
+cal interaction with structural disorder [1–3]. Topologi-
+cally protected edge modes can emerge inside a nontriv-
+ial bandgap, which is usually generated by gapping out
+a symmetry-protected Dirac cone.
+For example, time-
+reversal symmetry of photonic structures can be bro-
+ken by applying an external static magnetic field, lead-
+ing to an analogue quantum-Hall effect [1–4]. In addi-
+tion to breaking the time-reversal symmetry, the spatial-
+inversion symmetry can also be broken via spatial pertur-
+bations that are not invariant to the inversion symmetry
+transformation, resulting in an analogue quantum valley-
+Hall effect [1–3]. By emulating in photonics the valley
+degree of freedom introduced in solid state physics [5, 6],
+it has been suggested that two-dimensional (2D) honey-
+comb photonic lattices exhibit a valley-dependent topo-
+logical index, the so-called valley Chern number. This
+topological invariant is expressed in terms of the integral
+of the Berry curvature over the vicinity of the valleys
+located at the K, K′ symmetry points [7].
+When the
+difference across an interface between the valley Chern
+numbers of two valley-Hall topological photonic crys-
+tals (PhCs) is different from zero, topologically-protected
+valley modes can emerge at and propagate along the
+domain-wall interface separating the two PhCs with dif-
+ferent topology [8].
+To date, most of the studies of topological photonics
+have focused on passive optical systems operating in the
+∗ yupei.wang.18@ucl.ac.uk
+† Also at State Key Laboratory of Millimeter Waves, Department
+of Information Science and Engineering, Southeast University,
+Nanjing, 211189, China.
+linear regime [9]. However, introducing optical nonlinear
+effects to topological systems can lead to active photonic
+devices with new or improved functionalities, including
+ultra-short pulsed lasers, optical signal processing, and
+ultra-fast all-optical switches [10–12]. To this end, appli-
+cations of nonlinear topological photonics, such as topo-
+logical lasers [13, 14], lattice edge solitons [15, 16], op-
+tically tunable mode couplers [17], and frequency con-
+vertors [18–21], have already been proposed theoretically
+and in some cases successfully implemented in a variety
+of experimental platforms, including optical waveguides,
+optical resonators, and metamaterials [22]. Specifically,
+the combination of the Kerr nonlinearity and nontriv-
+ial topological characteristics can potentially lead to a
+new class of active photonic devices where the system
+topology plays a key rˆole. Since the Kerr coefficient of
+graphene is several orders of magnitude larger than that
+of bulk optical materials commonly used in practice [23],
+graphene-based topological platforms can have a major
+impact to the development of advanced ultra-fast active
+photonic devices.
+In this article, we demonstrate that an optical signal
+propagating in a topologically-protected valley mode of
+a graphene plasmonic crystal waveguide can be optically
+controlled through the Kerr effect induced by a pump
+beam injected in a bulk mode of the plasmonic crystal. In
+particular, by introducing additional holes with properly
+chosen size in a graphene metasurface with hexagonal
+lattice, so as it is no longer invariant to spatial-inversion
+symmetry transformations, one can create a nontriv-
+ial bandgap that originates from a symmetry-protected
+Dirac cone. We show that, as a result, topological in-
+terface modes presenting the familiar property of unidi-
+rectional light propagation are generated inside the non-
+trivial frequency bandgap. Employing this unidirection-
+ality feature in conjunction with the large nonlinear re-
+fractive index coefficient of graphene, it is demonstrated
+that an optical signal propagating in the proposed topo-
+logical waveguide can be optically controlled via an opti-
+arXiv:2301.01332v1  [physics.optics]  3 Jan 2023
+
+2
+cal pump beam propagating in one of the bulk modes of
+the metasurface. Moreover, our study indicates that the
+pump power required to switch ON/OFF the optical sig-
+nal is strongly dependent on the group-velocity (GV) of
+the pump, being significantly reduced when the proposed
+optical switch operates in the slow-light (SL) regime.
+The article is organized as follows. In the next section
+we present the geometrical configuration and properties
+of the photonic band structure of the proposed graphene
+plasmonic crystal. Then, in Section 3, we describe the
+operation of the optical switch and analyze quantitatively
+its optical response. The main conclusions of our study
+are presented in the last section of the article.
+II.
+BAND ANALYSIS OF GRAPHENE
+PLASMONIC WAVEGUIDE
+The schematic of the proposed graphene metasurface
+is presented in Fig. 1(a). It consists of a graphene sheet
+in which air nanoholes with two different radii are etched.
+The left and right semi-infinite metasurface domains are
+placed in a mirror-symmetric manner so as to generate
+a domain-wall interface along the x-axis, as illustrated
+by the yellow region in Fig. 1(a). Each domain contains
+the same unit cell, whereby two air holes with different
+radii, R and r, are arranged in a hexagonal array. The
+unit cell and the first Brillouin zone (FBZ) are shown in
+Figs. 1(b) and 1(c), respectively. In this study, we fix
+the lattice constant, a = 400
+√
+3 nm, and the radius of
+one of the nanoholes, R = 140 nm. The optical prop-
+erties of graphene are generally described by its surface
+conductivity, given by Kubo’s formula [24, 25].
+The band diagram of the graphene plasmonic crystal is
+calculated by the finite-element method (FEM) of Wave
+Optics Module in COMSOL® Multiphysics 5.6 [26] and
+(a)
+x
+y
+FBZ
+mirror symmetric interface
+y
+x
+(b)
+(c)
+(d)
+FIG. 1. (a) Schematic of the graphene plasmonic nanohole
+crystal with a domain-wall interface oriented along the x-
+axis.
+The left- and right-hand side domains are placed in
+a mirror-symmetric manner and contain the same unit cell.
+(b) Primitive unit cell of the graphene crystal with a lattice
+constant a, containing two air nanoholes with different radii
+R and r. (c) First Brillouin zone of the graphene plasmonic
+crystal showing the high-symmetry points Γ, K, and M. (d)
+Band diagram of the graphene plasmonic crystal determined
+for different radii r.
+validated using Synopsys® BandSOLVE tool [27].
+As
+shown in Fig. 1(d), the band diagrams were determined
+for different radii r. When r = 0, as per the black curves
+in Fig. 1(d), there is a Dirac cone at the K point, which
+is protected by the C6v symmetry of the hexagonal ar-
+rangement of holes with radius R.
+The first and sec-
+ond bands indeed linearly cross at Dirac points located
+at the frequency of 11.8 THz. In order to open up the
+inversion-symmetry-protected Dirac cone, additional air
+holes (r ̸= 0) are introduced into the graphene plas-
+monic crystal. This reduces the spatial-inversion sym-
+metry to the C3v point symmetry group [28].
+As a
+consequence, the C6v-symmetry-protected Dirac cone is
+gapped out, resulting in the formation of a nontrivial
+frequency bandgap, as illustrated by the red and blue
+curves in Fig. 1(d). Moreover, the variation of the width
+of the bandgap indicates its dependence on the radius
+of the added holes, r.
+Specifically, when r increases
+from 50 nmto80 nm, the spectral width of the bandgap
+increases by about 1 THz.
+This frequency shift is al-
+most entirely due to a blue-shift of the first band. In our
+subsequent computations, we consider graphene meta-
+surfaces with radius r fixed to r = 50 nm. This choice
+is guided by the fact that in this way one can achieve a
+relatively large nontrivial bandgap, which extends from
+11.1 THzto11.8 THz.
+Since the lattice of holes has hexagonal symmetry,
+it possesses two nonequivalent valleys in the reciprocal
+space. The integral of the Berry curvature around each
+of these valleys defines the valley Chern number, which
+among other things determines the number of possible
+topological edge states [8].
+In the wave vector space,
+around each valley, the distribution of the Berry curva-
+ture around the two nonequivalent high-symmetry points
+K and K′ defines two valley-dependent Chern numbers,
+which can be computationally evaluated by the Wilson-
+loop approach in a discretized Brillouin zone [29]. To this
+end, valley Chern numbers of the first band [see Fig. 1(d)]
+over the K and K′ valleys have been computed based on
+the FEM implemented in COMSOL. The results of these
+calculations, determined over a 18 × 18 computational
+grid covering the k-space, are plotted in Fig. 2.
+We show in Fig. 2(a) the Berry curvature distribution
+of the first band when r = 20 nm over the K and K′
+valleys. As expected, the distribution of Berry curvature
+shows a sharp peak with opposite signs at K and K′
+points. Specifically, the computed valley Chern numbers
+of the first band when r = 20 nm over K and K′ valleys
+are 0.49 and −0.49, respectively. The small deviation of
+0.01 from the theoretical value of valley Chern number,
+|C| = 1/2, illustrates the accuracy of the Wilson-loop
+computational method [30]. For r = 50 nm correspond-
+ing to a wider nontrivial bandgap in Fig. 1(d), the com-
+puted valley Chern numbers of the first band over K and
+K′ valleys decrease to 0.34 and −0.34, respectively, as
+indicated in Fig. 2(b).
+Note that when the frequency
+bandgap is relatively large, the distribution of the Berry
+curvature over the corners at K and K′ symmetry points
+
+a
+R
+ainterface
+XM
+K14
+Frequency (THz)
+12
+Bandgap
+10
+8
+r=0
+r=50 nm
+:r=80 nm
+6
+K
+M3
+1
+0
+-1-0.5
+0
+0.5
+1
+0
+-1-0.5
+0
+0.5
+(a)
+Ω (𝑎2)
+𝛿𝑘𝑦 (𝜋/𝑎)
+𝛿𝑘𝑥 (𝜋/𝑎)
+𝛿𝑘𝑦′ (𝜋/𝑎)
+𝛿𝑘𝑥′ (𝜋/𝑎)
+1
+0
+-1-0.5
+0
+(b)
+𝛿𝑘𝑦 (𝜋/𝑎)
+𝛿𝑘𝑥 (𝜋/𝑎)
+1
+0
+-1-0.5
+0
+0.5
+𝛿𝑘𝑦′ (𝜋/𝑎)
+𝛿𝑘𝑥′ (𝜋/𝑎)
+0.5
+𝐾 point
+𝐾′ point
+𝐾 point
+𝐾′ point
+Ω (𝑎2)
+FIG. 2. Computed Berry curvature distribution of the first
+band over the K and K′ valleys, determined for the radius of
+the additional hole (a) r = 20 nm and (b) r = 50 nm.
+of the Brillouin zone spreads significantly and overlaps
+with the Berry curvature distributions at neighbouring
+K and K′ symmetry points. This makes it more difficult
+to properly define the valley Chern number, as its calcu-
+lation cannot be extended to the entire FBZ. Therefore,
+the theoretical valley Chern number C = ±1/2 can only
+be obtained close to the Dirac point with an infinitesi-
+mally small perturbation [31].
+Following this analysis, and for the sake of simplic-
+ity of our further discussions, we fix the valley Chern
+number of the first band over the K and K′ valleys to
+CK = ±1/2 and CK′ = ∓1/2, respectively, values that
+correspond to an infinitesimally small perturbation. As
+a result, when a domain-wall interface with valley Chern
+number difference ∆C = ±1 is created by rotations of
+the graphene crystal by π/3, π, or 5π/3, a pair of valley
+modes is generated inside the bandgap. These topologi-
+cal modes propagate along the domain-wall interface in
+opposite direction, namely they have positive and nega-
+tive GV.
+We now consider two semi-infinite graphene metasur-
+faces placed together after one of them is rotated by π,
+thus forming a mirror-symmetric domain-wall interface,
+as shown in Fig. 3(a). The finite valley-dependent Chern
+number makes it possible to form valley-momentum
+locked interfacial modes, illustrated in the projected band
+diagram of Fig. 3(b). The blue regions represent the bulk
+modes, whereas a topological interface-mode band inside
+the nontrivial bandgap is marked by a red curve. In or-
+der to gain deeper physical insights into the properties
+of this topological mode, the corresponding field distri-
+bution is calculated at the frequency of 11.4 THz, which
+corresponds to the middle of the bandgap. The particu-
+lar topological mode is indicated by the symbol Es. As
+illustrated in Fig. 3(c), this topological mode propagates
+along the domain-wall interface and is highly confined at
+the interface.
+10
+11
+12
+13
+14
+9
+11.4 THz
+0
+0.2
+0.4
+0.6
+0.8
+x
+y
+x
+y
+𝑬𝒃𝟏
+𝑬𝒃𝟐𝑬𝒃𝟑
+𝑬𝒔
+topological mode
+bulk mode
+1
+Frequency (THz)
+(a)
+(b)
+(c)
+(d)
+FIG. 3. (a) Supercell of a finite graphene plasmonic waveguide
+with a domain-wall interface constructed from two mirror-
+symmetric domains.
+(b) Projected band diagram of the
+graphene plasmonic crystal waveguide corresponding to r =
+50 nm. A topologically protected interface-mode band (red
+line) exists inside the nontrivial bandgap. (c), (d) Unidirec-
+tional propagation of topological interfacial modes along the
+positive (negative) direction of the x-axis, when the waveguide
+is excited by a LCP (RCP) source at 11.4 THz, respectively.
+Furthermore,
+the unidirectional feature of valley-
+momentum locked interface modes is also investigated.
+To this end, six electric dipoles with increasing or de-
+creasing phase difference (±π/3) are placed together at
+the corners of a small hexagon, thus generating light with
+specific chirality. To be more specific, under the excita-
+tion of a left circularly-polarized (LCP) source at the fre-
+quency of 11.4 THz, see Fig. 3(c), the topologically pro-
+tected interfacial mode propagates along the domain-wall
+interface in the positive direction of the x-axis with a pos-
+itive group velocity, whereas the opposite is true for the
+topological interfacial mode excited by a right circularly-
+polarized (RCP) source with the same frequency, as per
+Fig. 3(d).
+III.
+ACTIVE ALL-OPTICALLY CONTROLABLE
+SWITCH
+Taking advantage of the unidirectional feature of the
+topological interface mode of the proposed graphene
+waveguide as well as the strong optical nonlinearity of
+graphene, a graphene-based all-optical switch is designed.
+To be more specific, we study the influence of the Kerr
+effect in graphene on the propagation characteristics of
+topological interface modes. As a versatile 2D material
+with large relaxation time (low optical losses) at THz fre-
+quencies, optical near-field enhancement [32], and large
+optical nonlinearity [33], graphene is ideally suited for
+nonlinear optics applications.
+The refractive index variation induced by the Kerr ef-
+fect in the graphene metasurface, in response to the elec-
+tric field generated by an optical pump, is given by [12]:
+∆ng(r) = 1
+2cϵ0ngn2|Ep(r)|2,
+(1)
+
+1.5
+1
+0.5
+0
+20
+20
+10
+10
+@
+020
+20
+10
+10
+@
+020
+15
+10
+5
+20
+20
+10
+10
+0
+@5
+10
+15
+20
+20
+20
+10
+10
+@
+0Ckx(π/a)4
+where ng is the refractive index of graphene, n2 =
+7.5 × 10−11 m2/W is the nonlinear refractive coefficient
+of graphene [34], and Ep(r) is the field amplitude of the
+pump. Moreover, the pump power per unit cell, Pp, car-
+ried by a bulk mode Eb is given by [35]:
+Pp = vg
+4a
+�
+Vcell
+∂
+∂ω [ωϵω(r)]|Eb(r)|2dV,
+(2)
+where vg = dω/dkx is the GV, Vcell is the volume of the
+unit cell, and ϵω(r) is the frequency-dependent permit-
+tivity distribution.
+To investigate the influence of the pump induced Kerr
+effect on the light propagation in the topological mode,
+several bulk modes with different GV are employed as
+pump modes.
+Since the power of the signal is much
+smaller than that of the pump, the contribution of the
+signal to the Kerr induced variation of the refractive in-
+dex is neglected. As a result, the signal propagation in
+the topological mode is solely controlled by the optical
+pump.
+The optical characteristics of the pump and signal
+modes are summarized in Fig. 4. For the bulk mode band
+indicated by the green curve in Fig. 3(b), the GV vg and
+group index, ng = c/vg, are shown in Fig. 4(a). The three
+bulk modes, Eb1 [kx = 0.55(π/a)], Eb2 [kx = 0.61(π/a)],
+and Eb3 [kx = 0.67(π/a)], are chosen in such a way that
+the first two are fast-light (FL) modes, whereas the last
+one is located in the SL region (the corresponding group
+index approaches 1000). Slow light can generally provide
+strong field enhancement and consequently can lead to in-
+creased nonlinear optical interactions [36]. Moreover, the
+corresponding field distributions of the signal and pump
+modes are plotted in Figs. 4(b) and 4(c), respectively.
+The field distribution of the topological valley mode Es,
+depicted in Fig. 3(b), shows that a signal generated by a
+LCP source with 11.4 THz is tightly confined along the
+domain-wall interface. Moreover, the spatial field pro-
+file of the bulk mode Eb1 with the largest GV among
+the three chosen bulk modes reveals a relatively uniform
+x
+y
+x
+y
+𝐸𝑏1
+𝐸𝑏2
+𝐸𝑏3
+v
+(b)
+(c)
+(a)
+FIG. 4. (a) Dependence of group velocity vg and group index
+ng = c/vg on kx, corresponding to the bulk mode containing
+Eb1, Eb2, and Eb3 [(green line in Fig. 3(b)]. (b) Field profile
+of the topological interface mode at 11.4 THz, indicated by
+Es in Fig. 3(b). (c) Field distribution of the pump injected
+in the bulk mode Eb1.
+11.4THz
+11.4THz
+Frequency (THz)
+1 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8
+1
+10
+11
+12
+13
+14
+9
+11.4THz
+0 0.2 0.4 0.6 0.8
+𝑃𝑝 = 0
+𝑃𝑝 = 3.25 𝜇𝑊
+𝑃𝑝 = 0.81 𝜇𝑊
+topological
+topological
+topological
+𝑬𝒃𝟏
+bulk mode
+(a)
+(b)
+(c)
+FIG. 5.
+(a), (b), (c) Projected band diagram of graphene
+nanohole plasmonic waveguide corresponding to the pump in-
+jected in the bulk mode Eb1, determined for the pump power
+Pp = 0, Pp = 0.81 µW, and Pp = 3.25 µW, respectively.
+field distribution that extends across the entire graphene
+metasurface. Note that our simulations produced similar
+electric field distributions for the other two bulk modes,
+Eb2 and Eb3, the main difference being the value of the
+field amplitude corresponding to a given pump power.
+Since the optical Kerr effect in the graphene metasur-
+face is induced by the pump, we investigated the depen-
+dence of the projected photonic band diagram on the
+pump power, Pp, the corresponding results being dis-
+played in Fig. 5.
+In order to determine the projected
+band structure corresponding to a pump power, Pp, we
+proceeded as follows. First, we computed the field dis-
+tribution of the pump mode, Eb(r), and its GV, vg, then
+scaled it using Eq. (2) in such a way that the optical
+power carried by the mode was Pp. Subsequently, using
+Eq. (1), we calculated the Kerr-induced variation of the
+index of refraction of graphene and the corresponding
+distribution of the electric permittivity of the graphene
+metasurface. In the final step, this nonlinear permittiv-
+ity was employed to determine the nonlinearly modified
+projected photonic band diagram of the metasurface. It
+should be noted that since the pump mode is periodic
+along the x-axis, a projected band structure can be de-
+fined in the optically pumped metasurface, too.
+In this analysis, we assumed that the pump power Pp
+was equal to 0 (linear regime), 0.81 µW, and 3.25 µW.
+The results of these computations indicate that as the
+pump power increases the frequency of the topological
+bandgap is blue-shifted by as much as 0.3 THz. There-
+fore, if the frequency of the signal mode is fixed to
+11.4 THz, by increasing the pump power Pp, we can
+switch the topological interface mode (originally located
+inside the bandgap) to a frequency region occupied by
+leaky bulk modes (outside the bandgap), namely a fre-
+quency at which the signal can no longer propagate in
+the waveguide.
+The threshold pump power needed to
+switch off the signal propagation was calculated to be
+
+kx(π/a)X106
+4
+1000
+2
+500
+(m/s)
+0
+0
+V
+-2
+-500
+-4
+-6
+-1000
+0
+0.59
+nkx(π/a)5
+𝑃𝑝 (𝜇𝑊)
+0
+5
+10
+15
+(b)
+𝐸𝑝 pump region
+x
+y
+L
+𝑷𝒔𝒊𝒏
+𝑷𝒔𝒐𝒖𝒕
+W
+(a)
+LCP signal source 
+FIG. 6. (a) Schematic of the active all-optical switch based on
+the graphene plasmonic waveguide. Light is pumped in the
+bulk mode Eb (yellow region), whereas the signal Es is gener-
+ated by a LCP source at 11.4 THz and carries an input power
+Psin and output power Psout.
+The length of the graphene
+waveguide is L = 35a and the device width is W = 19a. (b)
+Signal transmission, defined as η = Psout/Psin, vs. the pump
+power Pp, determined for the bulk modes with different GV,
+Eb1, Eb2, and Eb3, indicated in Fig. 4(a).
+Pp = 3.25 µW. It should be noted that we observed that
+the relative location of the bands did not change signifi-
+cantly as the pump power increased, although, as we just
+explained, their frequency varied.
+After the validation of the main idea on which our
+proposed optically controllable switch operates, namely
+the optical tuning of the band structure of the graphene
+metasurface via a pump beam, we proceeded to analyze
+quantitatively the optical characteristics of our optical
+switch. To this end, we considered the optical device de-
+picted schematically in Fig. 6(a), which is operated as fol-
+lows: a pump beam Ep (yellow region) with a frequency
+chosen in such a way that it propagates in a bulk mode,
+Eb, is injected into the graphene metasurface, while a low
+power LCP source with frequency 11.4 THz generates an
+optical signal (probe) Es. The length of the graphene
+plasmonic metasurface was L = 35a, which ensured that
+one achieves a relatively stable signal propagation at the
+domain-wall interface along the x-axis well beyond the
+transient region where the light is coupled from the LCP
+source to the signal mode. Due to the fact that the opti-
+cal signal with a frequency of 11.4 THz can be switched
+from a topological interface mode to leaky bulk modes by
+tuning the pump power, the optical signal can be turned
+ON/OFF when the pump power increases beyond a cer-
+tain threshold. To validate and quantify these ideas, we
+define the transmission of the signal beam as the ratio be-
+tween the output power of the signal, Psout, measured at
+the end of the graphene waveguide, and the input power
+of the signal, Psin, measured nearby the LCP source,
+namely η = Psout/Psin.
+Given that the power of the
+signal depends on the pump power, the transmission η
+depends implicitly on Pp, too.
+The results of our computational analysis of the pro-
+posed optical switch are summarized in Fig. 6(b), where
+we plot the dependence of the transmission of the sig-
+nal power η on the pump power Pp, determined for the
+cases when the pump power is injected in the bulk modes
+with different GV, Eb1 (red circles), Eb2 (blue triangles),
+and Eb3 (black stars), indicated in Fig. 4(a).
+By em-
+ploying the three pump modes, Eb1, Eb2, and Eb3, with
+decreasing GV approaching the SL regime, allowed us
+the investigate the influence of SL effects on the device
+characteristics. One conclusion of this analysis is that
+the signal transmission corresponding to pump modes
+with different GV presents a similar trend. Specifically,
+the signal transmission increases with the increase of the
+pump power, which is explained by the fact that, due to
+the Kerr-effect-induced increment of the refractive index
+of graphene waveguide, the signal can be more readily
+focused and coupled from the excitation source into the
+topological mode. Subsequently, as the pump power is
+further increased, the signal mode begins to couple to
+bulk modes resulting in a steep decrease to less than 0.1
+of the signal transmission.
+Another important fact revealed by the plots presented
+in Fig. 6(b) is that the pump power needed to switch
+ON/OFF the signal decreases dramatically when the GV
+of the pump mode is pushed into the SL regime. In par-
+ticular, more than 6× reduction of the switching optical
+pump power is observed in our numerical investigations
+when the pump mode is tuned from Eb1 to Eb3. This
+important result can be easily understood from the in-
+formation conveyed by Eq. (2).
+Thus, it can be seen
+from this equation that for a given pump power, Pp, the
+smaller the GV, vg, of the pump mode is, the larger is
+the corresponding electric field intensity |Eb| of the pump
+mode. This in turn implies that a larger Kerr-induce vari-
+ation of the index of refraction of graphene is achieved
+and consequently a larger frequency shift of the photonic
+bands is attained.
+IV.
+CONCLUSION
+We demonstrated an active optically-tunable switch
+based on the Kerr effect in a topologically protected
+valley-Hall
+graphene
+plasmonic
+metasurface.
+The
+spatial-inversion symmetry breaking of the graphene
+nanohole metasurface is realized by introducing an extra
+hole, which opens up a symmetry-protected Dirac cone.
+Consequently, a topological interface mode is formed in-
+side the nontrivial bandgap and propagates along the
+
+0.7
+0.6
+m
+n
+0.5
+0
+S
+S
+Transmi
+0.4
+0.3
+0.2
+0.14o Eb1
+ Eb2
+* Eb36
+domain-wall interface in a unidirectional manner. Tak-
+ing advantage of a large nonlinear refractive index of the
+graphene, the Kerr effect induced in the graphene is used
+to shift the frequency of the nontrivial bandgap of the
+system, so that one can optically control the signal prop-
+agation in the proposed topological graphene waveguide.
+Importantly, our results show that the transmission of the
+optical signal sharply decreases as the the pump power
+increases, and the required switching pump power is sig-
+nificantly reduced when the all-optical switch operates in
+the slow-light regime.
+Funding European Research Council (ERC- 2014-
+CoG-648328); China Scholarship Council.
+Disclosures The authors declare no conflicts of inter-
+est.
+[1] L. Lu, J. D. Joannopoulos, and M. Soljacic, “Topological
+photonics,” Nat. Photonics 8(11), 821-829 (2014).
+[2] A. B. Khanikaev and G. Shvets,
+“Two-dimensional
+topological photonics,” Nat. Photonics 11(12), 763-773
+(2017).
+[3] B. Y. Xie, et al. “Photonics meets topology,” Opt. Ex-
+press 26(19), 24531-24550 (2018).
+[4] Z. Qiao, S. A. Yang, W. Feng, W. K. Tse, J. Ding, Y.
+Yao, J. Wang, and Q. Niu, “Quantum anomalous Hall
+effect in graphene from Rashba and exchange effects,”
+Phys. Rev. B 82(16), 161414 (2010).
+[5] A. Rycerz, J. Tworzyd�lo, and C. W. J. Beenakker, “Val-
+ley filter and valley valve in graphene,” Nat. Phys. 3(3),
+172-175 (2007).
+[6] D. Xiao, Y. Wang, and N. Qian, “Valley-contrasting
+physics in graphene: magnetic moment and topological
+transport,” Phys. Rev. Lett. 99(23), 236809 (2007).
+[7] T. Ma and G. Shvets, “All-Si valley-Hall photonic topo-
+logical insulator,” New J. Phys. 18(2), 025012 (2016).
+[8] J. Noh, S. Huang, K. P. Chen, and M. C. Rechtsman,
+“Observation of photonic topological valley Hall edge
+states,” Phys. Rev. Lett. 120(6), 063902 (2018).
+[9] M. A. Foster, A. C. Turner, M. Lipson, and A. L. Gaeta,
+“Nonlinear optics in photonic nanowires,” Opt. Express
+16(2), 1300-1320 (2008).
+[10] C. Monat, M. De Sterke, and B. J. Eggleton, “Slow light
+enhanced nonlinear optics in periodic structures,” J. Opt.
+12(10), 104003 (2010).
+[11] N. C. Panoiu, M. Bahl, and R. M. Osgood, “Optically
+tunable superprism effect in nonlinear photonic crystals,”
+Opt. Lett. 28(24), 2503-2505 (2003).
+[12] R. W. Boyd, Nonlinear optics (Academic press, 2003).
+[13] G. Harari, M. A. Bandres, Y. Lumer, M. C. Rechtsman,
+Y. D. Chong, M. Khajavikhan, D. N. Christodoulides,
+and M. Segev, “Topological insulator laser: theory,” Sci-
+ence 359(6381), eaar4003 (2018).
+[14] M. A. Bandres, S. Wittek, G. Harari, M. Parto, J.
+Ren, M. Segev, D. N. Christodoulides, and M. Kha-
+javikhan, “Topological insulator laser:
+Experiments,”
+Science 359(6381), eaar4005 (2018).
+[15] S. Mukherjee and M. C. Rechtsman, “Observation of
+Floquet solitons in a topological bandgap,” Science
+368(6493), 856-859 (2020).
+[16] D.
+Leykam
+and
+Y.
+D.
+Chong,
+“Edge
+solitons
+in
+nonlinear-photonic topological insulators,” Phys. Rev.
+Lett. 117(14), 143901 (2016).
+[17] Y. Wang and N. C. Panoiu, “Optically controllable cou-
+pling between edge and topological interface modes of
+graphene metasurfaces,” J. Opt. 24(10), 104002 (2022).
+[18] Z. Lan, J. W. You, and N. C. Panoiu, “Nonlinear one-way
+edge-mode interactions for frequency mixing in topolog-
+ical photonic crystals,” Phys. Rev. B 101(15), 155422
+(2020).
+[19] Z. Lan, J. W. You, Q. Ren, W. E. I. Sha, and N. C.
+Panoiu, “Second-harmonic generation via double topo-
+logical valley-Hall kink modes in all-dielectric photonic
+crystals,” Phys. Rev. A 103(4), L041502 (2021).
+[20] D. Smirnova, S. Kruk, D. Leykam, E. Melik-Gaykazyan,
+D. Y. Choi, and Y. Kivshar, “Third-harmonic generation
+in photonic topological metasurfaces,” Phys. Rev. Lett.
+123(10), 103901 (2019).
+[21] J. W. You, Z. Lan, and N. C. Panoiu, “Four-wave mixing
+of topological edge plasmons in graphene metasurfaces,”
+Sci. Adv. 6(13), eaaz3910 (2020).
+[22] D. Smirnova, D. Leykam, Y. Chong, and Y. Kivshar,
+“Nonlinear topological photonics,” Appl. Phys. Rev.
+7(2), 021306 (2020).
+[23] A. N. Grigorenko, M. Polini, and K. S. Safavi-Novoselov,
+“Graphene plasmonics,” Nat. Photonics 6(11), 749-758
+(2012).
+[24] M. Dressel and G. Gruner, Electrodynamics of Solids
+(Cambridge University Press, 2002).
+[25] Y.
+Wang,
+J.
+W.
+You,
+Z.
+Lan,
+and
+N.
+C.
+Panoiu,“Topological
+valley
+plasmon
+transport
+in
+bilayer graphene metasurfaces for sensing applications,”
+Opt. Lett. 45(11), 3151-3154 (2020).
+[26] COMSOL
+Multiphysics®
+(available
+at:
+www.comsol.com).
+[27] Synopsys® (available at: www.synopsys.com).
+[28] J. W. You, Z. Lan, Q. Bao, and N. C. Panoiu,“Valley-Hall
+topological plasmons in a graphene nanohole plasmonic
+crystal waveguide,” IEEE J. Sel. Top. Quantum Electron.
+26(6), 4600308 (2020).
+[29] H. X. Wang, G. Y. Guo, and J. H. Jiang, “Band topol-
+ogy in classical waves: Wilson-loop approach to topolog-
+ical numbers and fragile topology,” New J. Phys. 21(9),
+093029 (2019).
+[30] M. I. Shalaev, W. Walasik, A. Tsukernik, Y. Xu, and N.
+M. Litchinitser, “Robust topologically protected trans-
+port in photonic crystals at telecommunication wave-
+lengths,” Nat. Nanotechnol. 14(1), 31-34 (2019).
+[31] S. Wong, M. Saba, O. Hess, and S. S. Oh, “Gapless uni-
+directional photonic transport using all-dielectric kagome
+lattices,” Phys. Rev. Res. 2(1), 012011 (2020).
+[32] J.
+W.
+You,
+S.
+R.
+Bongu,
+Q.
+Bao,
+and
+N.
+C.
+Panoiu,“Nonlinear optical properties and applications of
+2D materials:
+theoretical and experimental aspects,”
+Nanophotonics 8(1), 63-97 (2018).
+[33] S. Wu, L. Mao, A. M. Jones, W. Yao, C. Zhang, and
+X. Xu,“Quantum-enhanced tunable second-order opti-
+cal nonlinearity in bilayer graphene,” Nano Lett. 12(4),
+
+7
+2032-2036 (2012).
+[34] S. Thakur, B. Semnani, S. Safavi-Naeini, and A. H.
+Majedi, “Experimental characterization of the ultra-
+fast, tunable and broadband optical Kerr nonlinearity
+in graphene,” Sci. Rep. 9(1), 1-10 (2019).
+[35] S. Lavdas and N. C. Panoiu, “Theory of pulsed four-
+wave mixing in one-dimensional silicon photonic crystal
+slab waveguides,” Phys. Rev. B 93(11), 115435 (2016).
+[36] S. E. Harris and L. V. Hau, “Nonlinear optics at low light
+levels,” Phys. Rev. Lett. 82(23), 4611-4614 (1999).
+
diff --git a/V9AzT4oBgHgl3EQfYPyg/content/tmp_files/load_file.txt b/V9AzT4oBgHgl3EQfYPyg/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d7917cbe4c6c73eac1b1058e8c595a387dac7edf
--- /dev/null
+++ b/V9AzT4oBgHgl3EQfYPyg/content/tmp_files/load_file.txt
@@ -0,0 +1,545 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf,len=544
+page_content='All-optical control of topological valley transport in graphene metasurfaces  Yupei Wang,∗ Jian Wei You,† and Nicolae C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Panoiu  Department of Electronic and Electrical Engineering,  University College London, London WC1E 7JE, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  (Dated: January 5, 2023)  We demonstrate that the influence of Kerr effect on valley-Hall topological transport in graphene  metasurfaces can be used to implement an all-optical switch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' In particular, by taking advantage of  the large Kerr coefficient of graphene, the index of refraction of a topologically-protected graphene  metasurface can be tuned via a pump beam, which results in an optically controllable frequency shift  of the photonic bands of the metasurface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' This spectral variation can in turn be readily employed to  control and switch the propagation of an optical signal in certain waveguide modes of the graphene  metasurface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Importantly, our theoretical and computational analysis reveals that the threshold  pump power needed to optically switch ON/OFF the signal is strongly dependent on the group  velocity of the pump mode, especially when the device is operated in the slow-light regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' This  study could open up new routes towards active photonic nanodevices whose underlying functionality  stems from their topological characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  INTRODUCTION  Topological plasmonic edge states have recently at-  tracted a great deal of attention, particularly due to  their unique and robust optical properties, including  unidirectional propagation and backscattering-free opti-  cal interaction with structural disorder [1–3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Topologi-  cally protected edge modes can emerge inside a nontriv-  ial bandgap, which is usually generated by gapping out  a symmetry-protected Dirac cone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  For example, time-  reversal symmetry of photonic structures can be bro-  ken by applying an external static magnetic field, lead-  ing to an analogue quantum-Hall effect [1–4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' In addi-  tion to breaking the time-reversal symmetry, the spatial-  inversion symmetry can also be broken via spatial pertur-  bations that are not invariant to the inversion symmetry  transformation, resulting in an analogue quantum valley-  Hall effect [1–3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' By emulating in photonics the valley  degree of freedom introduced in solid state physics [5, 6],  it has been suggested that two-dimensional (2D) honey-  comb photonic lattices exhibit a valley-dependent topo-  logical index, the so-called valley Chern number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' This  topological invariant is expressed in terms of the integral  of the Berry curvature over the vicinity of the valleys  located at the K, K′ symmetry points [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  When the  difference across an interface between the valley Chern  numbers of two valley-Hall topological photonic crys-  tals (PhCs) is different from zero, topologically-protected  valley modes can emerge at and propagate along the  domain-wall interface separating the two PhCs with dif-  ferent topology [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  To date, most of the studies of topological photonics  have focused on passive optical systems operating in the  ∗ yupei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='18@ucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='uk  † Also at State Key Laboratory of Millimeter Waves, Department  of Information Science and Engineering, Southeast University,  Nanjing, 211189, China.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  linear regime [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' However, introducing optical nonlinear  effects to topological systems can lead to active photonic  devices with new or improved functionalities, including  ultra-short pulsed lasers, optical signal processing, and  ultra-fast all-optical switches [10–12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' To this end, appli-  cations of nonlinear topological photonics, such as topo-  logical lasers [13, 14], lattice edge solitons [15, 16], op-  tically tunable mode couplers [17], and frequency con-  vertors [18–21], have already been proposed theoretically  and in some cases successfully implemented in a variety  of experimental platforms, including optical waveguides,  optical resonators, and metamaterials [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Specifically,  the combination of the Kerr nonlinearity and nontriv-  ial topological characteristics can potentially lead to a  new class of active photonic devices where the system  topology plays a key rˆole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Since the Kerr coefficient of  graphene is several orders of magnitude larger than that  of bulk optical materials commonly used in practice [23],  graphene-based topological platforms can have a major  impact to the development of advanced ultra-fast active  photonic devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  In this article, we demonstrate that an optical signal  propagating in a topologically-protected valley mode of  a graphene plasmonic crystal waveguide can be optically  controlled through the Kerr effect induced by a pump  beam injected in a bulk mode of the plasmonic crystal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' In  particular, by introducing additional holes with properly  chosen size in a graphene metasurface with hexagonal  lattice, so as it is no longer invariant to spatial-inversion  symmetry transformations, one can create a nontriv-  ial bandgap that originates from a symmetry-protected  Dirac cone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' We show that, as a result, topological in-  terface modes presenting the familiar property of unidi-  rectional light propagation are generated inside the non-  trivial frequency bandgap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Employing this unidirection-  ality feature in conjunction with the large nonlinear re-  fractive index coefficient of graphene, it is demonstrated  that an optical signal propagating in the proposed topo-  logical waveguide can be optically controlled via an opti-  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='01332v1  [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='optics]  3 Jan 2023  2  cal pump beam propagating in one of the bulk modes of  the metasurface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Moreover, our study indicates that the  pump power required to switch ON/OFF the optical sig-  nal is strongly dependent on the group-velocity (GV) of  the pump, being significantly reduced when the proposed  optical switch operates in the slow-light (SL) regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  The article is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' In the next section  we present the geometrical configuration and properties  of the photonic band structure of the proposed graphene  plasmonic crystal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Then, in Section 3, we describe the  operation of the optical switch and analyze quantitatively  its optical response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' The main conclusions of our study  are presented in the last section of the article.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  BAND ANALYSIS OF GRAPHENE  PLASMONIC WAVEGUIDE  The schematic of the proposed graphene metasurface  is presented in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 1(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' It consists of a graphene sheet  in which air nanoholes with two different radii are etched.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  The left and right semi-infinite metasurface domains are  placed in a mirror-symmetric manner so as to generate  a domain-wall interface along the x-axis, as illustrated  by the yellow region in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 1(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Each domain contains  the same unit cell, whereby two air holes with different  radii, R and r, are arranged in a hexagonal array.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' The  unit cell and the first Brillouin zone (FBZ) are shown in  Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 1(b) and 1(c), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' In this study, we fix  the lattice constant, a = 400  √  3 nm, and the radius of  one of the nanoholes, R = 140 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' The optical prop-  erties of graphene are generally described by its surface  conductivity, given by Kubo’s formula [24, 25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  The band diagram of the graphene plasmonic crystal is  calculated by the finite-element method (FEM) of Wave  Optics Module in COMSOL® Multiphysics 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='6 [26] and  (a)  x  y  FBZ  mirror symmetric interface  y  x  (b)  (c)  (d)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' (a) Schematic of the graphene plasmonic nanohole  crystal with a domain-wall interface oriented along the x-  axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  The left- and right-hand side domains are placed in  a mirror-symmetric manner and contain the same unit cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  (b) Primitive unit cell of the graphene crystal with a lattice  constant a, containing two air nanoholes with different radii  R and r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' (c) First Brillouin zone of the graphene plasmonic  crystal showing the high-symmetry points Γ, K, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' (d)  Band diagram of the graphene plasmonic crystal determined  for different radii r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  validated using Synopsys® BandSOLVE tool [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  As  shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 1(d), the band diagrams were determined  for different radii r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' When r = 0, as per the black curves  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 1(d), there is a Dirac cone at the K point, which  is protected by the C6v symmetry of the hexagonal ar-  rangement of holes with radius R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  The first and sec-  ond bands indeed linearly cross at Dirac points located  at the frequency of 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='8 THz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' In order to open up the  inversion-symmetry-protected Dirac cone, additional air  holes (r ̸= 0) are introduced into the graphene plas-  monic crystal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' This reduces the spatial-inversion sym-  metry to the C3v point symmetry group [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  As a  consequence, the C6v-symmetry-protected Dirac cone is  gapped out, resulting in the formation of a nontrivial  frequency bandgap, as illustrated by the red and blue  curves in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 1(d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Moreover, the variation of the width  of the bandgap indicates its dependence on the radius  of the added holes, r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  Specifically, when r increases  from 50 nmto80 nm, the spectral width of the bandgap  increases by about 1 THz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  This frequency shift is al-  most entirely due to a blue-shift of the first band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' In our  subsequent computations, we consider graphene meta-  surfaces with radius r fixed to r = 50 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' This choice  is guided by the fact that in this way one can achieve a  relatively large nontrivial bandgap, which extends from  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='1 THzto11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='8 THz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  Since the lattice of holes has hexagonal symmetry,  it possesses two nonequivalent valleys in the reciprocal  space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' The integral of the Berry curvature around each  of these valleys defines the valley Chern number, which  among other things determines the number of possible  topological edge states [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  In the wave vector space,  around each valley, the distribution of the Berry curva-  ture around the two nonequivalent high-symmetry points  K and K′ defines two valley-dependent Chern numbers,  which can be computationally evaluated by the Wilson-  loop approach in a discretized Brillouin zone [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' To this  end, valley Chern numbers of the first band [see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 1(d)]  over the K and K′ valleys have been computed based on  the FEM implemented in COMSOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' The results of these  calculations, determined over a 18 × 18 computational  grid covering the k-space, are plotted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  We show in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 2(a) the Berry curvature distribution  of the first band when r = 20 nm over the K and K′  valleys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' As expected, the distribution of Berry curvature  shows a sharp peak with opposite signs at K and K′  points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Specifically, the computed valley Chern numbers  of the first band when r = 20 nm over K and K′ valleys  are 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='49 and −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='49, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' The small deviation of  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='01 from the theoretical value of valley Chern number,  |C| = 1/2, illustrates the accuracy of the Wilson-loop  computational method [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' For r = 50 nm correspond-  ing to a wider nontrivial bandgap in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 1(d), the com-  puted valley Chern numbers of the first band over K and  K′ valleys decrease to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='34 and −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='34, respectively, as  indicated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 2(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  Note that when the frequency  bandgap is relatively large, the distribution of the Berry  curvature over the corners at K and K′ symmetry points  a  R  ainterface  XM  K14  Frequency (THz)  12  Bandgap  10  8  r=0  r=50 nm  :r=80 nm  6  K  M3  1  0  1-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='5  1  0  1-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='5  (a)  Ω (𝑎2)  𝛿𝑘𝑦 (𝜋/𝑎)  𝛿𝑘𝑥 (𝜋/𝑎)  𝛿𝑘𝑦′ (𝜋/𝑎)  𝛿𝑘𝑥′ (𝜋/𝑎)  1  0  1-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='5  0  (b)  𝛿𝑘𝑦 (𝜋/𝑎)  𝛿𝑘𝑥 (𝜋/𝑎)  1  0  1-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='5  𝛿𝑘𝑦′ (𝜋/𝑎)  𝛿𝑘𝑥′ (𝜋/𝑎)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='5  𝐾 point  𝐾′ point  𝐾 point  𝐾′ point  Ω (𝑎2)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Computed Berry curvature distribution of the first  band over the K and K′ valleys, determined for the radius of  the additional hole (a) r = 20 nm and (b) r = 50 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  of the Brillouin zone spreads significantly and overlaps  with the Berry curvature distributions at neighbouring  K and K′ symmetry points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' This makes it more difficult  to properly define the valley Chern number, as its calcu-  lation cannot be extended to the entire FBZ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Therefore,  the theoretical valley Chern number C = ±1/2 can only  be obtained close to the Dirac point with an infinitesi-  mally small perturbation [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  Following this analysis, and for the sake of simplic-  ity of our further discussions, we fix the valley Chern  number of the first band over the K and K′ valleys to  CK = ±1/2 and CK′ = ∓1/2, respectively, values that  correspond to an infinitesimally small perturbation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' As  a result, when a domain-wall interface with valley Chern  number difference ∆C = ±1 is created by rotations of  the graphene crystal by π/3, π, or 5π/3, a pair of valley  modes is generated inside the bandgap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' These topologi-  cal modes propagate along the domain-wall interface in  opposite direction, namely they have positive and nega-  tive GV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  We now consider two semi-infinite graphene metasur-  faces placed together after one of them is rotated by π,  thus forming a mirror-symmetric domain-wall interface,  as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 3(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' The finite valley-dependent Chern  number makes it possible to form valley-momentum  locked interfacial modes, illustrated in the projected band  diagram of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 3(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' The blue regions represent the bulk  modes, whereas a topological interface-mode band inside  the nontrivial bandgap is marked by a red curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' In or-  der to gain deeper physical insights into the properties  of this topological mode, the corresponding field distri-  bution is calculated at the frequency of 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='4 THz, which  corresponds to the middle of the bandgap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' The particu-  lar topological mode is indicated by the symbol Es.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' As  illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 3(c), this topological mode propagates  along the domain-wall interface and is highly confined at  the interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  10  11  12  13  14  9  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='4 THz  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='8  x  y  x  y  𝑬𝒃𝟏  𝑬𝒃𝟐𝑬𝒃𝟑  𝑬𝒔  topological mode  bulk mode  1  Frequency (THz)  (a)  (b)  (c)  (d)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' (a) Supercell of a finite graphene plasmonic waveguide  with a domain-wall interface constructed from two mirror-  symmetric domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  (b) Projected band diagram of the  graphene plasmonic crystal waveguide corresponding to r =  50 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' A topologically protected interface-mode band (red  line) exists inside the nontrivial bandgap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' (c), (d) Unidirec-  tional propagation of topological interfacial modes along the  positive (negative) direction of the x-axis, when the waveguide  is excited by a LCP (RCP) source at 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='4 THz, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  Furthermore,  the unidirectional feature of valley-  momentum locked interface modes is also investigated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  To this end, six electric dipoles with increasing or de-  creasing phase difference (±π/3) are placed together at  the corners of a small hexagon, thus generating light with  specific chirality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' To be more specific, under the excita-  tion of a left circularly-polarized (LCP) source at the fre-  quency of 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='4 THz, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 3(c), the topologically pro-  tected interfacial mode propagates along the domain-wall  interface in the positive direction of the x-axis with a pos-  itive group velocity, whereas the opposite is true for the  topological interfacial mode excited by a right circularly-  polarized (RCP) source with the same frequency, as per  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 3(d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  ACTIVE ALL-OPTICALLY CONTROLABLE  SWITCH  Taking advantage of the unidirectional feature of the  topological interface mode of the proposed graphene  waveguide as well as the strong optical nonlinearity of  graphene, a graphene-based all-optical switch is designed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  To be more specific, we study the influence of the Kerr  effect in graphene on the propagation characteristics of  topological interface modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' As a versatile 2D material  with large relaxation time (low optical losses) at THz fre-  quencies, optical near-field enhancement [32], and large  optical nonlinearity [33], graphene is ideally suited for  nonlinear optics applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  The refractive index variation induced by the Kerr ef-  fect in the graphene metasurface, in response to the elec-  tric field generated by an optical pump, is given by [12]:  ∆ng(r) = 1  2cϵ0ngn2|Ep(r)|2,  (1)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='5  0  20  20  10  10  @  020  20  10  10  @  020  15  10  5  20  20  10  10  0  @5  10  15  20  20  20  10  10  @  0Ckx(π/a)4  where ng is the refractive index of graphene, n2 =  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='5 × 10−11 m2/W is the nonlinear refractive coefficient  of graphene [34], and Ep(r) is the field amplitude of the  pump.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Moreover, the pump power per unit cell, Pp, car-  ried by a bulk mode Eb is given by [35]:  Pp = vg  4a  �  Vcell  ∂  ∂ω [ωϵω(r)]|Eb(r)|2dV,  (2)  where vg = dω/dkx is the GV, Vcell is the volume of the  unit cell, and ϵω(r) is the frequency-dependent permit-  tivity distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  To investigate the influence of the pump induced Kerr  effect on the light propagation in the topological mode,  several bulk modes with different GV are employed as  pump modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  Since the power of the signal is much  smaller than that of the pump, the contribution of the  signal to the Kerr induced variation of the refractive in-  dex is neglected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' As a result, the signal propagation in  the topological mode is solely controlled by the optical  pump.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  The optical characteristics of the pump and signal  modes are summarized in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' For the bulk mode band  indicated by the green curve in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 3(b), the GV vg and  group index, ng = c/vg, are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 4(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' The three  bulk modes, Eb1 [kx = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='55(π/a)], Eb2 [kx = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='61(π/a)],  and Eb3 [kx = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='67(π/a)], are chosen in such a way that  the first two are fast-light (FL) modes, whereas the last  one is located in the SL region (the corresponding group  index approaches 1000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Slow light can generally provide  strong field enhancement and consequently can lead to in-  creased nonlinear optical interactions [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Moreover, the  corresponding field distributions of the signal and pump  modes are plotted in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 4(b) and 4(c), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  The field distribution of the topological valley mode Es,  depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 3(b), shows that a signal generated by a  LCP source with 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='4 THz is tightly confined along the  domain-wall interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Moreover, the spatial field pro-  file of the bulk mode Eb1 with the largest GV among  the three chosen bulk modes reveals a relatively uniform  x  y  x  y  𝐸𝑏1  𝐸𝑏2  𝐸𝑏3  v  (b)  (c)  (a)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' (a) Dependence of group velocity vg and group index  ng = c/vg on kx, corresponding to the bulk mode containing  Eb1, Eb2, and Eb3 [(green line in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 3(b)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' (b) Field profile  of the topological interface mode at 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='4 THz, indicated by  Es in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 3(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' (c) Field distribution of the pump injected  in the bulk mode Eb1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='4THz  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='4THz  Frequency (THz)  1 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='8 1 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='8  1  10  11  12  13  14  9  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='4THz  0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='8  𝑃𝑝 = 0  𝑃𝑝 = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='25 𝜇𝑊  𝑃𝑝 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='81 𝜇𝑊  topological  topological  topological  𝑬𝒃𝟏  bulk mode  (a)  (b)  (c)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  (a), (b), (c) Projected band diagram of graphene  nanohole plasmonic waveguide corresponding to the pump in-  jected in the bulk mode Eb1, determined for the pump power  Pp = 0, Pp = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='81 µW, and Pp = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='25 µW, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  field distribution that extends across the entire graphene  metasurface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Note that our simulations produced similar  electric field distributions for the other two bulk modes,  Eb2 and Eb3, the main difference being the value of the  field amplitude corresponding to a given pump power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  Since the optical Kerr effect in the graphene metasur-  face is induced by the pump, we investigated the depen-  dence of the projected photonic band diagram on the  pump power, Pp, the corresponding results being dis-  played in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  In order to determine the projected  band structure corresponding to a pump power, Pp, we  proceeded as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' First, we computed the field dis-  tribution of the pump mode, Eb(r), and its GV, vg, then  scaled it using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' (2) in such a way that the optical  power carried by the mode was Pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Subsequently, using  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' (1), we calculated the Kerr-induced variation of the  index of refraction of graphene and the corresponding  distribution of the electric permittivity of the graphene  metasurface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' In the final step, this nonlinear permittiv-  ity was employed to determine the nonlinearly modified  projected photonic band diagram of the metasurface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' It  should be noted that since the pump mode is periodic  along the x-axis, a projected band structure can be de-  fined in the optically pumped metasurface, too.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  In this analysis, we assumed that the pump power Pp  was equal to 0 (linear regime), 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='81 µW, and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='25 µW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  The results of these computations indicate that as the  pump power increases the frequency of the topological  bandgap is blue-shifted by as much as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='3 THz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' There-  fore, if the frequency of the signal mode is fixed to  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='4 THz, by increasing the pump power Pp, we can  switch the topological interface mode (originally located  inside the bandgap) to a frequency region occupied by  leaky bulk modes (outside the bandgap), namely a fre-  quency at which the signal can no longer propagate in  the waveguide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  The threshold pump power needed to  switch off the signal propagation was calculated to be  kx(π/a)X106  4  1000  2  500  (m/s)  0  0  V  2  500  4  6  1000  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='59  nkx(π/a)5  𝑃𝑝 (𝜇𝑊)  0  5  10  15  (b)  𝐸𝑝 pump region  x  y  L  𝑷𝒔𝒊𝒏  𝑷𝒔𝒐𝒖𝒕  W  (a)  LCP signal source  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' (a) Schematic of the active all-optical switch based on  the graphene plasmonic waveguide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Light is pumped in the  bulk mode Eb (yellow region), whereas the signal Es is gener-  ated by a LCP source at 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='4 THz and carries an input power  Psin and output power Psout.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  The length of the graphene  waveguide is L = 35a and the device width is W = 19a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' (b)  Signal transmission, defined as η = Psout/Psin, vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' the pump  power Pp, determined for the bulk modes with different GV,  Eb1, Eb2, and Eb3, indicated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 4(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  Pp = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='25 µW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' It should be noted that we observed that  the relative location of the bands did not change signifi-  cantly as the pump power increased, although, as we just  explained, their frequency varied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  After the validation of the main idea on which our  proposed optically controllable switch operates, namely  the optical tuning of the band structure of the graphene  metasurface via a pump beam, we proceeded to analyze  quantitatively the optical characteristics of our optical  switch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' To this end, we considered the optical device de-  picted schematically in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 6(a), which is operated as fol-  lows: a pump beam Ep (yellow region) with a frequency  chosen in such a way that it propagates in a bulk mode,  Eb, is injected into the graphene metasurface, while a low  power LCP source with frequency 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='4 THz generates an  optical signal (probe) Es.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' The length of the graphene  plasmonic metasurface was L = 35a, which ensured that  one achieves a relatively stable signal propagation at the  domain-wall interface along the x-axis well beyond the  transient region where the light is coupled from the LCP  source to the signal mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Due to the fact that the opti-  cal signal with a frequency of 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='4 THz can be switched  from a topological interface mode to leaky bulk modes by  tuning the pump power, the optical signal can be turned  ON/OFF when the pump power increases beyond a cer-  tain threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' To validate and quantify these ideas, we  define the transmission of the signal beam as the ratio be-  tween the output power of the signal, Psout, measured at  the end of the graphene waveguide, and the input power  of the signal, Psin, measured nearby the LCP source,  namely η = Psout/Psin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  Given that the power of the  signal depends on the pump power, the transmission η  depends implicitly on Pp, too.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  The results of our computational analysis of the pro-  posed optical switch are summarized in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 6(b), where  we plot the dependence of the transmission of the sig-  nal power η on the pump power Pp, determined for the  cases when the pump power is injected in the bulk modes  with different GV, Eb1 (red circles), Eb2 (blue triangles),  and Eb3 (black stars), indicated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 4(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  By em-  ploying the three pump modes, Eb1, Eb2, and Eb3, with  decreasing GV approaching the SL regime, allowed us  the investigate the influence of SL effects on the device  characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' One conclusion of this analysis is that  the signal transmission corresponding to pump modes  with different GV presents a similar trend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Specifically,  the signal transmission increases with the increase of the  pump power, which is explained by the fact that, due to  the Kerr-effect-induced increment of the refractive index  of graphene waveguide, the signal can be more readily  focused and coupled from the excitation source into the  topological mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Subsequently, as the pump power is  further increased, the signal mode begins to couple to  bulk modes resulting in a steep decrease to less than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='1  of the signal transmission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  Another important fact revealed by the plots presented  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 6(b) is that the pump power needed to switch  ON/OFF the signal decreases dramatically when the GV  of the pump mode is pushed into the SL regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' In par-  ticular, more than 6× reduction of the switching optical  pump power is observed in our numerical investigations  when the pump mode is tuned from Eb1 to Eb3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' This  important result can be easily understood from the in-  formation conveyed by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  Thus, it can be seen  from this equation that for a given pump power, Pp, the  smaller the GV, vg, of the pump mode is, the larger is  the corresponding electric field intensity |Eb| of the pump  mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' This in turn implies that a larger Kerr-induce vari-  ation of the index of refraction of graphene is achieved  and consequently a larger frequency shift of the photonic  bands is attained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  CONCLUSION  We demonstrated an active optically-tunable switch  based on the Kerr effect in a topologically protected  valley-Hall  graphene  plasmonic  metasurface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  The  spatial-inversion symmetry breaking of the graphene  nanohole metasurface is realized by introducing an extra  hole, which opens up a symmetry-protected Dirac cone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  Consequently, a topological interface mode is formed in-  side the nontrivial bandgap and propagates along the  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='6  m  n  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='5  0  S  S  Transmi  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='14o Eb1  Eb2  Eb36  domain-wall interface in a unidirectional manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Tak-  ing advantage of a large nonlinear refractive index of the  graphene, the Kerr effect induced in the graphene is used  to shift the frequency of the nontrivial bandgap of the  system, so that one can optically control the signal prop-  agation in the proposed topological graphene waveguide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  Importantly, our results show that the transmission of the  optical signal sharply decreases as the the pump power  increases, and the required switching pump power is sig-  nificantly reduced when the all-optical switch operates in  the slow-light regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  Funding European Research Council (ERC- 2014-  CoG-648328);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' China Scholarship Council.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  Disclosures The authors declare no conflicts of inter-  est.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  [1] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Lu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Joannopoulos, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Soljacic, “Topological  photonics,” Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Photonics 8(11), 821-829 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  [2] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Khanikaev and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Shvets,  “Two-dimensional  topological photonics,” Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Photonics 11(12), 763-773  (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  [3] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Xie, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' “Photonics meets topology,” Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Ex-  press 26(19), 24531-24550 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  [4] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Qiao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Yang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Feng, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Tse, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Ding, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  Yao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Wang, and Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Niu, “Quantum anomalous Hall  effect in graphene from Rashba and exchange effects,”  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' B 82(16), 161414 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  [5] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Rycerz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Tworzyd�lo, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Beenakker, “Val-  ley filter and valley valve in graphene,” Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 3(3),  172-175 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  [6] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Xiao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Wang, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Qian, “Valley-contrasting  physics in graphene: magnetic moment and topological  transport,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 99(23), 236809 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  [7] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Ma and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Shvets, “All-Si valley-Hall photonic topo-  logical insulator,” New J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 18(2), 025012 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  [8] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Noh, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Huang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Chen, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Rechtsman,  “Observation of photonic topological valley Hall edge  states,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 120(6), 063902 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  [9] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Foster, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Turner, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Lipson, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Gaeta,  “Nonlinear optics in photonic nanowires,” Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Express  16(2), 1300-1320 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  [10] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Monat, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' De Sterke, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Eggleton, “Slow light  enhanced nonlinear optics in periodic structures,” J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  12(10), 104003 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  [11] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Panoiu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Bahl, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Osgood, “Optically  tunable superprism effect in nonlinear photonic crystals,”  Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 28(24), 2503-2505 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  [12] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Boyd, Nonlinear optics (Academic press, 2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  [13] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Harari, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Bandres, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Lumer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Rechtsman,  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Chong, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Khajavikhan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Christodoulides,  and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Segev, “Topological insulator laser: theory,” Sci-  ence 359(6381), eaar4003 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  [14] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Bandres, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Wittek, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Harari, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Parto, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  Ren, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Segev, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Christodoulides, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Kha-  javikhan, “Topological insulator laser:  Experiments,”  Science 359(6381), eaar4005 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  [15] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Mukherjee and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Rechtsman, “Observation of  Floquet solitons in a topological bandgap,” Science  368(6493), 856-859 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  [16] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  Leykam  and  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  Chong,  “Edge  solitons  in  nonlinear-photonic topological insulators,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 117(14), 143901 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  [17] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Wang and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Panoiu, “Optically controllable cou-  pling between edge and topological interface modes of  graphene metasurfaces,” J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 24(10), 104002 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  [18] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Lan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' You, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Panoiu, “Nonlinear one-way  edge-mode interactions for frequency mixing in topolog-  ical photonic crystals,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' B 101(15), 155422  (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  [19] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Lan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' You, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Ren, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Sha, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  Panoiu, “Second-harmonic generation via double topo-  logical valley-Hall kink modes in all-dielectric photonic  crystals,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' A 103(4), L041502 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  [20] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Smirnova, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Kruk, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Leykam, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Melik-Gaykazyan,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Choi, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Kivshar, “Third-harmonic generation  in photonic topological metasurfaces,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  123(10), 103901 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  [21] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' You, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Lan, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Panoiu, “Four-wave mixing  of topological edge plasmons in graphene metasurfaces,”  Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 6(13), eaaz3910 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  [22] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Smirnova, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Leykam, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Chong, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Kivshar,  “Nonlinear topological photonics,” Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  7(2), 021306 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  [23] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Grigorenko, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Polini, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Safavi-Novoselov,  “Graphene plasmonics,” Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Photonics 6(11), 749-758  (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  [24] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Dressel and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Gruner, Electrodynamics of Solids  (Cambridge University Press, 2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  [25] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  Wang,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  You,  Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  Lan,  and  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  Panoiu,“Topological  valley  plasmon  transport  in  bilayer graphene metasurfaces for sensing applications,”  Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 45(11), 3151-3154 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  [26] COMSOL  Multiphysics®  (available  at:  www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='comsol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='com).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  [27] Synopsys® (available at: www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='synopsys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='com).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  [28] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' You, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Lan, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Bao, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Panoiu,“Valley-Hall  topological plasmons in a graphene nanohole plasmonic  crystal waveguide,” IEEE J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Sel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Top.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Quantum Electron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  26(6), 4600308 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  [29] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Wang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Guo, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Jiang, “Band topol-  ogy in classical waves: Wilson-loop approach to topolog-  ical numbers and fragile topology,” New J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 21(9),  093029 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  [30] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Shalaev, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Walasik, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Tsukernik, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Xu, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Litchinitser, “Robust topologically protected trans-  port in photonic crystals at telecommunication wave-  lengths,” Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Nanotechnol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 14(1), 31-34 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  [31] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Wong, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Saba, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Hess, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Oh, “Gapless uni-  directional photonic transport using all-dielectric kagome  lattices,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 2(1), 012011 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  [32] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  You,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  Bongu,  Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  Bao,  and  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  Panoiu,“Nonlinear optical properties and applications of  2D materials:  theoretical and experimental aspects,”  Nanophotonics 8(1), 63-97 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  [33] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Wu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Mao, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Jones, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Yao, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Zhang, and  X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Xu,“Quantum-enhanced tunable second-order opti-  cal nonlinearity in bilayer graphene,” Nano Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 12(4),  7  2032-2036 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  [34] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Thakur, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Semnani, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Safavi-Naeini, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  Majedi, “Experimental characterization of the ultra-  fast, tunable and broadband optical Kerr nonlinearity  in graphene,” Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 9(1), 1-10 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  [35] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Lavdas and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Panoiu, “Theory of pulsed four-  wave mixing in one-dimensional silicon photonic crystal  slab waveguides,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' B 93(11), 115435 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content='  [36] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Harris and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Hau, “Nonlinear optics at low light  levels,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
+page_content=' 82(23), 4611-4614 (1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9AzT4oBgHgl3EQfYPyg/content/2301.01332v1.pdf'}
diff --git a/VNE0T4oBgHgl3EQf2wJn/vector_store/index.faiss b/VNE0T4oBgHgl3EQf2wJn/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..6ab3acbc32f52a0cb6cf8a5cfd14cad63709ded6
--- /dev/null
+++ b/VNE0T4oBgHgl3EQf2wJn/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c880025de7a260a84b038231ae7d63c2ead31d2659978412cad5721ed9839706
+size 4128813
diff --git a/VNE0T4oBgHgl3EQf2wJn/vector_store/index.pkl b/VNE0T4oBgHgl3EQf2wJn/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..6c35bf22c7744f596f9d7fa58492cd4446c90739
--- /dev/null
+++ b/VNE0T4oBgHgl3EQf2wJn/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1ad89dea7f3995ce520a28f3fa700732525716dd9e891961ea5dd27e367d79d3
+size 132425
diff --git a/WtE2T4oBgHgl3EQfDga8/content/2301.03626v1.pdf b/WtE2T4oBgHgl3EQfDga8/content/2301.03626v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..0d36323cc7b8c709196eb552ce6890686d446195
--- /dev/null
+++ b/WtE2T4oBgHgl3EQfDga8/content/2301.03626v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1ad06bdb4eeb283a9714086d81b743acc42214536254a8f12e5499bbce294f56
+size 1313122
diff --git a/WtE2T4oBgHgl3EQfDga8/vector_store/index.faiss b/WtE2T4oBgHgl3EQfDga8/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..c4954105033f0ec41e09bed4fbbacf21c69ee293
--- /dev/null
+++ b/WtE2T4oBgHgl3EQfDga8/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4de72c85f6fcb91b13763e0ad8829b0888bd153eb25c870472a25903c535ecd9
+size 6619181
diff --git a/WtE2T4oBgHgl3EQfDga8/vector_store/index.pkl b/WtE2T4oBgHgl3EQfDga8/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..2028a3a15c112887a73e6e3d1a3a9eab9423bbb7
--- /dev/null
+++ b/WtE2T4oBgHgl3EQfDga8/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:93a6e690e9c095e0a298c614cc2f3fae5ead6ef7656bd94b787893434b4c0916
+size 231308
diff --git a/X9AyT4oBgHgl3EQf9foH/content/2301.00873v1.pdf b/X9AyT4oBgHgl3EQf9foH/content/2301.00873v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..4bf8448bd457b3e1529f391778f0c7568a6fcaf3
--- /dev/null
+++ b/X9AyT4oBgHgl3EQf9foH/content/2301.00873v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1280e74c89a684997320f45a18c70480376ebd197bb690c164e76248acf57e4d
+size 1942169
diff --git a/X9AyT4oBgHgl3EQf9foH/vector_store/index.pkl b/X9AyT4oBgHgl3EQf9foH/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..a89889c0ba22be51ebb04605940620c3b95ca01a
--- /dev/null
+++ b/X9AyT4oBgHgl3EQf9foH/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:508259b599741de99be5c319a90f32fc03089a505d5e07df8dc449917a8ce54c
+size 130845
diff --git a/X9E5T4oBgHgl3EQfdQ8b/content/2301.05609v1.pdf b/X9E5T4oBgHgl3EQfdQ8b/content/2301.05609v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..789e72d5f5111717da68f6743f45d635272086aa
--- /dev/null
+++ b/X9E5T4oBgHgl3EQfdQ8b/content/2301.05609v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9c072d9bbccd7f337a3a90082761104bc286f68578873fc066acb3b24b6d7ff0
+size 12929294
diff --git a/X9E5T4oBgHgl3EQfdQ8b/vector_store/index.faiss b/X9E5T4oBgHgl3EQfdQ8b/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..2b9a96c20e4b97515ac53f9bf6c660e16e3ef5e1
--- /dev/null
+++ b/X9E5T4oBgHgl3EQfdQ8b/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9d18e121e77c35c14f6ee61afc9614050313a1ac9757ea9142a6dcdadaebdf80
+size 3342381
diff --git a/XNE0T4oBgHgl3EQfmQGx/content/tmp_files/2301.02497v1.pdf.txt b/XNE0T4oBgHgl3EQfmQGx/content/tmp_files/2301.02497v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..669c9617cb7c26cab1eeb7c87873eadbfbbd0ffd
--- /dev/null
+++ b/XNE0T4oBgHgl3EQfmQGx/content/tmp_files/2301.02497v1.pdf.txt
@@ -0,0 +1,1337 @@
+arXiv:2301.02497v1  [math.AT]  6 Jan 2023
+SOME ASYMPTOTIC FORMULAE FOR TORSION IN HOMOTOPY GROUPS
+GUY BOYDE AND RUIZHI HUANG
+Abstract. Inspired by a remarkable work of F´elix, Halperin and Thomas on the asymptotic
+estimation of the ranks of rational homotopy groups, and more recent works of Wu and the authors
+on local hyperbolicity, we prove two asymptotic formulae for torsion rank of homotopy groups,
+one using ordinary homology and one using K-theory. We use these to obtain explicit quantitative
+asymptotic lower bounds on the torsion rank of the homotopy groups for many interesting spaces
+after suspension, including Moore spaces, Eilenberg-MacLane spaces, complex projective spaces,
+complex Grassmannians, Milnor hypersurfaces and unitary groups.
+1. Introduction
+The homotopy groups of a simply connected CW-complex Y of finite type have the form
+πi(Y ) ∼= (⊕
+di
+Z) ⊕
+⊕
+prime p
+t∈Z+
+( ⊕
+kp,t
+Z/pt),
+where di and kp,t are the rank of the free summands and the Z/pt-summands of πi(Y ) respectively.
+Denote rank0(πi(Y )) := di and rankZ/pt(πi(Y )) := kp,t.
+In the remarkable work [FHT], F´elix, Halperin and Thomas proved an asymptotic formula for
+the ranks rank0(πi(Y )) of the free part of the homotopy groups. In particular, they showed that if
+Y is finite and rank0(πi(Y )) ̸= 0 for infinitely many i ∈ Z+, then there is a constant δ > 1 such that
+for N large enough
+N+dim(Y )
+�
+i=N+2
+rank0(πi(Y )) ≥ δN,
+which they interpret as a strong ‘regularity’ property for the ranks rank0(πi(Y )) of the free part of
+the homotopy groups. Concerning the ranks rankZ/pt(πi(Y )) of the torsion part of the homotopy
+groups, they further raised the following natural question, which was rephrased in an explicit form
+by Wu and the second author in [HW, Question 1.8].
+Question 1.1. Are there ‘regularity’ properties of the torsion subgroups of the homotopy groups
+πi(Y ) as i → ∞?
+In this paper, we study the above question by providing estimates for the ranks rankZ/pt(πi(Y )) in
+certain cases. In particular, we give quantitative refinements of results of the authors and Wu, from
+the papers [HW], [Boy1], and [Boy2]. The methods of these papers implied more than was stated
+2010 Mathematics Subject Classification. Primary 55Q52, 55Q05, Secondary 55Q15, 55P40.
+1
+
+2
+GUY BOYDE AND RUIZHI HUANG
+in the theorems: the statements were always that the volume of p-torsion in the homotopy groups
+of various spaces grows exponentially, but actually the methods were completely constructive, and
+with more work one can extract concrete exponential lower bounds. The extraction of these lower
+bounds is the business of this paper.
+The proof of each of our main theorems (1.2 and 1.7) begins with the combinatorics of free
+Lie algebras, which have been well understood since long before F´elix, Halperin, and Thomas’s
+celebrated theorem. We use in particular some results of Babenko [Bab] and Lambrechts [Lam],
+both of which are more general. From this common beginning, the proof of each theorem is then
+complicated in a different way; we elaborate briefly after each theorem statement.
+Recent work of Burklund and Senger [BS] has greatly advanced our understanding of these phe-
+nomena: they finish a story begun by Henn [Hen] and Iriye [Iri] and show that the radii of convergence
+of the p-local “homotopy” and “loop-homology” power series are equal. Again, we discuss each of
+our theorems in light of this.
+1.1. Results via homology. We first give our quantitative refinement of the main result of [Boy2].
+To state the results, for any integer q ≥ 2 define a function
+fq(x) = (1 −
+x
+x − 1
+1
+ϕ) · 1
+xϕx − cxϕ
+x
+2 − κ|ψ|x
+for x ≥ 2, where
+• ϕ is the unique positive real root of the degree q + 1 polynomial P(z) = zq+1 − z − 1,
+• c = 2(q + 2)(1 + ϕ), and
+• κ = (q + 1)(1 +
+1
+|ψ|) with ψ the next largest root of P(z) in absolute value.
+We have the properties
+• 2
+1
+q+1 < ϕ < 1 + 1
+q , and
+• for any ε > 0, once x is large enough we have
+fq(x) ≥ (1 − ε)(1 − 1
+ϕ) · 1
+xϕx > (1 − ε)(1 − 2−
+1
+q+1 ) · 1
+x2
+x
+q+1 .
+We will use the function fq(x) with its properties freely in this subsection.
+Let P q+1(pr) be the Moore space defined as the mapping cone of the degree pr map Sq → Sq.
+The following theorem provides an asymptotic formula for the p-local homotopy groups under a
+homological condition.
+Theorem 1.2. Let Y be a simply connected CW-complex, let p ̸= 2 be prime, and let s ≤ r ∈ Z+.
+If there exists a map
+µ : P q+1(pr) −→ Y
+for some q ≥ 2, such that the induced map
+(Ωµ)∗ : H∗(ΩP q+1(pr); Z/ps) −→ H∗(ΩY ; Z/ps)
+
+SOME ASYMPTOTIC FORMULAE FOR TORSION IN HOMOTOPY GROUPS
+3
+is an injection, then we have the bound
+r
+�
+t=s
+rankZ/pt(πN+1(Y )) ≥ fq(N).
+In particular, for any ε > 0, once N is large enough we have
+r
+�
+t=s
+rankZ/pt(πN+1(Y )) > (1 − ε)(1 − 2−
+1
+q+1 ) · 1
+N 2
+N
+q+1 .
+Algebraically, Theorem 1.2 depends on the structure of the module of boundaries in a free Lie
+algebra over a finite field. It is the need to take boundaries which complicates the story relative
+to Babenko and Lambrechts’s work. This is dealt with in Subsection 2.3, using a result of Cohen,
+Moore, and Neisendorfer [CMN].
+It follows from [Boy2] that the hypotheses of Theorem 1.2 simplify in the case that Y = ΣX is a
+suspension, as follows:
+Theorem 1.3. Let X be a connected CW-complex, let p ̸= 2 be prime, and let s ≤ r ∈ Z+. Suppose
+that H∗(X; Z/ps) has finite type. If there exists a map
+µ : P q+1(pr) −→ ΣX
+for some q ≥ 2, such that
+µ∗ : �H∗(P q+1(pr); Z/ps) −→ �H∗(ΣX; Z/ps)
+is an injection, then we have the bound
+r
+�
+t=s
+rankZ/pt(πN+1(ΣX)) ≥ fq(N).
+In particular, for any ε > 0, once N is large enough we have
+r
+�
+t=s
+rankZ/pt(πN+1(ΣX)) > (1 − ε)(1 − 2−
+1
+q+1 ) · 1
+N 2
+N
+q+1 .
+The spaces X and Y in Theorems 1.2 and 1.3 can be infinite. The asymptotic formulae in both
+theorems bound the ranks of the p-local homotopy groups from below by an exponential function. In
+particular, they strengthen a recent result of the first author on local hyperbolicity [Boy2, Theorem
+1.5 and 1.6].
+Theorem 1.3 has interesting applications. For instance, we can show the following corollary.
+Corollary 1.4. Let X be a (q − 2)-connected CW-complex with q ≥ 2, and let p ̸= 2 be prime.
+Suppose that H∗(X; Z/pr) has finite type and Hq(ΣX; Z) contains a Z/pr-summand. Then we have
+rankZ/pr(πN+1(ΣX)) ≥ fq(N).
+In particular, for any ε > 0, once N is large enough we have
+rankZ/pr(πN+1(ΣX)) > (1 − ε)(1 − 2−
+1
+q+1 ) · 1
+N 2
+N
+q+1 .
+□
+
+4
+GUY BOYDE AND RUIZHI HUANG
+Either Corollary 1.4 or Theorem 1.3 implies the following immediately for the Moore spaces.
+Corollary 1.5. Let p be an odd prime and q ≥ 2. Then
+rankZ/pr(πN+1(P q+1(pr)) ≥ fq(N).
+In particular, for any ε > 0, once N is large enough we have
+rankZ/pr(πN+1(P q+1(pr)) > (1 − ε)(1 − 2−
+1
+q+1 ) · 1
+N 2
+N
+q+1 .
+□
+This strengthens a result of Wu and the second author on the Z/pr-hyperbolicity of P q+1(pr)
+[HW, Theorem 1.6].
+It is enlightening to compare this result from what could be deduced already from Burklund
+and Senger’s work [BS]. It follows from their Corollary A.5 that the radius of convergence of the
+series �∞
+N=1 dimZ/p(πN(P q+1(pr)) ⊗ Z/p) · tN is precisely
+1
+ϕ. Since P q+1(pr) is rationally elliptic
+(being rationally contractible), this power series really is describing the torsion. Corollary 1.5 adds
+information in two ways: first by giving a concrete function as a lower bound for all N, and second
+by saying something about summands isomorphic to Z/pr in particular, rather than p-torsion in
+general.
+Another interesting example of Corollary 1.4 is Eilenberg-MacLane space after suspension. In
+particular, the following immediate corollary strengthens [Boy2, Example 2.5].
+Corollary 1.6. Let p be an odd prime and q ≥ 2. Then
+rankZ/pr(πN(ΣK(Z/pr, q − 1)) ≥ fq(N).
+In particular, for any ε > 0, once N is large enough we have
+rankZ/pr(πN(ΣK(Z/pr, q − 1)) > (1 − ε)(1 − 2−
+1
+q+1 ) · 1
+N 2
+N
+q+1 .
+□
+1.2. Results via K-theory. Denote by
+rankp(πi(ΣX)) =
+∞
+�
+t=1
+rankZ/pt(πi(ΣX))
+the rank of the p-torsion summands of πi(ΣX). Our other main result refines the main theorem of
+[Boy1] to a quantitative statement under a K-theoretical condition:
+Theorem 1.7 (Weak version of Theorem 3.3). Let p be an odd prime, and let X be a path connected
+space having the p-local homotopy type of a finite CW-complex. Suppose that there exists a map
+µ :
+ℓ�
+i=1
+mi
+�
+j=1
+Sqi+1 → ΣX
+with 1 ≤ q1 < q2 < · · · < qℓ, such that the map
+�K∗(ΣX) ⊗ Z/p
+µ∗
+−→ �K∗(
+ℓ�
+i=1
+mi
+�
+j=1
+Sqi+1) ⊗ Z/p ∼=
+ℓ
+�
+i=1
+mi
+�
+j=1
+Z/p
+
+SOME ASYMPTOTIC FORMULAE FOR TORSION IN HOMOTOPY GROUPS
+5
+is a surjection.
+Then for any ε > 0, once the multiple M = mg′ of
+g′ = gcd(q1, . . . qℓ, 2(p − 1))
+is large enough we have
+rankp(πM(ΣX)) ≥
+1
+M 1+ε ϕ( conn(X)+1
+dim(X)+1 )M,
+where ϕ is the unique positive real root of the degree qℓ polynomial
+zqℓ −
+ℓ
+�
+i=1
+mizqℓ−qi = 0,
+(in particular, ϕ ≥ (�ℓ
+i=0 mi)
+1
+qℓ = (�ℓ
+i=0 mi)
+1
+max(q1,...qℓ) ), conn(X) is the p-local connectivity of X,
+and dim(X) is the rational cohomological dimension of X.
+A stronger estimate is provided by Theorem 3.3 with Remark 3.4 at the end of the paper. In
+particular, the asymptotic formulae in both theorems bound the ranks of the p-local homotopy
+groups from below by an exponential function. Unlike with Theorem 1.2, it is not necessary to
+take boundaries to prove Theorem 1.7, but the topological picture is difficult. The difficulty arises
+ultimately from an interaction between the James construction and the Adams operations, which
+as far as the authors know originates in the paper [Sel] of Selick on which [Boy1] is modelled,
+and manifests combinatorially as Condition (*) in the last section. This condition means that the
+‘Lie algebra’ one is ultimately able to find a copy of in homotopy groups ‘lags’ - appearing in higher
+dimensions than one might expect. In the end, this shows up as for example the factor of ( conn(X)+1
+dim(X)+1 )
+in the exponent in Theorem 1.7.
+Theorem 1.7 has interesting applications. For instance, let Grk(Cn) be the Grassmannian of
+k-dimensional complex linear subspaces of Cn, which is simply connected and of complex dimension
+k(n − k). Recall Gr1(Cn) ∼= CP n−1. In [Boy1, Example 2.6], it is shown that when n ≥ 3 and
+0 < k < n there is a map
+S3 ∨ S5 −→ ΣGrk(Cn)
+which induces a surjection on �K∗( ) ⊗ Z/p for all odd primes p. Therefore, the following corollary
+follows immediately from Theorem 1.7, which strengthens [Boy1, Example 2.5 and 2.6].
+Corollary 1.8. Let p be an odd prime, n ≥ 3 and 0 < k < n. Then for any ε > 0, once m is large
+enough we have
+rankp(π2m(ΣGrk(Cn))) ≥
+1
+(2m)1+ε
+�3 +
+√
+5
+2
+�
+m
+2k(n−k)+1 .
+□
+Similarly, let Hn,ℓ be the Milnor hypersurface defined by
+Hn,ℓ = {([z], [w]) ∈ CP n × CP ℓ |
+min(n,ℓ)
+�
+i=0
+ziwi = 0},
+
+6
+GUY BOYDE AND RUIZHI HUANG
+which is simply connected and of complex dimension n + ℓ − 1. In [Boy1, Example 2.7], it is showed
+that when n ≥ 2 and ℓ ≥ 3 there is a map
+S3 ∨ S5 −→ ΣHn,ℓ
+which induces a surjection on �K∗( ) ⊗ Z/p for all odd primes p. Therefore, the following corollary
+follows immediately from Theorem 1.7, which strengthens [Boy1, Example 2.7].
+Corollary 1.9. Let p be an odd prime, n ≥ 2 and ℓ ≥ 3. Then for any ε > 0, once m is large
+enough we have
+rankp(π2m(ΣHn,ℓ)) ≥
+1
+(2m)1+ε
+�3 +
+√
+5
+2
+�
+m
+2(n+ℓ)−1 .
+□
+Consider the n-th unitary group U(n) which is connected and of real dimension n2. In [Boy1,
+Example 2.8], it is showed that when n ≥ 3 there is a map
+S3 ∨ S5 −→ U(n)
+which induces a surjection on �K∗( )⊗Z/p for all odd primes p. It is clear that this map can be lifted
+to the special unitary group SU(n), which is 2-connected and of real dimension n2 − 1. Therefore,
+the following corollary follows immediately from Theorem 1.7, which strengthens [Boy1, Example
+2.8].
+Corollary 1.10. Let p be an odd prime and n ≥ 3. Then for any ε > 0, once m is large enough we
+have
+rankp(πm(ΣU(n))) ≥
+1
+m1+ε ϕ
+m
+n2+1 >
+1
+m1+ε (1.19)
+m
+n2+1 ,
+rankp(πm(ΣSU(n))) ≥
+1
+m1+ε ϕ
+3m
+n2 >
+1
+m1+ε (1.70)
+m
+n2 ,
+where ϕ is the unique positive real root of z5 − z2 − 1 = 0.
+□
+The structure of this paper is as follows. Section 2 treats the algebra and combinatorics. Sub-
+section 2.2 treats free Lie algebras without a differential, and Subsection 2.3 studies the module
+of boundaries in the differential case. These results are then used to prove the main theorems in
+Section 3.
+Acknowledgements This paper was written while Guy Boyde was an EPSRC Doctoral Prize post-
+doc at the University of Southampton. He would like to thank Naomi Andrew, George Davenport,
+Lawk Mineh, and Stephen Theriault for many helpful conversations.
+Ruizhi Huang was supported in part by the National Natural Science Foundation of China (Grant
+nos. 11801544 and 12288201), the National Key R&D Program of China (No. 2021YFA1002300),
+the Youth Innovation Promotion Association of Chinese Academy Sciences, and the “Chen Jingrun”
+Future Star Program of AMSS.
+
+SOME ASYMPTOTIC FORMULAE FOR TORSION IN HOMOTOPY GROUPS
+7
+2. Algebra
+2.1. Complex arithmetic.
+Lemma 2.1. Let S be a finite set of positive integers, let g = gcd(S), and let η ∈ C be nonzero.
+Then ηg is a positive real if and only if ηi is a positive real for all i ∈ S.
+Proof. The ‘only if’ direction follows from the fact that g divides each member of S. For the ‘if’
+direction, Bezout’s Lemma gives αi ∈ Z for each i ∈ S such that �
+i αi · i = g. Thus, if each ηi is a
+positive real, we get
+ηg = η
+�
+i αi·i =
+�
+i
+(ηi)αi,
+which is a product of powers of positive reals, hence also a positive real.
+□
+Lemma 2.2. Let c0, . . . ck−1 ∈ Z≥0, with c0 ≥ 1. The polynomial
+P(z) = zk −
+k−1
+�
+i=0
+cizi
+has precisely one positive real root, ϕ, which occurs with multiplicity one, and satisfies ϕ ≥ 1. The
+other roots η satisfy |η| ≤ ϕ, with equality holding if and only if η is the product of ϕ with a g-th
+root of unity, where g = gcd({i | ci ̸= 0} ∪ {k}).
+Proof. The number of sign changes between consecutive coefficients in P is 1, so P has precisely one
+positive real root by Descartes’ rule of signs. Call this root ϕ. Rearranging, we have ϕk = �k−1
+i=0 ciϕi.
+Since c0 ≥ 1, we must have ϕk ≥ 1, so ϕ ≥ 1.
+Suppose that η ∈ C is a root of P. Taking modulus and applying the triangle inequality, we
+obtain
+|η|k = |ηk| = |
+k−1
+�
+i=0
+ciηi| ≤
+k−1
+�
+i=0
+ci|η|i.
+Equality holds in the above if and only if 1) ηi is a non-negative real for all i for which ci ̸= 0, and
+2) |η| is a root of P. By Lemma 2.1, the first condition is equivalent to ηg being a non-negative real,
+where g = gcd{i | ci ̸= 0}. The second condition is equivalent to |η| = ϕ, since |η| is a non-negative
+real. The root ϕ satisfies these conditions, and the other solutions are obtained as the product of ϕ
+with the g-th roots of unity.
+If the inequality is strict then we have P(|η|) < 0. Since the value of the polynomial P(|z|) is
+positive for sufficiently large |z|, and ϕ is the unique positive real root, P(|z|) > 0 for any |z| > ϕ.
+It follows that |η| < ϕ, as required.
+□
+For a polynomial P(z) of degree k, let η1, . . . , ηk be the roots of P, with multiplicity. The N-th
+Newton polynomial of P is the complex number ηN
+1 + · · · + ηN
+k . If P has real coefficients, then the
+roots occur in conjugate pairs and the Newton polynomials take real values. Lemma 2.2 controls
+the Newton polynomials quite tightly. In particular, the next lemma explains that when N = gn is
+
+8
+GUY BOYDE AND RUIZHI HUANG
+g-divisible they are well approximated asymptotically by gϕgn, and when N is not g-divisible they
+are approximated by zero with the same error.
+Lemma 2.3. Let c0, . . . ck−1 ∈ Z≥0, with c0 ≥ 1. As n → ∞, the Newton polynomials of
+P(z) = zk −
+k−1
+�
+i=0
+cizi
+satisfy
+• For N not divisible by g we have
+|ηN
+1 + · · · + ηN
+k | ≤ (k − g)|ψ|N.
+• When N = gn is g-divisible we have
+|gϕgn − (ηgn
+1
++ · · · + ηgn
+k )| ≤ (k − g)|ψ|gn,
+where ϕ is the unique positive real root of P(z), ψ is the next largest root in absolute value, and
+g = gcd({i | ci ̸= 0} ∪ {k}).
+By definition, rN is a sum of N-th powers of positive reals less than ϕ. This means that this
+lemma implies for example that (ηgn
+1
++ · · · + ηgn
+k ) ∼ gϕgn as n → ∞.
+Proof. By Lemma 2.2, roots of P(z) come in two kinds: those which are the product of ϕ with a
+g-th root of unity, and those roots η with |η| < ϕ (hence |η| ≤ |ψ|). The important point is that
+each root of the first kind occurs with multiplicity precisely 1.
+To see this, apply Lemma 2.2 to the polynomial
+P ′(z) = z
+k
+g −
+k−1
+�
+i=0
+ciz
+i
+g
+obtained by dividing all powers by g, and use the fact that roots of P(z) are precisely the g-th roots
+of the roots of P ′(z).
+Then, without loss of generality assume η1, . . . ηg are the roots of the first kind, so that |η1| =
+· · · = |ηg| = ϕ. From elementary complex analysis or group theory we have that ηN
+1 + · · · + ηN
+g =
+
+
+
+
+
+gϕN
+g | N,
+0
+g ∤ N,
+and the result then follows from the triangle inequality.
+□
+2.2. Free Lie algebras. We write the generating set X of a free Lie algebra L = L(X) over Z
+as follows. Write q1 < · · · < qℓ for the distinct degrees which contain an element of X. Write
+xi,1, xi,2, . . . , xi,mi for the distinct generators in degree qi, so that in particular the number of
+generators in degree qi is mi. Hilton [Hil] showed that L is free as a Z-module.
+
+SOME ASYMPTOTIC FORMULAE FOR TORSION IN HOMOTOPY GROUPS
+9
+Let µ : Z>0 −→ {−1, 0, 1} be the M¨obius inversion function, defined by
+µ(s) =
+
+
+
+
+
+
+
+
+
+
+
+1
+s = 1
+0
+s > 1 is not square free
+(−1)ℓ
+s > 1 is a product of ℓ distinct primes.
+Given a polynomial P(z) = a0 + a1z + · · · + akzk with a0 ̸= 0, the reciprocal of P(z) is ak +
+ak−1z + · · ·+ a0zk. For given P(z), let η1, . . . ηk be the complex roots of the reciprocal of P(z), with
+multiplicity (so P(z) = a0
+�k
+i=1(1 − ηiz)). Write
+SN(P(z)) := ηN
+1 + · · · + ηN
+k
+for the N-th Newton polynomial in the zeroes of the reciprocal.
+The following theorem is due to Babenko. Relative to his statement, we have changed variable
+using the fact that, for fixed N, d �→ N
+d is a self-bijection of the set of divisors of N.
+Theorem 2.4. [Bab, Proposition 1] Let L be the free graded Lie algebra over Z on a finite set of
+generators {xi,j}, with notation as above. Then
+rank(LN) = (−1)N
+N
+�
+d|N
+(−1)
+N
+d µ(d)S N
+d (1 −
+ℓ
+�
+i=1
+mizqi),
+where the sum is taken over the divisors d of N.
+□
+Our next theorem is essentially a result of Lambrechts [Lam, Proposition 1] in the special case of
+free Lie algebras. Our derivation of this result from Babenko’s is essentially the same as Lambrechts’s,
+but the situation is simpler and slightly more is true. The point of the theorem is that when g | N,
+rank(LN) is well-approximated by g
+N ϕN with an error term given by a sum of exponentials in smaller
+bases.
+Theorem 2.5. Let L be the free graded Lie algebra over Z on a finite set of generators X. As before,
+write q1 < · · · < qℓ for the distinct degrees which contain an element of X, and let g = gcd(qi). Let
+mi be the number of generators in degree qi.
+• If g ∤ N, then rank(LN) = 0.
+• If g | N, then |rank(LN) − g
+N ϕN| ≤ qℓ
+N |ψ|N + gϕ
+N
+2 + qℓ|ψ|
+N
+2 ,
+where ϕ is the unique positive real root of the degree qℓ polynomial
+P(z) = zqℓ −
+ℓ
+�
+i=1
+mizqℓ−qi = 0,
+and ψ is the next largest root in absolute value.
+In particular,
+ϕ
+≥
+(�ℓ
+i=0 mi)
+1
+qℓ
+=
+(�ℓ
+i=0 mi)
+1
+max(q1,...qℓ) .
+
+10
+GUY BOYDE AND RUIZHI HUANG
+If P(z) has no roots which are strictly smaller than ϕ in absolute value (i.e. ‘ψ does not exist’)
+then terms involving ψ may be disregarded: precisely, the inequality in the second bullet may be
+replaced by |rank(LN) − g
+N ϕN| ≤ gϕ
+N
+2 .
+Proof. The first bullet follows immediately from the fact that L is concentrated in degrees divisible
+by g.
+We will now prove the second bullet. The point is that the Babenko’s formula of Theorem 2.4 is
+dominated by the d = 1 term. Let N be divisible by g. By Theorem 2.4 (using that µ(1) = 1) we
+have
+rank(LN) = (−1)N
+N
+�
+d|N
+(−1)
+N
+d µ(d)S N
+d (1 −
+ℓ
+�
+i=1
+mizqi)
+= 1
+N SN(1 −
+ℓ
+�
+i=1
+mizqi) + (−1)N
+N
+�
+d|N
+d≥2
+(−1)
+N
+d µ(d)S N
+d (1 −
+ℓ
+�
+i=1
+mizqi).
+We name these two terms, writing SN = SN(1 − �ℓ
+i=1 mizqi) to simplify notation. Let
+AN := 1
+N SN,
+and let
+BN := (−1)N
+N
+�
+d|N
+d≥2
+(−1)
+N
+d µ(d)S N
+d .
+By Lemma 2.3 (with n = N
+g ), we have |SN − gϕN| ≤ (qℓ − g)|ψ|N ≤ qℓ|ψ|N for ϕ and ψ as in the
+theorem statement. It therefore suffices to show that |BN| ≤ gϕ
+N
+2 + qℓ|ψ|
+N
+2 .
+Since |µ(d)| ≤ 1, we have by Lemma 2.3 that
+|BN| = 1
+N |
+�
+d|N
+d≥2
+(−1)
+N
+d µ(d)S N
+d | ≤ 1
+N
+�
+d|N
+d≥2
+|S N
+d | ≤ 1
+N
+�
+d|N
+d≥2
+(gϕ
+N
+d + qℓ|ψ|
+N
+d ).
+The number of terms in this summation is at most the number of divisors of N, which is at most
+N. The term is a sum of exponentials in positive bases, hence is strictly increasing, and in particular
+for d ≥ 2 we have the termwise bound gϕ
+N
+d + qℓ|ψ|
+N
+d ≤ gϕ
+N
+2 + qℓ|ψ|
+N
+2 . Putting this together gives
+|BN| ≤ gϕ
+N
+2 + qℓ|ψ|
+N
+2 ,
+as required.
+Lastly, we check that ϕ ≥ (�ℓ
+i=0 mi)
+1
+qℓ . Since the polynomial P(z) = zqℓ − �ℓ
+i=1 mizqℓ−qi has
+a unique positive root by Lemma 2.2, it suffices to check that P((�ℓ
+i=0 mi)
+1
+qℓ ) is non-positive. For
+
+SOME ASYMPTOTIC FORMULAE FOR TORSION IN HOMOTOPY GROUPS
+11
+each i, qℓ−qi
+qℓ
+lies between 1 and 0, so for any x ≥ 1 we have x
+qℓ−qi
+qℓ
+≥ 1. It follows that
+P((
+ℓ
+�
+i=0
+mi)
+1
+qℓ ) = (
+ℓ
+�
+i=0
+mi) −
+ℓ
+�
+i=1
+mi(
+ℓ
+�
+i=0
+mi)
+qℓ−qi
+qℓ
+≤ (
+ℓ
+�
+i=0
+mi) −
+ℓ
+�
+i=1
+mi · 1 = 0,
+as required.
+□
+2.3. Free Lie algebras with differentials. Free Lie algebras over Z/pr are obtained by tensoring
+the corresponding free Lie algebra over Z with Z/pr, since this gives the correct universal property.
+In this subsection, we consider L = L(x, y) = L(x, dx), the free differential Lie algebra over Z/pr
+on the acyclic rank 2 free differential Z/pr-module on generators x and y (dx = y). Suppose that
+deg(x) = q + 1, so deg(y) = q. By Theorem 2.5, since gcd(q, q + 1) = 1, we know that
+rankZ/pr(LN) ∼ 1
+N ϕN,
+where ϕ is the unique positive real root of the degree q + 1 polynomial
+zq+1 − z − 1 = 0.
+The size of the error in this approximation is exponential in base depending on the next largest
+root ψ (in absolute value), and √ϕ.
+In this subsection we are instead interested in B := Im(d) ⊂ L, the module of boundaries. Our
+aim is to prove Theorem 2.11. The argument will go as follows. It is known (Theorem 2.7) that
+the differential on L is ‘almost acyclic’. A counting argument using the fact that rank(LN) ∼ 1
+N ϕN
+then shows that the rank of the module of boundaries must be asymptotically a fixed fraction of
+that of LN.
+We will first reduce to the case r = 1 by means of the following lemma, which is proven in [Boy2]
+as Lemma 7.10.
+Lemma 2.6. Let ϕ : M −→ N be a map of Z/pr-modules, with N free. Then rankZ/pr(Im(ϕ)) =
+rankZ/p(Im(ϕ ⊗ Z/p)).
+□
+Now assume r = 1. Let u be an even-dimensional class in a graded differential Lie algebra L over
+Z/p for p ̸= 2. Following [CMN], let
+τk(u) = adpk−1(u)(du),
+and let
+σk(u) = 1
+2
+pk−1
+�
+j=1
+1
+p
+�pk
+j
+�
+[adj−1(u)(du), adpk−1−j(u)(du)].
+From our point of view, the point of the next theorem is that free differential Lie algebras are
+almost acyclic.
+
+12
+GUY BOYDE AND RUIZHI HUANG
+Theorem 2.7. [CMN, Proposition 4.9] Let V be an acyclic differential Z/p-vector space. Write
+L(V ) ∼= HL(V ) ⊕ K, for an acyclic module K. If K has an acyclic basis, that is, a basis
+{xα, yα, zβ, wβ},
+where α and β range over index sets I and J respectively, and we have
+d(xα) = yα, deg(xα) even,
+d(zβ) = wβ, deg(zβ) odd,
+then HL(V ) has a basis
+{τk(xα), σk(xα)}α∈I ,k≥1.
+□
+The theorem implies that the differential on L can be modified slightly to make it acyclic. Namely,
+define a new differential d : L(V ) → L(V ) by setting d = d on K, and letting d(τk(xα)) = σk(xα),
+d(σk(xα)) = 0. Of course, d will no longer satisfy the Leibniz rule, but it will still be a vector space
+endomorphism of degree −1 which satisfies d
+2 = 0.
+Now let B := Im(d) ⊂ L, and let σ ⊂ L be the subspace spanned by the elements σk(x), for some
+even degree x ∈ L and k ∈ Z+. By definition of d we then have the following corollary.
+Corollary 2.8. We have BN ∼= BN ⊕ σN.
+□
+The next lemma justifies the approximation by providing a crude upper bound on σN.
+Lemma 2.9. We have the bound
+dimZ/p σN ≤ c1 · Nϕ
+N
+p ,
+where c1 = 2(q + 2)ϕ
+2
+p .
+Proof. By definition, σN is spanned by classes σk(xα), and we have deg(σk(xα)) = k deg(xα) − 2.
+We therefore have
+dimZ/pr σN ≤
+�
+M≤N
+pkM−2=N
+dimZ/p LM ≤
+�
+M≤N
+pkM−2=N
+( 1
+M ϕM + q + 1
+M |ψ|M + ϕ
+M
+2 + (q + 1)|ψ|
+M
+2 )
+≤
+�
+M≤N
+pkM−2=N
+((q + 2)ϕM + (q + 2)ϕ
+M
+2 ) ≤
+�
+M≤N
+pkM−2=N
+2(q + 2)ϕM.
+by Theorem 2.5 (we use |ψ| < ϕ, and then drop the factors of
+1
+M , to obtain a bound which is strictly
+increasing even for small M). This summation contains fewer than N terms, and since the value of
+a given term is increasing in M, the size of the largest term is controlled by M = N+2
+pk
+≤ N+2
+p , so
+dimZ/p σN ≤ N · 2(q + 2)ϕ
+N+2
+p ,
+as required.
+□
+
+SOME ASYMPTOTIC FORMULAE FOR TORSION IN HOMOTOPY GROUPS
+13
+We next estimate the size of dim BN.
+Lemma 2.10. Let ψ be the next largest (in absolute value) root of zq+1 − z − 1 after ϕ. We have
+dimZ/p BN ≥ (1 −
+N
+N − 1
+1
+ϕ) · 1
+N ϕN − κ|ψ|N − c2ϕ
+N
+2 ,
+where κ = (q + 1)(1 +
+1
+|ψ|) and c2 = (q + 2)(1 +
+1
+√ϕ) ≤ 2(q + 2).
+Proof. Since d is acyclic, we have BN = Ker(d : LN → LN−1). The First Isomorphism Theorem
+then gives that LN⧸BN
+∼= BN−1, and since BN−1 ⊂ LN−1 we get
+dimZ/p BN ≥ dimZ/p LN − dimZ/p LN−1.
+Theorem 2.5 gives (since g = 1 and |ψ| < ϕ)
+dimZ/p LN−1 ≤
+1
+N − 1ϕN−1 + q + 1
+N − 1|ψ|N−1 + (q + 2)ϕ
+N−1
+2 ,
+and
+dimZ/p LN ≥ 1
+N ϕN − q + 1
+N
+|ψ|N − (q + 2)ϕ
+N
+2 .
+Combining these inequalities gives the result.
+□
+We are now ready to state and prove the main theorem of this subsection.
+Theorem 2.11. Let L ⊗ Z/pr = L(x, dx) ⊗ Z/pr = L(x, y) ⊗ Z/pr be the free differential graded
+Lie algebra over Z/pr on two generators x and y satisfying y = dx.
+Let q = deg(y), so that
+deg(x) = q + 1. Let B = Im(d) ⊂ L ⊗ Z/pr be the submodule of boundaries. Then we have the bound
+rank(BN) ≥ (1 −
+N
+N − 1
+1
+ϕ) · 1
+N ϕN − cNϕ
+N
+2 − κ|ψ|N,
+where ϕ > 1 is the unique positive real root of the degree n polynomial
+zq+1 − z − 1 = 0,
+ψ is the next largest root in absolute value, c = 2(q + 2)(1 + ϕ), and κ = (q + 1)(1 +
+1
+|ψ|). We have
+the bounds 2
+1
+q+1 < ϕ < 1 + 1
+q .
+Proof. By Lemma 2.6, it suffices to prove the theorem in the case r = 1. By Lemma 2.8 we have
+dimZ/p BN ≥ dimZ/p BN − dimZ/p σN.
+Combining Lemmas 2.9 and 2.10 (c = c1 + c2) then gives the result.
+□
+
+14
+GUY BOYDE AND RUIZHI HUANG
+3. Topology
+3.1. Homology. We now prove Theorem 1.2.
+Proof of Theorem 1.2. In the proof of Theorem 1.5 of [Boy2] it is shown that there exists a commu-
+tative diagram (the details of the definitions of the maps need not concern us here):
+L′(x, y)
+θ◦d
+�
+βr◦Φr,r
+π
+� π∗(ΩP n+1(pr))
+(Ωµ)∗
+�
+h◦ρs
+�
+π∗(ΩY )
+h◦ρs
+�
+L(x, y) ⊗ Z/ps
+Φr,s
+H� H∗(ΩP n+1(pr); Z/ps)
+(Ωµ)∗ � H∗(ΩY ; Z/ps).
+In the diagram, L(x, dx) ⊗ Z/ps is the free differential Lie algebra (with dx = y , deg(x) = q + 1,
+deg(y) = q). The top-left entry L′(x, dx) is a certain module over Z/pr which is ‘almost’ a free
+differential Lie algebra.
+We now use various results from [Boy2].
+By the remark immediately before Corollary 8.9 of
+that paper, the image of the left hand vertical map θ ◦ d is precisely the module of boundaries
+BL.
+By Lemma 9.6 the map Φr,s
+H
+is an injection, and the induced map on homology, (Ωµ)∗,
+is an injection by assumption. It follows by commutativity that the image in the bottom-right,
+I := Im(h ◦ ρs ◦ (Ωµ)∗ ◦ βr ◦ Φr,r
+π ), is isomorphic to BL.
+The point is then that the homotopy groups of Y surject onto I, hence must be just as large.
+More precisely, we obtain that
+r
+�
+t=s
+rankZ/pt(πN(ΩY )) ≥ rankZ/ps(IN) = rankZ/ps(BLN)
+by Lemma 7.8 of [Boy2] applied to the part of the diagram consisting of
+πN(ΩY )
+�P
+P
+P
+P
+P
+P
+P
+P
+P
+P
+P
+P
+(L′(x, y))N
+�
+�
+HN(ΩY ; Z/ps).
+The loops on Y is just a degree shift on homotopy groups, so the result follows by Theorem 2.11
+of this paper.
+□
+3.2. K-theory. In this subsection, the following linear inequality relating integers j and N will
+arise often. We will refer to it as Condition (∗). Here, X is a fixed space, conn(X) is the p-local
+connectivity of X, and dim(X) is the largest d for which Hd(X; Q) ̸= 0.
+(*)
+j >
+1
+2(p − 1)( dim(X) + 1
+conn(X) + 1 − 1)N + ( dim(X) + 1
+conn(X) + 1)(conn(X) + 2) − 1),
+The next theorem refines and slightly generalises Theorem 1.4 of [Boy1].
+
+SOME ASYMPTOTIC FORMULAE FOR TORSION IN HOMOTOPY GROUPS
+15
+Theorem 3.1. Let p be an odd prime, and let X be a path connected space having the p-local
+homotopy type of a finite CW-complex. Suppose that there exists a map
+µ :
+ℓ�
+i=1
+mi
+�
+j=1
+Sqi+1 → ΣX
+with 1 ≤ q1 < q2 < · · · < qℓ, such that the map
+�K∗(ΣX) ⊗ Z/p
+µ∗
+−→ �K∗(
+ℓ�
+i=1
+mi
+�
+j=1
+Sqi+1) ⊗ Z/p ∼=
+ℓ
+�
+i=1
+mi
+�
+j=1
+Z/p
+is a surjection.
+Then for any N, j such that
+j >
+1
+2(p − 1)( dim(X) + 1
+conn(X) + 1 − 1)N + ( dim(X) + 1
+conn(X) + 1)(conn(X) + 2) + 1)
+(i.e. such that Condition (*) holds) we have
+∞
+�
+t=1
+rankZ/pt(πN+2j(p−1)−1(ΩΣX)) ≥ rankZ/pr(LN ⊗ Z/pr),
+where L is as in Theorem 2.5 (the free Lie algebra on generators corresponding to the spheres in
+the wedge), conn(X) is the p-local connectivity of X, dim(X) is the dimension of X as measured by
+rational cohomology, and g = gcd(q1, . . . , qℓ).
+Proof. This is essentially a more careful restatement of Theorem 1.4 of [Boy1]. Some of the arguments
+of that paper are given only for a wedge of two spheres, but all of them apply verbatim to any finite
+wedge. Construction 7.15 of that paper gives (in slightly different language) a diagram of the form
+πN(ΩΣX)
+�◆
+◆
+◆
+◆
+◆
+◆
+◆
+◆
+◆
+◆
+◆
+LN ⊗ Z/pr
+�
+�
+EN+2j(p−1)
+for some module E∗ whose definition need not concern us.
+Theorem 7.16 of that paper than says that the horizontal map is an injection, and hence, just
+as in the proof of Theorem 1.2, the conclusion holds, provided that there exists some ℓ ∈ Z≥0 such
+that ℓj(p−1)+ N−1
+2
+> λk
+ℓ , for an integer k which may be taken to be ⌈
+N+1
+conn(X)+1⌉.
+The inequality therefore rearranges to j >
+1
+p−1(⌈
+N+1
+conn(X)+1⌉ log(λℓ)
+log(ℓ) − N−1
+2 ). In [AA], it is shown
+that λℓ = ℓ⌈ dim(X)
+2
+⌉, so we may simplify to
+j >
+1
+p − 1(⌈
+N + 1
+conn(X) + 1⌉⌈dim(X)
+2
+⌉ − N − 1
+2
+),
+which is implied by Condition (*), using the fact that for an integer z we have ⌈ z
+2⌉ ≤ z+1
+2 . This
+completes the proof.
+□
+The next step is a simple application of Bezout’s Lemma.
+
+16
+GUY BOYDE AND RUIZHI HUANG
+Lemma 3.2. Let α, β ∈ Z with α, β > 0, and let a, b ∈ R with a > 0. Consider the set of linear
+combinations
+Sn = {nα + jβ | j ∈ Z≥0, j > an + b} ⊂ Z.
+Let g′ = gcd(α, β). There exists a constant B, independent of n, such that for each n, all multiples
+of g′ which are at least min(Sn) + B are contained in Si for some i which is close to n in the
+sense that n ≤ i < n + β(β + 1).
+Furthermore, there exists a suitable B satisfying the bound
+B ≤ β2(α + a(1 + β)) + β, and hence any B ≥ β2(α + a(1 + β)) + β is also suitable.
+If α and β are fixed (and j and n are allowed to vary) then it is a familiar fact that the set of
+integers of the form nα + jβ is precisely the multiples of g′. Our statement is essentially just a more
+complicated version of this.
+Proof. First consider the set Sn. If an integer j satisfies j > an+b (so that nα+jβ lies in Sn), then
+increasing the parameter j certainly does not violate this condition. Therefore, adding a positive
+multiple of β to an element of Sn yields another element of Sn. In particular, Sn already contains
+all integers which are obtained by increasing min(Sn) by a multiple of β.
+These values are by
+construction linear combinations of α and β, so they are all multiples of g′.
+It remains, then, to show that by increasing n ‘just a little’, we can ‘fill in’ the intermediate
+multiples of g′. We will do so by ‘giving ourselves enough room’, in the sense of an ad-hoc quantity
+which we now define. Define the excess of (j, n) to be j − (an + b). The condition j > an + b is then
+equivalent to (j, n) having positive excess.
+By Bezout’s Lemma, let x > 0 and y ≥ 0 be the solution of xα − yβ = g′ with smallest non-
+negative y. We have 0 < x ≤ g′
+α + β and 0 ≤ y ≤ α. Given an expression nα + jβ, replacing n by
+n + x and j by j − y increases the value of the linear combination nα + jβ by g′, and reduces the
+excess by the constant ax + y. We will use this to fill in the remaining multiples of g′.
+Let j0 realise the smallest member of Sn, in the sense that min(Sn) = nα + j0β. Now take any
+j ≥ j0+ β
+g′ (ax+y). The excess of (n, j0) was positive, so the excess of (n, j) is greater than β
+g′ (ax+y).
+We may therefore add (x, −y) to (n, j) up to β
+g′ times while retaining a positive excess (and keeping
+j non-negative). This shows that all multiples of g′ lying between nα + jβ and nα + (j + 1)β are
+contained in Si for some i satisfying n ≤ i < n + β
+g′ x, and we may perform this procedure for any
+j ≥ j0 + β
+g′ (ax + y). In particular, all multiples of g′ which are at least min(Sn) + β( β
+g′ (ax + y) + 1)
+are contained in Si for some i satisfying n ≤ i < n + β
+g′ x. The extra +1 here is because j must
+be an integer. This is essentially the result, and it remains only to establish that we may take the
+constants as in the statement.
+Now, g′
+α ≤ 1, so x ≤ 1 + β, and
+β
+g′ x ≤ βx ≤ β(1 + β). This establishes the bounds on i. The
+bound on B follows from these inequalities, together with y ≤ α. This completes the proof.
+□
+We now prove the following strong version of Theorem 1.7.
+
+SOME ASYMPTOTIC FORMULAE FOR TORSION IN HOMOTOPY GROUPS
+17
+Theorem 3.3. Let p be an odd prime, and let X be a path connected space having the p-local
+homotopy type of a finite CW-complex. Suppose that there exists a map
+µ :
+ℓ�
+i=1
+mi
+�
+j=1
+Sqi+1 → ΣX
+with 1 ≤ q1 < q2 < · · · < qℓ, such that the map
+�K∗(ΣX) ⊗ Z/p
+µ∗
+−→ �K∗(
+ℓ�
+i=1
+mi
+�
+j=1
+Sqi+1) ⊗ Z/p ∼=
+ℓ
+�
+i=1
+mi
+�
+j=1
+Z/p
+is a surjection.
+Then there exist constants τ, θ > 0 such that for multiples M = mg′ of
+g′ = gcd(q1, . . . qℓ, 2(p − 1))
+we have
+∞
+�
+t=1
+rankZ/pt(πM(ΣX)) ≥
+τ
+1
+g
+conn(X)+1
+dim(X)+1 M + θ
+ϕ( conn(X)+1
+dim(X)+1 )M − o( 1
+M ϕ( conn(X)+1
+dim(X)+1 )M),
+where ϕ is the unique positive real root of the degree qℓ polynomial
+zqℓ −
+ℓ
+�
+i=1
+mizqℓ−qi = 0,
+(in particular, ϕ ≥ (�ℓ
+i=0 mi)
+1
+qℓ = (�ℓ
+i=0 mi)
+1
+max(q1,...qℓ) ), conn(X) is the p-local connectivity of X,
+dim(X) is the rational cohomological dimension of X, and g = gcd(q1, . . . , qℓ).
+Proof. Let
+Sn
+be
+the
+set
+of
+dimensions
+M
+for
+which
+Theorem
+3.1
+tells
+us
+that
+�∞
+t=1 rankZ/pt(πM(ΣX)) ≥ dimZ/p(Lng ⊗ Z/pr). That is:
+Sn = {ng + j · 2(p − 1) | j ∈ Z, j > an + b} ⊂ Z,
+where a =
+g
+2(p−1)( dim(X)+1
+conn(X)+1 − 1) and b =
+1
+2(p−1)( dim(X)+1
+conn(X)+1(conn(X) + 2) + 1).
+By Lemma 3.2, there exists a constant B, which may be taken to be 4(p − 1)2(g + a(1 + 2(p −
+1))) + 2(p − 1) such that for each M = mg′ ≥ min(Sn) + B, we have �∞
+t=1 rankZ/pt(πM(ΣX)) ≥
+dimZ/p(Lig ⊗ Z/pr) for some i with n ≤ i < n + 8(p − 1)2. By Theorem 2.5,
+∞
+�
+t=1
+rankZ/pt(πM(ΣX)) ≥ 1
+i ϕig − qℓ|ψ|ig − gϕ
+ig
+2 − qℓ|ψ|
+ig
+2 .
+Regardless of whether |ψ| > 1, we have |ψ|
+ig
+2 < 1 + |ψ|ig < 2 + |ψ|(n+8(p−1)2)g, so the inequality
+implies
+(†)
+∞
+�
+t=1
+rankZ/pt(πM(ΣX)) ≥
+1
+n + 8(p − 1)2 ϕng − gϕ
+(n+8(p−1)2)g
+2
+− qℓ(3 + 2|ψ|(n+8(p−1)2)g).
+It remains only to find the dependency of n upon M, and convert this expression into one in terms
+of M.
+
+18
+GUY BOYDE AND RUIZHI HUANG
+The smallest member of Sn is obtained by taking the smallest j = jn satisfying Condition (*).
+By definition jn is the smallest integer with jn > an + b, so jn ≤ an + b + 1. Thus,
+min(Sn) = ng + 2jn(p − 1) ≤ g( dim(X) + 1
+conn(X) + 1)n + 2(p − 1)(b + 1).
+To conclude, for given M = mg′, let n = n(M) be the largest non-negative integer satisfying
+M ≥ g( dim(X)+1
+conn(X)+1)n + 2(p − 1)(b + 1) + B. Rearranging gives n ≤ M−(2(p−1)(b+1)+B)
+g
+( conn(X)+1
+dim(X)+1 ).
+Since n is the largest such integer, it is at least one less than this expression. Applying the bounds
+n ≤ i < n + 8(p − 1)2, now gives that
+1
+n + 8(p − 1)2 ϕng ≥
+τ
+1
+g
+conn(X)+1
+dim(X)+1 M + θ
+ϕ
+conn(X)+1
+dim(X)+1 M,
+for constants θ and τ, and shows that the other terms of the inequality † are o( 1
+M ϕ
+conn(X)+1
+dim(X)+1 ), as
+required.
+□
+Remark 3.4. In this remark we give the constants and error term for Theorem 3.3, and collect the
+other constants appearing in the proof.
+The positive integers q1, . . . qℓ are given in the hypotheses of Theorem 3.3 (or Theorem 2.5). Then
+g = gcd(q1, . . . , qℓ),
+and
+g′ = gcd(q1, . . . qℓ, 2(p − 1)) = gcd(g, 2(p − 1)).
+The space X and the prime p ̸= 2 are given in the hypotheses of Theorem 3.3, dim(X) is the
+rational dimension of X, and conn(X) is its p-local connectivity.
+The constants appearing in the proof of Theorem 3.3 are then
+a =
+g
+2(p − 1)( dim(X) + 1
+conn(X) + 1 − 1),
+b =
+1
+2(p − 1)( dim(X) + 1
+conn(X) + 1(conn(X) + 2) + 1), and
+B = 4(p − 1)2(g + a(1 + 2(p − 1))) + 2(p − 1).
+It then follows from the proof that the constants θ and τ of Theorem 3.3 may be taken as follows.
+θ = 8(p − 1)2 − (conn(X) + 1
+dim(X) + 1 )2(p − 1)(b + 1 + B)
+g
+≤ 8(p − 1)2, and
+τ = ϕ−g−( conn(X)+1
+dim(X)+1 )(2(p−1)(b+1)+B),
+where, as usual, ϕ is the unique positive root of the polynomial P(z) = zqℓ − �ℓ
+i=1 mizqℓ−qi = 0.
+The error term in the bound Theorem 3.3 is an unpleasant expression, and we restrict ourselves
+to noting that it is negative, and of the form
+−c1ϕ
+1
+2
+conn(X)+1
+dim(X)+1 M − c2|ψ|
+conn(X)+1
+dim(X)+1 M − 3qℓ,
+
+SOME ASYMPTOTIC FORMULAE FOR TORSION IN HOMOTOPY GROUPS
+19
+for constants ci, where ψ is the next largest root of P(z) after ϕ, in absolute value. The deviation
+of the bound from being a pleasant expression is therefore exponential in bases determined by the
+roots of P(z).
+References
+[AA]
+J. F. Adams and M. F. Atiyah, K-theory and the Hopf invariant, Quart. J. Math. Oxford Ser. (2) 17 (1966),
+31-38. 3.2
+[Bab]
+I.K. Babenko, Analytical properties of Poincar´e series of a loop space, Mat. Zametki 27 (5) (1980), 359-367.
+1, 2.4
+[Boy1] G. Boyde, p-hyperbolicity of homotopy groups via K-theory, to appear in Math. Z., 2021. arXiv: 2101.04591.
+1, 1.2, 1.2, 1.2, 1.2, 3.2, 3.2
+[Boy2] G. Boyde, Z/pr-hyperbolicity via homology, to appear in Isr. J. Math., 2021. arXiv: 2106.03516. 1, 1.1, 1.1,
+1.1, 1.1, 2.3, 3.1
+[BS]
+R. Burklund, How big are the stable homotopy groups of spheres, with an appendix joint with A. Senger,
+preprint, 2022. arXiv:2203.00670 1, 1.1
+[CMN] F. R. Cohen, J. C. Moore and J. A. Neisendorfer, Torsion in homotopy groups, Ann. of Math. (2) 109 (1)
+(1979), 121-168. 1.1, 2.3, 2.7
+[FHT] Y. F´elix, S. Halperin and J.-C. Thomas, Exponential growth and an asymptotic formula for the ranks of
+homotopy groups of a finite 1-connected complex, Ann. of Math. 170 (2009), 443-464. 1
+[Hen]
+Hans-Werner Henn, On the growth of homotopy groups, Manuscripta Math. 56 (2) (1986), pp. 235–245. 1
+[Hil]
+P. J. Hilton, On the homotopy groups of the union of spheres, J. London Math. Soc. 30 (1955), 154-172. 2.2
+[HW]
+R. Huang and J. Wu, Exponential growth of homotopy groups of suspended finite complexes, Math. Z. 295
+(2020), pp. 1301-1321. 1, 1, 1.1
+[Iri]
+Kouyemon Iriye, On the Ranks of Homotopy Groups of a Space, Publ. Res. Inst. Math. Sci. 23 (1) (1987),
+pp. 209-213. 1
+[Lam] P. Lambrechts, Analytic properties of Poincar´e series of spaces, Topology 37 (6) (1998), pp. 1363-1370. 1, 2.2
+[Sel]
+Paul Selick, On conjectures of Moore and Serre in the case of torsion-free suspensions, Math. Proc. Cambridge
+Philos. Soc. 94 (1) (1983), pp. 53-60. 1.2
+Mathematical Institute, Utrecht University, Heidelberglaan 8 3584 CS Utrecht, The Netherlands
+Email address: g.boyde@uu.nl
+Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences,
+Beijing 100190, China
+Email address: haungrz@amss.ac.cn
+URL: https://sites.google.com/site/hrzsea/
+
diff --git a/XNE0T4oBgHgl3EQfmQGx/content/tmp_files/load_file.txt b/XNE0T4oBgHgl3EQfmQGx/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b1ae35c4360f54f464f083ea917967c1bd0788ad
--- /dev/null
+++ b/XNE0T4oBgHgl3EQfmQGx/content/tmp_files/load_file.txt
@@ -0,0 +1,641 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf,len=640
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='02497v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='AT]  6 Jan 2023  SOME ASYMPTOTIC FORMULAE FOR TORSION IN HOMOTOPY GROUPS  GUY BOYDE AND RUIZHI HUANG  Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Inspired by a remarkable work of F´elix, Halperin and Thomas on the asymptotic  estimation of the ranks of rational homotopy groups, and more recent works of Wu and the authors  on local hyperbolicity, we prove two asymptotic formulae for torsion rank of homotopy groups,  one using ordinary homology and one using K-theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' We use these to obtain explicit quantitative  asymptotic lower bounds on the torsion rank of the homotopy groups for many interesting spaces  after suspension, including Moore spaces, Eilenberg-MacLane spaces, complex projective spaces,  complex Grassmannians, Milnor hypersurfaces and unitary groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Introduction  The homotopy groups of a simply connected CW-complex Y of finite type have the form  πi(Y ) ∼= (⊕  di  Z) ⊕  ⊕  prime p  t∈Z+  ( ⊕  kp,t  Z/pt),  where di and kp,t are the rank of the free summands and the Z/pt-summands of πi(Y ) respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Denote rank0(πi(Y )) := di and rankZ/pt(πi(Y )) := kp,t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  In the remarkable work [FHT], F´elix, Halperin and Thomas proved an asymptotic formula for  the ranks rank0(πi(Y )) of the free part of the homotopy groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' In particular, they showed that if  Y is finite and rank0(πi(Y )) ̸= 0 for infinitely many i ∈ Z+, then there is a constant δ > 1 such that  for N large enough  N+dim(Y )  �  i=N+2  rank0(πi(Y )) ≥ δN,  which they interpret as a strong ‘regularity’ property for the ranks rank0(πi(Y )) of the free part of  the homotopy groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Concerning the ranks rankZ/pt(πi(Y )) of the torsion part of the homotopy  groups, they further raised the following natural question, which was rephrased in an explicit form  by Wu and the second author in [HW, Question 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Question 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Are there ‘regularity’ properties of the torsion subgroups of the homotopy groups  πi(Y ) as i → ∞?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  In this paper, we study the above question by providing estimates for the ranks rankZ/pt(πi(Y )) in  certain cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' In particular, we give quantitative refinements of results of the authors and Wu, from  the papers [HW], [Boy1], and [Boy2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' The methods of these papers implied more than was stated  2010 Mathematics Subject Classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Primary 55Q52, 55Q05, Secondary 55Q15, 55P40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  1  2  GUY BOYDE AND RUIZHI HUANG  in the theorems: the statements were always that the volume of p-torsion in the homotopy groups  of various spaces grows exponentially, but actually the methods were completely constructive, and  with more work one can extract concrete exponential lower bounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' The extraction of these lower  bounds is the business of this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  The proof of each of our main theorems (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='2 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='7) begins with the combinatorics of free  Lie algebras, which have been well understood since long before F´elix, Halperin, and Thomas’s  celebrated theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' We use in particular some results of Babenko [Bab] and Lambrechts [Lam],  both of which are more general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' From this common beginning, the proof of each theorem is then  complicated in a different way;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' we elaborate briefly after each theorem statement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Recent work of Burklund and Senger [BS] has greatly advanced our understanding of these phe-  nomena: they finish a story begun by Henn [Hen] and Iriye [Iri] and show that the radii of convergence  of the p-local “homotopy” and “loop-homology” power series are equal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Again, we discuss each of  our theorems in light of this.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Results via homology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' We first give our quantitative refinement of the main result of [Boy2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  To state the results, for any integer q ≥ 2 define a function  fq(x) = (1 −  x  x − 1  1  ϕ) · 1  xϕx − cxϕ  x  2 − κ|ψ|x  for x ≥ 2, where  ϕ is the unique positive real root of the degree q + 1 polynomial P(z) = zq+1 − z − 1,  c = 2(q + 2)(1 + ϕ), and  κ = (q + 1)(1 +  1  |ψ|) with ψ the next largest root of P(z) in absolute value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  We have the properties  2  1  q+1 < ϕ < 1 + 1  q , and  for any ε > 0, once x is large enough we have  fq(x) ≥ (1 − ε)(1 − 1  ϕ) · 1  xϕx > (1 − ε)(1 − 2−  1  q+1 ) · 1  x2  x  q+1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  We will use the function fq(x) with its properties freely in this subsection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Let P q+1(pr) be the Moore space defined as the mapping cone of the degree pr map Sq → Sq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  The following theorem provides an asymptotic formula for the p-local homotopy groups under a  homological condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Let Y be a simply connected CW-complex, let p ̸= 2 be prime, and let s ≤ r ∈ Z+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  If there exists a map  µ : P q+1(pr) −→ Y  for some q ≥ 2, such that the induced map  (Ωµ)∗ : H∗(ΩP q+1(pr);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Z/ps) −→ H∗(ΩY ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Z/ps)  SOME ASYMPTOTIC FORMULAE FOR TORSION IN HOMOTOPY GROUPS  3  is an injection, then we have the bound  r  �  t=s  rankZ/pt(πN+1(Y )) ≥ fq(N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  In particular, for any ε > 0, once N is large enough we have  r  �  t=s  rankZ/pt(πN+1(Y )) > (1 − ε)(1 − 2−  1  q+1 ) · 1  N 2  N  q+1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Algebraically, Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='2 depends on the structure of the module of boundaries in a free Lie  algebra over a finite field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' It is the need to take boundaries which complicates the story relative  to Babenko and Lambrechts’s work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' This is dealt with in Subsection 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='3, using a result of Cohen,  Moore, and Neisendorfer [CMN].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  It follows from [Boy2] that the hypotheses of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='2 simplify in the case that Y = ΣX is a  suspension, as follows:  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Let X be a connected CW-complex, let p ̸= 2 be prime, and let s ≤ r ∈ Z+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Suppose  that H∗(X;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Z/ps) has finite type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' If there exists a map  µ : P q+1(pr) −→ ΣX  for some q ≥ 2, such that  µ∗ : �H∗(P q+1(pr);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Z/ps) −→ �H∗(ΣX;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Z/ps)  is an injection, then we have the bound  r  �  t=s  rankZ/pt(πN+1(ΣX)) ≥ fq(N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  In particular, for any ε > 0, once N is large enough we have  r  �  t=s  rankZ/pt(πN+1(ΣX)) > (1 − ε)(1 − 2−  1  q+1 ) · 1  N 2  N  q+1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  The spaces X and Y in Theorems 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='2 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='3 can be infinite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' The asymptotic formulae in both  theorems bound the ranks of the p-local homotopy groups from below by an exponential function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' In  particular, they strengthen a recent result of the first author on local hyperbolicity [Boy2, Theorem  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='5 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='3 has interesting applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' For instance, we can show the following corollary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Corollary 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Let X be a (q − 2)-connected CW-complex with q ≥ 2, and let p ̸= 2 be prime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Suppose that H∗(X;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Z/pr) has finite type and Hq(ΣX;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Z) contains a Z/pr-summand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Then we have  rankZ/pr(πN+1(ΣX)) ≥ fq(N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  In particular, for any ε > 0, once N is large enough we have  rankZ/pr(πN+1(ΣX)) > (1 − ε)(1 − 2−  1  q+1 ) · 1  N 2  N  q+1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  □  4  GUY BOYDE AND RUIZHI HUANG  Either Corollary 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='4 or Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='3 implies the following immediately for the Moore spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Corollary 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Let p be an odd prime and q ≥ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Then  rankZ/pr(πN+1(P q+1(pr)) ≥ fq(N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  In particular, for any ε > 0, once N is large enough we have  rankZ/pr(πN+1(P q+1(pr)) > (1 − ε)(1 − 2−  1  q+1 ) · 1  N 2  N  q+1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  □  This strengthens a result of Wu and the second author on the Z/pr-hyperbolicity of P q+1(pr)  [HW, Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  It is enlightening to compare this result from what could be deduced already from Burklund  and Senger’s work [BS].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' It follows from their Corollary A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='5 that the radius of convergence of the  series �∞  N=1 dimZ/p(πN(P q+1(pr)) ⊗ Z/p) · tN is precisely  1  ϕ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Since P q+1(pr) is rationally elliptic  (being rationally contractible), this power series really is describing the torsion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Corollary 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='5 adds  information in two ways: first by giving a concrete function as a lower bound for all N, and second  by saying something about summands isomorphic to Z/pr in particular, rather than p-torsion in  general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Another interesting example of Corollary 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='4 is Eilenberg-MacLane space after suspension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' In  particular, the following immediate corollary strengthens [Boy2, Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Corollary 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Let p be an odd prime and q ≥ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Then  rankZ/pr(πN(ΣK(Z/pr, q − 1)) ≥ fq(N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  In particular, for any ε > 0, once N is large enough we have  rankZ/pr(πN(ΣK(Z/pr, q − 1)) > (1 − ε)(1 − 2−  1  q+1 ) · 1  N 2  N  q+1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  □  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Results via K-theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Denote by  rankp(πi(ΣX)) =  ∞  �  t=1  rankZ/pt(πi(ΣX))  the rank of the p-torsion summands of πi(ΣX).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Our other main result refines the main theorem of  [Boy1] to a quantitative statement under a K-theoretical condition:  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='7 (Weak version of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Let p be an odd prime, and let X be a path connected  space having the p-local homotopy type of a finite CW-complex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Suppose that there exists a map  µ :  ℓ�  i=1  mi  �  j=1  Sqi+1 → ΣX  with 1 ≤ q1 < q2 < · · · < qℓ, such that the map  �K∗(ΣX) ⊗ Z/p  µ∗  −→ �K∗(  ℓ�  i=1  mi  �  j=1  Sqi+1) ⊗ Z/p ∼=  ℓ  �  i=1  mi  �  j=1  Z/p  SOME ASYMPTOTIC FORMULAE FOR TORSION IN HOMOTOPY GROUPS  5  is a surjection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Then for any ε > 0, once the multiple M = mg′ of  g′ = gcd(q1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' qℓ, 2(p − 1))  is large enough we have  rankp(πM(ΣX)) ≥  1  M 1+ε ϕ( conn(X)+1  dim(X)+1 )M,  where ϕ is the unique positive real root of the degree qℓ polynomial  zqℓ −  ℓ  �  i=1  mizqℓ−qi = 0,  (in particular, ϕ ≥ (�ℓ  i=0 mi)  1  qℓ = (�ℓ  i=0 mi)  1  max(q1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='qℓ) ), conn(X) is the p-local connectivity of X,  and dim(X) is the rational cohomological dimension of X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  A stronger estimate is provided by Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='3 with Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='4 at the end of the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' In  particular, the asymptotic formulae in both theorems bound the ranks of the p-local homotopy  groups from below by an exponential function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Unlike with Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='2, it is not necessary to  take boundaries to prove Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='7, but the topological picture is difficult.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' The difficulty arises  ultimately from an interaction between the James construction and the Adams operations, which  as far as the authors know originates in the paper [Sel] of Selick on which [Boy1] is modelled,  and manifests combinatorially as Condition (*) in the last section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' This condition means that the  ‘Lie algebra’ one is ultimately able to find a copy of in homotopy groups ‘lags’ - appearing in higher  dimensions than one might expect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' In the end, this shows up as for example the factor of ( conn(X)+1  dim(X)+1 )  in the exponent in Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='7 has interesting applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' For instance, let Grk(Cn) be the Grassmannian of  k-dimensional complex linear subspaces of Cn, which is simply connected and of complex dimension  k(n − k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Recall Gr1(Cn) ∼= CP n−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' In [Boy1, Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='6], it is shown that when n ≥ 3 and  0 < k < n there is a map  S3 ∨ S5 −→ ΣGrk(Cn)  which induces a surjection on �K∗( ) ⊗ Z/p for all odd primes p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Therefore, the following corollary  follows immediately from Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='7, which strengthens [Boy1, Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='5 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Corollary 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Let p be an odd prime, n ≥ 3 and 0 < k < n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Then for any ε > 0, once m is large  enough we have  rankp(π2m(ΣGrk(Cn))) ≥  1  (2m)1+ε  �3 +  √  5  2  �  m  2k(n−k)+1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  □  Similarly, let Hn,ℓ be the Milnor hypersurface defined by  Hn,ℓ = {([z], [w]) ∈ CP n × CP ℓ |  min(n,ℓ)  �  i=0  ziwi = 0},  6  GUY BOYDE AND RUIZHI HUANG  which is simply connected and of complex dimension n + ℓ − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' In [Boy1, Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='7], it is showed  that when n ≥ 2 and ℓ ≥ 3 there is a map  S3 ∨ S5 −→ ΣHn,ℓ  which induces a surjection on �K∗( ) ⊗ Z/p for all odd primes p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Therefore, the following corollary  follows immediately from Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='7, which strengthens [Boy1, Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Corollary 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Let p be an odd prime, n ≥ 2 and ℓ ≥ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Then for any ε > 0, once m is large  enough we have  rankp(π2m(ΣHn,ℓ)) ≥  1  (2m)1+ε  �3 +  √  5  2  �  m  2(n+ℓ)−1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  □  Consider the n-th unitary group U(n) which is connected and of real dimension n2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' In [Boy1,  Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='8], it is showed that when n ≥ 3 there is a map  S3 ∨ S5 −→ U(n)  which induces a surjection on �K∗( )⊗Z/p for all odd primes p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' It is clear that this map can be lifted  to the special unitary group SU(n), which is 2-connected and of real dimension n2 − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Therefore,  the following corollary follows immediately from Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='7, which strengthens [Boy1, Example  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Corollary 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Let p be an odd prime and n ≥ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Then for any ε > 0, once m is large enough we  have  rankp(πm(ΣU(n))) ≥  1  m1+ε ϕ  m  n2+1 >  1  m1+ε (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='19)  m  n2+1 ,  rankp(πm(ΣSU(n))) ≥  1  m1+ε ϕ  3m  n2 >  1  m1+ε (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='70)  m  n2 ,  where ϕ is the unique positive real root of z5 − z2 − 1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  □  The structure of this paper is as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Section 2 treats the algebra and combinatorics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Sub-  section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='2 treats free Lie algebras without a differential, and Subsection 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='3 studies the module  of boundaries in the differential case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' These results are then used to prove the main theorems in  Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Acknowledgements This paper was written while Guy Boyde was an EPSRC Doctoral Prize post-  doc at the University of Southampton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' He would like to thank Naomi Andrew, George Davenport,  Lawk Mineh, and Stephen Theriault for many helpful conversations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Ruizhi Huang was supported in part by the National Natural Science Foundation of China (Grant  nos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' 11801544 and 12288201), the National Key R&D Program of China (No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' 2021YFA1002300),  the Youth Innovation Promotion Association of Chinese Academy Sciences, and the “Chen Jingrun”  Future Star Program of AMSS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  SOME ASYMPTOTIC FORMULAE FOR TORSION IN HOMOTOPY GROUPS  7  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Algebra  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Complex arithmetic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Let S be a finite set of positive integers, let g = gcd(S), and let η ∈ C be nonzero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Then ηg is a positive real if and only if ηi is a positive real for all i ∈ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' The ‘only if’ direction follows from the fact that g divides each member of S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' For the ‘if’  direction, Bezout’s Lemma gives αi ∈ Z for each i ∈ S such that �  i αi · i = g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Thus, if each ηi is a  positive real, we get  ηg = η  �  i αi·i =  �  i  (ηi)αi,  which is a product of powers of positive reals, hence also a positive real.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  □  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Let c0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' ck−1 ∈ Z≥0, with c0 ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' The polynomial  P(z) = zk −  k−1  �  i=0  cizi  has precisely one positive real root, ϕ, which occurs with multiplicity one, and satisfies ϕ ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' The  other roots η satisfy |η| ≤ ϕ, with equality holding if and only if η is the product of ϕ with a g-th  root of unity, where g = gcd({i | ci ̸= 0} ∪ {k}).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' The number of sign changes between consecutive coefficients in P is 1, so P has precisely one  positive real root by Descartes’ rule of signs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Call this root ϕ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Rearranging, we have ϕk = �k−1  i=0 ciϕi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Since c0 ≥ 1, we must have ϕk ≥ 1, so ϕ ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Suppose that η ∈ C is a root of P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Taking modulus and applying the triangle inequality, we  obtain  |η|k = |ηk| = |  k−1  �  i=0  ciηi| ≤  k−1  �  i=0  ci|η|i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Equality holds in the above if and only if 1) ηi is a non-negative real for all i for which ci ̸= 0, and  2) |η| is a root of P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' By Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='1, the first condition is equivalent to ηg being a non-negative real,  where g = gcd{i | ci ̸= 0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' The second condition is equivalent to |η| = ϕ, since |η| is a non-negative  real.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' The root ϕ satisfies these conditions, and the other solutions are obtained as the product of ϕ  with the g-th roots of unity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  If the inequality is strict then we have P(|η|) < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Since the value of the polynomial P(|z|) is  positive for sufficiently large |z|, and ϕ is the unique positive real root, P(|z|) > 0 for any |z| > ϕ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  It follows that |η| < ϕ, as required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  □  For a polynomial P(z) of degree k, let η1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' , ηk be the roots of P, with multiplicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' The N-th  Newton polynomial of P is the complex number ηN  1 + · · · + ηN  k .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' If P has real coefficients, then the  roots occur in conjugate pairs and the Newton polynomials take real values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='2 controls  the Newton polynomials quite tightly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' In particular, the next lemma explains that when N = gn is  8  GUY BOYDE AND RUIZHI HUANG  g-divisible they are well approximated asymptotically by gϕgn, and when N is not g-divisible they  are approximated by zero with the same error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Let c0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' ck−1 ∈ Z≥0, with c0 ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' As n → ∞, the Newton polynomials of  P(z) = zk −  k−1  �  i=0  cizi  satisfy  For N not divisible by g we have  |ηN  1 + · · · + ηN  k | ≤ (k − g)|ψ|N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  When N = gn is g-divisible we have  |gϕgn − (ηgn  1  + · · · + ηgn  k )| ≤ (k − g)|ψ|gn,  where ϕ is the unique positive real root of P(z), ψ is the next largest root in absolute value, and  g = gcd({i | ci ̸= 0} ∪ {k}).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  By definition, rN is a sum of N-th powers of positive reals less than ϕ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' This means that this  lemma implies for example that (ηgn  1  + · · · + ηgn  k ) ∼ gϕgn as n → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' By Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='2, roots of P(z) come in two kinds: those which are the product of ϕ with a  g-th root of unity, and those roots η with |η| < ϕ (hence |η| ≤ |ψ|).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' The important point is that  each root of the first kind occurs with multiplicity precisely 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  To see this, apply Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='2 to the polynomial  P ′(z) = z  k  g −  k−1  �  i=0  ciz  i  g  obtained by dividing all powers by g, and use the fact that roots of P(z) are precisely the g-th roots  of the roots of P ′(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Then, without loss of generality assume η1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' ηg are the roots of the first kind, so that |η1| =  · · = |ηg| = ϕ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' From elementary complex analysis or group theory we have that ηN  1 + · · · + ηN  g =  \uf8f1  \uf8f4  \uf8f2  \uf8f4  \uf8f3  gϕN  g | N,  0  g ∤ N,  and the result then follows from the triangle inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  □  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Free Lie algebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' We write the generating set X of a free Lie algebra L = L(X) over Z  as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Write q1 < · · · < qℓ for the distinct degrees which contain an element of X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Write  xi,1, xi,2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' , xi,mi for the distinct generators in degree qi, so that in particular the number of  generators in degree qi is mi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Hilton [Hil] showed that L is free as a Z-module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  SOME ASYMPTOTIC FORMULAE FOR TORSION IN HOMOTOPY GROUPS  9  Let µ : Z>0 −→ {−1, 0, 1} be the M¨obius inversion function, defined by  µ(s) =  \uf8f1  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f2  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f3  1  s = 1  0  s > 1 is not square free  (−1)ℓ  s > 1 is a product of ℓ distinct primes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Given a polynomial P(z) = a0 + a1z + · · · + akzk with a0 ̸= 0, the reciprocal of P(z) is ak +  ak−1z + · · ·+ a0zk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' For given P(z), let η1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' ηk be the complex roots of the reciprocal of P(z), with  multiplicity (so P(z) = a0  �k  i=1(1 − ηiz)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Write  SN(P(z)) := ηN  1 + · · · + ηN  k  for the N-th Newton polynomial in the zeroes of the reciprocal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  The following theorem is due to Babenko.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Relative to his statement, we have changed variable  using the fact that, for fixed N, d �→ N  d is a self-bijection of the set of divisors of N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' [Bab, Proposition 1] Let L be the free graded Lie algebra over Z on a finite set of  generators {xi,j}, with notation as above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Then  rank(LN) = (−1)N  N  �  d|N  (−1)  N  d µ(d)S N  d (1 −  ℓ  �  i=1  mizqi),  where the sum is taken over the divisors d of N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  □  Our next theorem is essentially a result of Lambrechts [Lam, Proposition 1] in the special case of  free Lie algebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Our derivation of this result from Babenko’s is essentially the same as Lambrechts’s,  but the situation is simpler and slightly more is true.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' The point of the theorem is that when g | N,  rank(LN) is well-approximated by g  N ϕN with an error term given by a sum of exponentials in smaller  bases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Let L be the free graded Lie algebra over Z on a finite set of generators X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' As before,  write q1 < · · · < qℓ for the distinct degrees which contain an element of X, and let g = gcd(qi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Let  mi be the number of generators in degree qi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  If g ∤ N, then rank(LN) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  If g | N, then |rank(LN) − g  N ϕN| ≤ qℓ  N |ψ|N + gϕ  N  2 + qℓ|ψ|  N  2 ,  where ϕ is the unique positive real root of the degree qℓ polynomial  P(z) = zqℓ −  ℓ  �  i=1  mizqℓ−qi = 0,  and ψ is the next largest root in absolute value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  In particular,  ϕ  ≥  (�ℓ  i=0 mi)  1  qℓ  =  (�ℓ  i=0 mi)  1  max(q1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='qℓ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  10  GUY BOYDE AND RUIZHI HUANG  If P(z) has no roots which are strictly smaller than ϕ in absolute value (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' ‘ψ does not exist’)  then terms involving ψ may be disregarded: precisely, the inequality in the second bullet may be  replaced by |rank(LN) − g  N ϕN| ≤ gϕ  N  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' The first bullet follows immediately from the fact that L is concentrated in degrees divisible  by g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  We will now prove the second bullet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' The point is that the Babenko’s formula of Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='4 is  dominated by the d = 1 term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Let N be divisible by g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' By Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='4 (using that µ(1) = 1) we  have  rank(LN) = (−1)N  N  �  d|N  (−1)  N  d µ(d)S N  d (1 −  ℓ  �  i=1  mizqi)  = 1  N SN(1 −  ℓ  �  i=1  mizqi) + (−1)N  N  �  d|N  d≥2  (−1)  N  d µ(d)S N  d (1 −  ℓ  �  i=1  mizqi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  We name these two terms, writing SN = SN(1 − �ℓ  i=1 mizqi) to simplify notation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Let  AN := 1  N SN,  and let  BN := (−1)N  N  �  d|N  d≥2  (−1)  N  d µ(d)S N  d .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  By Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='3 (with n = N  g ), we have |SN − gϕN| ≤ (qℓ − g)|ψ|N ≤ qℓ|ψ|N for ϕ and ψ as in the  theorem statement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' It therefore suffices to show that |BN| ≤ gϕ  N  2 + qℓ|ψ|  N  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Since |µ(d)| ≤ 1, we have by Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='3 that  |BN| = 1  N |  �  d|N  d≥2  (−1)  N  d µ(d)S N  d | ≤ 1  N  �  d|N  d≥2  |S N  d | ≤ 1  N  �  d|N  d≥2  (gϕ  N  d + qℓ|ψ|  N  d ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  The number of terms in this summation is at most the number of divisors of N, which is at most  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' The term is a sum of exponentials in positive bases, hence is strictly increasing, and in particular  for d ≥ 2 we have the termwise bound gϕ  N  d + qℓ|ψ|  N  d ≤ gϕ  N  2 + qℓ|ψ|  N  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Putting this together gives  |BN| ≤ gϕ  N  2 + qℓ|ψ|  N  2 ,  as required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Lastly, we check that ϕ ≥ (�ℓ  i=0 mi)  1  qℓ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Since the polynomial P(z) = zqℓ − �ℓ  i=1 mizqℓ−qi has  a unique positive root by Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='2, it suffices to check that P((�ℓ  i=0 mi)  1  qℓ ) is non-positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' For  SOME ASYMPTOTIC FORMULAE FOR TORSION IN HOMOTOPY GROUPS  11  each i, qℓ−qi  qℓ  lies between 1 and 0, so for any x ≥ 1 we have x  qℓ−qi  qℓ  ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' It follows that  P((  ℓ  �  i=0  mi)  1  qℓ ) = (  ℓ  �  i=0  mi) −  ℓ  �  i=1  mi(  ℓ  �  i=0  mi)  qℓ−qi  qℓ  ≤ (  ℓ  �  i=0  mi) −  ℓ  �  i=1  mi · 1 = 0,  as required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  □  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Free Lie algebras with differentials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Free Lie algebras over Z/pr are obtained by tensoring  the corresponding free Lie algebra over Z with Z/pr, since this gives the correct universal property.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  In this subsection, we consider L = L(x, y) = L(x, dx), the free differential Lie algebra over Z/pr  on the acyclic rank 2 free differential Z/pr-module on generators x and y (dx = y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Suppose that  deg(x) = q + 1, so deg(y) = q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' By Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='5, since gcd(q, q + 1) = 1, we know that  rankZ/pr(LN) ∼ 1  N ϕN,  where ϕ is the unique positive real root of the degree q + 1 polynomial  zq+1 − z − 1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  The size of the error in this approximation is exponential in base depending on the next largest  root ψ (in absolute value), and √ϕ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  In this subsection we are instead interested in B := Im(d) ⊂ L, the module of boundaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Our  aim is to prove Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' The argument will go as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' It is known (Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='7) that  the differential on L is ‘almost acyclic’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' A counting argument using the fact that rank(LN) ∼ 1  N ϕN  then shows that the rank of the module of boundaries must be asymptotically a fixed fraction of  that of LN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  We will first reduce to the case r = 1 by means of the following lemma, which is proven in [Boy2]  as Lemma 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Let ϕ : M −→ N be a map of Z/pr-modules, with N free.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Then rankZ/pr(Im(ϕ)) =  rankZ/p(Im(ϕ ⊗ Z/p)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  □  Now assume r = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Let u be an even-dimensional class in a graded differential Lie algebra L over  Z/p for p ̸= 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Following [CMN], let  τk(u) = adpk−1(u)(du),  and let  σk(u) = 1  2  pk−1  �  j=1  1  p  �pk  j  �  [adj−1(u)(du), adpk−1−j(u)(du)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  From our point of view, the point of the next theorem is that free differential Lie algebras are  almost acyclic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  12  GUY BOYDE AND RUIZHI HUANG  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' [CMN, Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='9] Let V be an acyclic differential Z/p-vector space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Write  L(V ) ∼= HL(V ) ⊕ K, for an acyclic module K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' If K has an acyclic basis, that is, a basis  {xα, yα, zβ, wβ},  where α and β range over index sets I and J respectively, and we have  d(xα) = yα, deg(xα) even,  d(zβ) = wβ, deg(zβ) odd,  then HL(V ) has a basis  {τk(xα), σk(xα)}α∈I ,k≥1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  □  The theorem implies that the differential on L can be modified slightly to make it acyclic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Namely,  define a new differential d : L(V ) → L(V ) by setting d = d on K, and letting d(τk(xα)) = σk(xα),  d(σk(xα)) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Of course, d will no longer satisfy the Leibniz rule, but it will still be a vector space  endomorphism of degree −1 which satisfies d  2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Now let B := Im(d) ⊂ L, and let σ ⊂ L be the subspace spanned by the elements σk(x), for some  even degree x ∈ L and k ∈ Z+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' By definition of d we then have the following corollary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' We have BN ∼= BN ⊕ σN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  □  The next lemma justifies the approximation by providing a crude upper bound on σN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' We have the bound  dimZ/p σN ≤ c1 · Nϕ  N  p ,  where c1 = 2(q + 2)ϕ  2  p .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' By definition, σN is spanned by classes σk(xα), and we have deg(σk(xα)) = k deg(xα) − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  We therefore have  dimZ/pr σN ≤  �  M≤N  pkM−2=N  dimZ/p LM ≤  �  M≤N  pkM−2=N  ( 1  M ϕM + q + 1  M |ψ|M + ϕ  M  2 + (q + 1)|ψ|  M  2 )  ≤  �  M≤N  pkM−2=N  ((q + 2)ϕM + (q + 2)ϕ  M  2 ) ≤  �  M≤N  pkM−2=N  2(q + 2)ϕM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  by Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='5 (we use |ψ| < ϕ, and then drop the factors of  1  M , to obtain a bound which is strictly  increasing even for small M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' This summation contains fewer than N terms, and since the value of  a given term is increasing in M, the size of the largest term is controlled by M = N+2  pk  ≤ N+2  p , so  dimZ/p σN ≤ N · 2(q + 2)ϕ  N+2  p ,  as required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  □  SOME ASYMPTOTIC FORMULAE FOR TORSION IN HOMOTOPY GROUPS  13  We next estimate the size of dim BN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Let ψ be the next largest (in absolute value) root of zq+1 − z − 1 after ϕ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' We have  dimZ/p BN ≥ (1 −  N  N − 1  1  ϕ) · 1  N ϕN − κ|ψ|N − c2ϕ  N  2 ,  where κ = (q + 1)(1 +  1  |ψ|) and c2 = (q + 2)(1 +  1  √ϕ) ≤ 2(q + 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Since d is acyclic, we have BN = Ker(d : LN → LN−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' The First Isomorphism Theorem  then gives that LN⧸BN  ∼= BN−1, and since BN−1 ⊂ LN−1 we get  dimZ/p BN ≥ dimZ/p LN − dimZ/p LN−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='5 gives (since g = 1 and |ψ| < ϕ)  dimZ/p LN−1 ≤  1  N − 1ϕN−1 + q + 1  N − 1|ψ|N−1 + (q + 2)ϕ  N−1  2 ,  and  dimZ/p LN ≥ 1  N ϕN − q + 1  N  |ψ|N − (q + 2)ϕ  N  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Combining these inequalities gives the result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  □  We are now ready to state and prove the main theorem of this subsection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Let L ⊗ Z/pr = L(x, dx) ⊗ Z/pr = L(x, y) ⊗ Z/pr be the free differential graded  Lie algebra over Z/pr on two generators x and y satisfying y = dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Let q = deg(y), so that  deg(x) = q + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Let B = Im(d) ⊂ L ⊗ Z/pr be the submodule of boundaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Then we have the bound  rank(BN) ≥ (1 −  N  N − 1  1  ϕ) · 1  N ϕN − cNϕ  N  2 − κ|ψ|N,  where ϕ > 1 is the unique positive real root of the degree n polynomial  zq+1 − z − 1 = 0,  ψ is the next largest root in absolute value, c = 2(q + 2)(1 + ϕ), and κ = (q + 1)(1 +  1  |ψ|).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' We have  the bounds 2  1  q+1 < ϕ < 1 + 1  q .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' By Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='6, it suffices to prove the theorem in the case r = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' By Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='8 we have  dimZ/p BN ≥ dimZ/p BN − dimZ/p σN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Combining Lemmas 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='9 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='10 (c = c1 + c2) then gives the result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  □  14  GUY BOYDE AND RUIZHI HUANG  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Topology  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Homology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' We now prove Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' In the proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='5 of [Boy2] it is shown that there exists a commu-  tative diagram (the details of the definitions of the maps need not concern us here):  L′(x, y)  θ◦d  �  βr◦Φr,r  π  � π∗(ΩP n+1(pr))  (Ωµ)∗  �  h◦ρs  �  π∗(ΩY )  h◦ρs  �  L(x, y) ⊗ Z/ps  Φr,s  H� H∗(ΩP n+1(pr);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Z/ps)  (Ωµ)∗ � H∗(ΩY ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Z/ps).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  In the diagram, L(x, dx) ⊗ Z/ps is the free differential Lie algebra (with dx = y , deg(x) = q + 1,  deg(y) = q).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' The top-left entry L′(x, dx) is a certain module over Z/pr which is ‘almost’ a free  differential Lie algebra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  We now use various results from [Boy2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  By the remark immediately before Corollary 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='9 of  that paper, the image of the left hand vertical map θ ◦ d is precisely the module of boundaries  BL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  By Lemma 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='6 the map Φr,s  H  is an injection, and the induced map on homology, (Ωµ)∗,  is an injection by assumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' It follows by commutativity that the image in the bottom-right,  I := Im(h ◦ ρs ◦ (Ωµ)∗ ◦ βr ◦ Φr,r  π ), is isomorphic to BL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  The point is then that the homotopy groups of Y surject onto I, hence must be just as large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  More precisely, we obtain that  r  �  t=s  rankZ/pt(πN(ΩY )) ≥ rankZ/ps(IN) = rankZ/ps(BLN)  by Lemma 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='8 of [Boy2] applied to the part of the diagram consisting of  πN(ΩY )  �P  P  P  P  P  P  P  P  P  P  P  P  (L′(x, y))N  �  �  HN(ΩY ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Z/ps).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  The loops on Y is just a degree shift on homotopy groups, so the result follows by Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='11  of this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  □  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' K-theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' In this subsection, the following linear inequality relating integers j and N will  arise often.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' We will refer to it as Condition (∗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Here, X is a fixed space, conn(X) is the p-local  connectivity of X, and dim(X) is the largest d for which Hd(X;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Q) ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  (*)  j >  1  2(p − 1)( dim(X) + 1  conn(X) + 1 − 1)N + ( dim(X) + 1  conn(X) + 1)(conn(X) + 2) − 1),  The next theorem refines and slightly generalises Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='4 of [Boy1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  SOME ASYMPTOTIC FORMULAE FOR TORSION IN HOMOTOPY GROUPS  15  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Let p be an odd prime, and let X be a path connected space having the p-local  homotopy type of a finite CW-complex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Suppose that there exists a map  µ :  ℓ�  i=1  mi  �  j=1  Sqi+1 → ΣX  with 1 ≤ q1 < q2 < · · · < qℓ, such that the map  �K∗(ΣX) ⊗ Z/p  µ∗  −→ �K∗(  ℓ�  i=1  mi  �  j=1  Sqi+1) ⊗ Z/p ∼=  ℓ  �  i=1  mi  �  j=1  Z/p  is a surjection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Then for any N, j such that  j >  1  2(p − 1)( dim(X) + 1  conn(X) + 1 − 1)N + ( dim(X) + 1  conn(X) + 1)(conn(X) + 2) + 1)  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' such that Condition (*) holds) we have  ∞  �  t=1  rankZ/pt(πN+2j(p−1)−1(ΩΣX)) ≥ rankZ/pr(LN ⊗ Z/pr),  where L is as in Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='5 (the free Lie algebra on generators corresponding to the spheres in  the wedge), conn(X) is the p-local connectivity of X, dim(X) is the dimension of X as measured by  rational cohomology, and g = gcd(q1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' , qℓ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' This is essentially a more careful restatement of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='4 of [Boy1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Some of the arguments  of that paper are given only for a wedge of two spheres, but all of them apply verbatim to any finite  wedge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Construction 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='15 of that paper gives (in slightly different language) a diagram of the form  πN(ΩΣX)  �◆  ◆  ◆  ◆  ◆  ◆  ◆  ◆  ◆  ◆  ◆  LN ⊗ Z/pr  �  �  EN+2j(p−1)  for some module E∗ whose definition need not concern us.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='16 of that paper than says that the horizontal map is an injection, and hence, just  as in the proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='2, the conclusion holds, provided that there exists some ℓ ∈ Z≥0 such  that ℓj(p−1)+ N−1  2  > λk  ℓ , for an integer k which may be taken to be ⌈  N+1  conn(X)+1⌉.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  The inequality therefore rearranges to j >  1  p−1(⌈  N+1  conn(X)+1⌉ log(λℓ)  log(ℓ) − N−1  2 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' In [AA], it is shown  that λℓ = ℓ⌈ dim(X)  2  ⌉, so we may simplify to  j >  1  p − 1(⌈  N + 1  conn(X) + 1⌉⌈dim(X)  2  ⌉ − N − 1  2  ),  which is implied by Condition (*), using the fact that for an integer z we have ⌈ z  2⌉ ≤ z+1  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' This  completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  □  The next step is a simple application of Bezout’s Lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  16  GUY BOYDE AND RUIZHI HUANG  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Let α, β ∈ Z with α, β > 0, and let a, b ∈ R with a > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Consider the set of linear  combinations  Sn = {nα + jβ | j ∈ Z≥0, j > an + b} ⊂ Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Let g′ = gcd(α, β).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' There exists a constant B, independent of n, such that for each n, all multiples  of g′ which are at least min(Sn) + B are contained in Si for some i which is close to n in the  sense that n ≤ i < n + β(β + 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Furthermore, there exists a suitable B satisfying the bound  B ≤ β2(α + a(1 + β)) + β, and hence any B ≥ β2(α + a(1 + β)) + β is also suitable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  If α and β are fixed (and j and n are allowed to vary) then it is a familiar fact that the set of  integers of the form nα + jβ is precisely the multiples of g′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Our statement is essentially just a more  complicated version of this.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' First consider the set Sn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' If an integer j satisfies j > an+b (so that nα+jβ lies in Sn), then  increasing the parameter j certainly does not violate this condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Therefore, adding a positive  multiple of β to an element of Sn yields another element of Sn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' In particular, Sn already contains  all integers which are obtained by increasing min(Sn) by a multiple of β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  These values are by  construction linear combinations of α and β, so they are all multiples of g′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  It remains, then, to show that by increasing n ‘just a little’, we can ‘fill in’ the intermediate  multiples of g′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' We will do so by ‘giving ourselves enough room’, in the sense of an ad-hoc quantity  which we now define.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Define the excess of (j, n) to be j − (an + b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' The condition j > an + b is then  equivalent to (j, n) having positive excess.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  By Bezout’s Lemma, let x > 0 and y ≥ 0 be the solution of xα − yβ = g′ with smallest non-  negative y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' We have 0 < x ≤ g′  α + β and 0 ≤ y ≤ α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Given an expression nα + jβ, replacing n by  n + x and j by j − y increases the value of the linear combination nα + jβ by g′, and reduces the  excess by the constant ax + y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' We will use this to fill in the remaining multiples of g′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Let j0 realise the smallest member of Sn, in the sense that min(Sn) = nα + j0β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Now take any  j ≥ j0+ β  g′ (ax+y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' The excess of (n, j0) was positive, so the excess of (n, j) is greater than β  g′ (ax+y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  We may therefore add (x, −y) to (n, j) up to β  g′ times while retaining a positive excess (and keeping  j non-negative).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' This shows that all multiples of g′ lying between nα + jβ and nα + (j + 1)β are  contained in Si for some i satisfying n ≤ i < n + β  g′ x, and we may perform this procedure for any  j ≥ j0 + β  g′ (ax + y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' In particular, all multiples of g′ which are at least min(Sn) + β( β  g′ (ax + y) + 1)  are contained in Si for some i satisfying n ≤ i < n + β  g′ x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' The extra +1 here is because j must  be an integer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' This is essentially the result, and it remains only to establish that we may take the  constants as in the statement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Now, g′  α ≤ 1, so x ≤ 1 + β, and  β  g′ x ≤ βx ≤ β(1 + β).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' This establishes the bounds on i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' The  bound on B follows from these inequalities, together with y ≤ α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' This completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  □  We now prove the following strong version of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  SOME ASYMPTOTIC FORMULAE FOR TORSION IN HOMOTOPY GROUPS  17  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Let p be an odd prime, and let X be a path connected space having the p-local  homotopy type of a finite CW-complex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Suppose that there exists a map  µ :  ℓ�  i=1  mi  �  j=1  Sqi+1 → ΣX  with 1 ≤ q1 < q2 < · · · < qℓ, such that the map  �K∗(ΣX) ⊗ Z/p  µ∗  −→ �K∗(  ℓ�  i=1  mi  �  j=1  Sqi+1) ⊗ Z/p ∼=  ℓ  �  i=1  mi  �  j=1  Z/p  is a surjection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Then there exist constants τ, θ > 0 such that for multiples M = mg′ of  g′ = gcd(q1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' qℓ, 2(p − 1))  we have  ∞  �  t=1  rankZ/pt(πM(ΣX)) ≥  τ  1  g  conn(X)+1  dim(X)+1 M + θ  ϕ( conn(X)+1  dim(X)+1 )M − o( 1  M ϕ( conn(X)+1  dim(X)+1 )M),  where ϕ is the unique positive real root of the degree qℓ polynomial  zqℓ −  ℓ  �  i=1  mizqℓ−qi = 0,  (in particular, ϕ ≥ (�ℓ  i=0 mi)  1  qℓ = (�ℓ  i=0 mi)  1  max(q1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='qℓ) ), conn(X) is the p-local connectivity of X,  dim(X) is the rational cohomological dimension of X, and g = gcd(q1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' , qℓ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Let  Sn  be  the  set  of  dimensions  M  for  which  Theorem  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='1  tells  us  that  �∞  t=1 rankZ/pt(πM(ΣX)) ≥ dimZ/p(Lng ⊗ Z/pr).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' That is:  Sn = {ng + j · 2(p − 1) | j ∈ Z, j > an + b} ⊂ Z,  where a =  g  2(p−1)( dim(X)+1  conn(X)+1 − 1) and b =  1  2(p−1)( dim(X)+1  conn(X)+1(conn(X) + 2) + 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  By Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='2, there exists a constant B, which may be taken to be 4(p − 1)2(g + a(1 + 2(p −  1))) + 2(p − 1) such that for each M = mg′ ≥ min(Sn) + B, we have �∞  t=1 rankZ/pt(πM(ΣX)) ≥  dimZ/p(Lig ⊗ Z/pr) for some i with n ≤ i < n + 8(p − 1)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' By Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='5,  ∞  �  t=1  rankZ/pt(πM(ΣX)) ≥ 1  i ϕig − qℓ|ψ|ig − gϕ  ig  2 − qℓ|ψ|  ig  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Regardless of whether |ψ| > 1, we have |ψ|  ig  2 < 1 + |ψ|ig < 2 + |ψ|(n+8(p−1)2)g, so the inequality  implies  (†)  ∞  �  t=1  rankZ/pt(πM(ΣX)) ≥  1  n + 8(p − 1)2 ϕng − gϕ  (n+8(p−1)2)g  2  − qℓ(3 + 2|ψ|(n+8(p−1)2)g).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  It remains only to find the dependency of n upon M, and convert this expression into one in terms  of M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  18  GUY BOYDE AND RUIZHI HUANG  The smallest member of Sn is obtained by taking the smallest j = jn satisfying Condition (*).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  By definition jn is the smallest integer with jn > an + b, so jn ≤ an + b + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Thus,  min(Sn) = ng + 2jn(p − 1) ≤ g( dim(X) + 1  conn(X) + 1)n + 2(p − 1)(b + 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  To conclude, for given M = mg′, let n = n(M) be the largest non-negative integer satisfying  M ≥ g( dim(X)+1  conn(X)+1)n + 2(p − 1)(b + 1) + B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Rearranging gives n ≤ M−(2(p−1)(b+1)+B)  g  ( conn(X)+1  dim(X)+1 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  Since n is the largest such integer, it is at least one less than this expression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Applying the bounds  n ≤ i < n + 8(p − 1)2, now gives that  1  n + 8(p − 1)2 ϕng ≥  τ  1  g  conn(X)+1  dim(X)+1 M + θ  ϕ  conn(X)+1  dim(X)+1 M,  for constants θ and τ, and shows that the other terms of the inequality † are o( 1  M ϕ  conn(X)+1  dim(X)+1 ), as  required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  □  Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' In this remark we give the constants and error term for Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='3, and collect the  other constants appearing in the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  The positive integers q1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' qℓ are given in the hypotheses of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='3 (or Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Then  g = gcd(q1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' , qℓ),  and  g′ = gcd(q1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' qℓ, 2(p − 1)) = gcd(g, 2(p − 1)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  The space X and the prime p ̸= 2 are given in the hypotheses of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='3, dim(X) is the  rational dimension of X, and conn(X) is its p-local connectivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  The constants appearing in the proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='3 are then  a =  g  2(p − 1)( dim(X) + 1  conn(X) + 1 − 1),  b =  1  2(p − 1)( dim(X) + 1  conn(X) + 1(conn(X) + 2) + 1), and  B = 4(p − 1)2(g + a(1 + 2(p − 1))) + 2(p − 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  It then follows from the proof that the constants θ and τ of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='3 may be taken as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  θ = 8(p − 1)2 − (conn(X) + 1  dim(X) + 1 )2(p − 1)(b + 1 + B)  g  ≤ 8(p − 1)2, and  τ = ϕ−g−( conn(X)+1  dim(X)+1 )(2(p−1)(b+1)+B),  where, as usual, ϕ is the unique positive root of the polynomial P(z) = zqℓ − �ℓ  i=1 mizqℓ−qi = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  The error term in the bound Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='3 is an unpleasant expression, and we restrict ourselves  to noting that it is negative, and of the form  −c1ϕ  1  2  conn(X)+1  dim(X)+1 M − c2|ψ|  conn(X)+1  dim(X)+1 M − 3qℓ,  SOME ASYMPTOTIC FORMULAE FOR TORSION IN HOMOTOPY GROUPS  19  for constants ci, where ψ is the next largest root of P(z) after ϕ, in absolute value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' The deviation  of the bound from being a pleasant expression is therefore exponential in bases determined by the  roots of P(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  References  [AA]  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Adams and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Atiyah, K-theory and the Hopf invariant, Quart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Oxford Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' (2) 17 (1966),  31-38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='2  [Bab]  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Babenko, Analytical properties of Poincar´e series of a loop space, Mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Zametki 27 (5) (1980), 359-367.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  1, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='4  [Boy1] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Boyde, p-hyperbolicity of homotopy groups via K-theory, to appear in Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=', 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' arXiv: 2101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='04591.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='  1, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='2, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='2, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='2, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='2, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='2, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='2  [Boy2] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Boyde, Z/pr-hyperbolicity via homology, to appear in Isr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=', 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' arXiv: 2106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='03516.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' 1, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='1, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='1,  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='1, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='1, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='3, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='1  [BS]  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Burklund, How big are the stable homotopy groups of spheres, with an appendix joint with A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Senger,  preprint, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' arXiv:2203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='00670 1, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='1  [CMN] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Cohen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Moore and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Neisendorfer, Torsion in homotopy groups, Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' of Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' (2) 109 (1)  (1979), 121-168.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='1, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='3, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='7  [FHT] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' F´elix, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Halperin and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Thomas, Exponential growth and an asymptotic formula for the ranks of  homotopy groups of a finite 1-connected complex, Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' of Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' 170 (2009), 443-464.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' 1  [Hen]  Hans-Werner Henn, On the growth of homotopy groups, Manuscripta Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' 56 (2) (1986), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' 235–245.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' 1  [Hil]  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Hilton, On the homotopy groups of the union of spheres, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' London Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' 30 (1955), 154-172.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='2  [HW]  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Huang and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Wu, Exponential growth of homotopy groups of suspended finite complexes, Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' 295  (2020), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' 1301-1321.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' 1, 1, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='1  [Iri]  Kouyemon Iriye, On the Ranks of Homotopy Groups of a Space, Publ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Inst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' 23 (1) (1987),  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' 209-213.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' 1  [Lam] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Lambrechts, Analytic properties of Poincar´e series of spaces, Topology 37 (6) (1998), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' 1363-1370.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' 1, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='2  [Sel]  Paul Selick, On conjectures of Moore and Serre in the case of torsion-free suspensions, Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Cambridge  Philos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' 94 (1) (1983), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' 53-60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='2  Mathematical Institute, Utrecht University, Heidelberglaan 8 3584 CS Utrecht, The Netherlands  Email address: g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='boyde@uu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='nl  Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences,  Beijing 100190, China  Email address: haungrz@amss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='cn  URL: https://sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='google.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
+page_content='com/site/hrzsea/' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE0T4oBgHgl3EQfmQGx/content/2301.02497v1.pdf'}
diff --git a/XNE2T4oBgHgl3EQfYgch/content/2301.03854v1.pdf b/XNE2T4oBgHgl3EQfYgch/content/2301.03854v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..23efde5d31380a95b2a09326ecdd86a2df53cb67
--- /dev/null
+++ b/XNE2T4oBgHgl3EQfYgch/content/2301.03854v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6dc1eb31d0e9f4369c4b8ccbf02bb031a61efb81ef3ad7815fd3f6e950fcbcbd
+size 4686130
diff --git a/XNE2T4oBgHgl3EQfYgch/vector_store/index.faiss b/XNE2T4oBgHgl3EQfYgch/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..892e9da362e28d20825b9e0f93f8534102bc0e82
--- /dev/null
+++ b/XNE2T4oBgHgl3EQfYgch/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:25a809e2731f2c24a61167839c34697b49c98c34a34f9707be030d31c81d3cc5
+size 2555949
diff --git a/XNE2T4oBgHgl3EQfYgch/vector_store/index.pkl b/XNE2T4oBgHgl3EQfYgch/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..9cb855511d8c3fed7e8768eb7150c8dbfca319b1
--- /dev/null
+++ b/XNE2T4oBgHgl3EQfYgch/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0a86d1f56055d8e414c0b479057d93edf1551ef7e325d4d70f03e42f72899a97
+size 90630
diff --git a/YdE2T4oBgHgl3EQfZAcJ/content/tmp_files/2301.03859v1.pdf.txt b/YdE2T4oBgHgl3EQfZAcJ/content/tmp_files/2301.03859v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2945dc3275820a336cb267a11ac1cdab4b5d88a5
--- /dev/null
+++ b/YdE2T4oBgHgl3EQfZAcJ/content/tmp_files/2301.03859v1.pdf.txt
@@ -0,0 +1,1105 @@
+Robust mutual synchronization in long spin Hall nano-oscillator chains
+Akash Kumar,1, ∗ Himanshu Fulara,2 Roman Khymyn,1 Mohammad Zahedinejad,3 Mona Rajabali,3
+Xiaotian Zhao,1 Nilamani Behera,1 Afshin Houshang,1 Ahmad A. Awad,1 and Johan ˚Akerman1, †
+1Physics Department, University of Gothenburg, 412 96 Gothenburg, Sweden.
+2Department of Physics, Indian Institute of Technology Roorkee, Roorkee 247667, India
+3NanOsc AB, Kista, Sweden.
+(Dated: January 11, 2023)
+Mutual synchronization of N serially connected spintronic nano-oscillators increases their coher-
+ence by a factor N and their output power by N 2. Increasing the number of mutually synchronized
+nano-oscillators in chains is hence of great importance for better signal quality and also for emerging
+applications such as oscillator-based neuromorphic computing and Ising machines where larger N
+can tackle larger problems. Here we fabricate spin Hall nano-oscillator chains of up to 50 serially
+connected nano-constrictions in W/NiFe, W/CoFeB/MgO, and NiFe/Pt stacks and demonstrate
+robust and complete mutual synchronization of up to 21 nano-constrictions, reaching linewidths of
+below 200 kHz and quality factors beyond 79,000, while operating at 10 GHz. We also find a square
+increase in the peak power with the increasing number of mutually synchronized oscillators, result-
+ing in a factor of 400 higher peak power in long chains compared to individual nano-constrictions.
+Although chains longer than 21 nano-constrictions also show complete mutual synchronization, it
+is not as robust and their signal quality does not improve as much as they prefer to break up into
+partially synchronized states. The low current and low field operation of these oscillators along with
+their wide frequency tunability (2-28 GHz) with both current and magnetic fields, make them ideal
+candidates for on-chip GHz-range applications and neuromorphic computing.
+I.
+INTRODUCTION
+Since the advent of spin transfer torque driven mag-
+netization precession in metallic spin valves [1–4], the
+interest in spintronic microwave oscillators has steadily
+increased [5]. Mutual synchronization of these non-linear
+microwave oscillators is of utmost importance for various
+applications such as efficient ultra-broadband signal gen-
+erators [6], wireless communication, ultra-fast microwave
+spectral analysis [7, 8] and recently developed interest
+in neuromorphic computing among others [9, 10]. More-
+over, researchers have recently demonstrated energy har-
+vesting from wireless signals using synchronized oscil-
+lators in series [11].
+There have been many attempts
+to synchronize these oscillators over short and long
+ranges [6, 10, 12–14]. However, the complex fabrication
+process of spin torque nano-oscillators (STNOs) raises a
+technological issue to scale their synchronization for high
+frequency applications and hence the progress of synchro-
+nizing many STNOs has been rather slow [6, 11, 14].
+Thanks to the spin Hall effect [15–17], a new class of
+spintronic oscillators, known as spin Hall nano-oscillators
+(SHNOs), has emerged [18–21]. Compared to STNOs,
+they rely on the current flowing in-plane, which makes
+their fabrication easier and allows for a much larger
+number of SHNOs to synchronize. In particular, nano-
+constriction based SHNOs [18, 19] can be easily fabri-
+cated into 1D chains [22] and 2D arrays [23].
+Earlier
+work has shown that up to nine SHNOs, separated by
+300 nm, can be mutually synchronized to generate both
+∗ akash.kumar@physics.gu.se
+† johan.akerman@physics.gu.se
+θ
+φ
+H
+x
+y
+z
+500 nm
+FIG. 1.
+Schematic representation of 21 nano-constriction
+SHNOs in a chain fabricated from a non-magnet/ferromagnet
+bilayer. Blue arrows with yellow spheres represent the local
+magnetization and its magneto-dynamical precession in each
+nano-constriction. The charge current is applied in-plane and
+the magnetic field at an oblique angle.
+The inset shows a
+scanning electron microscope image of an actual SHNO chain.
+higher output power and a narrower linewidth [22]. Sim-
+ilarly, 2D arrays of up to 8×8 oscillators [23] were found
+to synchronize completely. The number of synchronized
+oscillators along a dimension is hence limited to single
+digits.
+arXiv:2301.03859v1  [cond-mat.mes-hall]  10 Jan 2023
+
+Non-magnet2
+0
+5
+10
+15
+20
+0
+1
+2
+3
+4
+5
+6
+Resistance (kW)
+N
+ W/CoFeB/MgO
+ W/NiFe
+264 W
+105 W
+Spectrum Analyzer
+LNA
+IDC
+f
+Bias-T
+SHNO
+(a)
+(b)
+P
+FIG. 2.
+(a) Resistance of the SHNO chains vs. number of nano-constrictions (N ), showing the expected linear dependence,
+with each W/NiFe and W/CoFeB/MgO nano-constriction adding 105 Ω and 264 Ω, respectively. The inset shows an SEM
+image of the Ground-Signal-Ground pads connecting to the SHNO chain. (b) Schematic representation of the auto-oscillation
+measurement set-up. The drive current is provided via a bias-T, which also picks up the generated microwave voltage and feeds
+it to a low-noise amplifier before being recorded by a spectrum analyzer.
+In this work, we study mutual synchronization in
+much longer SHNO chains of up to 50 serially connected
+nano-constrictions fabricated from W(5 mm)/CoFeB(1.4
+nm)/MgO(2 nm) [24–27], W(5 nm)/NiFe(3 nm) [28], and
+NiFe(5 nm)/Pt(5 nm) [22, 23] material stacks (the order
+represents the actual stack sequence), focusing primarily
+on the W based SHNOs with their much lower threshold
+current. We find that robust and complete mutual syn-
+chronization can persist in chains of up to 21 oscillators,
+resulting in a significantly lower linewidth and higher out-
+put power compared to single SHNOs. We also observe
+mutual synchronization in the longer chains but with de-
+teriorated parameters, which we find to originate from a
+tendency for the longer chains to separate into shorter
+mutually synchronized sections.
+II.
+RESULTS AND DISCUSSION
+A.
+SHNO chains and measurement set-up
+Figure 1 shows the layout for a chain of nano-
+constriction SHNOs made from a non-magnet (NM) –
+ferromagnet (FM) bilayer. The inset shows a scanning
+electron micrograph of an actual SHNO chain. A charge
+current flows in the film plane and a magnetic field is
+applied at an oblique OOP angle, θ. The spin Hall ef-
+fect of the NM layer converts the charge current into a
+transverse spin current exerting an anti-damping torque
+on the FM layer, which above a certain threshold cur-
+rent can generate auto-oscillations of the local magneti-
+zation in each nano-constriction. In this work, we ex-
+plore 150 nm wide nano-constrictions separated by 200
+nm center-to-center separation and chain lengths of up to
+50 nano-constrictions. We primarily study and compare
+chains made from W/CoFeB/MgO and W/NiFe material
+stacks, where W was chosen for its very large spin-Hall
+angle (θSH = -0.44, for details see supplementary file)
+and the FM layers for their low damping of αCoF eB =
+0.025 and αNiF e = 0.032. We also compare our results
+with 21 synchronized nano-constrictions in the widely
+studied NiFe/Pt [22, 23] system (shown in the supple-
+mentary file), where a much larger charge current den-
+sity is required because of the lower spin Hall angle of Pt
+thin films. Figure 2(a) shows how the resistance of the
+SHNO chains increases linearly with the number of nano-
+constrictions, each nano-constriction adding 105 ohm and
+264 ohm of resistance for W/NiFe and W/CoFeB/MgO,
+respectively. A schematic of the measurement set-up is
+shown in Fig. 2(b). Further details can be found in the
+Methods section.
+B.
+Mutual Synchronization for N = 1–21
+Figure 3 shows the power spectral density (PSD) of
+auto-oscillation in W/CoFeB/MgO (a-f) and W/NiFe (g-
+l) based SHNOs with N = 1–21. The behavior of chains
+with N ≥ 30 will be discussed in a later section below.
+Both types of SHNOs show a positive non-linearity, at
+given applied field magnitude and angles. As discussed
+in Ref. [24], the perpendicular magnetic anisotropy of the
+W/CoFeB/MgO stack increases its non-linearity com-
+pared to W/NiFe. The non-linearity is also substantially
+higher for N ≥ 5 than for the single and double nano-
+constrictions, which indicates spin waves emission out of
+the nano-constriction regions. Thus, there are relatively
+substantial energy losses for the low number of oscilla-
+
+3
+1 NC
+2 NC
+5 NC
+10 NC
+15 NC
+21 NC
+H = 0.8 T, θ=80o 
+, φ = 20o
+W/NiFe
+0
+14
+0
+16
+0
+19
+0
+20
+0
+20
+0
+20
+(g)
+(h)
+(i)
+(j)
+(k)
+(l)
+5 NC
+(c)
+10 NC
+(d)
+2 NC
+15 NC
+21 NC
+0
+9
+0
+10
+0
+12
+0
+15
+0
+14
+0
+15
+1 NC
+(a)
+(b)
+(e)
+(f)
+W/CoFeB/MgO
+H = 0.8 T,  θ=65o 
+, φ = 20o
+FIG. 3.
+Power spectral density (PSD) of the microwave signal generated by a single nano-constriction and up to 21 mutually
+synchronized nano-constriction SHNOs for (a-f) W/CoFeB/MgO and (g-l) W/NiFe, respectively.
+tors by a spin wave emission, which limits the nonlinear
+frequency shift. Meanwhile, for the larger N the emitted
+waves contribute energy to the neighboring oscillators,
+increasing the non-linearity. The increased non-linearity
+is, at higher currents, accompanied by a change from a
+concave to a convex current dependence.
+All chains show complete synchronization towards
+higher currents. The maximum peak power (indicated
+by the dB over noise scale) also increases with N. At
+lower currents, partial synchronization into primarily two
+separate signals can be clearly observed. It is notewor-
+thy that the fully synchronized state coincides roughly
+with the change in curvature. As the change in curva-
+ture is only observed in chains and becomes more pro-
+nounced for larger N, this suggests that, at higher cur-
+rents, the auto-oscillation mode changes character due to
+the chain geometry. The robust mutual synchronization
+is governed by a combination of dipolar and spin wave-
+mediated coupling. The role of propagating spin waves
+and their comparison to dipolar coupling was first studied
+theoretically in nano-contact STNOs [29], where analyti-
+cal calculations suggested a dominant role of propagating
+spin waves at separations larger than 100 nm. Spin wave
+beams were also responsible for robust synchronization
+of up to five nano-contact STNOs [13]. Similar to nano-
+contact STNOs, nano-constriction SHNOs share a com-
+mon ferromagnetic layer, which suggests that the same
+arguments should apply.
+Following Ref. [29], the spin
+wave coupling strength should then be about twice that
+of dipolar coupling at a 200 nm separation.
+C.
+Analysis of linewidth and output power
+The microwave signal is fitted with a single Lorentzian
+function to extract the power and linewidth.
+Fig-
+ure 4 summarizes and compares the linewidth and
+peak power of 21 mutually synchronized oscillators for
+W/CoFeB/MgO and W/NiFe thin films, respectively;
+results for NiFe/Pt thin films are shown in the supple-
+
+10.8
+10.7
+10.6
+工
+GI
+10.5
+10.4
+10.3
+1.2
+1.4
+1.6
+1.8
+2
+(mA)10.8
+10.7
+N
+10.6
+10.5
+10.4
+10.3
+1.2
+1.4
+1.6
+1.8
+2
+(mA)19
+18.5
+(ZHD),
+18
+17.5
+17
+0.4
+0.6
+0.8
+(mA)19
+18.5
+(ZH))
+18
+17.5
+17
+0.4
+0.6
+0.8
+(mA)19
+18.5
+D
+18
+17.5
+17
+0.4
+0.6
+0.8
+(mA)19
+18.5
+(ZHD)
+18
+17.5
+17
+0.4
+0.6
+0.8
+(vw)19
+18.5
+(ZHO) J
+18
+17.5
+17
+0.4
+0.6
+0.8
+IDc (mA)19
+18.5
+ZHD)
+18
+17.5
+17
+0.4
+0.6
+0.8
+IDc (mA)10.8
+10.7
+10.6
+GH
+10.5
+10.4
+10.3
+1.2
+1.4
+1.6
+1.8
+2
+(mA)10.8
+10.7
+10.6
+10.5
+10.4
+10.3
+1.2
+1.4
+1.6
+1.8
+2
+(mA)10.8
+10.7
+10.6
+10.5
+10.4
+10.3
+1.2
+1.4
+1.6
+1.8
+2
+(mA)
+110.8
+10.7
+(ZHD)
+10.6
+10.5
+10.4
+10.3
+1.2
+1.4
+1.6
+1.8
+2
+DC
+(mA)4
+1.7
+1.8
+1.9
+2
+0.1
+1
+10
+Linewidth (MHz)
+IDC (mA)
+Df < 134 KHz
+Q > 79000
+H =0.8 T
+q = 80o, j = 20o
+W/NiFe
+(c)
+I
+II
+III
+1.7
+1.8
+1.9
+2
+0
+1k
+2k
+3k
+4k
+5k
+Peak Power (nV2/Hz)
+IDC (mA)
+(d)
+I
+II
+III
+0.45
+0.5
+0.55
+0.6
+0.1
+1
+10
+W/CoFeB/MgO
+Linewidth (MHz)
+IDC (mA)
+Df < 440 KHz
+Q > 41000
+H = 0.80 T
+q = 65o, j = 20o 
+(a)
+I
+II
+III
+0.45
+0.5
+0.55
+0.6
+0
+1k
+2k
+3k
+4k
+5k
+Peak Power (nV2/Hz)
+IDC (mA)
+(b)
+I
+II
+III
+FIG. 4.
+(a) and (b) Linewidth vs.
+IDC and peak power vs.
+IDC for 21 mutually synchronized W/CoFeB/MgO SHNOs. (c)
+and (d) Linewidth vs.
+IDC and peak power vs.
+IDC for 21 mutually synchronized W/NiFe SHNOs. The dashed blue line
+represents a complete mutual synchronization of 21 oscillators. The three color-coded regions represent the un-synchronized
+state (Blue), robustly synchronized state (Olive) and high current unstable synchronized state (pink).
+mentary.
+We observe the lowest linewidth of 134 kHz
+in the synchronized state of the W/NiFe based oscillator
+[Fig. 4(c)], with a peak power just above 4000 nV2/Hz
+[Fig. 4(d)]. The lowest linewidth of the W/CoFeB/MgO
+chain is 440 kHz [see Fig. 4(c)], also with peak power
+just above 4000 nV2/Hz [Fig. 4(d)]. For NiFe/Pt based
+SHNOs, we observe the lowest linewidth of 275 kHz with
+enormous peak power of 40,000 nV2/Hz (see supplemen-
+tary file).
+However, once this highest-quality signal is achieved,
+increasing the current further deteriorates the signal
+quality to intermediate values. This deterioration does
+not seem to be related to a loss of mutual synchroniza-
+tion as we only observe a single signal in all devices in
+this current range. Instead, this behavior coincides with
+the change in curvature described above, indicating that
+it could be due to a change in the auto-oscillating mode
+character.
+We hence define three different regions: I)
+incomplete partial synchronization with relatively poor
+signal quality, II) complete mutual synchronization with
+the best signal quality, and III) a possible different auto-
+oscillating regime with intermediate signal quality.
+Figure 5(a) and (b) shows the variation of linewidth
+and peak power with the number of oscillators for both
+the W/CoFeB/MgO and W/NiFe system. We observe a
+1/N dependence for the spectral linewidth, in agreement
+with the oscillator synchronization theory and depicts the
+enhancement of total mode volume. The peak power is
+found to follow a quadratic (N 2) dependence, also con-
+sistent with the nonlinear oscillator theory.
+D.
+Benchmarking the Quality Factor
+The combination of high auto-oscillation frequencies
+and low linewidths leads to very high quality factors
+(Q = f/∆f) for the synchronized chains. Figure 5(c)
+shows Q vs. N for both the W/CoFeB/MgO and W/NiFe
+systems. We observe Q > 79,000 for 21 mutually syn-
+chronized SHNOs in W/NiFe thin films, which is the
+highest quality factor reported for oscillators in a single
+chain (which also results in higher output power). This
+is comparable to the earlier observed Q of 170,000 in
+two-dimensional NiFe/Pt arrays of 8×8 oscillators. For
+
+5
+0
+0.2
+0.4
+0.6
+0.8
+1
+0
+2
+4
+6
+8
+Linewidth (MHz)
+1/N
+ W/CoFeB/MgO
+ W/NiFe
+(a)
+0
+100
+200
+300
+400
+0
+1k
+2k
+3k
+4k
+5k
+Peak Power (nV2/Hz)
+N2
+(b)
+0
+5
+10
+15
+20
+0
+25k
+50k
+75k
+100k
+Q-factor
+N
+Df = 134 KHz
+Q > 79000
+(c)
+FIG. 5.
+(a) Linewidth vs. inverse of number of nano-
+constrictions (1/N) in a chain of SHNOs for W/CoFeB/MgO
+and W/NiFe based oscillators.
+(b) Peak power vs. square
+of number of oscillators (N 2) for W/CoFeB/MgO and
+W/NiFe based oscillators, respectively.
+(C) Q−factor of
+SHNOs with number of oscillators (N), Black squares are for
+W/CoFeB/MgO and green circles represents W/NiFe. The
+red solid line represents linear fit.
+the W/CoFeB/MgO oscillators, we found a Q of 41,000,
+which is again the highest of any spintronic oscillator
+chains operating at frequencies higher than 15 GHz. For
+comparison with mutually synchronized oscillators based
+on magnetic tunnel junctions, recent demonstrations [6]
+of 8 mutually synchronized MTJs resulted in a Q−factor
+of 7400.
+It is interesting to compare Q−factor (and output
+power) more extensively with the literature. In Fig. 6,
+we show results from a large number of previous works,
+expressed as Q−factor vs. output power, for both single
+(hollow symbols) and synchronized (solid symbols) oscil-
+lators. Both here and further on we use the abbrevia-
+tions ’SHNOs’: spin Hall nano-oscillators (shown with
+triangles), ’MTJs’:
+nano-pillar magnetic tunnel junc-
+tions which include vortex oscillators (shown with cir-
+cular symbols), and ’Nano Contacts’: nano-contact spin
+valve structures (shown with rhombus). One can observe
+that the vortex oscillators [37–41] deliver the largest out-
+put power (most lie on the right side of the graph). How-
+ever, vortex oscillators mostly operate at much lower RF
+frequencies (0.1 GHz to 1.5 GHz) and hence result in
+lower quality factors. Other MTJs and nano-contact de-
+vices have larger frequency tunability but have lower out-
+put power and/or higher operational linewidth resulting
+in poor performance as signal generator. The synchro-
+nized MTJs have shown good results and are even em-
+ployed for power harvesting. Though they also end up
+with large linewidth and hence low Q−factor. The best
+Q−factor found for nano-contact spin valve was about
+18000 [42], which resulted in poor output power. The
+recently introduced SHNOs have already shown great
+promise with their narrow linewidth and high frequency
+operation, even a single oscillator results Q−factor in the
+range of 2000-4000 [20, 24, 47], though their output power
+is extremely low. In our previous work with 2D arrays
+of 64 oscillators, we observed an enormous Q−factor of
+179,000, though in a white noise regime (measured at
+short time scales).
+In the present work, we have im-
+proved our output power and can reach upto 200 pW with
+sustaining a high Q−factor of >79000 (for W/NiFe thin
+films). The NiFe/Pt system shows even higher output
+power of 300 pW with Q > 32,000. Further improvements
+in extending synchronization to rectangular arrays and
+fabricating tunneling magneto-resistance based readouts
+will bring these oscillators among the best-performing
+spintronic oscillators with large output power and high
+Q−factor.
+E.
+Synchronization beyond 21 SHNOs
+To investigate synchronization beyond 21 SHNOs, we
+fabricated 30, 40, and 50 nano-constrictions in series. It
+is noteworthy that we do observe single-frequency mi-
+crowave signal generation also in these much longer oscil-
+lator chains. However, no further linewidth reduction nor
+any further increase in the output power were observed.
+This could be due to an increasing out-of phase synchro-
+nization of SHNOs in the longer chains, as illustrated by
+the spins in Figure 1, if there is a small relative phase
+shift between individual nearest neighbor SHNOs that
+does not affect shorter chains but build up to a reduced
+total output power in the longer chains. Figure 7 shows
+the PSD for 30, 40 and 50 nano-constrictions in chain for
+W/CoFeB/MgO thin films. For 30 nano-constrictions in
+
+6
+: SHNOs
+: MTJs
+: Nano Contacts
+10−12
+10−11
+10−10
+10−9
+10−8
+10−7
+10−6
+10−5
+10−4
+102
+103
+104
+105
+27
+26
+39
+40
+41
+34
+35
+36
+33
+28
+37
+29
+30
+12
+38
+11
+6
+42
+42
+19
+31
+32
+13
+23
+21 *9 SHNOs chain
+22 *8x8 array
+This work
+This work
+This Work
+Q-factor
+Power (W)
+(W/NiFe)
+(W/CoFeB/MgO)
+(NiFe/Pt)
+FIG. 6.
+Bench-marking of spintronic oscillators: Q−factor vs. integrated output power of various spintronic oscillators
+and their synchronized systems (shown with filled symbols). The data comprise the best performance nano-pillar MTJs [6, 11,
+14, 30–36], vortex MTJs [37–41], Nano-contact spin valves [13, 42–45] and SHNOs [20, 22–24, 46].
+a chain [Fig. 7(a)], we found the lowest linewidth of 800
+kHz and a peak power of less than 400 nV2/Hz, which
+is one order of magnitude less than the robustly syn-
+chronized 21 SHNOs as shown in Fig. 5.
+Figure 7(b)
+shows the transition of partially synchronized microwave
+emissions into single synchronized mode at different IDC.
+However, as observed in the Fig. 7(b) the spectrum at
+450 µA and 490 µA (partially synchronized states) show
+lower linewidth and higher amplitude than fully synchro-
+nized states at 540 µA, 640 µA and 730 µA current. This
+clearly shows that the partial synchronization of oscilla-
+tors results in better spectral parameters than the full
+synchronization of oscillator chains with more than 30
+nano-constrictions.
+In other words, the longer chains
+may very well synchronize completely but be better de-
+scribed as weaker synchronization of partially synchro-
+nized sub-sections. This lack of robust synchronization
+for more than 21 nano-constrictions may arise from sta-
+tistical effects in a larger ensemble, or be due to larger
+Joule heating in longer chains, and/or result from the in-
+crease of an accumulative phase difference in the chains.
+Figure 7(c) and (d) show similar results for 40 and 50
+nano-constrictions in a chain, respectively. Though full
+synchronization in longer chains of more than 21 nano-
+constrictions is not very robust, it still shows a clear in-
+teraction between oscillators (either in-phase or out-of
+phase), which can be very useful for neuromorphic com-
+puting using a large number of spins (nano-constrictions).
+F.
+Perspective: Applications and Outlook
+We have successfully demonstrated the robust mutual
+synchronization of large number of SHNOs in a single
+chain.
+This observation leads to various applications
+that can be realized using these oscillators. The lower
+linewidth and the significantly larger output power en-
+able these oscillators for coherent frequency signal gen-
+eration applications, as well as for wireless communi-
+cations. Using the phase locked loop method, the mi-
+crowave oscillations in chains can be further stabilized,
+generating coherent oscillations that can be directly im-
+plemented in many microwave applications [48].
+The
+mutual synchronization of these oscillators in a chain
+can be explored for bio-inspired computing and be-
+yond [9, 23, 49] where each oscillator behaves as a neu-
+ron. Combined with voltage [26, 27, 50] and/or memris-
+tive [25] control of synchronization (synaptic weights),
+these large chains can be used to locally or globally
+control the coupling between oscillators (neurons). The
+present work also serves as a stepping stone in the direc-
+tion towards further scaling mutual synchronization to
+much larger square or rectangular arrays well beyond the
+previously demonstrated 64 oscillators. As these oscilla-
+tor arrays can be fabricated in a tiny area, it enables the
+possibility to scale/miniaturize the neuromorphic net-
+works based on these oscillators.
+The large frequency
+tunability with current also makes these oscillators ideal
+for ultrafast sweeping spectrum analysis, where neither
+
+7
+30 NC
+40 NC
+50 NC
+(a)
+(c)
+(d)
+0
+9
+0
+10
+0
+6
+30 NC
+(b)
+FIG. 7.
+(a) Power spectral density for synchronized 30 NC SHNOs in a chain. (b) The microwave spectrum for synchronized 30
+nano-constrictions in a chain for few current values (IDC) marked with arrows in Fig. (a). Power spectral density for mutually
+synchronized (c) 40 nano-constrictions and (d) 50 nano-constrictions SHNO in a chain for W/CoFeB/MgO thin films.
+vortex oscillators nor uniform MTJs can so far offer a
+wide resolution bandwidth [7, 8]. With recent demon-
+stration of energy-efficient spin Hall materials [51] and
+the reduction of constrictions size [21, 52], the required
+threshold current can be significantly reduced, operating
+these devices with ultra-low power.
+III.
+CONCLUSION
+In summary, we show that robust in-phase mutual syn-
+chronization of nano-constriction based SHNOs can be
+achieved in very long chains. The long-range synchro-
+nization not only shows an enhanced output power but
+also an improved linewidth of as low as 130 kHz for
+W/NiFe based heterostructures.
+The low current and
+low field operation of these oscillators along with their
+large frequency tunability, with both current and mag-
+netic field, make them ideal for various spintronic appli-
+cations such as neuromorphic computing. In the longest
+chains, mutual synchronization is less effective in im-
+proving the microwave signal properties with evidence
+of partial and/or increasingly out-of-phase synchroniza-
+tion. These results not only enhance our understanding
+of the mutual synchronization of these oscillators but also
+paves the way towards making larger networks of these
+oscillators for neuromorphic computing applications.
+METHODS
+Sample fabrication: We utilize the well studied W(5
+nm)/CoFeB(1.4 nm)/MgO (2 nm) and W(5 nm)/NiFe(3
+nm) heterostructures for the fabrication of microwave
+nano-constriction SHNOs used in the experiments. The
+NM/FM structures were deposited using magnetron
+sputtering on a high resistance intrinsic Si substrate (ρ >
+10,000 µohm-cm) at room temperature.
+The sample
+stacks were capped with 4 nm Al3O3 thin films.
+The
+growth of thin films was carried out using AJA Orion 8
+sputtering system with a base pressure of 3×10−8 Torr.
+The samples were then coated with 40 nm of hydrogen
+silsesquioxane (HSQ) negative tone electron beam resist.
+The SHNO chains used in the experiments were then fab-
+ricated using a combination of e-beam lithography (Raith
+EBPG 5200) and Ar-ion etching: more details can be
+
+B/roise
+6
+-Dc (HA)
+3
+108
+found here [26]. The top contact pads are fabricated us-
+ing laser writer based direct lithography followed by de-
+position of Cu(800 nm)/Pt(20 nm) thin films for Ground-
+Signal-Ground co-planar waveguide. In this experiment,
+we utilize the SHNOs with 150 nm nano-constriction
+width and 200 nm separation between SHNOs in a chain.
+Experimental Set-up: All the measurements were
+performed at room temperature. The microwave mea-
+surements were performed using a custom-built probe
+station utilizing GSG probes manufactured by GGB In-
+dustries. Figure 2(c) shows the schematic representation
+of the measurement setup. All measurements are carried
+out at a fixed IP angle and an OOP rotatable sample
+stage between the electromagnet poles at room tempera-
+ture. Different OOP angles are used to generate positive
+non-linearity in the system. To excite microwave emis-
+sion, a positive DC current IDC was applied to the de-
+vices through the inductive port of a bias-tee, while the
+microwave signal was detected using high frequency port.
+The resulting power spectral density (PSD) of the auto-
+oscillating signal (after amplification using low-noise am-
+plifier) is captured using Rohde and Schwarz (10 Hz– 40
+GHz) spectrum analyzer. To calculate the PSD spectrum
+shown in Figure 3 and 7, we have taken into account the
+impedance mismatch and the losses from the RF compo-
+nent and corrected to the low noise amplifier gain.
+ACKNOWLEDGMENTS
+This work was partially supported by the Horizon 2020
+research and innovation program (ERC Advanced Grant
+No. 835068 “TOPSPIN”). This work was also partially
+supported by the Swedish Research Council (VR) and
+the Knut and Alice Wallenberg Foundation.
+[1] J. C. Slonczewski, J. Magn. Magn. Mater. 159, L1
+(1996).
+[2] L. Berger, Phys. Rev. B 54, 9353 (1996).
+[3] M. Tsoi, A. Jansen, J. Bass, W.-C. Chiang, V. Tsoi, and
+P. Wyder, Nature 406, 46 (2000).
+[4] S. I. Kiselev,
+J. Sankey,
+I. Krivorotov,
+N. Emley,
+R. Schoelkopf, R. Buhrman, and D. Ralph, Nature 425,
+380 (2003).
+[5] T. Chen, R. K. Dumas, A. Eklund, P. K. Muduli,
+A. Houshang, A. A. Awad, P. Durrenfeld, B. G. Malm,
+A. Rusu, and J. ˚Akerman, Proc. IEEE 104, 1919 (2016).
+[6] S. Tsunegi, T. Taniguchi, R. Lebrun, K. Yakushiji,
+V. Cros, J. Grollier, A. Fukushima, S. Yuasa,
+and
+H. Kubota, Sci. Rep. 8, 1 (2018).
+[7] A. Litvinenko, V. Iurchuk, P. Sethi, S. Louis, V. Ty-
+berkevych, J. Li, A. Jenkins, R. Ferreira, B. Dieny,
+A. Slavin, et al., Nano Lett. 20, 6104 (2020).
+[8] A. Litvinenko, A. Sidi El Valli, V. Iurchuk, S. Louis,
+V. Tyberkevych, B. Dieny, A. N. Slavin, and U. Ebels,
+Nano Lett. 22, 1874 (2022).
+[9] J. Torrejon, M. Riou, F. Abreu Araujo, S. Tsunegi,
+G.
+Khalsa,
+D.
+Querlioz,
+P.
+Bortolotti,
+V.
+Cros,
+A. Fukushima, H. Kubota, S. Yuasa, M. D. Stiles, and
+J. Grollier, Nature 547, 428 (2017).
+[10] M. Romera, P. Talatchian, S. Tsunegi, F. A. Araujo,
+V.
+Cros,
+P.
+Bortolotti,
+J.
+Trastoy,
+K.
+Yakushiji,
+A. Fukushima, H. Kubota, S. Yuasa, M. Ernoult, D. Vo-
+denicarevic, T. Hirtzlin, N. Locatelli, D. Querlioz, , and
+J. Grollier, Nature 563, 230 (2018).
+[11] R. Sharma, R. Mishra, T. Ngo, Y.-X. Guo, S. Fukami,
+H. Sato, H. Ohno,
+and H. Yang, Nat. Commun. 12, 1
+(2021).
+[12] S. Erokhin and D. Berkov, Phys. Rev. B 89, 144421
+(2014).
+[13] A. Houshang, E. Iacocca, P. D¨urrenfeld, S. R. Sani,
+J. ˚Akerman,
+and R. K. Dumas, Nat. Nano. 11, 280
+(2016).
+[14] R. Lebrun, S. Tsunegi, P. Bortolotti, H. Kubota, A. Jenk-
+ins, M. Romera, K. Yakushiji, A. Fukushima, J. Grollier,
+S. Yuasa, et al., Nat. Commun. 8, 1 (2017).
+[15] Y. Tserkovnyak, A. Brataas, and G. E. W. Bauer, Phys.
+Rev. Lett. 88, 117601 (2002).
+[16] J. E. Hirsch, Phys. Rev. Lett. 83, 1834 (1999).
+[17] J. Sinova, S. O. Valenzuela, J. Wunderlich, C. H. Back,
+and T. Jungwirth, Rev. Mod. Phys. 87, 1213 (2015).
+[18] V. E. Demidov, S. Urazhdin, H. Ulrichs, V. Tiberkevich,
+A. Slavin, D. Baither, G. Schmitz, and S. O. Demokritov,
+Nat. Mater. 11, 1028 (2012).
+[19] V. Demidov, S. Urazhdin, A. Zholud, A. Sadovnikov,
+and S. Demokritov, Appl. Phys. Lett. 105, 172410
+(2014).
+[20] Z. Duan, A. Smith, L. Yang, B. Youngblood, J. Lindner,
+V. E. Demidov, S. O. Demokritov, and I. N. Krivorotov,
+Nat. Commun. 5, 1 (2014).
+[21] P. D¨urrenfeld, A. a. Awad, A. Houshang, R. K. Dumas,
+and J. ˚Akerman, Nanoscale 9, 1285 (2017).
+[22] A. A. Awad, P. D¨urrenfeld, A. Houshang, M. Dvornik,
+E. Iacocca, R. K. Dumas, and J. ˚Akerman, Nat. Phys.
+13, 292 (2016).
+[23] M. Zahedinejad, A. A. Awad, S. Muralidhar, R. Khymyn,
+H. Fulara, H. Mazraati, M. Dvornik,
+and J. ˚Akerman,
+Nat. Nano. 15, 47 (2020).
+[24] H. Fulara, M. Zahedinejad, R. Khymyn, A. Awad, S. Mu-
+ralidhar, M. Dvornik,
+and J. ˚Akerman, Sci. Adv. 5,
+eaax8467 (2019).
+[25] M. Zahedinejad, H. Fulara, R. Khymyn, A. Houshang,
+M. Dvornik, S. Fukami, S. Kanai, H. Ohno,
+and
+J. ˚Akerman, Nat. Mater. 21, 81 (2022).
+[26] A. Kumar, M. Rajabali, V. H. Gonz´alez, M. Zahedine-
+jad, A. Houshang, and J. ˚Akerman, Nanoscale 14, 1432
+(2022).
+[27] H. Fulara, M. Zahedinejad, R. Khymyn, M. Dvornik,
+S. Fukami, S. Kanai, H. Ohno,
+and J. ˚Akerman, Nat.
+Commun. 11, 1 (2020).
+[28] H. Mazraati, S. Chung, A. Houshang, M. Dvornik, L. Pi-
+azza, F. Qejvanaj, S. Jiang, T. Q. Le, J. Weissenrieder,
+and J. ˚Akerman, Appl. Phys. Lett. 109, 242402 (2016).
+[29] A. Slavin and V. Tiberkevich, IEEE Trans. Magn. 45,
+1875 (2009).
+[30] D. Houssameddine, S. Florez, J. Katine, J.-P. Michel,
+
+9
+U. Ebels, D. Mauri, O. Ozatay, B. Delaet, B. Viala,
+L. Folks, B. D. Terris,
+and M.-C. Cyrille, Appl. Phys.
+Lett. 93, 022505 (2008).
+[31] H. Kubota, K. Yakushiji, A. Fukushima, S. Tamaru,
+M. Konoto, T. Nozaki, S. Ishibashi, T. Saruya, S. Yuasa,
+T. Taniguchi, H. Arai,
+and H. Imamura, Appl. Phys.
+Exp. 6, 103003 (2013).
+[32] Z. Zeng, P. K. Amiri, I. N. Krivorotov, H. Zhao, G. Finoc-
+chio, J.-P. Wang, J. A. Katine, Y. Huai, J. Langer,
+K. Galatsis, K. L. Wang,
+and H. Jiang, ACS Nano 6,
+6115 (2012).
+[33] A. M. Deac, A. Fukushima, H. Kubota, H. Maehara,
+Y. Suzuki, S. Yuasa, Y. Nagamine, K. Tsunekawa, D. D.
+Djayaprawira,
+and N. Watanabe, Nat. Phys. 4, 803
+(2008).
+[34] Z. Zeng, P. Upadhyaya, P. Khalili Amiri, K. Cheung,
+J. Katine, J. Langer, K. Wang,
+and H. Jiang, Appl.
+Phys. Lett. 99, 032503 (2011).
+[35] J. D. Costa, S. Serrano-Guisan, B. Lacoste, A. S. Jenkins,
+T. B¨ohnert, M. Tarequzzaman, J. Borme, F. L. Deepak,
+E. Paz, J. Ventura, R. Ferreira,
+and P. P. Freitas, Sci.
+Rep. 7, 1 (2017).
+[36] T. Seki, Y. Sakuraba, H. Arai, M. Ueda, R. Okura,
+H. Imamura, and K. Takanashi, Appl. Phys. Lett. 105,
+092406 (2014).
+[37] V. Pribiag,
+I. Krivorotov,
+G. Fuchs,
+P. Braganca,
+O. Ozatay, J. Sankey, D. Ralph, and R. Buhrman, Nat.
+Phys. 3, 498 (2007).
+[38] S. Tsunegi,
+H. Kubota,
+K. Yakushiji,
+M. Konoto,
+S. Tamaru,
+A. Fukushima,
+H. Arai,
+H. Imamura,
+E. Grimaldi, R. Lebrun, J. Grollier, V. Cros,
+and
+S. Yuasa, Appl. Phys. Exp. 7, 063009 (2014).
+[39] S. Tsunegi, K. Yakushiji, A. Fukushima, S. Yuasa, and
+H. Kubota, Appl. Phys. Lett. 109, 252402 (2016).
+[40] A. Dussaux, E. Grimaldi, B. Rache Salles, A. S. Jenkins,
+A. V. Khvalkovskiy, P. Bortolotti, J. Grollier, H. Kubota,
+A. Fukushima, K. Yakushiji, S. Yuasa, V. Cros,
+and
+A. Fert, Appl. Phys. Lett. 105, 022404 (2014).
+[41] A. Dussaux, B. Georges, J. Grollier, V. Cros, A. V.
+Khvalkovskiy, A. Fukushima, M. Konoto, H. Kubota,
+K. Yakushiji, S. Yuasa, K. A. Zvezdin, K. Ando,
+and
+A. Fert, Nat. Commun. 1, 1 (2010).
+[42] W. H. Rippard, M. R. Pufall, S. Kaka, T. J. Silva, and
+S. E. Russek, Phys. Rev. B 70, 100406 (2004).
+[43] H.
+Maehara,
+H.
+Kubota,
+Y.
+Suzuki,
+T.
+Seki,
+K.
+Nishimura,
+Y.
+Nagamine,
+K.
+Tsunekawa,
+A. Fukushima, A. M. Deac, K. Ando,
+and S. Yuasa,
+Appl. Phys. Exp. 6, 113005 (2013).
+[44] H.
+Maehara,
+H.
+Kubota,
+Y.
+Suzuki,
+T.
+Seki,
+K.
+Nishimura,
+Y.
+Nagamine,
+K.
+Tsunekawa,
+A. Fukushima, H. Arai, T. Taniguchi, H. Imamura,
+K. Ando,
+and S. Yuasa, Appl. Phys. Exp. 7, 023003
+(2014).
+[45] S. Sani, J. Persson, S. M. Mohseni, Y. Pogoryelov,
+P. Muduli, A. Eklund, G. Malm, M. K¨all, A. Dmitriev,
+and J. ˚Akerman, Nat. Commun. 4, 1 (2013).
+[46] J.-R. Chen, A. Smith, E. A. Montoya, J. G. Lu,
+and
+I. N. Krivorotov, Commun. Phys. 3, 1 (2020).
+[47] M. Zahedinejad, H. Mazraati, H. Fulara, J. Yue, S. Jiang,
+A. Awad,
+and J. ˚Akerman, Appl. Phys. Lett. 112,
+132404 (2018).
+[48] S. Tamaru, H. Kubota, K. Yakushiji, S. Yuasa,
+and
+A. Fukushima, Sci. Rep. 5, 1 (2015).
+[49] A.
+Houshang,
+M.
+Zahedinejad,
+S.
+Muralidhar,
+J. Ch¸eci´nski, R. Khymyn, M. Rajabali, H. Fulara,
+A. A. Awad, M. Dvornik, and J. ˚Akerman, Phys. Rev.
+Appl. 17, 014003 (2022).
+[50] J.-G. Choi, J. Park, M.-G. Kang, D. Kim, J.-S. Rieh, K.-
+J. Lee, K.-J. Kim, and B.-G. Park, Nat. Commun. 13,
+3783 (2022).
+[51] N. Behera, H. Fulara, L. Bainsla, A. Kumar, M. Za-
+hedinejad, A. Houshang,
+and J. ˚Akerman, Phys. Rev.
+Appl. 18, 024017 (2022).
+[52] A. A. Awad, A. Houshang, M. Zahedinejad, R. Khymyn,
+and J. ˚Akerman, Appl. Phys. Lett. 116, 232401 (2020).
+
diff --git a/YdE2T4oBgHgl3EQfZAcJ/content/tmp_files/load_file.txt b/YdE2T4oBgHgl3EQfZAcJ/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..aec78f502f3a460d2b847381c4e1fea7a4bead97
--- /dev/null
+++ b/YdE2T4oBgHgl3EQfZAcJ/content/tmp_files/load_file.txt
@@ -0,0 +1,966 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf,len=965
+page_content='Robust mutual synchronization in long spin Hall nano-oscillator chains  Akash Kumar,1, ∗ Himanshu Fulara,2 Roman Khymyn,1 Mohammad Zahedinejad,3 Mona Rajabali,3  Xiaotian Zhao,1 Nilamani Behera,1 Afshin Houshang,1 Ahmad A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Awad,1 and Johan ˚Akerman1, †  1Physics Department, University of Gothenburg, 412 96 Gothenburg, Sweden.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  2Department of Physics, Indian Institute of Technology Roorkee, Roorkee 247667, India  3NanOsc AB, Kista, Sweden.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  (Dated: January 11, 2023)  Mutual synchronization of N serially connected spintronic nano-oscillators increases their coher-  ence by a factor N and their output power by N 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Increasing the number of mutually synchronized  nano-oscillators in chains is hence of great importance for better signal quality and also for emerging  applications such as oscillator-based neuromorphic computing and Ising machines where larger N  can tackle larger problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Here we fabricate spin Hall nano-oscillator chains of up to 50 serially  connected nano-constrictions in W/NiFe, W/CoFeB/MgO, and NiFe/Pt stacks and demonstrate  robust and complete mutual synchronization of up to 21 nano-constrictions, reaching linewidths of  below 200 kHz and quality factors beyond 79,000, while operating at 10 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' We also find a square  increase in the peak power with the increasing number of mutually synchronized oscillators, result-  ing in a factor of 400 higher peak power in long chains compared to individual nano-constrictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Although chains longer than 21 nano-constrictions also show complete mutual synchronization, it  is not as robust and their signal quality does not improve as much as they prefer to break up into  partially synchronized states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' The low current and low field operation of these oscillators along with  their wide frequency tunability (2-28 GHz) with both current and magnetic fields, make them ideal  candidates for on-chip GHz-range applications and neuromorphic computing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  INTRODUCTION  Since the advent of spin transfer torque driven mag-  netization precession in metallic spin valves [1–4], the  interest in spintronic microwave oscillators has steadily  increased [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Mutual synchronization of these non-linear  microwave oscillators is of utmost importance for various  applications such as efficient ultra-broadband signal gen-  erators [6], wireless communication, ultra-fast microwave  spectral analysis [7, 8] and recently developed interest  in neuromorphic computing among others [9, 10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' More-  over, researchers have recently demonstrated energy har-  vesting from wireless signals using synchronized oscil-  lators in series [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  There have been many attempts  to synchronize these oscillators over short and long  ranges [6, 10, 12–14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' However, the complex fabrication  process of spin torque nano-oscillators (STNOs) raises a  technological issue to scale their synchronization for high  frequency applications and hence the progress of synchro-  nizing many STNOs has been rather slow [6, 11, 14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Thanks to the spin Hall effect [15–17], a new class of  spintronic oscillators, known as spin Hall nano-oscillators  (SHNOs), has emerged [18–21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Compared to STNOs,  they rely on the current flowing in-plane, which makes  their fabrication easier and allows for a much larger  number of SHNOs to synchronize.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' In particular, nano-  constriction based SHNOs [18, 19] can be easily fabri-  cated into 1D chains [22] and 2D arrays [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Earlier  work has shown that up to nine SHNOs, separated by  300 nm, can be mutually synchronized to generate both  ∗ akash.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='kumar@physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='gu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='se  † johan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='akerman@physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='gu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='se  θ  φ  H  x  y  z  500 nm  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Schematic representation of 21 nano-constriction  SHNOs in a chain fabricated from a non-magnet/ferromagnet  bilayer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Blue arrows with yellow spheres represent the local  magnetization and its magneto-dynamical precession in each  nano-constriction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' The charge current is applied in-plane and  the magnetic field at an oblique angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  The inset shows a  scanning electron microscope image of an actual SHNO chain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  higher output power and a narrower linewidth [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Sim-  ilarly, 2D arrays of up to 8×8 oscillators [23] were found  to synchronize completely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' The number of synchronized  oscillators along a dimension is hence limited to single  digits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='03859v1  [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='mes-hall]  10 Jan 2023  Non-magnet2  0  5  10  15  20  0  1  2  3  4  5  6  Resistance (kW)  N  W/CoFeB/MgO  W/NiFe  264 W  105 W  Spectrum Analyzer  LNA  IDC  f  Bias-T  SHNO  (a)  (b)  P  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  (a) Resistance of the SHNO chains vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' number of nano-constrictions (N ), showing the expected linear dependence,  with each W/NiFe and W/CoFeB/MgO nano-constriction adding 105 Ω and 264 Ω, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' The inset shows an SEM  image of the Ground-Signal-Ground pads connecting to the SHNO chain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' (b) Schematic representation of the auto-oscillation  measurement set-up.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' The drive current is provided via a bias-T, which also picks up the generated microwave voltage and feeds  it to a low-noise amplifier before being recorded by a spectrum analyzer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  In this work, we study mutual synchronization in  much longer SHNO chains of up to 50 serially connected  nano-constrictions fabricated from W(5 mm)/CoFeB(1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='4  nm)/MgO(2 nm) [24–27], W(5 nm)/NiFe(3 nm) [28], and  NiFe(5 nm)/Pt(5 nm) [22, 23] material stacks (the order  represents the actual stack sequence), focusing primarily  on the W based SHNOs with their much lower threshold  current.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' We find that robust and complete mutual syn-  chronization can persist in chains of up to 21 oscillators,  resulting in a significantly lower linewidth and higher out-  put power compared to single SHNOs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' We also observe  mutual synchronization in the longer chains but with de-  teriorated parameters, which we find to originate from a  tendency for the longer chains to separate into shorter  mutually synchronized sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  RESULTS AND DISCUSSION  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  SHNO chains and measurement set-up  Figure 1 shows the layout for a chain of nano-  constriction SHNOs made from a non-magnet (NM) –  ferromagnet (FM) bilayer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' The inset shows a scanning  electron micrograph of an actual SHNO chain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' A charge  current flows in the film plane and a magnetic field is  applied at an oblique OOP angle, θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' The spin Hall ef-  fect of the NM layer converts the charge current into a  transverse spin current exerting an anti-damping torque  on the FM layer, which above a certain threshold cur-  rent can generate auto-oscillations of the local magneti-  zation in each nano-constriction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' In this work, we ex-  plore 150 nm wide nano-constrictions separated by 200  nm center-to-center separation and chain lengths of up to  50 nano-constrictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' We primarily study and compare  chains made from W/CoFeB/MgO and W/NiFe material  stacks, where W was chosen for its very large spin-Hall  angle (θSH = -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='44, for details see supplementary file)  and the FM layers for their low damping of αCoF eB =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='025 and αNiF e = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='032.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' We also compare our results  with 21 synchronized nano-constrictions in the widely  studied NiFe/Pt [22, 23] system (shown in the supple-  mentary file), where a much larger charge current den-  sity is required because of the lower spin Hall angle of Pt  thin films.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Figure 2(a) shows how the resistance of the  SHNO chains increases linearly with the number of nano-  constrictions, each nano-constriction adding 105 ohm and  264 ohm of resistance for W/NiFe and W/CoFeB/MgO,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' A schematic of the measurement set-up is  shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 2(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Further details can be found in the  Methods section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Mutual Synchronization for N = 1–21  Figure 3 shows the power spectral density (PSD) of  auto-oscillation in W/CoFeB/MgO (a-f) and W/NiFe (g-  l) based SHNOs with N = 1–21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' The behavior of chains  with N ≥ 30 will be discussed in a later section below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Both types of SHNOs show a positive non-linearity, at  given applied field magnitude and angles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' As discussed  in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' [24], the perpendicular magnetic anisotropy of the  W/CoFeB/MgO stack increases its non-linearity com-  pared to W/NiFe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' The non-linearity is also substantially  higher for N ≥ 5 than for the single and double nano-  constrictions, which indicates spin waves emission out of  the nano-constriction regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Thus, there are relatively  substantial energy losses for the low number of oscilla-  3  1 NC  2 NC  5 NC  10 NC  15 NC  21 NC  H = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='8 T, θ=80o  , φ = 20o  W/NiFe  0  14  0  16  0  19  0  20  0  20  0  20  (g)  (h)  (i)  (j)  (k)  (l)  5 NC  (c)  10 NC  (d)  2 NC  15 NC  21 NC  0  9  0  10  0  12  0  15  0  14  0  15  1 NC  (a)  (b)  (e)  (f)  W/CoFeB/MgO  H = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='8 T,  θ=65o  , φ = 20o  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Power spectral density (PSD) of the microwave signal generated by a single nano-constriction and up to 21 mutually  synchronized nano-constriction SHNOs for (a-f) W/CoFeB/MgO and (g-l) W/NiFe, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  tors by a spin wave emission, which limits the nonlinear  frequency shift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Meanwhile, for the larger N the emitted  waves contribute energy to the neighboring oscillators,  increasing the non-linearity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' The increased non-linearity  is, at higher currents, accompanied by a change from a  concave to a convex current dependence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  All chains show complete synchronization towards  higher currents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' The maximum peak power (indicated  by the dB over noise scale) also increases with N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' At  lower currents, partial synchronization into primarily two  separate signals can be clearly observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' It is notewor-  thy that the fully synchronized state coincides roughly  with the change in curvature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' As the change in curva-  ture is only observed in chains and becomes more pro-  nounced for larger N, this suggests that, at higher cur-  rents, the auto-oscillation mode changes character due to  the chain geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' The robust mutual synchronization  is governed by a combination of dipolar and spin wave-  mediated coupling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' The role of propagating spin waves  and their comparison to dipolar coupling was first studied  theoretically in nano-contact STNOs [29], where analyti-  cal calculations suggested a dominant role of propagating  spin waves at separations larger than 100 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Spin wave  beams were also responsible for robust synchronization  of up to five nano-contact STNOs [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Similar to nano-  contact STNOs, nano-constriction SHNOs share a com-  mon ferromagnetic layer, which suggests that the same  arguments should apply.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Following Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' [29], the spin  wave coupling strength should then be about twice that  of dipolar coupling at a 200 nm separation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Analysis of linewidth and output power  The microwave signal is fitted with a single Lorentzian  function to extract the power and linewidth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Fig-  ure 4 summarizes and compares the linewidth and  peak power of 21 mutually synchronized oscillators for  W/CoFeB/MgO and W/NiFe thin films, respectively;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  results for NiFe/Pt thin films are shown in the supple-  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='8  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='7  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='6  工  GI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='4  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='8  2  (mA)10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='8  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='7  N  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='6  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='4  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='8  2  (mA)19  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='5  (ZHD),  18  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='5  17  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='8  (mA)19  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='5  (ZH))  18  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='5  17  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='8  (mA)19  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='5  D  18  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='5  17  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='8  (mA)19  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='5  (ZHD)  18  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='5  17  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='8  (vw)19  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='5  (ZHO) J  18  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='5  17  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='8  IDc (mA)19  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='5  ZHD)  18  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='5  17  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='8  IDc (mA)10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='8  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='7  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='6  GH  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='4  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='8  2  (mA)10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='8  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='7  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='6  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='4  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='8  2  (mA)10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='8  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='7  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='6  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='4  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='8  2  (mA)  110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='8  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='7  (ZHD)  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='6  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='4  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='8  2  DC  (mA)4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='7  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='9  2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='1  1  10  Linewidth (MHz)  IDC (mA)  Df < 134 KHz  Q > 79000  H =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='8 T  q = 80o, j = 20o  W/NiFe  (c)  I  II  III  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='7  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='9  2  0  1k  2k  3k  4k  5k  Peak Power (nV2/Hz)  IDC (mA)  (d)  I  II  III  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='45  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='55  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='1  1  10  W/CoFeB/MgO  Linewidth (MHz)  IDC (mA)  Df < 440 KHz  Q > 41000  H = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='80 T  q = 65o, j = 20o  (a)  I  II  III  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='45  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='55  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='6  0  1k  2k  3k  4k  5k  Peak Power (nV2/Hz)  IDC (mA)  (b)  I  II  III  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  (a) and (b) Linewidth vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  IDC and peak power vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  IDC for 21 mutually synchronized W/CoFeB/MgO SHNOs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' (c)  and (d) Linewidth vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  IDC and peak power vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  IDC for 21 mutually synchronized W/NiFe SHNOs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' The dashed blue line  represents a complete mutual synchronization of 21 oscillators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' The three color-coded regions represent the un-synchronized  state (Blue), robustly synchronized state (Olive) and high current unstable synchronized state (pink).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  mentary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  We observe the lowest linewidth of 134 kHz  in the synchronized state of the W/NiFe based oscillator  [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 4(c)], with a peak power just above 4000 nV2/Hz  [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 4(d)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' The lowest linewidth of the W/CoFeB/MgO  chain is 440 kHz [see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 4(c)], also with peak power  just above 4000 nV2/Hz [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 4(d)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' For NiFe/Pt based  SHNOs, we observe the lowest linewidth of 275 kHz with  enormous peak power of 40,000 nV2/Hz (see supplemen-  tary file).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  However, once this highest-quality signal is achieved,  increasing the current further deteriorates the signal  quality to intermediate values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' This deterioration does  not seem to be related to a loss of mutual synchroniza-  tion as we only observe a single signal in all devices in  this current range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Instead, this behavior coincides with  the change in curvature described above, indicating that  it could be due to a change in the auto-oscillating mode  character.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  We hence define three different regions: I)  incomplete partial synchronization with relatively poor  signal quality, II) complete mutual synchronization with  the best signal quality, and III) a possible different auto-  oscillating regime with intermediate signal quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Figure 5(a) and (b) shows the variation of linewidth  and peak power with the number of oscillators for both  the W/CoFeB/MgO and W/NiFe system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' We observe a  1/N dependence for the spectral linewidth, in agreement  with the oscillator synchronization theory and depicts the  enhancement of total mode volume.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' The peak power is  found to follow a quadratic (N 2) dependence, also con-  sistent with the nonlinear oscillator theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Benchmarking the Quality Factor  The combination of high auto-oscillation frequencies  and low linewidths leads to very high quality factors  (Q = f/∆f) for the synchronized chains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Figure 5(c)  shows Q vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' N for both the W/CoFeB/MgO and W/NiFe  systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' We observe Q > 79,000 for 21 mutually syn-  chronized SHNOs in W/NiFe thin films, which is the  highest quality factor reported for oscillators in a single  chain (which also results in higher output power).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' This  is comparable to the earlier observed Q of 170,000 in  two-dimensional NiFe/Pt arrays of 8×8 oscillators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' For  5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='8  1  0  2  4  6  8  Linewidth (MHz)  1/N  W/CoFeB/MgO  W/NiFe  (a)  0  100  200  300  400  0  1k  2k  3k  4k  5k  Peak Power (nV2/Hz)  N2  (b)  0  5  10  15  20  0  25k  50k  75k  100k  Q-factor  N  Df = 134 KHz  Q > 79000  (c)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  (a) Linewidth vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' inverse of number of nano-  constrictions (1/N) in a chain of SHNOs for W/CoFeB/MgO  and W/NiFe based oscillators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  (b) Peak power vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' square  of number of oscillators (N 2) for W/CoFeB/MgO and  W/NiFe based oscillators, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  (C) Q−factor of  SHNOs with number of oscillators (N), Black squares are for  W/CoFeB/MgO and green circles represents W/NiFe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' The  red solid line represents linear fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  the W/CoFeB/MgO oscillators, we found a Q of 41,000,  which is again the highest of any spintronic oscillator  chains operating at frequencies higher than 15 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' For  comparison with mutually synchronized oscillators based  on magnetic tunnel junctions, recent demonstrations [6]  of 8 mutually synchronized MTJs resulted in a Q−factor  of 7400.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  It is interesting to compare Q−factor (and output  power) more extensively with the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 6,  we show results from a large number of previous works,  expressed as Q−factor vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' output power, for both single  (hollow symbols) and synchronized (solid symbols) oscil-  lators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Both here and further on we use the abbrevia-  tions ’SHNOs’: spin Hall nano-oscillators (shown with  triangles), ’MTJs’:  nano-pillar magnetic tunnel junc-  tions which include vortex oscillators (shown with cir-  cular symbols), and ’Nano Contacts’: nano-contact spin  valve structures (shown with rhombus).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' One can observe  that the vortex oscillators [37–41] deliver the largest out-  put power (most lie on the right side of the graph).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' How-  ever, vortex oscillators mostly operate at much lower RF  frequencies (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='1 GHz to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='5 GHz) and hence result in  lower quality factors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Other MTJs and nano-contact de-  vices have larger frequency tunability but have lower out-  put power and/or higher operational linewidth resulting  in poor performance as signal generator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' The synchro-  nized MTJs have shown good results and are even em-  ployed for power harvesting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Though they also end up  with large linewidth and hence low Q−factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' The best  Q−factor found for nano-contact spin valve was about  18000 [42], which resulted in poor output power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' The  recently introduced SHNOs have already shown great  promise with their narrow linewidth and high frequency  operation, even a single oscillator results Q−factor in the  range of 2000-4000 [20, 24, 47], though their output power  is extremely low.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' In our previous work with 2D arrays  of 64 oscillators, we observed an enormous Q−factor of  179,000, though in a white noise regime (measured at  short time scales).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  In the present work, we have im-  proved our output power and can reach upto 200 pW with  sustaining a high Q−factor of >79000 (for W/NiFe thin  films).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' The NiFe/Pt system shows even higher output  power of 300 pW with Q > 32,000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Further improvements  in extending synchronization to rectangular arrays and  fabricating tunneling magneto-resistance based readouts  will bring these oscillators among the best-performing  spintronic oscillators with large output power and high  Q−factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Synchronization beyond 21 SHNOs  To investigate synchronization beyond 21 SHNOs, we  fabricated 30, 40, and 50 nano-constrictions in series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' It  is noteworthy that we do observe single-frequency mi-  crowave signal generation also in these much longer oscil-  lator chains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' However, no further linewidth reduction nor  any further increase in the output power were observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  This could be due to an increasing out-of phase synchro-  nization of SHNOs in the longer chains, as illustrated by  the spins in Figure 1, if there is a small relative phase  shift between individual nearest neighbor SHNOs that  does not affect shorter chains but build up to a reduced  total output power in the longer chains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Figure 7 shows  the PSD for 30, 40 and 50 nano-constrictions in chain for  W/CoFeB/MgO thin films.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' For 30 nano-constrictions in  6  : SHNOs  : MTJs  : Nano Contacts  10−12  10−11  10−10  10−9  10−8  10−7  10−6  10−5  10−4  102  103  104  105  27  26  39  40  41  34  35  36  33  28  37  29  30  12  38  11  6  42  42  19  31  32  13  23  21 *9 SHNOs chain  22 *8x8 array  This work  This work  This Work  Q-factor  Power (W)  (W/NiFe)  (W/CoFeB/MgO)  (NiFe/Pt)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Bench-marking of spintronic oscillators: Q−factor vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' integrated output power of various spintronic oscillators  and their synchronized systems (shown with filled symbols).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' The data comprise the best performance nano-pillar MTJs [6, 11,  14, 30–36], vortex MTJs [37–41], Nano-contact spin valves [13, 42–45] and SHNOs [20, 22–24, 46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  a chain [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 7(a)], we found the lowest linewidth of 800  kHz and a peak power of less than 400 nV2/Hz, which  is one order of magnitude less than the robustly syn-  chronized 21 SHNOs as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Figure 7(b)  shows the transition of partially synchronized microwave  emissions into single synchronized mode at different IDC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  However, as observed in the Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 7(b) the spectrum at  450 µA and 490 µA (partially synchronized states) show  lower linewidth and higher amplitude than fully synchro-  nized states at 540 µA, 640 µA and 730 µA current.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' This  clearly shows that the partial synchronization of oscilla-  tors results in better spectral parameters than the full  synchronization of oscillator chains with more than 30  nano-constrictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  In other words, the longer chains  may very well synchronize completely but be better de-  scribed as weaker synchronization of partially synchro-  nized sub-sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' This lack of robust synchronization  for more than 21 nano-constrictions may arise from sta-  tistical effects in a larger ensemble, or be due to larger  Joule heating in longer chains, and/or result from the in-  crease of an accumulative phase difference in the chains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Figure 7(c) and (d) show similar results for 40 and 50  nano-constrictions in a chain, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Though full  synchronization in longer chains of more than 21 nano-  constrictions is not very robust, it still shows a clear in-  teraction between oscillators (either in-phase or out-of  phase), which can be very useful for neuromorphic com-  puting using a large number of spins (nano-constrictions).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Perspective: Applications and Outlook  We have successfully demonstrated the robust mutual  synchronization of large number of SHNOs in a single  chain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  This observation leads to various applications  that can be realized using these oscillators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' The lower  linewidth and the significantly larger output power en-  able these oscillators for coherent frequency signal gen-  eration applications, as well as for wireless communi-  cations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Using the phase locked loop method, the mi-  crowave oscillations in chains can be further stabilized,  generating coherent oscillations that can be directly im-  plemented in many microwave applications [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  The  mutual synchronization of these oscillators in a chain  can be explored for bio-inspired computing and be-  yond [9, 23, 49] where each oscillator behaves as a neu-  ron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Combined with voltage [26, 27, 50] and/or memris-  tive [25] control of synchronization (synaptic weights),  these large chains can be used to locally or globally  control the coupling between oscillators (neurons).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' The  present work also serves as a stepping stone in the direc-  tion towards further scaling mutual synchronization to  much larger square or rectangular arrays well beyond the  previously demonstrated 64 oscillators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' As these oscilla-  tor arrays can be fabricated in a tiny area, it enables the  possibility to scale/miniaturize the neuromorphic net-  works based on these oscillators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  The large frequency  tunability with current also makes these oscillators ideal  for ultrafast sweeping spectrum analysis, where neither  7  30 NC  40 NC  50 NC  (a)  (c)  (d)  0  9  0  10  0  6  30 NC  (b)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  (a) Power spectral density for synchronized 30 NC SHNOs in a chain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' (b) The microwave spectrum for synchronized 30  nano-constrictions in a chain for few current values (IDC) marked with arrows in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Power spectral density for mutually  synchronized (c) 40 nano-constrictions and (d) 50 nano-constrictions SHNO in a chain for W/CoFeB/MgO thin films.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  vortex oscillators nor uniform MTJs can so far offer a  wide resolution bandwidth [7, 8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' With recent demon-  stration of energy-efficient spin Hall materials [51] and  the reduction of constrictions size [21, 52], the required  threshold current can be significantly reduced, operating  these devices with ultra-low power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  CONCLUSION  In summary, we show that robust in-phase mutual syn-  chronization of nano-constriction based SHNOs can be  achieved in very long chains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' The long-range synchro-  nization not only shows an enhanced output power but  also an improved linewidth of as low as 130 kHz for  W/NiFe based heterostructures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  The low current and  low field operation of these oscillators along with their  large frequency tunability, with both current and mag-  netic field, make them ideal for various spintronic appli-  cations such as neuromorphic computing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' In the longest  chains, mutual synchronization is less effective in im-  proving the microwave signal properties with evidence  of partial and/or increasingly out-of-phase synchroniza-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' These results not only enhance our understanding  of the mutual synchronization of these oscillators but also  paves the way towards making larger networks of these  oscillators for neuromorphic computing applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  METHODS  Sample fabrication: We utilize the well studied W(5  nm)/CoFeB(1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='4 nm)/MgO (2 nm) and W(5 nm)/NiFe(3  nm) heterostructures for the fabrication of microwave  nano-constriction SHNOs used in the experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' The  NM/FM structures were deposited using magnetron  sputtering on a high resistance intrinsic Si substrate (ρ >  10,000 µohm-cm) at room temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  The sample  stacks were capped with 4 nm Al3O3 thin films.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  The  growth of thin films was carried out using AJA Orion 8  sputtering system with a base pressure of 3×10−8 Torr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  The samples were then coated with 40 nm of hydrogen  silsesquioxane (HSQ) negative tone electron beam resist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  The SHNO chains used in the experiments were then fab-  ricated using a combination of e-beam lithography (Raith  EBPG 5200) and Ar-ion etching: more details can be  B/roise  6  Dc (HA)  3  108  found here [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' The top contact pads are fabricated us-  ing laser writer based direct lithography followed by de-  position of Cu(800 nm)/Pt(20 nm) thin films for Ground-  Signal-Ground co-planar waveguide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' In this experiment,  we utilize the SHNOs with 150 nm nano-constriction  width and 200 nm separation between SHNOs in a chain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Experimental Set-up: All the measurements were  performed at room temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' The microwave mea-  surements were performed using a custom-built probe  station utilizing GSG probes manufactured by GGB In-  dustries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Figure 2(c) shows the schematic representation  of the measurement setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' All measurements are carried  out at a fixed IP angle and an OOP rotatable sample  stage between the electromagnet poles at room tempera-  ture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Different OOP angles are used to generate positive  non-linearity in the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' To excite microwave emis-  sion, a positive DC current IDC was applied to the de-  vices through the inductive port of a bias-tee, while the  microwave signal was detected using high frequency port.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  The resulting power spectral density (PSD) of the auto-  oscillating signal (after amplification using low-noise am-  plifier) is captured using Rohde and Schwarz (10 Hz– 40  GHz) spectrum analyzer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' To calculate the PSD spectrum  shown in Figure 3 and 7, we have taken into account the  impedance mismatch and the losses from the RF compo-  nent and corrected to the low noise amplifier gain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  ACKNOWLEDGMENTS  This work was partially supported by the Horizon 2020  research and innovation program (ERC Advanced Grant  No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 835068 “TOPSPIN”).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' This work was also partially  supported by the Swedish Research Council (VR) and  the Knut and Alice Wallenberg Foundation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [1] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Slonczewski, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Magn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Magn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 159, L1  (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [2] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Berger, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' B 54, 9353 (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [3] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Tsoi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Jansen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Bass, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Chiang, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Tsoi, and  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Wyder, Nature 406, 46 (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [4] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Kiselev,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Sankey,  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Krivorotov,  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Emley,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Schoelkopf, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Buhrman, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Ralph, Nature 425,  380 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [5] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Chen, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Dumas, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Eklund, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Muduli,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Houshang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Awad, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Durrenfeld, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Malm,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Rusu, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' ˚Akerman, Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' IEEE 104, 1919 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [6] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Tsunegi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Taniguchi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Lebrun, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Yakushiji,  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Cros, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Grollier, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Fukushima, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Yuasa,  and  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Kubota, Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 8, 1 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [7] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Litvinenko, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Iurchuk, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Sethi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Louis, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Ty-  berkevych, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Li, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Jenkins, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Ferreira, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Dieny,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Slavin, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=', Nano Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 20, 6104 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [8] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Litvinenko, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Sidi El Valli, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Iurchuk, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Louis,  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Tyberkevych, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Dieny, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Slavin, and U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Ebels,  Nano Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 22, 1874 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [9] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Torrejon, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Riou, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Abreu Araujo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Tsunegi,  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Khalsa,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Querlioz,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Bortolotti,  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Cros,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Fukushima, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Kubota, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Yuasa, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Stiles, and  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Grollier, Nature 547, 428 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [10] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Romera, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Talatchian, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Tsunegi, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Araujo,  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Cros,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Bortolotti,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Trastoy,  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Yakushiji,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Fukushima, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Kubota, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Yuasa, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Ernoult, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Vo-  denicarevic, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Hirtzlin, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Locatelli, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Querlioz, , and  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Grollier, Nature 563, 230 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [11] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Sharma, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Mishra, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Ngo, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Guo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Fukami,  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Sato, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Ohno,  and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Yang, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 12, 1  (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [12] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Erokhin and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Berkov, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' B 89, 144421  (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [13] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Houshang, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Iacocca, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' D¨urrenfeld, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Sani,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' ˚Akerman,  and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Dumas, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Nano.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 11, 280  (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [14] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Lebrun, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Tsunegi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Bortolotti, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Kubota, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Jenk-  ins, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Romera, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Yakushiji, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Fukushima, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Grollier,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Yuasa, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=', Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 8, 1 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [15] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Tserkovnyak, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Brataas, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Bauer, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 88, 117601 (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [16] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Hirsch, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 83, 1834 (1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [17] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Sinova, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Valenzuela, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Wunderlich, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Back,  and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Jungwirth, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 87, 1213 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [18] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Demidov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Urazhdin, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Ulrichs, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Tiberkevich,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Slavin, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Baither, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Schmitz, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Demokritov,  Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 11, 1028 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [19] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Demidov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Urazhdin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Zholud, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Sadovnikov,  and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Demokritov, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 105, 172410  (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [20] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Duan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Smith, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Yang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Youngblood, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Lindner,  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Demidov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Demokritov, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Krivorotov,  Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 5, 1 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [21] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' D¨urrenfeld, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Awad, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Houshang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Dumas,  and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' ˚Akerman, Nanoscale 9, 1285 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [22] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Awad, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' D¨urrenfeld, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Houshang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Dvornik,  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Iacocca, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Dumas, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' ˚Akerman, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  13, 292 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [23] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Zahedinejad, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Awad, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Muralidhar, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Khymyn,  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Fulara, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Mazraati, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Dvornik,  and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' ˚Akerman,  Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Nano.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 15, 47 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [24] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Fulara, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Zahedinejad, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Khymyn, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Awad, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Mu-  ralidhar, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Dvornik,  and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' ˚Akerman, Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 5,  eaax8467 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [25] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Zahedinejad, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Fulara, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Khymyn, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Houshang,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Dvornik, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Fukami, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Kanai, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Ohno,  and  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' ˚Akerman, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 21, 81 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [26] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Kumar, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Rajabali, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Gonz´alez, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Zahedine-  jad, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Houshang, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' ˚Akerman, Nanoscale 14, 1432  (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [27] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Fulara, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Zahedinejad, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Khymyn, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Dvornik,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Fukami, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Kanai, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Ohno,  and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' ˚Akerman, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 11, 1 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [28] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Mazraati, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Chung, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Houshang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Dvornik, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Pi-  azza, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Qejvanaj, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Jiang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Le, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Weissenrieder,  and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' ˚Akerman, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 109, 242402 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [29] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Slavin and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Tiberkevich, IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Magn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 45,  1875 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [30] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Houssameddine, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Florez, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Katine, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Michel,  9  U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Ebels, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Mauri, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Ozatay, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Delaet, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Viala,  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Folks, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Terris,  and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Cyrille, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 93, 022505 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [31] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Kubota, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Yakushiji, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Fukushima, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Tamaru,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Konoto, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Nozaki, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Ishibashi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Saruya, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Yuasa,  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Taniguchi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Arai,  and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Imamura, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Exp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 6, 103003 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [32] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Zeng, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Amiri, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Krivorotov, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Zhao, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Finoc-  chio, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Katine, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Huai, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Langer,  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Galatsis, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Wang,  and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Jiang, ACS Nano 6,  6115 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [33] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Deac, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Fukushima, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Kubota, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Maehara,  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Suzuki, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Yuasa, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Nagamine, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Tsunekawa, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Djayaprawira,  and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Watanabe, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 4, 803  (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [34] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Zeng, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Upadhyaya, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Khalili Amiri, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Cheung,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Katine, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Langer, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Wang,  and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Jiang, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 99, 032503 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [35] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Costa, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Serrano-Guisan, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Lacoste, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Jenkins,  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' B¨ohnert, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Tarequzzaman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Borme, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Deepak,  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Paz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Ventura, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Ferreira,  and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Freitas, Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 7, 1 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [36] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Seki, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Sakuraba, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Arai, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Ueda, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Okura,  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Imamura, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Takanashi, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 105,  092406 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [37] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Pribiag,  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Krivorotov,  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Fuchs,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Braganca,  O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Ozatay, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Sankey, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Ralph, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Buhrman, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 3, 498 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [38] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Tsunegi,  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Kubota,  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Yakushiji,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Konoto,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Tamaru,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Fukushima,  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Arai,  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Imamura,  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Grimaldi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Lebrun, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Grollier, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Cros,  and  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Yuasa, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Exp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 7, 063009 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [39] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Tsunegi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Yakushiji, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Fukushima, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Yuasa, and  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Kubota, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 109, 252402 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [40] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Dussaux, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Grimaldi, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Rache Salles, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Jenkins,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Khvalkovskiy, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Bortolotti, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Grollier, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Kubota,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Fukushima, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Yakushiji, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Yuasa, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Cros,  and  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Fert, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 105, 022404 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [41] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Dussaux, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Georges, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Grollier, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Cros, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Khvalkovskiy, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Fukushima, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Konoto, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Kubota,  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Yakushiji, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Yuasa, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Zvezdin, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Ando,  and  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Fert, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 1, 1 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [42] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Rippard, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Pufall, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Kaka, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Silva, and  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Russek, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' B 70, 100406 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [43] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Maehara,  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Kubota,  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Suzuki,  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Seki,  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Nishimura,  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Nagamine,  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Tsunekawa,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Fukushima, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Deac, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Ando,  and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Yuasa,  Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Exp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 6, 113005 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [44] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Maehara,  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Kubota,  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Suzuki,  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Seki,  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Nishimura,  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Nagamine,  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Tsunekawa,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Fukushima, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Arai, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Taniguchi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Imamura,  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Ando,  and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Yuasa, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Exp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 7, 023003  (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [45] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Sani, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Persson, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Mohseni, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Pogoryelov,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Muduli, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Eklund, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Malm, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' K¨all, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Dmitriev,  and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' ˚Akerman, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 4, 1 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [46] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='-R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Chen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Smith, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Montoya, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Lu,  and  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Krivorotov, Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 3, 1 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [47] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Zahedinejad, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Mazraati, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Fulara, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Yue, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Jiang,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Awad,  and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' ˚Akerman, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 112,  132404 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [48] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Tamaru, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Kubota, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Yakushiji, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Yuasa,  and  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Fukushima, Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 5, 1 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [49] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Houshang,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Zahedinejad,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Muralidhar,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Ch¸eci´nski, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Khymyn, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Rajabali, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Fulara,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Awad, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Dvornik, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' ˚Akerman, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 17, 014003 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [50] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Choi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Park, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Kang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Kim, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Rieh, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='-  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Lee, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Kim, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Park, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 13,  3783 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [51] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Behera, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Fulara, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Bainsla, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Kumar, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Za-  hedinejad, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Houshang,  and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' ˚Akerman, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 18, 024017 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content='  [52] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Awad, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Houshang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Zahedinejad, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Khymyn,  and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' ˚Akerman, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
+page_content=' 116, 232401 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YdE2T4oBgHgl3EQfZAcJ/content/2301.03859v1.pdf'}
diff --git a/ZNE5T4oBgHgl3EQfdw-l/content/2301.05614v1.pdf b/ZNE5T4oBgHgl3EQfdw-l/content/2301.05614v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..6bdc4f1f25da35a93df2e2d5cec3262ade6c80f4
--- /dev/null
+++ b/ZNE5T4oBgHgl3EQfdw-l/content/2301.05614v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ae2c7fff65b3487fa0b094f21759d6ed635900dfb08a030c588e3217531c1a1a
+size 2245820
diff --git a/ZNE5T4oBgHgl3EQfdw-l/vector_store/index.faiss b/ZNE5T4oBgHgl3EQfdw-l/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..f943ed3c7e51426ee4c2a816987f0a83834eecfd
--- /dev/null
+++ b/ZNE5T4oBgHgl3EQfdw-l/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:70f3906903eeb0b6c0999a8cf36eb540eab236230e77540c175c881ce32952db
+size 3407917
diff --git a/ZNE5T4oBgHgl3EQfdw-l/vector_store/index.pkl b/ZNE5T4oBgHgl3EQfdw-l/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..1d913148fe51144662076378eb8a0927866accab
--- /dev/null
+++ b/ZNE5T4oBgHgl3EQfdw-l/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a3ec5c0327329f8d85a30c0cecd42f7fcbe95ed07c66916ac8de584f31f24904
+size 110553
diff --git a/aNA0T4oBgHgl3EQfF__0/content/2301.02042v1.pdf b/aNA0T4oBgHgl3EQfF__0/content/2301.02042v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..add7acfab6a04fc532c3d7ca238cf163842e96ba
--- /dev/null
+++ b/aNA0T4oBgHgl3EQfF__0/content/2301.02042v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5834296656a86a16410d12d228b87b14840cb6facf45839bed6b98a740d901b8
+size 250023
diff --git a/aNA0T4oBgHgl3EQfF__0/vector_store/index.faiss b/aNA0T4oBgHgl3EQfF__0/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..5db98fed81713f9cd1629f283718d69c6dce853b
--- /dev/null
+++ b/aNA0T4oBgHgl3EQfF__0/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9710f63745b85bb11e18f4ca5084e57354530baff12da6a85b4116c6862ebaf4
+size 3342381
diff --git a/aNA0T4oBgHgl3EQfF__0/vector_store/index.pkl b/aNA0T4oBgHgl3EQfF__0/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..a35f648af04e4c308e6145056b72c2cfd3f9ac77
--- /dev/null
+++ b/aNA0T4oBgHgl3EQfF__0/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9226ed3c490bcf54806ede8b664c172684a76576d26accc36763ea6e7e0c3bf7
+size 122178
diff --git a/adAzT4oBgHgl3EQf2v4D/content/tmp_files/2301.01817v1.pdf.txt b/adAzT4oBgHgl3EQf2v4D/content/tmp_files/2301.01817v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2993309e5f16f4072fded6d8a79bd27d94319695
--- /dev/null
+++ b/adAzT4oBgHgl3EQf2v4D/content/tmp_files/2301.01817v1.pdf.txt
@@ -0,0 +1,1555 @@
+Evaluation of Induced Expert Knowledge in Causal Structure Learning
+by NOTEARS
+Jawad Chowdhury, Rezaur Rashid and Gabriel Terejanu
+Dept. of Computer Science, University of North Carolina at Charlotte, Charlotte, NC, USA
+mchowdh5@uncc.edu, mrashid1@uncc.edu, gabriel.terejanu@uncc.edu
+Keywords:
+Causality, Structured Prediction and Learning, Supervised Deep Learning, Optimization for Neural Networks.
+Abstract:
+Causal modeling provides us with powerful counterfactual reasoning and interventional mechanism to generate
+predictions and reason under various what-if scenarios. However, causal discovery using observation data
+remains a nontrivial task due to unobserved confounding factors, finite sampling, and changes in the data
+distribution. These can lead to spurious cause-effect relationships. To mitigate these challenges in practice,
+researchers augment causal learning with known causal relations. The goal of the paper is to study the impact
+of expert knowledge on causal relations in the form of additional constraints used in the formulation of the
+nonparametric NOTEARS. We provide a comprehensive set of comparative analyses of biasing the model
+using different types of knowledge. We found that (i) knowledge that correct the mistakes of the NOTEARS
+model can lead to statistically significant improvements, (ii) constraints on active edges have a larger positive
+impact on causal discovery than inactive edges, and surprisingly, (iii) the induced knowledge does not correct
+on average more incorrect active and/or inactive edges than expected. We also demonstrate the behavior of the
+model and the effectiveness of domain knowledge on a real-world dataset.
+1
+INTRODUCTION
+Machine learning models have been breaking records
+in terms of achieving higher predictive accuracy.
+Nevertheless, out-of-distribution (OOD) generaliza-
+tion remains a challenge. One solution is adopting
+causal structures (Lake et al., 2017) to constrain the
+models and remove spurious correlations. The un-
+derlying causal knowledge of the problem of inter-
+est can significantly help with domain adaptability
+and OOD generalization (Magliacane et al., 2017).
+Furthermore, causal models go beyond the capability
+of correlation-based models to produce predictions.
+They provide us with the powerful counterfactual rea-
+soning and interventional mechanism to reason under
+various what-if scenarios (Pearl, 2009).
+Two of the most prominent approaches in ob-
+servational causal discovery are constraint-based and
+score-based methods (Spirtes et al., 2000; Pearl and
+Verma, 1995; Colombo et al., 2012; Chickering,
+2002; Ramsey et al., 2017). Although these meth-
+ods are quite robust if the underlying assumptions
+are true, they are computationally expensive and their
+computational complexity increases with the number
+of system variables due to the combinatorial nature
+of the DAG constraint.
+NOTEARS (Zheng et al.,
+2018) tackles this problem with an algebraic char-
+acterization of acyclicity which reduces the combi-
+natorial problem to a continuous constrained opti-
+mization.
+Different approaches (Yu et al., 2019;
+Lachapelle et al., 2019; Ng et al., 2019; Zheng et al.,
+2020) have been proposed as the nonlinear or non-
+parametric extensions of this linear continuous opti-
+mization, which provides flexibility in modeling dif-
+ferent causal mechanisms.
+Learning the causal structure purely based on ob-
+servational data is not a trivial task due to various
+limitations such as finite sampling, unobserved con-
+founding factors, selection bias, and measurement er-
+rors (Cooper, 1995; Elkan, 2001; Zadrozny, 2004).
+These can result in spurious cause-effect relation-
+ships. To mitigate these challenges in practice, re-
+searchers augment causal learning with prior causal
+relations as featured in software packages such as
+CausalNex1, causal-learn2, bnlearn (Scutari, 2009),
+gCastle (Zhang et al., 2021), and DoWhy (Sharma
+and Kiciman, 2020). Heindorf et al. (Heindorf et al.,
+2020) in their work attempts to construct the first large
+scale open domain causality graph that can be in-
+1https://github.com/quantumblacklabs/causalnex
+2https://https://github.com/cmu-phil/causal-learn
+arXiv:2301.01817v1  [cs.LG]  4 Jan 2023
+
+cluded in the existing knowledge bases. The work
+further analyze and demonstrates the benefits of large
+scale causality graph in causal reasoning. Given a
+partial ancestral graph (PAG), representing the qual-
+itative knowledge of the causal structure, Jaber et
+al. (Jaber et al., 2018) in their study compute the inter-
+ventional distribution from observational data. Com-
+bining expert knowledge with structural learning fur-
+ther constrains the search space minimizing the num-
+ber of spurious mechanisms (Wei et al., 2020) and
+researchers often leverage these background knowl-
+edge by exploiting them as additional constraints
+for knowledge-enhanced event causality identifica-
+tion (Liu et al., 2021). O’Donnell et al. (O’Donnell
+et al., 2006) use expert knowledge as prior probabili-
+ties in learning Bayesian Network (BN) and Gencoglu
+and Gruber (Gencoglu and Gruber, 2020) use the lin-
+ear NOTEARS model to incorporate knowledge to
+detect how different characteristics of the COVID-19
+pandemic are causally related to each other. Differ-
+ent experts’ causal judgments can be aggregated into
+collective ones (Bradley et al., 2014) and Alrajeh et
+al. (Alrajeh et al., 2020) in their work, studied how
+these judgments can be combined to determine ef-
+fective interventions. An interesting exploration by
+Andrews et al. (Andrews et al., 2020) defines tiered
+background knowledge and shows that with this type
+of background knowledge the FCI algorithm (Spirtes
+et al., 2000) is sound and complete.
+However, understanding how to effectively incor-
+porate and evaluating the impact of induced knowl-
+edge is yet to be explored and we believe knowledge
+regarding this can mitigate some of the challenges
+of observational causal discovery. Human expertise
+can play a vital role to assess the learned model in
+causal structure learning (Bhattacharjya et al., 2021;
+Li et al., 2021). In practice, human assessment and
+validation process often take place in an iterative or
+sequential manner (Holzinger, 2016; Xin et al., 2018;
+Yang et al., 2019). In structure learning, this is more
+realistic for a sufficiently large causal network where
+one can learn, validate, and induce newly formed
+knowledge-set in the learning process following se-
+quential feedback loops. The goal of this paper is not
+to create a new causal discovery algorithm but rather
+to study this iterative interaction between prior causal
+knowledge from domain experts that takes the form of
+model constraints and a state-of-the-art causal struc-
+ture learning algorithm. Wei et al. (Wei et al., 2020)
+have been the first to augment NOTEARS with addi-
+tional optimization constraints to satisfy the Karush-
+Kuhn-Tucker (KKT) optimality conditions and Fang
+et al. (Fang et al., 2020) in their work leverages the
+low rank assumption in the context of causal DAG
+learning by augmented NOTEARS that shows signif-
+icant improvements.
+However, none of them have
+studied the impact of induced knowledge on causal
+structure learning by augmenting NOTEARS with the
+optimization constraints. For completeness, in Sec-
+tion 3, we do provide our formulation of nonparamet-
+ric NOTEARS (Zheng et al., 2020) with functionality
+to incorporate causal knowledge in the form of known
+direct causal and non-causal relations. Nevertheless,
+in this work, we aim to study the impact of expert
+causal knowledge on causal structure learning.
+The main contributions are summarized as fol-
+lows.
+(1) We demonstrate an iterative modeling
+framework to learn causal relations, impose causal
+knowledge to constrain the causal graphs, and fur-
+ther evaluate the model’s behavior and performance.
+(2) We empirically evaluate and demonstrate that: (a)
+knowledge that corrects model’s mistake can lead to
+statistically significant improvements, (b) constraints
+on active edges have a larger positive impact on causal
+discovery than inactive edges, and (c) the induced
+knowledge does not correct on average more incorrect
+active and/or inactive edges than expected. Finally,
+we illustrate the impact of additional knowledge in
+causal discovery on a real-world dataset.
+This paper is structured as follows: Section 2 in-
+troduces the background on causal graphical models
+(CGMs), score-based structure recovery methods, and
+a study using the score-based approach formulated
+as a continuous optimization and its recent nonpara-
+metric extension. In Section 3, we present our ex-
+tension of the nonparametric continuous optimization
+to incorporate causal knowledge in structure learning
+and detail the proposed knowledge induction process.
+Section 4 shows the empirical evaluations and com-
+parative analyses of the impact of expert knowledge
+on the model’s performance. Finally, in Section 5, we
+summarize our findings and provide a brief discussion
+on future work.
+2
+BACKGROUND
+In this section, we review the basic concepts related
+to causal structure learning and briefly cover a recent
+score-based continuous causal discovery approach us-
+ing structural equation models (SEMs).
+2.1
+Causal Graphical Model (CGM)
+A directed acyclic graph (DAG) is a directed graph
+without any directed cyclic paths (Spirtes et al.,
+2000). A causal graphical model CGM(PX,G) can
+be defined as a pair of a graph G and an observa-
+
+tional distribution PX over a set of random variables
+X = (X1,...,Xd). The distribution PX is Markovian
+with respect to G where G = (V,E) is a DAG that
+encodes the causal structures among the random vari-
+ables Xi ∈ X (Peters et al., 2017). The node i ∈ V
+corresponds to the random variable Xi ∈ X and edges
+(i, j) ∈ E correspond to the causal relations encoded
+by G. In a causal graphical model, the joint distri-
+bution Px can be factorized as p(x) = ∏d
+i=1 p(xi|xG
+pai)
+where XG
+pai refers to the set of parents (direct causes)
+for the variable Xi in DAG G and for each Xj ∈ XG
+pai
+there is an edge (Xj → Xi) ∈ E (Peters et al., 2017).
+2.2
+Score-based Structure Recovery
+In a structure recovery method, given n i.i.d. obser-
+vations in the data matrix X = [x1|...|xd] ∈ Rn×d,
+our goal is to learn the underlying causal relations
+encoded by the DAG G. Most of the approaches fol-
+low either a constraint-based or a score-based strategy
+for observational causal discovery. A score-based ap-
+proach typically concentrates on identifying the DAG
+model G that fits the observed set of data X accord-
+ing to some scoring criterion S(G,X) over the discrete
+space of DAGs D where G ∈ D (Chickering, 2002).
+The optimization problem for structure recovery in
+this case can be defined as follows:
+min
+G
+S(G,X)
+subject to
+G ∈ D
+(1)
+The challenge with Eq. 1 is that the acyclicity con-
+straint in the optimization is combinatorial in nature
+and scales exponentially with the number of nodes d
+in the graph. This makes the optimization problem
+NP-hard (Chickering, 1996; Chickering et al., 2004).
+2.3
+NOTEARS: Continuous
+Optimization for Structure
+Learning
+NOTEARS (Zheng et al., 2018) is a score-based
+structure learning approach which reformulates the
+combinatorial optimization problem to a continu-
+ous one through an algebraic characterization of the
+acyclicity constraint in Eq. 1 via trace exponen-
+tial. This method encodes the graph G defined over
+the d nodes to a weighted adjacency matrix W =
+[w1|...|wd] ∈ Rd×d where wi j ̸= 0 if there is an ac-
+tive edge Xi → Xj and wi j = 0 if there is not. The
+weighted adjacency matrix W entails a linear SEM by
+Xi = fi(X) + Ni = wT
+i X + Ni; where Ni is the associ-
+ated noise. The authors define a smooth score func-
+tion on the weighted matrix as h(W) = tr(eW◦W) − d
+where ◦ is the Hadamard product and eM is the ma-
+trix exponential of M. This embedding of the graph
+G and the characterization of acyclicity turns the op-
+timization in Eq. 1 into its equivalent:
+min
+W∈Rd×d
+L(W)
+subject to
+h(W) = 0
+(2)
+where L(W) is the least square loss over W and h(W)
+score defines the DAG-ness of the graph.
+2.4
+Nonparametric Extension of
+NOTEARS
+A nonparametric extension of the continuous opti-
+mization suggested by a subsequent study (Zheng
+et al., 2020) uses partial derivatives for asserting the
+dependency of f j on the random variables. The au-
+thors define f j ∈ H1(Rd) ⊂ L2(Rd) over the Sobolev
+space of square integrable functions whose deriva-
+tives are also square integrable. The authors show
+that f j can be independent of random variable Xi if
+and only if ||∂i f j||L2 = 0 where ∂i denotes partial
+derivative with respect to the i-th variable. This re-
+defines the weighted adjacency matrix with W(f) =
+W( f1,..., fd) ∈ Rd×d where each Wij encodes the
+partial dependency of f j on variable Xi. As a result,
+we can equivalently write Eq. 2 as follows:
+min
+f:f j∈H1(Rd),∀ j∈[d]
+L( f)
+subject to
+h(W( f)) = 0
+(3)
+for all Xj ∈ X.
+Two of the general instances pro-
+posed by (Zheng et al., 2020) are:
+NOTEARS-
+MLP and NOTEARS-Sob.
+A multilayer percep-
+tron having h number of hidden layers and σ :
+R → R activation function can be defined as
+M(X;L) = σ(L(h)σ(...σ(L(1)X)) where L(l) denotes
+the parameters associated with l-th hidden layer.
+The authors in (Zheng et al., 2020) show that if
+||i-th column of L(1)
+j ||2 = 0 then M j(X;L) will be
+independent of variable Xi which replaces the as-
+sociation of partial derivatives in Eq. 3 and rede-
+fines the adjacency matrix as W(θ) with W(θ)ij =
+||i-th column of L(1)
+j ||2 where θ = (θ1,...,θd); θk de-
+noting the set of parameters for the Mk(X;L) (k-
+th MLP). With the usage of neural networks and
+the augmented Lagrangian method (Bertsekas, 1997)
+NOTEARS-MLP solves the constrained problem in
+Eq. 3 as follows:
+min
+θ F(θ)+λ||θ||1
+F(θ) = L(θ)+ ρ
+2|h(W(θ))|2 +αh(W(θ))
+(4)
+
+Figure 1: Knowledge induction process. We induce knowl-
+edge by carrying over the existing knowledge set along with
+a new random correction informed by model mistakes.
+3
+KNOWLEDGE INDUCTION
+In our formulation, we use the multilayer perceptrons
+of NOTEARS-MLP proposed by (Zheng et al., 2020)
+as our estimators. We extend this framework to incor-
+porate causal knowledge by characterizing the extra
+information as additional constraints in the optimiza-
+tion in Eq. 3.
+Knowledge Type.
+We distinguish between these
+two types of knowledge: (i) known inactive is knowl-
+edge from the true inactive edges (absence of direct
+causal relation), and (ii) known active is knowledge
+from the true active edges (presence of direct causal
+relation).
+Knowledge Induction Process.
+We adopt an inter-
+active induction process, where the expert knowledge
+is informed by the outcome of the causal discovery
+model. Namely, the knowledge is induced to correct
+the mistakes of the model in the causal structure, in
+the hope that the new structure is closer to the true
+causal graph. This process is applied sequentially by
+correcting the mistakes of the model at each step.
+In the following subsections we present the formu-
+lation of the NOTEARS optimization with constrains
+and detail the sequential induction process.
+3.1
+Expert Knowledge as Constraints
+An induced knowledge associated with a true ac-
+tive edge, Xi → Xj (known active) enforces the cor-
+responding cell in the adjacency matrix to be non-
+zero, [W(θ)]ij ̸= 0. We consider this knowledge as
+inequality constraint in our extension of the optimiza-
+tion such that the following statement holds:
+hp
+ineq(W(θ)) > 0
+(5)
+Figure 2: Expected graph formulation: (a) true graph, Gtrue,
+(b) predicted graph by model at step k, Gk
+pred, (c) induced
+knowledge at step (k+1), (d) expected graph at step (k+1),
+Gk+1
+exp . Three different examples of many possible predicted
+graphs at step (k +1), Gk+1
+pred where the model performs (e)
+less than expectation, (f) par with expectation, and (g) more
+than expectation.
+where p enumerates over all the inequality constraints
+due to induction from the set of known active and
+hineq is the penalty score associated with the viola-
+tion of these inequality constraints.
+On the other
+hand, knowledge associated with true inactive edge,
+Xi ↛ Xj (known inactive) enforces the related cell in
+W(θ) to be equal to zero, [W(θ)]ij = 0 if the induction
+implies there should not be an edge from Xi to Xj. We
+consider this knowledge as equality constraint in our
+optimization such as:
+hq
+eq(W(θ)) = 0
+(6)
+where q enumerates over all the equality constraints,
+induced from the set of known inactive and heq is the
+penalty score associated with the violation of these
+equality constraints. With these additional constraints
+in Eqs. 5, 6 we extend Eq. 3 to incorporate causal
+knowledge in the optimization as follows:
+min
+f:f j∈H1(Rd),∀ j∈[d]
+L( f)
+subject to
+h(W(θ)) = 0,
+hq
+eq(W(θ)) = 0,
+hp
+ineq(W(θ)) > 0
+(7)
+NOTEARS uses a thresholding step on the estimated
+edge weights to reduce false discoveries by pruning
+all the edges with weights falling below a certain
+threshold. Because of this, in practice, even the equal-
+ity constraints in Eq. 6 become inequalities to allow
+for small weights. Finally, slack variables are intro-
+duced in the implementation to transform the inequal-
+ity constraints into equality constraints (see detailed
+formulation in Appendix A).
+By using the similar strategy suggested by Zheng
+et al. (Zheng et al., 2020) with augmented Lagrangian
+method the reframed constrained optimization of
+
+knowledge to
+knowledge to
+correct mistake
+correct mistake
+SHD
+'pred
+ASHL
+pred
+0
+2
+1
+# induced knowledgeX
+X
+X
+ induction
+(a)
+(c)
+(d)
+X
+X
+X
+(b)
+(e)
+(f)
+(g)Eq. 4 takes the following form:
+min
+θ F(θ)+λ||θ||1
+F(θ) = L(θ)+ ρ
+2|h(W(θ))|2 +αh(W(θ))
++∑
+p
+(ρineq
+2
+|hp
+ineq(W(θ))|2 +αphp
+ineq(W(θ)))
++∑
+q
+(ρeq
+2 |hq
+eq(W(θ))|2 +αqhq
+eq(W(θ)))
+(8)
+3.2
+Sequential Knowledge Induction
+In case of knowledge induction, the optimization is
+run in a sequential manner where the constraints are
+informed by the causal mistakes made by the model
+in the previous step. We start with our baseline model
+without imposing any additional knowledge from the
+true DAG and get the predicted causal graph denoted
+by G0
+pred in Figure 1.
+Then at each iterative step
+(k + 1), based on the mistakes in the causal graph
+Gk
+pred predicted by the NOTEARS-MLP, we select
+one additional random piece of knowledge to correct
+one of the mistakes, and add it to the set of con-
+straints identified in the previous k steps, and rerun
+NOTEARS. We note that a batch of corrections can
+also be selected, however for this work we have fo-
+cused on estimating the contribution of each piece of
+knowledge in the form of known active/inactive edge.
+Our observations are illustrated in Section 4.1, Sec-
+tion 4.2, Section 4.3, and Section 4.4.
+Expected Causal Graph.
+We consider the ex-
+pected causal graph, Gk+1
+exp at step (k+1) by consider-
+ing the case where all the knowledge has successfully
+been induced without impacting any other edges. Fig-
+ure 2d illustrates an example of how we formulate
+our expected graph for a particular step in the itera-
+tive process. We note that the correction might yield
+a directed graph (Expected Causal Graph) that is not
+necessary a DAG. The objective is to compare the
+performance between the causal graph predicted by
+NOTEARS and the expected causal graph. Our intu-
+ition is that the induced knowledge will probably cor-
+rect additional incorrect edges, see Figure 2g, yield-
+ing a performance better than expected.
+4
+EXPERIMENTS
+To empirically evaluate the impact of additional
+causal knowledge on causal learning and to keep our
+experimental setup similar to the study in Ref. (Zheng
+Table 1: Performance metrics considered with their corre-
+sponding desirability.
+Metric
+Desirability
+∆FDR
+Lower is better
+∆TPR
+Higher is better
+∆FPR
+Lower is better
+∆SHD
+Lower is better
+Table 2: Results for inducing redundant knowledge.
+Metric
+Mean ± Stderr.
+Remarks
+∆FDR
+-0.00030 ± 0.00017
+No harm
+∆TPR
+-0.00035 ± 0.00027
+No harm
+∆FPR
+-0.00097 ± 0.00059
+No harm
+∆SHD
+-0.00154 ± 0.00167
+No harm
+et al., 2020), we have used an MLP with 10 hid-
+den units and sigmoid activation functions. In all our
+experimental setup, we assume the prior knowledge
+is correct (agrees with the true DAG). Despite the
+known sensitivity of the NOTEARS algorithm to data
+scaling, as demonstrated in previous study (Reisach
+et al., 2021), we have conducted experiments using
+both unscaled and scaled data to ensure the robustness
+of our findings and we are pleased to report that our
+conclusions remain unchanged regardless of the scal-
+ing of the data, indicating the stability and reliability
+of our results. While we present the results using the
+unscaled data for consistency with the original imple-
+mentation of NOTEARS (Zheng et al., 2020), it is
+important to note that our conclusions hold true even
+when the data is scaled.
+Simulation.
+We investigate the performance of our
+formulation and the impact of induced knowledge by
+comparing the DAG estimates with the ground truths.
+For our simulations with synthetic data, we have con-
+sidered 16 different combinations following the sim-
+ulation criteria: two random graph models, Erdos-
+Renyi (ER) and Scale-Free (SF), number of nodes,
+d = {10,20}, sample size, n = {200,1000}, edge
+density, s0 = {1d,4d}. For each of these combina-
+tions, we have generated 10 different random graphs
+or true DAGs (as 10 trials for a particular combina-
+tion) and corresponding data by following nonlinear
+data generating process with index models (similar
+to the study in Ref. (Zheng et al., 2020) for which
+the underlying true DAGs are identifiable. The results
+are summarized over all these 160 random true DAGs
+and datasets. In our simulations, we have considered
+the regularization parameter, λ = 0.01. We evaluate
+the performance of causal learning based on the mean
+and the standard error of different metrics. For sta-
+tistical significance analysis, we have used t-test with
+α = 0.05 as the significance level.
+
+Table 3: Results for inducing knowledge that corrects model’s mistake.
+Metric
+Knowledge
+Mean ± Stderr.
+Improvement
+∆FDR
+inactive
+-0.018 ± 0.002
+Significant
+∆FDR
+active
+-0.008 ± 0.001
+Significant
+∆TPR
+inactive
+-0.007 ± 0.003
+Not significant
+∆TPR
+active
+0.024 ± 0.003
+Significant
+∆FPR
+inactive
+-0.023 ± 0.004
+Significant
+∆FPR
+active
+-0.008 ± 0.003
+Significant
+∆SHD
+inactive
+-0.032 ± 0.012
+Significant
+∆SHD
+active
+-0.071 ± 0.011
+Significant
+Metrics.
+For the comparative analysis, we consider
+the following performance metrics: False Discovery
+Rate (FDR), True Positive Rate (TPR), False Posi-
+tive Rate (FPR), and Structural Hamming Distance
+(SHD). However, since we are evaluating the perfor-
+mance over all these 160 random graphs of varying
+sizes, we consider Structural Hamming Distance per
+node (SHD/d) as our SHD measure that scales with
+the number of nodes (FDR, TPR, and FPR scale by
+definition). To evaluate the impact of induced knowl-
+edge, we calculate the differences in the metrics at
+different steps (where we have different sizes of in-
+duced knowledge set) and referred them as ∆FDR,
+∆TPR, ∆FPR, and ∆SHD, see also Table 1. For ex-
+ample, based on our model’s prediction we calculate
+the impact of inducing one additional piece of knowl-
+edge on the metric SHD (∆SHDpred) as follows:
+∆SHDpred = SHD(Gk+1
+pred)−SHD(Gk
+pred)
+(9)
+Sanity Check - Redundant Knowledge Does No
+Harm.
+As part of our sanity check, we investigate
+the impact of induced knowledge that matches the
+causal relationships successfully discovered by the
+NOTEARS-MLP. Therefore, in this section, we con-
+sider the set of edges that our baseline model cor-
+rectly classifies as our knowledge source. Here, we do
+not distinguish between the edge types of our induced
+knowledge (known inactive & active) since our goal
+is to investigate whether having redundant knowl-
+edge as additional constraints affects model’s perfor-
+mance or not. The results are illustrated in Table 2.
+Our empirical evaluation shows that adding redun-
+dant knowledge does not deteriorate the performance
+of NOTEARS-MLP. Our performed statistical test re-
+flects that the results after inducing the knowledge
+from the correctly classified edge set are not statis-
+tically different than the results from the model with-
+out these knowledge inductions. However, we have
+noticed that the performance gets worse with highly
+regularized models. This is consistent with observa-
+tions by Ng et al. (Ng et al., 2020) where sparse DAGs
+result in missing some of the true active edges.
+4.1
+Knowledge that Corrects Model’s
+Mistake
+We first investigate the role of randomly chosen
+knowledge that corrects model’s mistake based on
+the cause-effect relations of the true graph. There-
+fore, in this case, we consider the set of misclassified
+edges from the estimated causal graph as the knowl-
+edge source for biasing the model. The results are
+illustrated in Table 3. Our empirical result shows sta-
+tistically significant improvements whenever the in-
+duced knowledge corrects misclassified edges in the
+estimated causal graph except for the case of ∆TPR
+with known inactive edges. However, this behavior is
+not totally unexpected since knowledge from known
+inactive edges helps to get rid of false discoveries or
+false positives, which hardly have impact on true pos-
+itives.
+4.2
+Known Inactive vs Known Active
+In this subsection, we are interested in understanding
+the impact of different types of induced knowledge
+on causal discovery to correct the mistakes in the es-
+timated causal graph. As a result, the experimental
+setup is similar to Section 4.1 where we consider the
+misclassified edge set as the knowledge source. We
+consider both known inactive and known active types
+of knowledge to induce separately and analyze the
+differences of their impact on the performance. The
+results are illustrated in Table 4. Based on our statis-
+tical test, we have found that inducing known inactive
+is more effective when we compare the performance
+based on FDR and FPR as misclassification of inac-
+tive edges has more impact on these metrics. On the
+other hand, the results show that inducing known ac-
+tive is more effective on TPR as misclassification of
+active edges has more impact on this metric. Inter-
+estingly, we have found that known active provides a
+
+significant improvement over known inactive in terms
+of SHD. This can be attributed to the fact that the
+induced knowledge based on the true inactive edge
+(known inactive) between two random variables, i.e.
+from Xi to Xj allows for two extra degrees of freedom
+since it is still possible to have no edge at all or an ac-
+tive edge from Xj to Xi. However, the induced knowl-
+edge based on the true active edge doesn’t allow any
+degrees of freedom. This type of knowledge is more
+restraining for causal graph discovery and therefore
+carries more information.
+4.3
+Empirical Performance vs
+Expectation
+In this subsection, we are interested in understand-
+ing whether inducing knowledge to correct model’s
+mistakes exceeds expected improvement.
+The ex-
+perimental setup is similar to Section 4.1 and Sec-
+tion 4.2 where we consider the misclassified edge set
+as the knowledge source. We have conducted the ex-
+periments using both known inactive and known ac-
+tive types of knowledge separately.
+The expected
+causal graph, Gexp is formulated in a similar man-
+ner described in Fig. 2.
+Table 5 shows the sum-
+mary of the performance comparison in these cases
+with the expected results. Our statistical test shows
+that the induced correct knowledge does not cor-
+rect on average more incorrect active and/or inactive
+edges than expected. Therefore, using the informa-
+tion from induced knowledge does not have addi-
+tional impact than expected in the global optimiza-
+tion scheme. However, this is likely due to the fact
+that the structure of the expected causal graph, Gexp
+is not well-posed. It’s worth noting that Gexp isn’t
+necessarily a DAG since there isn’t any constraining
+mechanism to enforce acyclicity as compared to Gpred
+(NOTEARS imposes hard acyclicity constaint in the
+continuous optimization). Although it is to be noted
+here that solving an acyclicity constrained optimiza-
+tion problem does not guarantee to return a DAG and
+Ng et al. (Ng et al., 2022) in their study illustrates on
+this behavior and proposes the convergence guarantee
+with a DAG solution.
+4.4
+Real Data
+We evaluate the implication of incorporating expert
+knowledge on the dataset from study in Ref. (Sachs
+et al., 2005), which is largely used in the literature of
+probabilistic graphical models with a consensus net-
+work accepted by the biological community.
+This
+dataset contains the expression levels of phosphory-
+lated proteins and phospholipids in human cells under
+different conditions. The dataset has d = 11 cell types
+along with n = 7466 samples of expression levels. As
+for the ground truth of the underlying causal graph,
+we considered s0 = 20 active edges as suggested by
+the study (Sachs et al., 2005).
+We have opted for
+∆TPR, the percentage difference of edges in agree-
+ment (higher is better), and the percentage difference
+of reversed edges (lower is better) as the evaluation
+metrics since the performance on these metrics would
+indicate the significance more distinctively. Similar
+to the synthetic data analysis, we had 10 trials that
+we used to summarize our evaluation. Our empiri-
+cal result (Mean ± Stderr.) shows: ∆TPR as 0.020
+± 0.004, the percentage difference of edges in agree-
+ment as 0.393 ± 0.086, and the percentage difference
+of reversed edges as -0.073 ± 0.030. We have found
+that with the help of induced knowledge the model
+shows statistically significant improvement by cor-
+rectly identifying more active edges and by reducing
+the number of edges identified in the reverse direc-
+tion. Due to the limitation of having access only to a
+subset of the true active edges, our analyses could not
+include a comparative study on known inactive edges
+as in the synthetic data case. We assume the perfor-
+mance could have been improved by fine-tuning the
+model’s parameters but since our main focus of this
+study is entirely based on the analyses regarding the
+impact of induced knowledge of different types and
+from different sources on structure learning, we kept
+the parameter setup similar for all consecutive steps
+in the knowledge induction process.
+5
+CONCLUSIONS
+We have studied the impact of expert causal knowl-
+edge on causal structure learning and provided a set
+Table 4: Comparison between the impact of inducing knowledge regarding inactive vs active edges.
+Metric
+Inactive
+Active
+Better
+∆FDR
+-0.019 ± 0.002
+-0.008 ± 0.001
+inactive
+∆TPR
+-0.007 ± 0.003
+0.024 ± 0.003
+active
+∆FPR
+-0.023 ± 0.004
+-0.009 ± 0.004
+inactive
+∆SHD
+-0.033 ± 0.013
+-0.072 ± 0.011
+active
+
+Table 5: Comparison between the empirical performance vs expectation.
+Metric
+Knowledge
+Empirical
+Expected
+Remarks
+∆FDR
+inactive
+-0.019 ± 0.002
+-0.016 ± 0.002
+No difference
+∆FDR
+active
+-0.008 ± 0.001
+-0.006 ± 0.001
+No difference
+∆TPR
+inactive
+-0.007 ± 0.003
+-0.002 ± 0.003
+No difference
+∆TPR
+active
+0.024 ± 0.003
+0.022 ± 0.002
+No difference
+∆FPR
+inactive
+-0.023 ± 0.004
+-0.021 ± 0.004
+No difference
+∆FPR
+active
+-0.009 ± 0.003
+-0.007 ± 0.003
+No difference
+∆SHD
+inactive
+-0.033 ± 0.013
+-0.047 ± 0.010
+No difference
+∆SHD
+active
+-0.072 ± 0.011
+-0.056 ± 0.010
+No difference
+of comparative analyses of biasing the model using
+different types of knowledge. Our findings show that
+knowledge that corrects model’s mistakes yields sig-
+nificant improvements and it does no harm even in the
+case of redundant knowledge that results in redundant
+constraints. This suggest that the practitioners should
+consider incorporating domain knowledge whenever
+available.
+More importantly, we have found that
+knowledge related to active edges has a larger positive
+impact on causal discovery than knowledge related to
+inactive edges which can mostly be attributed to the
+difference between the number of degrees of freedom
+each case reduces. This finding suggest that the prac-
+titioners may want to prioritize incorporating knowl-
+edge regarding presence of an edge whenever appli-
+cable. Furthermore, our experimental analysis shows
+that the induced knowledge does not correct on av-
+erage more incorrect active and/or inactive edges than
+expected. This finding is rather surprising to us, as we
+have expected that every constraint based on a known
+active/inactive edge to impact and correct more than
+one edge on average.
+Our work points to the importance of the human-
+in-the-loop in causal discovery that we would like to
+further explore in our future studies. Also, we would
+like to mention that in our study we adopted hard con-
+straints to accommodate the prior knowledge since we
+have assumed our priors to be correct. An interesting
+future direction would be to accommodate the contin-
+uous optimization with functionality to allow differ-
+ent levels of confidence on the priors.
+ACKNOWLEDGEMENTS
+Research was sponsored by the Army Research Of-
+fice and was accomplished under Grant Number
+W911NF-22-1-0035. The views and conclusions con-
+tained in this document are those of the authors and
+should not be interpreted as representing the official
+policies, either expressed or implied, of the Army
+Research Office or the U.S. Government. The U.S.
+Government is authorized to reproduce and distribute
+reprints for Government purposes notwithstanding
+any copyright notation herein.
+REFERENCES
+Alrajeh, D., Chockler, H., and Halpern, J. Y. (2020). Com-
+bining experts’ causal judgments.
+Artificial Intelli-
+gence, 288:103355.
+Andrews, B., Spirtes, P., and Cooper, G. F. (2020). On the
+completeness of causal discovery in the presence of la-
+tent confounding with tiered background knowledge.
+In International Conference on Artificial Intelligence
+and Statistics, pages 4002–4011. PMLR.
+Bertsekas, D. P. (1997). Nonlinear programming. Journal
+of the Operational Research Society, 48(3):334–334.
+Bhattacharjya, D., Gao, T., Mattei, N., and Subramanian, D.
+(2021). Cause-effect association between event pairs
+in event datasets. In Proceedings of the Twenty-Ninth
+International Conference on International Joint Con-
+ferences on Artificial Intelligence, pages 1202–1208.
+Bradley, R., Dietrich, F., and List, C. (2014). Aggregating
+causal judgments. Philosophy of Science, 81(4):491–
+515.
+Chickering, D. M. (1996). Learning Bayesian networks is
+NP-complete. In Learning from data, pages 121–130.
+Springer.
+Chickering, D. M. (2002). Optimal structure identification
+with greedy search. Journal of machine learning re-
+search, 3(Nov):507–554.
+Chickering, M., Heckerman, D., and Meek, C. (2004).
+Large-sample learning of Bayesian networks is NP-
+hard. Journal of Machine Learning Research, 5.
+Colombo, D., Maathuis, M. H., Kalisch, M., and Richard-
+son, T. S. (2012). Learning high-dimensional directed
+acyclic graphs with latent and selection variables. The
+Annals of Statistics, pages 294–321.
+Cooper, G. (1995). Causal discovery from data in the pres-
+ence of selection bias.
+In Proceedings of the Fifth
+International Workshop on Artificial Intelligence and
+Statistics, pages 140–150.
+Elkan, C. (2001). The foundations of cost-sensitive learn-
+ing. In International joint conference on artificial in-
+telligence, volume 17, pages 973–978. Lawrence Erl-
+baum Associates Ltd.
+
+Fang, Z., Zhu, S., Zhang, J., Liu, Y., Chen, Z., and He, Y.
+(2020). Low rank directed acyclic graphs and causal
+structure learning. arXiv preprint arXiv:2006.05691.
+Gencoglu, O. and Gruber, M. (2020).
+Causal modeling
+of twitter activity during Covid-19.
+Computation,
+8(4):85.
+Heindorf,
+S.,
+Scholten,
+Y.,
+Wachsmuth,
+H.,
+Ngonga Ngomo, A.-C., and Potthast, M. (2020).
+Causenet: Towards a causality graph extracted from
+the web.
+In Proceedings of the 29th ACM Inter-
+national Conference on Information & Knowledge
+Management, pages 3023–3030.
+Holzinger, A. (2016).
+Interactive machine learning for
+health informatics: when do we need the human-in-
+the-loop? Brain Informatics, 3(2):119–131.
+Jaber, A., Zhang, J., and Bareinboim, E. (2018). Causal
+identification under Markov equivalence.
+arXiv
+preprint arXiv:1812.06209.
+Lachapelle, S., Brouillard, P., Deleu, T., and Lacoste-Julien,
+S. (2019). Gradient-based neural DAG learning. arXiv
+preprint arXiv:1906.02226.
+Lake, B. M., Ullman, T. D., Tenenbaum, J. B., and Gersh-
+man, S. J. (2017). Building machines that learn and
+think like people. Behavioral and brain sciences, 40.
+Li, Z., Ding, X., Liu, T., Hu, J. E., and Van Durme, B.
+(2021). Guided generation of cause and effect. arXiv
+preprint arXiv:2107.09846.
+Liu, J., Chen, Y., and Zhao, J. (2021). Knowledge enhanced
+event causality identification with mention masking
+generalizations. In Proceedings of the Twenty-Ninth
+International Conference on International Joint Con-
+ferences on Artificial Intelligence, pages 3608–3614.
+Magliacane, S., van Ommen, T., Claassen, T., Bongers,
+S., Versteeg, P., and Mooij, J. M. (2017).
+Do-
+main adaptation by using causal inference to pre-
+dict invariant conditional distributions. arXiv preprint
+arXiv:1707.06422.
+Ng, I., Fang, Z., Zhu, S., Chen, Z., and Wang, J.
+(2019). Masked gradient-based causal structure learn-
+ing. arXiv preprint arXiv:1910.08527.
+Ng, I., Ghassami, A., and Zhang, K. (2020). On the role
+of sparsity and DAG constraints for learning linear
+DAGs. arXiv preprint arXiv:2006.10201.
+Ng, I., Lachapelle, S., Ke, N. R., Lacoste-Julien, S., and
+Zhang, K. (2022). On the convergence of continuous
+constrained optimization for structure learning. In In-
+ternational Conference on Artificial Intelligence and
+Statistics, pages 8176–8198. PMLR.
+O’Donnell, R. T., Nicholson, A. E., Han, B., Korb, K. B.,
+Alam, M. J., and Hope, L. R. (2006). Causal discov-
+ery with prior information. In Australasian Joint Con-
+ference on Artificial Intelligence, pages 1162–1167.
+Springer.
+Pearl, J. (2009). Causality. Cambridge university press.
+Pearl, J. and Verma, T. S. (1995). A theory of inferred cau-
+sation.
+In Studies in Logic and the Foundations of
+Mathematics, volume 134, pages 789–811. Elsevier.
+Peters, J., Janzing, D., and Sch¨olkopf, B. (2017). Elements
+of causal inference: foundations and learning algo-
+rithms. The MIT Press.
+Ramsey, J., Glymour, M., Sanchez-Romero, R., and Gly-
+mour, C. (2017). A million variables and more: the
+Fast Greedy Equivalence Search algorithm for learn-
+ing high-dimensional graphical causal models, with
+an application to functional magnetic resonance im-
+ages. International journal of data science and ana-
+lytics, 3(2):121–129.
+Reisach, A., Seiler, C., and Weichwald, S. (2021). Beware
+of the simulated dag! causal discovery benchmarks
+may be easy to game. Advances in Neural Information
+Processing Systems, 34:27772–27784.
+Sachs, K., Perez, O., Pe’er, D., Lauffenburger, D. A., and
+Nolan, G. P. (2005).
+Causal protein-signaling net-
+works derived from multiparameter single-cell data.
+Science, 308(5721):523–529.
+Scutari, M. (2009). Learning bayesian networks with the
+bnlearn r package. arXiv preprint arXiv:0908.3817.
+Sharma, A. and Kiciman, E. (2020).
+Dowhy: An end-
+to-end library for causal inference.
+arXiv preprint
+arXiv:2011.04216.
+Spirtes, P., Glymour, C. N., Scheines, R., and Heckerman,
+D. (2000). Causation, prediction, and search. MIT
+press.
+Wei, D., Gao, T., and Yu, Y. (2020). Dags with no fears:
+A closer look at continuous optimization for learning
+bayesian networks. arXiv preprint arXiv:2010.09133.
+Xin, D., Ma, L., Liu, J., Macke, S., Song, S., and
+Parameswaran, A. (2018).
+Accelerating human-in-
+the-loop machine learning: Challenges and opportu-
+nities. In Proceedings of the second workshop on data
+management for end-to-end machine learning, pages
+1–4.
+Yang, Y., Kandogan, E., Li, Y., Sen, P., and Lasecki, W. S.
+(2019). A study on interaction in human-in-the-loop
+machine learning for text analytics. In IUI Workshops.
+Yu, Y., Chen, J., Gao, T., and Yu, M. (2019). DAG-GNN:
+DAG structure learning with graph neural networks.
+In International Conference on Machine Learning,
+pages 7154–7163. PMLR.
+Zadrozny, B. (2004).
+Learning and evaluating classi-
+fiers under sample selection bias. In Proceedings of
+the twenty-first international conference on Machine
+learning, page 114.
+Zhang, K., Zhu, S., Kalander, M., Ng, I., Ye, J., Chen, Z.,
+and Pan, L. (2021).
+gcastle: A python toolbox for
+causal discovery. arXiv preprint arXiv:2111.15155.
+Zheng, X., Aragam, B., Ravikumar, P., and Xing, E. P.
+(2018).
+DAGs with no tears:
+Continuous op-
+timization for structure learning.
+arXiv preprint
+arXiv:1803.01422.
+Zheng, X., Dan, C., Aragam, B., Ravikumar, P., and Xing,
+E. (2020).
+Learning sparse nonparametric DAGs.
+In International Conference on Artificial Intelligence
+and Statistics, pages 3414–3425. PMLR.
+
+APPENDIX
+A. Threshold Incorporation and Slack Variables
+In Eq. 5, we have seen that our inequality constraint
+takes the following form:
+hp
+ineq(W(θ)) > 0
+where p enumerates over each induced knowledge as-
+sociated with true active edge (known active) Xi → Xj
+imposing [W(θ)]i j ̸= 0. NOTEARS uses a threshold-
+ing step that reduces false discoveries where any edge
+weight below the threshold value, wthresh in its ab-
+solute value is set to zero. Thus, for any induction
+from true active edges (Xi → Xj) we have the follow-
+ing constraint:
+[W(θ)]2
+i j ≥ W 2
+thresh.
+We convert inequality constraints in our optimization
+to equality by introducing a set of slack variables yp
+such that:
+−[W(θ)]2
+i j +W 2
+thresh +yp = 0
+s.t.
+yp ≥ 0
+(10)
+In a similar manner, using the threshold value,
+Wthresh our equality constraints (associated with
+known inactive edges) take the form as:
+[W(θ)]2
+ij −W 2
+thresh +yq = 0
+s.t.
+yq ≥ 0
+(11)
+where q enumerates over each induction asso-
+ciated with true inactive edge Xi ↛ Xj imposing
+[W(θ)]ij = 0.
+B. Additional Results and Summary Statistics
+We illustrate here the detailed performance with sum-
+mary statistics of induced knowledge from our em-
+pirical evaluation (∆FDR, ∆TPR, ∆FPR, and ∆SHD
+for both ∆=1 and ∆=2).
+Similar to one additional
+knowledge (∆=1), we calculate the impact of induc-
+ing two additional piece of knowledge (∆=2) based
+on our model’s prediction i.e.
+on the metric SHD
+(∆SHD2
+pred) as follows:
+∆SHD2
+pred = SHD(Gk+2
+pred)−SHD(Gk
+pred)
+(12)
+Table 6 shows the results for inducing redundant
+knowledge or knowledge that is correctly classified
+by NOTEARS-MLP.
+Table 7 shows the detailed results for inducing
+knowledge that corrects model’s mistake.
+Table 8
+shows the detailed results of the difference between
+the impact of ‘known inactive’ (knowledge induced
+from inactive edges) and ‘known active’ (knowledge
+induced from active edges) using misclassified edge
+set as the knowledge source. Table 9 shows the de-
+tailed results of the difference between empirical im-
+provements due to knowledge induction vs expected
+outcomes using misclassified edge set as the knowl-
+edge source. Table 10 shows the detailed results for
+inducing knowledge on the real dataset (from (Sachs
+et al., 2005)).
+
+Table 6: Full results for inducing redundant knowledge (Sanity Check).
+Metric
+∆
+Mean ± Stderr.
+p-value
+t-stat
+Remarks
+∆FDR
+1
+-0.00030 ± 0.00017
+0.076
+-1.770
+No harm
+∆FDR
+2
+-0.00060 ± 0.00021
+0.004
+-2.850
+No harm
+∆TPR
+1
+-0.00035 ± 0.00027
+0.205
+-1.260
+No harm
+∆TPR
+2
+-0.00036 ± 0.00029
+0.227
+-1.210
+No harm
+∆FPR
+1
+-0.00097 ± 0.00059
+0.100
+-1.630
+No harm
+∆FPR
+2
+-0.00183 ± 0.00069
+0.008
+-2.660
+No harm
+∆SHD
+1
+-0.00154 ± 0.00167
+0.356
+-0.920
+No harm
+∆SHD
+2
+-0.00357 ± 0.00188
+0.050
+-1.900
+No harm
+Table 7: Full results for inducing knowledge that corrects model’s mistake (Section 4.1).
+Metric
+∆
+Knowledge
+Mean ± Stderr.
+p-value
+t-stat
+Improvement
+∆FDR
+1
+inactive
+-0.018, 0.002
+3.41E-14
+-7.800
+Significant
+∆FDR
+1
+active
+-0.008, 0.001
+2.51E-08
+-5.657
+Significant
+∆FDR
+2
+inactive
+-0.023, 0.003
+2.74E-15
+-8.221
+Significant
+∆FDR
+2
+active
+-0.011, 0.002
+9.06E-08
+-5.448
+Significant
+∆TPR
+1
+inactive
+-0.007, 0.003
+3.10E-02
+-2.164
+Not significant
+∆TPR
+1
+active
+0.024, 0.003
+8.58E-19
+9.191
+Significant
+∆TPR
+2
+inactive
+-0.001, 0.003
+8.25E-01
+-0.222
+Not significant
+∆TPR
+2
+active
+0.035, 0.004
+1.16E-19
+9.580
+Significant
+∆FPR
+1
+inactive
+-0.023, 0.004
+3.81E-08
+-5.583
+Significant
+∆FPR
+1
+active
+-0.008, 0.003
+1.21E-02
+-2.517
+Significant
+∆FPR
+2
+inactive
+-0.021, 0.003
+1.04E-08
+-5.845
+Significant
+∆FPR
+2
+active
+-0.015, 0.005
+6.73E-03
+-2.724
+Significant
+∆SHD
+1
+inactive
+-0.032, 0.012
+9.74E-03
+-2.594
+Significant
+∆SHD
+1
+active
+-0.071, 0.011
+1.61E-10
+-6.522
+Significant
+∆SHD
+2
+inactive
+-0.082, 0.012
+1.93E-10
+-6.533
+Significant
+∆SHD
+2
+active
+-0.126, 0.016
+3.41E-14
+-7.875
+Significant
+Table 8: Full results of comparison between the impact of inducing knowledge regarding inactive vs active edges. (Sec-
+tion 4.2).
+Metric
+∆
+Inactive
+Active
+p-value
+t-stat
+Better
+∆FDR
+1
+-0.019 ± 0.002
+-0.008 ± 0.001
+1.30E-04
+-3.85
+Inactive
+∆FDR
+2
+-0.023 ± 0.002
+-0.011 ± 0.001
+5.58E-04
+-3.47
+Inactive
+∆TPR
+1
+-0.007 ± 0.003
+0.024 ± 0.003
+8.13E-14
+-7.57
+Active
+∆TPR
+2
+-0.001 ± 0.003
+0.035 ± 0.004
+2.84E-13
+-7.43
+Active
+∆FPR
+1
+-0.023 ± 0.004
+-0.009 ± 0.004
+7.28E-03
+-2.69
+Inactive
+∆FPR
+2
+-0.021 ± 0.004
+-0.015 ± 0.005
+3.23E-01
+-0.99
+No difference
+∆SHD
+1
+-0.033 ± 0.013
+-0.072 ± 0.011
+1.90E-02
+2.35
+Active
+∆SHD
+2
+-0.082 ± 0.013
+-0.126 ± 0.016
+3.28E-02
+2.14
+Active
+
+Table 9: Full results of comparison between the empirical performance vs expectation (Section 4.3).
+Metric
+∆
+Knowledge
+Empirical
+Expected
+p-value
+t-stat
+Remarks
+∆FDR
+1
+inactive
+-0.019 ± 0.002
+-0.016 ± 0.002
+0.51
+-0.65
+No difference
+∆FDR
+1
+active
+-0.008 ± 0.001
+-0.006 ± 0.001
+0.21
+-1.25
+No difference
+∆FDR
+2
+inactive
+-0.023 ± 0.002
+-0.025 ± 0.002
+0.60
+0.53
+No difference
+∆FDR
+2
+active
+-0.011 ± 0.002
+-0.010 ± 0.002
+0.75
+-0.32
+No difference
+∆TPR
+1
+inactive
+-0.007 ± 0.003
+-0.002 ± 0.003
+0.22
+-1.23
+No difference
+∆TPR
+1
+active
+0.024 ± 0.003
+0.022 ± 0.002
+0.48
+0.70
+No difference
+∆TPR
+2
+inactive
+-0.001 ± 0.003
+-0.006 ± 0.003
+0.24
+1.17
+No difference
+∆TPR
+2
+active
+0.035 ± 0.004
+0.028 ± 0.004
+0.18
+1.34
+No difference
+∆FPR
+1
+inactive
+-0.023 ± 0.004
+-0.021 ± 0.004
+0.62
+-0.50
+No difference
+∆FPR
+1
+active
+-0.009 ± 0.003
+-0.007 ± 0.003
+0.79
+-0.27
+No difference
+∆FPR
+2
+inactive
+-0.021 ± 0.004
+-0.030 ± 0.005
+0.18
+1.34
+No difference
+∆FPR
+2
+active
+-0.015 ± 0.005
+-0.018 ± 0.005
+0.61
+0.51
+No difference
+∆SHD
+1
+inactive
+-0.033 ± 0.013
+-0.047 ± 0.010
+0.36
+0.91
+No difference
+∆SHD
+1
+active
+-0.072 ± 0.011
+-0.056 ± 0.010
+0.30
+-1.04
+No difference
+∆SHD
+2
+inactive
+-0.082 ± 0.013
+-0.086 ± 0.013
+0.82
+0.23
+No difference
+∆SHD
+2
+active
+-0.126 ± 0.016
+-0.100 ± 0.017
+0.28
+-1.09
+No difference
+Table 10: Full results for inducing knowledge in real data (Section 4.4).
+Metric
+∆
+Mean ± Stderr.
+p-value
+t-stat
+Remarks
+∆TPR
+1
+0.020 ± 0.004
+8.10E-06
+4.60
+Improvement
+∆TPR
+2
+0.036 ± 0.005
+1.77E-12
+7.62
+Improvement
+∆ % edge in agreement
+1
+0.393 ± 0.086
+8.10E-06
+4.60
+Improvement
+∆ % edge in agreement
+2
+0.714 ± 0.094
+1.77E-12
+7.62
+Improvement
+∆ % edge reversed
+1
+-0.073 ± 0.030
+1.54E-02
+-2.45
+Improvement
+∆ % edge reversed
+2
+-0.107 ± 0.033
+1.29E-03
+-3.27
+Improvement
+
diff --git a/adAzT4oBgHgl3EQf2v4D/content/tmp_files/load_file.txt b/adAzT4oBgHgl3EQf2v4D/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0ffaaef9b7abc4faf8a5f942493ae81f18f8c9bc
--- /dev/null
+++ b/adAzT4oBgHgl3EQf2v4D/content/tmp_files/load_file.txt
@@ -0,0 +1,1012 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf,len=1011
+page_content='Evaluation of Induced Expert Knowledge in Causal Structure Learning  by NOTEARS  Jawad Chowdhury, Rezaur Rashid and Gabriel Terejanu  Dept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' of Computer Science, University of North Carolina at Charlotte, Charlotte, NC, USA  mchowdh5@uncc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='edu, mrashid1@uncc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='edu, gabriel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='terejanu@uncc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='edu  Keywords:  Causality, Structured Prediction and Learning, Supervised Deep Learning, Optimization for Neural Networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Abstract:  Causal modeling provides us with powerful counterfactual reasoning and interventional mechanism to generate  predictions and reason under various what-if scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' However, causal discovery using observation data  remains a nontrivial task due to unobserved confounding factors, finite sampling, and changes in the data  distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' These can lead to spurious cause-effect relationships.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' To mitigate these challenges in practice,  researchers augment causal learning with known causal relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' The goal of the paper is to study the impact  of expert knowledge on causal relations in the form of additional constraints used in the formulation of the  nonparametric NOTEARS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' We provide a comprehensive set of comparative analyses of biasing the model  using different types of knowledge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' We found that (i) knowledge that correct the mistakes of the NOTEARS  model can lead to statistically significant improvements, (ii) constraints on active edges have a larger positive  impact on causal discovery than inactive edges, and surprisingly, (iii) the induced knowledge does not correct  on average more incorrect active and/or inactive edges than expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' We also demonstrate the behavior of the  model and the effectiveness of domain knowledge on a real-world dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  1  INTRODUCTION  Machine learning models have been breaking records  in terms of achieving higher predictive accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Nevertheless, out-of-distribution (OOD) generaliza-  tion remains a challenge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' One solution is adopting  causal structures (Lake et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2017) to constrain the  models and remove spurious correlations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' The un-  derlying causal knowledge of the problem of inter-  est can significantly help with domain adaptability  and OOD generalization (Magliacane et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Furthermore, causal models go beyond the capability  of correlation-based models to produce predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  They provide us with the powerful counterfactual rea-  soning and interventional mechanism to reason under  various what-if scenarios (Pearl, 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Two of the most prominent approaches in ob-  servational causal discovery are constraint-based and  score-based methods (Spirtes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2000;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Pearl and  Verma, 1995;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Colombo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Chickering,  2002;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Ramsey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Although these meth-  ods are quite robust if the underlying assumptions  are true, they are computationally expensive and their  computational complexity increases with the number  of system variables due to the combinatorial nature  of the DAG constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  NOTEARS (Zheng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=',  2018) tackles this problem with an algebraic char-  acterization of acyclicity which reduces the combi-  natorial problem to a continuous constrained opti-  mization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Different approaches (Yu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Lachapelle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Ng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Zheng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=',  2020) have been proposed as the nonlinear or non-  parametric extensions of this linear continuous opti-  mization, which provides flexibility in modeling dif-  ferent causal mechanisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Learning the causal structure purely based on ob-  servational data is not a trivial task due to various  limitations such as finite sampling, unobserved con-  founding factors, selection bias, and measurement er-  rors (Cooper, 1995;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Elkan, 2001;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Zadrozny, 2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  These can result in spurious cause-effect relation-  ships.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' To mitigate these challenges in practice, re-  searchers augment causal learning with prior causal  relations as featured in software packages such as  CausalNex1, causal-learn2, bnlearn (Scutari, 2009),  gCastle (Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2021), and DoWhy (Sharma  and Kiciman, 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Heindorf et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (Heindorf et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=',  2020) in their work attempts to construct the first large  scale open domain causality graph that can be in-  1https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='com/quantumblacklabs/causalnex  2https://https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='com/cmu-phil/causal-learn  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='01817v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='LG]  4 Jan 2023  cluded in the existing knowledge bases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' The work  further analyze and demonstrates the benefits of large  scale causality graph in causal reasoning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Given a  partial ancestral graph (PAG), representing the qual-  itative knowledge of the causal structure, Jaber et  al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (Jaber et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2018) in their study compute the inter-  ventional distribution from observational data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Com-  bining expert knowledge with structural learning fur-  ther constrains the search space minimizing the num-  ber of spurious mechanisms (Wei et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2020) and  researchers often leverage these background knowl-  edge by exploiting them as additional constraints  for knowledge-enhanced event causality identifica-  tion (Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' O’Donnell et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (O’Donnell  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2006) use expert knowledge as prior probabili-  ties in learning Bayesian Network (BN) and Gencoglu  and Gruber (Gencoglu and Gruber, 2020) use the lin-  ear NOTEARS model to incorporate knowledge to  detect how different characteristics of the COVID-19  pandemic are causally related to each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Differ-  ent experts’ causal judgments can be aggregated into  collective ones (Bradley et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2014) and Alrajeh et  al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (Alrajeh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2020) in their work, studied how  these judgments can be combined to determine ef-  fective interventions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' An interesting exploration by  Andrews et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (Andrews et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2020) defines tiered  background knowledge and shows that with this type  of background knowledge the FCI algorithm (Spirtes  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2000) is sound and complete.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  However, understanding how to effectively incor-  porate and evaluating the impact of induced knowl-  edge is yet to be explored and we believe knowledge  regarding this can mitigate some of the challenges  of observational causal discovery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Human expertise  can play a vital role to assess the learned model in  causal structure learning (Bhattacharjya et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' In practice, human assessment and  validation process often take place in an iterative or  sequential manner (Holzinger, 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Xin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' In structure learning, this is more  realistic for a sufficiently large causal network where  one can learn, validate, and induce newly formed  knowledge-set in the learning process following se-  quential feedback loops.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' The goal of this paper is not  to create a new causal discovery algorithm but rather  to study this iterative interaction between prior causal  knowledge from domain experts that takes the form of  model constraints and a state-of-the-art causal struc-  ture learning algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Wei et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (Wei et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2020)  have been the first to augment NOTEARS with addi-  tional optimization constraints to satisfy the Karush-  Kuhn-Tucker (KKT) optimality conditions and Fang  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (Fang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2020) in their work leverages the  low rank assumption in the context of causal DAG  learning by augmented NOTEARS that shows signif-  icant improvements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  However, none of them have  studied the impact of induced knowledge on causal  structure learning by augmenting NOTEARS with the  optimization constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' For completeness, in Sec-  tion 3, we do provide our formulation of nonparamet-  ric NOTEARS (Zheng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2020) with functionality  to incorporate causal knowledge in the form of known  direct causal and non-causal relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Nevertheless,  in this work, we aim to study the impact of expert  causal knowledge on causal structure learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  The main contributions are summarized as fol-  lows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  (1) We demonstrate an iterative modeling  framework to learn causal relations, impose causal  knowledge to constrain the causal graphs, and fur-  ther evaluate the model’s behavior and performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  (2) We empirically evaluate and demonstrate that: (a)  knowledge that corrects model’s mistake can lead to  statistically significant improvements, (b) constraints  on active edges have a larger positive impact on causal  discovery than inactive edges, and (c) the induced  knowledge does not correct on average more incorrect  active and/or inactive edges than expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Finally,  we illustrate the impact of additional knowledge in  causal discovery on a real-world dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  This paper is structured as follows: Section 2 in-  troduces the background on causal graphical models  (CGMs), score-based structure recovery methods, and  a study using the score-based approach formulated  as a continuous optimization and its recent nonpara-  metric extension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' In Section 3, we present our ex-  tension of the nonparametric continuous optimization  to incorporate causal knowledge in structure learning  and detail the proposed knowledge induction process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Section 4 shows the empirical evaluations and com-  parative analyses of the impact of expert knowledge  on the model’s performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Finally, in Section 5, we  summarize our findings and provide a brief discussion  on future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  2  BACKGROUND  In this section, we review the basic concepts related  to causal structure learning and briefly cover a recent  score-based continuous causal discovery approach us-  ing structural equation models (SEMs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='1  Causal Graphical Model (CGM)  A directed acyclic graph (DAG) is a directed graph  without any directed cyclic paths (Spirtes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=',  2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' A causal graphical model CGM(PX,G) can  be defined as a pair of a graph G and an observa-  tional distribution PX over a set of random variables  X = (X1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=',Xd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' The distribution PX is Markovian  with respect to G where G = (V,E) is a DAG that  encodes the causal structures among the random vari-  ables Xi ∈ X (Peters et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' The node i ∈ V  corresponds to the random variable Xi ∈ X and edges  (i, j) ∈ E correspond to the causal relations encoded  by G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' In a causal graphical model, the joint distri-  bution Px can be factorized as p(x) = ∏d  i=1 p(xi|xG  pai)  where XG  pai refers to the set of parents (direct causes)  for the variable Xi in DAG G and for each Xj ∈ XG  pai  there is an edge (Xj → Xi) ∈ E (Peters et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='2  Score-based Structure Recovery  In a structure recovery method, given n i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' obser-  vations in the data matrix X = [x1|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='|xd] ∈ Rn×d,  our goal is to learn the underlying causal relations  encoded by the DAG G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Most of the approaches fol-  low either a constraint-based or a score-based strategy  for observational causal discovery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' A score-based ap-  proach typically concentrates on identifying the DAG  model G that fits the observed set of data X accord-  ing to some scoring criterion S(G,X) over the discrete  space of DAGs D where G ∈ D (Chickering, 2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  The optimization problem for structure recovery in  this case can be defined as follows:  min  G  S(G,X)  subject to  G ∈ D  (1)  The challenge with Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' 1 is that the acyclicity con-  straint in the optimization is combinatorial in nature  and scales exponentially with the number of nodes d  in the graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' This makes the optimization problem  NP-hard (Chickering, 1996;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Chickering et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='3  NOTEARS: Continuous  Optimization for Structure  Learning  NOTEARS (Zheng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2018) is a score-based  structure learning approach which reformulates the  combinatorial optimization problem to a continu-  ous one through an algebraic characterization of the  acyclicity constraint in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' 1 via trace exponen-  tial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' This method encodes the graph G defined over  the d nodes to a weighted adjacency matrix W =  [w1|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='|wd] ∈ Rd×d where wi j ̸= 0 if there is an ac-  tive edge Xi → Xj and wi j = 0 if there is not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' The  weighted adjacency matrix W entails a linear SEM by  Xi = fi(X) + Ni = wT  i X + Ni;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' where Ni is the associ-  ated noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' The authors define a smooth score func-  tion on the weighted matrix as h(W) = tr(eW◦W) − d  where ◦ is the Hadamard product and eM is the ma-  trix exponential of M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' This embedding of the graph  G and the characterization of acyclicity turns the op-  timization in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' 1 into its equivalent:  min  W∈Rd×d  L(W)  subject to  h(W) = 0  (2)  where L(W) is the least square loss over W and h(W)  score defines the DAG-ness of the graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='4  Nonparametric Extension of  NOTEARS  A nonparametric extension of the continuous opti-  mization suggested by a subsequent study (Zheng  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2020) uses partial derivatives for asserting the  dependency of f j on the random variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' The au-  thors define f j ∈ H1(Rd) ⊂ L2(Rd) over the Sobolev  space of square integrable functions whose deriva-  tives are also square integrable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' The authors show  that f j can be independent of random variable Xi if  and only if ||∂i f j||L2 = 0 where ∂i denotes partial  derivative with respect to the i-th variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' This re-  defines the weighted adjacency matrix with W(f) =  W( f1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', fd) ∈ Rd×d where each Wij encodes the  partial dependency of f j on variable Xi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' As a result,  we can equivalently write Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' 2 as follows:  min  f:f j∈H1(Rd),∀ j∈[d]  L( f)  subject to  h(W( f)) = 0  (3)  for all Xj ∈ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Two of the general instances pro-  posed by (Zheng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2020) are:  NOTEARS-  MLP and NOTEARS-Sob.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  A multilayer percep-  tron having h number of hidden layers and σ :  R → R activation function can be defined as  M(X;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='L) = σ(L(h)σ(.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='σ(L(1)X)) where L(l) denotes  the parameters associated with l-th hidden layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  The authors in (Zheng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2020) show that if  ||i-th column of L(1)  j ||2 = 0 then M j(X;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='L) will be  independent of variable Xi which replaces the as-  sociation of partial derivatives in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' 3 and rede-  fines the adjacency matrix as W(θ) with W(θ)ij =  ||i-th column of L(1)  j ||2 where θ = (θ1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=',θd);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' θk de-  noting the set of parameters for the Mk(X;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='L) (k-  th MLP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' With the usage of neural networks and  the augmented Lagrangian method (Bertsekas, 1997)  NOTEARS-MLP solves the constrained problem in  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' 3 as follows:  min  θ F(θ)+λ||θ||1  F(θ) = L(θ)+ ρ  2|h(W(θ))|2 +αh(W(θ))  (4)  Figure 1: Knowledge induction process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' We induce knowl-  edge by carrying over the existing knowledge set along with  a new random correction informed by model mistakes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  3  KNOWLEDGE INDUCTION  In our formulation, we use the multilayer perceptrons  of NOTEARS-MLP proposed by (Zheng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2020)  as our estimators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' We extend this framework to incor-  porate causal knowledge by characterizing the extra  information as additional constraints in the optimiza-  tion in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Knowledge Type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  We distinguish between these  two types of knowledge: (i) known inactive is knowl-  edge from the true inactive edges (absence of direct  causal relation), and (ii) known active is knowledge  from the true active edges (presence of direct causal  relation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Knowledge Induction Process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  We adopt an inter-  active induction process, where the expert knowledge  is informed by the outcome of the causal discovery  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Namely, the knowledge is induced to correct  the mistakes of the model in the causal structure, in  the hope that the new structure is closer to the true  causal graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' This process is applied sequentially by  correcting the mistakes of the model at each step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  In the following subsections we present the formu-  lation of the NOTEARS optimization with constrains  and detail the sequential induction process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='1  Expert Knowledge as Constraints  An induced knowledge associated with a true ac-  tive edge, Xi → Xj (known active) enforces the cor-  responding cell in the adjacency matrix to be non-  zero, [W(θ)]ij ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' We consider this knowledge as  inequality constraint in our extension of the optimiza-  tion such that the following statement holds:  hp  ineq(W(θ)) > 0  (5)  Figure 2: Expected graph formulation: (a) true graph, Gtrue,  (b) predicted graph by model at step k, Gk  pred, (c) induced  knowledge at step (k+1), (d) expected graph at step (k+1),  Gk+1  exp .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Three different examples of many possible predicted  graphs at step (k +1), Gk+1  pred where the model performs (e)  less than expectation, (f) par with expectation, and (g) more  than expectation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  where p enumerates over all the inequality constraints  due to induction from the set of known active and  hineq is the penalty score associated with the viola-  tion of these inequality constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  On the other  hand, knowledge associated with true inactive edge,  Xi ↛ Xj (known inactive) enforces the related cell in  W(θ) to be equal to zero, [W(θ)]ij = 0 if the induction  implies there should not be an edge from Xi to Xj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' We  consider this knowledge as equality constraint in our  optimization such as:  hq  eq(W(θ)) = 0  (6)  where q enumerates over all the equality constraints,  induced from the set of known inactive and heq is the  penalty score associated with the violation of these  equality constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' With these additional constraints  in Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' 5, 6 we extend Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' 3 to incorporate causal  knowledge in the optimization as follows:  min  f:f j∈H1(Rd),∀ j∈[d]  L( f)  subject to  h(W(θ)) = 0,  hq  eq(W(θ)) = 0,  hp  ineq(W(θ)) > 0  (7)  NOTEARS uses a thresholding step on the estimated  edge weights to reduce false discoveries by pruning  all the edges with weights falling below a certain  threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Because of this, in practice, even the equal-  ity constraints in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' 6 become inequalities to allow  for small weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Finally, slack variables are intro-  duced in the implementation to transform the inequal-  ity constraints into equality constraints (see detailed  formulation in Appendix A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  By using the similar strategy suggested by Zheng  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (Zheng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=", 2020) with augmented Lagrangian  method the reframed constrained optimization of  knowledge to  knowledge to  correct mistake  correct mistake  SHD  'pred  ASHL  pred  0  2  1  # induced knowledgeX  X  X  induction  (a)  (c)  (d)  X  X  X  (b)  (e)  (f)  (g)Eq." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' 4 takes the following form:  min  θ F(θ)+λ||θ||1  F(θ) = L(θ)+ ρ  2|h(W(θ))|2 +αh(W(θ))  +∑  p  (ρineq  2  |hp  ineq(W(θ))|2 +αphp  ineq(W(θ)))  +∑  q  (ρeq  2 |hq  eq(W(θ))|2 +αqhq  eq(W(θ)))  (8)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='2  Sequential Knowledge Induction  In case of knowledge induction, the optimization is  run in a sequential manner where the constraints are  informed by the causal mistakes made by the model  in the previous step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' We start with our baseline model  without imposing any additional knowledge from the  true DAG and get the predicted causal graph denoted  by G0  pred in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Then at each iterative step  (k + 1), based on the mistakes in the causal graph  Gk  pred predicted by the NOTEARS-MLP, we select  one additional random piece of knowledge to correct  one of the mistakes, and add it to the set of con-  straints identified in the previous k steps, and rerun  NOTEARS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' We note that a batch of corrections can  also be selected, however for this work we have fo-  cused on estimating the contribution of each piece of  knowledge in the form of known active/inactive edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Our observations are illustrated in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='1, Sec-  tion 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='2, Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='3, and Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Expected Causal Graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  We consider the ex-  pected causal graph, Gk+1  exp at step (k+1) by consider-  ing the case where all the knowledge has successfully  been induced without impacting any other edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Fig-  ure 2d illustrates an example of how we formulate  our expected graph for a particular step in the itera-  tive process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' We note that the correction might yield  a directed graph (Expected Causal Graph) that is not  necessary a DAG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' The objective is to compare the  performance between the causal graph predicted by  NOTEARS and the expected causal graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Our intu-  ition is that the induced knowledge will probably cor-  rect additional incorrect edges, see Figure 2g, yield-  ing a performance better than expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  4  EXPERIMENTS  To empirically evaluate the impact of additional  causal knowledge on causal learning and to keep our  experimental setup similar to the study in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (Zheng  Table 1: Performance metrics considered with their corre-  sponding desirability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Metric  Desirability  ∆FDR  Lower is better  ∆TPR  Higher is better  ∆FPR  Lower is better  ∆SHD  Lower is better  Table 2: Results for inducing redundant knowledge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Metric  Mean ± Stderr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Remarks  ∆FDR  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='00030 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='00017  No harm  ∆TPR  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='00035 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='00027  No harm  ∆FPR  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='00097 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='00059  No harm  ∆SHD  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='00154 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='00167  No harm  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2020), we have used an MLP with 10 hid-  den units and sigmoid activation functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' In all our  experimental setup, we assume the prior knowledge  is correct (agrees with the true DAG).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Despite the  known sensitivity of the NOTEARS algorithm to data  scaling, as demonstrated in previous study (Reisach  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2021), we have conducted experiments using  both unscaled and scaled data to ensure the robustness  of our findings and we are pleased to report that our  conclusions remain unchanged regardless of the scal-  ing of the data, indicating the stability and reliability  of our results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' While we present the results using the  unscaled data for consistency with the original imple-  mentation of NOTEARS (Zheng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2020), it is  important to note that our conclusions hold true even  when the data is scaled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  We investigate the performance of our  formulation and the impact of induced knowledge by  comparing the DAG estimates with the ground truths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  For our simulations with synthetic data, we have con-  sidered 16 different combinations following the sim-  ulation criteria: two random graph models, Erdos-  Renyi (ER) and Scale-Free (SF), number of nodes,  d = {10,20}, sample size, n = {200,1000}, edge  density, s0 = {1d,4d}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' For each of these combina-  tions, we have generated 10 different random graphs  or true DAGs (as 10 trials for a particular combina-  tion) and corresponding data by following nonlinear  data generating process with index models (similar  to the study in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (Zheng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2020) for which  the underlying true DAGs are identifiable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' The results  are summarized over all these 160 random true DAGs  and datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' In our simulations, we have considered  the regularization parameter, λ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' We evaluate  the performance of causal learning based on the mean  and the standard error of different metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' For sta-  tistical significance analysis, we have used t-test with  α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='05 as the significance level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Table 3: Results for inducing knowledge that corrects model’s mistake.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Metric  Knowledge  Mean ± Stderr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Improvement  ∆FDR  inactive  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='018 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='002  Significant  ∆FDR  active  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='008 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='001  Significant  ∆TPR  inactive  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='007 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='003  Not significant  ∆TPR  active  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='024 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='003  Significant  ∆FPR  inactive  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='023 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='004  Significant  ∆FPR  active  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='008 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='003  Significant  ∆SHD  inactive  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='032 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='012  Significant  ∆SHD  active  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='071 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='011  Significant  Metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  For the comparative analysis, we consider  the following performance metrics: False Discovery  Rate (FDR), True Positive Rate (TPR), False Posi-  tive Rate (FPR), and Structural Hamming Distance  (SHD).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' However, since we are evaluating the perfor-  mance over all these 160 random graphs of varying  sizes, we consider Structural Hamming Distance per  node (SHD/d) as our SHD measure that scales with  the number of nodes (FDR, TPR, and FPR scale by  definition).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' To evaluate the impact of induced knowl-  edge, we calculate the differences in the metrics at  different steps (where we have different sizes of in-  duced knowledge set) and referred them as ∆FDR,  ∆TPR, ∆FPR, and ∆SHD, see also Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' For ex-  ample, based on our model’s prediction we calculate  the impact of inducing one additional piece of knowl-  edge on the metric SHD (∆SHDpred) as follows:  ∆SHDpred = SHD(Gk+1  pred)−SHD(Gk  pred)  (9)  Sanity Check - Redundant Knowledge Does No  Harm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  As part of our sanity check, we investigate  the impact of induced knowledge that matches the  causal relationships successfully discovered by the  NOTEARS-MLP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Therefore, in this section, we con-  sider the set of edges that our baseline model cor-  rectly classifies as our knowledge source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Here, we do  not distinguish between the edge types of our induced  knowledge (known inactive & active) since our goal  is to investigate whether having redundant knowl-  edge as additional constraints affects model’s perfor-  mance or not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' The results are illustrated in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Our empirical evaluation shows that adding redun-  dant knowledge does not deteriorate the performance  of NOTEARS-MLP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Our performed statistical test re-  flects that the results after inducing the knowledge  from the correctly classified edge set are not statis-  tically different than the results from the model with-  out these knowledge inductions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' However, we have  noticed that the performance gets worse with highly  regularized models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' This is consistent with observa-  tions by Ng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (Ng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2020) where sparse DAGs  result in missing some of the true active edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='1  Knowledge that Corrects Model’s  Mistake  We first investigate the role of randomly chosen  knowledge that corrects model’s mistake based on  the cause-effect relations of the true graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' There-  fore, in this case, we consider the set of misclassified  edges from the estimated causal graph as the knowl-  edge source for biasing the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' The results are  illustrated in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Our empirical result shows sta-  tistically significant improvements whenever the in-  duced knowledge corrects misclassified edges in the  estimated causal graph except for the case of ∆TPR  with known inactive edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' However, this behavior is  not totally unexpected since knowledge from known  inactive edges helps to get rid of false discoveries or  false positives, which hardly have impact on true pos-  itives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='2  Known Inactive vs Known Active  In this subsection, we are interested in understanding  the impact of different types of induced knowledge  on causal discovery to correct the mistakes in the es-  timated causal graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' As a result, the experimental  setup is similar to Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='1 where we consider the  misclassified edge set as the knowledge source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' We  consider both known inactive and known active types  of knowledge to induce separately and analyze the  differences of their impact on the performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' The  results are illustrated in Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Based on our statis-  tical test, we have found that inducing known inactive  is more effective when we compare the performance  based on FDR and FPR as misclassification of inac-  tive edges has more impact on these metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' On the  other hand, the results show that inducing known ac-  tive is more effective on TPR as misclassification of  active edges has more impact on this metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Inter-  estingly, we have found that known active provides a  significant improvement over known inactive in terms  of SHD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' This can be attributed to the fact that the  induced knowledge based on the true inactive edge  (known inactive) between two random variables, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  from Xi to Xj allows for two extra degrees of freedom  since it is still possible to have no edge at all or an ac-  tive edge from Xj to Xi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' However, the induced knowl-  edge based on the true active edge doesn’t allow any  degrees of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' This type of knowledge is more  restraining for causal graph discovery and therefore  carries more information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='3  Empirical Performance vs  Expectation  In this subsection, we are interested in understand-  ing whether inducing knowledge to correct model’s  mistakes exceeds expected improvement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  The ex-  perimental setup is similar to Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='1 and Sec-  tion 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='2 where we consider the misclassified edge set  as the knowledge source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' We have conducted the ex-  periments using both known inactive and known ac-  tive types of knowledge separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  The expected  causal graph, Gexp is formulated in a similar man-  ner described in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Table 5 shows the sum-  mary of the performance comparison in these cases  with the expected results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Our statistical test shows  that the induced correct knowledge does not cor-  rect on average more incorrect active and/or inactive  edges than expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Therefore, using the informa-  tion from induced knowledge does not have addi-  tional impact than expected in the global optimiza-  tion scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' However, this is likely due to the fact  that the structure of the expected causal graph, Gexp  is not well-posed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' It’s worth noting that Gexp isn’t  necessarily a DAG since there isn’t any constraining  mechanism to enforce acyclicity as compared to Gpred  (NOTEARS imposes hard acyclicity constaint in the  continuous optimization).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Although it is to be noted  here that solving an acyclicity constrained optimiza-  tion problem does not guarantee to return a DAG and  Ng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (Ng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2022) in their study illustrates on  this behavior and proposes the convergence guarantee  with a DAG solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='4  Real Data  We evaluate the implication of incorporating expert  knowledge on the dataset from study in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (Sachs  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2005), which is largely used in the literature of  probabilistic graphical models with a consensus net-  work accepted by the biological community.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  This  dataset contains the expression levels of phosphory-  lated proteins and phospholipids in human cells under  different conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' The dataset has d = 11 cell types  along with n = 7466 samples of expression levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' As  for the ground truth of the underlying causal graph,  we considered s0 = 20 active edges as suggested by  the study (Sachs et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  We have opted for  ∆TPR, the percentage difference of edges in agree-  ment (higher is better), and the percentage difference  of reversed edges (lower is better) as the evaluation  metrics since the performance on these metrics would  indicate the significance more distinctively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Similar  to the synthetic data analysis, we had 10 trials that  we used to summarize our evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Our empiri-  cal result (Mean ± Stderr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=') shows: ∆TPR as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='020  ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='004, the percentage difference of edges in agree-  ment as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='393 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='086, and the percentage difference  of reversed edges as -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='073 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='030.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' We have found  that with the help of induced knowledge the model  shows statistically significant improvement by cor-  rectly identifying more active edges and by reducing  the number of edges identified in the reverse direc-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Due to the limitation of having access only to a  subset of the true active edges, our analyses could not  include a comparative study on known inactive edges  as in the synthetic data case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' We assume the perfor-  mance could have been improved by fine-tuning the  model’s parameters but since our main focus of this  study is entirely based on the analyses regarding the  impact of induced knowledge of different types and  from different sources on structure learning, we kept  the parameter setup similar for all consecutive steps  in the knowledge induction process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  5  CONCLUSIONS  We have studied the impact of expert causal knowl-  edge on causal structure learning and provided a set  Table 4: Comparison between the impact of inducing knowledge regarding inactive vs active edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Metric  Inactive  Active  Better  ∆FDR  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='019 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='002  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='008 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='001  inactive  ∆TPR  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='007 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='003  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='024 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='003  active  ∆FPR  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='023 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='004  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='009 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='004  inactive  ∆SHD  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='033 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='013  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='072 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='011  active  Table 5: Comparison between the empirical performance vs expectation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Metric  Knowledge  Empirical  Expected  Remarks  ∆FDR  inactive  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='019 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='002  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='016 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='002  No difference  ∆FDR  active  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='008 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='001  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='006 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='001  No difference  ∆TPR  inactive  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='007 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='003  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='002 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='003  No difference  ∆TPR  active  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='024 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='003  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='022 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='002  No difference  ∆FPR  inactive  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='023 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='004  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='021 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='004  No difference  ∆FPR  active  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='009 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='003  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='007 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='003  No difference  ∆SHD  inactive  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='033 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='013  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='047 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='010  No difference  ∆SHD  active  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='072 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='011  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='056 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='010  No difference  of comparative analyses of biasing the model using  different types of knowledge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Our findings show that  knowledge that corrects model’s mistakes yields sig-  nificant improvements and it does no harm even in the  case of redundant knowledge that results in redundant  constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' This suggest that the practitioners should  consider incorporating domain knowledge whenever  available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  More importantly, we have found that  knowledge related to active edges has a larger positive  impact on causal discovery than knowledge related to  inactive edges which can mostly be attributed to the  difference between the number of degrees of freedom  each case reduces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' This finding suggest that the prac-  titioners may want to prioritize incorporating knowl-  edge regarding presence of an edge whenever appli-  cable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Furthermore, our experimental analysis shows  that the induced knowledge does not correct on av-  erage more incorrect active and/or inactive edges than  expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' This finding is rather surprising to us, as we  have expected that every constraint based on a known  active/inactive edge to impact and correct more than  one edge on average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Our work points to the importance of the human-  in-the-loop in causal discovery that we would like to  further explore in our future studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Also, we would  like to mention that in our study we adopted hard con-  straints to accommodate the prior knowledge since we  have assumed our priors to be correct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' An interesting  future direction would be to accommodate the contin-  uous optimization with functionality to allow differ-  ent levels of confidence on the priors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  ACKNOWLEDGEMENTS  Research was sponsored by the Army Research Of-  fice and was accomplished under Grant Number  W911NF-22-1-0035.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' The views and conclusions con-  tained in this document are those of the authors and  should not be interpreted as representing the official  policies, either expressed or implied, of the Army  Research Office or the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Government.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' The U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Government is authorized to reproduce and distribute  reprints for Government purposes notwithstanding  any copyright notation herein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  REFERENCES  Alrajeh, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Chockler, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', and Halpern, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Com-  bining experts’ causal judgments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Artificial Intelli-  gence, 288:103355.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Andrews, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Spirtes, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', and Cooper, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' On the  completeness of causal discovery in the presence of la-  tent confounding with tiered background knowledge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  In International Conference on Artificial Intelligence  and Statistics, pages 4002–4011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' PMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Bertsekas, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Nonlinear programming.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Journal  of the Operational Research Society, 48(3):334–334.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Bhattacharjya, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Gao, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Mattei, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', and Subramanian, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Cause-effect association between event pairs  in event datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' In Proceedings of the Twenty-Ninth  International Conference on International Joint Con-  ferences on Artificial Intelligence, pages 1202–1208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Bradley, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Dietrich, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', and List, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Aggregating  causal judgments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Philosophy of Science, 81(4):491–  515.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Chickering, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Learning Bayesian networks is  NP-complete.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' In Learning from data, pages 121–130.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Springer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Chickering, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Optimal structure identification  with greedy search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Journal of machine learning re-  search, 3(Nov):507–554.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Chickering, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Heckerman, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', and Meek, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Large-sample learning of Bayesian networks is NP-  hard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Journal of Machine Learning Research, 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Colombo, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Maathuis, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Kalisch, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', and Richard-  son, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Learning high-dimensional directed  acyclic graphs with latent and selection variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' The  Annals of Statistics, pages 294–321.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Cooper, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Causal discovery from data in the pres-  ence of selection bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  In Proceedings of the Fifth  International Workshop on Artificial Intelligence and  Statistics, pages 140–150.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Elkan, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' The foundations of cost-sensitive learn-  ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' In International joint conference on artificial in-  telligence, volume 17, pages 973–978.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Lawrence Erl-  baum Associates Ltd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Fang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Zhu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Zhang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Chen, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', and He, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Low rank directed acyclic graphs and causal  structure learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' arXiv preprint arXiv:2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='05691.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Gencoglu, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' and Gruber, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Causal modeling  of twitter activity during Covid-19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Computation,  8(4):85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Heindorf,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=',  Scholten,  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=',  Wachsmuth,  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=',  Ngonga Ngomo, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', and Potthast, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Causenet: Towards a causality graph extracted from  the web.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  In Proceedings of the 29th ACM Inter-  national Conference on Information & Knowledge  Management, pages 3023–3030.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Holzinger, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Interactive machine learning for  health informatics: when do we need the human-in-  the-loop?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Brain Informatics, 3(2):119–131.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Jaber, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Zhang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', and Bareinboim, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Causal  identification under Markov equivalence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  arXiv  preprint arXiv:1812.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='06209.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Lachapelle, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Brouillard, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Deleu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', and Lacoste-Julien,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Gradient-based neural DAG learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' arXiv  preprint arXiv:1906.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='02226.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Lake, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Ullman, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Tenenbaum, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', and Gersh-  man, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Building machines that learn and  think like people.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Behavioral and brain sciences, 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Li, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Ding, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Liu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Hu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', and Van Durme, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Guided generation of cause and effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' arXiv  preprint arXiv:2107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='09846.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Liu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Chen, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', and Zhao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Knowledge enhanced  event causality identification with mention masking  generalizations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' In Proceedings of the Twenty-Ninth  International Conference on International Joint Con-  ferences on Artificial Intelligence, pages 3608–3614.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Magliacane, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', van Ommen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Claassen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Bongers,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Versteeg, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', and Mooij, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Do-  main adaptation by using causal inference to pre-  dict invariant conditional distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' arXiv preprint  arXiv:1707.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='06422.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Ng, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Fang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Zhu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Chen, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', and Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Masked gradient-based causal structure learn-  ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' arXiv preprint arXiv:1910.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='08527.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Ng, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Ghassami, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', and Zhang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' On the role  of sparsity and DAG constraints for learning linear  DAGs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' arXiv preprint arXiv:2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='10201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Ng, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Lachapelle, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Ke, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Lacoste-Julien, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', and  Zhang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' On the convergence of continuous  constrained optimization for structure learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' In In-  ternational Conference on Artificial Intelligence and  Statistics, pages 8176–8198.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' PMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  O’Donnell, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Nicholson, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Han, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Korb, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=',  Alam, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', and Hope, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Causal discov-  ery with prior information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' In Australasian Joint Con-  ference on Artificial Intelligence, pages 1162–1167.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Springer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Pearl, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Causality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Cambridge university press.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Pearl, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' and Verma, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' A theory of inferred cau-  sation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  In Studies in Logic and the Foundations of  Mathematics, volume 134, pages 789–811.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Peters, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Janzing, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', and Sch¨olkopf, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Elements  of causal inference: foundations and learning algo-  rithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' The MIT Press.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Ramsey, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Glymour, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Sanchez-Romero, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', and Gly-  mour, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' A million variables and more: the  Fast Greedy Equivalence Search algorithm for learn-  ing high-dimensional graphical causal models, with  an application to functional magnetic resonance im-  ages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' International journal of data science and ana-  lytics, 3(2):121–129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Reisach, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Seiler, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', and Weichwald, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Beware  of the simulated dag!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' causal discovery benchmarks  may be easy to game.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Advances in Neural Information  Processing Systems, 34:27772–27784.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Sachs, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Perez, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Pe’er, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Lauffenburger, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', and  Nolan, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Causal protein-signaling net-  works derived from multiparameter single-cell data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Science, 308(5721):523–529.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Scutari, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Learning bayesian networks with the  bnlearn r package.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' arXiv preprint arXiv:0908.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='3817.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Sharma, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' and Kiciman, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Dowhy: An end-  to-end library for causal inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  arXiv preprint  arXiv:2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='04216.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Spirtes, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Glymour, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Scheines, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', and Heckerman,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Causation, prediction, and search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' MIT  press.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Wei, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Gao, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', and Yu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Dags with no fears:  A closer look at continuous optimization for learning  bayesian networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' arXiv preprint arXiv:2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='09133.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Xin, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Ma, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Liu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Macke, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Song, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', and  Parameswaran, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Accelerating human-in-  the-loop machine learning: Challenges and opportu-  nities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' In Proceedings of the second workshop on data  management for end-to-end machine learning, pages  1–4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Yang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Kandogan, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Sen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', and Lasecki, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' A study on interaction in human-in-the-loop  machine learning for text analytics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' In IUI Workshops.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Yu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Gao, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', and Yu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' DAG-GNN:  DAG structure learning with graph neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  In International Conference on Machine Learning,  pages 7154–7163.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' PMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Zadrozny, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Learning and evaluating classi-  fiers under sample selection bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' In Proceedings of  the twenty-first international conference on Machine  learning, page 114.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Zhang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Zhu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Kalander, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Ng, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Ye, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Chen, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=',  and Pan, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  gcastle: A python toolbox for  causal discovery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' arXiv preprint arXiv:2111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='15155.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Zheng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Aragam, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Ravikumar, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', and Xing, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  DAGs with no tears:  Continuous op-  timization for structure learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  arXiv preprint  arXiv:1803.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='01422.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Zheng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Dan, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Aragam, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', Ravikumar, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', and Xing,  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Learning sparse nonparametric DAGs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  In International Conference on Artificial Intelligence  and Statistics, pages 3414–3425.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' PMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  APPENDIX  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Threshold Incorporation and Slack Variables  In Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' 5, we have seen that our inequality constraint  takes the following form:  hp  ineq(W(θ)) > 0  where p enumerates over each induced knowledge as-  sociated with true active edge (known active) Xi → Xj  imposing [W(θ)]i j ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' NOTEARS uses a threshold-  ing step that reduces false discoveries where any edge  weight below the threshold value, wthresh in its ab-  solute value is set to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Thus, for any induction  from true active edges (Xi → Xj) we have the follow-  ing constraint:  [W(θ)]2  i j ≥ W 2  thresh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  We convert inequality constraints in our optimization  to equality by introducing a set of slack variables yp  such that:  −[W(θ)]2  i j +W 2  thresh +yp = 0  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  yp ≥ 0  (10)  In a similar manner, using the threshold value,  Wthresh our equality constraints (associated with  known inactive edges) take the form as:  [W(θ)]2  ij −W 2  thresh +yq = 0  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  yq ≥ 0  (11)  where q enumerates over each induction asso-  ciated with true inactive edge Xi ↛ Xj imposing  [W(θ)]ij = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Additional Results and Summary Statistics  We illustrate here the detailed performance with sum-  mary statistics of induced knowledge from our em-  pirical evaluation (∆FDR, ∆TPR, ∆FPR, and ∆SHD  for both ∆=1 and ∆=2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Similar to one additional  knowledge (∆=1), we calculate the impact of induc-  ing two additional piece of knowledge (∆=2) based  on our model’s prediction i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  on the metric SHD  (∆SHD2  pred) as follows:  ∆SHD2  pred = SHD(Gk+2  pred)−SHD(Gk  pred)  (12)  Table 6 shows the results for inducing redundant  knowledge or knowledge that is correctly classified  by NOTEARS-MLP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Table 7 shows the detailed results for inducing  knowledge that corrects model’s mistake.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Table 8  shows the detailed results of the difference between  the impact of ‘known inactive’ (knowledge induced  from inactive edges) and ‘known active’ (knowledge  induced from active edges) using misclassified edge  set as the knowledge source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Table 9 shows the de-  tailed results of the difference between empirical im-  provements due to knowledge induction vs expected  outcomes using misclassified edge set as the knowl-  edge source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' Table 10 shows the detailed results for  inducing knowledge on the real dataset (from (Sachs  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=', 2005)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Table 6: Full results for inducing redundant knowledge (Sanity Check).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Metric  ∆  Mean ± Stderr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  p-value  t-stat  Remarks  ∆FDR  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='00030 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='00017  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='076  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='770  No harm  ∆FDR  2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='00060 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='00021  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='004  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='850  No harm  ∆TPR  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='00035 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='00027  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='205  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='260  No harm  ∆TPR  2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='00036 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='00029  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='227  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='210  No harm  ∆FPR  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='00097 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='00059  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='100  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='630  No harm  ∆FPR  2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='00183 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='00069  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='008  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='660  No harm  ∆SHD  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='00154 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='00167  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='356  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='920  No harm  ∆SHD  2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='00357 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='00188  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='050  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='900  No harm  Table 7: Full results for inducing knowledge that corrects model’s mistake (Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Metric  ∆  Knowledge  Mean ± Stderr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  p-value  t-stat  Improvement  ∆FDR  1  inactive  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='018, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='002  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='41E-14  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='800  Significant  ∆FDR  1  active  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='008, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='001  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='51E-08  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='657  Significant  ∆FDR  2  inactive  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='023, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='003  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='74E-15  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='221  Significant  ∆FDR  2  active  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='011, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='002  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='06E-08  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='448  Significant  ∆TPR  1  inactive  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='007, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='003  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='10E-02  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='164  Not significant  ∆TPR  1  active  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='024, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='003  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='58E-19  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='191  Significant  ∆TPR  2  inactive  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='001, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='003  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='25E-01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='222  Not significant  ∆TPR  2  active  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='035, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='004  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='16E-19  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='580  Significant  ∆FPR  1  inactive  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='023, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='004  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='81E-08  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='583  Significant  ∆FPR  1  active  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='008, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='003  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='21E-02  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='517  Significant  ∆FPR  2  inactive  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='021, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='003  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='04E-08  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='845  Significant  ∆FPR  2  active  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='015, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='005  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='73E-03  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='724  Significant  ∆SHD  1  inactive  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='032, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='012  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='74E-03  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='594  Significant  ∆SHD  1  active  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='071, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='011  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='61E-10  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='522  Significant  ∆SHD  2  inactive  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='082, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='012  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='93E-10  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='533  Significant  ∆SHD  2  active  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='126, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='016  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='41E-14  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='875  Significant  Table 8: Full results of comparison between the impact of inducing knowledge regarding inactive vs active edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content=' (Sec-  tion 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Metric  ∆  Inactive  Active  p-value  t-stat  Better  ∆FDR  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='019 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='002  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='008 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='001  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='30E-04  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='85  Inactive  ∆FDR  2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='023 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='002  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='011 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='001  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='58E-04  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='47  Inactive  ∆TPR  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='007 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='003  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='024 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='003  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='13E-14  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='57  Active  ∆TPR  2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='001 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='003  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='035 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='004  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='84E-13  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='43  Active  ∆FPR  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='023 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='004  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='009 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='004  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='28E-03  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='69  Inactive  ∆FPR  2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='021 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='004  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='015 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='005  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='23E-01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='99  No difference  ∆SHD  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='033 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='013  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='072 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='011  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='90E-02  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='35  Active  ∆SHD  2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='082 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='013  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='126 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='016  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='28E-02  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='14  Active  Table 9: Full results of comparison between the empirical performance vs expectation (Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Metric  ∆  Knowledge  Empirical  Expected  p-value  t-stat  Remarks  ∆FDR  1  inactive  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='019 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='002  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='016 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='002  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='51  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='65  No difference  ∆FDR  1  active  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='008 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='001  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='006 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='001  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='21  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='25  No difference  ∆FDR  2  inactive  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='023 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='002  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='025 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='002  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='53  No difference  ∆FDR  2  active  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='011 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='002  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='010 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='002  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='32  No difference  ∆TPR  1  inactive  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='007 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='003  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='002 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='003  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='22  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='23  No difference  ∆TPR  1  active  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='024 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='003  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='022 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='002  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='48  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='70  No difference  ∆TPR  2  inactive  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='001 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='003  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='006 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='003  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='24  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='17  No difference  ∆TPR  2  active  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='035 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='004  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='028 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='004  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='18  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='34  No difference  ∆FPR  1  inactive  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='023 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='004  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='021 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='004  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='62  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='50  No difference  ∆FPR  1  active  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='009 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='003  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='007 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='003  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='79  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='27  No difference  ∆FPR  2  inactive  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='021 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='004  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='030 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='18  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='34  No difference  ∆FPR  2  active  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='015 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='018 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='61  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='51  No difference  ∆SHD  1  inactive  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='033 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='013  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='047 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='010  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='36  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='91  No difference  ∆SHD  1  active  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='072 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='011  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='056 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='010  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='30  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='04  No difference  ∆SHD  2  inactive  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='082 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='013  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='086 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='013  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='82  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='23  No difference  ∆SHD  2  active  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='126 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='016  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='100 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='017  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='28  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='09  No difference  Table 10: Full results for inducing knowledge in real data (Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  Metric  ∆  Mean ± Stderr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='  p-value  t-stat  Remarks  ∆TPR  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='020 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='004  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='10E-06  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='60  Improvement  ∆TPR  2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='036 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='005  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='77E-12  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='62  Improvement  ∆ % edge in agreement  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='393 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='086  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='10E-06  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='60  Improvement  ∆ % edge in agreement  2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='714 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='094  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='77E-12  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='62  Improvement  ∆ % edge reversed  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='073 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='030  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='54E-02  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='45  Improvement  ∆ % edge reversed  2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='107 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='033  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='29E-03  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
+page_content='27  Improvement' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/adAzT4oBgHgl3EQf2v4D/content/2301.01817v1.pdf'}
diff --git a/btAyT4oBgHgl3EQf-PpJ/content/2301.00888v1.pdf b/btAyT4oBgHgl3EQf-PpJ/content/2301.00888v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..2251119a3157b6e88b7d6ca94b8fc32a1d932380
--- /dev/null
+++ b/btAyT4oBgHgl3EQf-PpJ/content/2301.00888v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5f9c98b19c5be1aab6a11cac7b67aa1b508e4607cb61935089579d025ac78dbf
+size 3320164
diff --git a/btAyT4oBgHgl3EQf-PpJ/vector_store/index.faiss b/btAyT4oBgHgl3EQf-PpJ/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..16505517bd57fb52bd33a07549dc8a55348495be
--- /dev/null
+++ b/btAyT4oBgHgl3EQf-PpJ/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6181aa0e58abfdf9362f72aff4715f845b9ae6903d2201c1de5fcebd645a19b7
+size 3735597
diff --git a/btAyT4oBgHgl3EQf-PpJ/vector_store/index.pkl b/btAyT4oBgHgl3EQf-PpJ/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..fc2aa141e83d33af9274b48448d2bb3ddc898241
--- /dev/null
+++ b/btAyT4oBgHgl3EQf-PpJ/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:effef630e7a3e29614c37afe3a4aa08fe6be58d927a22777ac837c7640deae57
+size 143316
diff --git a/btFPT4oBgHgl3EQfBDTK/content/2301.12984v1.pdf b/btFPT4oBgHgl3EQfBDTK/content/2301.12984v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..ed5fa7ea6c8c70e6ff3d52105e1d953556e5ce3e
--- /dev/null
+++ b/btFPT4oBgHgl3EQfBDTK/content/2301.12984v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1d5ff97349f322996cb34b13ff2a4ea97103e563512087ab976b689e5161b973
+size 1882627
diff --git a/btFPT4oBgHgl3EQfBDTK/vector_store/index.faiss b/btFPT4oBgHgl3EQfBDTK/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..63c6368f90bce39f72e67f3c39853edb781244ca
--- /dev/null
+++ b/btFPT4oBgHgl3EQfBDTK/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:92ab3793feb008b3b06120949830ac6c1578e50d7ab7dc2142849e50dc318d5d
+size 4063277
diff --git a/btFPT4oBgHgl3EQfBDTK/vector_store/index.pkl b/btFPT4oBgHgl3EQfBDTK/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..5b22d59ceeb0c71da5299134e5e10659ee43321f
--- /dev/null
+++ b/btFPT4oBgHgl3EQfBDTK/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:64cf060b6cc3fe5fbdf56e05afb7c8b781292880896144781986e85c49854238
+size 149816
diff --git a/c9FJT4oBgHgl3EQfRiy-/content/2301.11496v1.pdf b/c9FJT4oBgHgl3EQfRiy-/content/2301.11496v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..c9dde48bcd3beda863b288a1761ae426f785318a
--- /dev/null
+++ b/c9FJT4oBgHgl3EQfRiy-/content/2301.11496v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:cd28562a2e7b5f8c88e6b1ccf91d7de0c742ccc929cc6ff46a33c0683cc9694d
+size 672414
diff --git a/c9FJT4oBgHgl3EQfRiy-/vector_store/index.faiss b/c9FJT4oBgHgl3EQfRiy-/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..a42e756415b13746aa7f3779b7f08bbd8e9b3058
--- /dev/null
+++ b/c9FJT4oBgHgl3EQfRiy-/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f522cf60a2cb02531ebb4a2f09688478c58cad4b2a0a80614bef09c1b547a264
+size 4522029
diff --git a/c9FJT4oBgHgl3EQfRiy-/vector_store/index.pkl b/c9FJT4oBgHgl3EQfRiy-/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..3a61a7cc34a1857bd807319febd45c61215bf4e4
--- /dev/null
+++ b/c9FJT4oBgHgl3EQfRiy-/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b23103d625f644df1e06865b29f7a85f02f9f05c62a6267430577dd9b9533ad3
+size 180108
diff --git a/cNE0T4oBgHgl3EQfWQCi/content/2301.02276v1.pdf b/cNE0T4oBgHgl3EQfWQCi/content/2301.02276v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..3f7a4014e5bdc4b1af21ad40ddb9eac32f184a92
--- /dev/null
+++ b/cNE0T4oBgHgl3EQfWQCi/content/2301.02276v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ace0942561e3ff84cdce4596f9e6e3a981d3789828e9d55472dc4501d8dde9da
+size 917416
diff --git a/cNE0T4oBgHgl3EQfWQCi/vector_store/index.pkl b/cNE0T4oBgHgl3EQfWQCi/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..88b7fb650f1c8ff95c288ede6934874f37e827c4
--- /dev/null
+++ b/cNE0T4oBgHgl3EQfWQCi/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:abcc521f5b1664786a2d9b053536394fd232b8b73d695b6db4f5abd7804ceff0
+size 373614
diff --git a/cdE5T4oBgHgl3EQffg9z/content/2301.05627v1.pdf b/cdE5T4oBgHgl3EQffg9z/content/2301.05627v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..908a8527fa9b3b42cf057bf9dad4ced0a994c6e4
--- /dev/null
+++ b/cdE5T4oBgHgl3EQffg9z/content/2301.05627v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d46993dd56f64aefec568a4ba37de12b23a7f82ed358d76aaa86905661e43d04
+size 675196
diff --git a/cdE5T4oBgHgl3EQffg9z/vector_store/index.pkl b/cdE5T4oBgHgl3EQffg9z/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..f691213c23aa035d6615a52cc9f6d7fcf3f7c368
--- /dev/null
+++ b/cdE5T4oBgHgl3EQffg9z/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:37fc6fbdb5cf1a6ba4879287941903a3bddf3a3e1608f67def8d3285a4be69cd
+size 85502
diff --git a/d9E1T4oBgHgl3EQfeAT4/content/2301.03203v1.pdf b/d9E1T4oBgHgl3EQfeAT4/content/2301.03203v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..91833b3adc9c6b96bf345e887910250d511ab497
--- /dev/null
+++ b/d9E1T4oBgHgl3EQfeAT4/content/2301.03203v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9b4f6efb6ed546900032198e97981fcb70eb9c6cc93911f15f5d20166e9e1ef5
+size 2406348
diff --git a/ddE1T4oBgHgl3EQfLQO1/content/2301.02975v1.pdf b/ddE1T4oBgHgl3EQfLQO1/content/2301.02975v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..d868561e253dc550a1c1e368408dc4866db6877a
--- /dev/null
+++ b/ddE1T4oBgHgl3EQfLQO1/content/2301.02975v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a16b4bfbdbc2c3b7ad9a6bd1e7f06bb6dafac04fc90e6e735aebbcc7934aad86
+size 319391
diff --git a/ddE1T4oBgHgl3EQfLQO1/vector_store/index.pkl b/ddE1T4oBgHgl3EQfLQO1/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..15cc771d9851f0d7122111663b5fa462d1b66ccc
--- /dev/null
+++ b/ddE1T4oBgHgl3EQfLQO1/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f37ff94a1b5fa80d7b354ef60b779228fa1e2bc20dde91d0a0f03119de863cd5
+size 414714
diff --git a/eNAzT4oBgHgl3EQf3f7y/content/tmp_files/2301.01832v1.pdf.txt b/eNAzT4oBgHgl3EQf3f7y/content/tmp_files/2301.01832v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b575b869933baa672a84a852c27e4ad85b9236ee
--- /dev/null
+++ b/eNAzT4oBgHgl3EQf3f7y/content/tmp_files/2301.01832v1.pdf.txt
@@ -0,0 +1,851 @@
+Availability Adversarial Attack and
+Countermeasures for Deep Learning-based Load
+Forecasting
+Wangkun Xu
+Electrical and Electronic Engineering
+Imperial College London
+London, UK
+wangkun.xu18@imperial.ac.uk
+Fei Teng
+Electrical and Electronic Engineering
+Imperial College London
+London, UK
+f.teng@imperial.ac.uk
+Abstract—The forecast of electrical loads is essential for the
+planning and operation of the power system. Recently, advances
+in deep learning have enabled more accurate forecasts. However,
+deep neural networks are prone to adversarial attacks. Although
+most of the literature focuses on integrity-based attacks, this
+paper proposes availability-based adversarial attacks, which can
+be more easily implemented by attackers. For each forecast
+instance, the availability attack position is optimally solved by
+mixed-integer reformulation of the artificial neural network. To
+tackle this attack, an adversarial training algorithm is proposed.
+In simulation, a realistic load forecasting dataset is considered
+and the attack performance is compared to the integrity-based
+attack. Meanwhile, the adversarial training algorithm is shown
+to significantly improve robustness against availability attacks.
+All codes are available at https://github.com/xuwkk/AAA Load
+Forecast.
+Index Terms—load forecasting, adversarial attack, availability
+attack, adversarial training.
+I. INTRODUCTION
+A. Load Forecasting
+Load forecasting plays an essential role in the operation and
+control of the power system. With more distributed resources
+embedded in the grid, accurate load forecasting also benefits
+the demand-side response. Plenty of researches have been
+done for load forecasting, both deterministic and probabilistic
+[1]. Regression-based models and their variants dominates
+the long-term forecasting while machine learning algorithms,
+such as artificial neural network (ANN) gains more attention
+for short-term forecasting due to its efficiency on feature
+extraction [2]. For instance, feedforward neural network is
+applied in [3]. In addition, long short-term memory (LSTM)
+and convolutional neural net (CNN) are used to remember tem-
+poral information, which can result in state-of-the-art accuracy
+[4].
+B. Adversarial Attack
+The concept of adversarial attack against deep neural net-
+work was firstly discovered by Szegedy et al. [5] where it has
+been shown that a small amount of perturbation on the image
+pixels can result in wrong classification. To generate the attack,
+fast gradient sign method (FGSM) was proposed by assuming
+the local linearity of the loss surface [6]. Although the FGSM
+can reduce the computational burden, it can only produces
+sub-optimal attack vectors. Projected gradient descent (PGD)
+extends the idea of FGSM in which the attack vector is
+solved in a multistep manner to approach the global optima
+[7]. In addition, the most effective approach to combating
+adversarial attacks is to minimize the loss of adversarial
+examples generated at each epoch, which is named adversarial
+training [7].
+Recently, adversarial attacks on time series, especially the
+load forecasting applications, have gained more attention [8].
+Starting from the linear model, Luo et al. compares four
+load forecasting algorithms that can easily fail under data
+integrity attacks [9]. The authors then introduce regularization
+to address the challenge [10]. However, the integrity attacks
+considered in [9], [10] are not specifically designed by the
+forecasting model. In [11], a robust linear regression for data
+availability attack is proposed through min-max optimization.
+In the deep learning era, a cost-oriented integrity attack is
+established to maximize operational cost [12]. In [13], the
+robustness of the deep load forecasting model is guaranteed
+through Bayesian inference.
+C. Contribution
+We observe that the integrity attack is the main source
+of adversarial attacks in deep learning-based load forecasting
+models, and the availability attack is only considered for linear
+models. Considering a ‘man-in-the-middle’ scenario, availabil-
+ity attack is much cheaper than integrity attack as the attacker
+does not need to manipulate the data and repackage the
+packets [14]. Meanwhile, missing data are more common, as
+measurements can be temporally unavailable due to equipment
+failure. To fill this research gap, first, we design the availability
+adversarial attack targeting on piecewise linear neural network
+(PLNN). The optimality of the attack is guaranteed by refor-
+mulating the PLNN into mixed integer linear programming
+(MILP). Second, an adversarial training algorithm is proposed
+that considers both clean and attack accuracy to improve
+arXiv:2301.01832v1  [cs.LG]  4 Jan 2023
+
+the robustness of the PLNN. In the simulation, we compare
+the performance of the availability adversarial attack with
+its integrity counterpart and demonstrate the effectiveness of
+the proposed adversarial training algorithm in a realistic load
+forecasting task.
+II. LOAD FORECASTING MODEL
+Load forecasting problem is defined as a supervised learning
+task where the input to the model is a collection of features,
+such as temperature, and the output is the true load con-
+sumption. Define a dataset space X × Y where X represents
+the input space and Y represents the target load space. To
+train a load forecasting model, a dataset X × Y
+can be
+sample from X × Y where X = [x1, x2, · · · , xN] ∈ RN×p
+and Y = [y1, y2, · · · , yN] ∈ RN. In this paper, the dataset
+from [15] is used which consists of data from the four-year
+metropolitan load at a resolution of one hour. The forecast
+features include K1: air pressure (kW), K2: cloud cover in
+%, K3: humidity in %, K4: temperature in ◦C, K5: wind
+direction in degrees, k6: wind speed in km/h, and K7: temporal
+information. Temporal information that includes the month,
+date, and time is further converted into sine and cosine values
+on the basis of different periods. Consequently, the above
+setting results in p = 12 number of features.
+A deep neural network f(·; θ) : X → Y parameterized on
+θ can be trained to minimize the mean squared error (MSE)
+loss between the targeted and predicted loads:
+L(θ) = 1
+N
+N
+�
+n=1
+(yn − f(xn; θ))2
+(1)
+Stochastic gradient descent (SGD) is broadly used to find
+the local minima θ∗ of (1). At each epoch, the gradient is
+found in a batch Bn of the dataset:
+θ := θ −
+α
+|Bn|∇θ
+�
+�
+�
+(x,y)∈Bn
+(y − f(x; θ))2
+�
+�
+(2)
+where α is a user-defined learning rate.
+Specifically, this paper considers a piecewise linear neural
+network structure with ReLU activation functions before the
+last layer. Therefore, the neural network f(x; θ) with d + 1
+layers (d ≥ 2) can be explicitly written as:
+z1 = x
+zi+1 = max {0, Wizi + bi},
+i = 1, · · · , d − 1
+zd+1 = Wdzd + bd
+(3)
+where Wi and bi are the weight and bias of the i-th layer.
+III. ADVERSARIAL ATTACKS ON LOAD FORECASTING
+In the literature, adversarial attack commonly refers to
+maliciously perturbing a small value in the input data xn,
+that is, integrity adversarial attack. The ‘adversarial’ implies
+that the attacker can maliciously design the attack vector for
+a specific trained ANN and data instance under a white-box
+assumption. However, in this paper, we propose availability
+adversarial attack where the attacker can block part or all of
+the input features.
+A. Integrity Adversarial Attacks
+Referring to the loss function (1), the objective of the
+adversarial attack is to increase the forecast error by perturbing
+δ on the input xn subject to a predefined lp ball ∥ · ∥p. After
+obtaining the trained model θ∗, the integrity adversarial attack
+on (xn, yn) can be written as
+max
+∥δ∥p≤ϵ(yn − f(xn + δ; θ∗))2
+(4)
+Projected gradient descent (PGD)1 can be used to solve (4).
+At each iteration, normalized gradient ascents are operated and
+the resulting data xn + δ is clamped by the norm ball [7].
+Although PGD has proven to be efficient, it is hard to
+obtain the global optima due to the non-convexity of the neural
+network. To approach the global optimality, multi-run strategy
+can be applied. However, it is possible to find global optima
+for small sized neural network under certain structure. Firstly,
+since the square loss in (4) is convex, to formulate a convex
+problem, we can maximize and minimize the forecast values.
+Second, l∞-norm is considered in which each feature can be
+maximally injected by ϵ. Referring to (3), (4) can be rewritten
+as:
+min / maxz1,...,zd+1zd+1
+s.t.
+∥z1 − x∥∞ ≤ ϵ
+zi+1 = max {0, Wizi + bi},
+i = 1, · · · , d − 1
+zd+1 = Wdzd + bd
+(5)
+The optimization problem (5) is non-convex due to the
+maximization constraint caused by ReLU. However, it can
+be easily transformed into an MILP using the big-M method.
+Specifically, (5) is equivalent to [16]:
+min / maxz1,...,zd+1,v1,...,vd−1zd+1
+s.t.
+zi+1 ≥ Wizi + bi,
+i = 1, . . . , d − 1
+zi+1 ≥ 0,
+i = 1, . . . , d − 1
+ui · vi ≥ zi+1,
+i = 1, . . . , d − 1
+Wizi + bi ≥ zi+1 + (1 − vi)li,
+i = 1, . . . , d − 1
+vi ∈ {0, 1}|vi|,
+i = 1, . . . , d − 1
+z1 ≤ x + δ
+z1 ≥ x − δ
+zd+1 = Wdzd + bd
+(6)
+where vi is the auxiliary integer variable related to the ReLU
+activation functions; ui and li are the upper and lower bounds
+for the output of the i-th layer, i.e., li ≤ Wizi + bi ≤ ui, i =
+1, · · · , d−1, which are designed by the user. All the inequality
+constraints in (6) are element-wise. If the inequality is satisfied
+for some optimal solution zi = z∗
+i , i = 1, · · · , d − 1 of (5),
+then the optimal solution of (6) is also an optimal solution of
+(5) [17]. A detailed conversion from (5) to (6) can be found
+in [18].
+1Though the objective of (4) is to maximize the loss; it is common to name
+it descent in the literature.
+
+B. Availability Adversarial Attack
+The integrity attack with the MILP reformulation has been
+well studied in the literature. However, it requires the attackers
+not only hijack the sensor measurements from the remote
+server, but also have the ability to manipulate their values and
+send them back to the operator. Compared to the integrity
+attack, the availability attack is much cheaper, as it only
+requires the attackers to block measurements [14].
+First, the temporal information, such as month, date and
+time, cannot be attacked as it can be easily obtained and
+verified by the operator. Therefore, only K1-K6 features are
+prone to attack (flexible feature, indexed by Iflex) while the
+temporal feature is fixed (indexed by Ifix). Second, once the
+K1-K6 features are blocked, the operator can have different
+choices to impute the missing value(s). In detail, defining
+an integer vector m ∈ {0, 1}|Iflex| and vector c ∈ Rp, the
+imputed input data can be represented as z1 = diag([m, 1]) ·
+x + diag([1 − m, 0]) · c where 1 and 0 are all one and zero
+vectors with proper dimensions2. The imputed vector c reflects
+the operator’s choice to compensate for the missing features.
+When m(i) = 0, this feature is unavailable and z1(i) = c(i).
+For simplicity, c can be chosen as 0 or the average value
+1
+N
+�
+n xn in this paper.
+Similarly to (5), the optimal availability adversarial attack
+can be obtained by solving the following optimization prob-
+lem:
+min / maxm,z1,...,zd+1zd+1
+s.t.
+z1 = diag([m, 1]) · x + diag([1 − m, 0]) · c
+zi+1 = max {0, Wizi + bi},
+i = 1, · · · , d − 1
+zd+1 = Wdzd + bd
+m ∈ {0, 1}|Iflex|
+|Iflex| −
+�
+m ≤ β
+(7)
+in which the last constraint represents the attacker’s budget.
+For example, at most β number of features can be blocked.
+Using the same big-M technique in (6), (7) can also be
+reformulated as MILP:
+min / maxm,z1,...,zd+1,v1,...,vd−1zd+1
+s.t.
+zi+1 ≥ Wizi + bi,
+i = 1, . . . , d − 1
+zi+1 ≥ 0,
+i = 1, . . . , d − 1
+ui · vi ≥ zi+1,
+i = 1, . . . , d − 1
+Wizi + bi ≥ zi+1 + (1 − vi)li,
+i = 1, . . . , d − 1
+vi ∈ {0, 1}|vi|,
+i = 1, . . . , d − 1
+z1 = diag([m, 1]) · x + diag([1 − m, 0]) · c
+m ∈ {0, 1}|Iflex|
+|Iflex| −
+�
+m ≤ β
+zd+1 = Wdzd + bd
+(8)
+2Without losing generality, we assume that the flexible features are con-
+catenated in front of the fixed features.
+The user-defined layer output bounds ui and li are essential
+to solve (7). First, the solution of (8) may be sub-optimal to
+(7) if the bounds do not cover the output of layer i at the
+optimal value of (7). Second, if the bounds are too large, the
+MILP can be slow to converge. To inform proper bounds on
+the output of each linear layer, convex bound propagation can
+be applied as follows. First, define l0 = u0 = x. Then the
+initial bounds on z1 can be defined as follows:
+l0[Iflex] = min {c, x}
+u0[Iflex] = max {c, x}
+(9)
+Considering (3), the bounds on the output of each layer
+before the last can be propagated by
+ˆli = max {0, li}
+ˆui = max {0, ui}
+li+1 = max {0, Wi} · ˆli + min {0, Wi} · ˆui + bi
+ui+1 = min {0, Wi} · ˆli + max {0, Wi} · ˆui + bi
+(10)
+for i = 0, · · · , d − 2. By the above formulation, there should
+be at least two layers in the network. Otherwise, the ANN will
+become a linear regression.
+Remark 1: A small value can be subtracted and added
+on l0[Iflex] and u0[Iflex] respectively to avoid numerical
+instability when solving MILP.
+IV. ADVERSARIAL TRAINING AGAINST AVAILABILITY
+ATTACK
+To overcome the availability attack defined in (7) and (8),
+adversarial training can be implemented in which the loss of
+the worst-case attack is minimized in each epoch. Defining
+zn = M(m) = diag([m, 1]) · xn + diag([1 − m, 0]) · cn, the
+adversarial loss function is written as
+Ladv(θ) = max
+m
+1
+N
+N
+�
+n=1
+(yn − f(zn; θ))2
+(11)
+Similarly to SGD in clean training (2), (11) can be mini-
+mized iteratively as
+θ := θ −
+α
+|Bn|
+�
+(x,y)∈Bn
+∇θ max
+m (y − f(z; θ))2
+(12)
+According to Danskin’s Theorem [7], the gradient of the
+maximization problem equals the gradient of the loss function
+at the maxima. Therefore,
+∇θ max
+m (y − f(z; θ))2 = ∇θ(y − f(z∗; θ))2
+(13)
+where z∗ is calculated from the optimal solution m∗ of
+the adversarial loss (11). Consequently, the loss function of
+adversarial training for availability attacks can be written as
+Lavai(θ) = L(θ) + βmaxLadv
+max(θ) + βminLadv
+min(θ)
+(14)
+In (14), L(·), Ladv
+max(·), and Ladv
+min(·) represent the clean
+loss, maximization, and minimization of adversarial loss (11)
+respectively. Instead of solely training on the adversarial
+instance, the clean loss is also added to improve the accuracy
+on clean dataset [19].
+
+Remark 2: Although the proposed availability adversarial
+attack and adversarial training are based on feedforward neural
+networks, they can also be extended to other types of piecewise
+linear layer, such as the convolutional layer. Due to the page
+limit, the discussion on convolutional neural networks will be
+left for future work.
+V. SIMULATION AND RESULT
+The optimal integrity and availability adversarial attacks are
+constructed using CVXPY [20] with Gurobi solver. Python
+muti-processing is used to accelerate the MILP optimization in
+(6) and (8). The deep load forecasting model is trained using
+PyTorch on an RTX 3090 graphic card. The outputs of the
+layers in ANN are 40-20-10-1. Adam optimizer is used with
+initial learning rate of 0.0005 and cosine annealing. For the
+original dataset [15], outliers beyond three-sigma are removed
+and we randomly separate the dataset into train and test with
+proportion 8:2. Flexible features are scaled into [0,1]. We train
+the model for 150 epochs and store the weights with best test
+set performance. For adversarial training, the hyperparameters
+are set to βmax = βmin = 1. The accuracy of the load
+forecasting model is reported by mean absolute percentage
+error (MAPE). For clean samples, we measure the distance
+between forecasted and ground-truth loads:
+MAPE = 1
+N
+N
+�
+n=1
+|yclean,n
+pred
+− yn
+true|
+yn
+true
+× 100%
+(15)
+For adversarial samples, we use the mean percentage error
+(MPE) to evaluate their output against the output of the clean
+sample:
+MPE = 1
+N
+N
+�
+n=1
+yadv,n
+pred − yclean,n
+pred
+yclean,n
+pred
+× 100%
+(16)
+as the adversarial attack is formulated on the trained neural
+network.
+In the following discussion, the model trained on clean
+dataset is referred as Clean Model, while the model trained
+through adversarial training is referred as Adver Model.
+Furthermore, to distinguish different attack attempts, we use
+AVAI(mode, c, β) to represent the availability adversarial
+attack with mode∈{max,min} and c ∈ {0, mean}. Similarly,
+INTE(mode, ϵ) represents the integrity adversarial attack with
+attack strength ϵ.
+A. Performance of Availability Adversarial Attack
+Fig. 1 compares the MPE deviation on the clean model un-
+der the availability adversarial attacks. In each of the box plot,
+the box represents the inter-quartile range (IQR) extending
+from the first quartile to the third of the data. The median of
+the data is indicated by the orange line. The whiskers cover
+the whole range of data. First, increasing the attack budget
+β can increase the output deviations. However, this trend is
+not significant when β ≥ 3. The output deviations with zero
+imputation c = 0 is more intense than average imputation as
+no feature information can be extracted. Second, different data
+can have different vulnerabilities on the availability attack. For
+example, some samples can maintain the output with MPE=0
+while others are altered significantly.
+1
+2
+3
+4
+5
+6
+0
+10
+20
+30
+MPE
+(a) AVAI(max, 0, β)
+1
+2
+3
+4
+5
+6
+0
+10
+20
+30
+MPE
+(b) AVAI(max, mean, β)
+1
+2
+3
+4
+5
+6
+80
+60
+40
+20
+0
+MPE
+(c) AVAI(min, 0, β)
+1
+2
+3
+4
+5
+6
+80
+60
+40
+20
+0
+MPE
+(d) AVAI(min, mean, β)
+Fig. 1: MPEs on the clean model under availability adversarial
+attacks.
+To better see the dependency of attack performance on the
+attack budget β, Fig. 2 records the number of actual missing
+features under AVAI(min, mean, β) attack (corresponding to
+Fig. 1(d)). First, it is clearly shown that a small proportion
+of data cannot be attacked regardless of the choices of β,
+which results in MPE=0. These data points are least sensitive
+to AVAI(min, mean, β) attack, as blocking any subset of their
+features can only increase the load forecast. Second, most of
+the actual missing numbers locate at 3 even when β = 6. This
+further implies that in most cases, blocking more features may
+not result in a stronger attack, although increasing β can have
+more flexibility to allocate the attack position.
+Fig. 3 records the MPE of integrity adversarial attacks
+solved by MILP (6). The median MPEs of availability attacks
+with β = 6 are also plotted as a reference. When maximizing
+the load forecast (Fig. 3(a)), availability attacks can give output
+deviations comparable to integrity attacks when ϵ is small, e.g.
+with ϵ = 0.1. However, when ϵ increases, the MPE of the
+integrity attack is much higher than the availability attacks.
+When minimizing the load forecast (Fig. 3(b)), AVAI(min,
+mean, 6) can persistently outperform integrity attacks. Since
+the input features are scaled into [0, 1], it is not realistic to
+have ϵ larger than 0.2. Meanwhile, as it is is much cheaper
+than the integrity attack, the availability attack is a promising
+attack strategy for the attacker. However, how to balance the
+cost and impact of this attack is unsolved and we will leave
+it for future work.
+Solving the MILP can be time consuming, especially when
+the number of integer variables is large. The computational
+time of both availability attacks are summarized in Table I. As
+adversarial training requires solving the optimal availability
+attacks, faster computation is beneficial to efficient training.
+
+0
+1
+2
+3
+4
+5
+6
+Actual Missing No.
+0
+1000
+2000
+3000
+4000
+5000
+6000
+Data No.
+(a) β = 1
+0
+1
+2
+3
+4
+5
+6
+Actual Missing No.
+0
+1000
+2000
+3000
+4000
+5000
+6000
+Data No.
+(b) β = 2
+0
+1
+2
+3
+4
+5
+6
+Actual Missing No.
+0
+1000
+2000
+3000
+4000
+5000
+6000
+Data No.
+(c) β = 3
+0
+1
+2
+3
+4
+5
+6
+Actual Missing No.
+0
+1000
+2000
+3000
+4000
+5000
+6000
+Data No.
+(d) β = 4
+0
+1
+2
+3
+4
+5
+6
+Actual Missing No.
+0
+1000
+2000
+3000
+4000
+5000
+6000
+Data No.
+(e) β = 5
+0
+1
+2
+3
+4
+5
+6
+Actual Missing No.
+0
+1000
+2000
+3000
+4000
+5000
+6000
+Data No.
+(f) β = 6
+Fig. 2: Actual missing numbers under different attack budget
+β. The AVAI(min, mean, β) attack strategy is used.
+0.1
+0.2
+0.3
+0.4
+0.5
+0
+10
+20
+30
+40
+50
+MPE
+AVAI(max,0,6)
+AVAI(max,mean,6)
+(a) INTE(max, ϵ)
+0.1
+0.2
+0.3
+0.4
+0.5
+60
+50
+40
+30
+20
+10
+0
+MPE
+AVAI(min,0,6)
+AVAI(min,mean,6)
+(b) INTE(min, ϵ)
+Fig. 3: MPE on the clean model under integrity adversarial
+attacks.
+Recall that the size of the dataset is 32k, which requires
+half hour to train single epoch. After using parallel compu-
+tation, the computational time is significantly reduced to 1.7
+min/epoch, which is acceptable for a real-time application.
+TABLE I: Average Computational Time (ms/sample)
+Attack Types
+Time
+AVAI-Parallel
+3.16
+AVAI-Sequential
+49.73
+B. Performance of Adversarial Training
+Adversarial training is implemented in this section. Since
+there are two imputation strategies discussed in this paper, the
+performances are reported on both models trained adversarially
+with c = 0 and c = mean. In addition, the attack budget is
+set to β = 6 in adversarial training.
+First, the MAPEs on the clean samples for both clean
+model and adversarial model are summarized in Table II.
+Adversarial training can inevitably deteriorate the performance
+of the model in clean samples by 1.0%. As c = 0 is a stronger
+attack attempt than c = mean, model trained on AVAI(mode,
+0, 6) has higher MAPE than it trained on AVAI(mode, mean,
+6).
+Second, the MPE on the adversarially attacked samples
+under different training situations are summarized in Fig. 4.
+After the adversarial training, the MPEs are reduced by more
+than 50% in general. The stronger adversarial training situation
+with c = 0 can have better robustness, but sacrifices more in
+clean accuracy (Table II). It is interesting to observe that the
+model trained with c = 0 can also have better performance
+on AVAI(mode, mean, 6) than the model trained directly with
+c = mean. Moreover, the performance of model trained with
+c = 0 has slightly higher MPEs than the model trained with
+c = mean. Referring to (14), both AVAI(max, c, 6) and
+AVAI(min, c, 6) attacks contribute equally to the adversarial
+loss function. Therefore, the gradient descent tries to balance
+them during the training, although the AVAI(min, 0, 6) is
+much stronger than AVAI(max, 0, 6). To solve the problem,
+the hyperparameters can be set to βmax > 1 > βmin > 0 in
+(14).
+TABLE II: MAPE on clean samples (in %).
+Clean
+Adver (c=0)
+Adver (c=mean)
+Train
+5.81
+6.83
+6.76
+Test
+6.07
+6.95
+6.88
+1
+2
+3
+4
+5
+6
+0
+1
+2
+3
+4
+MPE
+Clean
+Adver c = 0.0
+Adver c = mean
+(a) AVAI(max, 0, β)
+1
+2
+3
+4
+5
+6
+0
+1
+2
+3
+4
+MPE
+Clean
+Adver c = 0.0
+Adver c = mean
+(b) AVAI(max, mean, β)
+1
+2
+3
+4
+5
+6
+20
+15
+10
+5
+0
+MPE
+Clean
+Adver c = 0.0
+Adver c = mean
+(c) AVAI(min, 0, β)
+1
+2
+3
+4
+5
+6
+3.0
+2.5
+2.0
+1.5
+1.0
+0.5
+0.0
+MPE
+Clean
+Adver c = 0.0
+Adver c = mean
+(d) AVAI(min, mean, β)
+Fig. 4: Performances of adversarial training on availability
+attacks. The medians are taken for all samples in test dataset.
+VI. CONCLUSION
+This paper proposes a new availability adversarial attack
+on load forecasting model constructed by piece-wise linear
+
+neural network. The attack is optimally found through MILP
+subject to certain attack budget, and a countermeasure is
+given through adversarial training. The simulation results show
+that the availability attack can achieve attack performance
+comparable to that of the integrity counterpart. Meanwhile,
+adversarial training can effectively reduce MPE by more than
+50% on the adversarial samples while only increasing 1%
+MAPE on the clean samples.
+REFERENCES
+[1] T. Hong and S. Fan, “Probabilistic electric load forecasting: A tutorial
+review,” International Journal of Forecasting, vol. 32, no. 3, pp. 914–
+938, 2016.
+[2] C. Kuster, Y. Rezgui, and M. Mourshed, “Electrical load forecasting
+models: A critical systematic review,” Sustainable cities and society,
+vol. 35, pp. 257–270, 2017.
+[3] J. Zhang, Y. Wang, and G. Hug, “Cost-oriented load forecasting,”
+Electric Power Systems Research, vol. 205, p. 107723, 2022.
+[4] S. H. Rafi, Nahid-Al-Masood, S. R. Deeba, and E. Hossain, “A short-
+term load forecasting method using integrated cnn and lstm network,”
+IEEE Access, vol. 9, pp. 32 436–32 448, 2021.
+[5] C. Szegedy, W. Zaremba, I. Sutskever, J. Bruna, D. Erhan, I. Goodfellow,
+and R. Fergus, “Intriguing properties of neural networks,” arXiv preprint
+arXiv:1312.6199, 2013.
+[6] I. J. Goodfellow, J. Shlens, and C. Szegedy, “Explaining and harnessing
+adversarial examples,” arXiv preprint arXiv:1412.6572, 2014.
+[7] A. Madry, A. Makelov, L. Schmidt, D. Tsipras, and A. Vladu, “Towards
+deep learning models resistant to adversarial attacks,” arXiv preprint
+arXiv:1706.06083, 2017.
+[8] H. I. Fawaz, G. Forestier, J. Weber, L. Idoumghar, and P.-A. Muller, “Ad-
+versarial attacks on deep neural networks for time series classification,”
+in 2019 International Joint Conference on Neural Networks (IJCNN).
+IEEE, 2019, pp. 1–8.
+[9] J. Luo, T. Hong, and S.-C. Fang, “Benchmarking robustness of load
+forecasting models under data integrity attacks,” International Journal
+of Forecasting, vol. 34, no. 1, pp. 89–104, 2018.
+[10] ——, “Robust regression models for load forecasting,” IEEE Transac-
+tions on Smart Grid, vol. 10, no. 5, pp. 5397–5404, 2018.
+[11] A. Stratigakos, P. Andrianesis, A. Michiorri, and G. Kariniotakis,
+“Towards resilient energy forecasting: A robust optimization approach,”
+2022.
+[12] Y. Chen, M. Sun, Z. Chu, S. Camal, G. Kariniotakis, and F. Teng,
+“Vulnerability and impact of machine learning-based inertia forecasting
+under cost-oriented data integrity attack,” IEEE Transactions on Smart
+Grid, 2022.
+[13] Y. Zhou, Z. Ding, Q. Wen, and Y. Wang, “Robust load forecasting
+towards adversarial attacks via bayesian learning,” IEEE Transactions
+on Power Systems, 2022.
+[14] K. Pan, A. Teixeira, M. Cvetkovic, and P. Palensky, “Cyber risk analysis
+of combined data attacks against power system state estimation,” IEEE
+Transactions on Smart Grid, vol. 10, no. 3, pp. 3044–3056, 2018.
+[15] M. Farrokhabadi, J. Browell, Y. Wang, S. Makonin, W. Su, and
+H. Zareipour, “Day-ahead electricity demand forecasting competition:
+Post-covid paradigm,” IEEE Open Access Journal of Power and Energy,
+vol. 9, pp. 185–191, 2022.
+[16] X. Liu, X. Han, N. Zhang, and Q. Liu, “Certified monotonic neural
+networks,” Advances in Neural Information Processing Systems, vol. 33,
+pp. 15 427–15 438, 2020.
+[17] A. Teixeira, K. C. Sou, H. Sandberg, and K. H. Johansson, “Secure
+control systems: A quantitative risk management approach,” IEEE
+Control Systems Magazine, vol. 35, no. 1, pp. 24–45, 2015.
+[18] Z. Kolter and A. Madry, “Adversarial robustness - theory and practice,”
+2022. [Online]. Available: https://adversarial-ml-tutorial.org/
+[19] H. Zhang, Y. Yu, J. Jiao, E. Xing, L. El Ghaoui, and M. Jordan,
+“Theoretically principled trade-off between robustness and accuracy,”
+in International conference on machine learning.
+PMLR, 2019, pp.
+7472–7482.
+[20] S. Diamond and S. Boyd, “Cvxpy: A python-embedded modeling
+language for convex optimization,” The Journal of Machine Learning
+Research, vol. 17, no. 1, pp. 2909–2913, 2016.
+
diff --git a/eNAzT4oBgHgl3EQf3f7y/content/tmp_files/load_file.txt b/eNAzT4oBgHgl3EQf3f7y/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3daafcdcf18f83759fa76ebf6df4949a4661d29b
--- /dev/null
+++ b/eNAzT4oBgHgl3EQf3f7y/content/tmp_files/load_file.txt
@@ -0,0 +1,447 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf,len=446
+page_content='Availability Adversarial Attack and  Countermeasures for Deep Learning-based Load  Forecasting  Wangkun Xu  Electrical and Electronic Engineering  Imperial College London  London, UK  wangkun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='xu18@imperial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='uk  Fei Teng  Electrical and Electronic Engineering  Imperial College London  London, UK  f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='teng@imperial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='uk  Abstract—The forecast of electrical loads is essential for the  planning and operation of the power system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Recently, advances  in deep learning have enabled more accurate forecasts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' However,  deep neural networks are prone to adversarial attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Although  most of the literature focuses on integrity-based attacks, this  paper proposes availability-based adversarial attacks, which can  be more easily implemented by attackers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' For each forecast  instance, the availability attack position is optimally solved by  mixed-integer reformulation of the artificial neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' To  tackle this attack, an adversarial training algorithm is proposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  In simulation, a realistic load forecasting dataset is considered  and the attack performance is compared to the integrity-based  attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Meanwhile, the adversarial training algorithm is shown  to significantly improve robustness against availability attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  All codes are available at https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='com/xuwkk/AAA Load  Forecast.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  Index Terms—load forecasting, adversarial attack, availability  attack, adversarial training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' INTRODUCTION  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Load Forecasting  Load forecasting plays an essential role in the operation and  control of the power system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' With more distributed resources  embedded in the grid, accurate load forecasting also benefits  the demand-side response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Plenty of researches have been  done for load forecasting, both deterministic and probabilistic  [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Regression-based models and their variants dominates  the long-term forecasting while machine learning algorithms,  such as artificial neural network (ANN) gains more attention  for short-term forecasting due to its efficiency on feature  extraction [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' For instance, feedforward neural network is  applied in [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' In addition, long short-term memory (LSTM)  and convolutional neural net (CNN) are used to remember tem-  poral information, which can result in state-of-the-art accuracy  [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Adversarial Attack  The concept of adversarial attack against deep neural net-  work was firstly discovered by Szegedy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' [5] where it has  been shown that a small amount of perturbation on the image  pixels can result in wrong classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' To generate the attack,  fast gradient sign method (FGSM) was proposed by assuming  the local linearity of the loss surface [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Although the FGSM  can reduce the computational burden, it can only produces  sub-optimal attack vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Projected gradient descent (PGD)  extends the idea of FGSM in which the attack vector is  solved in a multistep manner to approach the global optima  [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' In addition, the most effective approach to combating  adversarial attacks is to minimize the loss of adversarial  examples generated at each epoch, which is named adversarial  training [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  Recently, adversarial attacks on time series, especially the  load forecasting applications, have gained more attention [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  Starting from the linear model, Luo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' compares four  load forecasting algorithms that can easily fail under data  integrity attacks [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' The authors then introduce regularization  to address the challenge [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' However, the integrity attacks  considered in [9], [10] are not specifically designed by the  forecasting model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' In [11], a robust linear regression for data  availability attack is proposed through min-max optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  In the deep learning era, a cost-oriented integrity attack is  established to maximize operational cost [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' In [13], the  robustness of the deep load forecasting model is guaranteed  through Bayesian inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Contribution  We observe that the integrity attack is the main source  of adversarial attacks in deep learning-based load forecasting  models, and the availability attack is only considered for linear  models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Considering a ‘man-in-the-middle’ scenario, availabil-  ity attack is much cheaper than integrity attack as the attacker  does not need to manipulate the data and repackage the  packets [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Meanwhile, missing data are more common, as  measurements can be temporally unavailable due to equipment  failure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' To fill this research gap, first, we design the availability  adversarial attack targeting on piecewise linear neural network  (PLNN).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' The optimality of the attack is guaranteed by refor-  mulating the PLNN into mixed integer linear programming  (MILP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Second, an adversarial training algorithm is proposed  that considers both clean and attack accuracy to improve  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='01832v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='LG]  4 Jan 2023  the robustness of the PLNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' In the simulation, we compare  the performance of the availability adversarial attack with  its integrity counterpart and demonstrate the effectiveness of  the proposed adversarial training algorithm in a realistic load  forecasting task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' LOAD FORECASTING MODEL  Load forecasting problem is defined as a supervised learning  task where the input to the model is a collection of features,  such as temperature, and the output is the true load con-  sumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Define a dataset space X × Y where X represents  the input space and Y represents the target load space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' To  train a load forecasting model, a dataset X × Y  can be  sample from X × Y where X = [x1, x2, · · · , xN] ∈ RN×p  and Y = [y1, y2, · · · , yN] ∈ RN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' In this paper, the dataset  from [15] is used which consists of data from the four-year  metropolitan load at a resolution of one hour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' The forecast  features include K1: air pressure (kW), K2: cloud cover in  %, K3: humidity in %, K4: temperature in ◦C, K5: wind  direction in degrees, k6: wind speed in km/h, and K7: temporal  information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Temporal information that includes the month,  date, and time is further converted into sine and cosine values  on the basis of different periods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Consequently, the above  setting results in p = 12 number of features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  A deep neural network f(·;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' θ) : X → Y parameterized on  θ can be trained to minimize the mean squared error (MSE)  loss between the targeted and predicted loads:  L(θ) = 1  N  N  �  n=1  (yn − f(xn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' θ))2  (1)  Stochastic gradient descent (SGD) is broadly used to find  the local minima θ∗ of (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' At each epoch, the gradient is  found in a batch Bn of the dataset:  θ := θ −  α  |Bn|∇θ  �  �  �  (x,y)∈Bn  (y − f(x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' θ))2  �  �  (2)  where α is a user-defined learning rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  Specifically, this paper considers a piecewise linear neural  network structure with ReLU activation functions before the  last layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Therefore, the neural network f(x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' θ) with d + 1  layers (d ≥ 2) can be explicitly written as:  z1 = x  zi+1 = max {0, Wizi + bi},  i = 1, · · · , d − 1  zd+1 = Wdzd + bd  (3)  where Wi and bi are the weight and bias of the i-th layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' ADVERSARIAL ATTACKS ON LOAD FORECASTING  In the literature, adversarial attack commonly refers to  maliciously perturbing a small value in the input data xn,  that is, integrity adversarial attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' The ‘adversarial’ implies  that the attacker can maliciously design the attack vector for  a specific trained ANN and data instance under a white-box  assumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' However, in this paper, we propose availability  adversarial attack where the attacker can block part or all of  the input features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Integrity Adversarial Attacks  Referring to the loss function (1), the objective of the  adversarial attack is to increase the forecast error by perturbing  δ on the input xn subject to a predefined lp ball ∥ · ∥p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' After  obtaining the trained model θ∗, the integrity adversarial attack  on (xn, yn) can be written as  max  ∥δ∥p≤ϵ(yn − f(xn + δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' θ∗))2  (4)  Projected gradient descent (PGD)1 can be used to solve (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  At each iteration, normalized gradient ascents are operated and  the resulting data xn + δ is clamped by the norm ball [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  Although PGD has proven to be efficient, it is hard to  obtain the global optima due to the non-convexity of the neural  network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' To approach the global optimality, multi-run strategy  can be applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' However, it is possible to find global optima  for small sized neural network under certain structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Firstly,  since the square loss in (4) is convex, to formulate a convex  problem, we can maximize and minimize the forecast values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  Second, l∞-norm is considered in which each feature can be  maximally injected by ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Referring to (3), (4) can be rewritten  as:  min / maxz1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=',zd+1zd+1  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  ∥z1 − x∥∞ ≤ ϵ  zi+1 = max {0, Wizi + bi},  i = 1, · · · , d − 1  zd+1 = Wdzd + bd  (5)  The optimization problem (5) is non-convex due to the  maximization constraint caused by ReLU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' However, it can  be easily transformed into an MILP using the big-M method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  Specifically, (5) is equivalent to [16]:  min / maxz1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=',zd+1,v1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=',vd−1zd+1  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  zi+1 ≥ Wizi + bi,  i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' , d − 1  zi+1 ≥ 0,  i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' , d − 1  ui · vi ≥ zi+1,  i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' , d − 1  Wizi + bi ≥ zi+1 + (1 − vi)li,  i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' , d − 1  vi ∈ {0, 1}|vi|,  i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' , d − 1  z1 ≤ x + δ  z1 ≥ x − δ  zd+1 = Wdzd + bd  (6)  where vi is the auxiliary integer variable related to the ReLU  activation functions;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' ui and li are the upper and lower bounds  for the output of the i-th layer, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=', li ≤ Wizi + bi ≤ ui, i =  1, · · · , d−1, which are designed by the user.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' All the inequality  constraints in (6) are element-wise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' If the inequality is satisfied  for some optimal solution zi = z∗  i , i = 1, · · · , d − 1 of (5),  then the optimal solution of (6) is also an optimal solution of  (5) [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' A detailed conversion from (5) to (6) can be found  in [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  1Though the objective of (4) is to maximize the loss;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' it is common to name  it descent in the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Availability Adversarial Attack  The integrity attack with the MILP reformulation has been  well studied in the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' However, it requires the attackers  not only hijack the sensor measurements from the remote  server, but also have the ability to manipulate their values and  send them back to the operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Compared to the integrity  attack, the availability attack is much cheaper, as it only  requires the attackers to block measurements [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  First, the temporal information, such as month, date and  time, cannot be attacked as it can be easily obtained and  verified by the operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Therefore, only K1-K6 features are  prone to attack (flexible feature, indexed by Iflex) while the  temporal feature is fixed (indexed by Ifix).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Second, once the  K1-K6 features are blocked, the operator can have different  choices to impute the missing value(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' In detail, defining  an integer vector m ∈ {0, 1}|Iflex| and vector c ∈ Rp, the  imputed input data can be represented as z1 = diag([m, 1]) ·  x + diag([1 − m, 0]) · c where 1 and 0 are all one and zero  vectors with proper dimensions2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' The imputed vector c reflects  the operator’s choice to compensate for the missing features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  When m(i) = 0, this feature is unavailable and z1(i) = c(i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  For simplicity, c can be chosen as 0 or the average value  1  N  �  n xn in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  Similarly to (5), the optimal availability adversarial attack  can be obtained by solving the following optimization prob-  lem:  min / maxm,z1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=',zd+1zd+1  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  z1 = diag([m, 1]) · x + diag([1 − m, 0]) · c  zi+1 = max {0, Wizi + bi},  i = 1, · · · , d − 1  zd+1 = Wdzd + bd  m ∈ {0, 1}|Iflex|  |Iflex| −  �  m ≤ β  (7)  in which the last constraint represents the attacker’s budget.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  For example, at most β number of features can be blocked.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  Using the same big-M technique in (6), (7) can also be  reformulated as MILP:  min / maxm,z1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=',zd+1,v1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=',vd−1zd+1  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  zi+1 ≥ Wizi + bi,  i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' , d − 1  zi+1 ≥ 0,  i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' , d − 1  ui · vi ≥ zi+1,  i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' , d − 1  Wizi + bi ≥ zi+1 + (1 − vi)li,  i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' , d − 1  vi ∈ {0, 1}|vi|,  i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' , d − 1  z1 = diag([m, 1]) · x + diag([1 − m, 0]) · c  m ∈ {0, 1}|Iflex|  |Iflex| −  �  m ≤ β  zd+1 = Wdzd + bd  (8)  2Without losing generality, we assume that the flexible features are con-  catenated in front of the fixed features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  The user-defined layer output bounds ui and li are essential  to solve (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' First, the solution of (8) may be sub-optimal to  (7) if the bounds do not cover the output of layer i at the  optimal value of (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Second, if the bounds are too large, the  MILP can be slow to converge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' To inform proper bounds on  the output of each linear layer, convex bound propagation can  be applied as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' First, define l0 = u0 = x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Then the  initial bounds on z1 can be defined as follows:  l0[Iflex] = min {c, x}  u0[Iflex] = max {c, x}  (9)  Considering (3), the bounds on the output of each layer  before the last can be propagated by  ˆli = max {0, li}  ˆui = max {0, ui}  li+1 = max {0, Wi} · ˆli + min {0, Wi} · ˆui + bi  ui+1 = min {0, Wi} · ˆli + max {0, Wi} · ˆui + bi  (10)  for i = 0, · · · , d − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' By the above formulation, there should  be at least two layers in the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Otherwise, the ANN will  become a linear regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  Remark 1: A small value can be subtracted and added  on l0[Iflex] and u0[Iflex] respectively to avoid numerical  instability when solving MILP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' ADVERSARIAL TRAINING AGAINST AVAILABILITY  ATTACK  To overcome the availability attack defined in (7) and (8),  adversarial training can be implemented in which the loss of  the worst-case attack is minimized in each epoch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Defining  zn = M(m) = diag([m, 1]) · xn + diag([1 − m, 0]) · cn, the  adversarial loss function is written as  Ladv(θ) = max  m  1  N  N  �  n=1  (yn − f(zn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' θ))2  (11)  Similarly to SGD in clean training (2), (11) can be mini-  mized iteratively as  θ := θ −  α  |Bn|  �  (x,y)∈Bn  ∇θ max  m (y − f(z;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' θ))2  (12)  According to Danskin’s Theorem [7], the gradient of the  maximization problem equals the gradient of the loss function  at the maxima.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Therefore,  ∇θ max  m (y − f(z;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' θ))2 = ∇θ(y − f(z∗;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' θ))2  (13)  where z∗ is calculated from the optimal solution m∗ of  the adversarial loss (11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Consequently, the loss function of  adversarial training for availability attacks can be written as  Lavai(θ) = L(θ) + βmaxLadv  max(θ) + βminLadv  min(θ)  (14)  In (14), L(·), Ladv  max(·), and Ladv  min(·) represent the clean  loss, maximization, and minimization of adversarial loss (11)  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Instead of solely training on the adversarial  instance, the clean loss is also added to improve the accuracy  on clean dataset [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  Remark 2: Although the proposed availability adversarial  attack and adversarial training are based on feedforward neural  networks, they can also be extended to other types of piecewise  linear layer, such as the convolutional layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Due to the page  limit, the discussion on convolutional neural networks will be  left for future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' SIMULATION AND RESULT  The optimal integrity and availability adversarial attacks are  constructed using CVXPY [20] with Gurobi solver.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Python  muti-processing is used to accelerate the MILP optimization in  (6) and (8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' The deep load forecasting model is trained using  PyTorch on an RTX 3090 graphic card.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' The outputs of the  layers in ANN are 40-20-10-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Adam optimizer is used with  initial learning rate of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='0005 and cosine annealing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' For the  original dataset [15], outliers beyond three-sigma are removed  and we randomly separate the dataset into train and test with  proportion 8:2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Flexible features are scaled into [0,1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' We train  the model for 150 epochs and store the weights with best test  set performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' For adversarial training, the hyperparameters  are set to βmax = βmin = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' The accuracy of the load  forecasting model is reported by mean absolute percentage  error (MAPE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' For clean samples, we measure the distance  between forecasted and ground-truth loads:  MAPE = 1  N  N  �  n=1  |yclean,n  pred  − yn  true|  yn  true  × 100%  (15)  For adversarial samples, we use the mean percentage error  (MPE) to evaluate their output against the output of the clean  sample:  MPE = 1  N  N  �  n=1  yadv,n  pred − yclean,n  pred  yclean,n  pred  × 100%  (16)  as the adversarial attack is formulated on the trained neural  network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  In the following discussion, the model trained on clean  dataset is referred as Clean Model, while the model trained  through adversarial training is referred as Adver Model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  Furthermore, to distinguish different attack attempts, we use  AVAI(mode, c, β) to represent the availability adversarial  attack with mode∈{max,min} and c ∈ {0, mean}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Similarly,  INTE(mode, ϵ) represents the integrity adversarial attack with  attack strength ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Performance of Availability Adversarial Attack  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 1 compares the MPE deviation on the clean model un-  der the availability adversarial attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' In each of the box plot,  the box represents the inter-quartile range (IQR) extending  from the first quartile to the third of the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' The median of  the data is indicated by the orange line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' The whiskers cover  the whole range of data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' First, increasing the attack budget  β can increase the output deviations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' However, this trend is  not significant when β ≥ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' The output deviations with zero  imputation c = 0 is more intense than average imputation as  no feature information can be extracted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Second, different data  can have different vulnerabilities on the availability attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' For  example, some samples can maintain the output with MPE=0  while others are altered significantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  1  2  3  4  5  6  0  10  20  30  MPE  (a) AVAI(max, 0, β)  1  2  3  4  5  6  0  10  20  30  MPE  (b) AVAI(max, mean, β)  1  2  3  4  5  6  80  60  40  20  0  MPE  (c) AVAI(min, 0, β)  1  2  3  4  5  6  80  60  40  20  0  MPE  (d) AVAI(min, mean, β)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 1: MPEs on the clean model under availability adversarial  attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  To better see the dependency of attack performance on the  attack budget β, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 2 records the number of actual missing  features under AVAI(min, mean, β) attack (corresponding to  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 1(d)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' First, it is clearly shown that a small proportion  of data cannot be attacked regardless of the choices of β,  which results in MPE=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' These data points are least sensitive  to AVAI(min, mean, β) attack, as blocking any subset of their  features can only increase the load forecast.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Second, most of  the actual missing numbers locate at 3 even when β = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' This  further implies that in most cases, blocking more features may  not result in a stronger attack, although increasing β can have  more flexibility to allocate the attack position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 3 records the MPE of integrity adversarial attacks  solved by MILP (6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' The median MPEs of availability attacks  with β = 6 are also plotted as a reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' When maximizing  the load forecast (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 3(a)), availability attacks can give output  deviations comparable to integrity attacks when ϵ is small, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  with ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' However, when ϵ increases, the MPE of the  integrity attack is much higher than the availability attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  When minimizing the load forecast (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 3(b)), AVAI(min,  mean, 6) can persistently outperform integrity attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Since  the input features are scaled into [0, 1], it is not realistic to  have ϵ larger than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Meanwhile, as it is is much cheaper  than the integrity attack, the availability attack is a promising  attack strategy for the attacker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' However, how to balance the  cost and impact of this attack is unsolved and we will leave  it for future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  Solving the MILP can be time consuming, especially when  the number of integer variables is large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' The computational  time of both availability attacks are summarized in Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' As  adversarial training requires solving the optimal availability  attacks, faster computation is beneficial to efficient training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  0  1  2  3  4  5  6  Actual Missing No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  0  1000  2000  3000  4000  5000  6000  Data No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  (a) β = 1  0  1  2  3  4  5  6  Actual Missing No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  0  1000  2000  3000  4000  5000  6000  Data No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  (b) β = 2  0  1  2  3  4  5  6  Actual Missing No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  0  1000  2000  3000  4000  5000  6000  Data No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  (c) β = 3  0  1  2  3  4  5  6  Actual Missing No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  0  1000  2000  3000  4000  5000  6000  Data No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  (d) β = 4  0  1  2  3  4  5  6  Actual Missing No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  0  1000  2000  3000  4000  5000  6000  Data No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  (e) β = 5  0  1  2  3  4  5  6  Actual Missing No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  0  1000  2000  3000  4000  5000  6000  Data No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  (f) β = 6  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 2: Actual missing numbers under different attack budget  β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' The AVAI(min, mean, β) attack strategy is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='5  0  10  20  30  40  50  MPE  AVAI(max,0,6)  AVAI(max,mean,6)  (a) INTE(max, ϵ)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='5  60  50  40  30  20  10  0  MPE  AVAI(min,0,6)  AVAI(min,mean,6)  (b) INTE(min, ϵ)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 3: MPE on the clean model under integrity adversarial  attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  Recall that the size of the dataset is 32k, which requires  half hour to train single epoch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' After using parallel compu-  tation, the computational time is significantly reduced to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='7  min/epoch, which is acceptable for a real-time application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  TABLE I: Average Computational Time (ms/sample)  Attack Types  Time  AVAI-Parallel  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='16  AVAI-Sequential  49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='73  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Performance of Adversarial Training  Adversarial training is implemented in this section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Since  there are two imputation strategies discussed in this paper, the  performances are reported on both models trained adversarially  with c = 0 and c = mean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' In addition, the attack budget is  set to β = 6 in adversarial training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  First, the MAPEs on the clean samples for both clean  model and adversarial model are summarized in Table II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  Adversarial training can inevitably deteriorate the performance  of the model in clean samples by 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='0%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' As c = 0 is a stronger  attack attempt than c = mean, model trained on AVAI(mode,  0, 6) has higher MAPE than it trained on AVAI(mode, mean,  6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  Second, the MPE on the adversarially attacked samples  under different training situations are summarized in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  After the adversarial training, the MPEs are reduced by more  than 50% in general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' The stronger adversarial training situation  with c = 0 can have better robustness, but sacrifices more in  clean accuracy (Table II).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' It is interesting to observe that the  model trained with c = 0 can also have better performance  on AVAI(mode, mean, 6) than the model trained directly with  c = mean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Moreover, the performance of model trained with  c = 0 has slightly higher MPEs than the model trained with  c = mean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Referring to (14), both AVAI(max, c, 6) and  AVAI(min, c, 6) attacks contribute equally to the adversarial  loss function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Therefore, the gradient descent tries to balance  them during the training, although the AVAI(min, 0, 6) is  much stronger than AVAI(max, 0, 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' To solve the problem,  the hyperparameters can be set to βmax > 1 > βmin > 0 in  (14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  TABLE II: MAPE on clean samples (in %).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  Clean  Adver (c=0)  Adver (c=mean)  Train  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='81  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='83  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='76  Test  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='07  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='95  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='88  1  2  3  4  5  6  0  1  2  3  4  MPE  Clean  Adver c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='0  Adver c = mean  (a) AVAI(max, 0, β)  1  2  3  4  5  6  0  1  2  3  4  MPE  Clean  Adver c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='0  Adver c = mean  (b) AVAI(max, mean, β)  1  2  3  4  5  6  20  15  10  5  0  MPE  Clean  Adver c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='0  Adver c = mean  (c) AVAI(min, 0, β)  1  2  3  4  5  6  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='0  MPE  Clean  Adver c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='0  Adver c = mean  (d) AVAI(min, mean, β)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 4: Performances of adversarial training on availability  attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' The medians are taken for all samples in test dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' CONCLUSION  This paper proposes a new availability adversarial attack  on load forecasting model constructed by piece-wise linear  neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' The attack is optimally found through MILP  subject to certain attack budget, and a countermeasure is  given through adversarial training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' The simulation results show  that the availability attack can achieve attack performance  comparable to that of the integrity counterpart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Meanwhile,  adversarial training can effectively reduce MPE by more than  50% on the adversarial samples while only increasing 1%  MAPE on the clean samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  REFERENCES  [1] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Hong and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Fan, “Probabilistic electric load forecasting: A tutorial  review,” International Journal of Forecasting, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 32, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 914–  938, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  [2] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Kuster, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Rezgui, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Mourshed, “Electrical load forecasting  models: A critical systematic review,” Sustainable cities and society,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 35, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 257–270, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  [3] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Wang, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Hug, “Cost-oriented load forecasting,”  Electric Power Systems Research, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 205, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 107723, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  [4] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Rafi, Nahid-Al-Masood, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Deeba, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Hossain, “A short-  term load forecasting method using integrated cnn and lstm network,”  IEEE Access, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 9, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 32 436–32 448, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  [5] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Szegedy, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Zaremba, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Sutskever, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Bruna, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Erhan, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Goodfellow,  and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Fergus, “Intriguing properties of neural networks,” arXiv preprint  arXiv:1312.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='6199, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  [6] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Goodfellow, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Shlens, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Szegedy, “Explaining and harnessing  adversarial examples,” arXiv preprint arXiv:1412.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='6572, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  [7] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Madry, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Makelov, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Schmidt, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Tsipras, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Vladu, “Towards  deep learning models resistant to adversarial attacks,” arXiv preprint  arXiv:1706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='06083, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  [8] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Fawaz, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Forestier, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Weber, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Idoumghar, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Muller, “Ad-  versarial attacks on deep neural networks for time series classification,”  in 2019 International Joint Conference on Neural Networks (IJCNN).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  IEEE, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 1–8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  [9] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Luo, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Hong, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Fang, “Benchmarking robustness of load  forecasting models under data integrity attacks,” International Journal  of Forecasting, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 34, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 89–104, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  [10] ——, “Robust regression models for load forecasting,” IEEE Transac-  tions on Smart Grid, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 10, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 5397–5404, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  [11] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Stratigakos, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Andrianesis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Michiorri, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Kariniotakis,  “Towards resilient energy forecasting: A robust optimization approach,”  2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  [12] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Chen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Sun, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Chu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Camal, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Kariniotakis, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Teng,  “Vulnerability and impact of machine learning-based inertia forecasting  under cost-oriented data integrity attack,” IEEE Transactions on Smart  Grid, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  [13] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Zhou, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Ding, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Wen, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Wang, “Robust load forecasting  towards adversarial attacks via bayesian learning,” IEEE Transactions  on Power Systems, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  [14] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Pan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Teixeira, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Cvetkovic, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Palensky, “Cyber risk analysis  of combined data attacks against power system state estimation,” IEEE  Transactions on Smart Grid, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 10, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 3044–3056, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  [15] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Farrokhabadi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Browell, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Wang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Makonin, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Su, and  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Zareipour, “Day-ahead electricity demand forecasting competition:  Post-covid paradigm,” IEEE Open Access Journal of Power and Energy,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 9, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 185–191, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  [16] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Liu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Han, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Zhang, and Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Liu, “Certified monotonic neural  networks,” Advances in Neural Information Processing Systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 33,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 15 427–15 438, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  [17] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Teixeira, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Sou, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Sandberg, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Johansson, “Secure  control systems: A quantitative risk management approach,” IEEE  Control Systems Magazine, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 35, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 24–45, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  [18] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Kolter and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Madry, “Adversarial robustness - theory and practice,”  2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Available: https://adversarial-ml-tutorial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='org/  [19] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Yu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Jiao, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Xing, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' El Ghaoui, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Jordan,  “Theoretically principled trade-off between robustness and accuracy,”  in International conference on machine learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  PMLR, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  7472–7482.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content='  [20] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Diamond and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' Boyd, “Cvxpy: A python-embedded modeling  language for convex optimization,” The Journal of Machine Learning  Research, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 17, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
+page_content=' 2909–2913, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNAzT4oBgHgl3EQf3f7y/content/2301.01832v1.pdf'}
diff --git a/fdE5T4oBgHgl3EQfhQ8n/content/2301.05639v1.pdf b/fdE5T4oBgHgl3EQfhQ8n/content/2301.05639v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..dfd08bd3d728ff4dbcdba25d41ade4b533226a3d
--- /dev/null
+++ b/fdE5T4oBgHgl3EQfhQ8n/content/2301.05639v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:450c9f9e41bd6c5caa680e21bc037dcb209076654fdc69704db6c28ad80fa0e5
+size 982723
diff --git a/fdE5T4oBgHgl3EQfhQ8n/vector_store/index.faiss b/fdE5T4oBgHgl3EQfhQ8n/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..fee5e8ccfe25542465b0de0513b479e59b1fbc16
--- /dev/null
+++ b/fdE5T4oBgHgl3EQfhQ8n/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6fcf20293ded3b72104fbfce7b3987a67f3644bdfc274e0a0800d306e415aba2
+size 6750253
diff --git a/fdE5T4oBgHgl3EQfhQ8n/vector_store/index.pkl b/fdE5T4oBgHgl3EQfhQ8n/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..83abfcf97d2eb3dbe5b16f27a8268fd0f3834a71
--- /dev/null
+++ b/fdE5T4oBgHgl3EQfhQ8n/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:dcb62bccc87ec7b1764083eba3e557dec951bee2075162f05ec8b5ddc726d4bb
+size 194372
diff --git a/htE3T4oBgHgl3EQf4Quq/content/2301.04771v1.pdf b/htE3T4oBgHgl3EQf4Quq/content/2301.04771v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..0920a34deba547335b6aca29f085e0c6f8461327
--- /dev/null
+++ b/htE3T4oBgHgl3EQf4Quq/content/2301.04771v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7e6793fa85999f42c7c5c3a48e0589834e35c0839f6293d18b24c8b5a12b12e5
+size 888506
diff --git a/htE3T4oBgHgl3EQf4Quq/vector_store/index.faiss b/htE3T4oBgHgl3EQf4Quq/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..77f95c10dba42bee1c610c4c85175c3fae91f7b1
--- /dev/null
+++ b/htE3T4oBgHgl3EQf4Quq/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ed3fe934026209cc9a29f5dc21a643c00f68d3a34eb089e731dee288c05040e1
+size 3735597
diff --git a/htE3T4oBgHgl3EQf4Quq/vector_store/index.pkl b/htE3T4oBgHgl3EQf4Quq/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..0fec3a38fbc82820c06080263698bb0b72cc1664
--- /dev/null
+++ b/htE3T4oBgHgl3EQf4Quq/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4cf5e2a8680ffcdfd672d7194f37e6fb127d42aa90cbc328ffa8b44fdd053cbc
+size 149418
diff --git a/itE2T4oBgHgl3EQfIAZX/content/2301.03674v1.pdf b/itE2T4oBgHgl3EQfIAZX/content/2301.03674v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..2b30dd668fc85d15223df07afcc1f21ec2f74b10
--- /dev/null
+++ b/itE2T4oBgHgl3EQfIAZX/content/2301.03674v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:753446ef7e722b4c73edd9f900cb7a0d0911f95871db39423cb0e000cf9c423f
+size 1170157
diff --git a/itE2T4oBgHgl3EQfIAZX/vector_store/index.pkl b/itE2T4oBgHgl3EQfIAZX/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..4d779a28e04ebdd98401e315f879415f5ec4dc61
--- /dev/null
+++ b/itE2T4oBgHgl3EQfIAZX/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2e0d37d7750db743842d65ad1fd6c6e89010f5d44789ce30dd103672d6a30fbd
+size 663398
diff --git a/j9AzT4oBgHgl3EQfbfze/content/tmp_files/2301.01388v1.pdf.txt b/j9AzT4oBgHgl3EQfbfze/content/tmp_files/2301.01388v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..86a09a1f25b68918c8ce878e0168ca9e64f13d08
--- /dev/null
+++ b/j9AzT4oBgHgl3EQfbfze/content/tmp_files/2301.01388v1.pdf.txt
@@ -0,0 +1,2002 @@
+Astronomy & Astrophysics manuscript no. main
+©ESO 2023
+January 5, 2023
+The cosmic web of X-ray active galactic nuclei
+seen through the eROSITA Final Equatorial Depth Survey (eFEDS)
+Johan Comparat1⋆, Wentao Luo2, 3, Andrea Merloni1, Surhud More4, 5, Mara Salvato1, Mirko Krumpe6, Takamitsu
+Miyaji7, William Brandt8, 9, 10, Antonis Georgakakis11, Masayuki Akiyama12, Johannes Buchner1, Tom Dwelly1,
+Toshihiro Kawaguchi19, Teng Liu1, Tohru Nagao15, Kirpal Nandra1, John Silverman13, 14, Yoshiki Toba16, 17, 18, 15, Scott
+F. Anderson20, Juna Kollmeier21
+1 Max-Planck-Institut für extraterrestrische Physik (MPE), Giessenbachstrasse 1, D-85748 Garching bei München, Germany
+2 Key Laboratory for Research in Galaxies and Cosmology, School of Astronomy and Space Science, University of Science and
+Technology of China, Hefei, Anhui 230026, China
+3 Department of Astronomy, School of Physical Sciences, University of Science and Technology of China, Hefei, Anhui 230026,
+China
+4 The Inter-University Centre for Astronomy and Astrophysics (IUCAA), Post Bag 4, Ganeshkhind, Pune 411007, India
+5 Kavli Institute for the Physics and Mathematics of the Universe (IPMU), 5-1-5 Kashiwanoha, Kashiwa-shi, Chiba 277-8583, Japan
+6 Leibniz-Institut für Astrophysik Potsdam, An der Sternwarte 16, 14482 Potsdam, Germany
+7 Instituto de Astronomía sede Ensenada, Universidad Nacional Autónoma de México, Km 107 Carretera Tijuana-Ensenada, 22860,
+Ensenada, Mexico
+8 Department of Astronomy and Astrophysics, 525 Davey Lab, The Pennsylvania State University, University Park, PA 16802, USA
+9 Institute for Gravitation and the Cosmos, The Pennsylvania State University, University Park, PA 16802, USA
+10 Department of Physics, 104 Davey Laboratory, The Pennsylvania State University, University Park, PA 16802, USA
+11 Institute for Astronomy and Astrophysics, National Observatory of Athens, V. Paulou & I. Metaxa, 11532, Greece
+12 Astronomical Institute, Tohoku University, 6-3 Aramaki, Aoba-ku, Sendai, Japan
+13 Kavli Institute for the Physics and Mathematics of the Universe, The University of Tokyo, Kashiwa, Japan 277-8583 (Kavli IPMU,
+WPI)
+14 Department of Astronomy, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan
+15 Research Center for Space and Cosmic Evolution, Ehime University, 2-5 Bunkyo-cho, Matsuyama, Ehime 790-8577, Japan
+16 National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
+17 Department of Astronomy, Kyoto University, Kitashirakawa-Oiwake-cho, Sakyo-ku, Kyoto, Kyoto 606-8502, Japan
+18 Academia Sinica Institute of Astronomy and Astrophysics, 11F Astronomy-Mathematics Building, AS/NTU, No.1, Section 4,
+Roosevelt Road, Taipei 10617, Taiwan
+19 Department of Economics, Management and Information Science, Onomichi City University, Hisayamada 1600-2, Onomichi,
+Hiroshima 722-8506, Japan
+20 Astronomy Department, University of Washington, Box 351580, Seattle, WA 98195, USA
+21 The Carnegie Observatories, 813 Santa Barbara Street, Pasadena, CA 91101, USA
+January 5, 2023
+ABSTRACT
+Which galaxies in the general population turn into active galactic nuclei (AGN) is a keystone of galaxy formation and evolution.
+Thanks to SRG/eROSITA’s contiguous 140 square degrees pilot survey field, we constructed a large, complete, and unbiased soft
+X-ray flux-limited AGN sample at low redshift 0.05 < z < 0.55. Two summary statistics, the clustering using spectra from SDSS-V
+and galaxy-galaxy lensing with imaging from HSC, are measured and interpreted with halo occupation distribution and abundance
+matching models. Both models successfully account for the observations. We obtain an exceptional complete view of the AGN
+halo occupation distribution. The population of AGN is broadly distributed among halos with a mean mass of 3.9+2.0
+−2.4 × 1012M⊙.
+This corresponds to a large-scale halo bias of b(z = 0.34) = 0.99+0.08
+−0.10. The central occupation has a large transition parameter
+σlog10(M) = 1.28 ± 0.2. The satellite occupation distribution is characterized by a shallow slope αsat = 0.73 ± 0.38. We find that
+AGNs in satellites are rare, with fsat < 20%. Most soft X-ray-selected AGNs are hosted by central galaxies in their dark matter
+halo. A weak correlation between soft X-ray luminosity and large-scale halo bias is confirmed (3.3σ). We discuss the implications of
+environmental-dependent AGN triggering. This study paves the way towards fully charting, in the coming decade, the co-evolution
+of X-ray AGN, their host galaxies, and dark matter haloes by combining eROSITA with SDSS-V, 4MOST, DESI, LSST, and Euclid.
+Key words. X-ray, active galactic nuclei
+⋆ E-mail: comparat@mpe.mpg.de
+1. Introduction
+Active galactic nuclei (AGN) are a keystone in galaxy evolu-
+tion. How they are triggered and are fueled are essential ques-
+Article number, page 1 of 17
+arXiv:2301.01388v1  [astro-ph.GA]  3 Jan 2023
+
+A&A proofs: manuscript no. main
+tions. Answering them will deepen our understanding of the
+co-evolution between galaxies, the gas surrounding them, and
+their central supermassive black holes (SMBH; see reviews from
+Padovani et al. 2017; Eckert et al. 2021). This article focuses
+on the large-scale environment of X-ray-selected AGN, namely
+the population of dark matter haloes hosting them. X-ray selec-
+tion provides AGN samples with higher completeness and purity
+than selections at different wavelengths (Hickox et al. 2009). As
+devised in simulations, this population is diverse (Georgakakis
+et al. 2018; Comparat et al. 2019). To infer the population of
+dark matter haloes hosting a sample of galaxies, the best tech-
+nique to date consists of interpreting the complementary signals
+from clustering and weak gravitational lensing (see for exam-
+ple Comparat et al. 2013; More et al. 2015; Coupon et al. 2015;
+Favole et al. 2016; Zhang et al. 2021).
+Previous studies of the clustering of X-ray-selected AGN
+were limited by the total number of X-ray AGN or the small
+survey area. They typically measured the large-scale halo bias
+of AGN selected in different fashions (Gilli et al. 2009; Cap-
+pelluti et al. 2010; Starikova et al. 2011; Koutoulidis et al.
+2013, 2018; Leauthaud et al. 2015; Viitanen et al. 2019; Alle-
+vato et al. 2019). The auto-correlation of X-ray-selected AGN
+was studied locally (z ∼ 0.045) with 199 AGN in the Swift-
+BAT all-sky survey (Cappelluti et al. 2010). They found these
+bright low redshift AGN to be hosted on average by dark mat-
+ter haloes of mass 1.6 − 2.5 × 1013h−1M⊙ corresponding to a
+large-scale halo bias of 1.2±0.1. At higher redshift (z ∼ 1) with
+deep pencil beam surveys (COSMOS observed with XMM and
+Chandra, Bootes, and Chandra compilations) and larger num-
+bers of AGN (ranging from 500 to 1,500), Gilli et al. (2009);
+Starikova et al. (2011); Koutoulidis et al. (2013); Viitanen et al.
+(2019); Allevato et al. (2019) inferred a large-scale halo bias of
+∼ 2 ± 0.2 corresponding to halo masses 4 − 9 × 1012h−1M⊙. In
+these studies, further splitting of the samples as a function of
+AGN type, luminosity, and host-galaxy properties, is not very
+conclusive due to small statistics. There are hints of correlation
+with X-ray luminosity and an indication of a low satellite frac-
+tion. The study of the angular auto-correlation of photometri-
+cally selected AGN, so with much larger samples, led to sim-
+ilar large-scale halo bias and typical dark matter halo masses
+(Myers et al. 2007; Donoso et al. 2014; Koutoulidis et al. 2018).
+Finally, Leauthaud et al. (2015) studied the galaxy-galaxy lens-
+ing signal around 382 X-ray-selected AGNs in the COSMOS
+field. They find that AGN host occupation is no different from
+that of galaxies. They explain the issue of quoting a mean for
+the halo mass when, instead, complete halo occupation distribu-
+tions should be discussed; see also Georgakakis et al. (2018) for
+an extended discussion. Also, after controlling for stellar mass,
+Yang et al. (2018a) found no clear dependence between the en-
+vironment and the sample-averaged SMBH accretion rate or the
+AGN fraction, which indicates that environment-related physical
+mechanisms might not significantly affect SMBH growth.
+To circumvent the low signal-to-noise ratio in the auto-
+correlation functions, the cross-correlation with a controlled
+galaxy population has been recently fruitful. Such studies re-
+late AGN populations to their host dark matter haloes (Krumpe
+et al. 2010, 2012, 2015, 2018; Mendez et al. 2016; Mountrichas
+et al. 2019; Zhang et al. 2021). They cross-correlated a similar
+number of X-ray-selected AGN (between 300 and 1500) with
+spectroscopic galaxy surveys: 2MASS, SDSS, VIPERS, COS-
+MOS (Skrutskie et al. 2006; York et al. 2000; Guzzo et al. 2014;
+Scoville et al. 2007). They obtain similar large-scale halo bias
+values as the auto-correlation studies and investigate the correla-
+tion with host-galaxy properties hinting at possible correlations
+with stellar mass. This powerful technique works only with ac-
+cess to a well-studied galaxy sample (Zehavi et al. 2011; Marulli
+et al. 2013). The limited signal-to-noise impedes establishing a
+clear definitive picture of how X-ray AGNs populate the cosmic
+web.
+With the advent of eROSITA (Predehl et al. 2021), the num-
+ber density of X-ray AGN increased to more than a hundred
+per square degree in the eROSITA Final Equatorial Depth Sur-
+vey (eFEDS, 140 deg2, ∼1,400 ks Brunner et al. 2022; Salvato
+et al. 2022). Accurate redshifts are required for precise cluster-
+ing and lensing analysis. The dedicated spectroscopic observa-
+tions of the X-ray sources detected in eFEDS (SDSS-IV, SDSS-
+V Abdurro’uf et al. 2022; Kollmeier et al. 2017, Merloni et al. in
+preparation) enabled the accurate measurement of redshifts for
+about eleven thousand X-ray point sources in eFEDS (i.e., for
+∼ 50% of the sources). This number of X-ray AGN with spec-
+tra is already comparable to its predecessor follow-up of ROSAT
+point sources (Comparat et al. 2020b).
+Outstanding weak-lensing data products are now available
+over wide areas thanks to the Hyper Suprime-Cam Subaru
+Strategic Program (HSC-SSP) (Aihara et al. 2019). They mea-
+sured accurate galaxy shapes for more than 20 source galaxies
+per square arc minute over vast areas (1,400 deg2), which almost
+completely cover the eFEDS field (Mandelbaum et al. 2018b).
+With these two outstanding observational advances, we mea-
+sure the auto-correlation function and the galaxy-galaxy lens-
+ing signal of X-ray-selected AGN to study their underlying dark
+matter halo distribution. We detail, in Sect. 2, the construction
+of the X-ray AGN sample, and the weak-lensing data products
+used. We describe the method to measure the clustering and
+galaxy-galaxy lensing in Sect. 3. The halo occupation distribu-
+tion and sub-halo abundance matching models used are detailed
+in Sect. 4. Results are discussed in Sect. 5, 6. Throughout, we as-
+sume a Flat LCDM cosmology with H0 = 67.74 km s−1 Mpc−1
+and Ωm(z = 0)=0.3089 (Planck Collaboration et al. 2020). The
+uncertainties are 1σ unless stated otherwise. Magnitudes are in
+the AB system (Oke & Gunn 1983). Throughout the article, we
+use AGN to designate X-ray-selected AGN.
+2. Data
+In this section, we describe the X-ray observations in Sect. 2.1
+and the weak-lensing data products in Sect. 2.2.
+2.1. eROSITA eFEDS
+We use the public Early Data Release eROSITA point
+source catalog of the eFEDS Performance Verification sur-
+vey (Brunner et al. 2022). The catalog contains 20,191 pri-
+mary sources, over 140 deg2, detected with a likelihood greater
+than 8 (ERO_DET_LIKE > 8) and with reliable counterpart
+(CTPquality ≥ 2) determined as described in Salvato et al. (2022).
+Simulations are only at X-ray wavelength and not in the optical,
+so the impact of the determination of the counterpart is stud-
+ied empirically in Sect. 4 of Salvato et al. (2022). The trade-off
+between purity and completeness study shows that counterparts
+with a threshold of CTPquality ≥ 2 (p_any > 0.035) have a purity
+and completeness both equal to 95%. We follow the recommen-
+dation of Salvato et al. (2022) and use the set of reliable coun-
+terparts above threshold with CTPquality ≥ 2. There are 1,219
+extra sources ERO_DET_LIKE > 8 & CTPquality < 2 that are
+then discarded. These sources are on the faint end of the X-ray
+flux distribution, inducing a 5% incompleteness at the faint end.
+Article number, page 2 of 17
+
+Comparat et al.: X-ray AGN HOD
+Fig. 1. Slice of the light cone sampled by the X-ray-selected eFEDS AGN sample in the redshift range 0.05 < z < 0.55 (blue crosses). The
+surrounding large-scale structure is sampled by GAMA galaxies (grey) and GAMA galaxy groups (purple) (Driver et al. 2022) as well as by
+eROSITA eFEDS clusters (red) (Liu et al. 2022a).
+Given the large distribution of fluxes (luminosities) considered
+here, we neglect this bias.
+2,160 sources are classified as stars either via astrometry, spec-
+troscopy, X-ray, and opt/IR colors or via a dedicated analysis as
+described in Schneider et al. (2022) and removed from the rest
+of the study.
+As shown by simulations (Liu et al. 2022c; Seppi et al. 2022),
+faint clusters are contaminants of the point source catalog. In
+eFEDS, 129 clusters are present in the point source catalog (Bul-
+bul et al. 2022). They are identified in Salvato et al. (2022) with
+the flag CLUSTER_CLASS ≥ 3 and are masked.
+After these cuts on the eFEDS point source catalog, we obtain
+17,902 AGN candidates over 140 deg2 (density of 127.9 per
+square degree). Fig. 1 illustrates the light cone considered in this
+analysis.
+2.1.1. Masks
+We must propagate the masks applied to the source catalog to the
+random catalog to estimate clustering. The random catalog is a
+set of un-clustered data points that cover the same sky area as
+the observations, see description in Sect. 2.1.4. As the masking
+radius for each detected source, we use its radius of maximum
+signal-to-noise augmented by 40 percent. This radius is deter-
+mined while extracting the X-ray spectrum of each source (Liu
+et al. 2022b), see Appendix A.1 for complete details.
+The edges of the survey have a lower exposure time. We
+find that trimming the survey edges by requiring a minimum ex-
+posure time of 830 seconds minimizes the KS test values (be-
+tween random and data vectors) with a minimal area loss, see
+Sec § 2.1.4. After applying the minimum exposure time cut, we
+are left with 16,308 AGN candidates over 128 deg2, resulting in
+a density of ∼127.4 deg−2.
+2.1.2. Photometric redshifts
+Photometric redshift estimation for galaxies hosting active
+galactic nuclei is complex (e.g. Salvato et al. 2018). In the
+eROSITA/eFEDs case, Salvato et al. (2022) measured photomet-
+ric redshifts to have σNMAD = 1.48 × median
+�
+|zspec−zphot|
+1+zspec
+�
+∼ 0.05
+and a fraction of outliers, with |zspec−zphot|
+1+zspec
+> 0.15, of the order of
+20%. At the bright end (r<21.5), we find that σNMAD decreases
+to ∼ 0.03 while the outlier fraction remains the same, 20%.
+With the help of the simulation from Comparat et al. (2019), we
+find that the measured clustering using photometric redshift with
+such dispersion and fraction of outliers would result in losing
+between one-third and one-half of the amplitude of the cluster-
+ing signal. So we will not use the photometric redshift to mea-
+sure clustering statistics; instead, we focus on the sub-sample of
+10,680 AGNs with spectroscopic observations, see the following
+Sect. 2.1.3.
+2.1.3. Spectroscopic redshifts
+The eFEDS field was observed with the SDSS infrastructure
+(Gunn et al. 2006; Smee et al. 2013) in March-April 2020 with
+both BOSS spectrographs (1000 fibers per plate, SDSS-IV, Blan-
+ton et al. 2017) and March-April 2021 with a single BOSS spec-
+trograph (500 fibers per plate, SDSS-V, Kollmeier et al. 2017,
+Merloni et al. in preparation). A total of 31 plates were ob-
+served, see Section ‘SPIDERS’ of Abdurro’uf et al. (2022) and
+the spectra are part of the SDSS DR18 (SDSS collaboration in
+preparation). The total area covered by SDSS-IV and V spec-
+troscopic observations is 133.77 deg2 (95% of the eFEDS area).
+The obtained spectroscopic redshift completeness depends on (i)
+the position in the sky; (ii) the optical magnitude of the source.
+We consider the z-band AB magnitude measured as in the legacy
+survey DR8 (Dey et al. 2019) and based on observations made
+with DECam (Flaugher et al. 2015). Although photometric red-
+shifts are not accurate enough for clustering studies, they are of
+sufficient quality to compare the distribution of magnitudes and
+fluxes in broad redshift bins. Overall, we find that at a z-band
+magnitude of 21.25 (19.0), the completeness is 50% (90%). We
+find that, up to redshift ∼0.55, the spectroscopic sample is a fair
+sub-sample (as a function of optical magnitude and X-ray flux)
+of the entire population. SDSS-V observations being limited to
+z-band magnitudes brighter than 21.5, beyond a redshift of 0.55,
+we are missing a significant fraction of the AGN that are opti-
+cally faint X-ray-selected AGN, see Fig. 2.
+We estimate the spectroscopic completeness in ∼3.5 deg2
+equal area pixels (half the size of an SDSS plate ∼7 deg2). The
+minimum (maximum) completeness measured in a pixel is 13%
+(69%). The relative variations of the spectroscopic redshift dis-
+tribution as a function of completeness are within the expected
+Article number, page 3 of 17
+
+eROSITA eFEDs
+0.45
+0.4
+144°
+Galaxies
+0.35
+AGN, LX>42
+0.3
+Redshift
+0.25
+x
+Qx
+Groups
+141°
+0
+0.2
+Clusters
+0.15
+×x
+0.1
++
+138°
+0.05
+.8
+x
+0.0
+x
+0
+xx
+136°
+0.0
+Q
+0*00
+0
+0.7
+X
+x
+x
+1.3
+*
+x
+133°
+xx
+0
+x
+1.9
+x
+x
+0*
+2.4
+x
+x
+x
+x
+x
+2.9
+x
+xO
+Lookback time
+130°
+3.4
+[Gyr]
+××
++
+x
+3.9
+4.3
+4.7
+127°A&A proofs: manuscript no. main
+Fig. 2. Spectroscopic completeness as a function of r-band magnitude
+vs. redshift (top) and soft X-ray luminosity (0.5-2 keV) vs. redshift (bot-
+tom). The completeness coverage is homogeneous below the redshift of
+0.6. At higher redshift, completeness at the faint end impacts the sample
+significantly.
+fluctuations for pixels with completeness levels above 40%. So,
+we discard areas with completeness lower than 40%. It removes
+about 20 deg2 of the area located at the edge of the eFEDs field
+(most of it overlaps with the low-exposure regions).
+To summarize, to measure the clustering, we create an AGN
+sample covering redshifts between 0.05 and 0.55, where the
+spectroscopic sample is not biased compared to the parent photo-
+z sample. We obtain a sample of 1,992 AGN with spectroscopic
+redshift covering 122.3 deg2. Figure 1 illustrates how the AGN
+considered in this analysis sample the large-scale structure ob-
+served with galaxies and groups from the GAMA survey and
+eROSITA eFEDS clusters. Table 1 summarizes the main proper-
+ties of the considered sample. The mean redshift of the sample
+is 0.34, with a standard deviation of 0.13. The sample’s mean
+X-ray luminosity in the soft 0.5–2 keV band is 42.91. The distri-
+bution around the mean is broad and has a standard deviation of
+0.65.
+Table 1. Properties of the sample. Minimum, mean, maximum, and
+standard deviation of the redshift, soft band X-ray luminosity, and g,
+r, z magnitudes from the legacy survey (Dey et al. 2019).
+property
+min
+mean
+max
+std
+redshift
+0.05
+0.34
+0.55
+0.13
+soft LX
+40.49
+42.91
+45.12
+0.65
+gAB
+15.16
+20.1
+23.13
+1.41
+rAB
+14.26
+19.23
+22.39
+1.35
+zAB
+13.62
+18.57
+21.82
+1.32
+We verified that the edges of the selection do not impact the
+clustering and lensing summary statistics: by moving the red-
+shift cut from 0.05 to 0.1 and from 0.55 to 0.5 and by adding
+a minimum luminosity threshold of 41.5. Further splitting the
+sample in soft X-ray luminosity-limited samples (or following a
+visual inspection of the optical spectra) significantly decreases
+the signal-to-noise in the measurements, and HOD model pa-
+rameters become unconstrained. Larger numbers of AGN with
+spectroscopic redshifts are required to investigate trends with pa-
+rameters defining the sample.
+Among the 1992 AGN studied here, 1648 (82.7%) have
+their spectroscopic redshift coming from SDSS observations.
+270 (13.5%) come from GAMA observations (Liske et al. 2015).
+Then in smaller numbers, spectroscopic redshifts originate from:
+46 from WiggleZ (Drinkwater et al. 2018), 8 from LAMOST
+DR5 v3 (Luo et al. 2015), 7 from 2SLAQ (Cannon et al. 2006), 5
+from 2MASS (Skrutskie et al. 2006), 3 from HCSC (Oguri et al.
+2018), 2 from 6dFGS (Jones et al. 2009), 1 from HYPERLEDA
+(Paturel et al. 2003), 1 from (Véron-Cetty & Véron 2010), and 1
+from RCSEDv2 (Chilingarian et al. 2021).
+2.1.4. Random catalogue
+To measure clustering, one compares the set of observed points
+to a group of points with no clustering but all other aspects equal
+(window function, redshift distribution). In this section, we ex-
+plain how the set of random points is constructed.
+We draw a set of random points with a large uniform den-
+sity of ∼81,000 deg−2 on the sky (about 11.5 million points on
+eFEDS). We first trim it to follow precisely the edges of the
+survey. We then follow the methodology of Georgakakis et al.
+(2008) to downsample the uniform random catalog with the sen-
+sitivity map, see details in Appendix A.2. Heuristically, this step
+applies the X-ray flux limit and its variations across the field
+to the set of random points. The total number of random points
+remaining after downsampling, masking (see the previous sec-
+tion), and trimming (low exposure time region) is 3,713,726.
+The density of random points, ∼ 30, 000 deg−2, is more than 200
+times larger than that of the data points (127.4 deg−2), which is
+largely sufficient.
+We downsample the random catalog to follow the spectro-
+scopic redshift completeness map and its dependency on R.A.
+and Dec. We cut the areas where spectroscopic completeness is
+lower than 40 %. As the relative variation in the redshift dis-
+tribution is independent of the completeness (see the previous
+section), we shuffle the set of observed redshifts and assign them
+to the random points, regardless of the completeness level.
+2.2. HSC-SSP weak-lensing data
+We use the HSC S19A weak-lensing products based on the
+HSC-SSP accumulated i-band imaging data from 2014 to 2019.
+Article number, page 4 of 17
+
+24
+1.0
+-
+0.8
+22
+TAB=21.5
+completeness
+0.6
+20
+0.4
+-
+18
+15
+-
+0.2
+10
+16
+0.0
+0.25
+0.50
+0.75
+1.00
+redshift45
+1.0
+44
+0.8
+eness
+43
+0.6
+letel
+compl
+42
+0.4
+41
+0.2
+z= 0.55
+40
+-
+0.0
+0.25
+0.50
+0.75
+1.00
+redshiftComparat et al.: X-ray AGN HOD
+The original HSC-SSP S19A wide-layer data covers about 512
+deg2, and it reduces to 433.48deg2 after the full-color full-depth
+(FCFD) selection. With the i-band magnitude cut of 24.5, the
+observed number density reaches up to 22.9 arcmin−2. The deep
+imaging data enable a comprehensive redshift coverage ranging
+from 0 to 3, and the calibrated bias residual shows no depen-
+dence on the redshift.
+There are several major updates in the shape catalog version
+from hscPipe4 to hscPipe7 (used here). These improvements
+include PSF modeling, image co-addition, bright star masking,
+and background subtraction.
+Due to the bad weather, volcanic activity, and other telescope
+downtimes, the observation time has significantly decreased. To
+compensate for the loss, besides the 30 nights additional obser-
+vation time, the survey strategy has been modified by (i) reduc-
+ing to 80% the time in the Deep/Ultra Deep fields, (ii) lowering
+the seeing conditions in i-band, (iii) changing the dither pattern
+from 6 to 5 in the i, z and y bands. The latter results in a 0.1 mag-
+nitude difference in the i-band depth. Altogether, the expected
+coverage should still reach up to 1200 deg2. We detail several
+essential aspects of the S19A imaging data below.
+2.2.1. Photometry
+The most important updates to the pipeline and data processing
+are (i) improved sky background subtraction; (ii) improved im-
+age co-addition warping kernel from Lanczos3 to Lanczos5; (iii)
+the addition of two new filters r2 and i2 that substitute the orig-
+inal r and i- band filters; (iv) improved Point Spread Function
+(PSF) based on PSFEx; (v) new masks around bright stars com-
+posed of ghosts, blooming, halo. About the sky subtraction algo-
+rithm, we apply the newest version based on Aihara et al. (2022)
+rather than the global-global algorithm Aihara et al. (2019). The
+latter leads to about 10% loss of extended source near the shape
+catalog cut at i-band magnitude equals 24.5.
+We use the Forward Global Calibration Method (FGCM;
+Burke et al. 2018) that was firstly developed for the Dark En-
+ergy Survey (DES; Sevilla-Noarbe et al. 2021) and now has been
+merged into the LSST/HSC pipeline. It starts with modeling
+the instrumental throughput measurements such as mirrors, fil-
+ters, and detectors. Then, the atmospheric model (MODTRAN4
+Berk et al. 1999) carries out detailed modeling of atmospheric
+throughput as a function of zenith distance at the location of the
+SUBARU telescope on Mauna Kea.
+The performance of the photometry is tested in two ways,
+an internal test by comparing the PSF magnitude to the Kron
+magnitude for a bright star sample (i<21.5) in the Wide XMM-
+LSS field. The standard deviation of the difference (PsfMag-
+KronMag) achieved is better than 1%, independently of the fil-
+ters and fields. One exception is the y-band, which shows a
+slightly larger scatter of 1.5%. In addition, the difference be-
+tween the CModel magnitude and PSF magnitude is below 0.2%.
+For the external test, PanSTARR1 stars brighter than r-band 20
+mag are used (PS1; Chambers et al. 2016). The scatter level is
+also at about the 1% level indicating good photometric perfor-
+mance. Observations are mixing the i (r) and the i2 (r2) fil-
+ters. It results in a small offset in the i (r) photometry in the
+Deep+UltraDeep fields and small regions of the Wide fields.
+Good photometric performance is a pre-condition for the red-
+shift calibration, described below.
+2.2.2. Photometric redshifts for sources
+The overlapping photometric and public spectroscopic surveys
+with HSC-SSP provide a wealth of data for photometric red-
+shift calibration. These data sets include zCOSMOS DR3 (Lilly
+et al. 2009), UDSz (Bradshaw et al. 2013; McLure et al. 2013),
+3D-HST (Skelton et al. 2014; Momcheva et al. 2016), FMOS-
+COSMOS (Silverman et al. 2015) and so forth. There are about
+170k spectroscopic redshifts (spec-z) and 37k g/prism-z with
+high-quality.
+To cover the wide range of photo-z methods (Tanaka et al.
+2018; Nishizawa et al. 2020) used different techniques on the
+HSC-SSP data: template-fitting, empirical-fitting, and machine
+learning. These include the Mizuki template-fitting method
+Tanaka (2015), MLK Self-Organise Map (SOM; More et al.
+in prep), NNPZ Nearest Neighbors P(z) (Cunha et al. 2009),
+FRANKEN-Z Flexible Regression over Associated Neighbors
+with Kernel dEnsity estimatioN for Redshifts, DEmP Direct Em-
+pirical Photometric code (Hsieh & Yee 2014) and Ephor Ex-
+tended Photometric Redshift (EPHOR). There is a newly de-
+veloped machine learning photometric method for HSC-SSP Y3
+shape catalog, i.e., dNNz (A. J. Nishizawa et al. in preparation).
+The metrics to quantify the performance of each method are
+the bias defined as ∆z = (zphot − zre f )/(1 + zre f ), the dispersion
+σzphot = 1.48 × MAD(δz) (MAD is the median absolute devia-
+tion), the outlier rate foutlier = N(∆z) > 0.15/Ntotal and the loss
+function L(∆z) = 1 − 1/(1 + (∆z/γ)2) with γ = 0.15. The pho-
+tometric redshift used in this work is based on dNNz method,
+which achieves an accuracy with a ∆z = 10−4 bias, a dispersion
+σzphot = 3%, and an outlier rate smaller than foutlier ≤ 10%.
+2.2.3. Shape catalog
+The
+HSC
+galaxy
+sample
+is
+selected
+following
+a
+se-
+ries of basic flag cuts, such as i_detect_isprimary,
+i_extendedness_value and i_sdsscentroid_flag. The
+detailed descriptions are listed in Table 2 of Li et al. (2022). The
+shapes of galaxies are measured with re-Gaussianization method
+(Hirata & Seljak 2003) (reGauss which has been merged to
+GalSim Rowe et al. (2015)), the PSF effects are corrected
+during the measurement process. HSC covers six discrete
+fields named after overlapping regions from previous surveys:
+XMM, HECTOMAP, WIDE12H, GAMA09H, GAMA15H,
+and VVDS. The eFEDS region overlaps with GAMA09H. Note
+that the HSC region GAMA09H covers a larger area than the
+original GAMA09H field and completely encompasses the
+eFEDS field.
+The final shape catalog contains the two components of the
+ellipticity:
+(e1, e2) = 1 − (b/a)2
+1 + (b/a)2 (cos2φ, sin2φ),
+(1)
+where b/a is the ratio between the minor axis and major axis,
+and φ is the position angle of the major axis with respect to the
+sky coordinates. The shear distortion, γi, is then related to the ei
+(i=1,2) such that
+γi = 1
+2R⟨ei⟩(i = 1, 2),
+(2)
+where R is the response of the galaxy ellipticity to a small distor-
+tion defined in Kaiser et al. (1995); Bernstein & Jarvis (2002).
+The response is calculated from the calibrated parameters erms
+Article number, page 5 of 17
+
+A&A proofs: manuscript no. main
+and σe based on simulations (Mandelbaum et al. 2018a; Li et al.
+2022) as follows
+R = 1 −
+�
+i wie2
+rms,i
+�
+i wi
+.
+(3)
+The weighting term wi in Eq.3 is composed of the per-
+component error from simulation due to photon noise σe;i, and
+the rms of galaxy shape distribution erms;i, wi = 1/(σ2
+e;i + e2
+rms;i).
+The reGauss algorithm suffers from several estimation bi-
+ases, e.g., model bias, noise bias, and selection bias which can be
+classified into multiplicative bias mi and additive bias ci (i=1,2),
+so that
+γi = (1 + mi)γtrue
+i
++ ci.
+(4)
+The final shear estimator is obtained with Eq. 5. It does not in-
+corporate the geometry factor Σcrit described in Sec.3.2.
+⟨γi⟩ =
+�
+j wiei;j
+2R(1 + ⟨mi⟩) �
+j wj
+−
+⟨ci⟩
+1 + ⟨m⟩.
+(5)
+Both multiplicative and additive biases are calibrated based on
+the simulations mentioned above. The two biases are then as-
+signed to each galaxy as a function of SNR and resolution R2.
+Additionally, there is selection bias as well as weight bias. The
+overall bias is quantified as the residuals for both multiplicative
+δm and additive bias δa, both of which can reach below 1% level
+for HSC-SSP Y3 shape catalog Li et al. (2022).
+3. Summary statistics
+Galaxy clustering and gravitational lensing probe the galaxy and
+matter over-density field’s auto and cross-correlations as a func-
+tion of scale via a biasing function (Tegmark & Peebles 1998;
+Tegmark & Bromley 1999; Dekel & Lahav 1999). These mea-
+surements are well suited to constrain the biasing function, also
+named more generically the galaxy-halo connection (Sheth &
+Tormen 1999; Wechsler & Tinker 2018). With the data described
+above, we compute two summary statistics: the AGN-AGN auto-
+correlation (clustering, Sect. 3.1) and galaxy-galaxy lensing with
+the AGN population being the lenses (Sect. 3.2).
+3.1. Clustering measurement
+We use the Landy & Szalay (1993) estimator to measure the
+projected two-point correlation function, labeled wp(rp) (for de-
+tailed definition, see e.g., Davis & Peebles 1983). To count
+pairs and integrate along the line of sight, we use the corrfunc
+software (Sinha & Garrison 2020). For the integration, we use
+πmax = 40 h−1Mpc. We carried out measurements with shorter
+and longer πmax and found that with 40, we would obtain the
+largest signal-to-noise in the clustering measurement.
+We randomly down-sample the catalog of random points for
+the clustering measurement to have twenty times the number
+of AGN. To have consistent 3D positions between the optical
+spectra and the X-ray sources, we compute the clustering using
+the position on the sky of the optical counterparts (Salvato et al.
+2022); we do not use the positions of the X-ray sources. The pro-
+jected correlation function obtained is shown in Fig. 3 (black er-
+ror bars). The clustering measurement’s uncertainty is estimated
+using the diagonal component of the covariance matrix obtained
+with 18 eFEDS simulated catalogs (Liu et al. 2022c). These sim-
+ulated eFEDS observations are based on the empirical models of
+Fig. 3. Projected clustering measurement of the X-ray flux-limited
+eFEDS AGN sample in the redshift range 0.05 < z < 0.55 (black).
+The prediction from the 18 eFEDS simulations appears in yellow. The
+best-fit model (jointly with weak-lensing observations) is in red.
+the X-ray cosmic web from Comparat et al. (2019, 2020a). The
+yellow shaded area in Fig. 3 shows the prediction from the 18
+mocks. We find that the forecast is faithful to the observations.
+Following Driver & Robotham (2010), we estimate the cos-
+mic variance in this field to be 1%, which we add as a constant
+systematic uncertainty at all scales to the clustering measure-
+ment. Note that it is small compared to statistical uncertainties.
+Using the eFEDS simulations, we find that clustering summary
+statistics are significantly biased low for separations rp >40
+h−1Mpc. This is due to the finite volume observed. So, we ex-
+clude from the fitting procedure clustering measurements with
+a separation larger than 40 h−1Mpc. The total signal-to-noise
+in the clustering measurement is 17.7, split into 11 radial bins.
+We sample the separation range with five bins per decade evenly
+log-spaced (0.2 dex steps) between 0.25 (10−0.6) and 39.8 (100.6)
+h−1Mpc.
+The fiber collision radius in SDSS is 62 arc seconds
+(∼0.25h−1Mpc at the mean redshift of the sample). The
+eROSITA PSF is 30 arc seconds, so X-ray-selected AGN pairs
+with a separation smaller than one arc minute are hardly de-
+tected. Moreover, since the AGN sample considered here is
+sparse (120 deg−2 ∼0.03 arc minutes−2) and spread over a long
+line of sight, AGN close pairs are small in numbers. Using the
+mock catalogs limited to redshifts 0.05 < z < 0.55, we estimate
+the number of expected pairs with an angular separation smaller
+than 62 arc seconds to be typically a handful: less than 10. Only
+half have physical separation smaller than 40 h−1Mpc. So, the
+number of missed pairs due to fiber collisions is negligible. So
+in our case, we consider that fiber collisions are not an issue, and
+we define our lowest separation bin at 0.25 h−1Mpc.
+3.2. Galaxy-galaxy lensing measurement
+The galaxy-galaxy lensing measurement is a cross-correlation
+between positions of foreground lenses (AGN in our case) and
+shapes of background galaxies acting as sources (HSC galax-
+ies), see reviews from Bartelmann & Schneider (2001); Re-
+fregier (2003). This measurement directly traces the galaxy halo
+Article number, page 6 of 17
+
+102
+101
+18mockcatalogs
+100
+Best-fit HOD
+eROSITAX-ray AGN
+10-1
+100
+101
+rp [h-1 Mpc]Comparat et al.: X-ray AGN HOD
+connection (e.g. Mandelbaum et al. 2005; Seljak et al. 2005).
+Numerous studies have used galaxy-galaxy lensing (sometimes
+combined with galaxy clustering) to trace the galaxy-halo con-
+nection in general (Leauthaud et al. 2011; Coupon et al. 2015;
+Zu & Mandelbaum 2015; Dvornik et al. 2018; Zacharegkas et al.
+2022).
+We combine the X-ray point sources from the eFEDS region
+and the HSC shape catalog to compute the galaxy-galaxy lensing
+using each source galaxy and its probability distribution function
+as a function of redshift (p(z)). The physical interpretation of the
+galaxy-galaxy lensing signal is the difference between the aver-
+age density inside a certain projected radius R and the average
+density at that same radius, so an excess surface density (ESD,
+∆Σ), that is
+∆Σ(R) = ¯Σ(≤ R) − Σ(R).
+(6)
+We follow the measurement procedure described in Miyatake
+et al. (2019); Luo et al. (2022), that
+∆Σ(R) =
+1
+2R(R)
+�Nl
+l wl
+�Ns
+s wlset,ls[⟨Σ−1
+cr ⟩]−1
+[1 + K(R)] �Nl
+l wl
+�Ns
+s wls
+.
+(7)
+In the above ESD estimator, R(R) is the response of the shape
+estimator, which, for this work, takes a value of 0.84. wls is the
+weight for each lens-source galaxy pair. wl is a weight assigned
+to each lens galaxy. Here we use wl = 1 in that there are no
+particular requirements on redshift, stellar mass or other proper-
+ties for the lens catalog. et,ls is the tangential component of the
+source galaxy shape with respect to the lens. The factor K(R)
+accounts for the multiplicative bias calibrated based on a suite
+of simulations developed in Mandelbaum et al. (2018a); Li et al.
+(2022).
+Two blinding schemes are provided for systematic sanity
+tests, the low and the high-accuracy blinding scheme. We use
+the former where a value of δm is added to the original cali-
+brated additive bias m where ei = (1 + mi)ei + ci (i=1,2). In the
+low accuracy scheme, only δm1 is added and encrypted for each
+user of the shape catalog. It is then decrypted and removed by
+subtracting δm1 term.
+An extra selection function for each lens-source pair is ap-
+plied following Medezinski et al. (2018) so that the accumulated
+probability of the P(z) satisfies
+P(zs ≥ zl + 0.2) =
+� ∞
+zl+0.2
+p(z)dz ≥ 0.98.
+(8)
+Fig. 4 shows the galaxy-galaxy lensing measurements ob-
+tained (black) as well as the best-fit HOD model (red). Measure-
+ments with a separation smaller than 20 h−1Mpc are included
+in the fitting procedure. The total signal-to-noise in the lensing
+measurement is 46, split into 15 radial bins. We sample the sep-
+aration range with 5.5 bins per decade evenly log-spaced (0.18
+dex) steps between 0.025 (10−1.6) and 8.3 (100.9) h−1Mpc. Com-
+pared to the clustering measurement, the measurement extends
+to ten times smaller separations. We measured the same using
+the public HSC one-year S16A (KIDS DR4) lensing products.
+They are consistent but have a lower total signal-to-noise of 21.4
+(6.5) compared to 46.
+4. Models
+We interpret the clustering and lensing summary statistics using
+models of halo occupation statistics (Cooray & Sheth 2002; Guo
+Fig. 4. Galaxy-galaxy lensing measurement. Excess surface mass den-
+sity measurement with HSC S19A data using as lenses the X-ray flux-
+limited eFEDS AGN sample in the redshift range 0.05 < z < 0.55
+(black). The best-fit model (jointly with clustering measurements) is
+shown in red.
+et al. 2010). There are three flavours of models: Halo Occupation
+Distribution (HOD; Berlind & Weinberg 2002; Kravtsov et al.
+2004; Zheng et al. 2005, 2007), Sub Halo Abundance Match-
+ing (SHAM; Conroy et al. 2006; Trujillo-Gomez et al. 2011;
+Klypin et al. 2013) and emulators of the large-scale structure
+of the Universe (e.g. DarkEmulator Nishimichi et al. 2019;
+Nishizawa et al. 2020). HOD and SHAM reproduce measure-
+ments of the galaxy clustering as a function of luminosity and
+color (Zehavi et al. 2011; Marulli et al. 2013). The exploration
+and parametrization of the assembly bias in such models is still a
+matter of debate (Contreras et al. 2021; Xu et al. 2021). Emula-
+tors enable a precise prediction of the cross-correlation between
+haloes and the dark matter, though due to the finite resolution
+of simulations they build upon, they are currently limited to pre-
+dict statistics at the high mass end (Nishimichi et al. 2019). So,
+first, we adjust the HOD model parameters to the measurements
+obtained in the previous section 4.1. Then, we compare mea-
+surements to the prediction of the SHAM model from Comparat
+et al. (2019) in Sect. 4.2.
+4.1. Halo occupation distribution model
+As a baseline, we use the HOD model formulated by More et al.
+(2015). It is described by the two equations below. ⟨NC⟩ (⟨NS ⟩)
+gives the average occupation of a dark matter halo of mass M
+by a central (satellite) galaxy. The model has 5 parameters θ =
+(Mmin, σlog10 M, αsat, Msat, M∗
+12).
+⟨NC⟩(M, θ) = fA
+2
+�
+1 + erf
+�(log10(M) − Mmin)
+σlog10 M
+��
+(9)
+⟨NS ⟩(M, θ) = ⟨NC⟩(M, θ)
+� M − 10Msat−1
+10Msat
+�αsat
+(10)
+Only a fraction of distinct haloes hosts a central galaxy with an
+AGN. The fA parameter, as introduced by Miyaji et al. (2011, Eq.
+24), can be interpreted as the duty cycle of halo centers being an
+Article number, page 7 of 17
+
+102
+101
+h
+100
+10-1
+Best-fit HOD
+eROSITA X-ray AGN
+10-2
+10-2
+10-1
+100
+101
+R [h-1 Mpc]A&A proofs: manuscript no. main
+Table 2. HOD parameters obtained (median of the posterior) by jointly
+fitting the auto-correlation function and the galaxy-galaxy lensing of
+the X-ray flux-limited AGN sample. The uncertainties quoted are 1σ
+(15.9–84.1 percentiles). Priors are flat in linear space.
+parameters
+min
+max
+0.05 < z < 0.55
+Mmin
+8.0
+15.0
+13.06 ± 0.44
+σlog10 M
+0.05
+1.5
+1.28 ± 0.2
+αsat
+0.1
+1.5
+0.73 ± 0.38
+Msat − Mmin
+-3.0
+2.45
+1.46 ± 0.52
+M∗
+12
+-4.0
+0.1
+-0.96 ± 0.45
+evidence (logZ)
+-39.88 ± 0.14
+deduced parameters
+b(z = ¯z) = 0.991+0.078
+−0.096
+b(z = 0.1) = 0.915+0.065
+−0.08
+fsat < 20.6%
+4-parameter fit, σlog10 M = 1.3
+Mmin
+13.09 ± 0.19
+αsat
+0.75 ± 0.39
+Msat − Mmin
+1.56 ± 0.46
+M∗
+12
+-0.97 ± 0.46
+evidence (logZ)
+-38.6 ± 0.12
+deduced parameters
+b(z = ¯z) = 1.001+0.075
+−0.094
+b(z = 0.1) = 0.918+0.065
+−0.076
+fsat < 16.8%
+4-parameter fit, σlog10 M = 1.0
+Mmin
+12.47 ± 0.26
+αsat
+0.75 ± 0.39
+Msat − Mmin
+1.84 ± 0.53
+M∗
+12
+-1.0 ± 0.5
+evidence (logZ)
+-40.34 ± 0.11
+deduced parameters
+b(z = ¯z) = 0.996+0.067
+−0.097
+b(z = 0.1) = 0.919+0.059
+−0.081
+fsat < 66.4%
+AGN. In this study, since the correlation function measurements
+do not depend on the normalization of the occupation distribu-
+tion, we arbitrarily set fA to 1.
+To avoid sampling un-physical values of Msat, the parame-
+ter passed to the fitting routine is Msat − Mmin with boundaries
+specified in Table 2.
+To fit for the ∆Σ measurement at small separations and ben-
+efit from the signal present, we need to add the prediction for a
+point-like mass term that represents the baryonic lensing mass
+of the AGN host galaxies. It adds the parameter M∗
+12 as follows:
+∆Σ∗(r) = 10M∗
+12+12
+πr2
+.
+(11)
+The posterior of this parameter represents the mean baryonic
+lensing mass of the galaxies hosting AGN. This mass is related
+to stellar mass (inferred with stellar population synthesis mod-
+els) but will also encompass gas in and around the galaxy. This
+baryonic lensing mass can be considered the upper limit of the
+mean stellar mass of galaxies hosting AGN.
+In total, we fit for five parameters on the two measurements
+∆Σ (wp(rp)) which have S/N=46 (17.7) in 15 (11) radial bins.
+The parameters are sampled with a flat prior (in linear space)
+within broad boundaries as specified in Table 2.
+4.2. Sub halo abundance matching models
+The Comparat et al. (2019, 2020b) empirical AGN model statis-
+tically links the dark matter haloes to the probability of hosting
+an AGN and its spectral energy distribution. By construction, it
+follows the X-ray luminosity function from Aird et al. (2015).
+Importantly for interpretation, the assignment is done regardless
+of the environment in which haloes live. The model has two pa-
+rameters: the fraction of AGN in satellites sub haloes and the
+scatter in the abundance matching relation between stellar mass
+and hard X-ray luminosity.
+We show the direct wr(rp) prediction from the mock cata-
+logues of Liu et al. (2022c) in Fig. 3. It is consistent with obser-
+vations. It was obtained with fsat = 10% (fraction of AGN being
+satellites) and σ = 1 (scatter in the abundance matching proce-
+dure between hard X-ray luminosity and stellar mass). These pa-
+rameters were chosen by hand by Comparat et al. (2019, 2020a).
+At that time (before this study), such parameters resulted in rea-
+sonable predictions.
+Creating a complete SHAM-base mock catalog is long (or-
+der of a few CPU hours) and thus impractical for fitting purposes.
+Furthermore, with current light cones constructed with replica-
+tions, predicting the galaxy-galaxy lensing signal is tedious as
+the dark matter particles are not kept. So, instead of predict-
+ing summary statistics as measured as a function of the SHAM
+parameters, we directly predict the halo occupation distribution
+curves as a function of fsat and σ. Thus, we sample a small and fi-
+nite number of (fsat, σ) combinations and create individual mock
+catalogs to predict the HOD curves.
+5. Results
+We discuss here the results of the fitting procedure and the
+comparison between models. In Sec. 5.1 (5.2), we discuss the
+results obtained with the HOD (SHAM) model. For the first
+time, we measure with relatively small uncertainties the com-
+plete halo occupation distribution of a low redshift flux-limited
+X-ray-selected sample of AGN. We obtain a global view of the
+distribution of haloes hosting X-ray AGN; see Fig. 6.
+5.1. HOD results
+We fit the parameters of the HOD model with a nested sampling
+method ultranest (Buchner 2021). The resulting parameters are
+given in Table 2. The constraints on the HOD parameters (when
+fitting individually each summary statistic or both jointly) are
+shown in Fig. 5. It illustrates the complementary nature of the
+two measurements. The comparison between the joint best-fit
+model and the clustering measurements and lensing measure-
+ments are shown in Figs. 3, 4. The models are sensible. They
+account for the observations.
+The five parameters are meaningful, although not precisely
+constrained by the joint fit of both summary statistics. For
+the central haloes, Mmin takes a median posterior value of
+13.06±0.44, the width of the error function is found at σlog10 M =
+1.3 ± 0.2. There is a low 1σ-level tension between the constraints
+on these parameters obtained by each summary statistic; see Fig.
+5. Due to the higher signal-to-noise on the lensing statistic, the
+combined best-fit values are closer to the individual best-fit value
+on the lensing statistic. For the satellites, the slope is best-fit at
+αsat =0.73±0.38 and the transition occurs in haloes 10 to 100
+times more massive than the typical halo : Msat − Mmin = 1.46
+± 0.52. Both summary statistics point to these parameter values
+(Fig. 5). The typical baryonic lensing mass of galaxies hosting
+Article number, page 8 of 17
+
+Comparat et al.: X-ray AGN HOD
+Fig. 5. Constraints were obtained on the HOD parameters when fitting only the clustering measurement (yellow), the lensing measurement (purple),
+or both jointly (blue). Contours show 1 and 2 σ constraints. Most of the constraining power comes from galaxy-galaxy lensing.
+these AGN is M∗
+12 = -0.96 ± 0.45. It sets an upper limit to the
+mean stellar mass of galaxies hosting AGN of ∼ 1011M⊙. The
+1σ boundaries encompass 3.9×1010 and 3.1×1011M⊙, which is
+in fair agreement with expectations from AGN host stellar mass
+function (Bongiorno et al. 2016; Yang et al. 2018b). This param-
+eter is not degenerate with others and is constrained only by the
+lensing measurements at small separations.
+We note a degeneracy between Mmin and σlog10 M, which
+we investigate. We decrease the number of parameters by fix-
+ing σlog10 M to 1.3 (similar to the best-fit value) and 1 (to force
+a less broad halo distribution, a sharper transition). We obtain
+a set of best-fit parameters (see Table 2) that are compatible
+with the 5-parameter fit. When fixing σlog10 M to 1.3, we ob-
+tain Mmin13.09 ± 0.19, similar value to the 5-parameter fit but
+with half the uncertainty. Results for other parameters remain
+unchanged. When fixing σlog10 M to 1, Mmin is logically forced to
+lower values to ∼ 12.5 to be able to fit the overall signal. The
+halo occupation distribution posterior is close to that of the five
+parameter fit, see Fig. 6 black and yellow/orange contours.
+We obtain a global view of the distribution of haloes hosting
+X-ray AGN; see Fig. 6. The 4-parameter best-fit model is within
+the 1σ uncertainty of the 5-parameter best-fit model. Due to the
+degeneracy between Mmin and σlog10 M, the 4-parameter fit HOD
+with σlog10 M = 1 is skewed towards lower masses compared to
+the 5-parameter fit. With the HOD model, we derive the average
+halo mass hosting central (central or satellite) AGN is 3.93+2.03
+−2.44×
+1012M⊙ (4.95+2.63
+−1.99 × 1012M⊙). These values are comparable to
+the findings of Rodríguez-Torres et al. (2017). We measure that
+Article number, page 9 of 17
+
+Wp(rp)
+Combined
+1.5
+wo6ol0
+1.0
+0.5
+0.0
+1.5
+1.0
+0.5
+0.0
+2
+-2
+0
+-2
+-4
+8
+10
+12
+14
+0.0
+0.5
+1.0
+1.5
+0.0
+0.5
+1.0
+1.5
+-2
+0
+-4
+~2
+0
+Mmin
+OiogroM
+αsat
+Msat  Mmin
+Mi2A&A proofs: manuscript no. main
+Fig. 6. Inferred halo occupation distribution (solid) split into central (dashes) and satellite (dots) for the 4 and 5 parameter HOD fits (yellow/orange
+and black). The 4-parameter best-fit model is within the 1σ uncertainty of the 5-parameter best-fit model. Due to the degeneracy between Mmin
+and σlog10 M, the 4-parameter fit HOD with σlog10 M = 1 is skewed towards lower masses compared to the 5-parameter fit. The direct predictions
+from mock catalogs from Leauthaud et al. (2015); Georgakakis et al. (2018); Comparat et al. (2019) are shown on the right panel. They are within
+the fitted contours obtained. The mocks from Leauthaud et al. (2015); Georgakakis et al. (2018) have a lower σlog10 M value (sharper transition)
+and are thus more in line with the 4-parameter fit. The mock from Comparat et al. (2019) has a higher σlog10 M value and is comparable to the
+5-parameter fit.
+the distribution of halo masses is broad. We thus confirm that
+quoting a typical halo mass will be extremely sensitive to the
+definition of what ‘typical’ means; see discussion in Leauthaud
+et al. (2015).
+The direct HOD predictions from mock catalogs from Leau-
+thaud et al. (2015); Georgakakis et al. (2018); Comparat et al.
+(2019) are shown on the right panel of Fig. 6. They are within
+the fitted contours obtained. The mocks from Leauthaud et al.
+(2015); Georgakakis et al. (2018) have a lower σlog10 M value
+(sharper transition) and are thus more in line with the 4-
+parameter fit. The mock from Comparat et al. (2019) has a higher
+σlog10 M value and is comparable to the 5-parameter fit (see more
+discussion in the SHAM section below). The normalization of
+⟨N(M)⟩ can be added as a parameter and possibly constrained
+by jointly fitting the clustering and lensing summary statistics
+with the stellar mass (or luminosity) function of galaxies hosting
+X-ray AGN to have a handle on the fraction of galaxies hosting
+an AGN. Though measuring reliable host-galaxy stellar masses
+in the case of type 1 AGN is complex (Ciesla et al. 2015; Zou
+et al. 2022), and is left for future studies.
+The large-scale halo bias inferred is given in Table 2 and
+shown in Figs. 7. At the mean redshift (0.34), it takes a value of
+b(¯z = 0.34) = 0.99+0.08
+−0.10, which extrapolated to redshift z = 0.1
+becomes b(z = 0.1) = 0.92+0.07
+−0.08. The deduced large-scale halo
+bias is the same if we fit the HOD model with 4 or 5 parame-
+ters, see Table 2. Krumpe et al. (2015) measured the bias of X-
+ray-selected AGN in a similar redshift range but for intrinsically
+more luminous AGN. With this analysis, we add a new measure-
+ment of the bias at lower soft X-ray luminosity: 8.1 × 1042 erg
+s−1. We confirm the weak positive correlation between bias and
+soft X-ray luminosity found by Krumpe et al. (2015), see Fig. 7
+bottom panel. We fit a linear relationship between the quantities
+and obtain b = (0.48 ± 0.14)LX + (−19.68 ± 6.17). The slope
+value obtained is 3.3σ (0.48/0.14=3.3) away from 0.
+Other X-ray-selected AGN clustering studies were either at
+lower redshift (Cappelluti et al. 2010) or higher redshift (Gilli
+et al. 2009; Starikova et al. 2011; Koutoulidis et al. 2013; Viita-
+nen et al. 2019; Allevato et al. 2019) and always covered higher
+luminosities. This new study is complementary to them.
+5.2. Halo abundance matching results
+The model has two parameters: the fraction of satellite AGNs
+and the scatter in the relation between stellar mass and X-
+ray luminosity. The predicted curves extend to halo masses of
+1011.5M⊙ (and not lower) due to the resolution of the simulation
+used. Both impact the shape and amplitude of the clustering sig-
+nal and the HOD. Figure 8 shows the predicted HOD curves for
+a subset of the parameter space explored. In the top left panel,
+the satellite fraction is fixed to 10%, and the σ parameter varies.
+The lower the σ, the sharper the transition is. The σ parameter
+from SHAM is related to the σlog10 M parameter from the HOD
+model. Mock catalogs with higher σ have a distribution of dark
+matter haloes more extended towards lower masses. In the top
+right panel, σ is fixed to 0.8, and the fsat varies. The higher the
+fsat, the steeper the slope of the satellite occupation curve (the
+larger the α parameter). The fsat parameter is related to both the
+αsat and the Msat HOD parameters.
+We compute a distance, denoted d, between each predicted
+HOD curve (NS HAM(M)) and the 50th precentile of the inferred
+HOD model as follows
+d = ΣM=15.5
+M=11.5
+�
+NS HAM(M, fsat, σ) − N50%
+HOD(M)
+�2
+�
+N84.1%
+HOD (M) − N15.9%
+HOD (M)
+�2
+.
+(12)
+Figure 8 (bottom panels) shows the distances as a function of σ
+and fsat. We find mock catalogs constructed with parameters sat-
+isfying σ < 2− fsat/10 predict halo occupation distributions well
+Article number, page 10 of 17
+
+HOD 4-p
+central
+HOD 5-p
+satellite
+101
+((W)N)
+100
+10-1
+10-2
+11
+12
+13
+14
+15
+log1o(Mhalo [M ])Mockcatalogues
+Comparat2019
+101
+Georgakakis201g
+Leauthaud 2015
+((W)N)
+100
+10-1
+10-2
+11
+12
+13
+14
+15
+log1o(Mhalo [M])Comparat et al.: X-ray AGN HOD
+Fig. 7. Inferred large-scale halo bias as a function of redshift (top panel)
+and luminosity (bottom panel) compared to (Krumpe et al. 2015) (red-
+shift range 0.16-0.36). We confirm the trend with soft X-ray luminosity
+and obtain a best-fit of y = (0.482±0.143)x+(−19.684±6.173) between
+the soft X-ray luminosity and the large-scale halo bias.
+within the contours of the 5-parameter best-fit HOD inferred
+from the observations (Fig. 8 bottom left panel). Parameter com-
+binations such as σ > 2 − fsat/10 are less preferred (top right
+corner of the bottom left panel). d is minimized for σ = 0.8 and
+fsat = 4%, see the star in the Figure. The six smallest distances
+are pointed out with empty circles. When comparing to the 4-
+parameter best-fit HOD contours (Fig. 8 bottom right panel), pa-
+rameters within σ < 2.4 − fsat/10 and σ > 0.5 are acceptable.
+Here we find that solutions with low σ are less preferred. In that
+case, d is minimized for σ = 1.2, and fsat = 4, see the star in the
+Figure. The six smallest distances are pointed out with empty
+circles. In both cases (comparing either to the 4-parameter of the
+5-parameter HOD fit), the best solutions point towards low fsat
+values.
+Mocks with both high σ and high fsat are far from the obser-
+vations and are ruled out.
+6. Summary and discussion
+This article provides a complete picture of how soft X-ray AGNs
+populate the cosmic web (Fig. 1). This achievement is possi-
+ble thanks to two factors: (i) the combination of the eROSITA
+eFEDS X-ray survey with its dedicated SDSS spectroscopic
+follow-up and with the HSC S19A lensing products (ii) the com-
+plementary nature of the two summary statistics fitted (Figs. 3,
+4). We obtain meaningful HOD constraints for an X-ray-selected
+AGN sample (Fig. 5, 6). We interpret the summary statistics with
+state-of-the-art HOD and SHAM models (Sect. 5). We set upon
+firm footage the fact that the mass distribution of haloes host-
+ing X-ray-selected AGN is broad, as hinted by previous studies.
+Both models point to a shallower satellite slope than for galaxy
+surveys meaning that the satellite fraction for X-ray-selected
+AGN is low, similar to the findings of Miyaji et al. (2011). Inter-
+estingly, we find a relatively large σlog10 M that is likely related to
+the width of the specific accretion rate distribution. Contrasting
+our results with those of Krumpe et al. (2015), the large-scale
+halo bias of X-ray-selected AGN appears to correlate (3.3σ sig-
+nificance) with soft band X-ray luminosity (Fig. 7). We compare
+the results with predictions from SHAM models and can rule out
+a portion of the parameter space (Fig. 8).
+6.1. On the σ and σlog10 M parameters
+The σ parameter in the SHAM model is the scatter in the abun-
+dance matching relation between the stellar mass of the galaxy
+hosting the AGN and the AGN hard X-ray luminosity (2–10
+keV). The probability distribution function of specific accre-
+tion rate resulting from a broad range of galaxy stellar masses
+(hosting AGN) is close to a power-law (with slope -1) in the
+range 31.5 < log10(λS AR) < 33.5 (see Fig. 5 of Comparat
+et al. (2019)). The distribution obtained deviates from the power
+law at high accretion rates. Indeed the scatter induces an expo-
+nential cut-off. The distribution at the faint end of the function
+would require higher-resolution simulations to be populated. The
+HOD results obtained here are compatible with SHAM models
+if σ ∈ [0.8, 1.2] and incompatible for low values of σ < 0.5
+(for the four parameters HOD fit) or high values (for the 5-
+parameter HOD fit). Indeed low values of σ induce a steeper
+probability distribution function of specific accretion rate, which
+are excluded by observations (Georgakakis et al. 2017). In the
+opposite regime, large values of σ induce a shallow (tending to
+become flat) probability distribution function of specific accre-
+tion rate when considering the entire population. In a sense, the
+σ SHAM parameter is related to how broad the distribution of
+specific accretion rate and its slope is.
+The σlog10 M parameter characterizes how broad the host halo
+distribution is. It is related to the diversity of host galaxies and
+their stellar mass via the stellar-to-halo mass relation (Moster
+et al. 2013; Behroozi et al. 2013). The relatively high σlog10 M ∼
+1.3 parameter obtained indicates that the host halo mass distribu-
+tion and, thus, the host stellar mass distribution are both broad.
+This is consistent with studies of the AGN host-galaxy stellar
+mass function (Bongiorno et al. 2016).
+So, it seems that both models point to the same general in-
+terpretation: the distribution of host-galaxy stellar mass and that
+of specific accretion rate are ‘broad’, which strengthens direct
+observations of these distributions (Bongiorno et al. 2016; Geor-
+gakakis et al. 2017), even if these might be subject to systematic
+effects in the measurement of the stellar mass of type 1 AGN
+(Ciesla et al. 2015).
+Article number, page 11 of 17
+
+2.0
+y=(0.482±0.143)x+(-19.684±6.173)
+1.8
++
+eFEDS
+Krumpe et al. 15
+1.6
+1.4
+1.2
+1.0
+0.8-
+0.6
+41
+42
+43
+44
+45
+log1o(L0.5 - 2 keV)2.0
+44.50
+1.8
+44.25
+1.6
+44.00
+- 2 keV)
+1.4
+43.75
+1.2
+43.50
+1.0
+43.25
+0.8
+43.00
+eROSITAeFEDS
+Krumpe et al. 15
+42.75
+0.6
+0.0
+0.2
+0.4
+0.6
+ZA&A proofs: manuscript no. main
+Fig. 8. SHAM predictions plotted with the fitted HOD model 1 σ contour of the 4 and 5 parameters HOD fit results. On the top left panel, the
+satellite fraction is fixed to 10%, and the σ parameter is varied. On the top right panel, σ is fixed to 0.8, and the fsat is varied. On the bottom left
+(right) panel is shown, as a function of σ and fsat, the distance between the HOD predicted by SHAM models and the 5-parameter (4-parameter)
+HOD inferred from the observations. The black dashed line on the bottom left panel corresponds to σ = 2 − fsat/10. When comparing to the
+5-parameter HOD fit, the bottom left half, below the σ < 2 − fsat/10 line of the parameter space, is preferred. Compared to the 4-parameter HOD
+fit (bottom right panel), the bottom left half is also preferred. The dashed line represents σ = 2.4 − fsat/10. The star identifies the lowest distance
+model. Empty circles identify the six lowest distance models.
+With the innermost lensing measurements, we measure the
+baryonic lensing mass for this sample (M∗
+12) to be within 4×1010
+and 3 × 1011M⊙. From the mock catalog, we predict a broad
+stellar mass distribution of AGN host galaxies with a median
+4 × 1010M⊙ and a large standard deviation of 0.6 dex. So, the
+SHAM predicted stellar mass being smaller than the HOD in-
+ferred baryonic lensing mass; we find that interpretations from
+the two models are consistent.
+6.2. On the satellite occupation
+As suggested in Leauthaud et al. (2015), the combination of clus-
+tering and lensing best constraints satellite occupation statistics.
+Compared to previous studies, we take here a significant step for-
+ward. Indeed satellite fractions inferred from clustering studies
+are limited by the precision of redshift in the presence of broad
+line AGNs, and for example Shen et al. (2013) or Rodríguez-
+Torres et al. (2017) could not constrain it. Lensing studies were
+limited by small numbers of X-ray-selected AGN (Leauthaud
+et al. 2015) and showed large uncertainties in the satellite occu-
+pation statistics. By combining eFEDS with HSC, we find a pref-
+erence for low satellite fractions (HOD upper limit is fsat < 20%
+and SHAM best fits are with fsat < 12%). The HOD result shows
+a preference for a shallow satellite slope (∼ 0.75) that is smaller
+than measured for galaxy samples (α ∼ 1−1.1 and fsat of 40% for
+galaxies with a stellar mass of 3×1010M⊙) (Zehavi et al. 2011;
+Zu & Mandelbaum 2015).
+The low satellite fraction could, in part, be due to the soft
+X-ray selection of the AGN. Indeed, satellite AGN could be ob-
+scured and only detectable in hard X-ray or the infrared (Ko-
+cevski et al. 2015; Krumpe et al. 2018). Krumpe et al. (2018)
+Article number, page 12 of 17
+
+1.6
+101
+1.4
+1.2
+100
+(M)
+1.06
+ONX
+0.8
+10-1
+HOD 5-p
+HOD 4-p =1
+0.6
+Mock, fsat = 10
+10-2
+0.4
+12
+14
+log1o(Mhalo [M  J)16
+101
+14
+12
+100
+(N(M))
+10
+8
+10-1
+HOD 5-p
+HOD4-p=1
+6
+Mock,=0.8
+10-2
+4
+12
+14
+log1o(Mhalo [M ])1.6
+1.5
+1.4
+1.0
+1.2
+0.5
+6 1.0
+0.0
+0.8
+-0.5
+0.6
+0.4
+-1.0
+5
+10
+15
+fsat1.6
+1.4
+0.5
+HOD
+1.2
+0.0
+4-p
+6 1.0
+(d2)
+0.5
+0.8
+0.6
+1.0
+0.4
+5
+10
+15
+fsatComparat et al.: X-ray AGN HOD
+compared the cross-correlation functions (CCF) of Swift BAT
+AGNs with 2MASS redshift survey galaxies and their HODs.
+Since Swift BAT AGN sample is hard (14-195 keV) X-ray-
+selected, it contains a larger fraction of type 2 obscured AGN
+than eROSITA-based samples. They found clear suppression of
+the 1-halo term in type 1 AGN CCF compared to type 2. The
+HOD analysis shows α ∼ 1 for the type 2 AGN HOD while that
+of the type 1 AGN was α <∼ 0.6. Powell et al. (2018) obtained
+similar results. A possible scenario causing the low α is the sup-
+pression of sub-halo mergers in high velocity encounters in high
+mass halos (Altamirano-Dévora et al. 2016; Oogi et al. 2020).
+An alternative interpretation of the apparent shallow slope is that
+the satellite HOD slope is not shallow, but the satellite distribu-
+tion profile within the dark matter halo does not follow the mass
+density profile assumed in the HOD modeling. If the satellite
+distribution is suppressed towards the outer part of the halo, the
+ordinary HOD modeling would result in low fitted α. Indeed, it
+would appear as if the satellites were suppressed in high-mass
+halos with large virial radii. However, one should be cautious as
+such interpretations are still a debate.
+6.3. Triggering mechanism for soft X-ray AGN in the cosmic
+web
+The general SHAM scheme applied to populate mock catalogs
+with AGN accounts for the observations satisfactorily. One im-
+portant assumption made in the SHAM model is that the assign-
+ment of an AGN to a galaxy is independent of the environment: it
+ignores the properties of the neighboring haloes. It implies that,
+to the first order, the larger scale environment, beyond the galaxy
+host halo, is not the primary driver to turn on the AGN. Instead,
+the local environment (within the virial radius) i.e., the circum-
+galactic medium, the interstellar medium, and the stellar popu-
+lations, are likely more decisive parameters. It agrees with the
+findings of Yang et al. (2018a); Allevato et al. (2019); Siudek
+et al. (2023). It emphasizes internal processes and their role as
+AGN triggers, for example, disc instabilities (e.g. Bournaud et al.
+2011) or the presence of bars (e.g. Ohta et al. 2007).
+The fact that the satellite slope is shallower than that of galaxies
+with equivalent stellar mass means that the in-fall of a satellite on
+a larger structure makes it less likely to host an AGN, even more,
+when structures are larger. It likely illustrates that the gas strip-
+ping from satellite galaxies in deep potential wells suppresses
+AGN. It is compatible with the environment quenching mecha-
+nism described by Peng et al. (2010, 2012).
+6.4. Outlook
+The eROSITA eFEDs observations constitute about 1% of the
+full eROSITA All-Sky Survey (eRASS). This study paves the
+way towards charting the co-evolution of X-ray AGN and their
+host galaxies and dark matter haloes.
+In the coming decade, by combining eROSITA with SDSS-
+V, 4MOST, and DESI spectroscopic redshifts (Kollmeier et al.
+2017; Merloni et al. 2019; DESI Collaboration et al. 2016) and
+with LSST and Euclid lensing products, one will be able to
+carry out the similar analysis over a larger area and on an ex-
+tended redshift range, up to z=1. Between eFEDS (120 deg2,
+z < 0.55) and future analysis (13,000 deg2, z < 1), the comoving
+volume will increase by a factor 450. HOD parameters should
+be inferred to the percent level. We will accurately measure the
+halo occupation distributions as a function of host-galaxy prop-
+erties and AGN properties towards characterizing possible cor-
+relations between HOD parameters and host-galaxy, AGN, and
+environmental properties. With that, one should unravel the role
+of AGN in shaping the galaxy population and its hot circum-
+galactic medium (Hopkins et al. 2006; Comparat et al. 2022).
+Complementary to HOD analysis is the direct or partial cor-
+relations with host galaxy properties; see reviews from Brandt &
+Yang (2021); Brandt & Alexander (2015). In recent years, spec-
+tral energy distribution fitting has dramatically improved in re-
+trieving unbiased galaxy stellar parameters of galaxies hosting
+AGN (e.g., Mountrichas et al. 2021; Yang et al. 2022, Buchner
+et al. in prep). The upcoming Rubin observatory LSST survey1
+(Ivezi´c et al. 2019) will provide deep multi-band imaging to be
+used to determine host galaxy properties. In addition, the future
+Euclid2 imaging space mission (Laureijs et al. 2011) will en-
+able accurate morphological measurements of AGN hosts on a
+significant fraction of the extra-galactic sky. Together these will
+allow charting of the physics of the connection between AGN,
+host galaxy morphology, and stellar properties (e.g. Yang et al.
+2019; Ni et al. 2019) and give further insight on the ecology of
+the cosmic web of X-ray AGN.
+References
+Abdurro’uf, Accetta, K., Aerts, C., et al. 2022, ApJS, 259, 35
+Aihara, H., AlSayyad, Y., Ando, M., et al. 2019, PASJ, 71, 114
+Aihara, H., AlSayyad, Y., Ando, M., et al. 2022, PASJ, 74, 247
+Aird, J., Coil, A. L., Georgakakis, A., et al. 2015, MNRAS, 451, 1892
+Allevato, V., Viitanen, A., Finoguenov, A., et al. 2019, A&A, 632, A88
+Altamirano-Dévora, L., Miyaji, T., Aceves, H., et al. 2016, Rev. Mexicana As-
+tron. Astrofis., 52, 11
+Bartelmann, M. & Schneider, P. 2001, Phys. Rep., 340, 291
+Behroozi, P., Wechsler, R., & Wu, H.-Y. 2013, ApJ, 762, 109
+Berk, A., Anderson, G. P., Bernstein, L. S., et al. 1999, in Society of Photo-
+Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 3756, Op-
+tical Spectroscopic Techniques and Instrumentation for Atmospheric and
+Space Research III, ed. A. M. Larar, 348–353
+Berlind, A. A. & Weinberg, D. H. 2002, ApJ, 575, 587
+Bernstein, G. M. & Jarvis, M. 2002, AJ, 123, 583
+Blanton, M. R., Bershady, M. A., Abolfathi, B., et al. 2017, AJ, 154, 28
+Bongiorno, A., Schulze, A., Merloni, A., et al. 2016, A&A, 588, A78
+Bournaud, F., Dekel, A., Teyssier, R., et al. 2011, ApJ, 741, L33
+Bradshaw, E. J., Almaini, O., Hartley, W. G., et al. 2013, MNRAS, 433, 194
+Brandt, W. N. & Alexander, D. M. 2015, Astronomy and Astrophysics Review,
+23, 1
+Brandt, W. N. & Yang, G. 2021, arXiv e-prints, arXiv:2111.01156
+Brunner, H., Liu, T., Lamer, G., et al. 2022, A&A, 661, A1
+Buchner, J. 2021, The Journal of Open Source Software, 6, 3001
+Bulbul, E., Liu, A., Pasini, T., et al. 2022, A&A, 661, A10
+Burke, D. L., Rykoff, E. S., Allam, S., et al. 2018, AJ, 155, 41
+Cannon, R., Drinkwater, M., Edge, A., et al. 2006, MNRAS, 372, 425
+Cappelluti, N., Ajello, M., Burlon, D., et al. 2010, ApJ, 716, L209
+Chambers, K. C., Magnier, E. A., Metcalfe, N., et al. 2016, arXiv e-prints,
+arXiv:1612.05560
+Chilingarian, I., Borisov, S., Goradzhanov, V., et al. 2021, arXiv e-prints,
+arXiv:2112.04866
+Ciesla, L., Charmandaris, V., Georgakakis, A., et al. 2015, A&A, 576, A10
+Comparat, J., Eckert, D., Finoguenov, A., et al. 2020a, The Open Journal of
+Astrophysics, 3, 13
+Comparat, J., Jullo, E., Kneib, J.-P., et al. 2013, MNRAS, 433, 1146
+Comparat, J., Merloni, A., Dwelly, T., et al. 2020b, A&A, 636, A97
+Comparat, J., Merloni, A., Salvato, M., et al. 2019, MNRAS, 487, 2005
+Comparat, J., Truong, N., Merloni, A., et al. 2022, A&A, 666, A156
+Conroy, C., Wechsler, R. H., & Kravtsov, A. V. 2006, ApJ, 647, 201
+Contreras, S., Angulo, R. E., & Zennaro, M. 2021, MNRAS, 504, 5205
+Cooray, A. & Sheth, R. 2002, Phys. Rep., 372, 1
+Coupon, J., Arnouts, S., van Waerbeke, L., et al. 2015, MNRAS, 449, 1352
+Cunha, C. E., Lima, M., Oyaizu, H., Frieman, J., & Lin, H. 2009, MNRAS, 396,
+2379
+Davis, M. & Peebles, P. J. E. 1983, ApJ, 267, 465
+Dekel, A. & Lahav, O. 1999, ApJ, 520, 24
+1 https://www.lsst.org
+2 https://www.cosmos.esa.int/web/euclid
+Article number, page 13 of 17
+
+A&A proofs: manuscript no. main
+DESI Collaboration, Aghamousa, A., Aguilar, J., et al. 2016, ArXiv e-prints
+[arXiv:1611.00036]
+Dey, A., Schlegel, D. J., Lang, D., et al. 2019, AJ, 157, 168
+Donoso, E., Yan, L., Stern, D., & Assef, R. J. 2014, ApJ, 789, 44
+Drinkwater, M. J., Byrne, Z. J., Blake, C., et al. 2018, MNRAS, 474, 4151
+Driver, S. P., Bellstedt, S., Robotham, A. S. G., et al. 2022, MNRAS, 513, 439
+Driver, S. P. & Robotham, A. S. G. 2010, MNRAS, 407, 2131
+Dvornik, A., Hoekstra, H., Kuijken, K., et al. 2018, MNRAS, 479, 1240
+Eckert, D., Gaspari, M., Gastaldello, F., Le Brun, A. M. C., & O’Sullivan, E.
+2021, Universe, 7, 142
+Favole, G., Comparat, J., Prada, F., et al. 2016, MNRAS, 461, 3421
+Flaugher, B., Diehl, H. T., Honscheid, K., et al. 2015, AJ, 150, 150
+Georgakakis, A., Aird, J., Schulze, A., et al. 2017, MNRAS, 471, 1976
+Georgakakis, A., Comparat, J., Merloni, A., et al. 2018, MNRAS, 3272
+Georgakakis, A., Nandra, K., Laird, E. S., Aird, J., & Trichas, M. 2008, MNRAS,
+388, 1205
+Gilli, R., Zamorani, G., Miyaji, T., et al. 2009, A&A, 494, 33
+Gunn, J. E., Siegmund, W. A., Mannery, E. J., et al. 2006, AJ, 131, 2332
+Guo, Q., White, S., Li, C., & Boylan-Kolchin, M. 2010, MNRAS, 404, 1111
+Guzzo, L., Scodeggio, M., Garilli, B., et al. 2014, A&A, 566, A108
+Hickox, R. C., Jones, C., Forman, W. R., et al. 2009, ApJ, 696, 891
+Hirata, C. & Seljak, U. 2003, MNRAS, 343, 459
+Hopkins, P. F., Hernquist, L., Cox, T. J., et al. 2006, ApJS, 163, 1
+Hsieh, B. C. & Yee, H. K. C. 2014, ApJ, 792, 102
+Ivezi´c, Ž., Kahn, S. M., Tyson, J. A., et al. 2019, ApJ, 873, 111
+Jones, D. H., Read, M. A., Saunders, W., et al. 2009, MNRAS, 399, 683
+Kaiser, N., Squires, G., & Broadhurst, T. 1995, ApJ, 449, 460
+Klypin, A., Prada, F., Yepes, G., Hess, S., & Gottlober, S. 2013, ArXiv e-prints
+[arXiv:1310.3740]
+Kocevski, D. D., Brightman, M., Nandra, K., et al. 2015, ApJ, 814, 104
+Kollmeier, J. A., Zasowski, G., Rix, H.-W., et al. 2017, arXiv e-prints
+[arXiv:1711.03234]
+Koutoulidis, L., Georgantopoulos, I., Mountrichas, G., et al. 2018, MNRAS, 481,
+3063
+Koutoulidis, L., Plionis, M., Georgantopoulos, I., & Fanidakis, N. 2013, MN-
+RAS, 428, 1382
+Kravtsov, A. V., Berlind, A. A., Wechsler, R. H., et al. 2004, ApJ, 609, 35
+Krumpe, M., Miyaji, T., & Coil, A. L. 2010, ApJ, 713, 558
+Krumpe, M., Miyaji, T., Coil, A. L., & Aceves, H. 2012, ApJ, 746, 1
+Krumpe, M., Miyaji, T., Coil, A. L., & Aceves, H. 2018, MNRAS, 474, 1773
+Krumpe, M., Miyaji, T., Husemann, B., et al. 2015, ApJ, 815, 21
+Landy, S. D. & Szalay, A. S. 1993, ApJ, 412, 64
+Laureijs, R., Amiaux, J., Arduini, S., et al. 2011, arXiv e-prints, arXiv:1110.3193
+Leauthaud, A., J. Benson, A., Civano, F., et al. 2015, MNRAS, 446, 1874
+Leauthaud, A., Tinker, J., Behroozi, P. S., Busha, M. T., & Wechsler, R. H. 2011,
+ApJ, 738, 45
+Li, X., Miyatake, H., Luo, W., et al. 2022, PASJ, 74, 421
+Lilly, S. J., Le Brun, V., Maier, C., et al. 2009, ApJS, 184, 218
+Liske, J., Baldry, I. K., Driver, S. P., et al. 2015, MNRAS, 452, 2087
+Liu, A., Bulbul, E., Ghirardini, V., et al. 2022a, A&A, 661, A2
+Liu, T., Buchner, J., Nandra, K., et al. 2022b, A&A, 661, A5
+Liu, T., Merloni, A., Comparat, J., et al. 2022c, A&A, 661, A27
+Luo, A. L., Zhao, Y.-H., Zhao, G., et al. 2015, Research in Astronomy and As-
+trophysics, 15, 1095
+Luo, W., Silverman, J. D., More, S., et al. 2022, arXiv e-prints, arXiv:2204.03817
+Mandelbaum, R., Lanusse, F., Leauthaud, A., et al. 2018a, MNRAS, 481, 3170
+Mandelbaum, R., Miyatake, H., Hamana, T., et al. 2018b, PASJ, 70, S25
+Mandelbaum, R., Tasitsiomi, A., Seljak, U., Kravtsov, A. V., & Wechsler, R. H.
+2005, MNRAS, 362, 1451
+Marulli, F., Bolzonella, M., Branchini, E., et al. 2013, A&A, 557, A17
+McLure, R. J., Cirasuolo, M., Dunlop, J. S., Almaini, O., & Foucaud, S. 2013, in
+Astrophysics and Space Science Proceedings, Vol. 37, Thirty Years of Astro-
+nomical Discovery with UKIRT, 323
+Medezinski, E., Oguri, M., Nishizawa, A. J., et al. 2018, PASJ, 70, 30
+Mendez, A. J., Coil, A. L., Aird, J., et al. 2016, ApJ, 821, 55
+Merloni, A., Alexander, D. A., Banerji, M., et al. 2019, The Messenger, 175, 42
+Miyaji, T., Krumpe, M., Coil, A. L., & Aceves, H. 2011, ApJ, 726, 83
+Miyatake, H., Battaglia, N., Hilton, M., et al. 2019, ApJ, 875, 63
+Momcheva, I. G., Brammer, G. B., van Dokkum, P. G., et al. 2016, ApJS, 225,
+27
+More, S., Miyatake, H., Mandelbaum, R., et al. 2015, ApJ, 806, 2
+Moster, B. P., Naab, T., & White, S. D. M. 2013, MNRAS, 428, 3121
+Mountrichas, G., Buat, V., Yang, G., et al. 2021, A&A, 646, A29
+Mountrichas, G., Georgakakis, A., & Georgantopoulos, I. 2019, MNRAS, 483,
+1374
+Myers, A. D., Brunner, R. J., Nichol, R. C., et al. 2007, ApJ, 658, 85
+Ni, Q., Yang, G., Brandt, W. N., et al. 2019, MNRAS, 490, 1135
+Nishimichi, T., Takada, M., Takahashi, R., et al. 2019, The Astrophysical Jour-
+nal, 884, 29
+Nishizawa, A. J., Hsieh, B.-C., Tanaka, M., & Takata, T. 2020, arXiv e-prints,
+arXiv:2003.01511
+Oguri, M., Lin, Y.-T., Lin, S.-C., et al. 2018, PASJ, 70, S20
+Ohta, K., Aoki, K., Kawaguchi, T., & Kiuchi, G. 2007, ApJS, 169, 1
+Oke, J. B. & Gunn, J. E. 1983, ApJ, 266, 713
+Oogi, T., Shirakata, H., Nagashima, M., et al. 2020, MNRAS, 497, 1
+Padovani, P., Alexander, D. M., Assef, R. J., et al. 2017, A&A Rev., 25, 2
+Paturel, G., Petit, C., Prugniel, P., et al. 2003, A&A, 412, 45
+Peng, Y.-j., Lilly, S. J., Kovaˇc, K., et al. 2010, ApJ, 721, 193
+Peng, Y.-j., Lilly, S. J., Renzini, A., & Carollo, M. 2012, ApJ, 757, 4
+Planck Collaboration, Aghanim, N., Akrami, Y., et al. 2020, A&A, 641, A6
+Powell, M. C., Cappelluti, N., Urry, C. M., et al. 2018, ApJ, 858, 110
+Predehl, P., Andritschke, R., Arefiev, V., et al. 2021, A&A, 647, A1
+Refregier, A. 2003, ARA&A, 41, 645
+Rodríguez-Torres, S. A., Comparat, J., Prada, F., et al. 2017, MNRAS, 468, 728
+Rowe, B. T. P., Jarvis, M., Mandelbaum, R., et al. 2015, Astronomy and Com-
+puting, 10, 121
+Salvato, M., Ilbert, O., & Hoyle, B. 2018, Nature Astronomy, 68
+Salvato, M., Wolf, J., Dwelly, T., et al. 2022, A&A, 661, A3
+Schneider, P. C., Freund, S., Czesla, S., et al. 2022, A&A, 661, A6
+Scoville, N., Aussel, H., Brusa, M., et al. 2007, ApJS, 172, 1
+Seljak, U., Makarov, A., Mandelbaum, R., et al. 2005, Phys. Rev. D, 71, 043511
+Seppi, R., Comparat, J., Bulbul, E., et al. 2022, A&A, 665, A78
+Sevilla-Noarbe, I., Bechtol, K., Carrasco Kind, M., et al. 2021, ApJS, 254, 24
+Shen, Y., McBride, C. K., White, M., et al. 2013, ApJ, 778, 98
+Sheth, R. K. & Tormen, G. 1999, MNRAS, 308, 119
+Silverman, J. D., Kashino, D., Sanders, D., et al. 2015, ApJS, 220, 12
+Sinha, M. & Garrison, L. H. 2020, MNRAS, 491, 3022
+Siudek, M., Mezcua, M., & Krywult, J. 2023, MNRAS, 518, 724
+Skelton, R. E., Whitaker, K. E., Momcheva, I. G., et al. 2014, ApJS, 214, 24
+Skrutskie, M. F., Cutri, R. M., Stiening, R., et al. 2006, AJ, 131, 1163
+Smee, S. A., Gunn, J. E., Uomoto, A., et al. 2013, AJ, 146, 32
+Starikova, S., Cool, R., Eisenstein, D., et al. 2011, ApJ, 741, 15
+Tanaka, M. 2015, ApJ, 801, 20
+Tanaka, M., Coupon, J., Hsieh, B.-C., et al. 2018, PASJ, 70, S9
+Tegmark, M. & Bromley, B. C. 1999, ApJ, 518, L69
+Tegmark, M. & Peebles, P. J. E. 1998, ApJ, 500, L79
+Trujillo-Gomez, S., Klypin, A., Primack, J., & Romanowsky, A. J. 2011, ApJ,
+742, 16
+Véron-Cetty, M.-P. & Véron, P. 2010, A&A, 518, A10
+Viitanen, A., Allevato, V., Finoguenov, A., et al. 2019, A&A, 629, A14
+Wechsler, R. H. & Tinker, J. L. 2018, ARA&A, 56, 435
+Xu, X., Zehavi, I., & Contreras, S. 2021, MNRAS, 502, 3242
+Yang, G., Boquien, M., Brandt, W. N., et al. 2022, ApJ, 927, 192
+Yang, G., Brandt, W. N., Alexander, D. M., et al. 2019, MNRAS, 485, 3721
+Yang, G., Brandt, W. N., Darvish, B., et al. 2018a, MNRAS, 480, 1022
+Yang, G., Brandt, W. N., Vito, F., et al. 2018b, MNRAS, 475, 1887
+York, D. G., Adelman, J., Anderson, Jr., J. E., et al. 2000, AJ, 120, 1579
+Zacharegkas, G., Chang, C., Prat, J., et al. 2022, MNRAS, 509, 3119
+Zehavi, I., Zheng, Z., Weinberg, D. H., et al. 2011, ApJ, 736, 59
+Zhang, Z., Wang, H., Luo, W., et al. 2021, A&A, 650, A155
+Zheng, Z., Berlind, A. A., Weinberg, D. H., et al. 2005, ApJ, 633, 791
+Zheng, Z., Coil, A. L., & Zehavi, I. 2007, ApJ, 667, 760
+Zou, F., Brandt, W. N., Chen, C.-T., et al. 2022, ApJS, 262, 15
+Zu, Y. & Mandelbaum, R. 2015, MNRAS, 454, 1161
+Acknowledgements. MK is supported by the DFG grant KR 3338/4-1. T. M. is
+supported by UNAM-DGAPA PAPIIT 111319 and CONACyT Ciencias Básica
+252531.
+This work is based on data from eROSITA, the soft X-ray instrument aboard
+SRG, a joint Russian-German science mission supported by the Russian Space
+Agency (Roskosmos), in the interests of the Russian Academy of Sciences rep-
+resented by its Space Research Institute (IKI), and the Deutsches Zentrum für
+Luft- und Raumfahrt (DLR). The SRG spacecraft was built by Lavochkin Asso-
+ciation (NPOL) and its subcontractors, and is operated by NPOL with support
+from the Max Planck Institute for Extraterrestrial Physics (MPE).
+The development and construction of the eROSITA X-ray instrument was led
+by MPE, with contributions from the Dr. Karl Remeis Observatory Bamberg
+& ECAP (FAU Erlangen-Nuernberg), the University of Hamburg Observatory,
+the Leibniz Institute for Astrophysics Potsdam (AIP), and the Institute for As-
+tronomy and Astrophysics of the University of Tübingen, with the support of
+DLR and the Max Planck Society. The Argelander Institute for Astronomy of
+the University of Bonn and the Ludwig Maximilians Universität Munich also
+participated in the science preparation for eROSITA.
+The eROSITA data shown here were processed using the eSASS/NRTA software
+system developed by the German eROSITA consortium.
+The Hyper Suprime-Cam (HSC) collaboration includes the astronomical com-
+munities of Japan and Taiwan, and Princeton University. The HSC instrumen-
+tation and software were developed by the National Astronomical Observatory
+of Japan (NAOJ), the Kavli Institute for the Physics and Mathematics of the
+Article number, page 14 of 17
+
+Comparat et al.: X-ray AGN HOD
+Universe (Kavli IPMU), the University of Tokyo, the High Energy Accelerator
+Research Organization (KEK), the Academia Sinica Institute for Astronomy and
+Astrophysics in Taiwan (ASIAA), and Princeton University. Funding was con-
+tributed by the FIRST program from the Japanese Cabinet Office, the Ministry
+of Education, Culture, Sports, Science and Technology (MEXT), the Japan Soci-
+ety for the Promotion of Science (JSPS), Japan Science and Technology Agency
+(JST), the Toray Science Foundation, NAOJ, Kavli IPMU, KEK, ASIAA, and
+Princeton University.
+This paper makes use of software developed for Vera C. Rubin Observatory. We
+thank the Rubin Observatory for making their code available as free software at
+http://pipelines.lsst.io/.
+This paper is based on data collected at the Subaru Telescope and retrieved from
+the HSC data archive system, which is operated by the Subaru Telescope and
+Astronomy Data Center (ADC) at NAOJ. Data analysis was in part carried out
+with the cooperation of Center for Computational Astrophysics (CfCA), NAOJ.
+We are honored and grateful for the opportunity of observing the Universe from
+Maunakea, which has the cultural, historical and natural significance in Hawaii.
+Funding for the Sloan Digital Sky Survey V has been provided by the Alfred P.
+Sloan Foundation, the Heising-Simons Foundation, the National Science Foun-
+dation, and the Participating Institutions. SDSS acknowledges support and re-
+sources from the Center for High-Performance Computing at the University of
+Utah. The SDSS web site is www.sdss5.org.
+SDSS is managed by the Astrophysical Research Consortium for the Participat-
+ing Institutions of the SDSS Collaboration, including the Carnegie Institution
+for Science, Chilean National Time Allocation Committee (CNTAC) ratified
+researchers, the Gotham Participation Group, Harvard University, Heidelberg
+University, The Johns Hopkins University, L’Ecole polytechnique fédérale de
+Lausanne (EPFL), Leibniz-Institut für Astrophysik Potsdam (AIP), Max-Planck-
+Institut für Astronomie (MPIA Heidelberg), Max-Planck-Institut für Extrater-
+restrische Physik (MPE), Nanjing University, National Astronomical Observa-
+tories of China (NAOC), New Mexico State University, The Ohio State Uni-
+versity, Pennsylvania State University, Smithsonian Astrophysical Observatory,
+Space Telescope Science Institute (STScI), the Stellar Astrophysics Participa-
+tion Group, Universidad Nacional Autónoma de México, University of Arizona,
+University of Colorado Boulder, University of Illinois at Urbana-Champaign,
+University of Toronto, University of Utah, University of Virginia, Yale Univer-
+sity, and Yunnan University.
+Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred
+P. Sloan Foundation, the U.S. Department of Energy Office of Science, and the
+Participating Institutions. SDSS acknowledges support and resources from the
+Center for High-Performance Computing at the University of Utah. The SDSS
+web site is www.sdss.org.
+SDSS is managed by the Astrophysical Research Consortium for the Partici-
+pating Institutions of the SDSS Collaboration including the Brazilian Participa-
+tion Group, the Carnegie Institution for Science, Carnegie Mellon University,
+Center for Astrophysics | Harvard & Smithsonian (CfA), the Chilean Partici-
+pation Group, the French Participation Group, Instituto de Astrofísica de Ca-
+narias, The Johns Hopkins University, Kavli Institute for the Physics and Math-
+ematics of the Universe (IPMU) / University of Tokyo, the Korean Participation
+Group, Lawrence Berkeley National Laboratory, Leibniz Institut für Astrophysik
+Potsdam (AIP), Max-Planck-Institut für Astronomie (MPIA Heidelberg), Max-
+Planck-Institut für Astrophysik (MPA Garching), Max-Planck-Institut für Ex-
+traterrestrische Physik (MPE), National Astronomical Observatories of China,
+New Mexico State University, New York University, University of Notre Dame,
+Observatório Nacional / MCTI, The Ohio State University, Pennsylvania State
+University, Shanghai Astronomical Observatory, United Kingdom Participation
+Group, Universidad Nacional Autónoma de México, University of Arizona, Uni-
+versity of Colorado Boulder, University of Oxford, University of Portsmouth,
+University of Utah, University of Virginia, University of Washington, University
+of Wisconsin, Vanderbilt University, and Yale University.
+Article number, page 15 of 17
+
+A&A proofs: manuscript no. main
+Appendix A: X-ray data analysis
+Appendix A.1: X-ray mask
+We use the region files created by eSASS/srctool to create X-
+ray masks for point sources (PS) and extended sources (EXT)
+(Liu et al. 2022b,a). Each source has its signal-to-noise ratio
+measured as a function of radius (circular apertures). An optimal
+radius for source extraction is found by maximizing the signal-
+to-noise ratio given the local background surface brightness. It is
+clipped to a minimum radius of 10′′(MINIMUM_SOURCE_RADIUS
+parameter) and a maximum radius of the 99% energy enclosed
+fraction radius of the point spread function. We use this maxi-
+mum signal-to-noise radius as a starting point to determine the
+area to be masked around sources.
+We measure the cross-correlation as a function of scale be-
+tween events (0.2-2.3 keV) and sources in the catalog. We mea-
+sure it for bins of the number of counts measured per source
+in the detection band. The cross-correlation becomes constant
+above a particular angular scale, which corresponds to a con-
+servative masking radius of a source (with a given number of
+counts), i.e., its average imprint on the sky, see Fig. A.1 top pan-
+els. For each cross-correlation curve, we measure the radius at
+which its value is between 1.25 and two times that of the constant
+values measured at large separation. This brackets the masking
+radius within the black vertical error bars shown in Fig. A.1 bot-
+tom panels. We find that this cross-correlation masking radius for
+point sources is, on average, 40 percent (20 for extended sources)
+larger than the eSASS/srctool radius of maximum signal-to-
+noise, see Fig. A.1 bottom panels. The srctool mask is likely not
+conservative enough for our purpose. For instance, the detection
+of a point source just beyond the eSASS/srctool masking ra-
+dius of another point source will be subject to biases due to the
+residual events measured via the cross-correlation. Though, if
+we followed the average masking radius suggested by the cross-
+correlation (Fig. A.1 bottom panels), the large scatter in the re-
+lation between the maximum signal-to-noise radius and the total
+number of counts would be missed. So to have a conservative
+mask that closely follows the data, we multiply the masking radii
+from eSASS/srctool by a factor of 1.4 (this is more conserva-
+tive than required for the extended sources, but it simplifies the
+procedure). In that way, the masking radius will reach, on aver-
+age, the line obtained from the cross-correlation. Doing so en-
+sures no remaining correlation between the set of events outside
+the mask and the source catalog. We are conservatively masking
+both point sources and extended sources individually.
+After applying the mask, we are left with 17,523 AGN can-
+didates. We are using the fraction of random points (see § 2.1.4)
+that fall in the masks, we estimate the area of the observed X-ray
+sky effectively occupied by sources. In all, sources occupy 9.805
+deg2 out of 141.97 deg2. AGN occupy 6.914 deg2, stars 0.988
+deg2, and extended sources 2.057 deg2.
+Appendix A.2: Random catalogue
+We use the sensitivity map produced by the eROSITA pipeline
+Brunner et al. (eSASS, apetool 2022) with a parameter Pthres =
+e−8 = 0.00033 (the Poisson probability threshold below which
+an excess of counts is considered a source), corresponding to a
+detection likelihood of 8. It is a pixelated fits image with size
+[0, 9000)×[0, 18000) containing the sensitivity limit (in counts).
+Each random point falls in a pixel of this map, and we attach the
+corresponding count limit Clim
+X to the random number. We draw a
+large set of redshift and X-ray fluxes ( fx, z) from the AGN X-ray
+luminosity function projection to assign to each random point
+Aird et al. (2015); Comparat et al. (2019). It is sampled down
+to 2 × 10−15erg cm−2 s−1, a flux value at which the area curve
+is smaller than 0.5 deg2. We convert the flux into an expected
+number of counts
+CT expected = fx × ECF × EEF × texp + CT background.
+(A.1)
+where the energy conversion factor is ECF = 1.164 × 1012. The
+encircled energy fraction is set to EEF = 0.65. The exposure
+time, texp, is obtained with the exposure map. CT background is ob-
+tained from the background map. We draw a random Poisson
+variable Rv for each CT expected. If this value exceeds the count
+limit, Rv > Clim
+X , the point is accepted in the random sample. We
+remove the shallower areas at the edge of the field through a min-
+imum exposure time threshold to minimize the maximum offset
+between the normalized cumulative distribution of the data sam-
+ple and the random sample. We find that an 830 seconds thresh-
+old minimizes the KS-test values at 0.19% (0.81%) for R.A.
+(Dec.). It removes ∼ 10 deg2. It is sufficiently accurate to es-
+timate clustering on the photometric sample. After masking ex-
+tended sources and stars and trimming the low exposure time re-
+gion, the total number of random points remaining is 3,713,726.
+Article number, page 16 of 17
+
+Comparat et al.: X-ray AGN HOD
+Fig. A.1. Cross-correlation between sources and events as a function of angular separation for extended (EXT, top left) and point-like (PS, top right)
+X-ray sources. Bottom. Masking radius v.s. log10 of the counts measured (bottom). Average masking radius obtained with the cross-correlation
+(black line). The masking radius obtained with eSASS/srctool for individual sources is systematically lower than the black line. Its best-fit
+polynomial (blue dashed) is multiplied by 1.2 (extended sources) or 1.4 (point sources) to align with the black line.
+Article number, page 17 of 17
+
+EXT
+1, 3 pixels
+371.1-622.7
+46.8-78.6
+1753.1-2941.5
+221.2-371.1
+27.9-46.8
+1044.8-1753.1
+131.8-221.2
+1.25,1.5,2
+ofevents
+622.7-1044.8
+78.6-131.8
+relative density
+101
+100
+101
+102
+103
+separationtosource[arcseconds]PS
+1, 3 pixels
+547.2-763.8
+53.0-74.0
+103
+4047.9-5650.3
+392.0-547.2
+38.0-53.0
+2899.9-4047.9
+280.8-392.0
+27.2-38.0
+events
+2077.5-2899.9
+201.2-280.8
+19.5-27.2
+1488.3-2077.5
+144.1-201.2
+14.0-19.5
+1066.2-1488.3
+103.3-144.1
+10.0-14.0
+densityof
+102
+763.8-1066.2
+74.0-103.3
+1.25,1.5,2
+relative
+101
+100
+101
+102
+103
+separationtosource[arcseconds]EXT
+[arc seconds]
+102
+Iradius
+masking
+eFEDs extended sources
+y=15.948x2.+0.046x+.34.124
+x1.2
+y=44.425x2+-79.217x+77.263
+EVTxSRC
+101
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+3.5
+4.0
+log1o(Count 0.2-2.3keV)PS
+eFEDspoint-like sources
+y=10.754x2+ -8.989x+ 24.49
+seconds]
+x1.4
+y=10.842x2+ 8.71x+2.75
+EVTxSRC
+arc
+102
+Iradius
+masking
+101
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+3.5
+4.0
+log1o(Count0.2-2.3keV)
\ No newline at end of file
diff --git a/j9AzT4oBgHgl3EQfbfze/content/tmp_files/load_file.txt b/j9AzT4oBgHgl3EQfbfze/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..61983817394b5ce07e6cb7d13dc3be943caaad6d
--- /dev/null
+++ b/j9AzT4oBgHgl3EQfbfze/content/tmp_files/load_file.txt
@@ -0,0 +1,2437 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf,len=2436
+page_content='Astronomy & Astrophysics manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' main  ©ESO 2023  January 5, 2023  The cosmic web of X-ray active galactic nuclei  seen through the eROSITA Final Equatorial Depth Survey (eFEDS)  Johan Comparat1⋆, Wentao Luo2, 3, Andrea Merloni1, Surhud More4, 5, Mara Salvato1, Mirko Krumpe6, Takamitsu  Miyaji7, William Brandt8, 9, 10, Antonis Georgakakis11, Masayuki Akiyama12, Johannes Buchner1, Tom Dwelly1,  Toshihiro Kawaguchi19, Teng Liu1, Tohru Nagao15, Kirpal Nandra1, John Silverman13, 14, Yoshiki Toba16, 17, 18, 15, Scott  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Anderson20,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Juna Kollmeier21  1 Max-Planck-Institut für extraterrestrische Physik (MPE),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Giessenbachstrasse 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' D-85748 Garching bei München,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Germany  2 Key Laboratory for Research in Galaxies and Cosmology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' School of Astronomy and Space Science,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' University of Science and  Technology of China,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Hefei,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Anhui 230026,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' China  3 Department of Astronomy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' School of Physical Sciences,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' University of Science and Technology of China,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Hefei,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Anhui 230026,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  China  4 The Inter-University Centre for Astronomy and Astrophysics (IUCAA),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Post Bag 4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Ganeshkhind,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Pune 411007,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' India  5 Kavli Institute for the Physics and Mathematics of the Universe (IPMU),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 5-1-5 Kashiwanoha,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Kashiwa-shi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Chiba 277-8583,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Japan  6 Leibniz-Institut für Astrophysik Potsdam,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' An der Sternwarte 16,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 14482 Potsdam,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Germany  7 Instituto de Astronomía sede Ensenada,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Universidad Nacional Autónoma de México,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Km 107 Carretera Tijuana-Ensenada,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 22860,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Ensenada,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Mexico  8 Department of Astronomy and Astrophysics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 525 Davey Lab,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The Pennsylvania State University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' University Park,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' PA 16802,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' USA  9 Institute for Gravitation and the Cosmos,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The Pennsylvania State University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' University Park,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' PA 16802,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' USA  10 Department of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 104 Davey Laboratory,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The Pennsylvania State University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' University Park,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' PA 16802,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' USA  11 Institute for Astronomy and Astrophysics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' National Observatory of Athens,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Paulou & I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Metaxa,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 11532,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Greece  12 Astronomical Institute,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Tohoku University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 6-3 Aramaki,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Aoba-ku,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Sendai,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Japan  13 Kavli Institute for the Physics and Mathematics of the Universe,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The University of Tokyo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Kashiwa,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Japan 277-8583 (Kavli IPMU,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  WPI)  14 Department of Astronomy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' School of Science,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The University of Tokyo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 7-3-1 Hongo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Bunkyo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Tokyo 113-0033,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Japan  15 Research Center for Space and Cosmic Evolution,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Ehime University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2-5 Bunkyo-cho,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Matsuyama,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Ehime 790-8577,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Japan  16 National Astronomical Observatory of Japan,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2-21-1 Osawa,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Mitaka,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Tokyo 181-8588,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Japan  17 Department of Astronomy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Kyoto University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Kitashirakawa-Oiwake-cho,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Sakyo-ku,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Kyoto,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Kyoto 606-8502,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Japan  18 Academia Sinica Institute of Astronomy and Astrophysics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 11F Astronomy-Mathematics Building,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' AS/NTU,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Section 4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Roosevelt Road,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Taipei 10617,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Taiwan  19 Department of Economics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Management and Information Science,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Onomichi City University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Hisayamada 1600-2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Onomichi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Hiroshima 722-8506,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Japan  20 Astronomy Department,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' University of Washington,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Box 351580,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Seattle,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' WA 98195,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' USA  21 The Carnegie Observatories,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 813 Santa Barbara Street,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Pasadena,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' CA 91101,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' USA  January 5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2023  ABSTRACT  Which galaxies in the general population turn into active galactic nuclei (AGN) is a keystone of galaxy formation and evolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Thanks to SRG/eROSITA’s contiguous 140 square degrees pilot survey field, we constructed a large, complete, and unbiased soft  X-ray flux-limited AGN sample at low redshift 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='05 < z < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Two summary statistics, the clustering using spectra from SDSS-V  and galaxy-galaxy lensing with imaging from HSC, are measured and interpreted with halo occupation distribution and abundance  matching models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Both models successfully account for the observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We obtain an exceptional complete view of the AGN  halo occupation distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The population of AGN is broadly distributed among halos with a mean mass of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='9+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='4 × 1012M⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  This corresponds to a large-scale halo bias of b(z = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='34) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='99+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='08  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The central occupation has a large transition parameter  σlog10(M) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='28 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The satellite occupation distribution is characterized by a shallow slope αsat = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='73 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We find that  AGNs in satellites are rare, with fsat < 20%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Most soft X-ray-selected AGNs are hosted by central galaxies in their dark matter  halo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' A weak correlation between soft X-ray luminosity and large-scale halo bias is confirmed (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='3σ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We discuss the implications of  environmental-dependent AGN triggering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' This study paves the way towards fully charting, in the coming decade, the co-evolution  of X-ray AGN, their host galaxies, and dark matter haloes by combining eROSITA with SDSS-V, 4MOST, DESI, LSST, and Euclid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Key words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' X-ray, active galactic nuclei  ⋆ E-mail: comparat@mpe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='mpg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='de  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Introduction  Active galactic nuclei (AGN) are a keystone in galaxy evolu-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' How they are triggered and are fueled are essential ques-  Article number, page 1 of 17  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='01388v1  [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='GA]  3 Jan 2023  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' main  tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Answering them will deepen our understanding of the  co-evolution between galaxies, the gas surrounding them, and  their central supermassive black holes (SMBH;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' see reviews from  Padovani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Eckert et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' This article focuses  on the large-scale environment of X-ray-selected AGN, namely  the population of dark matter haloes hosting them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' X-ray selec-  tion provides AGN samples with higher completeness and purity  than selections at different wavelengths (Hickox et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' As  devised in simulations, this population is diverse (Georgakakis  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Comparat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' To infer the population of  dark matter haloes hosting a sample of galaxies, the best tech-  nique to date consists of interpreting the complementary signals  from clustering and weak gravitational lensing (see for exam-  ple Comparat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' More et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Coupon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Favole et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Previous studies of the clustering of X-ray-selected AGN  were limited by the total number of X-ray AGN or the small  survey area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' They typically measured the large-scale halo bias  of AGN selected in different fashions (Gilli et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Cap-  pelluti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Starikova et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Koutoulidis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  2013, 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Leauthaud et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Viitanen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Alle-  vato et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The auto-correlation of X-ray-selected AGN  was studied locally (z ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='045) with 199 AGN in the Swift-  BAT all-sky survey (Cappelluti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' They found these  bright low redshift AGN to be hosted on average by dark mat-  ter haloes of mass 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='6 − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5 × 1013h−1M⊙ corresponding to a  large-scale halo bias of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' At higher redshift (z ∼ 1) with  deep pencil beam surveys (COSMOS observed with XMM and  Chandra, Bootes, and Chandra compilations) and larger num-  bers of AGN (ranging from 500 to 1,500), Gilli et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2009);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Starikova et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2011);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Koutoulidis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2013);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Viitanen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  (2019);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Allevato et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2019) inferred a large-scale halo bias of  ∼ 2 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2 corresponding to halo masses 4 − 9 × 1012h−1M⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' In  these studies, further splitting of the samples as a function of  AGN type, luminosity, and host-galaxy properties, is not very  conclusive due to small statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' There are hints of correlation  with X-ray luminosity and an indication of a low satellite frac-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The study of the angular auto-correlation of photometri-  cally selected AGN, so with much larger samples, led to sim-  ilar large-scale halo bias and typical dark matter halo masses  (Myers et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Donoso et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Koutoulidis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Finally, Leauthaud et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2015) studied the galaxy-galaxy lens-  ing signal around 382 X-ray-selected AGNs in the COSMOS  field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' They find that AGN host occupation is no different from  that of galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' They explain the issue of quoting a mean for  the halo mass when, instead, complete halo occupation distribu-  tions should be discussed;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' see also Georgakakis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2018) for  an extended discussion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Also, after controlling for stellar mass,  Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2018a) found no clear dependence between the en-  vironment and the sample-averaged SMBH accretion rate or the  AGN fraction, which indicates that environment-related physical  mechanisms might not significantly affect SMBH growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  To circumvent the low signal-to-noise ratio in the auto-  correlation functions, the cross-correlation with a controlled  galaxy population has been recently fruitful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Such studies re-  late AGN populations to their host dark matter haloes (Krumpe  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2010, 2012, 2015, 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Mendez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Mountrichas  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' They cross-correlated a similar  number of X-ray-selected AGN (between 300 and 1500) with  spectroscopic galaxy surveys: 2MASS, SDSS, VIPERS, COS-  MOS (Skrutskie et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' York et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2000;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Guzzo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Scoville et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' They obtain similar large-scale halo bias  values as the auto-correlation studies and investigate the correla-  tion with host-galaxy properties hinting at possible correlations  with stellar mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' This powerful technique works only with ac-  cess to a well-studied galaxy sample (Zehavi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Marulli  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The limited signal-to-noise impedes establishing a  clear definitive picture of how X-ray AGNs populate the cosmic  web.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  With the advent of eROSITA (Predehl et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2021), the num-  ber density of X-ray AGN increased to more than a hundred  per square degree in the eROSITA Final Equatorial Depth Sur-  vey (eFEDS, 140 deg2, ∼1,400 ks Brunner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Salvato  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Accurate redshifts are required for precise cluster-  ing and lensing analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The dedicated spectroscopic observa-  tions of the X-ray sources detected in eFEDS (SDSS-IV, SDSS-  V Abdurro’uf et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Kollmeier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2017, Merloni et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' in  preparation) enabled the accurate measurement of redshifts for  about eleven thousand X-ray point sources in eFEDS (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', for  ∼ 50% of the sources).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' This number of X-ray AGN with spec-  tra is already comparable to its predecessor follow-up of ROSAT  point sources (Comparat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2020b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Outstanding weak-lensing data products are now available  over wide areas thanks to the Hyper Suprime-Cam Subaru  Strategic Program (HSC-SSP) (Aihara et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' They mea-  sured accurate galaxy shapes for more than 20 source galaxies  per square arc minute over vast areas (1,400 deg2), which almost  completely cover the eFEDS field (Mandelbaum et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2018b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  With these two outstanding observational advances, we mea-  sure the auto-correlation function and the galaxy-galaxy lens-  ing signal of X-ray-selected AGN to study their underlying dark  matter halo distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We detail, in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2, the construction  of the X-ray AGN sample, and the weak-lensing data products  used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We describe the method to measure the clustering and  galaxy-galaxy lensing in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The halo occupation distribu-  tion and sub-halo abundance matching models used are detailed  in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Results are discussed in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 5, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Throughout, we as-  sume a Flat LCDM cosmology with H0 = 67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='74 km s−1 Mpc−1  and Ωm(z = 0)=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='3089 (Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The  uncertainties are 1σ unless stated otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Magnitudes are in  the AB system (Oke & Gunn 1983).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Throughout the article, we  use AGN to designate X-ray-selected AGN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Data  In this section, we describe the X-ray observations in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1  and the weak-lensing data products in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' eROSITA eFEDS  We use the public Early Data Release eROSITA point  source catalog of the eFEDS Performance Verification sur-  vey (Brunner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The catalog contains 20,191 pri-  mary sources, over 140 deg2, detected with a likelihood greater  than 8 (ERO_DET_LIKE > 8) and with reliable counterpart  (CTPquality ≥ 2) determined as described in Salvato et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Simulations are only at X-ray wavelength and not in the optical,  so the impact of the determination of the counterpart is stud-  ied empirically in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 4 of Salvato et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The trade-off  between purity and completeness study shows that counterparts  with a threshold of CTPquality ≥ 2 (p_any > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='035) have a purity  and completeness both equal to 95%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We follow the recommen-  dation of Salvato et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2022) and use the set of reliable coun-  terparts above threshold with CTPquality ≥ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' There are 1,219  extra sources ERO_DET_LIKE > 8 & CTPquality < 2 that are  then discarded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' These sources are on the faint end of the X-ray  flux distribution, inducing a 5% incompleteness at the faint end.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Article number, page 2 of 17  Comparat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' : X-ray AGN HOD  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Slice of the light cone sampled by the X-ray-selected eFEDS AGN sample in the redshift range 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='05 < z < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='55 (blue crosses).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The  surrounding large-scale structure is sampled by GAMA galaxies (grey) and GAMA galaxy groups (purple) (Driver et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2022) as well as by  eROSITA eFEDS clusters (red) (Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2022a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Given the large distribution of fluxes (luminosities) considered  here, we neglect this bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  2,160 sources are classified as stars either via astrometry, spec-  troscopy, X-ray, and opt/IR colors or via a dedicated analysis as  described in Schneider et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2022) and removed from the rest  of the study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  As shown by simulations (Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2022c;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Seppi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2022),  faint clusters are contaminants of the point source catalog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' In  eFEDS, 129 clusters are present in the point source catalog (Bul-  bul et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' They are identified in Salvato et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2022) with  the flag CLUSTER_CLASS ≥ 3 and are masked.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  After these cuts on the eFEDS point source catalog, we obtain  17,902 AGN candidates over 140 deg2 (density of 127.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='9 per  square degree).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 1 illustrates the light cone considered in this  analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Masks  We must propagate the masks applied to the source catalog to the  random catalog to estimate clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The random catalog is a  set of un-clustered data points that cover the same sky area as  the observations, see description in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' As the masking  radius for each detected source, we use its radius of maximum  signal-to-noise augmented by 40 percent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' This radius is deter-  mined while extracting the X-ray spectrum of each source (Liu  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2022b), see Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1 for complete details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  The edges of the survey have a lower exposure time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We  find that trimming the survey edges by requiring a minimum ex-  posure time of 830 seconds minimizes the KS test values (be-  tween random and data vectors) with a minimal area loss, see  Sec § 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' After applying the minimum exposure time cut, we  are left with 16,308 AGN candidates over 128 deg2, resulting in  a density of ∼127.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='4 deg−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Photometric redshifts  Photometric redshift estimation for galaxies hosting active  galactic nuclei is complex (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Salvato et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' In the  eROSITA/eFEDs case, Salvato et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2022) measured photomet-  ric redshifts to have σNMAD = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='48 × median  �  |zspec−zphot|  1+zspec  �  ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='05  and a fraction of outliers, with |zspec−zphot|  1+zspec  > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='15, of the order of  20%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' At the bright end (r<21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5), we find that σNMAD decreases  to ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='03 while the outlier fraction remains the same, 20%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  With the help of the simulation from Comparat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2019), we  find that the measured clustering using photometric redshift with  such dispersion and fraction of outliers would result in losing  between one-third and one-half of the amplitude of the cluster-  ing signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' So we will not use the photometric redshift to mea-  sure clustering statistics;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' instead, we focus on the sub-sample of  10,680 AGNs with spectroscopic observations, see the following  Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Spectroscopic redshifts  The eFEDS field was observed with the SDSS infrastructure  (Gunn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Smee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2013) in March-April 2020 with  both BOSS spectrographs (1000 fibers per plate, SDSS-IV, Blan-  ton et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2017) and March-April 2021 with a single BOSS spec-  trograph (500 fibers per plate, SDSS-V, Kollmeier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2017,  Merloni et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' in preparation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' A total of 31 plates were ob-  served, see Section ‘SPIDERS’ of Abdurro’uf et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2022) and  the spectra are part of the SDSS DR18 (SDSS collaboration in  preparation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The total area covered by SDSS-IV and V spec-  troscopic observations is 133.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='77 deg2 (95% of the eFEDS area).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  The obtained spectroscopic redshift completeness depends on (i)  the position in the sky;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (ii) the optical magnitude of the source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  We consider the z-band AB magnitude measured as in the legacy  survey DR8 (Dey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2019) and based on observations made  with DECam (Flaugher et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Although photometric red-  shifts are not accurate enough for clustering studies, they are of  sufficient quality to compare the distribution of magnitudes and  fluxes in broad redshift bins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Overall, we find that at a z-band  magnitude of 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='25 (19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0), the completeness is 50% (90%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We  find that, up to redshift ∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='55, the spectroscopic sample is a fair  sub-sample (as a function of optical magnitude and X-ray flux)  of the entire population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' SDSS-V observations being limited to  z-band magnitudes brighter than 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5, beyond a redshift of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='55,  we are missing a significant fraction of the AGN that are opti-  cally faint X-ray-selected AGN, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  We estimate the spectroscopic completeness in ∼3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5 deg2  equal area pixels (half the size of an SDSS plate ∼7 deg2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The  minimum (maximum) completeness measured in a pixel is 13%  (69%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The relative variations of the spectroscopic redshift dis-  tribution as a function of completeness are within the expected  Article number, page 3 of 17  eROSITA eFEDs  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='45  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='4  144°  Galaxies  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='35  AGN, LX>42  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='3  Redshift  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='25  x  Qx  Groups  141°  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2  Clusters  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='15  ×x  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1  +  138°  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='05  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='8  x  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  x  0  xx  136°  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  Q  0*00  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='7  X  x  x  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='3 x  133°  xx  0  x  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='9  x  x  0*  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='4  x  x  x  x  x  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='9  x  xO  Lookback time  130°  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='4  [Gyr]  ××  +  x  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='9  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='3  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='7  127°A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' main  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Spectroscopic completeness as a function of r-band magnitude  vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' redshift (top) and soft X-ray luminosity (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5-2 keV) vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' redshift (bot-  tom).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The completeness coverage is homogeneous below the redshift of  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' At higher redshift, completeness at the faint end impacts the sample  significantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  fluctuations for pixels with completeness levels above 40%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' So,  we discard areas with completeness lower than 40%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' It removes  about 20 deg2 of the area located at the edge of the eFEDs field  (most of it overlaps with the low-exposure regions).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  To summarize, to measure the clustering, we create an AGN  sample covering redshifts between 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='05 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='55, where the  spectroscopic sample is not biased compared to the parent photo-  z sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We obtain a sample of 1,992 AGN with spectroscopic  redshift covering 122.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='3 deg2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Figure 1 illustrates how the AGN  considered in this analysis sample the large-scale structure ob-  served with galaxies and groups from the GAMA survey and  eROSITA eFEDS clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Table 1 summarizes the main proper-  ties of the considered sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The mean redshift of the sample  is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='34, with a standard deviation of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The sample’s mean  X-ray luminosity in the soft 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5–2 keV band is 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The distri-  bution around the mean is broad and has a standard deviation of  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Properties of the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Minimum, mean, maximum, and  standard deviation of the redshift, soft band X-ray luminosity, and g,  r, z magnitudes from the legacy survey (Dey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  property  min  mean  max  std  redshift  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='34  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='55  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='13  soft LX  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='49  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='91  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='12  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='65  gAB  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='16  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='13  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='41  rAB  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='26  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='23  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='39  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='35  zAB  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='62  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='57  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='82  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='32  We verified that the edges of the selection do not impact the  clustering and lensing summary statistics: by moving the red-  shift cut from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='05 to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1 and from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='55 to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5 and by adding  a minimum luminosity threshold of 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Further splitting the  sample in soft X-ray luminosity-limited samples (or following a  visual inspection of the optical spectra) significantly decreases  the signal-to-noise in the measurements, and HOD model pa-  rameters become unconstrained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Larger numbers of AGN with  spectroscopic redshifts are required to investigate trends with pa-  rameters defining the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Among the 1992 AGN studied here, 1648 (82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='7%) have  their spectroscopic redshift coming from SDSS observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  270 (13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5%) come from GAMA observations (Liske et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Then in smaller numbers, spectroscopic redshifts originate from:  46 from WiggleZ (Drinkwater et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2018), 8 from LAMOST  DR5 v3 (Luo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2015), 7 from 2SLAQ (Cannon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2006), 5  from 2MASS (Skrutskie et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2006), 3 from HCSC (Oguri et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  2018), 2 from 6dFGS (Jones et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2009), 1 from HYPERLEDA  (Paturel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2003), 1 from (Véron-Cetty & Véron 2010), and 1  from RCSEDv2 (Chilingarian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Random catalogue  To measure clustering, one compares the set of observed points  to a group of points with no clustering but all other aspects equal  (window function, redshift distribution).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' In this section, we ex-  plain how the set of random points is constructed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  We draw a set of random points with a large uniform den-  sity of ∼81,000 deg−2 on the sky (about 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5 million points on  eFEDS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We first trim it to follow precisely the edges of the  survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We then follow the methodology of Georgakakis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  (2008) to downsample the uniform random catalog with the sen-  sitivity map, see details in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Heuristically, this step  applies the X-ray flux limit and its variations across the field  to the set of random points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The total number of random points  remaining after downsampling, masking (see the previous sec-  tion), and trimming (low exposure time region) is 3,713,726.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  The density of random points, ∼ 30, 000 deg−2, is more than 200  times larger than that of the data points (127.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='4 deg−2), which is  largely sufficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  We downsample the random catalog to follow the spectro-  scopic redshift completeness map and its dependency on R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  and Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We cut the areas where spectroscopic completeness is  lower than 40 %.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' As the relative variation in the redshift dis-  tribution is independent of the completeness (see the previous  section), we shuffle the set of observed redshifts and assign them  to the random points, regardless of the completeness level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' HSC-SSP weak-lensing data  We use the HSC S19A weak-lensing products based on the  HSC-SSP accumulated i-band imaging data from 2014 to 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Article number, page 4 of 17  24  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='8  22  TAB=21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5  completeness  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='6  20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='4 18  15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2  10  16  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='75  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='00  redshift45  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  44  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='8  eness  43  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='6  letel  compl  42  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='4  41  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2  z= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='55  40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='75  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='00  redshiftComparat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' : X-ray AGN HOD  The original HSC-SSP S19A wide-layer data covers about 512  deg2, and it reduces to 433.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='48deg2 after the full-color full-depth  (FCFD) selection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' With the i-band magnitude cut of 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5, the  observed number density reaches up to 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='9 arcmin−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The deep  imaging data enable a comprehensive redshift coverage ranging  from 0 to 3, and the calibrated bias residual shows no depen-  dence on the redshift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  There are several major updates in the shape catalog version  from hscPipe4 to hscPipe7 (used here).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' These improvements  include PSF modeling, image co-addition, bright star masking,  and background subtraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Due to the bad weather, volcanic activity, and other telescope  downtimes, the observation time has significantly decreased.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' To  compensate for the loss, besides the 30 nights additional obser-  vation time, the survey strategy has been modified by (i) reduc-  ing to 80% the time in the Deep/Ultra Deep fields, (ii) lowering  the seeing conditions in i-band, (iii) changing the dither pattern  from 6 to 5 in the i, z and y bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The latter results in a 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1 mag-  nitude difference in the i-band depth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Altogether, the expected  coverage should still reach up to 1200 deg2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We detail several  essential aspects of the S19A imaging data below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Photometry  The most important updates to the pipeline and data processing  are (i) improved sky background subtraction;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (ii) improved im-  age co-addition warping kernel from Lanczos3 to Lanczos5;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (iii)  the addition of two new filters r2 and i2 that substitute the orig-  inal r and i- band filters;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (iv) improved Point Spread Function  (PSF) based on PSFEx;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (v) new masks around bright stars com-  posed of ghosts, blooming, halo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' About the sky subtraction algo-  rithm, we apply the newest version based on Aihara et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2022)  rather than the global-global algorithm Aihara et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The  latter leads to about 10% loss of extended source near the shape  catalog cut at i-band magnitude equals 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  We use the Forward Global Calibration Method (FGCM;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Burke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2018) that was firstly developed for the Dark En-  ergy Survey (DES;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Sevilla-Noarbe et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2021) and now has been  merged into the LSST/HSC pipeline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' It starts with modeling  the instrumental throughput measurements such as mirrors, fil-  ters, and detectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Then, the atmospheric model (MODTRAN4  Berk et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 1999) carries out detailed modeling of atmospheric  throughput as a function of zenith distance at the location of the  SUBARU telescope on Mauna Kea.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  The performance of the photometry is tested in two ways,  an internal test by comparing the PSF magnitude to the Kron  magnitude for a bright star sample (i<21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5) in the Wide XMM-  LSS field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The standard deviation of the difference (PsfMag-  KronMag) achieved is better than 1%, independently of the fil-  ters and fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' One exception is the y-band, which shows a  slightly larger scatter of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' In addition, the difference be-  tween the CModel magnitude and PSF magnitude is below 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  For the external test, PanSTARR1 stars brighter than r-band 20  mag are used (PS1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Chambers et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The scatter level is  also at about the 1% level indicating good photometric perfor-  mance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Observations are mixing the i (r) and the i2 (r2) fil-  ters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' It results in a small offset in the i (r) photometry in the  Deep+UltraDeep fields and small regions of the Wide fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Good photometric performance is a pre-condition for the red-  shift calibration, described below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Photometric redshifts for sources  The overlapping photometric and public spectroscopic surveys  with HSC-SSP provide a wealth of data for photometric red-  shift calibration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' These data sets include zCOSMOS DR3 (Lilly  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2009), UDSz (Bradshaw et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' McLure et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2013),  3D-HST (Skelton et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Momcheva et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2016), FMOS-  COSMOS (Silverman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2015) and so forth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' There are about  170k spectroscopic redshifts (spec-z) and 37k g/prism-z with  high-quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  To cover the wide range of photo-z methods (Tanaka et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Nishizawa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2020) used different techniques on the  HSC-SSP data: template-fitting, empirical-fitting, and machine  learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' These include the Mizuki template-fitting method  Tanaka (2015), MLK Self-Organise Map (SOM;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' More et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  in prep), NNPZ Nearest Neighbors P(z) (Cunha et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2009),  FRANKEN-Z Flexible Regression over Associated Neighbors  with Kernel dEnsity estimatioN for Redshifts, DEmP Direct Em-  pirical Photometric code (Hsieh & Yee 2014) and Ephor Ex-  tended Photometric Redshift (EPHOR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' There is a newly de-  veloped machine learning photometric method for HSC-SSP Y3  shape catalog, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', dNNz (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Nishizawa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' in preparation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  The metrics to quantify the performance of each method are  the bias defined as ∆z = (zphot − zre f )/(1 + zre f ), the dispersion  σzphot = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='48 × MAD(δz) (MAD is the median absolute devia-  tion), the outlier rate foutlier = N(∆z) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='15/Ntotal and the loss  function L(∆z) = 1 − 1/(1 + (∆z/γ)2) with γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The pho-  tometric redshift used in this work is based on dNNz method,  which achieves an accuracy with a ∆z = 10−4 bias, a dispersion  σzphot = 3%, and an outlier rate smaller than foutlier ≤ 10%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Shape catalog  The  HSC  galaxy  sample  is  selected  following  a  se-  ries of basic flag cuts, such as i_detect_isprimary,  i_extendedness_value and i_sdsscentroid_flag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The  detailed descriptions are listed in Table 2 of Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The  shapes of galaxies are measured with re-Gaussianization method  (Hirata & Seljak 2003) (reGauss which has been merged to  GalSim Rowe et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2015)), the PSF effects are corrected  during the measurement process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' HSC covers six discrete  fields named after overlapping regions from previous surveys:  XMM, HECTOMAP, WIDE12H, GAMA09H, GAMA15H,  and VVDS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The eFEDS region overlaps with GAMA09H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Note  that the HSC region GAMA09H covers a larger area than the  original GAMA09H field and completely encompasses the  eFEDS field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  The final shape catalog contains the two components of the  ellipticity:  (e1, e2) = 1 − (b/a)2  1 + (b/a)2 (cos2φ, sin2φ),  (1)  where b/a is the ratio between the minor axis and major axis,  and φ is the position angle of the major axis with respect to the  sky coordinates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The shear distortion, γi, is then related to the ei  (i=1,2) such that  γi = 1  2R⟨ei⟩(i = 1, 2),  (2)  where R is the response of the galaxy ellipticity to a small distor-  tion defined in Kaiser et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (1995);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Bernstein & Jarvis (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  The response is calculated from the calibrated parameters erms  Article number, page 5 of 17  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' main  and σe based on simulations (Mandelbaum et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2018a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  2022) as follows  R = 1 −  �  i wie2  rms,i  �  i wi  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  (3)  The weighting term wi in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='3 is composed of the per-  component error from simulation due to photon noise σe;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='i, and  the rms of galaxy shape distribution erms;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='i, wi = 1/(σ2  e;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='i + e2  rms;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  The reGauss algorithm suffers from several estimation bi-  ases, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', model bias, noise bias, and selection bias which can be  classified into multiplicative bias mi and additive bias ci (i=1,2),  so that  γi = (1 + mi)γtrue  i  + ci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  (4)  The final shear estimator is obtained with Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' It does not in-  corporate the geometry factor Σcrit described in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  ⟨γi⟩ =  �  j wiei;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='j  2R(1 + ⟨mi⟩) �  j wj  −  ⟨ci⟩  1 + ⟨m⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  (5)  Both multiplicative and additive biases are calibrated based on  the simulations mentioned above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The two biases are then as-  signed to each galaxy as a function of SNR and resolution R2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Additionally, there is selection bias as well as weight bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The  overall bias is quantified as the residuals for both multiplicative  δm and additive bias δa, both of which can reach below 1% level  for HSC-SSP Y3 shape catalog Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Summary statistics  Galaxy clustering and gravitational lensing probe the galaxy and  matter over-density field’s auto and cross-correlations as a func-  tion of scale via a biasing function (Tegmark & Peebles 1998;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Tegmark & Bromley 1999;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Dekel & Lahav 1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' These mea-  surements are well suited to constrain the biasing function, also  named more generically the galaxy-halo connection (Sheth &  Tormen 1999;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Wechsler & Tinker 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' With the data described  above, we compute two summary statistics: the AGN-AGN auto-  correlation (clustering, Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1) and galaxy-galaxy lensing with  the AGN population being the lenses (Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Clustering measurement  We use the Landy & Szalay (1993) estimator to measure the  projected two-point correlation function, labeled wp(rp) (for de-  tailed definition, see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Davis & Peebles 1983).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' To count  pairs and integrate along the line of sight, we use the corrfunc  software (Sinha & Garrison 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' For the integration, we use  πmax = 40 h−1Mpc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We carried out measurements with shorter  and longer πmax and found that with 40, we would obtain the  largest signal-to-noise in the clustering measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  We randomly down-sample the catalog of random points for  the clustering measurement to have twenty times the number  of AGN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' To have consistent 3D positions between the optical  spectra and the X-ray sources, we compute the clustering using  the position on the sky of the optical counterparts (Salvato et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  2022);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' we do not use the positions of the X-ray sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The pro-  jected correlation function obtained is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 3 (black er-  ror bars).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The clustering measurement’s uncertainty is estimated  using the diagonal component of the covariance matrix obtained  with 18 eFEDS simulated catalogs (Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2022c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' These sim-  ulated eFEDS observations are based on the empirical models of  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Projected clustering measurement of the X-ray flux-limited  eFEDS AGN sample in the redshift range 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='05 < z < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='55 (black).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  The prediction from the 18 eFEDS simulations appears in yellow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The  best-fit model (jointly with weak-lensing observations) is in red.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  the X-ray cosmic web from Comparat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2019, 2020a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The  yellow shaded area in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 3 shows the prediction from the 18  mocks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We find that the forecast is faithful to the observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Following Driver & Robotham (2010), we estimate the cos-  mic variance in this field to be 1%, which we add as a constant  systematic uncertainty at all scales to the clustering measure-  ment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Note that it is small compared to statistical uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Using the eFEDS simulations, we find that clustering summary  statistics are significantly biased low for separations rp >40  h−1Mpc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' This is due to the finite volume observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' So, we ex-  clude from the fitting procedure clustering measurements with  a separation larger than 40 h−1Mpc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The total signal-to-noise  in the clustering measurement is 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='7, split into 11 radial bins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  We sample the separation range with five bins per decade evenly  log-spaced (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2 dex steps) between 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='25 (10−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='6) and 39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='8 (100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='6)  h−1Mpc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  The fiber collision radius in SDSS is 62 arc seconds  (∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='25h−1Mpc at the mean redshift of the sample).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The  eROSITA PSF is 30 arc seconds, so X-ray-selected AGN pairs  with a separation smaller than one arc minute are hardly de-  tected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Moreover, since the AGN sample considered here is  sparse (120 deg−2 ∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='03 arc minutes−2) and spread over a long  line of sight, AGN close pairs are small in numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Using the  mock catalogs limited to redshifts 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='05 < z < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='55, we estimate  the number of expected pairs with an angular separation smaller  than 62 arc seconds to be typically a handful: less than 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Only  half have physical separation smaller than 40 h−1Mpc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' So, the  number of missed pairs due to fiber collisions is negligible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' So  in our case, we consider that fiber collisions are not an issue, and  we define our lowest separation bin at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='25 h−1Mpc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Galaxy-galaxy lensing measurement  The galaxy-galaxy lensing measurement is a cross-correlation  between positions of foreground lenses (AGN in our case) and  shapes of background galaxies acting as sources (HSC galax-  ies), see reviews from Bartelmann & Schneider (2001);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Re-  fregier (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' This measurement directly traces the galaxy halo  Article number, page 6 of 17  102  101  18mockcatalogs  100  Best-fit HOD  eROSITAX-ray AGN  10-1  100  101  rp [h-1 Mpc]Comparat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' : X-ray AGN HOD  connection (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Mandelbaum et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Seljak et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Numerous studies have used galaxy-galaxy lensing (sometimes  combined with galaxy clustering) to trace the galaxy-halo con-  nection in general (Leauthaud et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Coupon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Zu & Mandelbaum 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Dvornik et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Zacharegkas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  We combine the X-ray point sources from the eFEDS region  and the HSC shape catalog to compute the galaxy-galaxy lensing  using each source galaxy and its probability distribution function  as a function of redshift (p(z)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The physical interpretation of the  galaxy-galaxy lensing signal is the difference between the aver-  age density inside a certain projected radius R and the average  density at that same radius, so an excess surface density (ESD,  ∆Σ), that is  ∆Σ(R) = ¯Σ(≤ R) − Σ(R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  (6)  We follow the measurement procedure described in Miyatake  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2019);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Luo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2022), that  ∆Σ(R) =  1  2R(R)  �Nl  l wl  �Ns  s wlset,ls[⟨Σ−1  cr ⟩]−1  [1 + K(R)] �Nl  l wl  �Ns  s wls  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  (7)  In the above ESD estimator, R(R) is the response of the shape  estimator, which, for this work, takes a value of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' wls is the  weight for each lens-source galaxy pair.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' wl is a weight assigned  to each lens galaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Here we use wl = 1 in that there are no  particular requirements on redshift, stellar mass or other proper-  ties for the lens catalog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' et,ls is the tangential component of the  source galaxy shape with respect to the lens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The factor K(R)  accounts for the multiplicative bias calibrated based on a suite  of simulations developed in Mandelbaum et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2018a);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Two blinding schemes are provided for systematic sanity  tests, the low and the high-accuracy blinding scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We use  the former where a value of δm is added to the original cali-  brated additive bias m where ei = (1 + mi)ei + ci (i=1,2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' In the  low accuracy scheme, only δm1 is added and encrypted for each  user of the shape catalog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' It is then decrypted and removed by  subtracting δm1 term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  An extra selection function for each lens-source pair is ap-  plied following Medezinski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2018) so that the accumulated  probability of the P(z) satisfies  P(zs ≥ zl + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2) =  � ∞  zl+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2  p(z)dz ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  (8)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 4 shows the galaxy-galaxy lensing measurements ob-  tained (black) as well as the best-fit HOD model (red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Measure-  ments with a separation smaller than 20 h−1Mpc are included  in the fitting procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The total signal-to-noise in the lensing  measurement is 46, split into 15 radial bins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We sample the sep-  aration range with 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5 bins per decade evenly log-spaced (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='18  dex) steps between 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='025 (10−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='6) and 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='3 (100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='9) h−1Mpc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Com-  pared to the clustering measurement, the measurement extends  to ten times smaller separations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We measured the same using  the public HSC one-year S16A (KIDS DR4) lensing products.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  They are consistent but have a lower total signal-to-noise of 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='4  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5) compared to 46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Models  We interpret the clustering and lensing summary statistics using  models of halo occupation statistics (Cooray & Sheth 2002;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Guo  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Galaxy-galaxy lensing measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Excess surface mass den-  sity measurement with HSC S19A data using as lenses the X-ray flux-  limited eFEDS AGN sample in the redshift range 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='05 < z < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='55  (black).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The best-fit model (jointly with clustering measurements) is  shown in red.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' There are three flavours of models: Halo Occupation  Distribution (HOD;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Berlind & Weinberg 2002;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Kravtsov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  2004;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Zheng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2005, 2007), Sub Halo Abundance Match-  ing (SHAM;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Conroy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Trujillo-Gomez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Klypin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2013) and emulators of the large-scale structure  of the Universe (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' DarkEmulator Nishimichi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Nishizawa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' HOD and SHAM reproduce measure-  ments of the galaxy clustering as a function of luminosity and  color (Zehavi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Marulli et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The exploration  and parametrization of the assembly bias in such models is still a  matter of debate (Contreras et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Xu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Emula-  tors enable a precise prediction of the cross-correlation between  haloes and the dark matter, though due to the finite resolution  of simulations they build upon, they are currently limited to pre-  dict statistics at the high mass end (Nishimichi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' So,  first, we adjust the HOD model parameters to the measurements  obtained in the previous section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Then, we compare mea-  surements to the prediction of the SHAM model from Comparat  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2019) in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Halo occupation distribution model  As a baseline, we use the HOD model formulated by More et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' It is described by the two equations below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' ⟨NC⟩ (⟨NS ⟩)  gives the average occupation of a dark matter halo of mass M  by a central (satellite) galaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The model has 5 parameters θ =  (Mmin, σlog10 M, αsat, Msat, M∗  12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  ⟨NC⟩(M, θ) = fA  2  �  1 + erf  �(log10(M) − Mmin)  σlog10 M  ��  (9)  ⟨NS ⟩(M, θ) = ⟨NC⟩(M, θ)  � M − 10Msat−1  10Msat  �αsat  (10)  Only a fraction of distinct haloes hosts a central galaxy with an  AGN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The fA parameter, as introduced by Miyaji et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2011, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  24), can be interpreted as the duty cycle of halo centers being an  Article number, page 7 of 17  102  101  h  100  10-1  Best-fit HOD  eROSITA X-ray AGN  10-2  10-2  10-1  100  101  R [h-1 Mpc]A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' main  Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' HOD parameters obtained (median of the posterior) by jointly  fitting the auto-correlation function and the galaxy-galaxy lensing of  the X-ray flux-limited AGN sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The uncertainties quoted are 1σ  (15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='9–84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1 percentiles).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Priors are flat in linear space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  parameters  min  max  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='05 < z < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='55  Mmin  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='06 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='44  σlog10 M  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='05  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='28 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2  αsat  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='73 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='38  Msat − Mmin  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='45  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='46 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='52  M∗  12  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='96 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='45  evidence (logZ)  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='88 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='14  deduced parameters  b(z = ¯z) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='991+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='078  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='096  b(z = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='915+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='065  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='08  fsat < 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='6%  4-parameter fit, σlog10 M = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='3  Mmin  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='09 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='19  αsat  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='75 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='39  Msat − Mmin  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='56 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='46  M∗  12  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='97 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='46  evidence (logZ)  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='6 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='12  deduced parameters  b(z = ¯z) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='001+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='075  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='094  b(z = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='918+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='065  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='076  fsat < 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='8%  4-parameter fit, σlog10 M = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  Mmin  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='47 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='26  αsat  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='75 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='39  Msat − Mmin  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='84 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='53  M∗  12  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5  evidence (logZ)  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='34 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='11  deduced parameters  b(z = ¯z) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='996+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='067  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='097  b(z = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='919+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='059  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='081  fsat < 66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='4%  AGN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' In this study, since the correlation function measurements  do not depend on the normalization of the occupation distribu-  tion, we arbitrarily set fA to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  To avoid sampling un-physical values of Msat, the parame-  ter passed to the fitting routine is Msat − Mmin with boundaries  specified in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  To fit for the ∆Σ measurement at small separations and ben-  efit from the signal present, we need to add the prediction for a  point-like mass term that represents the baryonic lensing mass  of the AGN host galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' It adds the parameter M∗  12 as follows:  ∆Σ∗(r) = 10M∗  12+12  πr2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  (11)  The posterior of this parameter represents the mean baryonic  lensing mass of the galaxies hosting AGN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' This mass is related  to stellar mass (inferred with stellar population synthesis mod-  els) but will also encompass gas in and around the galaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' This  baryonic lensing mass can be considered the upper limit of the  mean stellar mass of galaxies hosting AGN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  In total, we fit for five parameters on the two measurements  ∆Σ (wp(rp)) which have S/N=46 (17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='7) in 15 (11) radial bins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  The parameters are sampled with a flat prior (in linear space)  within broad boundaries as specified in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Sub halo abundance matching models  The Comparat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2019, 2020b) empirical AGN model statis-  tically links the dark matter haloes to the probability of hosting  an AGN and its spectral energy distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' By construction, it  follows the X-ray luminosity function from Aird et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Importantly for interpretation, the assignment is done regardless  of the environment in which haloes live.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The model has two pa-  rameters: the fraction of AGN in satellites sub haloes and the  scatter in the abundance matching relation between stellar mass  and hard X-ray luminosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  We show the direct wr(rp) prediction from the mock cata-  logues of Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2022c) in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' It is consistent with obser-  vations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' It was obtained with fsat = 10% (fraction of AGN being  satellites) and σ = 1 (scatter in the abundance matching proce-  dure between hard X-ray luminosity and stellar mass).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' These pa-  rameters were chosen by hand by Comparat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2019, 2020a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  At that time (before this study), such parameters resulted in rea-  sonable predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Creating a complete SHAM-base mock catalog is long (or-  der of a few CPU hours) and thus impractical for fitting purposes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Furthermore, with current light cones constructed with replica-  tions, predicting the galaxy-galaxy lensing signal is tedious as  the dark matter particles are not kept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' So, instead of predict-  ing summary statistics as measured as a function of the SHAM  parameters, we directly predict the halo occupation distribution  curves as a function of fsat and σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Thus, we sample a small and fi-  nite number of (fsat, σ) combinations and create individual mock  catalogs to predict the HOD curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Results  We discuss here the results of the fitting procedure and the  comparison between models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1 (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2), we discuss the  results obtained with the HOD (SHAM) model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' For the first  time, we measure with relatively small uncertainties the com-  plete halo occupation distribution of a low redshift flux-limited  X-ray-selected sample of AGN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We obtain a global view of the  distribution of haloes hosting X-ray AGN;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' HOD results  We fit the parameters of the HOD model with a nested sampling  method ultranest (Buchner 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The resulting parameters are  given in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The constraints on the HOD parameters (when  fitting individually each summary statistic or both jointly) are  shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' It illustrates the complementary nature of the  two measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The comparison between the joint best-fit  model and the clustering measurements and lensing measure-  ments are shown in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 3, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The models are sensible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' They  account for the observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  The five parameters are meaningful, although not precisely  constrained by the joint fit of both summary statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' For  the central haloes, Mmin takes a median posterior value of  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='06±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='44, the width of the error function is found at σlog10 M =  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='3 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' There is a low 1σ-level tension between the constraints  on these parameters obtained by each summary statistic;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Due to the higher signal-to-noise on the lensing statistic, the  combined best-fit values are closer to the individual best-fit value  on the lensing statistic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' For the satellites, the slope is best-fit at  αsat =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='73±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='38 and the transition occurs in haloes 10 to 100  times more massive than the typical halo : Msat − Mmin = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='46  ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Both summary statistics point to these parameter values  (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The typical baryonic lensing mass of galaxies hosting  Article number, page 8 of 17  Comparat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' : X-ray AGN HOD  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Constraints were obtained on the HOD parameters when fitting only the clustering measurement (yellow), the lensing measurement (purple),  or both jointly (blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Contours show 1 and 2 σ constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Most of the constraining power comes from galaxy-galaxy lensing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  these AGN is M∗  12 = -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='96 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' It sets an upper limit to the  mean stellar mass of galaxies hosting AGN of ∼ 1011M⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The  1σ boundaries encompass 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='9×1010 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1×1011M⊙, which is  in fair agreement with expectations from AGN host stellar mass  function (Bongiorno et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2018b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' This param-  eter is not degenerate with others and is constrained only by the  lensing measurements at small separations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  We note a degeneracy between Mmin and σlog10 M, which  we investigate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We decrease the number of parameters by fix-  ing σlog10 M to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='3 (similar to the best-fit value) and 1 (to force  a less broad halo distribution, a sharper transition).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We obtain  a set of best-fit parameters (see Table 2) that are compatible  with the 5-parameter fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' When fixing σlog10 M to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='3, we ob-  tain Mmin13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='09 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='19, similar value to the 5-parameter fit but  with half the uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Results for other parameters remain  unchanged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' When fixing σlog10 M to 1, Mmin is logically forced to  lower values to ∼ 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5 to be able to fit the overall signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The  halo occupation distribution posterior is close to that of the five  parameter fit, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 6 black and yellow/orange contours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  We obtain a global view of the distribution of haloes hosting  X-ray AGN;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The 4-parameter best-fit model is within  the 1σ uncertainty of the 5-parameter best-fit model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Due to the  degeneracy between Mmin and σlog10 M, the 4-parameter fit HOD  with σlog10 M = 1 is skewed towards lower masses compared to  the 5-parameter fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' With the HOD model, we derive the average  halo mass hosting central (central or satellite) AGN is 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='93+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='03  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='44×  1012M⊙ (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='95+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='63  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='99 × 1012M⊙).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' These values are comparable to  the findings of Rodríguez-Torres et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We measure that  Article number, page 9 of 17  Wp(rp)  Combined  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5  wo6ol0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  2  2  0  2  4  8  10  12  14  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5  2  0  4  ~2  0  Mmin  OiogroM  αsat  Msat  Mmin  Mi2A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' main  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Inferred halo occupation distribution (solid) split into central (dashes) and satellite (dots) for the 4 and 5 parameter HOD fits (yellow/orange  and black).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The 4-parameter best-fit model is within the 1σ uncertainty of the 5-parameter best-fit model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Due to the degeneracy between Mmin  and σlog10 M, the 4-parameter fit HOD with σlog10 M = 1 is skewed towards lower masses compared to the 5-parameter fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The direct predictions  from mock catalogs from Leauthaud et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2015);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Georgakakis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2018);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Comparat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2019) are shown on the right panel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' They are within  the fitted contours obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The mocks from Leauthaud et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2015);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Georgakakis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2018) have a lower σlog10 M value (sharper transition)  and are thus more in line with the 4-parameter fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The mock from Comparat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2019) has a higher σlog10 M value and is comparable to the  5-parameter fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  the distribution of halo masses is broad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We thus confirm that  quoting a typical halo mass will be extremely sensitive to the  definition of what ‘typical’ means;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' see discussion in Leauthaud  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  The direct HOD predictions from mock catalogs from Leau-  thaud et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2015);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Georgakakis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2018);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Comparat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  (2019) are shown on the right panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' They are within  the fitted contours obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The mocks from Leauthaud et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  (2015);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Georgakakis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2018) have a lower σlog10 M value  (sharper transition) and are thus more in line with the 4-  parameter fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The mock from Comparat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2019) has a higher  σlog10 M value and is comparable to the 5-parameter fit (see more  discussion in the SHAM section below).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The normalization of  ⟨N(M)⟩ can be added as a parameter and possibly constrained  by jointly fitting the clustering and lensing summary statistics  with the stellar mass (or luminosity) function of galaxies hosting  X-ray AGN to have a handle on the fraction of galaxies hosting  an AGN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Though measuring reliable host-galaxy stellar masses  in the case of type 1 AGN is complex (Ciesla et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Zou  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2022), and is left for future studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  The large-scale halo bias inferred is given in Table 2 and  shown in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' At the mean redshift (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='34), it takes a value of  b(¯z = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='34) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='99+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='08  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='10, which extrapolated to redshift z = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1  becomes b(z = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='92+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='07  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='08.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The deduced large-scale halo  bias is the same if we fit the HOD model with 4 or 5 parame-  ters, see Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Krumpe et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2015) measured the bias of X-  ray-selected AGN in a similar redshift range but for intrinsically  more luminous AGN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' With this analysis, we add a new measure-  ment of the bias at lower soft X-ray luminosity: 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1 × 1042 erg  s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We confirm the weak positive correlation between bias and  soft X-ray luminosity found by Krumpe et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2015), see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 7  bottom panel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We fit a linear relationship between the quantities  and obtain b = (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='48 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='14)LX + (−19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='68 ± 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='17).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The slope  value obtained is 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='3σ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='48/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='14=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='3) away from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Other X-ray-selected AGN clustering studies were either at  lower redshift (Cappelluti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2010) or higher redshift (Gilli  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Starikova et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Koutoulidis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Viita-  nen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Allevato et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2019) and always covered higher  luminosities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' This new study is complementary to them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Halo abundance matching results  The model has two parameters: the fraction of satellite AGNs  and the scatter in the relation between stellar mass and X-  ray luminosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The predicted curves extend to halo masses of  1011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5M⊙ (and not lower) due to the resolution of the simulation  used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Both impact the shape and amplitude of the clustering sig-  nal and the HOD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Figure 8 shows the predicted HOD curves for  a subset of the parameter space explored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' In the top left panel,  the satellite fraction is fixed to 10%, and the σ parameter varies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  The lower the σ, the sharper the transition is.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The σ parameter  from SHAM is related to the σlog10 M parameter from the HOD  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Mock catalogs with higher σ have a distribution of dark  matter haloes more extended towards lower masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' In the top  right panel, σ is fixed to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='8, and the fsat varies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The higher the  fsat, the steeper the slope of the satellite occupation curve (the  larger the α parameter).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The fsat parameter is related to both the  αsat and the Msat HOD parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  We compute a distance, denoted d, between each predicted  HOD curve (NS HAM(M)) and the 50th precentile of the inferred  HOD model as follows  d = ΣM=15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5  M=11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5  �  NS HAM(M, fsat, σ) − N50%  HOD(M)  �2  �  N84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1%  HOD (M) − N15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='9%  HOD (M)  �2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  (12)  Figure 8 (bottom panels) shows the distances as a function of σ  and fsat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We find mock catalogs constructed with parameters sat-  isfying σ < 2− fsat/10 predict halo occupation distributions well  Article number, page 10 of 17  HOD 4-p  central  HOD 5-p  satellite  101  ((W)N)  100  10-1  10-2  11  12  13  14  15  log1o(Mhalo [M ])Mockcatalogues  Comparat2019  101  Georgakakis201g  Leauthaud 2015  ((W)N)  100  10-1  10-2  11  12  13  14  15  log1o(Mhalo [M])Comparat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' : X-ray AGN HOD  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Inferred large-scale halo bias as a function of redshift (top panel)  and luminosity (bottom panel) compared to (Krumpe et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2015) (red-  shift range 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='16-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='36).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We confirm the trend with soft X-ray luminosity  and obtain a best-fit of y = (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='482±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='143)x+(−19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='684±6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='173) between  the soft X-ray luminosity and the large-scale halo bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  within the contours of the 5-parameter best-fit HOD inferred  from the observations (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 8 bottom left panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Parameter com-  binations such as σ > 2 − fsat/10 are less preferred (top right  corner of the bottom left panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' d is minimized for σ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='8 and  fsat = 4%, see the star in the Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The six smallest distances  are pointed out with empty circles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' When comparing to the 4-  parameter best-fit HOD contours (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 8 bottom right panel), pa-  rameters within σ < 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='4 − fsat/10 and σ > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5 are acceptable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Here we find that solutions with low σ are less preferred.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' In that  case, d is minimized for σ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2, and fsat = 4, see the star in the  Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The six smallest distances are pointed out with empty  circles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' In both cases (comparing either to the 4-parameter of the  5-parameter HOD fit), the best solutions point towards low fsat  values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Mocks with both high σ and high fsat are far from the obser-  vations and are ruled out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Summary and discussion  This article provides a complete picture of how soft X-ray AGNs  populate the cosmic web (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' This achievement is possi-  ble thanks to two factors: (i) the combination of the eROSITA  eFEDS X-ray survey with its dedicated SDSS spectroscopic  follow-up and with the HSC S19A lensing products (ii) the com-  plementary nature of the two summary statistics fitted (Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 3,  4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We obtain meaningful HOD constraints for an X-ray-selected  AGN sample (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 5, 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We interpret the summary statistics with  state-of-the-art HOD and SHAM models (Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We set upon  firm footage the fact that the mass distribution of haloes host-  ing X-ray-selected AGN is broad, as hinted by previous studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Both models point to a shallower satellite slope than for galaxy  surveys meaning that the satellite fraction for X-ray-selected  AGN is low, similar to the findings of Miyaji et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Inter-  estingly, we find a relatively large σlog10 M that is likely related to  the width of the specific accretion rate distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Contrasting  our results with those of Krumpe et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2015), the large-scale  halo bias of X-ray-selected AGN appears to correlate (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='3σ sig-  nificance) with soft band X-ray luminosity (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We compare  the results with predictions from SHAM models and can rule out  a portion of the parameter space (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' On the σ and σlog10 M parameters  The σ parameter in the SHAM model is the scatter in the abun-  dance matching relation between the stellar mass of the galaxy  hosting the AGN and the AGN hard X-ray luminosity (2–10  keV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The probability distribution function of specific accre-  tion rate resulting from a broad range of galaxy stellar masses  (hosting AGN) is close to a power-law (with slope -1) in the  range 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5 < log10(λS AR) < 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5 (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 5 of Comparat  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2019)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The distribution obtained deviates from the power  law at high accretion rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Indeed the scatter induces an expo-  nential cut-off.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The distribution at the faint end of the function  would require higher-resolution simulations to be populated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The  HOD results obtained here are compatible with SHAM models  if σ ∈ [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='8, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2] and incompatible for low values of σ < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5  (for the four parameters HOD fit) or high values (for the 5-  parameter HOD fit).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Indeed low values of σ induce a steeper  probability distribution function of specific accretion rate, which  are excluded by observations (Georgakakis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' In the  opposite regime, large values of σ induce a shallow (tending to  become flat) probability distribution function of specific accre-  tion rate when considering the entire population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' In a sense, the  σ SHAM parameter is related to how broad the distribution of  specific accretion rate and its slope is.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  The σlog10 M parameter characterizes how broad the host halo  distribution is.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' It is related to the diversity of host galaxies and  their stellar mass via the stellar-to-halo mass relation (Moster  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Behroozi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The relatively high σlog10 M ∼  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='3 parameter obtained indicates that the host halo mass distribu-  tion and, thus, the host stellar mass distribution are both broad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  This is consistent with studies of the AGN host-galaxy stellar  mass function (Bongiorno et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  So, it seems that both models point to the same general in-  terpretation: the distribution of host-galaxy stellar mass and that  of specific accretion rate are ‘broad’, which strengthens direct  observations of these distributions (Bongiorno et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Geor-  gakakis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2017), even if these might be subject to systematic  effects in the measurement of the stellar mass of type 1 AGN  (Ciesla et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Article number, page 11 of 17  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  y=(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='482±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='143)x+(-19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='684±6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='173)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='8  +  eFEDS  Krumpe et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 15  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='8-  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='6  41  42  43  44  45  log1o(L0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5 - 2 keV)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='50  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='8  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='25  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='6  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='00  2 keV)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='4  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='75  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='50  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='8  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='00  eROSITAeFEDS  Krumpe et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 15  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='6  ZA&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' main  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' SHAM predictions plotted with the fitted HOD model 1 σ contour of the 4 and 5 parameters HOD fit results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' On the top left panel, the  satellite fraction is fixed to 10%, and the σ parameter is varied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' On the top right panel, σ is fixed to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='8, and the fsat is varied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' On the bottom left  (right) panel is shown, as a function of σ and fsat, the distance between the HOD predicted by SHAM models and the 5-parameter (4-parameter)  HOD inferred from the observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The black dashed line on the bottom left panel corresponds to σ = 2 − fsat/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' When comparing to the  5-parameter HOD fit, the bottom left half, below the σ < 2 − fsat/10 line of the parameter space, is preferred.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Compared to the 4-parameter HOD  fit (bottom right panel), the bottom left half is also preferred.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The dashed line represents σ = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='4 − fsat/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The star identifies the lowest distance  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Empty circles identify the six lowest distance models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  With the innermost lensing measurements, we measure the  baryonic lensing mass for this sample (M∗  12) to be within 4×1010  and 3 × 1011M⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' From the mock catalog, we predict a broad  stellar mass distribution of AGN host galaxies with a median  4 × 1010M⊙ and a large standard deviation of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='6 dex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' So, the  SHAM predicted stellar mass being smaller than the HOD in-  ferred baryonic lensing mass;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' we find that interpretations from  the two models are consistent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' On the satellite occupation  As suggested in Leauthaud et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2015), the combination of clus-  tering and lensing best constraints satellite occupation statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Compared to previous studies, we take here a significant step for-  ward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Indeed satellite fractions inferred from clustering studies  are limited by the precision of redshift in the presence of broad  line AGNs, and for example Shen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2013) or Rodríguez-  Torres et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2017) could not constrain it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Lensing studies were  limited by small numbers of X-ray-selected AGN (Leauthaud  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2015) and showed large uncertainties in the satellite occu-  pation statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' By combining eFEDS with HSC, we find a pref-  erence for low satellite fractions (HOD upper limit is fsat < 20%  and SHAM best fits are with fsat < 12%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The HOD result shows  a preference for a shallow satellite slope (∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='75) that is smaller  than measured for galaxy samples (α ∼ 1−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1 and fsat of 40% for  galaxies with a stellar mass of 3×1010M⊙) (Zehavi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Zu & Mandelbaum 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  The low satellite fraction could, in part, be due to the soft  X-ray selection of the AGN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Indeed, satellite AGN could be ob-  scured and only detectable in hard X-ray or the infrared (Ko-  cevski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Krumpe et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Krumpe et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2018)  Article number, page 12 of 17  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='6  101  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2  100  (M)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='06  ONX  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='8  10-1  HOD 5-p  HOD 4-p =1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='6  Mock, fsat = 10  10-2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='4  12  14  log1o(Mhalo [M  J)16  101  14  12  100  (N(M))  10  8  10-1  HOD 5-p  HOD4-p=1  6  Mock,=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='8  10-2  4  12  14  log1o(Mhalo [M ])1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5  6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  5  10  15  fsat1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5  HOD  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  4-p  6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  (d2)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='4  5  10  15  fsatComparat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' : X-ray AGN HOD  compared the cross-correlation functions (CCF) of Swift BAT  AGNs with 2MASS redshift survey galaxies and their HODs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Since Swift BAT AGN sample is hard (14-195 keV) X-ray-  selected, it contains a larger fraction of type 2 obscured AGN  than eROSITA-based samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' They found clear suppression of  the 1-halo term in type 1 AGN CCF compared to type 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The  HOD analysis shows α ∼ 1 for the type 2 AGN HOD while that  of the type 1 AGN was α <∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Powell et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2018) obtained  similar results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' A possible scenario causing the low α is the sup-  pression of sub-halo mergers in high velocity encounters in high  mass halos (Altamirano-Dévora et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Oogi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  An alternative interpretation of the apparent shallow slope is that  the satellite HOD slope is not shallow, but the satellite distribu-  tion profile within the dark matter halo does not follow the mass  density profile assumed in the HOD modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' If the satellite  distribution is suppressed towards the outer part of the halo, the  ordinary HOD modeling would result in low fitted α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Indeed, it  would appear as if the satellites were suppressed in high-mass  halos with large virial radii.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' However, one should be cautious as  such interpretations are still a debate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Triggering mechanism for soft X-ray AGN in the cosmic  web  The general SHAM scheme applied to populate mock catalogs  with AGN accounts for the observations satisfactorily.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' One im-  portant assumption made in the SHAM model is that the assign-  ment of an AGN to a galaxy is independent of the environment: it  ignores the properties of the neighboring haloes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' It implies that,  to the first order, the larger scale environment, beyond the galaxy  host halo, is not the primary driver to turn on the AGN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Instead,  the local environment (within the virial radius) i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', the circum-  galactic medium, the interstellar medium, and the stellar popu-  lations, are likely more decisive parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' It agrees with the  findings of Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2018a);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Allevato et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2019);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Siudek  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2023).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' It emphasizes internal processes and their role as  AGN triggers, for example, disc instabilities (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Bournaud et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  2011) or the presence of bars (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Ohta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  The fact that the satellite slope is shallower than that of galaxies  with equivalent stellar mass means that the in-fall of a satellite on  a larger structure makes it less likely to host an AGN, even more,  when structures are larger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' It likely illustrates that the gas strip-  ping from satellite galaxies in deep potential wells suppresses  AGN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' It is compatible with the environment quenching mecha-  nism described by Peng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2010, 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Outlook  The eROSITA eFEDs observations constitute about 1% of the  full eROSITA All-Sky Survey (eRASS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' This study paves the  way towards charting the co-evolution of X-ray AGN and their  host galaxies and dark matter haloes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  In the coming decade, by combining eROSITA with SDSS-  V, 4MOST, and DESI spectroscopic redshifts (Kollmeier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Merloni et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' DESI Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2016) and  with LSST and Euclid lensing products, one will be able to  carry out the similar analysis over a larger area and on an ex-  tended redshift range, up to z=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Between eFEDS (120 deg2,  z < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='55) and future analysis (13,000 deg2, z < 1), the comoving  volume will increase by a factor 450.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' HOD parameters should  be inferred to the percent level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We will accurately measure the  halo occupation distributions as a function of host-galaxy prop-  erties and AGN properties towards characterizing possible cor-  relations between HOD parameters and host-galaxy, AGN, and  environmental properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' With that, one should unravel the role  of AGN in shaping the galaxy population and its hot circum-  galactic medium (Hopkins et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Comparat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Complementary to HOD analysis is the direct or partial cor-  relations with host galaxy properties;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' see reviews from Brandt &  Yang (2021);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Brandt & Alexander (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' In recent years, spec-  tral energy distribution fitting has dramatically improved in re-  trieving unbiased galaxy stellar parameters of galaxies hosting  AGN (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Mountrichas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2022, Buchner  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' in prep).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The upcoming Rubin observatory LSST survey1  (Ivezi´c et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2019) will provide deep multi-band imaging to be  used to determine host galaxy properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' In addition, the future  Euclid2 imaging space mission (Laureijs et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2011) will en-  able accurate morphological measurements of AGN hosts on a  significant fraction of the extra-galactic sky.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Together these will  allow charting of the physics of the connection between AGN,  host galaxy morphology, and stellar properties (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Ni et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2019) and give further insight on the ecology of  the cosmic web of X-ray AGN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  References  Abdurro’uf, Accetta, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Aerts, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2022, ApJS, 259, 35  Aihara, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', AlSayyad, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Ando, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2019, PASJ, 71, 114  Aihara, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', AlSayyad, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Ando, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2022, PASJ, 74, 247  Aird, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Coil, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Georgakakis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2015, MNRAS, 451, 1892  Allevato, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Viitanen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Finoguenov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2019, A&A, 632, A88  Altamirano-Dévora, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Miyaji, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Aceves, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2016, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Mexicana As-  tron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Astrofis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', 52, 11  Bartelmann, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' & Schneider, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2001, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', 340, 291  Behroozi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Wechsler, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', & Wu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2013, ApJ, 762, 109  Berk, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Anderson, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Bernstein, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 1999, in Society of Photo-  Optical Instrumentation Engineers (SPIE) Conference Series, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 3756, Op-  tical Spectroscopic Techniques and Instrumentation for Atmospheric and  Space Research III, ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Larar, 348–353  Berlind, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' & Weinberg, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2002, ApJ, 575, 587  Bernstein, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' & Jarvis, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2002, AJ, 123, 583  Blanton, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Bershady, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Abolfathi, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2017, AJ, 154, 28  Bongiorno, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Schulze, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Merloni, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2016, A&A, 588, A78  Bournaud, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Dekel, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Teyssier, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2011, ApJ, 741, L33  Bradshaw, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Almaini, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Hartley, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2013, MNRAS, 433, 194  Brandt, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' & Alexander, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2015, Astronomy and Astrophysics Review,  23, 1  Brandt, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' & Yang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2021, arXiv e-prints, arXiv:2111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='01156  Brunner, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Liu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Lamer, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2022, A&A, 661, A1  Buchner, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2021, The Journal of Open Source Software, 6, 3001  Bulbul, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Liu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Pasini, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2022, A&A, 661, A10  Burke, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Rykoff, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Allam, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2018, AJ, 155, 41  Cannon, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Drinkwater, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Edge, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2006, MNRAS, 372, 425  Cappelluti, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Ajello, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Burlon, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2010, ApJ, 716, L209  Chambers, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Magnier, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Metcalfe, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2016, arXiv e-prints,  arXiv:1612.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='05560  Chilingarian, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Borisov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Goradzhanov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2021, arXiv e-prints,  arXiv:2112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='04866  Ciesla, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Charmandaris, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Georgakakis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2015, A&A, 576, A10  Comparat, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Eckert, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Finoguenov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2020a, The Open Journal of  Astrophysics, 3, 13  Comparat, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Jullo, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Kneib, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2013, MNRAS, 433, 1146  Comparat, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Merloni, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Dwelly, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2020b, A&A, 636, A97  Comparat, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Merloni, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Salvato, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2019, MNRAS, 487, 2005  Comparat, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Truong, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Merloni, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2022, A&A, 666, A156  Conroy, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Wechsler, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', & Kravtsov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2006, ApJ, 647, 201  Contreras, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Angulo, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', & Zennaro, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2021, MNRAS, 504, 5205  Cooray, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' & Sheth, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2002, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', 372, 1  Coupon, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Arnouts, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', van Waerbeke, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2015, MNRAS, 449, 1352  Cunha, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Lima, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Oyaizu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Frieman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', & Lin, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2009, MNRAS, 396,  2379  Davis, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' & Peebles, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 1983, ApJ, 267, 465  Dekel, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' & Lahav, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 1999, ApJ, 520, 24  1 https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='lsst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='org  2 https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='cosmos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='esa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='int/web/euclid  Article number, page 13 of 17  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' main  DESI Collaboration, Aghamousa, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Aguilar, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2016, ArXiv e-prints  [arXiv:1611.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='00036]  Dey, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Schlegel, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Lang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2019, AJ, 157, 168  Donoso, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Yan, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Stern, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', & Assef, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2014, ApJ, 789, 44  Drinkwater, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Byrne, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Blake, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2018, MNRAS, 474, 4151  Driver, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Bellstedt, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Robotham, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2022, MNRAS, 513, 439  Driver, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' & Robotham, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2010, MNRAS, 407, 2131  Dvornik, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Hoekstra, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Kuijken, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2018, MNRAS, 479, 1240  Eckert, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Gaspari, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Gastaldello, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Le Brun, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', & O’Sullivan, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  2021, Universe, 7, 142  Favole, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Comparat, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Prada, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2016, MNRAS, 461, 3421  Flaugher, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Diehl, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Honscheid, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2015, AJ, 150, 150  Georgakakis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Aird, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Schulze, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2017, MNRAS, 471, 1976  Georgakakis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Comparat, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Merloni, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2018, MNRAS, 3272  Georgakakis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Nandra, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Laird, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Aird, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', & Trichas, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2008, MNRAS,  388, 1205  Gilli, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Zamorani, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Miyaji, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2009, A&A, 494, 33  Gunn, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Siegmund, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Mannery, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2006, AJ, 131, 2332  Guo, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', White, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Li, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', & Boylan-Kolchin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2010, MNRAS, 404, 1111  Guzzo, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Scodeggio, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Garilli, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2014, A&A, 566, A108  Hickox, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Jones, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Forman, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2009, ApJ, 696, 891  Hirata, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' & Seljak, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2003, MNRAS, 343, 459  Hopkins, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Hernquist, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Cox, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2006, ApJS, 163, 1  Hsieh, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' & Yee, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2014, ApJ, 792, 102  Ivezi´c, Ž.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Kahn, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Tyson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2019, ApJ, 873, 111  Jones, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Read, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Saunders, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2009, MNRAS, 399, 683  Kaiser, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Squires, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', & Broadhurst, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 1995, ApJ, 449, 460  Klypin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Prada, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Yepes, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Hess, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', & Gottlober, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2013, ArXiv e-prints  [arXiv:1310.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='3740]  Kocevski, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Brightman, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Nandra, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2015, ApJ, 814, 104  Kollmeier, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Zasowski, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Rix, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2017, arXiv e-prints  [arXiv:1711.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='03234]  Koutoulidis, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Georgantopoulos, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Mountrichas, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2018, MNRAS, 481,  3063  Koutoulidis, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Plionis, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Georgantopoulos, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', & Fanidakis, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2013, MN-  RAS, 428, 1382  Kravtsov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Berlind, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Wechsler, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2004, ApJ, 609, 35  Krumpe, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Miyaji, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', & Coil, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2010, ApJ, 713, 558  Krumpe, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Miyaji, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Coil, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', & Aceves, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2012, ApJ, 746, 1  Krumpe, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Miyaji, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Coil, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', & Aceves, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2018, MNRAS, 474, 1773  Krumpe, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Miyaji, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Husemann, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2015, ApJ, 815, 21  Landy, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' & Szalay, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 1993, ApJ, 412, 64  Laureijs, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Amiaux, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Arduini, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2011, arXiv e-prints, arXiv:1110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='3193  Leauthaud, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Benson, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Civano, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2015, MNRAS, 446, 1874  Leauthaud, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Tinker, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Behroozi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Busha, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', & Wechsler, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2011,  ApJ, 738, 45  Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Miyatake, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Luo, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2022, PASJ, 74, 421  Lilly, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Le Brun, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Maier, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2009, ApJS, 184, 218  Liske, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Baldry, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Driver, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2015, MNRAS, 452, 2087  Liu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Bulbul, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Ghirardini, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2022a, A&A, 661, A2  Liu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Buchner, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Nandra, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2022b, A&A, 661, A5  Liu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Merloni, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Comparat, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2022c, A&A, 661, A27  Luo, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Zhao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Zhao, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2015, Research in Astronomy and As-  trophysics, 15, 1095  Luo, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Silverman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', More, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2022, arXiv e-prints, arXiv:2204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='03817  Mandelbaum, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Lanusse, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Leauthaud, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2018a, MNRAS, 481, 3170  Mandelbaum, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Miyatake, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Hamana, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2018b, PASJ, 70, S25  Mandelbaum, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Tasitsiomi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Seljak, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Kravtsov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', & Wechsler, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  2005, MNRAS, 362, 1451  Marulli, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Bolzonella, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Branchini, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2013, A&A, 557, A17  McLure, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Cirasuolo, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Dunlop, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Almaini, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', & Foucaud, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2013, in  Astrophysics and Space Science Proceedings, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 37, Thirty Years of Astro-  nomical Discovery with UKIRT, 323  Medezinski, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Oguri, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Nishizawa, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2018, PASJ, 70, 30  Mendez, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Coil, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Aird, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2016, ApJ, 821, 55  Merloni, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Alexander, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Banerji, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2019, The Messenger, 175, 42  Miyaji, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Krumpe, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Coil, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', & Aceves, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2011, ApJ, 726, 83  Miyatake, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Battaglia, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Hilton, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2019, ApJ, 875, 63  Momcheva, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Brammer, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', van Dokkum, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2016, ApJS, 225,  27  More, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Miyatake, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Mandelbaum, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2015, ApJ, 806, 2  Moster, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Naab, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', & White, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2013, MNRAS, 428, 3121  Mountrichas, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Buat, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Yang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2021, A&A, 646, A29  Mountrichas, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Georgakakis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', & Georgantopoulos, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2019, MNRAS, 483,  1374  Myers, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Brunner, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Nichol, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2007, ApJ, 658, 85  Ni, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Yang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Brandt, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2019, MNRAS, 490, 1135  Nishimichi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Takada, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Takahashi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2019, The Astrophysical Jour-  nal, 884, 29  Nishizawa, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Hsieh, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Tanaka, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', & Takata, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2020, arXiv e-prints,  arXiv:2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='01511  Oguri, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Lin, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='-T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Lin, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2018, PASJ, 70, S20  Ohta, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Aoki, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Kawaguchi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', & Kiuchi, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2007, ApJS, 169, 1  Oke, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' & Gunn, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 1983, ApJ, 266, 713  Oogi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Shirakata, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Nagashima, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2020, MNRAS, 497, 1  Padovani, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Alexander, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Assef, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2017, A&A Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', 25, 2  Paturel, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Petit, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Prugniel, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2003, A&A, 412, 45  Peng, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='-j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Lilly, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Kovaˇc, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2010, ApJ, 721, 193  Peng, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='-j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Lilly, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Renzini, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', & Carollo, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2012, ApJ, 757, 4  Planck Collaboration, Aghanim, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Akrami, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2020, A&A, 641, A6  Powell, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Cappelluti, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Urry, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2018, ApJ, 858, 110  Predehl, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Andritschke, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Arefiev, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2021, A&A, 647, A1  Refregier, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2003, ARA&A, 41, 645  Rodríguez-Torres, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Comparat, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Prada, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2017, MNRAS, 468, 728  Rowe, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Jarvis, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Mandelbaum, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2015, Astronomy and Com-  puting, 10, 121  Salvato, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Ilbert, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', & Hoyle, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2018, Nature Astronomy, 68  Salvato, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Wolf, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Dwelly, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2022, A&A, 661, A3  Schneider, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Freund, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Czesla, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2022, A&A, 661, A6  Scoville, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Aussel, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Brusa, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2007, ApJS, 172, 1  Seljak, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Makarov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Mandelbaum, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2005, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' D, 71, 043511  Seppi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Comparat, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Bulbul, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2022, A&A, 665, A78  Sevilla-Noarbe, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Bechtol, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Carrasco Kind, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2021, ApJS, 254, 24  Shen, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', McBride, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', White, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2013, ApJ, 778, 98  Sheth, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' & Tormen, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 1999, MNRAS, 308, 119  Silverman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Kashino, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Sanders, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2015, ApJS, 220, 12  Sinha, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' & Garrison, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2020, MNRAS, 491, 3022  Siudek, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Mezcua, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', & Krywult, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2023, MNRAS, 518, 724  Skelton, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Whitaker, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Momcheva, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2014, ApJS, 214, 24  Skrutskie, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Cutri, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Stiening, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2006, AJ, 131, 1163  Smee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Gunn, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Uomoto, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2013, AJ, 146, 32  Starikova, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Cool, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Eisenstein, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2011, ApJ, 741, 15  Tanaka, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2015, ApJ, 801, 20  Tanaka, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Coupon, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Hsieh, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2018, PASJ, 70, S9  Tegmark, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' & Bromley, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 1999, ApJ, 518, L69  Tegmark, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' & Peebles, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 1998, ApJ, 500, L79  Trujillo-Gomez, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Klypin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Primack, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', & Romanowsky, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2011, ApJ,  742, 16  Véron-Cetty, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' & Véron, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2010, A&A, 518, A10  Viitanen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Allevato, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Finoguenov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2019, A&A, 629, A14  Wechsler, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' & Tinker, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2018, ARA&A, 56, 435  Xu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Zehavi, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', & Contreras, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2021, MNRAS, 502, 3242  Yang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Boquien, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Brandt, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2022, ApJ, 927, 192  Yang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Brandt, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Alexander, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2019, MNRAS, 485, 3721  Yang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Brandt, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Darvish, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2018a, MNRAS, 480, 1022  Yang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Brandt, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Vito, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2018b, MNRAS, 475, 1887  York, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Adelman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Anderson, Jr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2000, AJ, 120, 1579  Zacharegkas, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Chang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Prat, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2022, MNRAS, 509, 3119  Zehavi, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Zheng, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Weinberg, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2011, ApJ, 736, 59  Zhang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Luo, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2021, A&A, 650, A155  Zheng, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Berlind, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Weinberg, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2005, ApJ, 633, 791  Zheng, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Coil, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', & Zehavi, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2007, ApJ, 667, 760  Zou, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Brandt, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', Chen, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='-T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2022, ApJS, 262, 15  Zu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' & Mandelbaum, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2015, MNRAS, 454, 1161  Acknowledgements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' MK is supported by the DFG grant KR 3338/4-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' is  supported by UNAM-DGAPA PAPIIT 111319 and CONACyT Ciencias Básica  252531.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  This work is based on data from eROSITA, the soft X-ray instrument aboard  SRG, a joint Russian-German science mission supported by the Russian Space  Agency (Roskosmos), in the interests of the Russian Academy of Sciences rep-  resented by its Space Research Institute (IKI), and the Deutsches Zentrum für  Luft- und Raumfahrt (DLR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The SRG spacecraft was built by Lavochkin Asso-  ciation (NPOL) and its subcontractors, and is operated by NPOL with support  from the Max Planck Institute for Extraterrestrial Physics (MPE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  The development and construction of the eROSITA X-ray instrument was led  by MPE, with contributions from the Dr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Karl Remeis Observatory Bamberg  & ECAP (FAU Erlangen-Nuernberg), the University of Hamburg Observatory,  the Leibniz Institute for Astrophysics Potsdam (AIP), and the Institute for As-  tronomy and Astrophysics of the University of Tübingen, with the support of  DLR and the Max Planck Society.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The Argelander Institute for Astronomy of  the University of Bonn and the Ludwig Maximilians Universität Munich also  participated in the science preparation for eROSITA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  The eROSITA data shown here were processed using the eSASS/NRTA software  system developed by the German eROSITA consortium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  The Hyper Suprime-Cam (HSC) collaboration includes the astronomical com-  munities of Japan and Taiwan, and Princeton University.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The HSC instrumen-  tation and software were developed by the National Astronomical Observatory  of Japan (NAOJ), the Kavli Institute for the Physics and Mathematics of the  Article number, page 14 of 17  Comparat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' : X-ray AGN HOD  Universe (Kavli IPMU), the University of Tokyo, the High Energy Accelerator  Research Organization (KEK), the Academia Sinica Institute for Astronomy and  Astrophysics in Taiwan (ASIAA), and Princeton University.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Funding was con-  tributed by the FIRST program from the Japanese Cabinet Office, the Ministry  of Education, Culture, Sports, Science and Technology (MEXT), the Japan Soci-  ety for the Promotion of Science (JSPS), Japan Science and Technology Agency  (JST), the Toray Science Foundation, NAOJ, Kavli IPMU, KEK, ASIAA, and  Princeton University.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  This paper makes use of software developed for Vera C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Rubin Observatory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We  thank the Rubin Observatory for making their code available as free software at  http://pipelines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='lsst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='io/.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  This paper is based on data collected at the Subaru Telescope and retrieved from  the HSC data archive system, which is operated by the Subaru Telescope and  Astronomy Data Center (ADC) at NAOJ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Data analysis was in part carried out  with the cooperation of Center for Computational Astrophysics (CfCA), NAOJ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  We are honored and grateful for the opportunity of observing the Universe from  Maunakea, which has the cultural, historical and natural significance in Hawaii.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Funding for the Sloan Digital Sky Survey V has been provided by the Alfred P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Sloan Foundation, the Heising-Simons Foundation, the National Science Foun-  dation, and the Participating Institutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' SDSS acknowledges support and re-  sources from the Center for High-Performance Computing at the University of  Utah.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The SDSS web site is www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='sdss5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='org.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  SDSS is managed by the Astrophysical Research Consortium for the Participat-  ing Institutions of the SDSS Collaboration,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' including the Carnegie Institution  for Science,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Chilean National Time Allocation Committee (CNTAC) ratified  researchers,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' the Gotham Participation Group,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Harvard University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Heidelberg  University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The Johns Hopkins University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' L’Ecole polytechnique fédérale de  Lausanne (EPFL),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Leibniz-Institut für Astrophysik Potsdam (AIP),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Max-Planck-  Institut für Astronomie (MPIA Heidelberg),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Max-Planck-Institut für Extrater-  restrische Physik (MPE),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Nanjing University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' National Astronomical Observa-  tories of China (NAOC),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' New Mexico State University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The Ohio State Uni-  versity,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Pennsylvania State University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Smithsonian Astrophysical Observatory,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Space Telescope Science Institute (STScI),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' the Stellar Astrophysics Participa-  tion Group,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Universidad Nacional Autónoma de México,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' University of Arizona,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  University of Colorado Boulder,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' University of Illinois at Urbana-Champaign,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  University of Toronto,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' University of Utah,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' University of Virginia,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Yale Univer-  sity,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' and Yunnan University.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Sloan Foundation, the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Department of Energy Office of Science, and the  Participating Institutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' SDSS acknowledges support and resources from the  Center for High-Performance Computing at the University of Utah.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The SDSS  web site is www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='sdss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='org.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  SDSS is managed by the Astrophysical Research Consortium for the Partici-  pating Institutions of the SDSS Collaboration including the Brazilian Participa-  tion Group,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' the Carnegie Institution for Science,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Carnegie Mellon University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Center for Astrophysics | Harvard & Smithsonian (CfA),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' the Chilean Partici-  pation Group,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' the French Participation Group,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Instituto de Astrofísica de Ca-  narias,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The Johns Hopkins University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Kavli Institute for the Physics and Math-  ematics of the Universe (IPMU) / University of Tokyo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' the Korean Participation  Group,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Lawrence Berkeley National Laboratory,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Leibniz Institut für Astrophysik  Potsdam (AIP),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Max-Planck-Institut für Astronomie (MPIA Heidelberg),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Max-  Planck-Institut für Astrophysik (MPA Garching),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Max-Planck-Institut für Ex-  traterrestrische Physik (MPE),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' National Astronomical Observatories of China,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  New Mexico State University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' New York University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' University of Notre Dame,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Observatório Nacional / MCTI,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The Ohio State University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Pennsylvania State  University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Shanghai Astronomical Observatory,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' United Kingdom Participation  Group,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Universidad Nacional Autónoma de México,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' University of Arizona,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Uni-  versity of Colorado Boulder,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' University of Oxford,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' University of Portsmouth,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  University of Utah,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' University of Virginia,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' University of Washington,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' University  of Wisconsin,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Vanderbilt University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' and Yale University.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Article number, page 15 of 17  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' main  Appendix A: X-ray data analysis  Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1: X-ray mask  We use the region files created by eSASS/srctool to create X-  ray masks for point sources (PS) and extended sources (EXT)  (Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' 2022b,a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Each source has its signal-to-noise ratio  measured as a function of radius (circular apertures).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' An optimal  radius for source extraction is found by maximizing the signal-  to-noise ratio given the local background surface brightness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' It is  clipped to a minimum radius of 10′′(MINIMUM_SOURCE_RADIUS  parameter) and a maximum radius of the 99% energy enclosed  fraction radius of the point spread function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We use this maxi-  mum signal-to-noise radius as a starting point to determine the  area to be masked around sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  We measure the cross-correlation as a function of scale be-  tween events (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='3 keV) and sources in the catalog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We mea-  sure it for bins of the number of counts measured per source  in the detection band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The cross-correlation becomes constant  above a particular angular scale, which corresponds to a con-  servative masking radius of a source (with a given number of  counts), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=', its average imprint on the sky, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1 top pan-  els.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' For each cross-correlation curve, we measure the radius at  which its value is between 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='25 and two times that of the constant  values measured at large separation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' This brackets the masking  radius within the black vertical error bars shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1 bot-  tom panels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We find that this cross-correlation masking radius for  point sources is, on average, 40 percent (20 for extended sources)  larger than the eSASS/srctool radius of maximum signal-to-  noise, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1 bottom panels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The srctool mask is likely not  conservative enough for our purpose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' For instance, the detection  of a point source just beyond the eSASS/srctool masking ra-  dius of another point source will be subject to biases due to the  residual events measured via the cross-correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Though, if  we followed the average masking radius suggested by the cross-  correlation (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1 bottom panels), the large scatter in the re-  lation between the maximum signal-to-noise radius and the total  number of counts would be missed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' So to have a conservative  mask that closely follows the data, we multiply the masking radii  from eSASS/srctool by a factor of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='4 (this is more conserva-  tive than required for the extended sources, but it simplifies the  procedure).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' In that way, the masking radius will reach, on aver-  age, the line obtained from the cross-correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Doing so en-  sures no remaining correlation between the set of events outside  the mask and the source catalog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We are conservatively masking  both point sources and extended sources individually.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  After applying the mask, we are left with 17,523 AGN can-  didates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We are using the fraction of random points (see § 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='4)  that fall in the masks, we estimate the area of the observed X-ray  sky effectively occupied by sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' In all, sources occupy 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='805  deg2 out of 141.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='97 deg2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' AGN occupy 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='914 deg2, stars 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='988  deg2, and extended sources 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='057 deg2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2: Random catalogue  We use the sensitivity map produced by the eROSITA pipeline  Brunner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (eSASS, apetool 2022) with a parameter Pthres =  e−8 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='00033 (the Poisson probability threshold below which  an excess of counts is considered a source), corresponding to a  detection likelihood of 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' It is a pixelated fits image with size  [0, 9000)×[0, 18000) containing the sensitivity limit (in counts).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Each random point falls in a pixel of this map, and we attach the  corresponding count limit Clim  X to the random number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We draw a  large set of redshift and X-ray fluxes ( fx, z) from the AGN X-ray  luminosity function projection to assign to each random point  Aird et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2015);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Comparat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' It is sampled down  to 2 × 10−15erg cm−2 s−1, a flux value at which the area curve  is smaller than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5 deg2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We convert the flux into an expected  number of counts  CT expected = fx × ECF × EEF × texp + CT background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1)  where the energy conversion factor is ECF = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='164 × 1012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The  encircled energy fraction is set to EEF = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The exposure  time, texp, is obtained with the exposure map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' CT background is ob-  tained from the background map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We draw a random Poisson  variable Rv for each CT expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' If this value exceeds the count  limit, Rv > Clim  X , the point is accepted in the random sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We  remove the shallower areas at the edge of the field through a min-  imum exposure time threshold to minimize the maximum offset  between the normalized cumulative distribution of the data sam-  ple and the random sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' We find that an 830 seconds thresh-  old minimizes the KS-test values at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='19% (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='81%) for R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  (Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' It removes ∼ 10 deg2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' It is sufficiently accurate to es-  timate clustering on the photometric sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' After masking ex-  tended sources and stars and trimming the low exposure time re-  gion, the total number of random points remaining is 3,713,726.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Article number, page 16 of 17  Comparat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' : X-ray AGN HOD  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Cross-correlation between sources and events as a function of angular separation for extended (EXT, top left) and point-like (PS, top right)  X-ray sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Bottom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Masking radius v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' log10 of the counts measured (bottom).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Average masking radius obtained with the cross-correlation  (black line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' The masking radius obtained with eSASS/srctool for individual sources is systematically lower than the black line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content=' Its best-fit  polynomial (blue dashed) is multiplied by 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2 (extended sources) or 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='4 (point sources) to align with the black line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='  Article number, page 17 of 17  EXT  1, 3 pixels  371.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1-622.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='7  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='8-78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='6  1753.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1-2941.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5  221.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2-371.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='9-46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='8  1044.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='8-1753.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1  131.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='8-221.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='25,1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5,2  ofevents  622.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='7-1044.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='8  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='6-131.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='8  relative density  101  100  101  102  103  separationtosource[arcseconds]PS  1, 3 pixels  547.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2-763.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='8  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0-74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  103  4047.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='9-5650.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='3  392.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0-547.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0-53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  2899.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='9-4047.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='9  280.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='8-392.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2-38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  events  2077.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5-2899.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='9  201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2-280.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='8  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5-27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2  1488.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='3-2077.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5  144.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1-201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0-19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5  1066.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2-1488.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='3  103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='3-144.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='1  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0-14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  densityof  102  763.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='8-1066.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0-103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='25,1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5,2  relative  101  100  101  102  103  separationtosource[arcseconds]EXT  [arc seconds]  102  Iradius  masking  eFEDs extended sources  y=15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='948x2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='046x+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='124  x1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2  y=44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='425x2+-79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='217x+77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='263  EVTxSRC  101  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  log1o(Count 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='3keV)PS  eFEDspoint-like sources  y=10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='754x2+ -8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='989x+ 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='49  seconds]  x1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='4  y=10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='842x2+ 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='71x+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='75  EVTxSRC  arc  102  Iradius  masking  101  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='5  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='0  log1o(Count0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='2-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
+page_content='3keV)' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/j9AzT4oBgHgl3EQfbfze/content/2301.01388v1.pdf'}
diff --git a/jNAyT4oBgHgl3EQfx_lt/content/2301.00676v1.pdf b/jNAyT4oBgHgl3EQfx_lt/content/2301.00676v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..0d9aa4a98401973b52d5c089157c9180dbd0c67b
--- /dev/null
+++ b/jNAyT4oBgHgl3EQfx_lt/content/2301.00676v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:389ecd01cf0e7a03f9f06669b2c3c9017d744fd0412db9b46413b73eacfcbaaa
+size 706777
diff --git a/jNAyT4oBgHgl3EQfx_lt/vector_store/index.pkl b/jNAyT4oBgHgl3EQfx_lt/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..7ef8223b22340ea87fb0c2b0633843dc18d10426
--- /dev/null
+++ b/jNAyT4oBgHgl3EQfx_lt/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9376beb73e354271c023015f844bc8a6d72cc9c502ba53f33c24a7a519780dc6
+size 125112
diff --git a/jNE1T4oBgHgl3EQfNQMV/content/tmp_files/2301.02998v1.pdf.txt b/jNE1T4oBgHgl3EQfNQMV/content/tmp_files/2301.02998v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b87aed2ef9fd7dc1911cf4f9a98b0b654c280969
--- /dev/null
+++ b/jNE1T4oBgHgl3EQfNQMV/content/tmp_files/2301.02998v1.pdf.txt
@@ -0,0 +1,1264 @@
+arXiv:2301.02998v1  [cs.IR]  8 Jan 2023
+InPars-Light: Cost-Effective Unsupervised Training of Efficient
+Rankers
+Leonid Boytsov∗
+leo@boytsov.info
+Amazon AWS AI Labs
+Pittsburgh, USA
+Preksha Patel†
+Vivek Sourabh†
+Riddhi Nisar†
+Sayani Kundu†
+Ramya Ramanathan†
+Carnegie Mellon University
+Pittsburgh, USA
+Eric Nyberg
+ehn@cs.cmu.edu
+Carnegie Mellon University
+Pittsburgh, USA
+ABSTRACT
+We carried out a reproducibility study of InPars recipe for unsuper-
+vised training of neural rankers [4]. As a by-product of this study,
+we developed a simple-yet-effective modification of InPars, which
+we called InPars-light. Unlike InPars, InPars-light uses only a freely
+available language model BLOOM and 7x-100x smaller ranking
+models. On all five English retrieval collections (used in the origi-
+nal InPars study) we obtained substantial (7-30%) and statistically
+significant improvements over BM25 in nDCG or MRR using only a
+30M parameter six-layer MiniLM ranker. In contrast, in the InPars
+study only a 100x larger MonoT5-3B model consistently outper-
+formed BM25, whereas their smaller MonoT5-220M model (which
+is still 7x larger than our MiniLM ranker), outperformedBM25 only
+on MS MARCO and TREC DL 2020. In a purely unsupervised set-
+ting, our 435M parameter DeBERTA v3 ranker was roughly at par
+with the 7x larger MonoT5-3B: In fact, on three out of five datasets,
+it slightly outperformed MonoT5-3B. Finally, these good results
+were achieved by re-ranking only 100 candidate documents com-
+pared to 1000 used in InPars. We believe that InPars-light is the first
+truly cost-effective prompt-based unsupervised recipe to train and
+deploy neural ranking models that outperform BM25.
+CCS CONCEPTS
+• Information systems → Retrieval models and ranking.
+KEYWORDS
+unsupervised training, neural information retrieval, ranking
+1
+INTRODUCTION
+Training effective neural IR models often requires abundant in-
+domain training data, which can be quite costly to obtain: Judging
+a single document-query pair takes at least one minute on aver-
+age [13, 19] and a single query typically needs at least 50 of such
+judgements [7].1 In that, models trained on out-of-domain data
+and/or fine-tuned using a small number of in-domain queries are
+often worse or perform only marginally better [31, 47] than simple
+non-neural BM25 rankers.
+∗Work done outside of the scope of employment.
+†Equal contribution: Work done while studying at Carnegie Mellon University.
+1Robust04 and TREC-COVID collections used in our study have about 1K judgements
+per query.
+A recent trend to deal with this problem consists in generat-
+ing synthetic in-domain training data via prompting of Large Lan-
+guage Models (LLMs) [4, 9, 43], However, proposed solutions are
+not cost effective. Furthermore, because researchers used primarily
+proprietary LLMs—whose training procedure was not controlled
+by the scientific community—or instruction-finetuned LLMs there
+is a question of whether information retrieval capabilities emerge,
+indeed, from a large scale training with a next-token-prediction
+objective.
+To enable a practical solution for a large scale LLM-based gen-
+eration of training data for IR systems, as well as to answer this
+key scientific question, we carry out a reproducibility study of In-
+Pars [4] using medium-size (at most 7B parameters) open-source
+LLMs [44, 50]. In addition, our study employs more practical and
+more commonly used BERT-based cross-encoder models having as
+little as 30 million parameters. In contrast, the original study em-
+ployed large MonoT5 rankers of which only MonoT5-3B ranker
+(with 3 billion parameters) performed well [35].
+We discover that in a purely unsupervised setting we can re-
+place an impractical three-billion parameter MonoT5-3B model [35]
+with a 7x smaller bi-directional BERT model while obtaining com-
+parable results. Moreover, unlike the original InPars study where
+a 220M million MonoT5 model fails to outperform BM25 on three
+out of five datasets, we show that a much smaller MiniLM model
+with only 30 million parameters [53] can always outperform BM25
+by 7-30% in key metrics (nDCG@K or MRR).
+In that, obtaining these good results required re-ranking only
+100 candidate documents compared to 1000 in the InPars study [4].
+Compared to InPars, our recipe—which we call InPars-Light—is
+substantially more cost effective in three dimensions: (a) synthetic
+data generation, (b) model training, and (c) inference.
+In our study we ask the following research questions:
+• RQ1: Do information retrieval (IR) capabilities emerge merely
+from a large-scale next-token-prediction training? Although,
+prior studies (see § 2) provide limited evidence to answer
+this question positively, we believed that additional evidenced
+was required.
+• RQ2: Are open-source models more or less useful for gener-
+ation of synthetic IR training data compared to the similar-
+size GPT-3 model?
+
+• RQ3: Does consistency checking proposed by Dai et al. [9],
+indeed, beneficial. Is it applicable in the re-ranking setting
+(as opposed to using it with retrievers as in [9])?
+• RQ4: Can we match performance of a large MonoT5-3B
+ranker using much smaller BERT models?
+• RQ5: In particular, can we substantially outperform BM25
+using a small and fast ranker such as a MiniLM ranker with
+merely 30 million parameters?
+We obtain the following results:
+• RQ1 & RQ2: Not only open-source LLMs BLOOM [44] and
+GPT-J [50] trained in a fully unsupervised fashion can be
+prompted to generate effective synthetic queries, but using
+them leads to consistent improvement compared to GPT-3
+Curie model [6]. At the same time, we estimate that genera-
+tion of synthetic queries using open-source models is about
+10x cheaper. Note that in the concurrent work, Jeronymo
+et al. [18] also obtained good results using an open-source
+generation models, but they do not have an ablation that
+focuses specifically on replacing GPT-3 Curie with open-
+source models.
+• RQ3: Although we confirm the effectiveness of the InPars
+training recipe, fine-tuning the model using consistency-checked
+data always produced a better model;
+• RQ4 & RQ5: We confirm the finding of Bonifacio et al. [4]
+that the InPars-recipe (even if combined with consistency
+checking) does not work well for small models. We never-
+theless discover that a combination of pre-training on all
+queries (from all datasets) and in-domain finetuning on consistency-
+checked data produces a small MiniLM-30M model that al-
+ways outperformedBM25 by 7-30% in key metrics (nDCG@k
+or MRR);
+2
+RELATED WORK
+Neural information retrieval has become a busy research area. An
+overview of the recent approaches and trends we address the reader
+to the survey by Lin et al. [24]. Likewise, prompting methods have
+gained quite a bit of popularity in NLP (see, e.g., [26] for a recent
+survey), but they were scarcely used in IR: We know only three
+papers directly related to our work.
+Sachan et al. [43] were probably the first to demonstrate effec-
+tiveness of LLMs in the document ranking task. In their approach,
+which they named UPR, they concatenate a document, a special
+prompt such as "please write a question for this document" and the
+query itself. Then, UPR uses a pre-trained LLM model to compute
+the likelihood of generating the query given the passage text. How-
+ever, they evaluate only on QA (but not IR) datasets and their main
+results are for an impractical three-billion parameter instruction-
+finetuned model, which is used essentially as a re-ranker (in a zero-
+shot sceanrio). Because this LLM was instruction fine-tuned these
+experiments do not permit definitive conclusions about RQ1. Al-
+though they also demonstrated the effectiveness of a standard (i.e.,
+just next-token-prediction training) 2.7B GPT-Neo LLM [3], this
+was done only for a single QA dataset, namely Natural Questions
+[19].
+The smallest model that they used had 250 million parameters
+(compared to our 30-million MiniLM model): The evaluated it only
+on the Natural Questions [19] collection, where it outperformed
+BM25 only by about 10%.
+Bonifacio et al. [4] proposed an InPars method, which relied
+on few-shot prompting. The study had a convincing evaluation
+on five datasets where only one dataset, namely NQ, is a typical
+QA collection. Unlike Sachan et al. [43] Bonifacio et al. used few-
+shot prompting to distill an LLM into smaller rankers. To this end,
+few-shot prompting was used to generate synthetic queries for
+randomly sampled documents. For each collection they generated
+100K synthetic queries and retained only 10K with the highest av-
+erage log-probabilities.
+However, they obtained good results only for a huge MonoT5-
+3B parameter model. Moreover, the used a proprietary GPT-3 model,
+which can be quite costly to use. In a follow-up study, which is con-
+current with this work, Jeronymo et. al [18] introduced a modifica-
+tion of InPars—dubbed InPars v2—where GPT-3 Curie [6] was re-
+placed with an open-source model GPT-J [50]. However, this model
+swap is “entangled” with at least two other modifications in the
+training recipe:
+• A new filtering condition that employs an MS MARCO trained
+MonoT5-3B model.
+• The vanilla prompt (which was used in InPars and our ex-
+periments) was replaced with the Guided by Bad Question
+prompt (introduced in [4]).
+Thus, it is not possible to fairly assess the impact of replacing GPT-
+3 Curie with GPT-J [50].
+An important disadvantage of InPars v2 recipe is that it is still
+not cost-effect as authors use a huge MonoT5-3B model. The fil-
+tering check uses a MonoT5-3B model trained on MS MARCO cor-
+pus, which is not always possible in a commercial setting due to
+licensing issues (MS MARCO is a research-only collection). More-
+over, the MonoT5-3B model trained on MS MARCO—albeit being
+impractical—has excellent zero-shot transferability: Fine-tuning MonoT5-
+3B model trained on MS MARCO with InPars v2 only improves the
+average BEIR score only by 2.4%: from 0.538 to 0.551.
+Dai et al. [9] used an InPars-like method called Promptagator
+and created synthetic training data using a huge proprietary FLAN
+model with 137 billion parameters. Although they used modestly
+sized models with 110 million parameters, Dai et al. [9] generated
+as many as million synthetic training queries for each dataset. In
+contrast, InPars used only 100K queries per dataset, which is much
+less expensive (see a discussion in § 5.2).
+Importantly, Dai et al [9] proposed to use consistency checking
+[1] to filter-out potentially spurious queries, which was not previ-
+ously done in the IR context. We use a variant of this procedure as
+well.
+In addition, to prompt-based generation of training data, there
+are multipleproposals for self-supervised adaptation of out-of-domain
+models using generative pseudo-labeling [22, 38, 51]. To this end,
+questions or queries are generated using a pretrained seq2seq model
+(though an LLMs can be used as well) and negative examples are
+mined using either BM25 or an out-of-domain retriever or ranker.
+Unsupervised domain adaptation is complementary to the approaches
+considered in this work.
+The disadvantage of such approaches is that they may need a
+reasonably effective out-of-domain model. However, such models
+
+Table 1: The format of the vanilla 3-shot InPars prompt
+Example 1:
+Document: <text of the first example document>
+Relevant Query: <text of the first relevant query>
+Example 2:
+Document: <text of the second example document>
+Relevant Query: <text of the second relevant query>
+Example 3:
+Document: <text of the third example document>
+Relevant Query: <text of the third relevant query>
+Example 4:
+Document: <real in-domain document text placeholder>
+Relevant Query:
+Notes: To generate a synthetic query, we first insert a text of a
+chosen real in-domain document after the prefix “Document:”
+in example four. Then, we “ask” an LLM to generate a comple-
+tion.
+can be hard to obtain due to licensing issues and poor transferabil-
+ity from other domains. For example, MS MARCO models have rea-
+sonable transferability [31, 47], but MS MARCO cannot be used to
+train models in a commercial context (without extra licensing from
+Microsoft). In contrast, the Natural Questions (NQ) collection [19]
+has a permissive license2, but models trained on NQ can fail to
+transfer to datasets that are not based on Wikipedia [31].
+Another potentially complementary approach is LLM-assisted
+query expansion. In particular Gao et al. prompt a 175B Instruct-
+GPT model to generate a hypothetical answer to a question [12].
+Then this answer is encoded and together with the encoding of the
+original question they are compared with encoded documents. In
+a purely unsupervised setting—-using the Contriever bi-encoder
+training without supervision [17]—they were able to outperform
+BM25 by as much as 20%.
+Despite strong results, a serious disadvantage of this approach is
+its dependence on the external proprietary model that is costly and
+has long generation times. Although we could not find any reliable
+benchmarks, a folklore opinion is that generation latency is a few
+seconds. To verify this, we used the OpenAI playground3 to gener-
+ate a few hypothetical answers using the prompt in Gao et al. [12]
+and a sample of TREC DL 2020 queries. With a maximum genera-
+tion length of 256 tokens (a default setting), the latency exceeded
+four seconds.
+Quite interestingly, Gao et al. [12] tried to replace a 175B GPT-
+3 model with smaller open-source models on TREC DL 2019 and
+TREC DL 2020 (see Table 4 in their study), but failed to obtain con-
+sistent and substantial gains with models having fewer than 50B
+parameters.
+3
+METHODS
+3.1
+Information Retrieval Pipeline
+We use a variant of a classic filter-and-refine multi-stage retrieval
+pipeline [30, 36, 52], where top-푘 candidate documents retrieved
+by a fast BM25 ranker [40] are re-ranked using a slower neural
+re-ranker. For collections where document have titles, the BM25
+retriever itself has two stages: In the first stage we retrieve 1K
+documents using a Lucene index built over the concatenation of
+all document fields. In the second stage, these candidates are re-
+ranked using equally weighted BM25 scores computed separately
+for each field.
+Our neural rankers are cross-encoder models [24, 34], which
+operate on queries concatenated with documents. Concatenated
+texts are passed to a backbone bi-directional encoder-only Trans-
+former model [10] equipped with an additional ranking head (a
+fully-connected layer), which produces a relevance score (using
+the last-layer contextualized embedding of a CLS-token [34]). In
+contrast, authors of InPars [4] use a T5 [37] cross-encoding re-
+ranker [35], which is a full Transformer model [48]. It uses both the
+encoder and the decoder. The T5 ranking Transformer is trained
+to generate labels “true” and “false”, which represent relevant and
+non-relevant document-query pairs, respectively.
+Backbone Transformer models can differ in the number of pa-
+rameters and pre-training approaches (including pre-training datasets).
+In this paper we evaluated the following models, all of which were
+pre-trained in the self-supervised fashion without using IR-specific
+pre-training or supervision with IR datasets:
+• A six-layer MiniLM-L6 model [53]. It is a tiny (by modern
+standards) 30-million parameter model, which was distilled
+[15, 21, 41] from Roberta [27]. We download model L6xH384
+MiniLMv2 from the Microsoft website.4
+• A 24-layer (large) ERNIE v2 model from the HuggingFace
+hub [46]5. It has 335 million parameters.
+• A 24-layer (large) DeBERTA v3 model with 435 million pa-
+rameters [14] from the HuggingFace hub 6.
+We choose ERNIE v2 and DeBERTA v3 because (from our prior ex-
+perience) we knew they had strong performance on the MS MARCO
+dataset (better than BERT large [10] and several other models that
+we tested in the past). Both models performedcomparably well (see
+Table 4) in the preliminary experiments, but we chose DeBERTA
+for main experiments because it is more effective on MS MARCO
+and TREC-DL 2020.
+However, both of these models are quite large and we aspired to
+show that an InPars-like training recipe can be used with smaller
+models too. In contrast, Bonifacio et al. [4] were able to show that
+only a big T5-3B model with 3B parameters outperformedBM25 on
+all five datasets, while the smaller (but still quite large) T5-200M
+ranker with “merely” 200 million parameters did not outperform
+BM25 on three datasets (it only worked on MS MARCO and TREC-
+DL 2020).
+2https://github.com/google-research-datasets/natural-questions/blob/master/LICENSE
+3https://beta.openai.com/playground
+4https://github.com/microsoft/unilm/tree/master/minilm
+5https://huggingface.co/nghuyong/ernie-2.0-large-en
+6https://huggingface.co/microsoft/deberta-v3-large
+
+3.2
+Generation of Synthetic Training Data
+In-domain training data is generated using a well-known few-shot
+prompting approach introduced by Brown et al. [6]. In the IR do-
+main, it was first used by Bonifacio et al. [4] who re-branded it as
+InPars. The key idea is to “prompt” a large language model with a
+few-shot textual demonstration of known relevant query-document
+pairs. To produce a novel query-document pair, Bonifacio et al. ap-
+pend an in-domain document to the prompt and “ask” the model to
+complete the text. We use the so-called vanilla prompt (see Table 1)
+created by Bonifacio et al. [4]. Like in the InPars study, we gener-
+ated 100K queries for each dataset with exception of MS MARCO
+and TREC DL. Because both datasets use the same set of passages
+they share the same set of 100K generated queries.
+Repeating this procedure for many in-domain documents pro-
+duces a large training set, but it can be quite imperfect: We carried
+out spot-checking and found quite a few queries that were spuri-
+ous or only tangentially relevant to the passage from which they
+were generated.
+Many spurious queries can be filtered out automatically. To this
+end, in InPars Bonifacio et al. [4] used only 10% of the queries
+with the highest log-probabilities (averaged over query tokens). In
+Promptagator Dai et al. [9] introduced a different filtering proce-
+dure, which was a variant of consistency checking [1]. Dai et al.
+first trained a retriever model using all the generated queries. Then,
+for each query they retrieved a set of documents. The query passed
+the consistency check if the first retrieved document was the doc-
+ument from which the query was generated.
+Dai et al. [9] used consistency checking with bi-encoding re-
+trieval models, but it is applicable to cross-encoding re-ranking
+models as well. Another straightforward modification of this ap-
+proach is to check if a generated document is present in a set of
+top-푘 (푘 > 1) candidates with the highest relevance scores (as com-
+puted by the re-ranking or retrieval model).
+3.3
+InPars-Light Training Recipe
+The InPars-Light is a modification of the original InPars, but it is
+substantially more cost effective for generation of synthetic queries,
+training the models, and inference. InPars-Light has the following
+main “ingredients”:
+• Using open-source models instead of GPT-3;
+• Using much smaller ranking models;
+• Fine-tuning models on consistency-checked training data;
+• Optional pre-training of models using all generated queries
+from all collections.
+• Re-ranking only 100 candidate documents instead of 1000;
+To obtain consistency-checked queries for a given dataset, a
+model trained on InPars-generated queries (for this dataset) was
+used to re-rank output of all original queries (for a given dataset).
+Then, all the queries where the query-generating-document did
+not appear among top-푘 scored documents was discarded. In our
+study, we experimented with 푘 from one to three (but only on
+MS MARCO).7 Although 푘 = 1 worked pretty well, using 푘 = 3
+lead to a small boost in accuracy. Consistency-checking was car-
+ried out using DeBERTA-v3-435M [14]. We want to emphasize that
+7We did not want to optimize this parameter for all collections and, thus, to commit
+a sin of tuning hyper-parameters on the complete test set.
+consistency-checked training data was used in addition to origi-
+nal InPars-generated data (but not instead), namely, to fine-tune a
+model initially trained on InPars generated data.
+Also, quite interestingly, a set of consistency-checked queries
+had only a modest (about 20-30%) overlap with the set of queries
+that were selected according to their average log-probabilities. Thus,
+consistency-checking increased the amount of available training
+data. It might seem appealing to achieve the same objective by sim-
+ply picking a larger number of queries (with highest average log-
+probabilities). However, preliminary experiments on MS MARCO
+showed that a naive increase of the number of queries degraded
+effectiveness (which is consistent with the InPars study [4]).
+Although, the original InPars recipe with open-source models
+and consistency checking allowed us to train strong DeBERTA-
+v3-435M models, performance of MiniLM models was lackluster
+(roughly at BM25 level for all collections).
+Because bigger models performed quite well, it may be possible
+to distill [15, 21, 41] their parameters into a much smaller MiniLM-
+30M model. Distillation is known to be successful in the IR domain
+[16, 25]. However, it failed in our case due to overfitting. We left
+investigation of the failure reasons for the future and used the fol-
+lowing workaround:
+• First we carried out an all-domain pre-training without any
+filtering (i.e., using all queries from all collections);
+• Then, we fine-tuned all-domain pre-trained models on the
+consistency-checked in-domain data.
+3.4
+Miscellaneous
+Experiments were carried out using the framework FlexNeuART
+[5], which provided support for basic indexing, retrieval, and neu-
+ral ranking. The neural models are implemented using PyTorch
+and Huggingface [54]. The models were trained using an InfoNCE
+loss [20]. In a single training epoch, we selected randomly one pair
+of positive and three negative examples per query (negatives are
+sampled from 1000 documents with highest BM25 scores). Note
+that, however, that during inference we re-ranked only 100 docu-
+ments. A number of negatives was not tuned: We used as much as
+we can while ensuring we do not run out of GPU memory during
+training on any collection.
+We used an AdamW [28] optimizer with a small weight decay
+(10−7), a warm-up schedule, and a batch size of 16.8 We used differ-
+ent base rates for the fully-connected prediction head (2·10−4) and
+for the main Transformer layers (2 · 10−5). Also note that the loss
+reduction mode was “sum”: To use this recipe with the reduction
+mode “mean” the learning rates need to be multiplied by the batch
+size.
+We trained each model using three seeds and reported the aver-
+age results (unless specified otherwise). To compute statistical sig-
+nificance, we first obtained an “average” run where for each query
+we averaged query-specific metric values over three seeds. Note
+that we compute exactly the same metric values as in [4]. For sta-
+tistical significance testing we used a paired two-sided t-test. For
+query sets with a large number of queries (name MS MARCO devel-
+opment set and BEIR Natural Questions) we used a lower threshold
+8The learning rate grows linearly from zero for 20% of the steps until it reaches the
+base learning rate [32, 45] and then goes back to zero (also linearly).
+
+of 0.01. For small query sets (Robust04 and TREC-COVID), the sta-
+tistical significance threshold was set to 0.05.
+We implemented our query generation module using the Auto-
+ModelForCasualLM interface from HuggingFace. We used a three-
+shot vanilla prompt template used by [4] (also shown in Table
+1). The output was generated via greedy decoding. The maximum
+number of new tokens generated for each example was set to 32.
+4
+DATASETS
+Because we aimed to reproduce the main results of InPars [4], we
+used exactly the same set of queries and datasets, which are de-
+scribed below. Except MS MARCO (which was processed directly
+using FlexNeuART [5] scripts), datasets were ingested with a help
+of the IR datasets packages [29].
+Some of the collections below have multiple text fields, which
+were used differently by a BM25 and neural ranker. All collections
+except Robust04 have exactly one query field. Robust04 queries
+have the following parts: title, description, and narrative. For the
+purpose of BM25 retrieval and ranker, we use only the title field,
+but the neural ranker is used the description field (which is consis-
+tent with [4]). The narrative field is not used.
+Two collectionshave documents with both the title and the main
+body text fields. The neural rankers operate on concatenation of
+these fields. If this concatenation is longer than 477 BERT tokens,
+it is truncated (queries longer than 32 BERT tokens are truncated
+as well). For BM25 scoring, we index the concatenated fields as well
+(in Lucene). However, after retrieving 1000 candidates, we re-rank
+them using the sum of BM25 scores computed for the title and the
+main body text fields separately (using FlexNeuART [5]).
+Synthetically Generated Training Queries. For each of the
+datasets, Bonifacio et al. [4] provided both the GPT-3-generated
+queries (using GPT-3 Curie model) and the documents that are
+used to generate the queries. This permits an apples-to-apples com-
+parison of the quality of training data generated using GPT-3 Curie
+with the quality of synthetic training data generated using open-
+source models GPT-J [50] and BLOOM [44]. According to the es-
+timates of Bonifacio et al. [4], the Curie model has 6B parameters,
+which is close to the estimate made by by Gao from EleutherAI [11].
+Thus, we used GPT-J [50] and BLOOM [44] models with 6 and 7 bil-
+lion parameters, respectively. Although other open-source models
+can potentially be used, generation of synthetic queries is quite ex-
+pensive and exploring other open-source options is left for future
+work.
+MS MARCO sparse and TREC DL 2020. MS MARCO is col-
+lection of 8.8M passages extracted from approximately 3.6M Web
+documents, which was derived from the MS MARCO reading com-
+prehension dataset [2, 8]. It “ships“ with more than half a million
+of question-like queries sampled from the Bing search engine log
+with subsequent filtering. The queries are not necessarily proper
+English questions, e.g., “lyme disease symptoms mood”, but they
+are answerable by a short passage retrieved from a set of about
+3.6M Web documents [2]. Relevance judgements are quite sparse
+(about one relevant passage per query) and a positive label indi-
+cates that the passage can answer the respective question.
+The MS MARCO collections has several development and test
+query sets of which we use only a development set with approx-
+imately 6.9K sparsely-judged queries and the TREC DL 2020 [8]
+collection of 54 densely judged queries. Henceforth, for simplic-
+ity when we discuss the MS MARCO development set we use a
+shortened name MS MARCO, which is also consistent with Boni-
+facio al. [4].
+Note that the MS MARCO collection has a large training set, but
+we do not use it in the fully unsupervised scenario. We do use it
+though in the hybrid setting (see § 5.1).
+Robust04 [49] is a small (but commonly used) collection that
+has about 500K news wire documents. It comes with a small but
+densely judged set of 250 queries, which have about 1.2K judge-
+ments on average.
+Natural Questions(NQ) BEIR [19] is an open domain Wikipedia-
+based Question Answering (QA) dataset. Similar to MS MARCO,
+it has real user queries (submitted to Google). We use a BEIR’s
+variant of NQ [47], which has about 2.6M short passages from
+Wikipedia and 3.4K sparsely-judged queries (about 1.2 relevant
+documents per query).
+TREC COVID BEIR [39] is a small corpus that has 171K sci-
+entific articles on the topic of COVID-19 and 50 densely-judged
+queries (1.3K judged documents per query on average). It was cre-
+ated for a NIST challenge whose objective was to develop informa-
+tion retrieval methods tailored for the COVID-19 domain (with a
+hope to be a useful tool during COVID-19 pandemic). We use the
+BEIR’s version of this dataset [47].
+5
+RESULTS
+5.1
+Main Results
+Our main experimental results are presented in Table 2. We or-
+ganize them into multiple sections, where we show effectiveness
+numbers for various supervised, unsupervised, and hybrid approaches.
+In addition to our own measurements, we copy key results from
+the work by Bonifacio et al. [4], which include results for BM25, re-
+ranking using OpenAI API, as well as results for Mono-T5 rankers
+[35] trained in the unsupervised, supervised, and hybrid manner.
+Because there is a substantial variability of results among seeds (in-
+cluding one case of extremely poorconvergence), for unsupervised-
+only training we also present our-best seed results in Table 3. In
+Table 4, we show effectiveness of InPars for three types of models
+to generate synthetic training queries (including OpenAI GPT-3
+model). In our experiments, we statistically test several statistical
+hypotheses, which are explained separately at the bottom of each
+table.
+BM25 baselines. Comparing effectiveness of FlexNeuART [5]
+BM25 with effectiveness of Pyserini [23] BM25—used the InPars
+study [4]—we can see that on all datasets except TREC DL 2020
+we closely match (within 1.5%) Pyserini numbers. On TREC DL
+2020 our BM25 is 6% more effective in nNDCG@10 and 25% more
+effective in MAP.
+Reproducibility Notes. In addition to BM25 performance, we
+can reproduce some of the key findings from prior work. In what
+follows we discuss these (and other findings) in more detail:
+
+Table 2: Main Results (averaged over three seeds)
+MS MARCO
+TREC DL 2020
+Robust04
+NQ
+TREC COVID
+MRR
+MAP nDCG@10
+MAP nDCG@20 nDCG@10
+nDCG@10
+BM25 [4]
+0.1874
+0.2876
+0.4876
+0.2531
+0.4240
+0.3290
+0.6880
+BM25 (ours)
+0.1867
+0.3612
+0.5159
+0.2555
+0.4285
+0.3248
+0.6767
+OpenAI Ranking API: re-ranking 100 Documents [4]
+Curie (6B) [4]
+$
+0.3296
+0.5422
+0.2785
+0.5053
+0.4171
+0.7251
+Davinci (175B) [4]
+$
+0.3163
+0.5366
+0.2790
+0.5103
+$
+0.6918
+Unsupervised: InPars-based Training Data
+monoT5-220M (InPars) [4]
+0.2585
+0.3599
+0.5764
+0.2490
+0.4268
+0.3354
+0.6666
+monoT5-3B (InPars) [4]
+0.2967
+0.4334
+0.6612
+0.3180
+0.5181
+0.5133
+0.7835
+MiniLM-L6-30M (InPars)
+푏푎0.2117
+푏0.3482
+푏0.4953
+푏푎0.2263
+푏푎0.3802
+푏푎0.2187
+푏0.6361
+MiniLM-L6-30M (InPars ◮ consist. check)
+푐푏푎0.2336
+푐푏0.3769
+푐푏0.5543
+푐푏0.2556
+푐푏0.4440
+푐푏0.3239
+푐푏0.6926
+MiniLM-L6-30M (InPars all ◮ consist. check)
+푐푎0.2468
+푐푎0.3929
+푐푎0.5726
+푐0.2639
+푐푎0.4599
+푐푎0.3747
+푐푎0.7688
+DeBERTA-v3-435M (InPars)
+푏푎0.2746
+푏푎0.4385
+푎0.6649
+푏푎0.2811
+푏푎0.4987
+푏푎0.4476
+푎0.8022
+DeBERTA-v3-435M (InPars ◮ consist. check)
+푐푏푎0.2815 푐푏푎0.4446
+푐푎0.6717 푐푏푎0.3009 푐푏푎0.5360
+푐푏푎0.4621
+푐푎0.8183
+DeBERTA-v3-435M (InPars all ◮ consist. check)
+푐푎0.1957
+푐0.3607
+푐0.5007
+푐0.2518
+푐0.4320
+푐0.3267
+푐0.6953
+Supervised and Hybrid: transfer from MS MARCO with an optional fine-tuning on consistency-checked InPars data
+MiniLM-L6-30M (MS MARCO)
+푑푎0.3080
+푎0.4370
+푎0.6662
+푑푎0.2295
+푑푎0.3923
+푑푎0.4646
+푑푎0.7476
+MiniLM-L6-30M (MS MARCO ◮ consist. check)
+푑푎0.2944
+푎0.4311
+푎0.6501
+푑푎0.2692
+푑푎0.4730
+푑푎0.4320
+푑푎0.7898
+DeBERTA-v3-435M (MS MARCO)
+푑푎0.3508
+푎0.4679
+푑푎0.7269
+푎0.2986
+푎0.5304
+푑푎0.5616
+푎0.8304
+DeBERTA-v3-435M (MS MARCO ◮ consist. check)
+푑푎0.3166
+푎0.4553
+푑푎0.6912
+푎0.3011
+푎0.5371
+푑푎0.5075
+푎0.8165
+monoT5-220M (MS MARCO) [35]
+0.3810
+0.4909
+0.7141
+0.3279
+0.5298
+0.5674
+0.7775
+monoT5-3B (MS MARCO) [35]
+0.3980
+0.5281
+0.7508
+0.3876
+0.6091
+0.6334
+0.7948
+monoT5-3B (MS MARCO ◮ InPars) [4]
+0.3894
+0.5087
+0.7439
+0.3967
+0.6227
+0.6297
+0.8471
+OpenAI API ranking results are copied from Bonifacio et al. [4]. In that, $ denotes experiments that were too expensive to run.
+InPars denotes the original query-generation method with filtering-out 90% of queries having lowest average log-probabilities.
+InPars all denotes the query-generation method without query filtering, which was used in all-domain pretraining.
+Consist. check denotes consistency filtering of all generated queries using a model trained on InPars-generated data.
+Best unsupervised and hybrid-training results are marked by bold font (separately for unsupervised and hybrid-training).
+Super-scripted labels denote the following statistically significant differences (thresholds are given in the main text):
+a: between a neural model and BM25;
+b: between training with and without fine-tuning on consistency-checked data (for the same model type).
+c: between pre-training using all generated queries for all collections and only filtered in-domain queries (for the same model type).
+d: between 0-shot transferring an MS MARCO model & fine-tuning this model on filtered in-domain queries (for the same model type).
+• Generation of synthetic in-domain data using an InPars-like
+recipe can permit training very strong in-domain rankers
+without any human-provided supervision data;
+• Without additional tricks such as all-domain pre-training
+and consistency checking, only a sufficiently larger model
+can outperform BM25;
+• A consistency checking introducedby Promptagator [9] does
+lead to a substantial gain in accuracy;
+• Replacing the proprietary GPT-3 Curie model with BLOOM
+[44] can improve performance, which is in line with findings
+of Jeronymo et al. [18]. However, unlike our study, they do
+not directly assess the impact of replacing the generating
+model alone.
+Unsupervised-only training. In a purely unsupervised set-
+ting, we obtain comparable or better results using much smaller
+ranking models. With DeBERTA-v3-435M we obtain comparable
+(somewhat better or worse) effectiveness to MonoT5-3B on four
+collections out of five (MonoT5-3B has 7x more parameters). Our
+biggest gap is for the NQ collection. However, this is the collec-
+tion where we already obtain a substantial 15-30% gain over BM25.
+Moreover, there is quite a bit of variability across model seeds, and
+our best-seed NQ model is quite close to the average performance
+of MonoT5-3B (see Table 3).
+Our smallest MiniLM-L6-30M model with all-domain pretrain-
+ing and finetuning on consistency-checked data (InPars all ◮ con-
+sist. check) roughly matches the 7x larger MonoT5-220M on MS
+MARCO and TREC DL 2020, but it is substantially better than
+
+Table 3: Best-Seed Results for Unsupervised Training
+MS MARCO
+TREC DL 2020
+Robust04
+NQ
+TREC COVID
+MRR
+MAP nDCG@10
+MAP nDCG@20 nDCG@10
+nDCG@10
+BM25 (ours)
+0.1867
+0.3612
+0.5159
+0.2555
+0.4285
+0.3248
+0.6767
+MiniLM results
+MiniLM-L6-30M (InPars)
+푏푎0.2197
+푏0.3562
+푏0.5151 푏푎0.2380
+푏푎0.4029
+푏푎0.2415
+푏0.6732
+MiniLM-L6-30M (InPars ◮ consist. check)
+푐푏푎0.2422
+푏0.3844
+푏푎0.5753
+푐푏0.2615
+푐푏푎0.4554
+푐푏0.3297
+푏푎0.7483
+MiniLM-L6-30M (InPars all ◮ consist. check)
+푐푎0.2517
+푎0.3945
+푎0.5769
+푐0.2671
+푐푎0.4691
+푐푎0.3800
+푎0.7709
+DeBERTA results
+DeBERTA-v3-435M (InPars)
+푏푎0.2748
+푎0.4437
+푎0.6779 푏푎0.2874
+푏푎0.5131
+푎0.4872
+푎0.8118
+DeBERTA-v3-435M (InPars ◮ consist. check)
+푏푎0.2847
+푎0.4479
+푎0.6813
+푏푎0.3043
+푏푎0.5417
+푐푎0.4924
+푎0.8305
+DeBERTA-v3-435M (InPars all ◮ consist. check)
+푎0.2804
+푎0.4414
+푎0.6575
+푎0.3076
+푎0.5505
+푐푎0.4746
+푎0.8259
+Super-scripted labels denote the following statistically significant differences (thresholds are given in the main text):
+a: between a neural model and BM25;
+b: between training with and without fine-tuning on consistency-checked data (for the same model type).
+c: between pre-training using all generated queries and only filtered in-domain queries (for the same model type).
+Notes: Best results (separately for each model are marked by bold font.
+MonoT5-220M on the remaining datasets, where MonoT5-220M ef-
+fectiveness is largely at BM25 level. MiniLM-L6-30M outperforms
+BM25 on all collections and all metrics. In all but one case these dif-
+ferences are also statistically significant. In terms of nDCG and/or
+MRR, it is 7-30% more effective.
+Impact of consistency checking and all-domain pre-training.
+It is crucial to note, however, on its own the InPars recipe does
+not produce a strong MiniLM-L6-30M model, which is in line with
+finding of the InPars study where only MonoT5-3B (but not a much
+smaller MonoT5-220M) outperformedBM25 on all collections. Strong
+performance of MiniLM-L6-30M was due to additional training
+with consistency-checked data and pre-training on all-domain (all
+queries from all collections) data. Therefore, we carry out ablation
+experiments to assess effectiveness of these procedures.
+We can see that for both MiniLM-L6-30M and DeBERTA-v3-
+435M,fine-tunining on consistency-checked data improves outcomes:
+For 12 measurements out of 14, these differences are also statisti-
+cally significant (denoted by super-script label “b”). Moreover, all-
+domain pretraining (instead of training on data generated by the
+original InPars recipe) further boosts accuracy of MiniLM-L6-30M
+in all cases. Moreover, all the differences are statistically significant
+(denoted by super-script label “c”). However, all-domain pretrain-
+ing substantially degrades performance of DeBERTA-v3-435M.
+An in-depth investigation showed that for one seed (out of three),
+the model failed to converge properly. Although, we could have
+also chosen a different seed and present better results, we felt that
+this failure to converge (which was the only case out of many ex-
+periments we ran!) was an indication that all-domain pretraining
+dit not work well for DeBERTA-v3-435M. To further verify this hy-
+pothesis, we also checked the best-seed outcomes, which are pre-
+sented in Table 3. For MiniLM-L6-30M, the all-domain pre-training
+improves the best-seed results in all cases, though we have fewer
+statistically significant difference now (this is expected, because
+using average-seed runs leads to more stable measurements). For
+DeBERTA-v3-435M, there is either a substantial degradation or
+a small decrease/increase that is not statistically significant (de-
+noted by super-script label “c”). Thus, our biggest model—unlike
+15x smaller MiniLM-L6-30M— does not benefit from all-domain
+pretraining. In fact this pretraining leads to performance degrada-
+tion (including potential decrease in training stability).
+Supervisedand hybrid training. We find that for ourdatasets,
+a model trained on MS MARCO (both MiniLM-L6-30M and DeBERTA-
+v3-435M) transfers well to other collections, except for transfer
+of MiniLM-L6-30M to Robust04. However, similar to all-domain
+pre-training the 15x smaller MiniLM-L6-30M benefits more from
+in-domain fine-tuning with consistency-checked data: There are
+substantial and statistically significant improvements for Robust04
+and TREC-COVID (but a degradation for MS MARCO, TREC DL
+2020 and NQ, whereas in the case of DeBERTA-v3-435M such fine-
+tuning noticeably degrades accuracy in most cases.
+Also note that DeBERTA-v3-435M roughly matches MonoT5-
+220M while still lagging behind MonoT5-3B. This is in line with
+prior finding that large ranking models have better zero-shot trans-
+ferring effectiveness [33, 42]. However, using multi-billion param-
+eter ranking models is not a practical choice.
+Model-Type Ablation To assess the impact of replacing GPT-3
+Curie with an open-source model, we carried out experiments us-
+ing ERNIE-v2 model [46]. Althoughwe generated synthetic queries
+only once, each ranker was trained with three different seeds. Thus,
+we compared systems where query-specific metric values were av-
+eraged over seeds. To our surprise (see Table 4), except for NQ
+where all models were nearly equally good, GPT-3 Curie under-
+performed both open-source models (out of 14 measurements 10
+are statistically significant as denoted by super-script “b”). The dif-
+ference was particularly big for Robust04.
+We then computed the average gain by (1) computing relative
+gain separately for each datasets and key metrics (nDCG or MRR)
+
+Table 4: Performance of InPars for Different Generating and Ranking Models (averaged over three seeds)
+MS MARCO
+TREC DL 2020
+Robust04
+NQ
+TREC COVID
+MRR
+MAP
+nDCG@10
+MAP
+nDCG@20
+nDCG@10
+nDCG@10
+BM25 (ours)
+0.1867
+0.3612
+0.5159
+0.2555
+0.4285
+0.3248
+0.6767
+ERNIE-v2-335M OpenAI Curie (6B)
+푎0.2538
+푎0.4140
+푎0.6229
+푎0.2357
+0.4016
+푎0.4277
+푎0.7411
+ERNIE-v2-335M GPT-J (6B)
+푏푎0.2608
+푏푎0.4286
+푎0.6367
+푐푏0.2691
+푐푏푎0.4724
+푎0.4248
+푏푎0.7750
+ERNIE-v2-335M BLOOM (7B)
+푑푏푎0.2605
+푏푎0.4286
+푎0.6407
+푐푏푎0.2852
+푑푐푏푎0.5102
+푑푎0.4215
+푏푎0.7871
+DeBERTA-v3-435M BLOOM (7B)
+푑푏푎0.2746
+푏푎0.4385
+푏푎0.6649
+푏푎0.2811
+푑푏푎0.4987
+푑푏푎0.4476
+푏푎0.8022
+Notes: Best results are in bold. Super-scripted labels denote statistically significant differences (thresholds are given in the main text):
+a: between a neural model and BM25;
+b: between a given neural model trained using queries from a given open-source models and ERNIE trained on queries from GPT-3;
+c: between using GPT-J-generated queries and BLOOM-generated queries (only for ERNIE);
+d: between the DeBERTA model and the ERNIE model (both trained using BLOOM-generated queries).
+and (2) averaging these relative gains. The resulting gains (not
+shown in the table) are 7.2% for BLOOM and 5.2% for GPT-J.
+In addition to the generation model, we assessed the impact of
+using DeBERTA-v3 instead of ERNIE-v2. This time around, both
+models were trained using BLOOM-generated queries. We can see
+that DeBERTA v3 was generally better than ERNIE-v2.
+5.2
+Cost and Efficiency
+In the following sub-section, we discuss both the ranking efficiency
+and query-generation cost. Although one may argue that the cost
+of generation using open-source models is negligibly small, in real-
+ity this is true only if one owns their own hardware and generates
+enough queries to justify the initial investment. Thus, we make a
+more reasonable assessment assuming that the user can employ a
+cheap cloud service.
+Efficiency of Re-ranking. A rather common opinion (in par-
+ticular expressed by anonymous reviewers on multiple occasions)
+is that using cross-encoders is not a practical option. This might be
+true for extremely constrained latency environments or very large
+models, but we think it is totally practical to use small models such
+as MiniLM-L6-30M for applications such as enterprise search. In
+particular, on a reasonably modern GPU (such as RTX 3090) and
+Pytorch MinLm-L6-30M re-ranking throughput exceeds 500 pas-
+sages per second (assuming truncation to the first 477 characters).
+Thus re-ranking 100 documents has an acceptable sub-second re-
+ranking latency.
+Cost of Model Training. Here, all training times are given
+with respect to a single RTX 3090 GPU. Training and evaluating
+MiniLM6-30M models had negligible costs dominated by all-domain
+pretraining, which took about two hours per seed. In contrast, the
+all-domain pretraining of DeBERTA-v3-435M took 28 hours. How-
+ever, only about 20-30% of queries were selected for training mod-
+els and fine-tuning them consistency checked data. Thus, without
+all-domain pretraining, the training time itself was rather small.
+Aside from all-domain pre-training, the two most time-consuming
+operations were validation of large query sets (MS MARCO and
+NQ), which jointly have about 10K queries, and consistency check-
+ing (using DeBERTA-v3-435M model). The total validation time for
+DeBERTA-v3-435 was about 6 hours (for all collections). The con-
+sistency checking, however, took about 48 hours. In the future, we
+should consider carrying out consistency checking using a much
+faster MiniLM-L6-30M model.
+Cost of Query Generation. For the original InPars [4], the cost
+of generation for the GPT-3 Curie model is $0.002 per one thou-
+sand tokens. The token count includes the length of the prompt
+and the prompting document.9 We estimate that (depending on
+the collection) a single generation involves 300 to 500 tokens: long-
+document collections Robust04 and TREC-COVID both have close
+to 500 tokens per generation.
+Taking an estimate of 500 tokens per generation, the cost of
+querying OpenAI GPT-3 Curie API can be up to $100 for Robust04
+and TREC-COVID. Assuming that sampling from 137-B FLAN model
+to be as expensive as from the largest GPT-3 model Davinci (which
+has a similar number of parameters), each generation in the Promp-
+tagator study [9], was 10x more expensive compared to InPars
+study [4]. Moreover, because Dai et al. [4] generated one million
+samples per collection, the Promptagator recipe was about two or-
+ders of magnitude expensive compared to InPars.
+In contrast, it takes only about 15 hours to generate 100K queries
+using RTX 3090 GPU. Extrapolating this estimate to A100, which is
+about 2x faster than RTX 309010, and using the pricing of Lambda
+GPU cloud, we estimate the cost of generation in our InPars-light
+study to be under $10 per collection. 11
+6
+CONCLUSION
+We carried out a reproducibility study of InPars recipe for unsuper-
+vised training of neural rankers. As a by-product of this study, we
+developed a simple-yet-effective modification of InPars, which we
+called InPars-light. Unlike InPars, InPars-light uses only a freely
+available language model BLOOM, 7x-100x smaller ranking mod-
+els, and re-ranks only 100 candidate records instead of 1000.
+Not only can we reproduce key findings from prior work, but
+combining the original InPars recipe [4] with (1) fine-tuning on
+consistency-checked data [9], (2) and all-domain pretraining, we
+9https://chengh.medium.com/understand-the-pricing-of-gpt3-e646b2d63320
+10https://lambdalabs.com/blog/nvidia-rtx-a6000-benchmarks
+11https://lambdalabs.com/service/gpu-cloud#pricing
+
+were able to train a very efficient and small model MiniLM-L6-30M
+that outperformed BM25 on all collections (in MRR or nDCG). Last
+but not least, with a larger DeBERTA-v3-435M model we could
+largely match performance of a 7x larger MonoT5-3B (even out-
+performing it on two datasets).
+ACKNOWLEDGMENTS
+REFERENCES
+[1] Chris Alberti, Daniel Andor, Emily Pitler, Jacob Devlin, and Michael Collins.
+2019. Synthetic QA Corpora Generation with Roundtrip Consistency. In Pro-
+ceedings of the 57th Annual Meeting of the Association for Computational Lin-
+guistics. Association for Computational Linguistics, Florence, Italy, 6168–6173.
+https://doi.org/10.18653/v1/P19-1620
+[2] Payal Bajaj, Daniel Campos, Nick Craswell, Li Deng, Jianfeng Gao, Xiaodong
+Liu, Rangan Majumder, Andrew McNamara, Bhaskar Mitra, Tri Nguyen, et al.
+2016. MS MARCO: A human generated machine reading comprehension dataset.
+arXiv preprint arXiv:1611.09268 (2016).
+[3] Sid Black, Leo Gao, Phil Wang, Connor Leahy, and Stella Biderman. 2021.
+GPT-Neo: Large Scale Autoregressive Language Modeling with Mesh-Tensorflow.
+https://doi.org/10.5281/zenodo.5297715
+[4] Luiz Henrique Bonifacio, Hugo Abonizio, Marzieh Fadaee, and Rodrigo
+Nogueira. 2022. InPars: Unsupervised Dataset Generation for Information Re-
+trieval. In SIGIR. ACM, 2387–2392.
+[5] Leonid Boytsov and Eric Nyberg. 2020.
+Flexible retrieval with NMSLIB and
+FlexNeuART. In Proceedings of Second Workshop for NLP Open Source Software
+(NLP-OSS). 32–43.
+[6] Tom B. Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared Ka-
+plan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry,
+Amanda Askell, Sandhini Agarwal, Ariel Herbert-Voss, Gretchen Krueger, Tom
+Henighan, Rewon Child, Aditya Ramesh, Daniel M. Ziegler, Jeffrey Wu, Clemens
+Winter, Christopher Hesse, Mark Chen, Eric Sigler, Mateusz Litwin, Scott Gray,
+Benjamin Chess, Jack Clark, Christopher Berner, Sam McCandlish, Alec Rad-
+ford, Ilya Sutskever, and Dario Amodei. 2020. Language Models are Few-Shot
+Learners. In NeurIPS.
+[7] Chris Buckley, Darrin Dimmick, Ian Soboroff, and Ellen M. Voorhees. 2007. Bias
+and the limits of pooling for large collections. Inf. Retr. 10, 6 (2007), 491–508.
+[8] Nick Craswell, Bhaskar Mitra, Emine Yilmaz, Daniel Campos, and Ellen M
+Voorhees. 2020. Overview of the TREC 2019 deep learning track. arXiv preprint
+arXiv:2003.07820 (2020).
+[9] Zhuyun Dai, Vincent Y. Zhao, Ji Ma, Yi Luan, Jianmo Ni, Jing Lu, Anton Bakalov,
+Kelvin Guu, Keith B. Hall, and Ming-Wei Chang. 2022. Promptagator: Few-shot
+Dense Retrieval From 8 Examples. CoRR abs/2209.11755 (2022).
+[10] Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. 2018. BERT:
+Pre-training of deep bidirectional transformers for language understanding.
+arXiv preprint arXiv:1810.04805 (2018).
+[11] Leo Gao. 2021. https://blog.eleuther.ai/gpt3-model-sizes/.
+[12] Luyu
+Gao,
+Xueguang
+Ma,
+Jimmy
+Lin,
+and
+Jamie
+Callan.
+2022.
+Precise
+Zero-Shot
+Dense
+Retrieval
+without
+Relevance
+Labels.
+https://doi.org/10.48550/ARXIV.2212.10496
+[13] Lei Han, Eddy Maddalena, Alessandro Checco, Cristina Sarasua, Ujwal Gadiraju,
+Kevin Roitero, and Gianluca Demartini. 2020. Crowd Worker Strategies in Rele-
+vance Judgment Tasks. In WSDM. ACM, 241–249.
+[14] Pengcheng He, Xiaodong Liu, Jianfeng Gao, and Weizhu Chen. 2021.
+De-
+berta: decoding-Enhanced Bert with Disentangled Attention. In ICLR. OpenRe-
+view.net.
+[15] Geoffrey E. Hinton, Oriol Vinyals, and Jeffrey Dean. 2015. Distilling the Knowl-
+edge in a Neural Network. CoRR abs/1503.02531 (2015).
+[16] Sebastian
+Hofstätter,
+Sophia
+Althammer,
+Michael
+Schröder,
+Mete
+Sertkan,
+and
+Allan
+Hanbury.
+2020.
+Improving
+Efficient
+Neural
+Ranking
+Models
+with
+Cross-Architecture
+Knowledge
+Distillation.
+https://doi.org/10.48550/ARXIV.2010.02666
+[17] Gautier Izacard, Mathilde Caron, Lucas Hosseini, Sebastian Riedel, Piotr Bo-
+janowski, Armand Joulin, and Edouard Grave. 2021.
+Towards Unsupervised
+Dense Information Retrieval with Contrastive Learning. CoRR abs/2112.09118
+(2021).
+[18] Vitor Jeronymo, Luiz Bonifacio, Hugo Abonizio, Marzieh Fadaee, Roberto
+Lotufo, Jakub Zavrel, and Rodrigo Nogueira. 2023.
+InPars-v2: Large Lan-
+guage Models as Efficient Dataset Generators for Information Retrieval.
+https://doi.org/10.48550/ARXIV.2301.01820
+[19] Tom Kwiatkowski, Jennimaria Palomaki, Olivia Redfield, Michael Collins, Ankur
+Parikh, Chris Alberti, Danielle Epstein, Illia Polosukhin, Jacob Devlin, Kenton
+Lee, et al. 2019. NaturalQuestions: a benchmarkfor question answering research.
+Transactions of the Association for Computational Linguistics 7 (2019), 453–466.
+[20] Phuc H. Le-Khac, Graham Healy, and Alan F. Smeaton. 2020. Contrastive Rep-
+resentation Learning: A Framework and Review. IEEE Access 8 (2020), 193907–
+193934.
+[21] Jinyu Li, Rui Zhao, Jui-Ting Huang, and Yifan Gong. 2014.
+Learning small-
+size DNN with output-distribution-based criteria. In INTERSPEECH. ISCA, 1910–
+1914.
+[22] Minghan Li and Éric Gaussier. 2022. Domain Adaptation for Dense Retrieval
+through Self-Supervision by Pseudo-Relevance Labeling. CoRR abs/2212.06552
+(2022).
+[23] Jimmy Lin, Xueguang Ma, Sheng-Chieh Lin, Jheng-Hong Yang, Ronak Pradeep,
+and Rodrigo Nogueira. 2021. Pyserini: A Python toolkit for reproducible infor-
+mation retrieval research with sparse and dense representations. In Proceedings
+of the 44th International ACM SIGIR Conference on Research and Development in
+Information Retrieval. 2356–2362.
+[24] Jimmy Lin, Rodrigo Nogueira, and Andrew Yates. 2021. Pretrained Transformers
+for Text Ranking: BERT and Beyond. Morgan & Claypool Publishers.
+[25] Sheng-Chieh Lin, Jheng-Hong Yang, and Jimmy Lin. 2020. Distilling Dense Rep-
+resentations for Ranking using Tightly-Coupled Teachers. CoRR abs/2010.11386
+(2020).
+[26] Pengfei Liu, Weizhe Yuan, Jinlan Fu, Zhengbao Jiang, Hiroaki Hayashi, and
+Graham Neubig. 2021.
+Pre-train, Prompt, and Predict: A Systematic Survey
+of Prompting Methods in Natural Language Processing. CoRR abs/2107.13586
+(2021).
+[27] Yinhan Liu, Myle Ott, Naman Goyal, Jingfei Du, Mandar Joshi, Danqi
+Chen, Omer Levy, Mike Lewis, Luke Zettlemoyer, and Veselin Stoyanov.
+2019.
+RoBERTa: A Robustly Optimized BERT Pretraining Approach.
+CoRR
+abs/1907.11692 (2019).
+[28] Ilya Loshchilov and Frank Hutter. 2017. Decoupled weight decay regularization.
+arXiv preprint arXiv:1711.05101 (2017).
+[29] Sean MacAvaney, Andrew Yates, Sergey Feldman, Doug Downey, Arman Cohan,
+and Nazli Goharian. 2021. Simplified Data Wrangling with ir_datasets. In SIGIR.
+[30] Irina Matveeva, Chris Burges, Timo Burkard, Andy Laucius, and Leon Wong.
+2006. High accuracy retrieval with multiple nested ranker. In SIGIR. ACM, 437–
+444.
+[31] Iurii Mokrii, Leonid Boytsov, and Pavel Braslavski. 2021. A Systematic Evalua-
+tion of Transfer Learning and Pseudo-labeling with BERT-based Ranking Mod-
+els. In SIGIR. ACM, 2081–2085.
+[32] Marius Mosbach, Maksym Andriushchenko, and Dietrich Klakow. 2020. On the
+Stability of Fine-tuning BERT: Misconceptions, Explanations, and Strong Base-
+lines. arXiv preprint arXiv:2006.04884 (2020).
+[33] Jianmo Ni, Chen Qu, Jing Lu, Zhuyun Dai, Gustavo Hern’andez ’Abrego, Ji Ma,
+Vincent Zhao, Yi Luan, Keith B. Hall, Ming-Wei Chang, and Yinfei Yang. 2021.
+Large DualEncoders Are Generalizable Retrievers. ArXiv abs/2112.07899 (2021).
+[34] Rodrigo Nogueira and Kyunghyun Cho. 2019. Passage Re-ranking with BERT.
+arXiv preprint arXiv:1901.04085 (2019).
+[35] Rodrigo Nogueira, Zhiying Jiang, and Jimmy Lin. 2020.
+Document ranking
+with a pretrained sequence-to-sequence model. arXiv preprint arXiv:2003.06713
+(2020).
+[36] John M. Prager. 2006. Open-Domain Question-Answering. Found. Trends Inf.
+Retr. 1, 2 (2006), 91–231.
+[37] Colin Raffel, Noam Shazeer, Adam Roberts, Katherine Lee, Sharan Narang,
+Michael Matena, Yanqi Zhou, Wei Li, and Peter J. Liu. 2020. Exploring the Limits
+of Transfer Learning with a Unified Text-to-Text Transformer. J. Mach. Learn.
+Res. 21 (2020), 140:1–140:67.
+[38] Revanth Gangi Reddy, Bhavani Iyer, Md. Arafat Sultan, Rong Zhang, Avirup Sil,
+Vittorio Castelli, Radu Florian, and Salim Roukos. 2021. Synthetic TargetDomain
+Supervision for Open Retrieval QA. In SIGIR. ACM, 1793–1797.
+[39] Kirk Roberts, Tasmeer Alam, Steven Bedrick, Dina Demner-Fushman, Kyle Lo,
+Ian Soboroff, Ellen M. Voorhees, Lucy Lu Wang, and William R. Hersh. 2020.
+TREC-COVID: rationale and structure of an information retrieval shared task
+for COVID-19. J. Am. Medical Informatics Assoc. 27, 9 (2020), 1431–1436.
+[40] Stephen Robertson. 2004. Understanding inverse document frequency: on the-
+oretical arguments for IDF.
+Journal of Documentation 60, 5 (2004), 503–520.
+https://doi.org/10.1108/00220410410560582
+[41] Adriana Romero, Nicolas Ballas, Samira Ebrahimi Kahou, Antoine Chassang,
+Carlo Gatta, and Yoshua Bengio. 2015. FitNets: Hints for Thin Deep Nets. In
+ICLR (Poster).
+[42] Guilherme Rosa, Luiz Bonifacio, Vitor Jeronymo, Hugo Abonizio, Marzieh
+Fadaee, Roberto Lotufo, and Rodrigo Nogueira. 2022.
+In Defense of Cross-
+Encoders for Zero-Shot Retrieval. https://doi.org/10.48550/ARXIV.2212.06121
+[43] Devendra Singh Sachan, Mike Lewis, Mandar Joshi, Armen Aghajanyan, Wen-
+tau Yih, Joelle Pineau, and Luke Zettlemoyer. 2022. Improving Passage Retrieval
+with Zero-Shot Question Generation. CoRR abs/2204.07496 (2022).
+[44] Teven Le Scao, Angela Fan, Christopher Akiki, Ellie Pavlick, Suzana Ilic, Daniel
+Hesslow, Roman Castagné, Alexandra Sasha Luccioni, François Yvon, Matthias
+Gallé, Jonathan Tow, Alexander M. Rush, Stella Biderman, Albert Webson,
+Pawan Sasanka Ammanamanchi, Thomas Wang, Benoît Sagot, Niklas Muen-
+nighoff, Albert Villanova del Moral, Olatunji Ruwase, Rachel Bawden, Stas Bek-
+man, Angelina McMillan-Major, Iz Beltagy, Huu Nguyen, Lucile Saulnier, Sam-
+son Tan, Pedro Ortiz Suarez, Victor Sanh, Hugo Laurençon, Yacine Jernite, Julien
+
+Launay,MargaretMitchell, Colin Raffel, Aaron Gokaslan, Adi Simhi, Aitor Soroa,
+Alham Fikri Aji, Amit Alfassy, Anna Rogers, Ariel Kreisberg Nitzav, Canwen
+Xu, Chenghao Mou, Chris Emezue, Christopher Klamm, Colin Leong, Daniel
+van Strien, David Ifeoluwa Adelani, and et al. 2022. BLOOM: A 176B-Parameter
+Open-Access Multilingual Language Model. CoRR abs/2211.05100 (2022).
+[45] Leslie N. Smith. 2017. Cyclical Learning Rates for Training Neural Networks. In
+WACV. 464–472.
+[46] Yu Sun, Shuohuan Wang, Yu-Kun Li, Shikun Feng, Hao Tian, Hua Wu, and
+Haifeng Wang. 2020. ERNIE 2.0: A Continual Pre-Training Framework for Lan-
+guage Understanding. In AAAI. AAAI Press, 8968–8975.
+[47] Nandan Thakur, Nils Reimers, Andreas Rücklé, Abhishek Srivastava, and Iryna
+Gurevych. 2021. BEIR: A Heterogenous Benchmark for Zero-shot Evaluation of
+Information Retrieval Models. arXiv preprint arXiv:2104.08663 (2021).
+[48] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones,
+Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin. 2017. Attention is All you
+Need. In NIPS. 5998–6008.
+[49] Ellen Voorhees. 2004. Overview of the TREC 2004 Robust Retrieval Track. In
+TREC.
+[50] Ben
+Wang
+and
+Aran
+Komatsuzaki.
+2021.
+GPT-J-6B:
+A
+6
+Billion
+Parameter
+Autoregressive
+Language
+Model.
+https://github.com/kingoflolz/mesh-transformer-jax.
+[51] Kexin Wang, Nandan Thakur, Nils Reimers, and Iryna Gurevych. 2022. GPL:
+Generative Pseudo Labeling for Unsupervised Domain Adaptation of Dense Re-
+trieval. In NAACL-HLT. Association for Computational Linguistics, 2345–2360.
+[52] Lidan Wang, Jimmy Lin, and Donald Metzler. 2011. A cascade ranking model
+for efficient ranked retrieval. In SIGIR. ACM, 105–114.
+[53] Wenhui Wang, Furu Wei, Li Dong, Hangbo Bao, Nan Yang, and Ming Zhou. 2020.
+MiniLM: Deep Self-Attention Distillation for Task-Agnostic Compression of Pre-
+Trained Transformers. In NeurIPS.
+[54] Thomas Wolf, Lysandre Debut, Victor Sanh, Julien Chaumond, Clement
+Delangue, Anthony
+Moi, Pierric Cistac, Tim Rault, Remi Louf, Mor-
+gan Funtowicz, Joe Davison, Sam Shleifer, Patrick von Platen, Clara Ma,
+Yacine Jernite, Julien Plu, Canwen Xu, Teven Le Scao, Sylvain Gugger,
+Mariama Drame, Quentin Lhoest, and Alexander Rush. 2020.
+Transform-
+ers: State-of-the-Art Natural Language Processing. In Proceedings of the
+2020 Conference on Empirical Methods in Natural Language Processing: Sys-
+tem Demonstrations. Association for Computational Linguistics, Online, 38–45.
+https://doi.org/10.18653/v1/2020.emnlp-demos.6
+
diff --git a/jNE1T4oBgHgl3EQfNQMV/content/tmp_files/load_file.txt b/jNE1T4oBgHgl3EQfNQMV/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7d3a340720d3dfd0ba666552f3e0a479dd1340d3
--- /dev/null
+++ b/jNE1T4oBgHgl3EQfNQMV/content/tmp_files/load_file.txt
@@ -0,0 +1,971 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf,len=970
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='02998v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='IR]  8 Jan 2023  InPars-Light: Cost-Effective Unsupervised Training of Efficient  Rankers  Leonid Boytsov∗  leo@boytsov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='info  Amazon AWS AI Labs  Pittsburgh, USA  Preksha Patel†  Vivek Sourabh†  Riddhi Nisar†  Sayani Kundu†  Ramya Ramanathan†  Carnegie Mellon University  Pittsburgh, USA  Eric Nyberg  ehn@cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='cmu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='edu  Carnegie Mellon University  Pittsburgh, USA  ABSTRACT  We carried out a reproducibility study of InPars recipe for unsuper-  vised training of neural rankers [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' As a by-product of this study,  we developed a simple-yet-effective modification of InPars, which  we called InPars-light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Unlike InPars, InPars-light uses only a freely  available language model BLOOM and 7x-100x smaller ranking  models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' On all five English retrieval collections (used in the origi-  nal InPars study) we obtained substantial (7-30%) and statistically  significant improvements over BM25 in nDCG or MRR using only a  30M parameter six-layer MiniLM ranker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In contrast, in the InPars  study only a 100x larger MonoT5-3B model consistently outper-  formed BM25, whereas their smaller MonoT5-220M model (which  is still 7x larger than our MiniLM ranker), outperformedBM25 only  on MS MARCO and TREC DL 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In a purely unsupervised set-  ting, our 435M parameter DeBERTA v3 ranker was roughly at par  with the 7x larger MonoT5-3B: In fact, on three out of five datasets,  it slightly outperformed MonoT5-3B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Finally, these good results  were achieved by re-ranking only 100 candidate documents com-  pared to 1000 used in InPars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' We believe that InPars-light is the first  truly cost-effective prompt-based unsupervised recipe to train and  deploy neural ranking models that outperform BM25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  CCS CONCEPTS  Information systems → Retrieval models and ranking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  KEYWORDS  unsupervised training, neural information retrieval, ranking  1  INTRODUCTION  Training effective neural IR models often requires abundant in-  domain training data, which can be quite costly to obtain: Judging  a single document-query pair takes at least one minute on aver-  age [13, 19] and a single query typically needs at least 50 of such  judgements [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='1 In that, models trained on out-of-domain data  and/or fine-tuned using a small number of in-domain queries are  often worse or perform only marginally better [31, 47] than simple  non-neural BM25 rankers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  ∗Work done outside of the scope of employment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  †Equal contribution: Work done while studying at Carnegie Mellon University.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  1Robust04 and TREC-COVID collections used in our study have about 1K judgements  per query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  A recent trend to deal with this problem consists in generat-  ing synthetic in-domain training data via prompting of Large Lan-  guage Models (LLMs) [4, 9, 43], However, proposed solutions are  not cost effective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Furthermore, because researchers used primarily  proprietary LLMs—whose training procedure was not controlled  by the scientific community—or instruction-finetuned LLMs there  is a question of whether information retrieval capabilities emerge,  indeed, from a large scale training with a next-token-prediction  objective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  To enable a practical solution for a large scale LLM-based gen-  eration of training data for IR systems, as well as to answer this  key scientific question, we carry out a reproducibility study of In-  Pars [4] using medium-size (at most 7B parameters) open-source  LLMs [44, 50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In addition, our study employs more practical and  more commonly used BERT-based cross-encoder models having as  little as 30 million parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In contrast, the original study em-  ployed large MonoT5 rankers of which only MonoT5-3B ranker  (with 3 billion parameters) performed well [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  We discover that in a purely unsupervised setting we can re-  place an impractical three-billion parameter MonoT5-3B model [35]  with a 7x smaller bi-directional BERT model while obtaining com-  parable results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Moreover, unlike the original InPars study where  a 220M million MonoT5 model fails to outperform BM25 on three  out of five datasets, we show that a much smaller MiniLM model  with only 30 million parameters [53] can always outperform BM25  by 7-30% in key metrics (nDCG@K or MRR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  In that, obtaining these good results required re-ranking only  100 candidate documents compared to 1000 in the InPars study [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Compared to InPars, our recipe—which we call InPars-Light—is  substantially more cost effective in three dimensions: (a) synthetic  data generation, (b) model training, and (c) inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  In our study we ask the following research questions:  RQ1: Do information retrieval (IR) capabilities emerge merely  from a large-scale next-token-prediction training?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Although,  prior studies (see § 2) provide limited evidence to answer  this question positively, we believed that additional evidenced  was required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  RQ2: Are open-source models more or less useful for gener-  ation of synthetic IR training data compared to the similar-  size GPT-3 model?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  RQ3: Does consistency checking proposed by Dai et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' [9],  indeed, beneficial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Is it applicable in the re-ranking setting  (as opposed to using it with retrievers as in [9])?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  RQ4: Can we match performance of a large MonoT5-3B  ranker using much smaller BERT models?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  RQ5: In particular, can we substantially outperform BM25  using a small and fast ranker such as a MiniLM ranker with  merely 30 million parameters?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  We obtain the following results:  RQ1 & RQ2: Not only open-source LLMs BLOOM [44] and  GPT-J [50] trained in a fully unsupervised fashion can be  prompted to generate effective synthetic queries, but using  them leads to consistent improvement compared to GPT-3  Curie model [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' At the same time, we estimate that genera-  tion of synthetic queries using open-source models is about  10x cheaper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Note that in the concurrent work, Jeronymo  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' [18] also obtained good results using an open-source  generation models, but they do not have an ablation that  focuses specifically on replacing GPT-3 Curie with open-  source models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  RQ3: Although we confirm the effectiveness of the InPars  training recipe, fine-tuning the model using consistency-checked  data always produced a better model;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  RQ4 & RQ5: We confirm the finding of Bonifacio et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' [4]  that the InPars-recipe (even if combined with consistency  checking) does not work well for small models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' We never-  theless discover that a combination of pre-training on all  queries (from all datasets) and in-domain finetuning on consistency-  checked data produces a small MiniLM-30M model that al-  ways outperformedBM25 by 7-30% in key metrics (nDCG@k  or MRR);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  2  RELATED WORK  Neural information retrieval has become a busy research area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' An  overview of the recent approaches and trends we address the reader  to the survey by Lin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Likewise, prompting methods have  gained quite a bit of popularity in NLP (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=', [26] for a recent  survey), but they were scarcely used in IR: We know only three  papers directly related to our work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Sachan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' [43] were probably the first to demonstrate effec-  tiveness of LLMs in the document ranking task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In their approach,  which they named UPR, they concatenate a document, a special  prompt such as "please write a question for this document" and the  query itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Then, UPR uses a pre-trained LLM model to compute  the likelihood of generating the query given the passage text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' How-  ever, they evaluate only on QA (but not IR) datasets and their main  results are for an impractical three-billion parameter instruction-  finetuned model, which is used essentially as a re-ranker (in a zero-  shot sceanrio).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Because this LLM was instruction fine-tuned these  experiments do not permit definitive conclusions about RQ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Al-  though they also demonstrated the effectiveness of a standard (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=',  just next-token-prediction training) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='7B GPT-Neo LLM [3], this  was done only for a single QA dataset, namely Natural Questions  [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  The smallest model that they used had 250 million parameters  (compared to our 30-million MiniLM model): The evaluated it only  on the Natural Questions [19] collection, where it outperformed  BM25 only by about 10%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Bonifacio et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' [4] proposed an InPars method, which relied  on few-shot prompting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' The study had a convincing evaluation  on five datasets where only one dataset, namely NQ, is a typical  QA collection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Unlike Sachan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' [43] Bonifacio et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' used few-  shot prompting to distill an LLM into smaller rankers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' To this end,  few-shot prompting was used to generate synthetic queries for  randomly sampled documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' For each collection they generated  100K synthetic queries and retained only 10K with the highest av-  erage log-probabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  However, they obtained good results only for a huge MonoT5-  3B parameter model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Moreover, the used a proprietary GPT-3 model,  which can be quite costly to use.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In a follow-up study, which is con-  current with this work, Jeronymo et.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' al [18] introduced a modifica-  tion of InPars—dubbed InPars v2—where GPT-3 Curie [6] was re-  placed with an open-source model GPT-J [50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' However, this model  swap is “entangled” with at least two other modifications in the  training recipe:  A new filtering condition that employs an MS MARCO trained  MonoT5-3B model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  The vanilla prompt (which was used in InPars and our ex-  periments) was replaced with the Guided by Bad Question  prompt (introduced in [4]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Thus, it is not possible to fairly assess the impact of replacing GPT-  3 Curie with GPT-J [50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  An important disadvantage of InPars v2 recipe is that it is still  not cost-effect as authors use a huge MonoT5-3B model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' The fil-  tering check uses a MonoT5-3B model trained on MS MARCO cor-  pus, which is not always possible in a commercial setting due to  licensing issues (MS MARCO is a research-only collection).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' More-  over, the MonoT5-3B model trained on MS MARCO—albeit being  impractical—has excellent zero-shot transferability: Fine-tuning MonoT5-  3B model trained on MS MARCO with InPars v2 only improves the  average BEIR score only by 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4%: from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='538 to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='551.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Dai et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' [9] used an InPars-like method called Promptagator  and created synthetic training data using a huge proprietary FLAN  model with 137 billion parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Although they used modestly  sized models with 110 million parameters, Dai et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' [9] generated  as many as million synthetic training queries for each dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In  contrast, InPars used only 100K queries per dataset, which is much  less expensive (see a discussion in § 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Importantly, Dai et al [9] proposed to use consistency checking  [1] to filter-out potentially spurious queries, which was not previ-  ously done in the IR context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' We use a variant of this procedure as  well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  In addition, to prompt-based generation of training data, there  are multipleproposals for self-supervised adaptation of out-of-domain  models using generative pseudo-labeling [22, 38, 51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' To this end,  questions or queries are generated using a pretrained seq2seq model  (though an LLMs can be used as well) and negative examples are  mined using either BM25 or an out-of-domain retriever or ranker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Unsupervised domain adaptation is complementary to the approaches  considered in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  The disadvantage of such approaches is that they may need a  reasonably effective out-of-domain model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' However,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' such models  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='Table 1: The format of the vanilla 3-shot InPars prompt  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='Example 1:  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='Document: <text of the first example document>  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='Relevant Query: <text of the first relevant query>  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='Example 2:  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='Document: <text of the second example document>  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='Relevant Query: <text of the second relevant query>  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='Example 3:  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='Document: <text of the third example document>  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='Relevant Query: <text of the third relevant query>  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='Example 4:  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='Document: <real in-domain document text placeholder>  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='Relevant Query:  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='Notes: To generate a synthetic query,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' we first insert a text of a  chosen real in-domain document after the prefix “Document:”  in example four.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Then, we “ask” an LLM to generate a comple-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  can be hard to obtain due to licensing issues and poor transferabil-  ity from other domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' For example, MS MARCO models have rea-  sonable transferability [31, 47], but MS MARCO cannot be used to  train models in a commercial context (without extra licensing from  Microsoft).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In contrast, the Natural Questions (NQ) collection [19]  has a permissive license2, but models trained on NQ can fail to  transfer to datasets that are not based on Wikipedia [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Another potentially complementary approach is LLM-assisted  query expansion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In particular Gao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' prompt a 175B Instruct-  GPT model to generate a hypothetical answer to a question [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Then this answer is encoded and together with the encoding of the  original question they are compared with encoded documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In  a purely unsupervised setting—-using the Contriever bi-encoder  training without supervision [17]—they were able to outperform  BM25 by as much as 20%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Despite strong results, a serious disadvantage of this approach is  its dependence on the external proprietary model that is costly and  has long generation times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Although we could not find any reliable  benchmarks, a folklore opinion is that generation latency is a few  seconds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' To verify this, we used the OpenAI playground3 to gener-  ate a few hypothetical answers using the prompt in Gao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' [12]  and a sample of TREC DL 2020 queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' With a maximum genera-  tion length of 256 tokens (a default setting), the latency exceeded  four seconds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Quite interestingly, Gao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' [12] tried to replace a 175B GPT-  3 model with smaller open-source models on TREC DL 2019 and  TREC DL 2020 (see Table 4 in their study), but failed to obtain con-  sistent and substantial gains with models having fewer than 50B  parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  3  METHODS  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='1  Information Retrieval Pipeline  We use a variant of a classic filter-and-refine multi-stage retrieval  pipeline [30, 36, 52], where top-푘 candidate documents retrieved  by a fast BM25 ranker [40] are re-ranked using a slower neural  re-ranker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' For collections where document have titles, the BM25  retriever itself has two stages: In the first stage we retrieve 1K  documents using a Lucene index built over the concatenation of  all document fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In the second stage, these candidates are re-  ranked using equally weighted BM25 scores computed separately  for each field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Our neural rankers are cross-encoder models [24, 34], which  operate on queries concatenated with documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Concatenated  texts are passed to a backbone bi-directional encoder-only Trans-  former model [10] equipped with an additional ranking head (a  fully-connected layer), which produces a relevance score (using  the last-layer contextualized embedding of a CLS-token [34]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In  contrast, authors of InPars [4] use a T5 [37] cross-encoding re-  ranker [35], which is a full Transformer model [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' It uses both the  encoder and the decoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' The T5 ranking Transformer is trained  to generate labels “true” and “false”, which represent relevant and  non-relevant document-query pairs, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Backbone Transformer models can differ in the number of pa-  rameters and pre-training approaches (including pre-training datasets).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  In this paper we evaluated the following models, all of which were  pre-trained in the self-supervised fashion without using IR-specific  pre-training or supervision with IR datasets:  A six-layer MiniLM-L6 model [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' It is a tiny (by modern  standards) 30-million parameter model, which was distilled  [15, 21, 41] from Roberta [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' We download model L6xH384  MiniLMv2 from the Microsoft website.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4  A 24-layer (large) ERNIE v2 model from the HuggingFace  hub [46]5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' It has 335 million parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  A 24-layer (large) DeBERTA v3 model with 435 million pa-  rameters [14] from the HuggingFace hub 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  We choose ERNIE v2 and DeBERTA v3 because (from our prior ex-  perience) we knew they had strong performance on the MS MARCO  dataset (better than BERT large [10] and several other models that  we tested in the past).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Both models performedcomparably well (see  Table 4) in the preliminary experiments, but we chose DeBERTA  for main experiments because it is more effective on MS MARCO  and TREC-DL 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  However, both of these models are quite large and we aspired to  show that an InPars-like training recipe can be used with smaller  models too.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In contrast, Bonifacio et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' [4] were able to show that  only a big T5-3B model with 3B parameters outperformedBM25 on  all five datasets, while the smaller (but still quite large) T5-200M  ranker with “merely” 200 million parameters did not outperform  BM25 on three datasets (it only worked on MS MARCO and TREC-  DL 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  2https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='com/google-research-datasets/natural-questions/blob/master/LICENSE  3https://beta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='openai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='com/playground  4https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='com/microsoft/unilm/tree/master/minilm  5https://huggingface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='co/nghuyong/ernie-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='0-large-en  6https://huggingface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='co/microsoft/deberta-v3-large  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2  Generation of Synthetic Training Data  In-domain training data is generated using a well-known few-shot  prompting approach introduced by Brown et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In the IR do-  main, it was first used by Bonifacio et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' [4] who re-branded it as  InPars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' The key idea is to “prompt” a large language model with a  few-shot textual demonstration of known relevant query-document  pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' To produce a novel query-document pair, Bonifacio et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' ap-  pend an in-domain document to the prompt and “ask” the model to  complete the text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' We use the so-called vanilla prompt (see Table 1)  created by Bonifacio et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Like in the InPars study, we gener-  ated 100K queries for each dataset with exception of MS MARCO  and TREC DL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Because both datasets use the same set of passages  they share the same set of 100K generated queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Repeating this procedure for many in-domain documents pro-  duces a large training set, but it can be quite imperfect: We carried  out spot-checking and found quite a few queries that were spuri-  ous or only tangentially relevant to the passage from which they  were generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Many spurious queries can be filtered out automatically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' To this  end, in InPars Bonifacio et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' [4] used only 10% of the queries  with the highest log-probabilities (averaged over query tokens).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In  Promptagator Dai et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' [9] introduced a different filtering proce-  dure, which was a variant of consistency checking [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Dai et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  first trained a retriever model using all the generated queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Then,  for each query they retrieved a set of documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' The query passed  the consistency check if the first retrieved document was the doc-  ument from which the query was generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Dai et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' [9] used consistency checking with bi-encoding re-  trieval models, but it is applicable to cross-encoding re-ranking  models as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Another straightforward modification of this ap-  proach is to check if a generated document is present in a set of  top-푘 (푘 > 1) candidates with the highest relevance scores (as com-  puted by the re-ranking or retrieval model).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3  InPars-Light Training Recipe  The InPars-Light is a modification of the original InPars, but it is  substantially more cost effective for generation of synthetic queries,  training the models, and inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' InPars-Light has the following  main “ingredients”:  Using open-source models instead of GPT-3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Using much smaller ranking models;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Fine-tuning models on consistency-checked training data;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Optional pre-training of models using all generated queries  from all collections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Re-ranking only 100 candidate documents instead of 1000;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  To obtain consistency-checked queries for a given dataset, a  model trained on InPars-generated queries (for this dataset) was  used to re-rank output of all original queries (for a given dataset).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Then, all the queries where the query-generating-document did  not appear among top-푘 scored documents was discarded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In our  study, we experimented with 푘 from one to three (but only on  MS MARCO).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='7 Although 푘 = 1 worked pretty well, using 푘 = 3  lead to a small boost in accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Consistency-checking was car-  ried out using DeBERTA-v3-435M [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' We want to emphasize that  7We did not want to optimize this parameter for all collections and, thus, to commit  a sin of tuning hyper-parameters on the complete test set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  consistency-checked training data was used in addition to origi-  nal InPars-generated data (but not instead), namely, to fine-tune a  model initially trained on InPars generated data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Also, quite interestingly, a set of consistency-checked queries  had only a modest (about 20-30%) overlap with the set of queries  that were selected according to their average log-probabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Thus,  consistency-checking increased the amount of available training  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' It might seem appealing to achieve the same objective by sim-  ply picking a larger number of queries (with highest average log-  probabilities).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' However, preliminary experiments on MS MARCO  showed that a naive increase of the number of queries degraded  effectiveness (which is consistent with the InPars study [4]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Although, the original InPars recipe with open-source models  and consistency checking allowed us to train strong DeBERTA-  v3-435M models, performance of MiniLM models was lackluster  (roughly at BM25 level for all collections).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Because bigger models performed quite well, it may be possible  to distill [15, 21, 41] their parameters into a much smaller MiniLM-  30M model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Distillation is known to be successful in the IR domain  [16, 25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' However, it failed in our case due to overfitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' We left  investigation of the failure reasons for the future and used the fol-  lowing workaround:  First we carried out an all-domain pre-training without any  filtering (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=', using all queries from all collections);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Then, we fine-tuned all-domain pre-trained models on the  consistency-checked in-domain data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4  Miscellaneous  Experiments were carried out using the framework FlexNeuART  [5], which provided support for basic indexing, retrieval, and neu-  ral ranking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' The neural models are implemented using PyTorch  and Huggingface [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' The models were trained using an InfoNCE  loss [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In a single training epoch, we selected randomly one pair  of positive and three negative examples per query (negatives are  sampled from 1000 documents with highest BM25 scores).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Note  that, however, that during inference we re-ranked only 100 docu-  ments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' A number of negatives was not tuned: We used as much as  we can while ensuring we do not run out of GPU memory during  training on any collection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  We used an AdamW [28] optimizer with a small weight decay  (10−7), a warm-up schedule, and a batch size of 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='8 We used differ-  ent base rates for the fully-connected prediction head (2·10−4) and  for the main Transformer layers (2 · 10−5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Also note that the loss  reduction mode was “sum”: To use this recipe with the reduction  mode “mean” the learning rates need to be multiplied by the batch  size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  We trained each model using three seeds and reported the aver-  age results (unless specified otherwise).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' To compute statistical sig-  nificance, we first obtained an “average” run where for each query  we averaged query-specific metric values over three seeds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Note  that we compute exactly the same metric values as in [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' For sta-  tistical significance testing we used a paired two-sided t-test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' For  query sets with a large number of queries (name MS MARCO devel-  opment set and BEIR Natural Questions) we used a lower threshold  8The learning rate grows linearly from zero for 20% of the steps until it reaches the  base learning rate [32, 45] and then goes back to zero (also linearly).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' For small query sets (Robust04 and TREC-COVID), the sta-  tistical significance threshold was set to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  We implemented our query generation module using the Auto-  ModelForCasualLM interface from HuggingFace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' We used a three-  shot vanilla prompt template used by [4] (also shown in Table  1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' The output was generated via greedy decoding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' The maximum  number of new tokens generated for each example was set to 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  4  DATASETS  Because we aimed to reproduce the main results of InPars [4], we  used exactly the same set of queries and datasets, which are de-  scribed below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Except MS MARCO (which was processed directly  using FlexNeuART [5] scripts), datasets were ingested with a help  of the IR datasets packages [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Some of the collections below have multiple text fields, which  were used differently by a BM25 and neural ranker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' All collections  except Robust04 have exactly one query field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Robust04 queries  have the following parts: title, description, and narrative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' For the  purpose of BM25 retrieval and ranker, we use only the title field,  but the neural ranker is used the description field (which is consis-  tent with [4]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' The narrative field is not used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Two collectionshave documents with both the title and the main  body text fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' The neural rankers operate on concatenation of  these fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' If this concatenation is longer than 477 BERT tokens,  it is truncated (queries longer than 32 BERT tokens are truncated  as well).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' For BM25 scoring, we index the concatenated fields as well  (in Lucene).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' However, after retrieving 1000 candidates, we re-rank  them using the sum of BM25 scores computed for the title and the  main body text fields separately (using FlexNeuART [5]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Synthetically Generated Training Queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' For each of the  datasets, Bonifacio et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' [4] provided both the GPT-3-generated  queries (using GPT-3 Curie model) and the documents that are  used to generate the queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' This permits an apples-to-apples com-  parison of the quality of training data generated using GPT-3 Curie  with the quality of synthetic training data generated using open-  source models GPT-J [50] and BLOOM [44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' According to the es-  timates of Bonifacio et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' [4], the Curie model has 6B parameters,  which is close to the estimate made by by Gao from EleutherAI [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Thus, we used GPT-J [50] and BLOOM [44] models with 6 and 7 bil-  lion parameters, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Although other open-source models  can potentially be used, generation of synthetic queries is quite ex-  pensive and exploring other open-source options is left for future  work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  MS MARCO sparse and TREC DL 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' MS MARCO is col-  lection of 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='8M passages extracted from approximately 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='6M Web  documents, which was derived from the MS MARCO reading com-  prehension dataset [2, 8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' It “ships“ with more than half a million  of question-like queries sampled from the Bing search engine log  with subsequent filtering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' The queries are not necessarily proper  English questions, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=', “lyme disease symptoms mood”, but they  are answerable by a short passage retrieved from a set of about  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='6M Web documents [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Relevance judgements are quite sparse  (about one relevant passage per query) and a positive label indi-  cates that the passage can answer the respective question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  The MS MARCO collections has several development and test  query sets of which we use only a development set with approx-  imately 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='9K sparsely-judged queries and the TREC DL 2020 [8]  collection of 54 densely judged queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Henceforth, for simplic-  ity when we discuss the MS MARCO development set we use a  shortened name MS MARCO, which is also consistent with Boni-  facio al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Note that the MS MARCO collection has a large training set, but  we do not use it in the fully unsupervised scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' We do use it  though in the hybrid setting (see § 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Robust04 [49] is a small (but commonly used) collection that  has about 500K news wire documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' It comes with a small but  densely judged set of 250 queries, which have about 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2K judge-  ments on average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Natural Questions(NQ) BEIR [19] is an open domain Wikipedia-  based Question Answering (QA) dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Similar to MS MARCO,  it has real user queries (submitted to Google).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' We use a BEIR’s  variant of NQ [47], which has about 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='6M short passages from  Wikipedia and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4K sparsely-judged queries (about 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2 relevant  documents per query).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  TREC COVID BEIR [39] is a small corpus that has 171K sci-  entific articles on the topic of COVID-19 and 50 densely-judged  queries (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3K judged documents per query on average).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' It was cre-  ated for a NIST challenge whose objective was to develop informa-  tion retrieval methods tailored for the COVID-19 domain (with a  hope to be a useful tool during COVID-19 pandemic).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' We use the  BEIR’s version of this dataset [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  5  RESULTS  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='1  Main Results  Our main experimental results are presented in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' We or-  ganize them into multiple sections, where we show effectiveness  numbers for various supervised, unsupervised, and hybrid approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  In addition to our own measurements, we copy key results from  the work by Bonifacio et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' [4], which include results for BM25, re-  ranking using OpenAI API, as well as results for Mono-T5 rankers  [35] trained in the unsupervised, supervised, and hybrid manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Because there is a substantial variability of results among seeds (in-  cluding one case of extremely poorconvergence), for unsupervised-  only training we also present our-best seed results in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In  Table 4, we show effectiveness of InPars for three types of models  to generate synthetic training queries (including OpenAI GPT-3  model).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In our experiments, we statistically test several statistical  hypotheses, which are explained separately at the bottom of each  table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  BM25 baselines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Comparing effectiveness of FlexNeuART [5]  BM25 with effectiveness of Pyserini [23] BM25—used the InPars  study [4]—we can see that on all datasets except TREC DL 2020  we closely match (within 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='5%) Pyserini numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' On TREC DL  2020 our BM25 is 6% more effective in nNDCG@10 and 25% more  effective in MAP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Reproducibility Notes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In addition to BM25 performance, we  can reproduce some of the key findings from prior work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In what  follows we discuss these (and other findings) in more detail:  Table 2: Main Results (averaged over three seeds)  MS MARCO  TREC DL 2020  Robust04  NQ  TREC COVID  MRR  MAP nDCG@10  MAP nDCG@20 nDCG@10  nDCG@10  BM25 [4]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='1874  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2876  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4876  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2531  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4240  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3290  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='6880  BM25 (ours)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='1867  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3612  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='5159  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2555  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4285  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3248  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='6767  OpenAI Ranking API: re-ranking 100 Documents [4]  Curie (6B) [4]  $  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3296  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='5422  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2785  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='5053  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4171  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='7251  Davinci (175B) [4]  $  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3163  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='5366  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2790  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='5103  $  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='6918  Unsupervised: InPars-based Training Data  monoT5-220M (InPars) [4]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2585  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3599  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='5764  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2490  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4268  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3354  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='6666  monoT5-3B (InPars) [4]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2967  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4334  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='6612  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3180  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='5181  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='5133  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='7835  MiniLM-L6-30M (InPars)  푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2117  푏0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3482  푏0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4953  푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2263  푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3802  푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2187  푏0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='6361  MiniLM-L6-30M (InPars ◮ consist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' check)  푐푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2336  푐푏0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3769  푐푏0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='5543  푐푏0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2556  푐푏0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4440  푐푏0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3239  푐푏0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='6926  MiniLM-L6-30M (InPars all ◮ consist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' check)  푐푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2468  푐푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3929  푐푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='5726  푐0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2639  푐푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4599  푐푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3747  푐푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='7688  DeBERTA-v3-435M (InPars)  푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2746  푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4385  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='6649  푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2811  푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4987  푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4476  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='8022  DeBERTA-v3-435M (InPars ◮ consist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' check)  푐푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2815 푐푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4446  푐푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='6717 푐푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3009 푐푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='5360  푐푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4621  푐푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='8183  DeBERTA-v3-435M (InPars all ◮ consist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' check)  푐푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='1957  푐0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3607  푐0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='5007  푐0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2518  푐0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4320  푐0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3267  푐0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='6953  Supervised and Hybrid: transfer from MS MARCO with an optional fine-tuning on consistency-checked InPars data  MiniLM-L6-30M (MS MARCO)  푑푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3080  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4370  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='6662  푑푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2295  푑푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3923  푑푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4646  푑푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='7476  MiniLM-L6-30M (MS MARCO ◮ consist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' check)  푑푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2944  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4311  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='6501  푑푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2692  푑푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4730  푑푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4320  푑푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='7898  DeBERTA-v3-435M (MS MARCO)  푑푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3508  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4679  푑푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='7269  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2986  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='5304  푑푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='5616  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='8304  DeBERTA-v3-435M (MS MARCO ◮ consist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' check)  푑푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3166  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4553  푑푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='6912  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3011  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='5371  푑푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='5075  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='8165  monoT5-220M (MS MARCO) [35]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3810  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4909  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='7141  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3279  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='5298  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='5674  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='7775  monoT5-3B (MS MARCO) [35]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3980  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='5281  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='7508  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3876  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='6091  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='6334  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='7948  monoT5-3B (MS MARCO ◮ InPars) [4]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3894  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='5087  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='7439  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3967  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='6227  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='6297  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='8471  OpenAI API ranking results are copied from Bonifacio et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In that, $ denotes experiments that were too expensive to run.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  InPars denotes the original query-generation method with filtering-out 90% of queries having lowest average log-probabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  InPars all denotes the query-generation method without query filtering, which was used in all-domain pretraining.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Consist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' check denotes consistency filtering of all generated queries using a model trained on InPars-generated data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Best unsupervised and hybrid-training results are marked by bold font (separately for unsupervised and hybrid-training).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Super-scripted labels denote the following statistically significant differences (thresholds are given in the main text):  a: between a neural model and BM25;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  b: between training with and without fine-tuning on consistency-checked data (for the same model type).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  c: between pre-training using all generated queries for all collections and only filtered in-domain queries (for the same model type).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  d: between 0-shot transferring an MS MARCO model & fine-tuning this model on filtered in-domain queries (for the same model type).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Generation of synthetic in-domain data using an InPars-like  recipe can permit training very strong in-domain rankers  without any human-provided supervision data;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Without additional tricks such as all-domain pre-training  and consistency checking, only a sufficiently larger model  can outperform BM25;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  A consistency checking introducedby Promptagator [9] does  lead to a substantial gain in accuracy;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Replacing the proprietary GPT-3 Curie model with BLOOM  [44] can improve performance, which is in line with findings  of Jeronymo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' However, unlike our study, they do  not directly assess the impact of replacing the generating  model alone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Unsupervised-only training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In a purely unsupervised set-  ting, we obtain comparable or better results using much smaller  ranking models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' With DeBERTA-v3-435M we obtain comparable  (somewhat better or worse) effectiveness to MonoT5-3B on four  collections out of five (MonoT5-3B has 7x more parameters).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Our  biggest gap is for the NQ collection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' However, this is the collec-  tion where we already obtain a substantial 15-30% gain over BM25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Moreover, there is quite a bit of variability across model seeds, and  our best-seed NQ model is quite close to the average performance  of MonoT5-3B (see Table 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Our smallest MiniLM-L6-30M model with all-domain pretrain-  ing and finetuning on consistency-checked data (InPars all ◮ con-  sist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' check) roughly matches the 7x larger MonoT5-220M on MS  MARCO and TREC DL 2020, but it is substantially better than  Table 3: Best-Seed Results for Unsupervised Training  MS MARCO  TREC DL 2020  Robust04  NQ  TREC COVID  MRR  MAP nDCG@10  MAP nDCG@20 nDCG@10  nDCG@10  BM25 (ours)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='1867  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3612  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='5159  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2555  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4285  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3248  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='6767  MiniLM results  MiniLM-L6-30M (InPars)  푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2197  푏0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3562  푏0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='5151 푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2380  푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4029  푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2415  푏0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='6732  MiniLM-L6-30M (InPars ◮ consist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' check)  푐푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2422  푏0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3844  푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='5753  푐푏0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2615  푐푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4554  푐푏0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3297  푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='7483  MiniLM-L6-30M (InPars all ◮ consist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' check)  푐푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2517  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3945  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='5769  푐0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2671  푐푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4691  푐푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3800  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='7709  DeBERTA results  DeBERTA-v3-435M (InPars)  푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2748  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4437  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='6779 푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2874  푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='5131  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4872  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='8118  DeBERTA-v3-435M (InPars ◮ consist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' check)  푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2847  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4479  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='6813  푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3043  푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='5417  푐푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4924  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='8305  DeBERTA-v3-435M (InPars all ◮ consist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' check)  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2804  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4414  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='6575  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3076  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='5505  푐푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4746  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='8259  Super-scripted labels denote the following statistically significant differences (thresholds are given in the main text):  a: between a neural model and BM25;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  b: between training with and without fine-tuning on consistency-checked data (for the same model type).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  c: between pre-training using all generated queries and only filtered in-domain queries (for the same model type).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Notes: Best results (separately for each model are marked by bold font.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  MonoT5-220M on the remaining datasets, where MonoT5-220M ef-  fectiveness is largely at BM25 level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' MiniLM-L6-30M outperforms  BM25 on all collections and all metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In all but one case these dif-  ferences are also statistically significant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In terms of nDCG and/or  MRR, it is 7-30% more effective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Impact of consistency checking and all-domain pre-training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  It is crucial to note, however, on its own the InPars recipe does  not produce a strong MiniLM-L6-30M model, which is in line with  finding of the InPars study where only MonoT5-3B (but not a much  smaller MonoT5-220M) outperformedBM25 on all collections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Strong  performance of MiniLM-L6-30M was due to additional training  with consistency-checked data and pre-training on all-domain (all  queries from all collections) data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Therefore, we carry out ablation  experiments to assess effectiveness of these procedures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  We can see that for both MiniLM-L6-30M and DeBERTA-v3-  435M,fine-tunining on consistency-checked data improves outcomes:  For 12 measurements out of 14, these differences are also statisti-  cally significant (denoted by super-script label “b”).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Moreover, all-  domain pretraining (instead of training on data generated by the  original InPars recipe) further boosts accuracy of MiniLM-L6-30M  in all cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Moreover, all the differences are statistically significant  (denoted by super-script label “c”).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' However, all-domain pretrain-  ing substantially degrades performance of DeBERTA-v3-435M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  An in-depth investigation showed that for one seed (out of three),  the model failed to converge properly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Although, we could have  also chosen a different seed and present better results, we felt that  this failure to converge (which was the only case out of many ex-  periments we ran!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=') was an indication that all-domain pretraining  dit not work well for DeBERTA-v3-435M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' To further verify this hy-  pothesis, we also checked the best-seed outcomes, which are pre-  sented in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' For MiniLM-L6-30M, the all-domain pre-training  improves the best-seed results in all cases, though we have fewer  statistically significant difference now (this is expected, because  using average-seed runs leads to more stable measurements).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' For  DeBERTA-v3-435M, there is either a substantial degradation or  a small decrease/increase that is not statistically significant (de-  noted by super-script label “c”).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Thus, our biggest model—unlike  15x smaller MiniLM-L6-30M— does not benefit from all-domain  pretraining.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In fact this pretraining leads to performance degrada-  tion (including potential decrease in training stability).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Supervisedand hybrid training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' We find that for ourdatasets,  a model trained on MS MARCO (both MiniLM-L6-30M and DeBERTA-  v3-435M) transfers well to other collections, except for transfer  of MiniLM-L6-30M to Robust04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' However, similar to all-domain  pre-training the 15x smaller MiniLM-L6-30M benefits more from  in-domain fine-tuning with consistency-checked data: There are  substantial and statistically significant improvements for Robust04  and TREC-COVID (but a degradation for MS MARCO, TREC DL  2020 and NQ, whereas in the case of DeBERTA-v3-435M such fine-  tuning noticeably degrades accuracy in most cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Also note that DeBERTA-v3-435M roughly matches MonoT5-  220M while still lagging behind MonoT5-3B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' This is in line with  prior finding that large ranking models have better zero-shot trans-  ferring effectiveness [33, 42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' However, using multi-billion param-  eter ranking models is not a practical choice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Model-Type Ablation To assess the impact of replacing GPT-3  Curie with an open-source model, we carried out experiments us-  ing ERNIE-v2 model [46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Althoughwe generated synthetic queries  only once, each ranker was trained with three different seeds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Thus,  we compared systems where query-specific metric values were av-  eraged over seeds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' To our surprise (see Table 4), except for NQ  where all models were nearly equally good, GPT-3 Curie under-  performed both open-source models (out of 14 measurements 10  are statistically significant as denoted by super-script “b”).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' The dif-  ference was particularly big for Robust04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  We then computed the average gain by (1) computing relative  gain separately for each datasets and key metrics (nDCG or MRR)  Table 4: Performance of InPars for Different Generating and Ranking Models (averaged over three seeds)  MS MARCO  TREC DL 2020  Robust04  NQ  TREC COVID  MRR  MAP  nDCG@10  MAP  nDCG@20  nDCG@10  nDCG@10  BM25 (ours)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='1867  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3612  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='5159  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2555  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4285  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='3248  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='6767  ERNIE-v2-335M OpenAI Curie (6B)  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2538  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4140  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='6229  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2357  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4016  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4277  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='7411  ERNIE-v2-335M GPT-J (6B)  푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2608  푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4286  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='6367  푐푏0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2691  푐푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4724  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4248  푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='7750  ERNIE-v2-335M BLOOM (7B)  푑푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2605  푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4286  푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='6407  푐푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2852  푑푐푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='5102  푑푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4215  푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='7871  DeBERTA-v3-435M BLOOM (7B)  푑푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2746  푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4385  푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='6649  푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2811  푑푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4987  푑푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='4476  푏푎0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='8022  Notes: Best results are in bold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Super-scripted labels denote statistically significant differences (thresholds are given in the main text):  a: between a neural model and BM25;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  b: between a given neural model trained using queries from a given open-source models and ERNIE trained on queries from GPT-3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  c: between using GPT-J-generated queries and BLOOM-generated queries (only for ERNIE);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  d: between the DeBERTA model and the ERNIE model (both trained using BLOOM-generated queries).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  and (2) averaging these relative gains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' The resulting gains (not  shown in the table) are 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2% for BLOOM and 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2% for GPT-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  In addition to the generation model, we assessed the impact of  using DeBERTA-v3 instead of ERNIE-v2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' This time around, both  models were trained using BLOOM-generated queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' We can see  that DeBERTA v3 was generally better than ERNIE-v2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2  Cost and Efficiency  In the following sub-section, we discuss both the ranking efficiency  and query-generation cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Although one may argue that the cost  of generation using open-source models is negligibly small, in real-  ity this is true only if one owns their own hardware and generates  enough queries to justify the initial investment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Thus, we make a  more reasonable assessment assuming that the user can employ a  cheap cloud service.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Efficiency of Re-ranking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' A rather common opinion (in par-  ticular expressed by anonymous reviewers on multiple occasions)  is that using cross-encoders is not a practical option.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' This might be  true for extremely constrained latency environments or very large  models, but we think it is totally practical to use small models such  as MiniLM-L6-30M for applications such as enterprise search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In  particular, on a reasonably modern GPU (such as RTX 3090) and  Pytorch MinLm-L6-30M re-ranking throughput exceeds 500 pas-  sages per second (assuming truncation to the first 477 characters).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Thus re-ranking 100 documents has an acceptable sub-second re-  ranking latency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Cost of Model Training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Here, all training times are given  with respect to a single RTX 3090 GPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Training and evaluating  MiniLM6-30M models had negligible costs dominated by all-domain  pretraining, which took about two hours per seed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In contrast, the  all-domain pretraining of DeBERTA-v3-435M took 28 hours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' How-  ever, only about 20-30% of queries were selected for training mod-  els and fine-tuning them consistency checked data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Thus, without  all-domain pretraining, the training time itself was rather small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Aside from all-domain pre-training, the two most time-consuming  operations were validation of large query sets (MS MARCO and  NQ), which jointly have about 10K queries, and consistency check-  ing (using DeBERTA-v3-435M model).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' The total validation time for  DeBERTA-v3-435 was about 6 hours (for all collections).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' The con-  sistency checking, however, took about 48 hours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In the future, we  should consider carrying out consistency checking using a much  faster MiniLM-L6-30M model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Cost of Query Generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' For the original InPars [4], the cost  of generation for the GPT-3 Curie model is $0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='002 per one thou-  sand tokens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' The token count includes the length of the prompt  and the prompting document.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='9 We estimate that (depending on  the collection) a single generation involves 300 to 500 tokens: long-  document collections Robust04 and TREC-COVID both have close  to 500 tokens per generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Taking an estimate of 500 tokens per generation, the cost of  querying OpenAI GPT-3 Curie API can be up to $100 for Robust04  and TREC-COVID.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Assuming that sampling from 137-B FLAN model  to be as expensive as from the largest GPT-3 model Davinci (which  has a similar number of parameters), each generation in the Promp-  tagator study [9], was 10x more expensive compared to InPars  study [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Moreover, because Dai et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' [4] generated one million  samples per collection, the Promptagator recipe was about two or-  ders of magnitude expensive compared to InPars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  In contrast, it takes only about 15 hours to generate 100K queries  using RTX 3090 GPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Extrapolating this estimate to A100, which is  about 2x faster than RTX 309010, and using the pricing of Lambda  GPU cloud, we estimate the cost of generation in our InPars-light  study to be under $10 per collection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 11  6  CONCLUSION  We carried out a reproducibility study of InPars recipe for unsuper-  vised training of neural rankers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' As a by-product of this study, we  developed a simple-yet-effective modification of InPars, which we  called InPars-light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Unlike InPars, InPars-light uses only a freely  available language model BLOOM, 7x-100x smaller ranking mod-  els, and re-ranks only 100 candidate records instead of 1000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Not only can we reproduce key findings from prior work, but  combining the original InPars recipe [4] with (1) fine-tuning on  consistency-checked data [9], (2) and all-domain pretraining, we  9https://chengh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='medium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='com/understand-the-pricing-of-gpt3-e646b2d63320  10https://lambdalabs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='com/blog/nvidia-rtx-a6000-benchmarks  11https://lambdalabs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='com/service/gpu-cloud#pricing  were able to train a very efficient and small model MiniLM-L6-30M  that outperformed BM25 on all collections (in MRR or nDCG).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Last  but not least, with a larger DeBERTA-v3-435M model we could  largely match performance of a 7x larger MonoT5-3B (even out-  performing it on two datasets).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  ACKNOWLEDGMENTS  REFERENCES  [1] Chris Alberti, Daniel Andor, Emily Pitler, Jacob Devlin, and Michael Collins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Synthetic QA Corpora Generation with Roundtrip Consistency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In Pro-  ceedings of the 57th Annual Meeting of the Association for Computational Lin-  guistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Association for Computational Linguistics, Florence, Italy, 6168–6173.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='18653/v1/P19-1620  [2] Payal Bajaj, Daniel Campos, Nick Craswell, Li Deng, Jianfeng Gao, Xiaodong  Liu, Rangan Majumder, Andrew McNamara, Bhaskar Mitra, Tri Nguyen, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' MS MARCO: A human generated machine reading comprehension dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  arXiv preprint arXiv:1611.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='09268 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [3] Sid Black, Leo Gao, Phil Wang, Connor Leahy, and Stella Biderman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  GPT-Neo: Large Scale Autoregressive Language Modeling with Mesh-Tensorflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='5281/zenodo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='5297715  [4] Luiz Henrique Bonifacio, Hugo Abonizio, Marzieh Fadaee, and Rodrigo  Nogueira.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' InPars: Unsupervised Dataset Generation for Information Re-  trieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In SIGIR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' ACM, 2387–2392.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [5] Leonid Boytsov and Eric Nyberg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Flexible retrieval with NMSLIB and  FlexNeuART.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In Proceedings of Second Workshop for NLP Open Source Software  (NLP-OSS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 32–43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [6] Tom B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared Ka-  plan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry,  Amanda Askell, Sandhini Agarwal, Ariel Herbert-Voss, Gretchen Krueger, Tom  Henighan, Rewon Child, Aditya Ramesh, Daniel M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Ziegler, Jeffrey Wu, Clemens  Winter, Christopher Hesse, Mark Chen, Eric Sigler, Mateusz Litwin, Scott Gray,  Benjamin Chess, Jack Clark, Christopher Berner, Sam McCandlish, Alec Rad-  ford, Ilya Sutskever, and Dario Amodei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Language Models are Few-Shot  Learners.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In NeurIPS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [7] Chris Buckley, Darrin Dimmick, Ian Soboroff, and Ellen M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Voorhees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Bias  and the limits of pooling for large collections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Retr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 10, 6 (2007), 491–508.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [8] Nick Craswell, Bhaskar Mitra, Emine Yilmaz, Daniel Campos, and Ellen M  Voorhees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Overview of the TREC 2019 deep learning track.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' arXiv preprint  arXiv:2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='07820 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [9] Zhuyun Dai, Vincent Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Zhao, Ji Ma, Yi Luan, Jianmo Ni, Jing Lu, Anton Bakalov,  Kelvin Guu, Keith B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Hall, and Ming-Wei Chang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Promptagator: Few-shot  Dense Retrieval From 8 Examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' CoRR abs/2209.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='11755 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [10] Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' BERT:  Pre-training of deep bidirectional transformers for language understanding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  arXiv preprint arXiv:1810.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='04805 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [11] Leo Gao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' https://blog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='eleuther.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='ai/gpt3-model-sizes/.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [12] Luyu  Gao,  Xueguang  Ma,  Jimmy  Lin,  and  Jamie  Callan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Precise  Zero-Shot  Dense  Retrieval  without  Relevance  Labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='48550/ARXIV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='10496  [13] Lei Han, Eddy Maddalena, Alessandro Checco, Cristina Sarasua, Ujwal Gadiraju,  Kevin Roitero, and Gianluca Demartini.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Crowd Worker Strategies in Rele-  vance Judgment Tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In WSDM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' ACM, 241–249.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [14] Pengcheng He, Xiaodong Liu, Jianfeng Gao, and Weizhu Chen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  De-  berta: decoding-Enhanced Bert with Disentangled Attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In ICLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' OpenRe-  view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='net.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [15] Geoffrey E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Hinton, Oriol Vinyals, and Jeffrey Dean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Distilling the Knowl-  edge in a Neural Network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' CoRR abs/1503.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='02531 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [16] Sebastian  Hofstätter,  Sophia  Althammer,  Michael  Schröder,  Mete  Sertkan,  and  Allan  Hanbury.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Improving  Efficient  Neural  Ranking  Models  with  Cross-Architecture  Knowledge  Distillation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='48550/ARXIV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='02666  [17] Gautier Izacard, Mathilde Caron, Lucas Hosseini, Sebastian Riedel, Piotr Bo-  janowski, Armand Joulin, and Edouard Grave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Towards Unsupervised  Dense Information Retrieval with Contrastive Learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' CoRR abs/2112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='09118  (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [18] Vitor Jeronymo, Luiz Bonifacio, Hugo Abonizio, Marzieh Fadaee, Roberto  Lotufo, Jakub Zavrel, and Rodrigo Nogueira.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  InPars-v2: Large Lan-  guage Models as Efficient Dataset Generators for Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='48550/ARXIV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='01820  [19] Tom Kwiatkowski, Jennimaria Palomaki, Olivia Redfield, Michael Collins, Ankur  Parikh, Chris Alberti, Danielle Epstein, Illia Polosukhin, Jacob Devlin, Kenton  Lee, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' NaturalQuestions: a benchmarkfor question answering research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Transactions of the Association for Computational Linguistics 7 (2019), 453–466.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [20] Phuc H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Le-Khac, Graham Healy, and Alan F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Smeaton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Contrastive Rep-  resentation Learning: A Framework and Review.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' IEEE Access 8 (2020), 193907–  193934.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [21] Jinyu Li, Rui Zhao, Jui-Ting Huang, and Yifan Gong.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Learning small-  size DNN with output-distribution-based criteria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In INTERSPEECH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' ISCA, 1910–  1914.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [22] Minghan Li and Éric Gaussier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Domain Adaptation for Dense Retrieval  through Self-Supervision by Pseudo-Relevance Labeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' CoRR abs/2212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='06552  (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [23] Jimmy Lin, Xueguang Ma, Sheng-Chieh Lin, Jheng-Hong Yang, Ronak Pradeep,  and Rodrigo Nogueira.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Pyserini: A Python toolkit for reproducible infor-  mation retrieval research with sparse and dense representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In Proceedings  of the 44th International ACM SIGIR Conference on Research and Development in  Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2356–2362.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [24] Jimmy Lin, Rodrigo Nogueira, and Andrew Yates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Pretrained Transformers  for Text Ranking: BERT and Beyond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Morgan & Claypool Publishers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [25] Sheng-Chieh Lin, Jheng-Hong Yang, and Jimmy Lin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Distilling Dense Rep-  resentations for Ranking using Tightly-Coupled Teachers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' CoRR abs/2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='11386  (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [26] Pengfei Liu, Weizhe Yuan, Jinlan Fu, Zhengbao Jiang, Hiroaki Hayashi, and  Graham Neubig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Pre-train, Prompt, and Predict: A Systematic Survey  of Prompting Methods in Natural Language Processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' CoRR abs/2107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='13586  (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [27] Yinhan Liu, Myle Ott, Naman Goyal, Jingfei Du, Mandar Joshi, Danqi  Chen, Omer Levy, Mike Lewis, Luke Zettlemoyer, and Veselin Stoyanov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  RoBERTa: A Robustly Optimized BERT Pretraining Approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  CoRR  abs/1907.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='11692 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [28] Ilya Loshchilov and Frank Hutter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Decoupled weight decay regularization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  arXiv preprint arXiv:1711.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='05101 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [29] Sean MacAvaney, Andrew Yates, Sergey Feldman, Doug Downey, Arman Cohan,  and Nazli Goharian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Simplified Data Wrangling with ir_datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In SIGIR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [30] Irina Matveeva, Chris Burges, Timo Burkard, Andy Laucius, and Leon Wong.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' High accuracy retrieval with multiple nested ranker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In SIGIR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' ACM, 437–  444.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [31] Iurii Mokrii, Leonid Boytsov, and Pavel Braslavski.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' A Systematic Evalua-  tion of Transfer Learning and Pseudo-labeling with BERT-based Ranking Mod-  els.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In SIGIR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' ACM, 2081–2085.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [32] Marius Mosbach, Maksym Andriushchenko, and Dietrich Klakow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' On the  Stability of Fine-tuning BERT: Misconceptions, Explanations, and Strong Base-  lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' arXiv preprint arXiv:2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='04884 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [33] Jianmo Ni, Chen Qu, Jing Lu, Zhuyun Dai, Gustavo Hern’andez ’Abrego, Ji Ma,  Vincent Zhao, Yi Luan, Keith B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Hall, Ming-Wei Chang, and Yinfei Yang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Large DualEncoders Are Generalizable Retrievers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' ArXiv abs/2112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='07899 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [34] Rodrigo Nogueira and Kyunghyun Cho.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Passage Re-ranking with BERT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  arXiv preprint arXiv:1901.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='04085 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [35] Rodrigo Nogueira, Zhiying Jiang, and Jimmy Lin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Document ranking  with a pretrained sequence-to-sequence model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' arXiv preprint arXiv:2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='06713  (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [36] John M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Prager.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Open-Domain Question-Answering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Trends Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Retr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 1, 2 (2006), 91–231.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [37] Colin Raffel, Noam Shazeer, Adam Roberts, Katherine Lee, Sharan Narang,  Michael Matena, Yanqi Zhou, Wei Li, and Peter J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Liu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Exploring the Limits  of Transfer Learning with a Unified Text-to-Text Transformer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Mach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Learn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 21 (2020), 140:1–140:67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [38] Revanth Gangi Reddy, Bhavani Iyer, Md.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Arafat Sultan, Rong Zhang, Avirup Sil,  Vittorio Castelli, Radu Florian, and Salim Roukos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Synthetic TargetDomain  Supervision for Open Retrieval QA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In SIGIR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' ACM, 1793–1797.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [39] Kirk Roberts, Tasmeer Alam, Steven Bedrick, Dina Demner-Fushman, Kyle Lo,  Ian Soboroff, Ellen M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Voorhees, Lucy Lu Wang, and William R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Hersh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  TREC-COVID: rationale and structure of an information retrieval shared task  for COVID-19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Am.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Medical Informatics Assoc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 27, 9 (2020), 1431–1436.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [40] Stephen Robertson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Understanding inverse document frequency: on the-  oretical arguments for IDF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Journal of Documentation 60, 5 (2004), 503–520.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='1108/00220410410560582  [41] Adriana Romero, Nicolas Ballas, Samira Ebrahimi Kahou, Antoine Chassang,  Carlo Gatta, and Yoshua Bengio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' FitNets: Hints for Thin Deep Nets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In  ICLR (Poster).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [42] Guilherme Rosa, Luiz Bonifacio, Vitor Jeronymo, Hugo Abonizio, Marzieh  Fadaee, Roberto Lotufo, and Rodrigo Nogueira.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  In Defense of Cross-  Encoders for Zero-Shot Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='48550/ARXIV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='2212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='06121  [43] Devendra Singh Sachan, Mike Lewis, Mandar Joshi, Armen Aghajanyan, Wen-  tau Yih, Joelle Pineau, and Luke Zettlemoyer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Improving Passage Retrieval  with Zero-Shot Question Generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' CoRR abs/2204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='07496 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [44] Teven Le Scao, Angela Fan, Christopher Akiki, Ellie Pavlick, Suzana Ilic, Daniel  Hesslow, Roman Castagné, Alexandra Sasha Luccioni, François Yvon, Matthias  Gallé, Jonathan Tow, Alexander M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Rush,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Stella Biderman,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Albert Webson,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Pawan Sasanka Ammanamanchi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Thomas Wang,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Benoît Sagot,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Niklas Muen-  nighoff,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Albert Villanova del Moral,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Olatunji Ruwase,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Rachel Bawden,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Stas Bek-  man,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Angelina McMillan-Major,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Iz Beltagy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Huu Nguyen,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Lucile Saulnier,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Sam-  son Tan,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Pedro Ortiz Suarez,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Victor Sanh,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Hugo Laurençon,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Yacine Jernite,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Julien  Launay,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='MargaretMitchell,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Colin Raffel,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Aaron Gokaslan,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Adi Simhi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Aitor Soroa,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Alham Fikri Aji,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Amit Alfassy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Anna Rogers,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Ariel Kreisberg Nitzav,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Canwen  Xu,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Chenghao Mou,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Chris Emezue,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Christopher Klamm,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Colin Leong,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Daniel  van Strien,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' David Ifeoluwa Adelani,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' and et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' BLOOM: A 176B-Parameter  Open-Access Multilingual Language Model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' CoRR abs/2211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='05100 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [45] Leslie N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Smith.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Cyclical Learning Rates for Training Neural Networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In  WACV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 464–472.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [46] Yu Sun, Shuohuan Wang, Yu-Kun Li, Shikun Feng, Hao Tian, Hua Wu, and  Haifeng Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' ERNIE 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='0: A Continual Pre-Training Framework for Lan-  guage Understanding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In AAAI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' AAAI Press, 8968–8975.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [47] Nandan Thakur, Nils Reimers, Andreas Rücklé, Abhishek Srivastava, and Iryna  Gurevych.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' BEIR: A Heterogenous Benchmark for Zero-shot Evaluation of  Information Retrieval Models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' arXiv preprint arXiv:2104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='08663 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [48] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones,  Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Attention is All you  Need.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In NIPS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 5998–6008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [49] Ellen Voorhees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Overview of the TREC 2004 Robust Retrieval Track.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In  TREC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [50] Ben  Wang  and  Aran  Komatsuzaki.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  GPT-J-6B:  A  6  Billion  Parameter  Autoregressive  Language  Model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='com/kingoflolz/mesh-transformer-jax.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [51] Kexin Wang, Nandan Thakur, Nils Reimers, and Iryna Gurevych.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' GPL:  Generative Pseudo Labeling for Unsupervised Domain Adaptation of Dense Re-  trieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In NAACL-HLT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Association for Computational Linguistics, 2345–2360.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [52] Lidan Wang, Jimmy Lin, and Donald Metzler.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' A cascade ranking model  for efficient ranked retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In SIGIR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' ACM, 105–114.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [53] Wenhui Wang, Furu Wei, Li Dong, Hangbo Bao, Nan Yang, and Ming Zhou.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  MiniLM: Deep Self-Attention Distillation for Task-Agnostic Compression of Pre-  Trained Transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In NeurIPS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  [54] Thomas Wolf, Lysandre Debut, Victor Sanh, Julien Chaumond, Clement  Delangue, Anthony  Moi, Pierric Cistac, Tim Rault, Remi Louf, Mor-  gan Funtowicz, Joe Davison, Sam Shleifer, Patrick von Platen, Clara Ma,  Yacine Jernite, Julien Plu, Canwen Xu, Teven Le Scao, Sylvain Gugger,  Mariama Drame, Quentin Lhoest, and Alexander Rush.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  Transform-  ers: State-of-the-Art Natural Language Processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' In Proceedings of the  2020 Conference on Empirical Methods in Natural Language Processing: Sys-  tem Demonstrations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content=' Association for Computational Linguistics, Online, 38–45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='18653/v1/2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='emnlp-demos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
+page_content='6' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE1T4oBgHgl3EQfNQMV/content/2301.02998v1.pdf'}
diff --git a/l9E2T4oBgHgl3EQfywj-/content/tmp_files/2301.04125v1.pdf.txt b/l9E2T4oBgHgl3EQfywj-/content/tmp_files/2301.04125v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..26821437047dc15c10c5f08f063e74737c8c7030
--- /dev/null
+++ b/l9E2T4oBgHgl3EQfywj-/content/tmp_files/2301.04125v1.pdf.txt
@@ -0,0 +1,637 @@
+arXiv:2301.04125v1  [hep-th]  10 Jan 2023
+Electric field-based quantization of the gauge invariant Proca theory
+Bogdan Damski
+Jagiellonian University, Institute of Theoretical Physics, �Lojasiewicza 11, 30-348 Krak´ow, Poland
+We consider the gauge invariant version of the Proca theory, where besides the real vector field
+there is also the real scalar field. We quantize the theory such that the commutator of the scalar field
+operator and the electric field operator is given by a predefined three-dimensional vector field, say E
+up to a global prefactor. This happens when the field operators of the gauge invariant Proca theory
+satisfy the proper gauge constraint. In particular, we show that E given by the classical Coulomb
+field leads to the Coulomb gauge constraint making the vector field operator divergenceless. We also
+show that physically unreadable gauge constraints can have a strikingly simple E-representation in
+our formalism. This leads to the discussion of Debye, Yukawa, etc. gauges. In general terms, we
+explore the mapping between classical vector fields and gauge constraints imposed on the operators
+of the studied theory.
+I.
+INTRODUCTION
+The Proca theory delivers the simplest relativistic de-
+scription of massive vector bosons [1, 2]. As a result of
+that, it is of both phenomenological and theoretical in-
+terest.
+In the phenomenological context, it captures some
+properties of ρ and ω mesons and the particles medi-
+ating weak interactions, W and Z bosons [1]. In addi-
+tion to that, it is regarded as a promising extension of
+Maxwell’s electrodynamics, the one taking into account
+the possibility that the photon may not be a massless
+particle after all. Thereby various upper bounds on the
+photon mass are obtained by comparing the predictions
+of the Proca theory to actual experimental data (see e.g.
+[2, 3] extensively discussing this physically rich topic). In
+the theoretical context, which is of main interest in this
+work, the Proca theory provides an elegant framework
+for the examination of various issues associated with the
+quantization of vector fields (see e.g. [1, 4, 5]).
+We are interested in the Proca theory of the real vector
+field. Its classical Lagrangian density can be written as
+L = −1
+4 (∂µVν − ∂νVµ)2 + m2
+2 (Vµ)2 ,
+(1)
+where V µ is the vector field and m is the mass of spin-1
+particles described by this theory after its quantization
+(see Appendix for our conventions).
+The important thing now is that theory (1) is mani-
+festly non-invariant with respect to the gauge transfor-
+mation. In fact, it is a gauge-fixed theory in the sense
+that field equations impose the Lorenz gauge constraint
+onto the vector field. This state of affairs can be easily
+changed by the replacement
+Vµ → Aµ + 1
+e∂µG,
+(2)
+where the vector field Aµ and the real scalar field G
+are supposed to simultaneously change under the gauge
+transformation. Namely,
+Aµ → Aµ + ∂µf, G → G − ef,
+(3)
+where f is a smooth real function of space-time coordi-
+nates and e is the unit of the electric charge.
+Imposing (2) on (1), we see that the resulting La-
+grangian density,
+L′ = −1
+4 (∂µAν − ∂νAµ)2 + m2
+2
+�
+Aµ + 1
+e∂µG
+�2
+,
+(4)
+is unaffected by the gauge transformation. For this rea-
+son, we will refer to the theory defined by (4) as the
+gauge invariant (GI) Proca theory. Such a theory was
+studied before, see e.g. [6, 7], and it bears similarity to
+the Stueckelberg theory, which is reviewed in [8].
+To proceed with the discussion of the GI Proca the-
+ory, one has to choose a gauge because the vector field
+is no longer Lorenz gauge fixed in (4). Besides the stan-
+dard Coulomb gauge choice, which was e.g. enforced with
+the Lagrange multiplier technique in [6], the following in-
+triguing gauge constraint was introduced in [7]
+e∇·AD = m2GD.
+(5)
+It was labelled as the Coulomb gauge choice [7], but the
+rationale behind such a name was not provided. We be-
+lieve that a proper name for such a gauge could be the
+Debye gauge, which will be carefully explained in this
+work. Anticipating this discussion, we have labelled the
+fields subjected to such a constraint with the appropri-
+ate subscript. Their quantization was studied in [7] by
+means of the Faddeev-Jackiw approach [9].
+Our goal is to develop and discuss the quantization for-
+malism, where gauge choices are labelled by the classical
+vector field E, which determines the commutator of the
+scalar and electric field operators. Thereby, we explore
+the mapping between such E and the field operators of
+the GI Proca theory.
+The outline of this paper is the following. The concise
+summary of basic results concerning the Proca theory is
+provided in Sec. II. Next, our quantization procedure is
+introduced in Sec. III. Its features are then discussed in
+Sec. IV, where the electric field context of the proposed
+approach is laid out along with several illustrative exam-
+ples. Finally, the summary of our work is presented in
+Sec. V, which is followed by Appendix listing our con-
+ventions.
+
+2
+II.
+BASICS
+We state below basic results concerning theories (1)
+and (4).
+To begin, the independent variables of Proca theory
+(1) are fields V i and their canonical conjugates
+πi = ∂iV0 − ∂0Vi.
+(6)
+Such a theory is canonically quantized by demanding that
+[1, 4, 5]
+[V i(t, x), πj(t, y)] = −iδijδ(y − x),
+(7)
+[V i(t, x), V j(t, y)] = [πi(t, x), πj(t, y)] = 0.
+(8)
+We note that
+V 0 = − 1
+m2 ∇·π,
+(9)
+which explains why V 0 is the dependent variable of the-
+ory (1). We also note that the canonical conjugate of V 0
+vanishes.
+Then, we remark that the variables of GI Proca theory
+(4), whose quantization will be discussed in Sec. III, are
+fields Ai and G as well as their canonical conjugates
+∂iA0 − ∂0Ai = πi
+(10)
+and
+˜π = m2
+e
+�
+A0 + 1
+e∂0G
+�
+= m2
+e V0,
+(11)
+respectively. We note that the right-hand sides of (10)
+and (11) follow from mapping (2), which we assume in
+this work.
+Finally, we have a few observations about π and ˜π.
+First, (9) and (11) imply that π and ˜π are linked via the
+field constraint [10]
+∇·π = −e˜π.
+(12)
+Second, π and ˜π are gauge invariant. This means that
+unlike A and G, they will not be equipped with a gauge-
+specific subscript below. Third, the physical content of
+π, and so also of ˜π due to (12), is best seen from the
+fact that π = E, where E = −∂0V − ∇V 0 = −∂0A −
+∇A0 is the electric field operator. Note that we use the
+same “electric field” terminology as in the theory of the
+massless electromagnetic field.
+III.
+GAUGE ANSATZ AND COMMUTATION
+RELATIONS
+We are interested in quantization of theory (4). In a
+nutshell, one may approach this problem in the following
+way.
+To begin, one chooses the gauge constraint for the
+fields.
+For example, one may decide to work in the
+Coulomb gauge
+∇·AC = 0,
+(13)
+where the subscript indicates the gauge choice. Natu-
+rally, there are uncountably many other gauge choices,
+see e.g. (5), whose implications are not so obvious.
+Then, one figures out commutation relations between
+the fields and their canonical conjugates, which is a non-
+trivial task. Indeed, as they have to be consistent with
+the chosen gauge constraint, they are expected to differ
+from the canonical commutation relations.
+We approach quantization of theory (4) somewhat dif-
+ferently. Namely, instead of imposing the specific gauge
+constraint in the form of the equation for the vector and
+scalar field operators, we require that
+GE(t, x) = e
+�
+d3z V (t, z) · E(z − x),
+(14a)
+AE = V + 1
+e∇GE,
+(14b)
+where E is a time-independent
+R3-valued vector field and
+the appropriate subscript has been added to the fields to
+indicate their dependence on E. Equation (14a) can be
+seen as the ansatz, whereas equation (14b) expresses the
+fact that we rely on mapping (2), which also leads to
+A0
+E =
+e
+m2 ˜π − 1
+e∂0GE.
+(15)
+All together, we will refer to (14) as the gauge ansatz.
+The field E, whose physical meaning will be discussed
+in Sec. IV, defines the gauge in our formalism. In fact, it
+is easy to see that under E → E′, GE and AE transform
+just as G and A in (3) with
+f(t, x) =
+�
+d3z V (t, z) · [E(z − x) − E′(z − x)].
+(16)
+This time, however, f is operator-valued. This is inter-
+esting because classical, i.e. c-number, gauge transfor-
+mations are typically discussed in the context of gauge
+theories (see e.g. Sec. 2.5.2 of [11] for relevant remarks).
+We are now ready to discuss equal-time commutators
+between the canonically-related operators introduced in
+Sec. II. The non-trivial ones are
+[GE(t, x), ˜π(t, y)] = i ∇·E(y − x),
+(17)
+[Ai
+E(t, x), ˜π(t, y)] = i
+e∂y
+i [δ(y − x) − ∇·E(y − x)], (18)
+[GE(t, x), πj(t, y)] = −ieEj(y − x),
+(19)
+[Ai
+E(t, x), πj(t, y)] = −iδijδ(y − x) + i∂y
+i Ej(y − x),
+(20)
+where ∂y
+i = ∂/∂yi. These expressions trigger the follow-
+ing comments.
+
+3
+First, in order to verify these commutators, one can
+replace GE and Ai
+E in (17)–(20) with (14) and then use
+(7) to simplify the resulting expressions. Similarly, one
+may verify with the help of (8) that the remaining equal-
+time commutators between GE, AE, π, and ˜π identically
+vanish.
+Second, we find these commutators remarkably com-
+pact and general. As expected, they do differ from canon-
+ical commutation relations: (17) is not equal to iδ(y−x),
+(20) is not equal to −iδijδ(y−x), and (18) as well as (19)
+do not vanish. The structure of (17)–(20) stems from the
+restrictions imposed by field constraint (12) and gauge
+ansatz (14); see Sec.
+IV C for additional relevant re-
+marks. In particular, one may easily notice that (17) and
+(19) are interrelated via (12). The same remark applies
+to (18) and (20).
+Third, we have independently verified the above results
+in the two already introduced gauges, (5) and (13), where
+E is given by (29) evaluated for M = m and (27), respec-
+tively. We have done it via the Dirac bracket quantization
+technique adopted so as to enforce gauge constraints (5)
+and (13) (see [5] for the textbook introduction to such a
+quantization approach and Sec. IV A for the explanation
+of the above-listed choices of E).
+IV.
+ELECTRIC FIELD PERSPECTIVE ON
+GAUGE ANSATZ
+The quantum GI Proca theory is built of the vector
+field AE and the scalar field GE. The role of AE is clear:
+the electric and magnetic field operators are expressed in
+terms of AE and so in such a sense this operator captures
+physics of the electromagnetic field. The question now
+is what is the role of GE? At first sight, it seems that
+the only role of GE is to enforce the gauge invariance of
+the Lagrangian density. However, by looking at commu-
+tator (19), we realize that GE also plays the role of the
+generator of the local shift of the electric field operator.
+To explain what we mean by saying so, we note that by
+combining (19) with the following well-known identity
+exp(X)Y exp(−X)
+= Y + [X, Y ] + 1
+2![X, [X, Y ]] + · · · ,
+(21)
+it can be formally shown that
+exp [iGE(t, x)] E(t, y) exp [−iGE(t, x)]
+= E(t, y) + eE(y − x).
+(22)
+As both (19) and (22) particularly clearly expose the
+electric field context of E, we see the quantization proce-
+dure based on (14) as the electric field-based quantization
+scheme. Two remarks are in order now.
+First, we use the term formal when we refer to
+(22) because we do not actually inquire if the operator
+exp[±iGE(t, x)] is well-defined. Second, we note that in
+the spirit of the Helmholtz theorem [12], one may con-
+sider the following decomposition of E
+E = −∇ΦE + ∇ × FE,
+(23)
+where ΦE and FE are classical time-independent scalar
+and vector fields, respectively. Formula (23) will guide
+our subsequent discussion.
+A.
+Curl-free E
+We study here gauges induced by
+E = −∇ΦE,
+(24)
+where ΦE is real-valued.
+To begin, we address the question of what is the rela-
+tion between GE and AE when (24) holds. After standard
+manipulations based on gauge ansatz (14), we find that
+e∇·AE = fE(−i∇)GE + ∆GE,
+(25)
+where fE is defined via
+ΦE(r) =
+�
+d3k
+(2π)3
+exp(−ik · r)
+fE(k)
+(26)
+and fE(k) = f ∗
+E(−k) to ensure the real value of the above
+integral. We will refer to (25) as the gauge constraint to
+distinguish it from field constraint (12) and gauge ansatz
+(14). The formal character of (25) will be commented
+upon in Sec. V. We are now ready to discuss the previ-
+ously mentioned Coulomb and Debye gauges.
+We say that E induces the Coulomb gauge when
+E = −∇ΦC, ΦC =
+1
+4πr ,
+(27)
+where ∇ = (∂/∂ri) and r = |r|.
+Such a terminology
+is supported by two observations.
+First, it is natural
+in our formalism because such E is given by the nega-
+tive gradient of the Coulomb potential originating from
+the unit charge. Second, a simple calculation shows that
+fE(−i∇) = −∆ here, which leads to the divergenceless
+vector field via (25). Properly labeling the fields, we have
+(GC, AC) = (GE, AE) for E = −∇ΦC,
+(28)
+where the vector field satisfies gauge constraint (13) in
+the traditional nomenclature.
+In full analogy to the above reasoning, the gauge in-
+duced by
+E = −∇ΦD, ΦD = exp(−Mr)
+4πr
+(29)
+will be called the Debye gauge (M > 0). We have pro-
+posed this name because such E is given by the negative
+gradient of the Debye potential describing the screening
+of the unit charge in plasmas and electrolytes.
+
+4
+As far as the relation between GE and AE is concerned,
+we find fE(−i∇) = −∆+ M 2 in the Debye gauge. Then,
+it follows from (25) that the fields in such a gauge satisfy
+e∇·AD = M 2GD.
+(30)
+Note that previously stated gauge constraint (5) is the
+M = m version of (30).
+Next, we observe that the gauge constraint satisfied by
+the fields non-trivially depends on the magnitude and the
+direction of E (the magnitude and the sign of ΦE). This
+can be illustrated by the introduction of the following
+two gauges.
+We define the primed Coulomb gauge by saying that
+it is induced in our formalism by
+E = −∇ΦC′, ΦC′ = βΦC =
+β
+4πr,
+(31)
+where β > 0. The sensitivity of the gauge constraint to
+the change of the magnitude of E is now seen by com-
+paring (13) to
+e∇·AC′ = β − 1
+β
+∆GC′,
+(32)
+which is satisfied by the fields in the primed Coulomb
+gauge.
+Furthermore, we consider the gauge induced by
+E = −∇ΦY , ΦY = −ΦD = −exp(−Mr)
+4πr
+,
+(33)
+where the subscript refers to the fact that such E is given
+by the negative gradient of the Yukawa potential ob-
+tained for the unit strength of the inter-nucleon inter-
+actions. The fields in so defined Yukawa gauge satisfy
+e∇·AY = 2∆GY − M 2GY .
+(34)
+The difference between (30) and (34) illustrates the sen-
+sitivity of the gauge constraint to the global change of
+the direction of E.
+Moving on, we note that new gauges can be obtained
+by superposing fields E.
+For fields E given by (24),
+this typically leads to the complicated relation between
+GE and AE due to the reciprocal additivity law for fE.
+Namely, if
+E = −∇ΦE′ − ∇ΦE′′ − · · · ,
+(35)
+then
+1
+fE
+=
+1
+fE′ +
+1
+fE′′ + · · · .
+(36)
+This can be illustrated by the consideration of the
+Coulomb-Yukawa gauge, which we define as the gauge
+induced by
+E = −∇ΦC − ∇ΦY = −∇
+� 1
+4πr − exp(−Mr)
+4πr
+�
+. (37)
+A quick calculation shows that in this case fE(−i∇) =
+(∆/M)2 − ∆, which results in
+e∇·ACY =
+1
+M 2 ∆(∆GCY ).
+(38)
+Note that such a gauge constraint resembles neither (13)
+nor (34) despite the fact that it is induced by the su-
+perposition of the fields E leading to the Coulomb and
+Yukawa gauges. This is the consequence of the fact that
+fE ̸= fE′ + fE′′ + · · · when (35) holds. We mention in
+passing that the M = m version of the operator GCY was
+used in [13] to construct the finite-energy charged state
+in Proca theory (1).
+Finally, we note the trivial possibility of choosing E =
+0. This sets GE = 0, removing the scalar field from the
+theory. Such a gauge choice is known in the literature as
+the unitary gauge (see e.g. [14]). In our formalism, the
+term null gauge seems to be more appropriate.
+B.
+Divergence-free E
+We briefly comment here upon gauges induced by
+E = ∇ × FE,
+(39)
+where FE is
+R3-valued.
+For a general function FE, we are unsure how to derive
+the closed-form expression for the gauge constraint akin
+to (25). Thus, we focus on the specific results inspired
+by the discussion from Sec. IV A. Namely, we consider
+FE(r) = d
+�
+d3k
+(2π)3
+exp(−ik · r)
+gE(k)
+,
+(40)
+where d ∈
+R3 is the constant vector and gE(k) = g∗
+E(−k).
+It can be then found via (14) that the fields of the
+GI Proca theory satisfy the following formal gauge con-
+straint
+ed · (∇ × AE) = gE(−i∇)GE.
+(41)
+To see how all this works in practice, one may choose
+FE to be given by
+d β
+4πr , ±dexp(−Mr)
+4πr
+, d
+� 1
+4πr − exp(−Mr)
+4πr
+�
+.
+(42)
+From the results presented in Sec. IV A, it is clear that
+these choices lead to gE(−i∇) equal to
+− 1
+β ∆, ±(−∆ + M 2), (∆/M)2 − ∆,
+(43)
+respectively.
+The corresponding gauge constraints are
+obtained by combining (41) with (43), the E fields asso-
+ciated with them are given by the curl of the vector fields
+listed in (42).
+
+5
+C.
+Gauge constraints vs. commutation relations
+Let’s consider a gauge constraint written in the form
+Υ = 0.
+We will say that it is consistent with equal-
+time commutation relations, written for the fields be-
+longing to some set X, when [Υ(t, x), X(t, y)] = 0 for
+all X ∈ X.
+For example, the consistency of gauge
+constraint (30) with commutation relations (17)–(20)
+requires [e∇·AD(t, x) − M 2GD(t, x), X(t, y)] = 0 for
+X = GD, AD, π, ˜π.
+We note that it can be easily verified that gauge con-
+straints (13), (30), (32), (34), and (38) are consistent with
+commutation relations (17)–(20). It goes without saying
+that this happens when the right-hand sides of (17)–(20)
+are evaluated with the corresponding fields E: (27), (29),
+(31), (33), and (37), respectively. For a general curl-free
+E given by (24), it can be formally shown that gauge
+constraint (25) is consistent with (17)–(20).
+We also note that similar self-consistency checks can
+be performed for the divergence-free E discussed in Sec.
+IV B. Namely, it can be shown that (41) is formally con-
+sistent with (17)–(20) when (40) holds, which can be also
+individually verified for the specific cases listed in (42).
+V.
+SUMMARY
+We have discussed how GI Proca theory (4) can be
+quantized with the help of gauge ansatz (14). Such an
+ansatz is parameterized by the classical vector field E,
+which determines the commutator of the scalar field op-
+erator and the electric field operator (19).
+In several special cases, we have found an explicit map-
+ping between the field E and the gauge constraint satis-
+fied by the fields of the GI Proca theory. In particular,
+we have discussed the mapping
+E = −∇
+� 1
+4πr
+�
+�→ ∇·AC = 0,
+(44)
+which gives a new meaning to the term Coulomb gauge,
+a very suggestive one in our opinion. While discussing
+other cases, we have found that unreadable gauge con-
+straints can have a strikingly simple E-representation in
+our formalism, which we find remarkable.
+One of the
+simplest illustrations supporting such an observation is
+the following
+E = −∇
+�exp(−Mr)
+4πr
+�
+�→ e∇·AD = M 2GD,
+(45)
+which defines the Debye gauge in our nomenclature. Fur-
+ther support for the above observation is provided by
+comparing gauge constraints (32), (34), and (38) to the
+fields E associated with them (31), (33), and (37), re-
+spectively. We note that, to the best of our knowledge,
+none of these three gauge constraints has been previ-
+ously mentioned in the literature.
+We also note that
+another batch of unusual gauge constraints, having sim-
+ple E-representation, can be obtained by combining (41)
+with (43).
+In a more general context, we have proposed the re-
+lation between curl-free E given by (24) and the gauge
+constraint satisfied by the fields of the GI Proca theory
+(25).
+Such a result has a formal character because it
+involves the pseudo-differential operator fE(−i∇), where
+the function fE can be in general non-analytic or singular
+for well-defined E. If such complications are present, then
+there is the question of what (25) really means. These
+somewhat intriguing ambiguities do not affect our gauge
+ansatz-based considerations (14), which do not rely on
+the form of the gauge constraint satisfied by the fields.
+Similar remarks apply to formal result (41), which has
+been obtained for the particular class of divergence-free
+E.
+Finally, we would like to emphasize the efficiency of the
+discussed formalism. Indeed, our quantization procedure
+is carried out all at once for different gauges labelled by
+E. In particular, this is well illustrated by the general
+character of commutation relations (17)–(20).
+ACKNOWLEDGMENTS
+These studies have been supported by the Pol-
+ish
+National
+Science
+Centre
+(NCN)
+Grant
+No.
+2019/35/B/ST2/00034.
+APPENDIX: CONVENTIONS
+We adopt the Heaviside-Lorentz system of units in its
+ℏ = c = 1 version. Greek and Latin indices of tensors
+take values 0, 1, 2, 3 and 1, 2, 3, respectively. The metric
+signature is (+ − −−).
+3-vectors are written in bold,
+e.g. x = (xµ) = (x0, x). We use the Einstein summation
+convention, (Xµ···)2 = Xµ···Xµ···, and ∆ = ∇ · ∇. The
+complex conjugation is denoted as ∗.
+[1] R.
+Greiner
+and
+J.
+Reinhardt,
+Field
+Quantization
+(Springer-Verlag, 1996).
+[2] A. S. Goldhaber and M. M. Nieto, Rev. Mod. Phys. 82,
+939 (2010).
+[3] L.-C. Tu, J. Luo, and G. T. Gillies, Rep. Prog. Phys. 68,
+77 (2005).
+[4] B. G.-g. Chen, D. Derbes, D. Griffiths, B. Hill, R. Sohn,
+and Y.-S. Ting, Lectures of Sidney Coleman on Quantum
+Field Theory (World Scientific, 2018).
+[5] S. Weinberg, The Quantum Theory of Fields, vol. I: Foun-
+
+6
+dations (Cambridge University Press, 2010).
+[6] G. S. Guralnik, C. R. Hagen, and T. W. B. Kibble, Adv.
+Part. Phys. 2, 567 (1968).
+[7] B. M. Pimentel and G. E. R. Zambrano, Nucl. Part. Phys.
+Proc. 267-269, 183 (2015).
+[8] H. Ruegg and M. Ruiz-Altaba, Int. J. Mod. Phys. A 19,
+3265 (2004).
+[9] L. Faddeev and R. Jackiw, Phys. Rev. Lett. 60, 1692
+(1988).
+[10] We call (12) the field constraint because it follows from
+the field equations of the Proca theory.
+[11] E. Leader and C. Lorc´e, Phys. Rep. 541, 163 (2014).
+[12] D. J. Griffiths, Introduction to Electrodynamics (Cam-
+bridge University Press, 2017).
+[13] B. Damski, arXiv:2212.01951.
+[14] A. Das, Lectures on Quantum Field Theory (World Sci-
+entific, 2008). We note that gauge invariant Proca theory
+(4) is called the Stueckelberg theory in this textbook. A
+bit different definition of the Stueckelberg theory is pre-
+sented in review [8], which explains why we do not refer
+to (4) as the Stueckelberg theory.
+
diff --git a/l9E2T4oBgHgl3EQfywj-/content/tmp_files/load_file.txt b/l9E2T4oBgHgl3EQfywj-/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ab9b94a44fe38f5baa6c659ccd89635348184ccd
--- /dev/null
+++ b/l9E2T4oBgHgl3EQfywj-/content/tmp_files/load_file.txt
@@ -0,0 +1,293 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf,len=292
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='04125v1  [hep-th]  10 Jan 2023  Electric field-based quantization of the gauge invariant Proca theory  Bogdan Damski  Jagiellonian University, Institute of Theoretical Physics, �Lojasiewicza 11, 30-348 Krak´ow, Poland  We consider the gauge invariant version of the Proca theory, where besides the real vector field  there is also the real scalar field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' We quantize the theory such that the commutator of the scalar field  operator and the electric field operator is given by a predefined three-dimensional vector field, say E  up to a global prefactor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' This happens when the field operators of the gauge invariant Proca theory  satisfy the proper gauge constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' In particular, we show that E given by the classical Coulomb  field leads to the Coulomb gauge constraint making the vector field operator divergenceless.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' We also  show that physically unreadable gauge constraints can have a strikingly simple E-representation in  our formalism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' This leads to the discussion of Debye, Yukawa, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' gauges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' In general terms, we  explore the mapping between classical vector fields and gauge constraints imposed on the operators  of the studied theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  INTRODUCTION  The Proca theory delivers the simplest relativistic de-  scription of massive vector bosons [1, 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' As a result of  that, it is of both phenomenological and theoretical in-  terest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  In the phenomenological context, it captures some  properties of ρ and ω mesons and the particles medi-  ating weak interactions, W and Z bosons [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' In addi-  tion to that, it is regarded as a promising extension of  Maxwell’s electrodynamics, the one taking into account  the possibility that the photon may not be a massless  particle after all.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Thereby various upper bounds on the  photon mass are obtained by comparing the predictions  of the Proca theory to actual experimental data (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  [2, 3] extensively discussing this physically rich topic).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' In  the theoretical context, which is of main interest in this  work, the Proca theory provides an elegant framework  for the examination of various issues associated with the  quantization of vector fields (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' [1, 4, 5]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  We are interested in the Proca theory of the real vector  field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Its classical Lagrangian density can be written as  L = −1  4 (∂µVν − ∂νVµ)2 + m2  2 (Vµ)2 ,  (1)  where V µ is the vector field and m is the mass of spin-1  particles described by this theory after its quantization  (see Appendix for our conventions).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  The important thing now is that theory (1) is mani-  festly non-invariant with respect to the gauge transfor-  mation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' In fact, it is a gauge-fixed theory in the sense  that field equations impose the Lorenz gauge constraint  onto the vector field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' This state of affairs can be easily  changed by the replacement  Vµ → Aµ + 1  e∂µG,  (2)  where the vector field Aµ and the real scalar field G  are supposed to simultaneously change under the gauge  transformation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Namely,  Aµ → Aµ + ∂µf, G → G − ef,  (3)  where f is a smooth real function of space-time coordi-  nates and e is the unit of the electric charge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  Imposing (2) on (1), we see that the resulting La-  grangian density,  L′ = −1  4 (∂µAν − ∂νAµ)2 + m2  2  �  Aµ + 1  e∂µG  �2  ,  (4)  is unaffected by the gauge transformation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' For this rea-  son, we will refer to the theory defined by (4) as the  gauge invariant (GI) Proca theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Such a theory was  studied before, see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' [6, 7], and it bears similarity to  the Stueckelberg theory, which is reviewed in [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  To proceed with the discussion of the GI Proca the-  ory, one has to choose a gauge because the vector field  is no longer Lorenz gauge fixed in (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Besides the stan-  dard Coulomb gauge choice, which was e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' enforced with  the Lagrange multiplier technique in [6], the following in-  triguing gauge constraint was introduced in [7]  e∇·AD = m2GD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  (5)  It was labelled as the Coulomb gauge choice [7], but the  rationale behind such a name was not provided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' We be-  lieve that a proper name for such a gauge could be the  Debye gauge, which will be carefully explained in this  work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Anticipating this discussion, we have labelled the  fields subjected to such a constraint with the appropri-  ate subscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Their quantization was studied in [7] by  means of the Faddeev-Jackiw approach [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  Our goal is to develop and discuss the quantization for-  malism, where gauge choices are labelled by the classical  vector field E, which determines the commutator of the  scalar and electric field operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Thereby, we explore  the mapping between such E and the field operators of  the GI Proca theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  The outline of this paper is the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' The concise  summary of basic results concerning the Proca theory is  provided in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Next, our quantization procedure is  introduced in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Its features are then discussed in  Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' IV, where the electric field context of the proposed  approach is laid out along with several illustrative exam-  ples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Finally, the summary of our work is presented in  Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' V, which is followed by Appendix listing our con-  ventions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  2  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  BASICS  We state below basic results concerning theories (1)  and (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  To begin, the independent variables of Proca theory  (1) are fields V i and their canonical conjugates  πi = ∂iV0 − ∂0Vi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  (6)  Such a theory is canonically quantized by demanding that  [1, 4, 5]  [V i(t, x), πj(t, y)] = −iδijδ(y − x),  (7)  [V i(t, x), V j(t, y)] = [πi(t, x), πj(t, y)] = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  (8)  We note that  V 0 = − 1  m2 ∇·π,  (9)  which explains why V 0 is the dependent variable of the-  ory (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' We also note that the canonical conjugate of V 0  vanishes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  Then, we remark that the variables of GI Proca theory  (4), whose quantization will be discussed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' III, are  fields Ai and G as well as their canonical conjugates  ∂iA0 − ∂0Ai = πi  (10)  and  ˜π = m2  e  �  A0 + 1  e∂0G  �  = m2  e V0,  (11)  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' We note that the right-hand sides of (10)  and (11) follow from mapping (2), which we assume in  this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  Finally, we have a few observations about π and ˜π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  First, (9) and (11) imply that π and ˜π are linked via the  field constraint [10]  ∇·π = −e˜π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  (12)  Second, π and ˜π are gauge invariant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' This means that  unlike A and G, they will not be equipped with a gauge-  specific subscript below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Third, the physical content of  π, and so also of ˜π due to (12), is best seen from the  fact that π = E, where E = −∂0V − ∇V 0 = −∂0A −  ∇A0 is the electric field operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Note that we use the  same “electric field” terminology as in the theory of the  massless electromagnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  GAUGE ANSATZ AND COMMUTATION  RELATIONS  We are interested in quantization of theory (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' In a  nutshell, one may approach this problem in the following  way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  To begin, one chooses the gauge constraint for the  fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  For example, one may decide to work in the  Coulomb gauge  ∇·AC = 0,  (13)  where the subscript indicates the gauge choice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Natu-  rally, there are uncountably many other gauge choices,  see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' (5), whose implications are not so obvious.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  Then, one figures out commutation relations between  the fields and their canonical conjugates, which is a non-  trivial task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Indeed, as they have to be consistent with  the chosen gauge constraint, they are expected to differ  from the canonical commutation relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  We approach quantization of theory (4) somewhat dif-  ferently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Namely, instead of imposing the specific gauge  constraint in the form of the equation for the vector and  scalar field operators, we require that  GE(t, x) = e  �  d3z V (t, z) · E(z − x),  (14a)  AE = V + 1  e∇GE,  (14b)  where E is a time-independent  R3-valued vector field and  the appropriate subscript has been added to the fields to  indicate their dependence on E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Equation (14a) can be  seen as the ansatz, whereas equation (14b) expresses the  fact that we rely on mapping (2), which also leads to  A0  E =  e  m2 ˜π − 1  e∂0GE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  (15)  All together, we will refer to (14) as the gauge ansatz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  The field E, whose physical meaning will be discussed  in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' IV, defines the gauge in our formalism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' In fact, it  is easy to see that under E → E′, GE and AE transform  just as G and A in (3) with  f(t, x) =  �  d3z V (t, z) · [E(z − x) − E′(z − x)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  (16)  This time, however, f is operator-valued.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' This is inter-  esting because classical, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' c-number, gauge transfor-  mations are typically discussed in the context of gauge  theories (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='2 of [11] for relevant remarks).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  We are now ready to discuss equal-time commutators  between the canonically-related operators introduced in  Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' The non-trivial ones are  [GE(t, x), ˜π(t, y)] = i ∇·E(y − x),  (17)  [Ai  E(t, x), ˜π(t, y)] = i  e∂y  i [δ(y − x) − ∇·E(y − x)], (18)  [GE(t, x), πj(t, y)] = −ieEj(y − x),  (19)  [Ai  E(t, x), πj(t, y)] = −iδijδ(y − x) + i∂y  i Ej(y − x),  (20)  where ∂y  i = ∂/∂yi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' These expressions trigger the follow-  ing comments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  3  First, in order to verify these commutators, one can  replace GE and Ai  E in (17)–(20) with (14) and then use  (7) to simplify the resulting expressions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Similarly, one  may verify with the help of (8) that the remaining equal-  time commutators between GE, AE, π, and ˜π identically  vanish.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  Second, we find these commutators remarkably com-  pact and general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' As expected, they do differ from canon-  ical commutation relations: (17) is not equal to iδ(y−x),  (20) is not equal to −iδijδ(y−x), and (18) as well as (19)  do not vanish.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' The structure of (17)–(20) stems from the  restrictions imposed by field constraint (12) and gauge  ansatz (14);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  IV C for additional relevant re-  marks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' In particular, one may easily notice that (17) and  (19) are interrelated via (12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' The same remark applies  to (18) and (20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  Third, we have independently verified the above results  in the two already introduced gauges, (5) and (13), where  E is given by (29) evaluated for M = m and (27), respec-  tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' We have done it via the Dirac bracket quantization  technique adopted so as to enforce gauge constraints (5)  and (13) (see [5] for the textbook introduction to such a  quantization approach and Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' IV A for the explanation  of the above-listed choices of E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  ELECTRIC FIELD PERSPECTIVE ON  GAUGE ANSATZ  The quantum GI Proca theory is built of the vector  field AE and the scalar field GE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' The role of AE is clear:  the electric and magnetic field operators are expressed in  terms of AE and so in such a sense this operator captures  physics of the electromagnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' The question now  is what is the role of GE?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' At first sight, it seems that  the only role of GE is to enforce the gauge invariance of  the Lagrangian density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' However, by looking at commu-  tator (19), we realize that GE also plays the role of the  generator of the local shift of the electric field operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  To explain what we mean by saying so, we note that by  combining (19) with the following well-known identity  exp(X)Y exp(−X)  = Y + [X, Y ] + 1  2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' [X, [X, Y ]] + · · · ,  (21)  it can be formally shown that  exp [iGE(t, x)] E(t, y) exp [−iGE(t, x)]  = E(t, y) + eE(y − x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  (22)  As both (19) and (22) particularly clearly expose the  electric field context of E, we see the quantization proce-  dure based on (14) as the electric field-based quantization  scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Two remarks are in order now.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  First, we use the term formal when we refer to  (22) because we do not actually inquire if the operator  exp[±iGE(t, x)] is well-defined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Second, we note that in  the spirit of the Helmholtz theorem [12], one may con-  sider the following decomposition of E  E = −∇ΦE + ∇ × FE,  (23)  where ΦE and FE are classical time-independent scalar  and vector fields, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Formula (23) will guide  our subsequent discussion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  Curl-free E  We study here gauges induced by  E = −∇ΦE,  (24)  where ΦE is real-valued.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  To begin, we address the question of what is the rela-  tion between GE and AE when (24) holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' After standard  manipulations based on gauge ansatz (14), we find that  e∇·AE = fE(−i∇)GE + ∆GE,  (25)  where fE is defined via  ΦE(r) =  �  d3k  (2π)3  exp(−ik · r)  fE(k)  (26)  and fE(k) = f ∗  E(−k) to ensure the real value of the above  integral.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' We will refer to (25) as the gauge constraint to  distinguish it from field constraint (12) and gauge ansatz  (14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' The formal character of (25) will be commented  upon in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' We are now ready to discuss the previ-  ously mentioned Coulomb and Debye gauges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  We say that E induces the Coulomb gauge when  E = −∇ΦC, ΦC =  1  4πr ,  (27)  where ∇ = (∂/∂ri) and r = |r|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  Such a terminology  is supported by two observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  First, it is natural  in our formalism because such E is given by the nega-  tive gradient of the Coulomb potential originating from  the unit charge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Second, a simple calculation shows that  fE(−i∇) = −∆ here, which leads to the divergenceless  vector field via (25).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Properly labeling the fields, we have  (GC, AC) = (GE, AE) for E = −∇ΦC,  (28)  where the vector field satisfies gauge constraint (13) in  the traditional nomenclature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  In full analogy to the above reasoning, the gauge in-  duced by  E = −∇ΦD, ΦD = exp(−Mr)  4πr  (29)  will be called the Debye gauge (M > 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' We have pro-  posed this name because such E is given by the negative  gradient of the Debye potential describing the screening  of the unit charge in plasmas and electrolytes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  4  As far as the relation between GE and AE is concerned,  we find fE(−i∇) = −∆+ M 2 in the Debye gauge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Then,  it follows from (25) that the fields in such a gauge satisfy  e∇·AD = M 2GD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  (30)  Note that previously stated gauge constraint (5) is the  M = m version of (30).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  Next, we observe that the gauge constraint satisfied by  the fields non-trivially depends on the magnitude and the  direction of E (the magnitude and the sign of ΦE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' This  can be illustrated by the introduction of the following  two gauges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  We define the primed Coulomb gauge by saying that  it is induced in our formalism by  E = −∇ΦC′, ΦC′ = βΦC =  β  4πr,  (31)  where β > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' The sensitivity of the gauge constraint to  the change of the magnitude of E is now seen by com-  paring (13) to  e∇·AC′ = β − 1  β  ∆GC′,  (32)  which is satisfied by the fields in the primed Coulomb  gauge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  Furthermore, we consider the gauge induced by  E = −∇ΦY , ΦY = −ΦD = −exp(−Mr)  4πr  ,  (33)  where the subscript refers to the fact that such E is given  by the negative gradient of the Yukawa potential ob-  tained for the unit strength of the inter-nucleon inter-  actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' The fields in so defined Yukawa gauge satisfy  e∇·AY = 2∆GY − M 2GY .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  (34)  The difference between (30) and (34) illustrates the sen-  sitivity of the gauge constraint to the global change of  the direction of E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  Moving on, we note that new gauges can be obtained  by superposing fields E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  For fields E given by (24),  this typically leads to the complicated relation between  GE and AE due to the reciprocal additivity law for fE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  Namely, if  E = −∇ΦE′ − ∇ΦE′′ − · · · ,  (35)  then  1  fE  =  1  fE′ +  1  fE′′ + · · · .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  (36)  This can be illustrated by the consideration of the  Coulomb-Yukawa gauge, which we define as the gauge  induced by  E = −∇ΦC − ∇ΦY = −∇  � 1  4πr − exp(−Mr)  4πr  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' (37)  A quick calculation shows that in this case fE(−i∇) =  (∆/M)2 − ∆, which results in  e∇·ACY =  1  M 2 ∆(∆GCY ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  (38)  Note that such a gauge constraint resembles neither (13)  nor (34) despite the fact that it is induced by the su-  perposition of the fields E leading to the Coulomb and  Yukawa gauges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' This is the consequence of the fact that  fE ̸= fE′ + fE′′ + · · · when (35) holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' We mention in  passing that the M = m version of the operator GCY was  used in [13] to construct the finite-energy charged state  in Proca theory (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  Finally, we note the trivial possibility of choosing E =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' This sets GE = 0, removing the scalar field from the  theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Such a gauge choice is known in the literature as  the unitary gauge (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' [14]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' In our formalism, the  term null gauge seems to be more appropriate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  Divergence-free E  We briefly comment here upon gauges induced by  E = ∇ × FE,  (39)  where FE is  R3-valued.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  For a general function FE, we are unsure how to derive  the closed-form expression for the gauge constraint akin  to (25).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Thus, we focus on the specific results inspired  by the discussion from Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' IV A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Namely, we consider  FE(r) = d  �  d3k  (2π)3  exp(−ik · r)  gE(k)  ,  (40)  where d ∈  R3 is the constant vector and gE(k) = g∗  E(−k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  It can be then found via (14) that the fields of the  GI Proca theory satisfy the following formal gauge con-  straint  ed · (∇ × AE) = gE(−i∇)GE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  (41)  To see how all this works in practice, one may choose  FE to be given by  d β  4πr , ±dexp(−Mr)  4πr  , d  � 1  4πr − exp(−Mr)  4πr  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  (42)  From the results presented in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' IV A, it is clear that  these choices lead to gE(−i∇) equal to  − 1  β ∆, ±(−∆ + M 2), (∆/M)2 − ∆,  (43)  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  The corresponding gauge constraints are  obtained by combining (41) with (43), the E fields asso-  ciated with them are given by the curl of the vector fields  listed in (42).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  5  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  Gauge constraints vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' commutation relations  Let’s consider a gauge constraint written in the form  Υ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  We will say that it is consistent with equal-  time commutation relations, written for the fields be-  longing to some set X, when [Υ(t, x), X(t, y)] = 0 for  all X ∈ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  For example, the consistency of gauge  constraint (30) with commutation relations (17)–(20)  requires [e∇·AD(t, x) − M 2GD(t, x), X(t, y)] = 0 for  X = GD, AD, π, ˜π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  We note that it can be easily verified that gauge con-  straints (13), (30), (32), (34), and (38) are consistent with  commutation relations (17)–(20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' It goes without saying  that this happens when the right-hand sides of (17)–(20)  are evaluated with the corresponding fields E: (27), (29),  (31), (33), and (37), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' For a general curl-free  E given by (24), it can be formally shown that gauge  constraint (25) is consistent with (17)–(20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  We also note that similar self-consistency checks can  be performed for the divergence-free E discussed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  IV B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Namely, it can be shown that (41) is formally con-  sistent with (17)–(20) when (40) holds, which can be also  individually verified for the specific cases listed in (42).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  SUMMARY  We have discussed how GI Proca theory (4) can be  quantized with the help of gauge ansatz (14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Such an  ansatz is parameterized by the classical vector field E,  which determines the commutator of the scalar field op-  erator and the electric field operator (19).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  In several special cases, we have found an explicit map-  ping between the field E and the gauge constraint satis-  fied by the fields of the GI Proca theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' In particular,  we have discussed the mapping  E = −∇  � 1  4πr  �  �→ ∇·AC = 0,  (44)  which gives a new meaning to the term Coulomb gauge,  a very suggestive one in our opinion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' While discussing  other cases, we have found that unreadable gauge con-  straints can have a strikingly simple E-representation in  our formalism, which we find remarkable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  One of the  simplest illustrations supporting such an observation is  the following  E = −∇  �exp(−Mr)  4πr  �  �→ e∇·AD = M 2GD,  (45)  which defines the Debye gauge in our nomenclature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Fur-  ther support for the above observation is provided by  comparing gauge constraints (32), (34), and (38) to the  fields E associated with them (31), (33), and (37), re-  spectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' We note that, to the best of our knowledge,  none of these three gauge constraints has been previ-  ously mentioned in the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  We also note that  another batch of unusual gauge constraints, having sim-  ple E-representation, can be obtained by combining (41)  with (43).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  In a more general context, we have proposed the re-  lation between curl-free E given by (24) and the gauge  constraint satisfied by the fields of the GI Proca theory  (25).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  Such a result has a formal character because it  involves the pseudo-differential operator fE(−i∇), where  the function fE can be in general non-analytic or singular  for well-defined E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' If such complications are present, then  there is the question of what (25) really means.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' These  somewhat intriguing ambiguities do not affect our gauge  ansatz-based considerations (14), which do not rely on  the form of the gauge constraint satisfied by the fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  Similar remarks apply to formal result (41), which has  been obtained for the particular class of divergence-free  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  Finally, we would like to emphasize the efficiency of the  discussed formalism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Indeed, our quantization procedure  is carried out all at once for different gauges labelled by  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' In particular, this is well illustrated by the general  character of commutation relations (17)–(20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  ACKNOWLEDGMENTS  These studies have been supported by the Pol-  ish  National  Science  Centre  (NCN)  Grant  No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  2019/35/B/ST2/00034.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  APPENDIX: CONVENTIONS  We adopt the Heaviside-Lorentz system of units in its  ℏ = c = 1 version.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Greek and Latin indices of tensors  take values 0, 1, 2, 3 and 1, 2, 3, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' The metric  signature is (+ − −−).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  3-vectors are written in bold,  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' x = (xµ) = (x0, x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' We use the Einstein summation  convention, (Xµ···)2 = Xµ···Xµ···, and ∆ = ∇ · ∇.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' The  complex conjugation is denoted as ∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  [1] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  Greiner  and  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  Reinhardt,  Field  Quantization  (Springer-Verlag, 1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  [2] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Goldhaber and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Nieto, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' 82,  939 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  [3] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Tu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Luo, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Gillies, Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' 68,  77 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  [4] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='-g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Chen, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Derbes, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Griffiths, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Hill, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Sohn,  and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Ting, Lectures of Sidney Coleman on Quantum  Field Theory (World Scientific, 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  [5] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Weinberg, The Quantum Theory of Fields, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' I: Foun-  6  dations (Cambridge University Press, 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  [6] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Guralnik, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Hagen, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Kibble, Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  Part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' 2, 567 (1968).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  [7] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Pimentel and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Zambrano, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' 267-269, 183 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  [8] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Ruegg and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Ruiz-Altaba, Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' A 19,  3265 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  [9] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Faddeev and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Jackiw, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' 60, 1692  (1988).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  [10] We call (12) the field constraint because it follows from  the field equations of the Proca theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  [11] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Leader and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Lorc´e, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' 541, 163 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  [12] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Griffiths, Introduction to Electrodynamics (Cam-  bridge University Press, 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  [13] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Damski, arXiv:2212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='01951.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content='  [14] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' Das, Lectures on Quantum Field Theory (World Sci-  entific, 2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' We note that gauge invariant Proca theory  (4) is called the Stueckelberg theory in this textbook.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
+page_content=' A  bit different definition of the Stueckelberg theory is pre-  sented in review [8], which explains why we do not refer  to (4) as the Stueckelberg theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfywj-/content/2301.04125v1.pdf'}
diff --git a/lNE2T4oBgHgl3EQfdwfJ/content/2301.03910v1.pdf b/lNE2T4oBgHgl3EQfdwfJ/content/2301.03910v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..e9c12a02c9958d69dd1e34cd575e0b0b310fbde1
--- /dev/null
+++ b/lNE2T4oBgHgl3EQfdwfJ/content/2301.03910v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:77b624405a410527f44942073693e107414a806b88b078fb362152f1abebdb66
+size 3101461
diff --git a/lNE2T4oBgHgl3EQfdwfJ/vector_store/index.faiss b/lNE2T4oBgHgl3EQfdwfJ/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..ed4613d86ec16a13782a72a59936a22711fb5b89
--- /dev/null
+++ b/lNE2T4oBgHgl3EQfdwfJ/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ec4c918bc54ecdfacfea1b7679739503d6d561ce68a159165dadc9eb7e4cf31d
+size 4194349
diff --git a/lNE2T4oBgHgl3EQfdwfJ/vector_store/index.pkl b/lNE2T4oBgHgl3EQfdwfJ/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..6b99d1e9209ad5b5ced139d33a7f8979d593615b
--- /dev/null
+++ b/lNE2T4oBgHgl3EQfdwfJ/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8b6fdf46965b0ec394834bb595ef6f7b06513bc9c54ca1ef1d841397212070f0
+size 141842
diff --git a/ltE5T4oBgHgl3EQfHQ5_/content/2301.05438v1.pdf b/ltE5T4oBgHgl3EQfHQ5_/content/2301.05438v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..9733e9f533e2e7f7918794daac49971e3344500f
--- /dev/null
+++ b/ltE5T4oBgHgl3EQfHQ5_/content/2301.05438v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:700908c42a2ff83caebe372532d8cdabe087c3e7c0c4160704e75213b23a37f2
+size 139139
diff --git a/ltE5T4oBgHgl3EQfHQ5_/vector_store/index.faiss b/ltE5T4oBgHgl3EQfHQ5_/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..08ff4853eedf71a426936621fbfe0cc625151d4e
--- /dev/null
+++ b/ltE5T4oBgHgl3EQfHQ5_/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:66a58e2392138a5f0f9a8d3a348d199f65c38675e37ee036bfa8580ecb89c244
+size 852013
diff --git a/ltE5T4oBgHgl3EQfHQ5_/vector_store/index.pkl b/ltE5T4oBgHgl3EQfHQ5_/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..29b3c90816d343db7f4f66b0c25a054b287a8fa9
--- /dev/null
+++ b/ltE5T4oBgHgl3EQfHQ5_/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a1a45c9c499eda5726eb4061ec94b6dd1b6fd7cd7c5ef5c74889bdd9fe90ee38
+size 28929
diff --git a/m9A0T4oBgHgl3EQfJv8c/content/tmp_files/2301.02093v1.pdf.txt b/m9A0T4oBgHgl3EQfJv8c/content/tmp_files/2301.02093v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ea85fef7226c48611e6aa833345312c5e8d08d55
--- /dev/null
+++ b/m9A0T4oBgHgl3EQfJv8c/content/tmp_files/2301.02093v1.pdf.txt
@@ -0,0 +1,2091 @@
+Double scaling limit of the prismatic tensor model
+T. Krajewski1, T. Muller2, and A. Tanasa2,3
+1Aix Marseille Univ, Université de Toulon, CNRS, CPT, Marseille,
+France, EU
+2Univ. Bordeaux, LaBRI CNRS UMR 5800, Talence, France, EU
+3DFT, H. Hulubei Nat. Inst. Phys. Nucl. Engineering, Magurele,
+Magurele, Romania, EU
+January 6, 2023
+Abstract
+In S. Giombi, I. Klebanov, F. Popov, S. Prakash and G. Tarnopolsky, Phys. Rev.
+D 98 (2018) 10, 105005, a prismatic tensor model was introduced. We study here
+the diagrammatics and the double scaling limit of this model, using the intermediate
+field method. We explicitly exhibit the next-to-leading order Feynman graphs in
+the 1/N expansion. Using appropriate combinatorial tools, we further study the
+general term of the 1/N expansion and we compute the 2−point function in the
+double scaling limit. We find that the double scaling limit mechanism implemented
+here is similar to the one implemented for various quartic tensor models.
+Contents
+1
+Introduction
+2
+2
+The prismatic model; intermediate field method
+4
+3
+Leading order graphs in the large N limit
+6
+3.1
+Leading order graphs in the tetrahedric representation . . . . . . . .
+7
+3.2
+Leading order graphs in the prismatic representation . . . . . . . . .
+8
+4
+Generating functions of leading order graphs
+8
+4.1
+Generating functions of melonic graphs . . . . . . . . . . . . . . . . .
+8
+4.2
+Generating function of LO graphs in the prismatic representation . .
+11
+5
+Diagrammatic Analysis
+12
+5.1
+Dipoles and their generating functions . . . . . . . . . . . . . . . . .
+13
+5.2
+Chains and their generating functions
+. . . . . . . . . . . . . . . . .
+14
+5.3
+Scheme decomposition . . . . . . . . . . . . . . . . . . . . . . . . . .
+19
+1
+arXiv:2301.02093v1  [hep-th]  5 Jan 2023
+
+6
+Next-to-leading order graphs
+21
+6.1
+Dipole-free 2 particle irreducible graphs
+. . . . . . . . . . . . . . . .
+22
+6.2
+2PI graphs with dipoles
+. . . . . . . . . . . . . . . . . . . . . . . . .
+22
+6.3
+2 particle reducible NLO graphs
+. . . . . . . . . . . . . . . . . . . .
+24
+7
+Double scaling limit of the 2-point function
+24
+8
+Concluding remarks
+30
+1
+Introduction
+Tensor models are zero-dimensional quantum field theoretical models where the
+fields are tensors of arbitrary rank (see the books [1] [2] or the review articles [3],
+[4], [5], [6] or [7]).
+Introduced as a generalization in dimension three and higher of the celebrated
+random matrix models (see [8] and the reviews [9, 10]), tensor models are currently
+studied in the context of mathematical physics, combinatorics and various other
+domains of mathematics. Thus, rank d tensor models are naturally linked to d di-
+mensional random geometries, as the Feynman graphs present in their perturbative
+expansion are dual to random triangulations. Moreover, such models were proven
+by Witten [11] and then by Klebanov and Tarnopolsky [12] to be related to the
+holographic Sachdev-Ye-Kitaev model [13].
+Initially proposed in the nineties (see, for example, [14]), tensor models lacked
+the implementation of the large N mechanism (N being in this context the size of the
+tensor). This changed in 2011, with the proposition of the so-called colored tensor
+model by Gurau [15], which he proved to have a well-defined large N expansion [16].
+Shortly after, a less restricted model (from the point of view of the class of Feynman
+graphs allowed by the perturbative expansion), the multi-orientable model [17] was
+proposed and proven to have a well-defined large N expansion [18].
+An O(N)3-invariant tensor model, was proposed in [19] (see also [20, 21] for
+various diagrammatic developments). We refer to this type of model as single field
+tetrahedric model, since one has only one tensor field in the action, and the inter-
+action is tetrahedric (its index structure has the topology of a tetrahedron).
+Let us also mention that the model proposed in [19] was later related by Klebanov
+and Tarnopolsky in [12] to the celebrated holographic SYK model.
+The case of sextic interactions for this type of O(N)3 invariant-tensor model was
+studied by Giombi et al. in [22]. This model was called prismatic since its large
+N limit is dominated by a positive-definite operator whose index structure has the
+topology of a prism. In this paper, we will study this prismatic model.
+The large N expansion of tensor models is controlled, as usually in tensor models,
+by a parameter ω called the degree. The large N expansion is dominated by graphs
+of vanishing degree. In [23], it was proven that the leading order (LO) graphs in
+the large N expansion of the prismatic model are not the usual melonic graphs one
+is used to from tensor model literature (see again the books [1] [2] or the review
+articles [3], [4], [5] or [7]). The role of the fundamental melon is played by a triple
+tadpole graph. Moreover, one now has two types of melonic insertions, one at the
+level of the propagator (as usually in tensor model literature), and another one at
+the level of the vertex, which is a new type of melonic move with respect to what it
+is known in the tensor model literature.
+2
+
+In this paper we give a different proof of the LO graph identification of [23]. Our
+proof relies on an extensive use of the intermediate field method, which expresses
+the prismatic model as a model with quartic tetrahedric interactions, but with two
+distinct tensor field (the initial tensor field and an intermediate field).
+Moreover, the intermediate field method used in this papers allows us to identify
+the next-to-leading (NLO) graphs in the large N expansion.
+The main result of this paper is then the implementation of the celebrated double
+scaling limit mechanism for the prismatic tensor model.
+Using a combinatorial
+scheme decomposition a la [24] allows to identify at any degree a sub-family of
+graphs, called dominant, whose amplitude is the most divergent when the coupling
+constant of the model goes to criticality. One then has, in this double scaling limit,
+contributions of Feynman graphs of any degree, as it was already noticed for the
+colored [25] model, the multi-orientable model [26] and the single field tetrahedric
+model [20].
+Note that in this paper we work with the 2−point function, and not with the
+free energy when implementing the double scaling mechanism. This comes from the
+fact that, from a combinatorial point of view, it is easier to work with the 2-point
+function, which correspond to what combinatorists call a rooted graph (and which
+has no symmetries). This is a standard tool in combinatorics and it has already
+been exported in mathematical physics for the study of quartic tensor models (see
+again [20], [26] and [25]). However, the results obtained here for the 2-point function
+can be extended, leading to an analogous behaviour, for the free energy (or for 2k-
+point function, k here being arbitrary, see [26], where this was implemented for the
+multi-orientable tensor model).
+Moreover, we prove that the 2-point function of the model is summable. This
+behaviour is different with respect to the matrix model case.
+In this paper, our overall strategy is the following:
+1. Apply the intermediate field method in order to reduce the sextic interaction
+of the prismatic model to the quartic, tetrahedric one. As mentioned above,
+by doing so, one now has two fields in the action, the original tensor field and
+the intermediate field (also a tensor field). We call this the tetrahedric repre-
+sentation of the model (by contrast to the "original" one, using the prismatic
+vertex, which we call the prismatic representation of the model).
+2. Generalize the results known in the case of the single field tetrahedric model
+mentioned above to the two-field model obtained via the use of the intermediate
+field method.
+3. When possible, deduce the results on the original prismatic model from the
+two field model above (thus somehow applying an "inverse" intermediate field
+method).
+The paper is structured in the following way. In the next section, we recall the
+definition of the prismatic model and the use of the intermediate field method in
+this case. In the third section, we exhibit the LO graphs, in both the tetrahedric
+and the prismatic representations of the model. In the following section, we study
+the generating functions of the LO graphs, in both representations of the model.
+In the fifth section we introduce appropriate diagrammatic tools in order to study,
+from a combinatorial point of view, the general term of the large N expansion of this
+model. We use these tools in the following sections, where the NLO Feynman graphs
+3
+
+are exhibited. In the seventh section we identify the dominant graphs and compute
+the 2−function is the double scaling limit. We end the paper with a concluding
+section.
+2
+The prismatic model; intermediate field method
+In this section we recall from [22] the definition of the prismatic tensor model and
+the implementation of the intermediate field method for this model.
+Let a random tensor Ti1i2i3 with three indices ranging from 1 to N ∈ N∗. The
+group O(N)3 acts in the following way on the tensor field
+Ti1i2i3 = O(1)
+i1j1O(2)
+i1j1O(3)
+i1j1Tj1j2j3,
+(1)
+where the O(k) are independent orthogonal matrices. The action of the model writes:
+SN = −1
+2
+�
+i,j,k
+TijkTijk
++tN −α
+6
+�
+a1,a2,a3,b1,b2,b3,c1,c2,c3
+Ta1b1c1Ta1b2c2Ta2b1c2Ta3b3c1Ta3b2c3Ta2b3c3,
+SN = −1
+2
+�
+i,j,k
+TijkTijk + tN −α
+6
+Ip(T).
+(2)
+Where
+Ip(T) =
+�
+a1,a2,a3,b1,b2,b3,c1,c2,c3
+Ta1b1c1Ta1b2c2Ta2b1c2Ta3b3c1Ta3b2c3Ta2b3c3
+(3)
+is the prismatic tensor invariant whose graphical representation is given in Fig
+1. Let us note here that the prismatic interaction above is positively defined.
+1
+3
+1
+3
+1
+3
+2
+2
+Ta1b1c1
+Ta3b3c1
+Ta1b2c2
+Ta2b1c2
+Ta2b3c3
+Ta3b2c3
+Figure 1: The prismatic interaction
+The partition function is then given by
+Z(t, N) =
+�
+[dT]e− 1
+2
+�
+i,j,k TijkTijk+ tN−α
+6
+Ip(T),
+(4)
+where [dT] is the tensor measure
+[dT] =
+N
+�
+i,j,k=1
+dTijk.
+(5)
+4
+
+Using the intermediate field method, the sextic interaction above can be reduced
+to a quartic interaction [27]. Recall that
+e
+tN−α
+6
+Ip(T) =
+�
+[dχ]
+(2π)N3/2 e− 1
+2
+�N
+i,j,k=1 χijkχijk
+e
+�
+2tN−α
+6
+�N
+a1,a2,b1,b2,c1,c2=1 Ta1b1c1Ta1b2c2Ta2b1c2χa2b2c1,
+=
+�
+[dχ]
+(2π)N3/2 e
+− 1
+2
+�N
+i,j,k=1 χijkχijk+
+�
+2tN−α
+6
+˜It(T,χ),
+(6)
+where
+˜It(T, χ) =
+N
+�
+a1,a2,b1,b2,c1,c2=1
+Ta1b1c1Ta1b2c2Ta2b1c2χa2b2c1.
+(7)
+The interaction obtained by using this intermediate field method is therefore a
+tetrahedron-type interaction coupling three T fields and one intermediate field χ.
+The graphical representation of this interaction is given in Fig 2.
+Ta1b1c1
+Ta1b2c2
+Ta2b1c2
+1
+3
+3
+1
+2
+χa2b2c1
+Figure 2: The tetrahedric interaction
+The partition function can therefore be written as
+Z(t, N) =
+�
+[dT]
+[dχ]
+(2π)N3/2 e
+− 1
+2
+�N
+i,j,k=1(TijkTijk+χijkχijk)+
+�
+2tN−α
+6
+˜It(T,χ),
+=
+�
+[dT]
+[dχ]
+(2π)N3/2 e− 1
+2
+�N
+i,j,k=1(TijkTijk+χijkχijk)+ λ′N−α′
+4
+˜It(T,χ),
+(8)
+where we made a redefinition of the coupling constant λ′N−α′
+4
+=
+�
+2tN−α
+6
+.
+The
+identification 2α′ = α indicates that the scaling of a prismatic interaction needs to
+be twice the one of a tetrahedron. Recall that the single field tetrahedron interaction
+is known to be equal to 3
+2 [19]. One thus has, for the scaling parameter of the
+prismatic interaction:
+α = 3.
+(9)
+In the sequel, when working with prismatic vertices, it will be stated that the
+analysis is performed in the prismatic representation. When working with the
+intermediate field representation, hence with tetrahedron interactions, we will refer
+to it as the tetrahedric representation.
+Using the intermediate field method described above, any prismatic vertex in a
+Feynman graph can be split into two tetrahedra vertices connected by an auxiliary
+field propagator χ as in Figure 3, where the field χ is represented by a curly line.
+One can prove that the Feynman amplitude of a vacuum graph is equal to
+AG = tnpN3−�
+l=1,2,3
+kl
+2 = tnpN3−ω(G),
+(10)
+5
+
+1
+3
+1
+3
+1
+3
+2
+2
+Ta1b1c1
+Ta3b3c1
+Ta1b2c2
+Ta2b1c2
+Ta2b3c3
+Ta3b2c3
+Ta1b1c1
+Ta1b2c2
+Ta2b1c2
+1
+3
+3
+1
+2
+2
+χa2b2c1
+3
+3
+1
+1
+χa4b4c4
+Ta3b3c4
+Ta3b4c3
+Ta4b3c3
+Figure 3: The intermediate field method for the prismatic tensor interaction.
+where np and resp. nt are the number of vertices of the prismatic and resp. tetra-
+hedric representation (recall that nt = 2np). Moreover, the parameter
+ω(G) =
+�
+l=1,2,3
+kl
+2 = 3 + 3np − fG = 3 + 3
+2nt − fG
+(11)
+is called the degree.
+Let us also notice that the tetrahedric representation can be linked to dimer
+models of the graphs present in the tetrahedric model. The dimer model is the
+study of the perfect matchings of a graph.
+Recall that a perfect matching of a
+graph is a configuration where all its vertices are paired with exactly one of their
+connected neighbours [28]. As each vertex possesses a single χ node, connecting two
+vertices with a χ propagator is equivalent to pairing them. Therefore, by considering
+the dimers of all the graphs in the tetrahedric model, one can derive all the graphs
+present in the tetrahedric representation of the prismatic model 1. An example of
+the perfect pairing of a graph in the tetrahedric model and its equivalent in the
+tetrahedric representation is given in Figure 4.
+Figure 4: On the left, a graph in the tetrahedric model and one of its perfect pairing. On
+the right is the corresponding graph in the tetrahedric representation.
+3
+Leading order graphs in the large N limit
+In this section, we study the 1
+N expansion of the prismatic model and we explicitly
+exhibit the dominant graphs, in both the tetrahedric and prismatic representation.
+1In a more general setting, replacing one of the fields in a single field interaction by an intermediate
+field is equivalent to consider the dimers of the graphs present in the original model.
+6
+
+Our study, as already mentioned in the Introduction, uses the intermediate field
+method.
+3.1
+Leading order graphs in the tetrahedric represen-
+tation
+Equation (11) above implies that the degree of the prismatic model is a non-negative
+integer. Hence, the LO Feynman graphs of the model are thus the ones satisfying
+the condition:
+ω(G) = 0.
+(12)
+Let us first identify these graphs in the tetrahedric representation. As usual in the
+tensor model literature, we call these graphs melonic graphs. One can prove that
+they are built by starting from the vacuum elementary melon shown in Figure 5 and
+by recursively inserting one of the elementary 2-points melons on arbitrary edges.
+The insertions possible on the two types of edges are shown in Figure 6.
+1
+3
+3
+1
+2
+3
+1
+2
+1
+3
+Figure 5: On the left, the vacuum elementary melon in the tetrahedric representation. On
+the right, a simplified graphical representation of the graph where the tetrahedric vertices
+are replaced by black dots.
+i
+i
+j
+j
+i
+j
+j
+i
+i
+j
+i
+j
+i
+j
+i
+j
+k
+k
+k
+k
+Figure 6: The melonic insertions on the two types of propagators.
+Let us give in Fig. 7 an example of melonic graphs obtained via melonic inser-
+tions on a T propagator, on the LHS, and on a χ propagator on the RHS.
+7
+
+Figure 7: Example of melonic graphs.
+3.2
+Leading order graphs in the prismatic representa-
+tion
+In the prismatic representation, the elementary melon of the tetrahedric representa-
+tion becomes a triple tadpole (see Figure 8 for its various graphical representations).
+We refer to this triple tadpole as the elementary triple tadpole.
+Let us now explain what the two melonic insertions in the tetrahedric represen-
+tation become in this prismatic representation. The insertion on a T propagator is
+equivalent to the insertion of a 2−point double tadpole (which is obtained by "cut-
+ting" an edge of the elementary triple tadpole). The insertion on a χ propagator is
+equivalent to an insertion at the level of a prismatic vertex. One needs to "split" a
+prismatic vertex into two prismatic vertices which are linked by T propagators (see
+Figure 9).
+Let us give in Figure 10 some examples of LO graphs in the prismatic repre-
+sentation. The first graph is the elementary triple tadpole. The second graph is
+obtained by a vertex splitting of the elementary triple tadpole vertex. The third
+graph is obtained by inserting a 2−point double tadpole on one of the edges of the
+first graph (the elementary triple tadpole) and so on.
+4
+Generating functions of leading order graphs
+4.1
+Generating functions of melonic graphs
+In this subsection we analyse the generating functions of melonic graphs in the
+tetrahedric representation, find its singularities and the behaviour of this generating
+function close to the singularity.
+As there are two types of 2−point functions (associated with the two propaga-
+tors), we denote by MT (t) and Mχ(t) the generating functions of the two sets of
+corresponding melon graphs. This is given in Figure 11.
+One has
+MT (t) = 1 + 3tM3
+T (t)Mχ(t),
+Mχ(t) = 1 + tM3
+T (t)Mχ(t),
+(13)
+where the factor 3 in the first equation above counts the three different choices of
+placing a χ propagator connecting the two vertices of the melonic graph. Substi-
+tuting Mχ(t) in the first equation gives
+1 + t(M4
+T (t) + 2M3
+T (t)) − MT (t) = 0.
+(14)
+8
+
+1
+3
+3
+1
+2
+1
+3
+3
+1
+2
+1
+1
+1
+2
+3
+3
+3
+Figure 8: On the left, the elementary vacuum melon in the two graphical representations.
+On the right, their prismatic equivalent. On the bottom right, the prismatic vertex is
+represented by a red square.
+,
+,
+,
+i
+i
+i
+j
+j
+j
+k
+i
+i
+j
+i
+j
+j
+i
+j
+i
+j
+i
+j
+i
+j
+j
+i
+i
+j
+k
+k
+Figure 9: The prismatic equivalent of the two melonic insertions.
+Figure 10: Examples of the LO graph in the prismatic representation.
+Finding the general solution of such equation is an involved task. However, one can
+derive its singularities, i. e. the points where the solution stops being analytic.
+One can consider the more general problem given by
+F(MT , t) = 0,
+(15)
+where one needs to find MT (t). Using the implicit function theorem [29], one can
+9
+
+MT
+MT
+MT
+Mχ
++
+=
+3
+MT
+MT
+MT
++
+=
+Mχ
+MT
+Mχ
+Figure 11: LO 2−point functions in the terahedric representation.
+write
+dMT (t)
+dt
+= − ∂F/∂t
+∂F/∂MT
+.
+(16)
+This implies that MT (t) ceases to be analytic when
+∂F
+∂MT = 0 as its derivative blows
+up.
+In the case of the melons, one has F(MT , t) = 1+t(MT (t)4 +2MT (t)3)−MT (t).
+One then has the following system of equations (we denote MT (tc) by MT,c):
+MT,c = 1 + tc(M4
+T,c + 2M3
+T,c),
+1 = tc(4M3
+T,c + 6M2
+T,c).
+(17)
+The second equation implies tc =
+1
+4M3
+T,c+6M2
+T,c , which can be substituted in the first
+one to give
+MT,c = 1 +
+M4
+T,c + 2M3
+T,c
+4M3
+T,c + 6M2
+T,c
+.
+(18)
+After some algebra, one finds M2
+T,c = 2.
+The singularities are then the points
+for which MT = ±
+√
+2 at tc =
+1
+12±8
+√
+2. Recall that Pringsheim’s theorem (see for
+example [29]) implies that the singularity closest to t = 0 defines the radius of
+convergence of the series expansion of MT (t) around the origin. This point is the
+dominant singularity. As
+1
+12+8
+√
+2 <
+1
+12−8
+√
+2, one has
+tc =
+1
+12 + 8
+√
+2 and MT (tc) =
+√
+2,
+(19)
+at the dominant singularity.
+Let us now find the behavior of the function MT (t) near this dominant singu-
+larity. In order to do this, one needs to Taylor expand the function F(MT , t) near
+a critical point.
+10
+
+Assuming that
+∂2F
+∂M2
+T ̸= 0,
+and using the conditions F(MT , t) = 0,
+∂F
+∂MT |tc = 0 and since ∂F
+∂t2 = 0, one has:
+∂F
+∂t |tc(tc − t) +
+∂2F
+∂t∂MT
+|tc(tc − t)(MT (t) − MT,c) + O(ϵ2)
+= ∂2F
+∂M2
+T
+|tc
+1
+2(MT (t) − MT,c)2.
+(20)
+In the limit t → tc (keeping only the LO term in the expansion), one has:
+MT (t) t→tc
+∼ MT,c ±
+�
+2
+∂F/∂t|tc
+∂2F/∂M2
+T |tc
+√tc − t.
+(21)
+Since MT (t) is the generating function of melonic graphs, this implies that MT (t)
+is an increasing function in t and this further implies that one needs to choose,
+amongst the two solutions (21), the solution with a negative sign.
+Thus, the function MT (t) behaves, near the dominant singularity, as
+MT (t) t→tc
+∼ MT,c −
+�
+�
+�
+� M4
+T,c + 2M3
+T,c
+6(M2
+T,c + MT,c)
+�
+1 − t/tc,
+MT (t) t→tc
+∼ MT,c − K
+�
+1 − t/tc.
+(22)
+Inserting the explicit expressions (19) of tc and MT,c, this behavior writes as
+MT (t) t→tc
+∼
+√
+2 −
+�√
+2
+3 (1 −
+t
+12 + 8
+√
+2).
+(23)
+4.2
+Generating function of LO graphs in the prismatic
+representation
+In this subsection, we analyze the generating function of LO graphs in the prismatic
+representation and we give an enumerative combinatorics result for the number of
+such LO graph at an arbitrary order in perturbation theory.
+Let us denote by P the generating function of the 2−point LO graphs. This
+expands as P = �
+n antn The coefficients an thus give us the number of LO graphs
+at a given order n in perturbation theory. In order to compute these coefficients,
+a closed equation for P needs to be found. This equation can be obtained in a
+diagrammatic way.
+Recall that we found two distinct insertions (one at the level of the propagator
+and one at the level of the prismatic vertex) which generate all the LO graphs in the
+prismatic representation. This translates in the diagrammatic equation represented
+in Fig. 12, for the 2−point and 6−point function.
+One has
+P = 1 + 3P 3Γ,
+Γ = t + tP 3Γ.
+(24)
+This leads to
+P − 1 = t(P 4 + 2P 3).
+(25)
+11
+
+=
++
+=
++
+P
+P
+P
+P
+Γ
+Γ
+Γ
+P
+P
+P
+i
+i
+�3
+i=1
+Figure 12: Graphical representation of the equations of the generating function P.
+Changing variable to y = P − 1 gives
+y = t
+�(y + 1)4 + 2(y + 1)3� = tf(y).
+(26)
+Using Lagrange inversion theorem (see again the book [29]), the coefficient an can
+be computed in the following way. Suppose that f(x) expands as f(x) = �
+k≥0 fkxk
+and f0 ̸= 0. Then the equation y = tf(y) admits a unique solution of the form
+y(t) = �
+n≥1 yntn with yn = 1
+n[xn−1]f(x)n, where the notation [xm]g(x) denotes the
+order m coefficient of g(x).
+Recall that, in the case considered here, f(y) = (y + 1)4 + 2(y + 1)3 = (y +
+1)3(y + 3). This implies that yn = 1
+n[xn−1]
+�(x + 1)3n(x + 3)n�. Using the binomial
+expansion, one can identify the coefficients as
+yn = 1
+n
+n−1
+�
+k≥0
+3n!
+k!(3n − k)!
+n!
+(n − k − 1)!(k + 1)!3k+1.
+(27)
+Since y = P − 1, one thus has
+P = 1 +
+�
+n≥1
+n−1
+�
+k≥0
+3n!
+k!(3n − k)!
+n!
+(n − k − 1)!(k + 1)!3k+1tn,
+(28)
+which finally leads to the identification of the number of LO graphs in the prismatic
+representation to be: a0 = 1 and an = yn, for any n ∈ N.
+5
+Diagrammatic Analysis
+In this section we introduce the diagrammatic tools needed to implement the double
+scaling limit of the model.
+12
+
+5.1
+Dipoles and their generating functions
+The notion of dipole was already introduced for the colored tensor model in [16], then
+for the MO tensor model in [30] and also for the O(N)3−invariant quartic model
+in [20]. In this subsection, we define a diagrammatic notion of dipole subgraph for
+the model studied here, in the tetrahedric representation.
+A dipole of color i is a subgraph formed by two tetrahedric vertices connected
+by two parallel edges such that the subgraph has a face of length two and of color i.
+For each given color i, there are five different types of dipoles. We call these
+types of dipoles types α, βL, βR, δL and δR, see Fig. 13.
+i
+i
+i
+i
+i
+i
+i
+i
+i
+i
+i
+i
+i
+i
+i
+αi
+βi,L
+δi,L
+i
+i
+i
++
+βi,R
+δi,R
+Figure 13: The five types of dipoles.
+To simplify the graphical representation, the dipoles can be replaced by the
+dipole-vertices shown in Figure 14.
+Dα,i
+DβR,i
+DδR,i
+DβL,i
+DδL,i
+Figure 14: The five types of dipole-vertices.
+Let us now exhibit the generating functions for the dipoles. One needs to insert
+the generating functions of melons on each edge and its square root on its half edges.
+This way of counting the melonic insertions on the edges allows us to avoid counting
+twice the melons when there are two adjacent dipoles.
+Thus, the generating functions of the five types of dipoles write:
+Dα = 2tMT (t)3Mχ = 2
+3(MT (t) − 1),
+DβL = DβR = Dβ = tMT (t)3Mχ(t) = 1
+3(MT (t) − 1)
+DδL = DδR = Dδ = tMT (t)3Mχ(t) = 1
+3(MT (t) − 1).
+(29)
+Note that the generating function of a dipole does not depend on the color.
+Notice also that the generating functions of the dipoles of type βL and βR as well
+as the generating functions of the dipoles of type δL and δR are the same. In the
+following, we will differentiate the generating function of these dipoles when writing
+the structure of the chains (in Section 5.2). However, when writing the contribution
+of the dominant graphs to the 2−point function (in Section 7), we will simply
+denote them by Dβ and Dδ. This allows us to clarify the structure of the chains
+while keeping a compact expression for the contribution of the dominant graphs.
+13
+
+From the expression of the different generating functions above, one can find
+that the critical points of the dipole generating functions are identical to the ones
+of the generating functions of the melon graphs.
+5.2
+Chains and their generating functions
+Chains are defined in an analogous way as in [20] [30] to be the 4−point graphs
+obtained by connecting at least two dipoles and by matching one side of a dipole to
+the corresponding side of the next dipole in the chain.
+A chain is said to be of length ℓ if it contains ℓ dipoles. Each chain of length ℓ
+contains subchains of length 2 ≤ ℓ′ ≤ ℓ. A chain is therefore said to be maximal if
+it cannot be included in a longer chain of the graph.
+Note that changing the length of a chain doesn’t change the degree of a graph.
+This can be proven by induction on the length of the chain, by inserting a dipole in
+a chain of length k, and by counting carefully the number of faces and vertices.
+Using the previous five types of dipoles, there are eight different possibilities for
+the external edges of a chain. We thus have eight types of chainsIf all the dipoles
+of a given chain are of color i, the respective chain is said to be an unbroken chain
+of color i. If the dipoles of the chain do not have the same color, we say that the
+respective chain is broken.
+Similar to the case of dipoles, in order to simplify the graphics, we represent
+unbroken chains of a given type and color i by a chain-vertex C, while broken chains
+are represented by chain-vertices B. The different types of unbroken chain-vertices
+are shown in Figure 15.
+Furthermore, we classify the chains into two families:
+• Family A, if the external legs are the same on each side of the chain.
+• Family B, if the external legs are different on each side of the chain.
+1
+2
+3
+4
+5
+A
+B
+C1,i
+C2L,i
+C3,i
+C4R,i
+C5L,i
+C2R,i
+5
+C5R,i
+4
+C4L,i
+2
+Figure 15: All the different types of broken chain-vertices.
+Let us now have a closer look at the dipole structure and the generating functions
+of each of these chains:
+Family A:
+The building block of the chains in the family A are the dipoles of
+type α, βL and βR. If a dipole of type βR doesn’t end a chain, it must be followed
+by a dipole of type βL.
+14
+
+All the possibilities of gluing up dipoles are given in Figure 16. The other types
+of chains of the family A follow directly from the type 1 chain as shown in Figure
+17.
+C1,i
+=
+Dα,i
+�
+k≥1
+DβR,i
+DβL,i
++
+Dα,i
++
+DβR,i
+DβL,i
+�
+k≥0
+DβR,i
+DβL,i
++
+Dα,i
+k
+k
+Figure 16: The structure of the chains of type 1.
+C2L,i
+=
+DβL,i
+C1,i
+Dα,i
++
+C3,i
+=
+C1,i
+Dα,i
++
+DβR,i
+DβL,i
++
+DβR,i
+DβL,i
+C2R,i
+=
+DβR,i
+C1,i
+Dα,i
++
+Figure 17: The structure of the chains of type 2, 3.
+The generating functions are then derived as following:
+C1 = Dα
+�
+k≥1
+(DβRDβL + Dα)k + DβRDβL
+�
+k≥0
+(DβRDβL + Dα)k,
+= (Dα + DβRDβL)
+�
+k≥0
+(D2
+β + Dα)k − Dα,
+=
+Dα + DβRDβL
+1 − (Dα + DβRDβL) − Dα,
+(30)
+and
+C2L = DβL(C1 + Dα) = DβL
+Dα + DβRDβL
+1 − (Dα + DβRDβL),
+C2R = DβR(C1 + Dα) = Dβ
+Dα + DβRDβL
+1 − (Dα + DβRDβL),
+C3 = DβL(1 + C1 + Dα)DβR =
+DβLDβR
+1 − (Dα + DβLDβR).
+(31)
+15
+
+The generating functions of the broken chains of type 1 can be derived from
+the expressions of the generating functions above by noticing that every chain of
+type 1 that is not of a given color must be broken. When building chains, there are
+three possible colors of dipoles to insert. Multiplying each generating functions of
+dipoles by a factor three, and subtracting the chains of color i, gives the generating
+functions of the broken chains B1. This writes as:
+B1 =
+3Dα + 9DβLDβR
+1 − (3Dα + 9DβLDβR) − 3Dα −
+�
+i=1,2,3
+C1,i.
+(32)
+The expressions of the remaining types of broken chains follow then from Figure 18
+and write:
+B2L = 6DβL(C1 + Dα) + 3DβLB1,
+B2R = 6(C1 + Dα)DβR + 3B1DβR,
+B3 = 18DβL(C1 + Dα)DβR + 6DβLDβR + 9DβLB1DβR.
+(33)
+B2L
+=
+DβL,i
+C1,j
+Dα,j
++
+B3
+=
+C1,j
+Dα,j
++
+DβR,k
+DβL,i
++
+DβR,j
+DβL,i
+�3
+i̸=j
++
+�3
+i=1
+DβL,i
+B1
+�3
+i̸=j
++
+DβR,j
+DβL,i
+�3
+i,j
+B1
+B2R
+=
+DβR,i
+C1,j
+Dα,j
++
+�3
+i̸=j
++
+�3
+i=1
+DβR,i
+B1
+i ̸= j ork ̸= i
+ork ̸= j
+� 3
+Figure 18: The structure of the broken chains of family A.
+After summing over the three colors in the last term of equation (32), and after
+16
+
+some further algebra, one gets:
+B1 = 6DβLDβR + 18(DβLDβR)2 + 6D2
+α + 24DαDβLDβR
+�1 − (3Dα + 9DβLDβR)
+��1 − (Dα + DβLDβR)
+�
+,
+B2L = DβL
+24DβLDβR + 6Dα
+�1 − (3Dα + 9DβLDβR)
+��1 − (Dα + DβLDβR)
+�,
+B2R = DβR
+24DβLDβR + 6Dα
+�1 − (3Dα + 9DβLDβR)
+��1 − (Dα + DβLDβR)
+�,
+B3 =
+3DβLDβR(2 + 6DβLDβR)
+�1 − (3Dα + 9DβLDβR)
+��1 − (Dα + DβLDβR)
+�.
+(34)
+Family B:
+As above, the structure of the chains in family B is derived from their
+building blocks that are dipoles of type δL and δR. If a dipole of type δL or resp.
+δR doesn’t end a chain, it must be followed by a dipole of type δR or resp. δL. All
+the possibilities for type 5 chains are then given in Figure 19.
+DδL,i
+DδR,i
+C5R,i
+=
+�
+k≥0
+DδL,i
+DδR,i
+k
+DδR,i
+DδL,i
+C5L,i
+=
+�
+k≥0
+DδR,i
+DδL,i
+k
+Figure 19: Structure of the chains of type 5.
+The structure of the others chains can then be deduced from the type 5 chains
+and is shown in Figure 20.
+DδR,i
+C4R,i
+=
+C5R,i
+DδL,i
+C4L,i
+=
+C5L,i
+DδR,i
+=
+C5L,i
+DδL,i
+=
+C5R,i
+Figure 20: Structure of the chains of type 4.
+The generating functions of family B chains write:
+C5L = C5R = DδLDδR
+�
+k≥0
+(DδLDδR)k =
+DδLDδR
+1 − DδLDδR
+,
+C4L = DδLC5L =
+D2
+δLDδR
+1 − DδLDδR
+,
+C4R = DδRC5R =
+DδLD2
+δR
+1 − DδLDδR
+.
+(35)
+17
+
+Using a similar argument as in the case of family A chains, the broken chains of
+this family are found to be
+B5L = B5R = DδLDδR
+6 + 18DδLDδR
+(1 − DδLDδR)(1 − 9DδLDδR),
+B4L =
+24D2
+δLDδR
+(1 − DδLDδR)(1 − 9DδLDδR),
+B4R =
+24DδLD2
+δR
+(1 − DδLDδR)(1 − 9DδLDδR).
+(36)
+The formulas obtained above for the generating functions of the various types
+of chains have therefore five different types of singular points:
+• As any dipole has the same singular points as the melons, the chains also have
+the same singular points as the melons.
+• For the unbroken and broken chains of family A, the points satisfying Dα +
+DβLDβR = 1 are singular points.
+• For the broken chains of family A, the points satisfying 3Dα + 9DβLDβR = 1
+are singular points.
+• For the colored and broken chains of family B, the points satisfying DδLDδR =
+1 are singular points.
+• For the broken chains of family B, the points satisfying 9DδLDδR = 1 are
+singular points.
+Inserting the expression of the generating functions of the dipoles in the singularity
+conditions above, one has:
+2
+3(MT (t) − 1) + 1
+9(MT (t) − 1)2 = 1,
+2(MT (t) − 1) + (MT (t) − 1)2 = 1,
+1
+9(MT (t) − 1)2 = 1,
+(MT (t) − 1)2 = 1.
+(37)
+Each condition leads to a 2nd order equation and the solutions of these equations are:
+MT = −2±3
+√
+2, MT = ±
+√
+2, MT = 4, −2 and resp. MT = 2, 0. The points where
+3Dα + 9D2
+β = 1 are therefore also points where the melons are singular. Recall that
+MT (t) was chosen to be an increasing function of t. This means that the singularity
+with the smallest |MT | is also the one with t closest to zero. Inserting MT = 0 in
+equation (14) gives 1 = 0 and is therefore impossible. The dominant singularity is
+then the point (MT,c, tc) = (
+√
+2,
+1
+8
+√
+2+12) which is a singular point for the generating
+functions of melons and broken chains of family A.
+Notice also from equation (34) that only the broken chains of type 2L,2R, 3 that
+are composed of a broken chain of type 1 are singular at the critical point. We
+denote these specific chains by a star such that B2∗
+L = 3DβLB1, B2∗
+R = 3DβRB1 and
+B3∗ = 9DβLB1DβR.
+Then, near the critical point, one gets:
+18
+
+B1
+t→tc
+≈
+3Dα + 9D2
+β
+1 − (3Dα + 9D2
+β)
+t→tc
+∼
+1
+2MT,cK
+�
+1 − t
+tc
+,
+B2L
+t→tc
+≈ B2∗
+L = 3DβLB1
+t→tc
+∼
+MT,c − 1
+MT,cK
+�
+1 − t
+tc
+,
+B2R
+t→tc
+≈ B2∗
+R = 3DβRB1
+t→tc
+∼
+MT,c − 1
+MT,cK
+�
+1 − t
+tc
+,
+B3
+t→tc
+≈ B3∗ = 9DβLDβRB1
+t→tc
+∼
+(MT,c − 1)2
+MT,cK
+�
+1 − t
+tc
+.
+(38)
+5.3
+Scheme decomposition
+As in [20] [30], the scheme S of a graph G is defined by eliminating from the respec-
+tive graph any 2-point melonic subgraph, and replacing each maximal chain by its
+corresponding chain-vertex and any dipole by its corresponding dipole-vertex.
+One can prove that the degree of the scheme ω(S) is then identical to the one
+of the initial graph ω(G) (see again [20] [30]).
+Each scheme represents then a family of graphs and any graph can be de-
+rived from its corresponding scheme by replacing/inserting back the corresponding
+dipoles, chains and melons.
+Let us give an example of a scheme and a Feynman graph corresponding to it
+in Fig. 21.
+C1,i
+DδR,j
+i
+i
+j
+Figure 21: Example of a graph (left) and its corresponding scheme (right).
+In [20] it was proven that the number of schemes at a given degree is finite
+in the O(N)3-invariant model. In order to obtain this result, it was proven that
+both the number of dipole/chain-vertices and the number of tetrahedric vertices
+was bounded.
+The schemes of the prismatic model can be obtained by decorating the edge that
+links pairs of vertices of the schemes present in the tetrahedric model. There is also
+only a finite number of ways to perform such decoration on a scheme with a given
+number of dipole-vertices, chain-vertices, and tetrahedric vertices. This implies that
+the number of schemes at a given degree in the prismatic model must be finite.
+19
+
+As the number of schemes at each degree is finite, we can use them to compact
+the infinite number of graphs at a fixed degree into a finite number of schemes.
+Thus, the sum over an infinite number of Feynman graphs in G2(t) can be written
+as a sum over a finite number of schemes. The 2−point function then writes
+G2(t) = MT (t) +
+�
+ω≥1
+N−ω �
+PS,ω(M, C),
+(39)
+where PS,ω(M, C) is a polynomial of the melons generating function and the chains
+generating functions. The sum in the formula above is performed on all the schemes
+of degree ω. The dominant singularity of G2(t) is then the singular point (MT,c, tc) =
+(
+√
+2,
+1
+8
+√
+2+12) of the broken chains of type 1, 2∗
+L, 2∗
+R and 3∗.
+Dipole/chain-vertex removal
+When studying the combinatorics schemes, a
+standard operation is to remove dipole/chain-vertices and to reconnect the half-
+edges together on each sides of the vertices as in Figure 22.
+C, B
+D
+e1
+e2
+e3
+e4
+e
+e′
+Figure 22: The process of dipole removal.
+A dipole/chain-vertex is said to be separating if its removal disconnects the
+scheme S.
+One can prove that the removal of a separating dipole/chain-vertex
+leads to a distribution of the degree between the two connected components (see
+again [20] and [30]). Thus, removing a separating dipole/chain-vertex leaves the
+degree invariant. Moreover, one has
+ω(S) = ω(S1) + ω(S2),
+(40)
+where S1 and S2 are the two connected components resulting from the removal.
+Let us denote by S′ the scheme obtained after a dipole removal in S. By carefully
+counting the number of faces and vertices, one can prove (see again [20] and [30])
+that removing a non separating dipole or chain of color i changes the degree as
+ω(S) − 1 ≥ ω(S′) ≥ ω(S) − 3.
+(41)
+Analogously, removing a non separating broken chain gives ω(S′) = ω(S) − 3
+Skeleton graphs
+When identifying the dominant schemes, a key role is played
+by skeleton graphs (see again [20]). These graphs are defined as follows.
+Consider a scheme S, its skeleton graph I(S) is obtained by removing all its
+broken chain-vertices of type 1 and by adding arrows (labeled by B1) between the
+edges formed in this way. Notice that the definition given here is slightly different
+than the one given in [20].
+An example of such a dipole-vertex removal is given in Figure 23. In a skeleton
+graph, the arrows play the role of the edges whereas the disconnected components
+Si, resulting from the removals, play the role of the vertices. However, these edges
+20
+
+B1
+B1
+Figure 23: The dipole removal in the construction of the skeleton graph.
+and vertices don’t contribute to the degree as in a Feynman graph. An example of
+a scheme and its skeleton graph is given in Figure 24.
+Skeleton graphs have several interesting properties (see again [20]):
+• If one of the components Si has degree 0, then this component has a valency
+greater or equal to 3.
+This can be proven by noticing that a degree 0 graph with valency 1 must be
+a melonic 2-point function and one with valency 2 must be a dipole or chain.
+None of these situations can occur for a skeleton graph.
+• Let S be a scheme with q non separating chain-vertices of type 1 and let S′
+the scheme obtained be removing these q chain-vertices. The skeleton graph
+I(S′) is a tree and its degree satisfies the inequality: ω(I(S)) ≤ ω(S) − q.
+This comes from the fact that, if a scheme has only separating dipole/chain-
+vertices no cycle can appear in its skeleton graph. The bound on ω(I(S)) is
+derived by using equation (41) and by recalling that the removal of a separating
+dipole/chain-vertex doesn’t change the degree.
+• If I(S) is a tree, its degree is equal to the one of its scheme and is given by
+the sum of the degree of its components
+ω(I(S)) =
+�
+i
+ω(Si).
+(42)
+This comes from the fact that, if I(S) is a tree, all its dipole/chain-vertices
+are separating. This is then a direct consequence of equation (40).
+6
+Next-to-leading order graphs
+In this section we explicitly identify the NLO Feynman graphs of the prismatic
+model. Recall from equation (11) that the degree of the prismatic model is a non-
+negative integer. Hence, if G is an NLO Feynman graph, one has: ω(G) = 1.
+The graphs of degree one for the tetrahedric model have been identified in [21].
+Using this analysis, one can derive the corresponding NLO Feynman graphs of the
+model considered here. This is done using the following strategy. We consider all
+the graphs of degree one identified in [21], and investigate all the ways to decorate
+each graph with a χ propagator per pair of vertices. Finally, by contracting the
+intermediate field propagator χ and discarding the potential redundancies, all the
+graphs of degree one in the prismatic representation are found.
+In the tetrahedric representation, the NLO graphs can be separated into three
+classes (see again [21]):
+1. 2PI, dipole-free Feynman graphs
+2. 2PI Feynman graphs with dipoles
+21
+
+C1,i
+B1
+B5L
+B1
+B1
+C1,i
+B5L
+B1
+Figure 24: An example of a scheme and its skeleton graph.
+3. 2PR Feynman graphs
+In the sequel, we give the schemes of the graphs in the tetrahedric representation
+and give some examples of Feynman graphs in both the tetrahedric and the prismatic
+representations. Recall that the number of tetrahedric vertices replacing a chain-
+vertex is arbitrary, and the same holds for the corresponding number prismatic
+vertices (when using the prismatic representation of the model).
+6.1
+Dipole-free 2 particle irreducible graphs
+It was derived in [21] that there is a unique dipole free scheme of degree one in the
+tetrahedric model. This scheme is given in Figure (25).
+Note that, since this scheme has no dipole-vertices and no chain-vertices, one
+can obtain the corresponding graphs by the usual melonic insertions on any of its
+edges.
+There are then 3 independent ways to place the χ propagator on this NLO graph,
+see Fig. 26.
+However, when contracting the χ propagators in order to obtain the prismatic
+representation NLO graphs, one can show that the three graphs of Fig. 26 lead to
+the unique graph of Fig. 27.
+The NLO graphs in the prismatic representation are thus obtained via the two
+prismatic melonic moves (see above) performed on the graph of Fig. 27.
+6.2
+2PI graphs with dipoles
+The schemes of the 2PI graphs with dipoles in the tetrahedric representation are
+given in Figure 28. The edges e and e′ can be of type T or χ, implying that s = 1
+22
+
+Figure 25: The unique 2PI dipole free scheme of degree one in the tetrahedric model.
+Figure 26: The different ways to place the χ propagators on the NLO graph of Fig. 25.
+i
+j
+j
+j
+j
+j
+j
+i
+i
+i
+i
+i
+i
+i
+j
+i
+j
+j
+k
+k
+k
+Figure 27: The only graph found by contracting the χ edges of the graphs in Figure 25.
+or 5 (the case s = 4 beeing equivalent to s = 1). The explicit schemes, with the
+23
+
+2
+7
+Fi=4
+F2 = 4
+F3 = 3
+w = 3＋ 6- 11= 1
+2
+2corresponding T or χ propagators, are given on the right side of Fig. 29.
+Let us end this subsection by giving some explicit examples of NLO 2PI graphs
+with dipoles (where we have replaced the chain-vertices by chains of length four),
+and their corresponding graphs in the prismatic representation - see Figure 30.
+Cs,i
+e
+e′
+Figure 28: The explicit schemes of the 2PI NLO graphs with dipoles.
+C5,i
+C1,i
+,
+Figure 29: The explicit schemes of the 2PI NLO graphs with dipoles.
+6.3
+2 particle reducible NLO graphs
+Recall from [21] that schemes of the 2PR graphs in the tetrahedric model are given
+in Fig. 31.
+When placing the χ propagators, the corresponding schemes are given in Fig. 32.
+The empty boxes in the figures can either be a dipole-vertex, a broken chain-vertex
+or a colored chain-vertex.
+Let us end this section by giving some examples of NLO 2PR graphs and the
+corresponding graph in the prismatic representation, see Figure 33. The first graph
+in the figure is the first graph of Fig. 32. The second graph is obtained from the
+second scheme of Fig. 32, where we have replaced the empty box by a chain of
+length four and color i. Finally, the third graph is obtained from the second scheme
+of Fig. 32, where we have replaced the empty box by a broken chain of length four.
+7
+Double scaling limit of the 2-point function
+Let us recall that the dominant singularity of G2(t, N) is the point (MT,c, tc) =
+(
+√
+2,
+1
+8
+√
+2+12) where the broken chains of type 1, 2∗
+L, 2∗
+R and 3∗ are singular. The
+dominant schemes are then the ones that maximize the number of these chains.
+24
+
+i
+i
+i
+i
+i
+i
+i
+j
+j
+j
+i
+i
+i
+i
+i
+j
+j
+j
+j
+i
+i
+i
+i
+j
+j
+j
+i
+Figure 30: Examples of NLO, 2PI graphs with dipoles in the tetrahedric (left) and pris-
+matic (right) representation.
+Figure 31: The schemes of the NLO 2PR graphs in the single field tetrahedric model.
+i
+j
+k
+i′
+j′
+k′
+i
+i
+k
+k
+j
+j
+i′
+j′
+k′
+k′
+j′
+i′
+Figure 32: The schemes of the NLO 2PR graphs.
+The general strategy used in this section is the following:
+• we remove all the non separating dipole/chain-vertices of a scheme S; we
+denote by S′ the resulting scheme.
+• we derive different bounds on the number of components of S′
+• finally, we use these bounds to obtain appropriate bounds on the sum of num-
+ber of broken chain-vertices of type 1, 2∗
+L, 2∗
+R and 3∗ of the original scheme
+25
+
+i
+i
+i
+i
+k
+k
+i
+j
+j
+i
+i
+i
+i
+j
+j
+j
+i
+k
+j
+i
+j
+i
+j
+j
+j
+i
+k
+k
+j
+i
+Figure 33: Examples of the degree 1, 2PR graphs in the tetrahedric (left) and the prismatic
+(right) representation.
+S.
+Thus, let us consider a scheme S with b the sum of the number of broken
+chains of type 1, 2∗
+L, 2∗
+R, 3∗.
+Note that these broken chains can be separating or
+non-separating, and we denote by p and resp. q the number of separating and resp.
+non-separating broken chains:
+b = p + q.
+(43)
+We need to find a bound on b. In order to do so, as explained above, we remove all
+the q non-separating broken chain-vertices and denote by S′ the resulting scheme.
+The degree of S′ is then ω(S′) = ω(S)−3q, and the resulting scheme has p separating
+broken chains of type 1, 2∗
+L, 2∗
+R, 3∗. We then split every broken chain-vertex of type
+2∗
+L resp. 2∗
+R into a dipole-vertex (of any color) of type βL resp. βR and a broken
+chain-vertex of type 1. Similarly, we split every broken chains-vertex of type 3∗ into
+two dipoles vertices of type β and a broken chain-vertex of type 1. The graphical
+representation of this splitting procedure is given in Figure 34. After this splitting,
+the scheme S′ has p separating broken chains-vertices of type 1.
+B2∗
+L
+B3∗
+DβL,i
+B1
+DβR,j
+DβL,i
+B1
+B2∗
+R
+DβR,i
+B1
+Figure 34: Splitting of the chains of type 2∗, 3∗.
+Consider the skeleton graphs I(S′) of S′. As S′ had only separating broken
+chains, I(S′) is a tree and its degree is given by the sum of the degree of its compo-
+26
+
+nents. Recall that the smallest positive degree possible for the components of I(S′)
+is one.
+The skeleton graph I(S′) has 3 types of connected components:
+• The rooted component, it is unique.
+• Non rooted components of positive degree, we denote their number by N+.
+• Non-rooted components of degree zero. Such components are said to be tracked
+if they are connected to a non separating broken chain-vertex of type 1 in
+S.
+Otherwise the components are said to be non-tracked.
+The number of
+non rooted degree 0 components is denoted by N0 = N0,t + N0,nt where N0,t
+resp. N0,nt is the number of tracked resp. non-tracked non-rooted degree 0
+components.
+Therefore, the number of components Nc of the skeleton graph reads
+Nc = N0,nt + N0,t + N+ + 1.
+(44)
+Recall that in the skeleton graph I(S), a degree 0 component has a valency at
+least equal to three. This implies that in I(S′) the valency of a tracked degree
+component is at least equal to one since it is at most connected to two separating
+broken chain-vertices of type 1 in S.
+Following [20], one can prove the following bounds:
+N0,t ≤ 2q,
+(45)
+N+ ≤ ω(S′),
+(46)
+2p ≥ 3N0,nt + N0,t + N+ + 1,
+(47)
+p = N0,nt + N0,t + N+.
+(48)
+After some algebra, one gets the following inequality
+p ≤ 2ω(S) − 2q − 1,
+(49)
+which further leads to:
+b ≤ 2ω(S) − q − 1.
+(50)
+Hence the maximal value for b is 2ω(S) − 1 (when q = 0). One can check that
+when b reaches the upper bound, the inequalities (45), (46) and (47) turn into
+equalities. This implies that N0,t = 0, N+ = ω(S) and that the valency of all degree
+0 components is 3, while the one of the positive degree components is 1.
+All positive components in I(S′) are of degree one, hence there are two possi-
+bilities. The components connected to a broken chain of type 1, 2∗
+L or 2∗
+R (on the
+T propagator side) before the removal are given by the NLO schemes described in
+Section 6.
+The components that are connected to a broken chain of type 3∗,2∗
+L or 2∗
+R (on
+the χ propagator side) are the NLO schemes described in Section 6 with a 2−point
+graph (obtained from the contraction of a dipole of type βL or βR as shown in Figure
+35) inserted in any of their χ propagator.
+The degree 0 components are all non tracked and have adjacency 3. They must
+then come from schemes of the form given by Figure 36 where s = 1, 2∗
+L, 2∗
+R, 3∗.
+27
+
+DβP
+Figure 35: Contraction of a type β dipole leading to a 2−point graph. (P = L or R)
+Bs
+Bs
+Bs
+Bs
+Bs
+Bs
+1
+2
+1
+2
+2
+1
+2
+1
+3
+3
+Figure 36: The different subschemes that can produce a component of degree 0 and
+adjacency 3 in the skeleton graph. Bt,A can be any broken chain of type s = 1, 2∗
+L, 2∗
+R, 3∗
+and family A.
+1
+2
+1
+2
+2
+1
+2
+1
+3
+3
+DβL,j
+DβR,i
+DβL,k
+1
+2
+1
+2
+2
+1
+2
+1
+3
+3
+DβP ,j
+Figure 37: The internal nodes of I′(S′)
+Finally, following [20], one gets that the skeleton graph I(S′) is a rooted binary
+tree with ω(S) leaves given by the rooted component or the degree 1 components
+and ω(S) − 1 inner nodes given by components of degree 0.
+As the schemes are fully encoded by their skeleton graphs, the dominant schemes
+are thus in bijection with the rooted binary trees described above.
+The generating function of these trees is
+Gω,T (t) = B1(t)2ω−1I(t)ω−1L(t)ω,
+(51)
+where I(t) resp. L(t) are the weights coming from the internal nodes resp. leaves.
+The expression of L(t) is derived by considering all the 2−point subschemes that
+lead to a component of degree and valency 1 in the skeleton graphs I′(S) of the
+scheme S. There is a consequent number of such subschemes, hence L(t) will be the
+sum of a consequent number of terms coming from these subschemes. By a tedious
+28
+
+but straightforward computation, one finds the following expressions:
+I(t) = 6tMT (t)3Mχ(t)(1 + 3Dβ) + 1 + (3Dβ)3,
+= 2(MT (t) − 1)(1 + 3Dβ) + 1 + (3D3
+β)
+(52)
+L(t) = 9MT (t)9Mχ(t)3(1 + Dβ(t)) + 3C1(t) + 6(C1(t) + Dα(t))M3
+T (t)Mχ(t)
++ 12(C2(t) + Dβ(t))MT (t)3Mχ(t) + 3C5(t) + 6(C4(t) + Dδ(t))M3
+T (t)Mχ(t)
++ 9Dβ(t)C5(t) + 9Dβ(t)C4(t) + 18C1(t)M3
+T (t)Mχ(t)
++ MT (t)3Mχ(t)
+�
+18 + 27Dβ(t) + 54Dβ(t) + 54C4(t) + 18B4(t) + 54C5(t)
++ 18B5(t)
+�
++ M3
+T (t)Mχ(t)27(1 + 3Dβ(t))
+�
+3D2
+β(t) + 3Dβ(t)(C4(t) + C5(t))
++ Dβ(t)(B4(t) + B5(t)) + 3
+2(C2
+4(t) + C2
+5(t)) + 3C4(t)C5(t)
++ C4(t)B5(t) + B4(t)C5(t))
+�
++ M3
+T (t)Mχ(t)9(1 + 3Dβ(t))(B2
+4(t) + B2
+5(t)
++ B4(t)B5(t)) + 54MT (t)6M2
+χ(t)
+�
+3Dβ(t) + 3C4(t) + B4(t) + 3C5(t)
++ 3Dβ(t)(3C4(t) + 3Dβ(t) + 3C5(t) + B4(t) + B5(t)) + B5(t) + 3C4(t)
+�
+3C5(t)
++ 3
+2C4(t) + B4(t) + B5(t)
+�
++ 3C5(t)(3
+2C5(t) + B4(t) + B5(t))
+�
+.
+(53)
+We can now sum over all the trees described above and add a melonic insertion at
+the root to find the generating function of the dominant Feynman graphs of a given
+degree ω
+Gω,dom(t) = MT (t)
+�
+T
+Gω,T = MT (t)Catω−1B1(t)2ω−1I(t)ω−1L(t)ω,
+(54)
+where Catω−1 is the (ω − 1)th Catalan number. Using equation (38) we find that
+Gω,dom
+t→tc
+∼ Catω−1MT,c
+�
+�
+1
+2MT,cK
+�
+1 − t
+tc
+�
+�
+2ω−1
+I(tc)ω−1L(tc)ω.
+(55)
+Let us now define the double scaling parameter κ(t, N) as
+κ(t, N) =
+I(tc)L(tc)
+4NM2
+T,cK2(1 − t
+tc ).
+(56)
+Recall that in the 1
+N expansion, the Feynman amplitude of a generic vacuum graph
+of degree ω scales as N3−ω, and the one of a 2-point function graph hence scales as
+N−ω (since, when cutting an edge of a vacuum graph in order to obatin a 2−point
+function graph, 3 faces, and hence a factor N3, are lost).
+The contribution of the dominant graphs of degree ω to the 2-point function in
+the double scaling limit then writes
+N−ωGω,dom = MT,cN5/2
+�L(tc)κ(t, N)
+I(tc)
+�1/2
+Catω−1κ(t, N)ω−1.
+(57)
+29
+
+Adding the contribution of the melons and summing over all the degrees, the
+2-point function in the double scaling limit is
+G2,DS(t, N) = MT,c +
+�
+ω>0
+N−ωGω,dom
+= MT,c + MT,cN− 1
+2
+�L(tc)κ(t, N)
+I(tc)
+�1/2 �
+ω∈N∗
+Catω−1κ(t, N)ω−1
+= MT,c
+�
+1 + N− 1
+2
+�L(tc)
+I(tc)
+�1/2 1 −
+�
+1 − 4κ(t, N)
+2κ(t, N)1/2
+�
+(58)
+Let us end this section by giving some interpretation of the result above. One
+can see that, in the double scaling limit, the 2-point function picks up contributions
+of all degrees, and not just from the vanishing degree (as it is the case for the large
+N limit). Moreover, one can notice that the higher it is the degree of the graph, the
+greater it is the contribution from the respective degree when the coupling constant
+tends to the critical value. Note also that, in the limit κ → 0 the large N limit is
+recovered. This behaviour is identical to the one of the matrix case.
+As the sum in equation (58) is convergent for κ ≤ 1/4, the double scaling limit
+series of the prismatic model is thus convergent. This is different from the matrix
+model case where the double scaling series diverge.
+The result obtained here is
+analogous to the one obtained for quartic tensor models (see again [20], [26] and
+[25]). Finally, let us mention that one could expect to obtain a similar double scaling
+limit behaviour for other sextic tensor models.
+8
+Concluding remarks
+In this paper, we studied the double scaling limit of the O(N)3 invariant-tensor
+model with a sextic prismatic interaction. Using the intermediate field method,
+this sextic interaction has been reduced to a quartic T 3χ tetrahedric one, χ beeing
+the intermediate field. This method allowed us to work in the so-called tetrahedric
+representation where all prismatic vertices of the Feynman graphs are split in pairs of
+tetrahedra vertices. In order to obtain our results, we thus generalised the methods
+used in the study of the single field model with T 4 tetrahedric interaction to the
+T 3χ case.
+This strategy allowed us to give a new method to identify the LO graphs explic-
+itly in the large N expansion of the model. In the tetrahedric representation, the LO
+graphs are melonic graphs with melonic insertions that can be performed on the two
+types of propagators. In the prismatic representation, the LO graphs are a different
+class of graphs. These graphs are obtained from the triple tadpole given in Figure
+8 and recursively inserting a 2−point double tadpole on any propagator or splitting
+any prismatic vertex into two such vertices linked by a pair of edges as in Figure
+9. We have then have introduced chains, dipoles and schemes and we used them
+to describe the general terms of the 1/N expansion of the model. We used them
+to exhibit both the NLO and the dominant graphs of the model in the tetrahedric
+representation. The schemes of the dominant graphs are in bijection with rooted
+binary trees whose leaves are the schemes of the NLO graphs and whose internal
+nodes are degree 0 components. Finally, we computed the 2-point function in the
+double scaling limit, see equation (58) above.
+30
+
+A natural follow up is to apply methods used in this paper to other sextic interac-
+tions, such as the sextic interactions considered (from a renormalization perspective)
+in [22]. For example, one could consider a model with the four interactions given in
+Figure 38. By using a real intermediate field, the interactions of the model can be
+λ1
+λ2
++
++
+all color
+permutations
+√λ1λ2
++
+all color
+permutations
+Figure 38: The internal nodes of I′(S′)
+reduced to a tetrahedric and pillows T 3χ interactions as in Figure 39. In this model,
+the tetrahedron interactions can be paired to pillow interactions. This renders the
+model somehow richer than the prismatic model with a more envolved combinatorial
+structure. Moreover, the study of this model could serve as an intermediate step
+toward the computation of the double scaling limit of the O(N)3-invariant tensor
+model containing all the sextic connected interactions.
+T
+T
+T
+i
+i
+χ
+T
+T
+T
+χ
+√λ1
+√λ2
++
+i = 1
+3
+Figure 39: The internal nodes of I′(S′)
+Acknowledgements. The authors have been partially supported by the ANR-
+20-CE48-0018 “3DMaps” grant.
+A. T. has been partially supported by the PN
+09370102 grant. The authors warmly acknowledge Victor Nador for useful discus-
+sions at various steps of this research project.
+References
+[1]
+R. G. Gurau. Random tensors. Oxford University Press, 2017.
+[2]
+A. Tanasa. Combinatorial Physics. Oxford University Press, 2021.
+[3]
+A. Tanasa. “The Multi-Orientable Random Tensor Model, a Review”. In:
+Symmetry, Integrability and Geometry: Methods and Applications (June
+2016). doi: 10.3842/sigma.2016.056.
+[4]
+A. Tanasa. “Tensor models, a quantum field theoretical particulariza-
+tion”. In: Proc. Rom. Acad. A 13.3 (2012), pp. 225–234. arXiv: 1211.
+4444 [math.CO].
+[5]
+R. Gurau. Notes on Tensor Models and Tensor Field Theories. 2019.
+doi: 10.48550/ARXIV.1907.03531.
+[6]
+R. G. Gurau. “Notes on tensor models and tensor field theories”. In:
+Ann. Inst. H. Poincare D Comb. Phys. Interact. 9.1 (2022), pp. 159–
+218. doi: 10.4171/aihpd/117. arXiv: 1907.03531 [hep-th].
+31
+
+[7]
+I. R. Klebanov, F. Popov, and G. Tarnopolsky. “TASI Lectures on Large
+N Tensor Models”. In: PoS TASI2017 (2018), p. 004. doi: 10.22323/
+1.305.0004. arXiv: 1808.09434 [hep-th].
+[8]
+J.-B. Zuber. Introduction to random matrices. 2011.
+[9]
+P. Francesco, P. Ginsparg, and J. Zinn-Justin. “2D gravity and random
+matrices”. In: Physics Reports 254.1-2 (Mar. 1995), pp. 1–133. doi: 10.
+1016/0370-1573(94)00084-g.
+[10]
+P. Di Francesco. 2D Quantum Gravity, Matrix Models and Graph Com-
+binatorics. 2004. doi: 10.48550/ARXIV.MATH-PH/0406013.
+[11]
+E. Witten. An SYK-Like Model Without Disorder. 2016. doi: 10.48550/
+ARXIV.1610.09758.
+[12]
+I. R. Klebanov and G. Tarnopolsky. “Uncolored random tensors, melon
+diagrams, and the Sachdev-Ye-Kitaev models”. In: Phys. Rev. D 95.4
+(2017), p. 046004. doi: 10.1103/PhysRevD.95.046004. arXiv: 1611.
+08915 [hep-th].
+[13]
+Kitaev. http://online.kitp.ucsb.edu/online/entangled15/kitaev/ , (talk at
+KITP).
+[14]
+J. Ambjørn, B. Durhuus, and T. Jónsson. “Three-Dimensional simplicial
+quantum gravity and generalized matrix models”. In: Modern Physics
+Letters A 06.12 (1991), pp. 1133–1146. doi: 10.1142/S0217732391001184.
+eprint: https://doi.org/10.1142/S0217732391001184.
+[15]
+R. Gurau. “Colored Group Field Theory”. In: Communications in Math-
+ematical Physics 304.1 (Mar. 2011), pp. 69–93. doi: 10.1007/s00220-
+011-1226-9.
+[16]
+R. Gurau. “The 1/N Expansion of Colored Tensor Models”. In: Annales
+Henri Poincaré 12.5 (Mar. 2011), pp. 829–847. doi: 10.1007/s00023-
+011-0101-8.
+[17]
+A. Tanasa. “Multi-orientable Group Field Theory”. In: J. Phys. A 45
+(2012), p. 165401. doi: 10.1088/1751-8113/45/16/165401. arXiv:
+1109.0694 [math.CO].
+[18]
+S. Dartois, V. Rivasseau, and A. Tanasa. “The 1/N Expansion of Multi-
+Orientable Random Tensor Models”. In: Annales Henri Poincaré 15.5
+(June 2013), pp. 965–984. doi: 10.1007/s00023-013-0262-8.
+[19]
+S. Carrozza and A. Tanasa. “O(N) Random Tensor Models”. In: Letters
+in Mathematical Physics 106.11 (Aug. 2016), pp. 1531–1559. doi: 10.
+1007/s11005-016-0879-x.
+[20]
+V. Bonzom, V. Nador, and A. Tanasa. “Double scaling limit for the
+O(N)3-invariant tensor model”. In: Journal of Physics A: Mathematical
+and Theoretical 55.13 (Mar. 2022), p. 135201. doi: 10.1088/1751-
+8121/ac4898.
+32
+
+[21]
+V. Bonzom, V. Nador, and A. Tanasa. “Diagrammatics of the quar-
+tic O(N)3 -invariant Sachdev-Ye-Kitaev-like tensor model”. In: Journal
+of Mathematical Physics 60 (July 2019), p. 072302. doi: 10.1063/1.
+5095248.
+[22]
+S. Giombi et al. “Prismatic large N models for bosonic tensors”. In:
+Physical Review D 98.10 (Nov. 2018). doi: 10.1103/physrevd.98.
+105005.
+[23]
+S. Prakash and R. Sinha. “Melonic dominance in subchromatic sextic
+tensor models”. In: Physical Review D 101.12 (June 2020). doi: 10.
+1103/physrevd.101.126001.
+[24]
+G. Chapuy, M. Marcus, and G. Schaeffer. “A bijection for rooted maps
+on orientable surfaces”. In: (2007). doi: 10.48550/ARXIV.0712.3649.
+[25]
+R. Gurau and G. Schaeffer. Regular colored graphs of positive degree.
+2013. doi: 10.48550/ARXIV.1307.5279.
+[26]
+R. Gurau, A. Tanasa, and D. R. Youmans. “The double scaling limit of
+the multi-orientable tensor model”. In: EPL (Europhysics Letters) 111.2
+(July 2015), p. 21002. doi: 10.1209/0295-5075/111/21002.
+[27]
+L. Lionni and V. Rivasseau. Intermediate Field Representation for Posi-
+tive Matrix and Tensor Interactions. 2016. doi: 10.48550/ARXIV.1609.
+05018.
+[28]
+R. Kenyon. An introduction to the dimer model. 2003. doi: 10.48550/
+ARXIV.MATH/0310326.
+[29]
+P. Flajolet and R. Sedgewick. Analytic Combinatorics. 1st ed. USA:
+Cambridge University Press, 2009. isbn: 0521898064.
+[30]
+E. Fusy and A. Tanasa. “Asymptotic expansion of the multi-orientable
+random tensor model”. In: (2014). doi: 10.48550/ARXIV.1408.5725.
+33
+
diff --git a/m9A0T4oBgHgl3EQfJv8c/content/tmp_files/load_file.txt b/m9A0T4oBgHgl3EQfJv8c/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d9328acb491239119889208cdb082b99958aa231
--- /dev/null
+++ b/m9A0T4oBgHgl3EQfJv8c/content/tmp_files/load_file.txt
@@ -0,0 +1,962 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf,len=961
+page_content='Double scaling limit of the prismatic tensor model  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Krajewski1, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Muller2, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Tanasa2,3  1Aix Marseille Univ, Université de Toulon, CNRS, CPT, Marseille,  France, EU  2Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Bordeaux, LaBRI CNRS UMR 5800, Talence, France, EU  3DFT, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Hulubei Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Inst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Engineering, Magurele,  Magurele, Romania, EU  January 6, 2023  Abstract  In S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Giombi, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Klebanov, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Popov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Prakash and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Tarnopolsky, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  D 98 (2018) 10, 105005, a prismatic tensor model was introduced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' We study here  the diagrammatics and the double scaling limit of this model, using the intermediate  field method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' We explicitly exhibit the next-to-leading order Feynman graphs in  the 1/N expansion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Using appropriate combinatorial tools, we further study the  general term of the 1/N expansion and we compute the 2−point function in the  double scaling limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' We find that the double scaling limit mechanism implemented  here is similar to the one implemented for various quartic tensor models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Contents  1  Introduction  2  2  The prismatic model;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' intermediate field method  4  3  Leading order graphs in the large N limit  6  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='1  Leading order graphs in the tetrahedric representation .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  7  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='2  Leading order graphs in the prismatic representation .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  8  4  Generating functions of leading order graphs  8  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='1  Generating functions of melonic graphs .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  8  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='2  Generating function of LO graphs in the prismatic representation .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  11  5  Diagrammatic Analysis  12  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='1  Dipoles and their generating functions .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  13  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='2  Chains and their generating functions  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  14  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='3  Scheme decomposition .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  19  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='02093v1  [hep-th]  5 Jan 2023  6  Next-to-leading order graphs  21  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='1  Dipole-free 2 particle irreducible graphs  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  22  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='2  2PI graphs with dipoles  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  22  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='3  2 particle reducible NLO graphs  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  24  7  Double scaling limit of the 2-point function  24  8  Concluding remarks  30  1  Introduction  Tensor models are zero-dimensional quantum field theoretical models where the  fields are tensors of arbitrary rank (see the books [1] [2] or the review articles [3],  [4], [5], [6] or [7]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Introduced as a generalization in dimension three and higher of the celebrated  random matrix models (see [8] and the reviews [9, 10]), tensor models are currently  studied in the context of mathematical physics, combinatorics and various other  domains of mathematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Thus, rank d tensor models are naturally linked to d di-  mensional random geometries, as the Feynman graphs present in their perturbative  expansion are dual to random triangulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Moreover, such models were proven  by Witten [11] and then by Klebanov and Tarnopolsky [12] to be related to the  holographic Sachdev-Ye-Kitaev model [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Initially proposed in the nineties (see, for example, [14]), tensor models lacked  the implementation of the large N mechanism (N being in this context the size of the  tensor).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' This changed in 2011, with the proposition of the so-called colored tensor  model by Gurau [15], which he proved to have a well-defined large N expansion [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Shortly after, a less restricted model (from the point of view of the class of Feynman  graphs allowed by the perturbative expansion), the multi-orientable model [17] was  proposed and proven to have a well-defined large N expansion [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  An O(N)3-invariant tensor model, was proposed in [19] (see also [20, 21] for  various diagrammatic developments).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' We refer to this type of model as single field  tetrahedric model, since one has only one tensor field in the action, and the inter-  action is tetrahedric (its index structure has the topology of a tetrahedron).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Let us also mention that the model proposed in [19] was later related by Klebanov  and Tarnopolsky in [12] to the celebrated holographic SYK model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  The case of sextic interactions for this type of O(N)3 invariant-tensor model was  studied by Giombi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' in [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' This model was called prismatic since its large  N limit is dominated by a positive-definite operator whose index structure has the  topology of a prism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' In this paper, we will study this prismatic model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  The large N expansion of tensor models is controlled, as usually in tensor models,  by a parameter ω called the degree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' The large N expansion is dominated by graphs  of vanishing degree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' In [23], it was proven that the leading order (LO) graphs in  the large N expansion of the prismatic model are not the usual melonic graphs one  is used to from tensor model literature (see again the books [1] [2] or the review  articles [3], [4], [5] or [7]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' The role of the fundamental melon is played by a triple  tadpole graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Moreover, one now has two types of melonic insertions, one at the  level of the propagator (as usually in tensor model literature), and another one at  the level of the vertex, which is a new type of melonic move with respect to what it  is known in the tensor model literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  2  In this paper we give a different proof of the LO graph identification of [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Our  proof relies on an extensive use of the intermediate field method, which expresses  the prismatic model as a model with quartic tetrahedric interactions, but with two  distinct tensor field (the initial tensor field and an intermediate field).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Moreover, the intermediate field method used in this papers allows us to identify  the next-to-leading (NLO) graphs in the large N expansion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  The main result of this paper is then the implementation of the celebrated double  scaling limit mechanism for the prismatic tensor model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Using a combinatorial  scheme decomposition a la [24] allows to identify at any degree a sub-family of  graphs, called dominant, whose amplitude is the most divergent when the coupling  constant of the model goes to criticality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' One then has, in this double scaling limit,  contributions of Feynman graphs of any degree, as it was already noticed for the  colored [25] model, the multi-orientable model [26] and the single field tetrahedric  model [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Note that in this paper we work with the 2−point function, and not with the  free energy when implementing the double scaling mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' This comes from the  fact that, from a combinatorial point of view, it is easier to work with the 2-point  function, which correspond to what combinatorists call a rooted graph (and which  has no symmetries).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' This is a standard tool in combinatorics and it has already  been exported in mathematical physics for the study of quartic tensor models (see  again [20], [26] and [25]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' However, the results obtained here for the 2-point function  can be extended, leading to an analogous behaviour, for the free energy (or for 2k-  point function, k here being arbitrary, see [26], where this was implemented for the  multi-orientable tensor model).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Moreover, we prove that the 2-point function of the model is summable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' This  behaviour is different with respect to the matrix model case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  In this paper, our overall strategy is the following:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Apply the intermediate field method in order to reduce the sextic interaction  of the prismatic model to the quartic, tetrahedric one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' As mentioned above,  by doing so, one now has two fields in the action, the original tensor field and  the intermediate field (also a tensor field).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' We call this the tetrahedric repre-  sentation of the model (by contrast to the "original" one, using the prismatic  vertex, which we call the prismatic representation of the model).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Generalize the results known in the case of the single field tetrahedric model  mentioned above to the two-field model obtained via the use of the intermediate  field method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' When possible, deduce the results on the original prismatic model from the  two field model above (thus somehow applying an "inverse" intermediate field  method).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  The paper is structured in the following way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' In the next section, we recall the  definition of the prismatic model and the use of the intermediate field method in  this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' In the third section, we exhibit the LO graphs, in both the tetrahedric  and the prismatic representations of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' In the following section, we study  the generating functions of the LO graphs, in both representations of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  In the fifth section we introduce appropriate diagrammatic tools in order to study,  from a combinatorial point of view, the general term of the large N expansion of this  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' We use these tools in the following sections, where the NLO Feynman graphs  3  are exhibited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' In the seventh section we identify the dominant graphs and compute  the 2−function is the double scaling limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' We end the paper with a concluding  section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  2  The prismatic model;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' intermediate field method  In this section we recall from [22] the definition of the prismatic tensor model and  the implementation of the intermediate field method for this model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Let a random tensor Ti1i2i3 with three indices ranging from 1 to N ∈ N∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' The  group O(N)3 acts in the following way on the tensor field  Ti1i2i3 = O(1)  i1j1O(2)  i1j1O(3)  i1j1Tj1j2j3,  (1)  where the O(k) are independent orthogonal matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' The action of the model writes:  SN = −1  2  �  i,j,k  TijkTijk  +tN −α  6  �  a1,a2,a3,b1,b2,b3,c1,c2,c3  Ta1b1c1Ta1b2c2Ta2b1c2Ta3b3c1Ta3b2c3Ta2b3c3,  SN = −1  2  �  i,j,k  TijkTijk + tN −α  6  Ip(T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (2)  Where  Ip(T) =  �  a1,a2,a3,b1,b2,b3,c1,c2,c3  Ta1b1c1Ta1b2c2Ta2b1c2Ta3b3c1Ta3b2c3Ta2b3c3  (3)  is the prismatic tensor invariant whose graphical representation is given in Fig  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Let us note here that the prismatic interaction above is positively defined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  1  3  1  3  1  3  2  2  Ta1b1c1  Ta3b3c1  Ta1b2c2  Ta2b1c2  Ta2b3c3  Ta3b2c3  Figure 1: The prismatic interaction  The partition function is then given by  Z(t, N) =  �  [dT]e− 1  2  �  i,j,k TijkTijk+ tN−α  6  Ip(T),  (4)  where [dT] is the tensor measure  [dT] =  N  �  i,j,k=1  dTijk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (5)  4  Using the intermediate field method, the sextic interaction above can be reduced  to a quartic interaction [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Recall that  e  tN−α  6  Ip(T) =  �  [dχ]  (2π)N3/2 e− 1  2  �N  i,j,k=1 χijkχijk  e  �  2tN−α  6  �N  a1,a2,b1,b2,c1,c2=1 Ta1b1c1Ta1b2c2Ta2b1c2χa2b2c1,  =  �  [dχ]  (2π)N3/2 e  − 1  2  �N  i,j,k=1 χijkχijk+  �  2tN−α  6  ˜It(T,χ),  (6)  where  ˜It(T, χ) =  N  �  a1,a2,b1,b2,c1,c2=1  Ta1b1c1Ta1b2c2Ta2b1c2χa2b2c1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (7)  The interaction obtained by using this intermediate field method is therefore a  tetrahedron-type interaction coupling three T fields and one intermediate field χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  The graphical representation of this interaction is given in Fig 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Ta1b1c1  Ta1b2c2  Ta2b1c2  1  3  3  1  2  χa2b2c1  Figure 2: The tetrahedric interaction  The partition function can therefore be written as  Z(t, N) =  �  [dT]  [dχ]  (2π)N3/2 e  − 1  2  �N  i,j,k=1(TijkTijk+χijkχijk)+  �  2tN−α  6  ˜It(T,χ),  =  �  [dT]  [dχ]  (2π)N3/2 e− 1  2  �N  i,j,k=1(TijkTijk+χijkχijk)+ λ′N−α′  4  ˜It(T,χ),  (8)  where we made a redefinition of the coupling constant λ′N−α′  4  =  �  2tN−α  6  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  The  identification 2α′ = α indicates that the scaling of a prismatic interaction needs to  be twice the one of a tetrahedron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Recall that the single field tetrahedron interaction  is known to be equal to 3  2 [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' One thus has, for the scaling parameter of the  prismatic interaction:  α = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (9)  In the sequel, when working with prismatic vertices, it will be stated that the  analysis is performed in the prismatic representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' When working with the  intermediate field representation, hence with tetrahedron interactions, we will refer  to it as the tetrahedric representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Using the intermediate field method described above, any prismatic vertex in a  Feynman graph can be split into two tetrahedra vertices connected by an auxiliary  field propagator χ as in Figure 3, where the field χ is represented by a curly line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  One can prove that the Feynman amplitude of a vacuum graph is equal to  AG = tnpN3−�  l=1,2,3  kl  2 = tnpN3−ω(G),  (10)  5  1  3  1  3  1  3  2  2  Ta1b1c1  Ta3b3c1  Ta1b2c2  Ta2b1c2  Ta2b3c3  Ta3b2c3  Ta1b1c1  Ta1b2c2  Ta2b1c2  1  3  3  1  2  2  χa2b2c1  3  3  1  1  χa4b4c4  Ta3b3c4  Ta3b4c3  Ta4b3c3  Figure 3: The intermediate field method for the prismatic tensor interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  where np and resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' nt are the number of vertices of the prismatic and resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' tetra-  hedric representation (recall that nt = 2np).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Moreover, the parameter  ω(G) =  �  l=1,2,3  kl  2 = 3 + 3np − fG = 3 + 3  2nt − fG  (11)  is called the degree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Let us also notice that the tetrahedric representation can be linked to dimer  models of the graphs present in the tetrahedric model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' The dimer model is the  study of the perfect matchings of a graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Recall that a perfect matching of a  graph is a configuration where all its vertices are paired with exactly one of their  connected neighbours [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' As each vertex possesses a single χ node, connecting two  vertices with a χ propagator is equivalent to pairing them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Therefore, by considering  the dimers of all the graphs in the tetrahedric model, one can derive all the graphs  present in the tetrahedric representation of the prismatic model 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' An example of  the perfect pairing of a graph in the tetrahedric model and its equivalent in the  tetrahedric representation is given in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Figure 4: On the left, a graph in the tetrahedric model and one of its perfect pairing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' On  the right is the corresponding graph in the tetrahedric representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  3  Leading order graphs in the large N limit  In this section, we study the 1  N expansion of the prismatic model and we explicitly  exhibit the dominant graphs, in both the tetrahedric and prismatic representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  1In a more general setting, replacing one of the fields in a single field interaction by an intermediate  field is equivalent to consider the dimers of the graphs present in the original model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  6  Our study, as already mentioned in the Introduction, uses the intermediate field  method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='1  Leading order graphs in the tetrahedric represen-  tation  Equation (11) above implies that the degree of the prismatic model is a non-negative  integer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Hence, the LO Feynman graphs of the model are thus the ones satisfying  the condition:  ω(G) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (12)  Let us first identify these graphs in the tetrahedric representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' As usual in the  tensor model literature, we call these graphs melonic graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' One can prove that  they are built by starting from the vacuum elementary melon shown in Figure 5 and  by recursively inserting one of the elementary 2-points melons on arbitrary edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  The insertions possible on the two types of edges are shown in Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  1  3  3  1  2  3  1  2  1  3  Figure 5: On the left, the vacuum elementary melon in the tetrahedric representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' On  the right, a simplified graphical representation of the graph where the tetrahedric vertices  are replaced by black dots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  i  i  j  j  i  j  j  i  i  j  i  j  i  j  i  j  k  k  k  k  Figure 6: The melonic insertions on the two types of propagators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Let us give in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 7 an example of melonic graphs obtained via melonic inser-  tions on a T propagator, on the LHS, and on a χ propagator on the RHS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  7  Figure 7: Example of melonic graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='2  Leading order graphs in the prismatic representa-  tion  In the prismatic representation, the elementary melon of the tetrahedric representa-  tion becomes a triple tadpole (see Figure 8 for its various graphical representations).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  We refer to this triple tadpole as the elementary triple tadpole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Let us now explain what the two melonic insertions in the tetrahedric represen-  tation become in this prismatic representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' The insertion on a T propagator is  equivalent to the insertion of a 2−point double tadpole (which is obtained by "cut-  ting" an edge of the elementary triple tadpole).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' The insertion on a χ propagator is  equivalent to an insertion at the level of a prismatic vertex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' One needs to "split" a  prismatic vertex into two prismatic vertices which are linked by T propagators (see  Figure 9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Let us give in Figure 10 some examples of LO graphs in the prismatic repre-  sentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' The first graph is the elementary triple tadpole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' The second graph is  obtained by a vertex splitting of the elementary triple tadpole vertex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' The third  graph is obtained by inserting a 2−point double tadpole on one of the edges of the  first graph (the elementary triple tadpole) and so on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  4  Generating functions of leading order graphs  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='1  Generating functions of melonic graphs  In this subsection we analyse the generating functions of melonic graphs in the  tetrahedric representation, find its singularities and the behaviour of this generating  function close to the singularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  As there are two types of 2−point functions (associated with the two propaga-  tors), we denote by MT (t) and Mχ(t) the generating functions of the two sets of  corresponding melon graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' This is given in Figure 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  One has  MT (t) = 1 + 3tM3  T (t)Mχ(t),  Mχ(t) = 1 + tM3  T (t)Mχ(t),  (13)  where the factor 3 in the first equation above counts the three different choices of  placing a χ propagator connecting the two vertices of the melonic graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Substi-  tuting Mχ(t) in the first equation gives  1 + t(M4  T (t) + 2M3  T (t)) − MT (t) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (14)  8  1  3  3  1  2  1  3  3  1  2  1  1  1  2  3  3  3  Figure 8: On the left, the elementary vacuum melon in the two graphical representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  On the right, their prismatic equivalent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' On the bottom right, the prismatic vertex is  represented by a red square.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  ,  ,  ,  i  i  i  j  j  j  k  i  i  j  i  j  j  i  j  i  j  i  j  i  j  j  i  i  j  k  k  Figure 9: The prismatic equivalent of the two melonic insertions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Figure 10: Examples of the LO graph in the prismatic representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Finding the general solution of such equation is an involved task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' However, one can  derive its singularities, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' the points where the solution stops being analytic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  One can consider the more general problem given by  F(MT , t) = 0,  (15)  where one needs to find MT (t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Using the implicit function theorem [29], one can  9  MT  MT  MT  Mχ  +  =  3  MT  MT  MT  +  =  Mχ  MT  Mχ  Figure 11: LO 2−point functions in the terahedric representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  write  dMT (t)  dt  = − ∂F/∂t  ∂F/∂MT  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (16)  This implies that MT (t) ceases to be analytic when  ∂F  ∂MT = 0 as its derivative blows  up.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  In the case of the melons, one has F(MT , t) = 1+t(MT (t)4 +2MT (t)3)−MT (t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  One then has the following system of equations (we denote MT (tc) by MT,c):  MT,c = 1 + tc(M4  T,c + 2M3  T,c),  1 = tc(4M3  T,c + 6M2  T,c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (17)  The second equation implies tc =  1  4M3  T,c+6M2  T,c , which can be substituted in the first  one to give  MT,c = 1 +  M4  T,c + 2M3  T,c  4M3  T,c + 6M2  T,c  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (18)  After some algebra, one finds M2  T,c = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  The singularities are then the points  for which MT = ±  √  2 at tc =  1  12±8  √  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Recall that Pringsheim’s theorem (see for  example [29]) implies that the singularity closest to t = 0 defines the radius of  convergence of the series expansion of MT (t) around the origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' This point is the  dominant singularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' As  1  12+8  √  2 <  1  12−8  √  2, one has  tc =  1  12 + 8  √  2 and MT (tc) =  √  2,  (19)  at the dominant singularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Let us now find the behavior of the function MT (t) near this dominant singu-  larity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' In order to do this, one needs to Taylor expand the function F(MT , t) near  a critical point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  10  Assuming that  ∂2F  ∂M2  T ̸= 0,  and using the conditions F(MT , t) = 0,  ∂F  ∂MT |tc = 0 and since ∂F  ∂t2 = 0, one has:  ∂F  ∂t |tc(tc − t) +  ∂2F  ∂t∂MT  |tc(tc − t)(MT (t) − MT,c) + O(ϵ2)  = ∂2F  ∂M2  T  |tc  1  2(MT (t) − MT,c)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (20)  In the limit t → tc (keeping only the LO term in the expansion), one has:  MT (t) t→tc  ∼ MT,c ±  �  2  ∂F/∂t|tc  ∂2F/∂M2  T |tc  √tc − t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (21)  Since MT (t) is the generating function of melonic graphs, this implies that MT (t)  is an increasing function in t and this further implies that one needs to choose,  amongst the two solutions (21), the solution with a negative sign.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Thus, the function MT (t) behaves, near the dominant singularity, as  MT (t) t→tc  ∼ MT,c −  �  �  �  � M4  T,c + 2M3  T,c  6(M2  T,c + MT,c)  �  1 − t/tc,  MT (t) t→tc  ∼ MT,c − K  �  1 − t/tc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (22)  Inserting the explicit expressions (19) of tc and MT,c, this behavior writes as  MT (t) t→tc  ∼  √  2 −  �√  2  3 (1 −  t  12 + 8  √  2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (23)  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='2  Generating function of LO graphs in the prismatic  representation  In this subsection, we analyze the generating function of LO graphs in the prismatic  representation and we give an enumerative combinatorics result for the number of  such LO graph at an arbitrary order in perturbation theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Let us denote by P the generating function of the 2−point LO graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' This  expands as P = �  n antn The coefficients an thus give us the number of LO graphs  at a given order n in perturbation theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' In order to compute these coefficients,  a closed equation for P needs to be found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' This equation can be obtained in a  diagrammatic way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Recall that we found two distinct insertions (one at the level of the propagator  and one at the level of the prismatic vertex) which generate all the LO graphs in the  prismatic representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' This translates in the diagrammatic equation represented  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 12, for the 2−point and 6−point function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  One has  P = 1 + 3P 3Γ,  Γ = t + tP 3Γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (24)  This leads to  P − 1 = t(P 4 + 2P 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (25)  11  =  +  =  +  P  P  P  P  Γ  Γ  Γ  P  P  P  i  i  �3  i=1  Figure 12: Graphical representation of the equations of the generating function P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Changing variable to y = P − 1 gives  y = t  �(y + 1)4 + 2(y + 1)3� = tf(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (26)  Using Lagrange inversion theorem (see again the book [29]), the coefficient an can  be computed in the following way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Suppose that f(x) expands as f(x) = �  k≥0 fkxk  and f0 ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Then the equation y = tf(y) admits a unique solution of the form  y(t) = �  n≥1 yntn with yn = 1  n[xn−1]f(x)n, where the notation [xm]g(x) denotes the  order m coefficient of g(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Recall that, in the case considered here, f(y) = (y + 1)4 + 2(y + 1)3 = (y +  1)3(y + 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' This implies that yn = 1  n[xn−1]  �(x + 1)3n(x + 3)n�.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Using the binomial  expansion, one can identify the coefficients as  yn = 1  n  n−1  �  k≥0  3n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' (3n − k)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (n − k − 1)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' (k + 1)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='3k+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (27)  Since y = P − 1, one thus has  P = 1 +  �  n≥1  n−1  �  k≥0  3n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' (3n − k)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (n − k − 1)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' (k + 1)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='3k+1tn,  (28)  which finally leads to the identification of the number of LO graphs in the prismatic  representation to be: a0 = 1 and an = yn, for any n ∈ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  5  Diagrammatic Analysis  In this section we introduce the diagrammatic tools needed to implement the double  scaling limit of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  12  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='1  Dipoles and their generating functions  The notion of dipole was already introduced for the colored tensor model in [16], then  for the MO tensor model in [30] and also for the O(N)3−invariant quartic model  in [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' In this subsection, we define a diagrammatic notion of dipole subgraph for  the model studied here, in the tetrahedric representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  A dipole of color i is a subgraph formed by two tetrahedric vertices connected  by two parallel edges such that the subgraph has a face of length two and of color i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  For each given color i, there are five different types of dipoles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' We call these  types of dipoles types α, βL, βR, δL and δR, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  i  i  i  i  i  i  i  i  i  i  i  i  i  i  i  αi  βi,L  δi,L  i  i  i  +  βi,R  δi,R  Figure 13: The five types of dipoles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  To simplify the graphical representation, the dipoles can be replaced by the  dipole-vertices shown in Figure 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Dα,i  DβR,i  DδR,i  DβL,i  DδL,i  Figure 14: The five types of dipole-vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Let us now exhibit the generating functions for the dipoles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' One needs to insert  the generating functions of melons on each edge and its square root on its half edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  This way of counting the melonic insertions on the edges allows us to avoid counting  twice the melons when there are two adjacent dipoles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Thus, the generating functions of the five types of dipoles write:  Dα = 2tMT (t)3Mχ = 2  3(MT (t) − 1),  DβL = DβR = Dβ = tMT (t)3Mχ(t) = 1  3(MT (t) − 1)  DδL = DδR = Dδ = tMT (t)3Mχ(t) = 1  3(MT (t) − 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (29)  Note that the generating function of a dipole does not depend on the color.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Notice also that the generating functions of the dipoles of type βL and βR as well  as the generating functions of the dipoles of type δL and δR are the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' In the  following, we will differentiate the generating function of these dipoles when writing  the structure of the chains (in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' However, when writing the contribution  of the dominant graphs to the 2−point function (in Section 7), we will simply  denote them by Dβ and Dδ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' This allows us to clarify the structure of the chains  while keeping a compact expression for the contribution of the dominant graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  13  From the expression of the different generating functions above, one can find  that the critical points of the dipole generating functions are identical to the ones  of the generating functions of the melon graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='2  Chains and their generating functions  Chains are defined in an analogous way as in [20] [30] to be the 4−point graphs  obtained by connecting at least two dipoles and by matching one side of a dipole to  the corresponding side of the next dipole in the chain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  A chain is said to be of length ℓ if it contains ℓ dipoles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Each chain of length ℓ  contains subchains of length 2 ≤ ℓ′ ≤ ℓ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' A chain is therefore said to be maximal if  it cannot be included in a longer chain of the graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Note that changing the length of a chain doesn’t change the degree of a graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  This can be proven by induction on the length of the chain, by inserting a dipole in  a chain of length k, and by counting carefully the number of faces and vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Using the previous five types of dipoles, there are eight different possibilities for  the external edges of a chain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' We thus have eight types of chainsIf all the dipoles  of a given chain are of color i, the respective chain is said to be an unbroken chain  of color i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' If the dipoles of the chain do not have the same color, we say that the  respective chain is broken.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Similar to the case of dipoles, in order to simplify the graphics, we represent  unbroken chains of a given type and color i by a chain-vertex C, while broken chains  are represented by chain-vertices B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' The different types of unbroken chain-vertices  are shown in Figure 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Furthermore, we classify the chains into two families:  Family A, if the external legs are the same on each side of the chain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Family B, if the external legs are different on each side of the chain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  1  2  3  4  5  A  B  C1,i  C2L,i  C3,i  C4R,i  C5L,i  C2R,i  5  C5R,i  4  C4L,i  2  Figure 15: All the different types of broken chain-vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Let us now have a closer look at the dipole structure and the generating functions  of each of these chains:  Family A:  The building block of the chains in the family A are the dipoles of  type α, βL and βR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' If a dipole of type βR doesn’t end a chain, it must be followed  by a dipole of type βL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  14  All the possibilities of gluing up dipoles are given in Figure 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' The other types  of chains of the family A follow directly from the type 1 chain as shown in Figure  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  C1,i  =  Dα,i  �  k≥1  DβR,i  DβL,i  +  Dα,i  +  DβR,i  DβL,i  �  k≥0  DβR,i  DβL,i  +  Dα,i  k  k  Figure 16: The structure of the chains of type 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  C2L,i  =  DβL,i  C1,i  Dα,i  +  C3,i  =  C1,i  Dα,i  +  DβR,i  DβL,i  +  DβR,i  DβL,i  C2R,i  =  DβR,i  C1,i  Dα,i  +  Figure 17: The structure of the chains of type 2, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  The generating functions are then derived as following:  C1 = Dα  �  k≥1  (DβRDβL + Dα)k + DβRDβL  �  k≥0  (DβRDβL + Dα)k,  = (Dα + DβRDβL)  �  k≥0  (D2  β + Dα)k − Dα,  =  Dα + DβRDβL  1 − (Dα + DβRDβL) − Dα,  (30)  and  C2L = DβL(C1 + Dα) = DβL  Dα + DβRDβL  1 − (Dα + DβRDβL),  C2R = DβR(C1 + Dα) = Dβ  Dα + DβRDβL  1 − (Dα + DβRDβL),  C3 = DβL(1 + C1 + Dα)DβR =  DβLDβR  1 − (Dα + DβLDβR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (31)  15  The generating functions of the broken chains of type 1 can be derived from  the expressions of the generating functions above by noticing that every chain of  type 1 that is not of a given color must be broken.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' When building chains, there are  three possible colors of dipoles to insert.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Multiplying each generating functions of  dipoles by a factor three, and subtracting the chains of color i, gives the generating  functions of the broken chains B1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' This writes as:  B1 =  3Dα + 9DβLDβR  1 − (3Dα + 9DβLDβR) − 3Dα −  �  i=1,2,3  C1,i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (32)  The expressions of the remaining types of broken chains follow then from Figure 18  and write:  B2L = 6DβL(C1 + Dα) + 3DβLB1,  B2R = 6(C1 + Dα)DβR + 3B1DβR,  B3 = 18DβL(C1 + Dα)DβR + 6DβLDβR + 9DβLB1DβR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (33)  B2L  =  DβL,i  C1,j  Dα,j  +  B3  =  C1,j  Dα,j  +  DβR,k  DβL,i  +  DβR,j  DβL,i  �3  i̸=j  +  �3  i=1  DβL,i  B1  �3  i̸=j  +  DβR,j  DβL,i  �3  i,j  B1  B2R  =  DβR,i  C1,j  Dα,j  +  �3  i̸=j  +  �3  i=1  DβR,i  B1  i ̸= j ork ̸= i  ork ̸= j  � 3  Figure 18: The structure of the broken chains of family A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  After summing over the three colors in the last term of equation (32), and after  16  some further algebra, one gets:  B1 = 6DβLDβR + 18(DβLDβR)2 + 6D2  α + 24DαDβLDβR  �1 − (3Dα + 9DβLDβR)  ��1 − (Dα + DβLDβR)  �  ,  B2L = DβL  24DβLDβR + 6Dα  �1 − (3Dα + 9DβLDβR)  ��1 − (Dα + DβLDβR)  �,  B2R = DβR  24DβLDβR + 6Dα  �1 − (3Dα + 9DβLDβR)  ��1 − (Dα + DβLDβR)  �,  B3 =  3DβLDβR(2 + 6DβLDβR)  �1 − (3Dα + 9DβLDβR)  ��1 − (Dα + DβLDβR)  �.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (34)  Family B:  As above, the structure of the chains in family B is derived from their  building blocks that are dipoles of type δL and δR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' If a dipole of type δL or resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  δR doesn’t end a chain, it must be followed by a dipole of type δR or resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' δL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' All  the possibilities for type 5 chains are then given in Figure 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  DδL,i  DδR,i  C5R,i  =  �  k≥0  DδL,i  DδR,i  k  DδR,i  DδL,i  C5L,i  =  �  k≥0  DδR,i  DδL,i  k  Figure 19: Structure of the chains of type 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  The structure of the others chains can then be deduced from the type 5 chains  and is shown in Figure 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  DδR,i  C4R,i  =  C5R,i  DδL,i  C4L,i  =  C5L,i  DδR,i  =  C5L,i  DδL,i  =  C5R,i  Figure 20: Structure of the chains of type 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  The generating functions of family B chains write:  C5L = C5R = DδLDδR  �  k≥0  (DδLDδR)k =  DδLDδR  1 − DδLDδR  ,  C4L = DδLC5L =  D2  δLDδR  1 − DδLDδR  ,  C4R = DδRC5R =  DδLD2  δR  1 − DδLDδR  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (35)  17  Using a similar argument as in the case of family A chains, the broken chains of  this family are found to be  B5L = B5R = DδLDδR  6 + 18DδLDδR  (1 − DδLDδR)(1 − 9DδLDδR),  B4L =  24D2  δLDδR  (1 − DδLDδR)(1 − 9DδLDδR),  B4R =  24DδLD2  δR  (1 − DδLDδR)(1 − 9DδLDδR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (36)  The formulas obtained above for the generating functions of the various types  of chains have therefore five different types of singular points:  As any dipole has the same singular points as the melons, the chains also have  the same singular points as the melons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  For the unbroken and broken chains of family A, the points satisfying Dα +  DβLDβR = 1 are singular points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  For the broken chains of family A, the points satisfying 3Dα + 9DβLDβR = 1  are singular points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  For the colored and broken chains of family B, the points satisfying DδLDδR =  1 are singular points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  For the broken chains of family B, the points satisfying 9DδLDδR = 1 are  singular points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Inserting the expression of the generating functions of the dipoles in the singularity  conditions above, one has:  2  3(MT (t) − 1) + 1  9(MT (t) − 1)2 = 1,  2(MT (t) − 1) + (MT (t) − 1)2 = 1,  1  9(MT (t) − 1)2 = 1,  (MT (t) − 1)2 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (37)  Each condition leads to a 2nd order equation and the solutions of these equations are:  MT = −2±3  √  2, MT = ±  √  2, MT = 4, −2 and resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' MT = 2, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' The points where  3Dα + 9D2  β = 1 are therefore also points where the melons are singular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Recall that  MT (t) was chosen to be an increasing function of t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' This means that the singularity  with the smallest |MT | is also the one with t closest to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Inserting MT = 0 in  equation (14) gives 1 = 0 and is therefore impossible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' The dominant singularity is  then the point (MT,c, tc) = (  √  2,  1  8  √  2+12) which is a singular point for the generating  functions of melons and broken chains of family A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Notice also from equation (34) that only the broken chains of type 2L,2R, 3 that  are composed of a broken chain of type 1 are singular at the critical point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' We  denote these specific chains by a star such that B2∗  L = 3DβLB1, B2∗  R = 3DβRB1 and  B3∗ = 9DβLB1DβR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Then, near the critical point, one gets:  18  B1  t→tc  ≈  3Dα + 9D2  β  1 − (3Dα + 9D2  β)  t→tc  ∼  1  2MT,cK  �  1 − t  tc  ,  B2L  t→tc  ≈ B2∗  L = 3DβLB1  t→tc  ∼  MT,c − 1  MT,cK  �  1 − t  tc  ,  B2R  t→tc  ≈ B2∗  R = 3DβRB1  t→tc  ∼  MT,c − 1  MT,cK  �  1 − t  tc  ,  B3  t→tc  ≈ B3∗ = 9DβLDβRB1  t→tc  ∼  (MT,c − 1)2  MT,cK  �  1 − t  tc  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (38)  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='3  Scheme decomposition  As in [20] [30], the scheme S of a graph G is defined by eliminating from the respec-  tive graph any 2-point melonic subgraph, and replacing each maximal chain by its  corresponding chain-vertex and any dipole by its corresponding dipole-vertex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  One can prove that the degree of the scheme ω(S) is then identical to the one  of the initial graph ω(G) (see again [20] [30]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Each scheme represents then a family of graphs and any graph can be de-  rived from its corresponding scheme by replacing/inserting back the corresponding  dipoles, chains and melons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Let us give an example of a scheme and a Feynman graph corresponding to it  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  C1,i  DδR,j  i  i  j  Figure 21: Example of a graph (left) and its corresponding scheme (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  In [20] it was proven that the number of schemes at a given degree is finite  in the O(N)3-invariant model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' In order to obtain this result, it was proven that  both the number of dipole/chain-vertices and the number of tetrahedric vertices  was bounded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  The schemes of the prismatic model can be obtained by decorating the edge that  links pairs of vertices of the schemes present in the tetrahedric model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' There is also  only a finite number of ways to perform such decoration on a scheme with a given  number of dipole-vertices, chain-vertices, and tetrahedric vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' This implies that  the number of schemes at a given degree in the prismatic model must be finite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  19  As the number of schemes at each degree is finite, we can use them to compact  the infinite number of graphs at a fixed degree into a finite number of schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Thus, the sum over an infinite number of Feynman graphs in G2(t) can be written  as a sum over a finite number of schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' The 2−point function then writes  G2(t) = MT (t) +  �  ω≥1  N−ω �  PS,ω(M, C),  (39)  where PS,ω(M, C) is a polynomial of the melons generating function and the chains  generating functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' The sum in the formula above is performed on all the schemes  of degree ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' The dominant singularity of G2(t) is then the singular point (MT,c, tc) =  (  √  2,  1  8  √  2+12) of the broken chains of type 1, 2∗  L, 2∗  R and 3∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Dipole/chain-vertex removal  When studying the combinatorics schemes, a  standard operation is to remove dipole/chain-vertices and to reconnect the half-  edges together on each sides of the vertices as in Figure 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  C, B  D  e1  e2  e3  e4  e  e′  Figure 22: The process of dipole removal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  A dipole/chain-vertex is said to be separating if its removal disconnects the  scheme S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  One can prove that the removal of a separating dipole/chain-vertex  leads to a distribution of the degree between the two connected components (see  again [20] and [30]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Thus, removing a separating dipole/chain-vertex leaves the  degree invariant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Moreover, one has  ω(S) = ω(S1) + ω(S2),  (40)  where S1 and S2 are the two connected components resulting from the removal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Let us denote by S′ the scheme obtained after a dipole removal in S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' By carefully  counting the number of faces and vertices, one can prove (see again [20] and [30])  that removing a non separating dipole or chain of color i changes the degree as  ω(S) − 1 ≥ ω(S′) ≥ ω(S) − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (41)  Analogously, removing a non separating broken chain gives ω(S′) = ω(S) − 3  Skeleton graphs  When identifying the dominant schemes, a key role is played  by skeleton graphs (see again [20]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' These graphs are defined as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Consider a scheme S, its skeleton graph I(S) is obtained by removing all its  broken chain-vertices of type 1 and by adding arrows (labeled by B1) between the  edges formed in this way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Notice that the definition given here is slightly different  than the one given in [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  An example of such a dipole-vertex removal is given in Figure 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' In a skeleton  graph, the arrows play the role of the edges whereas the disconnected components  Si, resulting from the removals, play the role of the vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' However, these edges  20  B1  B1  Figure 23: The dipole removal in the construction of the skeleton graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  and vertices don’t contribute to the degree as in a Feynman graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' An example of  a scheme and its skeleton graph is given in Figure 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Skeleton graphs have several interesting properties (see again [20]):  If one of the components Si has degree 0, then this component has a valency  greater or equal to 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  This can be proven by noticing that a degree 0 graph with valency 1 must be  a melonic 2-point function and one with valency 2 must be a dipole or chain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  None of these situations can occur for a skeleton graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Let S be a scheme with q non separating chain-vertices of type 1 and let S′  the scheme obtained be removing these q chain-vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' The skeleton graph  I(S′) is a tree and its degree satisfies the inequality: ω(I(S)) ≤ ω(S) − q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  This comes from the fact that, if a scheme has only separating dipole/chain-  vertices no cycle can appear in its skeleton graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' The bound on ω(I(S)) is  derived by using equation (41) and by recalling that the removal of a separating  dipole/chain-vertex doesn’t change the degree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  If I(S) is a tree, its degree is equal to the one of its scheme and is given by  the sum of the degree of its components  ω(I(S)) =  �  i  ω(Si).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (42)  This comes from the fact that, if I(S) is a tree, all its dipole/chain-vertices  are separating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' This is then a direct consequence of equation (40).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  6  Next-to-leading order graphs  In this section we explicitly identify the NLO Feynman graphs of the prismatic  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Recall from equation (11) that the degree of the prismatic model is a non-  negative integer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Hence, if G is an NLO Feynman graph, one has: ω(G) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  The graphs of degree one for the tetrahedric model have been identified in [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Using this analysis, one can derive the corresponding NLO Feynman graphs of the  model considered here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' This is done using the following strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' We consider all  the graphs of degree one identified in [21], and investigate all the ways to decorate  each graph with a χ propagator per pair of vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Finally, by contracting the  intermediate field propagator χ and discarding the potential redundancies, all the  graphs of degree one in the prismatic representation are found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  In the tetrahedric representation, the NLO graphs can be separated into three  classes (see again [21]):  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 2PI, dipole-free Feynman graphs  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 2PI Feynman graphs with dipoles  21  C1,i  B1  B5L  B1  B1  C1,i  B5L  B1  Figure 24: An example of a scheme and its skeleton graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 2PR Feynman graphs  In the sequel, we give the schemes of the graphs in the tetrahedric representation  and give some examples of Feynman graphs in both the tetrahedric and the prismatic  representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Recall that the number of tetrahedric vertices replacing a chain-  vertex is arbitrary, and the same holds for the corresponding number prismatic  vertices (when using the prismatic representation of the model).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='1  Dipole-free 2 particle irreducible graphs  It was derived in [21] that there is a unique dipole free scheme of degree one in the  tetrahedric model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' This scheme is given in Figure (25).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Note that, since this scheme has no dipole-vertices and no chain-vertices, one  can obtain the corresponding graphs by the usual melonic insertions on any of its  edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  There are then 3 independent ways to place the χ propagator on this NLO graph,  see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  However, when contracting the χ propagators in order to obtain the prismatic  representation NLO graphs, one can show that the three graphs of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 26 lead to  the unique graph of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  The NLO graphs in the prismatic representation are thus obtained via the two  prismatic melonic moves (see above) performed on the graph of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='2  2PI graphs with dipoles  The schemes of the 2PI graphs with dipoles in the tetrahedric representation are  given in Figure 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' The edges e and e′ can be of type T or χ, implying that s = 1  22  Figure 25: The unique 2PI dipole free scheme of degree one in the tetrahedric model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Figure 26: The different ways to place the χ propagators on the NLO graph of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  i  j  j  j  j  j  j  i  i  i  i  i  i  i  j  i  j  j  k  k  k  Figure 27: The only graph found by contracting the χ edges of the graphs in Figure 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  or 5 (the case s = 4 beeing equivalent to s = 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' The explicit schemes, with the  23  2  7  Fi=4  F2 = 4  F3 = 3  w = 3＋ 6- 11= 1  2  2corresponding T or χ propagators, are given on the right side of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Let us end this subsection by giving some explicit examples of NLO 2PI graphs  with dipoles (where we have replaced the chain-vertices by chains of length four),  and their corresponding graphs in the prismatic representation - see Figure 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Cs,i  e  e′  Figure 28: The explicit schemes of the 2PI NLO graphs with dipoles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  C5,i  C1,i  ,  Figure 29: The explicit schemes of the 2PI NLO graphs with dipoles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='3  2 particle reducible NLO graphs  Recall from [21] that schemes of the 2PR graphs in the tetrahedric model are given  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  When placing the χ propagators, the corresponding schemes are given in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  The empty boxes in the figures can either be a dipole-vertex, a broken chain-vertex  or a colored chain-vertex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Let us end this section by giving some examples of NLO 2PR graphs and the  corresponding graph in the prismatic representation, see Figure 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' The first graph  in the figure is the first graph of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' The second graph is obtained from the  second scheme of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 32, where we have replaced the empty box by a chain of  length four and color i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Finally, the third graph is obtained from the second scheme  of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 32, where we have replaced the empty box by a broken chain of length four.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  7  Double scaling limit of the 2-point function  Let us recall that the dominant singularity of G2(t, N) is the point (MT,c, tc) =  (  √  2,  1  8  √  2+12) where the broken chains of type 1, 2∗  L, 2∗  R and 3∗ are singular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' The  dominant schemes are then the ones that maximize the number of these chains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  24  i  i  i  i  i  i  i  j  j  j  i  i  i  i  i  j  j  j  j  i  i  i  i  j  j  j  i  Figure 30: Examples of NLO, 2PI graphs with dipoles in the tetrahedric (left) and pris-  matic (right) representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Figure 31: The schemes of the NLO 2PR graphs in the single field tetrahedric model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  i  j  k  i′  j′  k′  i  i  k  k  j  j  i′  j′  k′  k′  j′  i′  Figure 32: The schemes of the NLO 2PR graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  The general strategy used in this section is the following:  we remove all the non separating dipole/chain-vertices of a scheme S;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' we  denote by S′ the resulting scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  we derive different bounds on the number of components of S′  finally, we use these bounds to obtain appropriate bounds on the sum of num-  ber of broken chain-vertices of type 1, 2∗  L, 2∗  R and 3∗ of the original scheme  25  i  i  i  i  k  k  i  j  j  i  i  i  i  j  j  j  i  k  j  i  j  i  j  j  j  i  k  k  j  i  Figure 33: Examples of the degree 1, 2PR graphs in the tetrahedric (left) and the prismatic  (right) representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Thus, let us consider a scheme S with b the sum of the number of broken  chains of type 1, 2∗  L, 2∗  R, 3∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Note that these broken chains can be separating or  non-separating, and we denote by p and resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' q the number of separating and resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  non-separating broken chains:  b = p + q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (43)  We need to find a bound on b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' In order to do so, as explained above, we remove all  the q non-separating broken chain-vertices and denote by S′ the resulting scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  The degree of S′ is then ω(S′) = ω(S)−3q, and the resulting scheme has p separating  broken chains of type 1, 2∗  L, 2∗  R, 3∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' We then split every broken chain-vertex of type  2∗  L resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 2∗  R into a dipole-vertex (of any color) of type βL resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' βR and a broken  chain-vertex of type 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Similarly, we split every broken chains-vertex of type 3∗ into  two dipoles vertices of type β and a broken chain-vertex of type 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' The graphical  representation of this splitting procedure is given in Figure 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' After this splitting,  the scheme S′ has p separating broken chains-vertices of type 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  B2∗  L  B3∗  DβL,i  B1  DβR,j  DβL,i  B1  B2∗  R  DβR,i  B1  Figure 34: Splitting of the chains of type 2∗, 3∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Consider the skeleton graphs I(S′) of S′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' As S′ had only separating broken  chains, I(S′) is a tree and its degree is given by the sum of the degree of its compo-  26  nents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Recall that the smallest positive degree possible for the components of I(S′)  is one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  The skeleton graph I(S′) has 3 types of connected components:  The rooted component, it is unique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Non rooted components of positive degree, we denote their number by N+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Non-rooted components of degree zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Such components are said to be tracked  if they are connected to a non separating broken chain-vertex of type 1 in  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Otherwise the components are said to be non-tracked.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  The number of  non rooted degree 0 components is denoted by N0 = N0,t + N0,nt where N0,t  resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' N0,nt is the number of tracked resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' non-tracked non-rooted degree 0  components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Therefore, the number of components Nc of the skeleton graph reads  Nc = N0,nt + N0,t + N+ + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (44)  Recall that in the skeleton graph I(S), a degree 0 component has a valency at  least equal to three.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' This implies that in I(S′) the valency of a tracked degree  component is at least equal to one since it is at most connected to two separating  broken chain-vertices of type 1 in S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  Following [20], one can prove the following bounds:  N0,t ≤ 2q,  (45)  N+ ≤ ω(S′),  (46)  2p ≥ 3N0,nt + N0,t + N+ + 1,  (47)  p = N0,nt + N0,t + N+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (48)  After some algebra, one gets the following inequality  p ≤ 2ω(S) − 2q − 1,  (49)  which further leads to:  b ≤ 2ω(S) − q − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (50)  Hence the maximal value for b is 2ω(S) − 1 (when q = 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' One can check that  when b reaches the upper bound, the inequalities (45), (46) and (47) turn into  equalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' This implies that N0,t = 0, N+ = ω(S) and that the valency of all degree  0 components is 3, while the one of the positive degree components is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  All positive components in I(S′) are of degree one, hence there are two possi-  bilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' The components connected to a broken chain of type 1, 2∗  L or 2∗  R (on the  T propagator side) before the removal are given by the NLO schemes described in  Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  The components that are connected to a broken chain of type 3∗,2∗  L or 2∗  R (on  the χ propagator side) are the NLO schemes described in Section 6 with a 2−point  graph (obtained from the contraction of a dipole of type βL or βR as shown in Figure  35) inserted in any of their χ propagator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  The degree 0 components are all non tracked and have adjacency 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' They must  then come from schemes of the form given by Figure 36 where s = 1, 2∗  L, 2∗  R, 3∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  27  DβP  Figure 35: Contraction of a type β dipole leading to a 2−point graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' (P = L or R)  Bs  Bs  Bs  Bs  Bs  Bs  1  2  1  2  2  1  2  1  3  3  Figure 36: The different subschemes that can produce a component of degree 0 and  adjacency 3 in the skeleton graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Bt,A can be any broken chain of type s = 1, 2∗  L, 2∗  R, 3∗  and family A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  1  2  1  2  2  1  2  1  3  3  DβL,j  DβR,i  DβL,k  1  2  1  2  2  1  2  1  3  3  DβP ,j  Figure 37: The internal nodes of I′(S′)  Finally, following [20], one gets that the skeleton graph I(S′) is a rooted binary  tree with ω(S) leaves given by the rooted component or the degree 1 components  and ω(S) − 1 inner nodes given by components of degree 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  As the schemes are fully encoded by their skeleton graphs, the dominant schemes  are thus in bijection with the rooted binary trees described above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  The generating function of these trees is  Gω,T (t) = B1(t)2ω−1I(t)ω−1L(t)ω,  (51)  where I(t) resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' L(t) are the weights coming from the internal nodes resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' leaves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  The expression of L(t) is derived by considering all the 2−point subschemes that  lead to a component of degree and valency 1 in the skeleton graphs I′(S) of the  scheme S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' There is a consequent number of such subschemes, hence L(t) will be the  sum of a consequent number of terms coming from these subschemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' By a tedious  28  but straightforward computation,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' one finds the following expressions:  I(t) = 6tMT (t)3Mχ(t)(1 + 3Dβ) + 1 + (3Dβ)3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='= 2(MT (t) − 1)(1 + 3Dβ) + 1 + (3D3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='β)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='(52)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='L(t) = 9MT (t)9Mχ(t)3(1 + Dβ(t)) + 3C1(t) + 6(C1(t) + Dα(t))M3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='T (t)Mχ(t)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='+ 12(C2(t) + Dβ(t))MT (t)3Mχ(t) + 3C5(t) + 6(C4(t) + Dδ(t))M3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='T (t)Mχ(t)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='+ 9Dβ(t)C5(t) + 9Dβ(t)C4(t) + 18C1(t)M3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='T (t)Mχ(t)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='+ MT (t)3Mχ(t)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='18 + 27Dβ(t) + 54Dβ(t) + 54C4(t) + 18B4(t) + 54C5(t)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='+ 18B5(t)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='+ M3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='T (t)Mχ(t)27(1 + 3Dβ(t))  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='3D2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='β(t) + 3Dβ(t)(C4(t) + C5(t))  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='+ Dβ(t)(B4(t) + B5(t)) + 3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='2(C2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='4(t) + C2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='5(t)) + 3C4(t)C5(t)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='+ C4(t)B5(t) + B4(t)C5(t))  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='+ M3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='T (t)Mχ(t)9(1 + 3Dβ(t))(B2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='4(t) + B2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='5(t)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='+ B4(t)B5(t)) + 54MT (t)6M2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='χ(t)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='3Dβ(t) + 3C4(t) + B4(t) + 3C5(t)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='+ 3Dβ(t)(3C4(t) + 3Dβ(t) + 3C5(t) + B4(t) + B5(t)) + B5(t) + 3C4(t)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='3C5(t)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='+ 3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='2C4(t) + B4(t) + B5(t)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='+ 3C5(t)(3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='2C5(t) + B4(t) + B5(t))  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (53)  We can now sum over all the trees described above and add a melonic insertion at  the root to find the generating function of the dominant Feynman graphs of a given  degree ω  Gω,dom(t) = MT (t)  �  T  Gω,T = MT (t)Catω−1B1(t)2ω−1I(t)ω−1L(t)ω,  (54)  where Catω−1 is the (ω − 1)th Catalan number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Using equation (38) we find that  Gω,dom  t→tc  ∼ Catω−1MT,c  �  �  1  2MT,cK  �  1 − t  tc  �  �  2ω−1  I(tc)ω−1L(tc)ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (55)  Let us now define the double scaling parameter κ(t, N) as  κ(t, N) =  I(tc)L(tc)  4NM2  T,cK2(1 − t  tc ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (56)  Recall that in the 1  N expansion, the Feynman amplitude of a generic vacuum graph  of degree ω scales as N3−ω, and the one of a 2-point function graph hence scales as  N−ω (since, when cutting an edge of a vacuum graph in order to obatin a 2−point  function graph, 3 faces, and hence a factor N3, are lost).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  The contribution of the dominant graphs of degree ω to the 2-point function in  the double scaling limit then writes  N−ωGω,dom = MT,cN5/2  �L(tc)κ(t, N)  I(tc)  �1/2  Catω−1κ(t, N)ω−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  (57)  29  Adding the contribution of the melons and summing over all the degrees, the  2-point function in the double scaling limit is  G2,DS(t, N) = MT,c +  �  ω>0  N−ωGω,dom  = MT,c + MT,cN− 1  2  �L(tc)κ(t, N)  I(tc)  �1/2 �  ω∈N∗  Catω−1κ(t, N)ω−1  = MT,c  �  1 + N− 1  2  �L(tc)  I(tc)  �1/2 1 −  �  1 − 4κ(t, N)  2κ(t, N)1/2  �  (58)  Let us end this section by giving some interpretation of the result above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' One  can see that, in the double scaling limit, the 2-point function picks up contributions  of all degrees, and not just from the vanishing degree (as it is the case for the large  N limit).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Moreover, one can notice that the higher it is the degree of the graph, the  greater it is the contribution from the respective degree when the coupling constant  tends to the critical value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Note also that, in the limit κ → 0 the large N limit is  recovered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' This behaviour is identical to the one of the matrix case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  As the sum in equation (58) is convergent for κ ≤ 1/4, the double scaling limit  series of the prismatic model is thus convergent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' This is different from the matrix  model case where the double scaling series diverge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  The result obtained here is  analogous to the one obtained for quartic tensor models (see again [20], [26] and  [25]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Finally, let us mention that one could expect to obtain a similar double scaling  limit behaviour for other sextic tensor models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  8  Concluding remarks  In this paper, we studied the double scaling limit of the O(N)3 invariant-tensor  model with a sextic prismatic interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Using the intermediate field method,  this sextic interaction has been reduced to a quartic T 3χ tetrahedric one, χ beeing  the intermediate field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' This method allowed us to work in the so-called tetrahedric  representation where all prismatic vertices of the Feynman graphs are split in pairs of  tetrahedra vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' In order to obtain our results, we thus generalised the methods  used in the study of the single field model with T 4 tetrahedric interaction to the  T 3χ case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  This strategy allowed us to give a new method to identify the LO graphs explic-  itly in the large N expansion of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' In the tetrahedric representation, the LO  graphs are melonic graphs with melonic insertions that can be performed on the two  types of propagators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' In the prismatic representation, the LO graphs are a different  class of graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' These graphs are obtained from the triple tadpole given in Figure  8 and recursively inserting a 2−point double tadpole on any propagator or splitting  any prismatic vertex into two such vertices linked by a pair of edges as in Figure  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' We have then have introduced chains, dipoles and schemes and we used them  to describe the general terms of the 1/N expansion of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' We used them  to exhibit both the NLO and the dominant graphs of the model in the tetrahedric  representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' The schemes of the dominant graphs are in bijection with rooted  binary trees whose leaves are the schemes of the NLO graphs and whose internal  nodes are degree 0 components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Finally, we computed the 2-point function in the  double scaling limit, see equation (58) above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  30  A natural follow up is to apply methods used in this paper to other sextic interac-  tions, such as the sextic interactions considered (from a renormalization perspective)  in [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' For example, one could consider a model with the four interactions given in  Figure 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' By using a real intermediate field, the interactions of the model can be  λ1  λ2  +  +  all color  permutations  √λ1λ2  +  all color  permutations  Figure 38: The internal nodes of I′(S′)  reduced to a tetrahedric and pillows T 3χ interactions as in Figure 39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' In this model,  the tetrahedron interactions can be paired to pillow interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' This renders the  model somehow richer than the prismatic model with a more envolved combinatorial  structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Moreover, the study of this model could serve as an intermediate step  toward the computation of the double scaling limit of the O(N)3-invariant tensor  model containing all the sextic connected interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  T  T  T  i  i  χ  T  T  T  χ  √λ1  √λ2  +  i = 1  3  Figure 39: The internal nodes of I′(S′)  Acknowledgements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' The authors have been partially supported by the ANR-  20-CE48-0018 “3DMaps” grant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' has been partially supported by the PN  09370102 grant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' The authors warmly acknowledge Victor Nador for useful discus-  sions at various steps of this research project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  References  [1]  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Gurau.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Random tensors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Oxford University Press, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  [2]  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Tanasa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Combinatorial Physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Oxford University Press, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  [3]  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Tanasa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' “The Multi-Orientable Random Tensor Model, a Review”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' In:  Symmetry, Integrability and Geometry: Methods and Applications (June  2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='3842/sigma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='056.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  [4]  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Tanasa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' “Tensor models, a quantum field theoretical particulariza-  tion”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' In: Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Rom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Acad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' A 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='3 (2012), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 225–234.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' arXiv: 1211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  4444 [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  [5]  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Gurau.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Notes on Tensor Models and Tensor Field Theories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='48550/ARXIV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='1907.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='03531.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  [6]  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Gurau.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' “Notes on tensor models and tensor field theories”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' In:  Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Inst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Poincare D Comb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Interact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='1 (2022), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 159–  218.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='4171/aihpd/117.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' arXiv: 1907.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='03531 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  31  [7]  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Klebanov, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Popov, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Tarnopolsky.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' “TASI Lectures on Large  N Tensor Models”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' In: PoS TASI2017 (2018), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='22323/  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='305.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='0004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' arXiv: 1808.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='09434 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  [8]  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Zuber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Introduction to random matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  [9]  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Francesco, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Ginsparg, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Zinn-Justin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' “2D gravity and random  matrices”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' In: Physics Reports 254.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='1-2 (Mar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 1995), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 1–133.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  1016/0370-1573(94)00084-g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  [10]  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Di Francesco.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 2D Quantum Gravity, Matrix Models and Graph Com-  binatorics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='48550/ARXIV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='MATH-PH/0406013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  [11]  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Witten.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' An SYK-Like Model Without Disorder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='48550/  ARXIV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='1610.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='09758.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  [12]  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Klebanov and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Tarnopolsky.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' “Uncolored random tensors, melon  diagrams, and the Sachdev-Ye-Kitaev models”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' In: Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' D 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='4  (2017), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 046004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='046004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' arXiv: 1611.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  08915 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  [13]  Kitaev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' http://online.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='kitp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='ucsb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='edu/online/entangled15/kitaev/ , (talk at  KITP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  [14]  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Ambjørn, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Durhuus, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Jónsson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' “Three-Dimensional simplicial  quantum gravity and generalized matrix models”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' In: Modern Physics  Letters A 06.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='12 (1991), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 1133–1146.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='1142/S0217732391001184.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  eprint: https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='1142/S0217732391001184.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  [15]  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Gurau.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' “Colored Group Field Theory”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' In: Communications in Math-  ematical Physics 304.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='1 (Mar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 2011), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 69–93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='1007/s00220-  011-1226-9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  [16]  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Gurau.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' “The 1/N Expansion of Colored Tensor Models”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' In: Annales  Henri Poincaré 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='5 (Mar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 2011), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 829–847.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='1007/s00023-  011-0101-8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  [17]  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Tanasa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' “Multi-orientable Group Field Theory”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' In: J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' A 45  (2012), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 165401.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='1088/1751-8113/45/16/165401.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' arXiv:  1109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='0694 [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  [18]  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Dartois, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Rivasseau, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Tanasa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' “The 1/N Expansion of Multi-  Orientable Random Tensor Models”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' In: Annales Henri Poincaré 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='5  (June 2013), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 965–984.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='1007/s00023-013-0262-8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  [19]  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Carrozza and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Tanasa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' “O(N) Random Tensor Models”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' In: Letters  in Mathematical Physics 106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='11 (Aug.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 2016), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 1531–1559.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  1007/s11005-016-0879-x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  [20]  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Bonzom, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Nador, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Tanasa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' “Double scaling limit for the  O(N)3-invariant tensor model”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' In: Journal of Physics A: Mathematical  and Theoretical 55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='13 (Mar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 2022), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 135201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='1088/1751-  8121/ac4898.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  32  [21]  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Bonzom, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Nador, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Tanasa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' “Diagrammatics of the quar-  tic O(N)3 -invariant Sachdev-Ye-Kitaev-like tensor model”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' In: Journal  of Mathematical Physics 60 (July 2019), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 072302.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  5095248.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  [22]  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Giombi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' “Prismatic large N models for bosonic tensors”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' In:  Physical Review D 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='10 (Nov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='1103/physrevd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  105005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  [23]  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Prakash and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Sinha.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' “Melonic dominance in subchromatic sextic  tensor models”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' In: Physical Review D 101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='12 (June 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  1103/physrevd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='126001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  [24]  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Chapuy, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Marcus, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Schaeffer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' “A bijection for rooted maps  on orientable surfaces”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' In: (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='48550/ARXIV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='0712.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='3649.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  [25]  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Gurau and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Schaeffer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Regular colored graphs of positive degree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='48550/ARXIV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='1307.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='5279.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  [26]  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Gurau, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Tanasa, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Youmans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' “The double scaling limit of  the multi-orientable tensor model”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' In: EPL (Europhysics Letters) 111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='2  (July 2015), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 21002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='1209/0295-5075/111/21002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  [27]  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Lionni and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Rivasseau.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Intermediate Field Representation for Posi-  tive Matrix and Tensor Interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='48550/ARXIV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='1609.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  05018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  [28]  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Kenyon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' An introduction to the dimer model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='48550/  ARXIV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='MATH/0310326.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  [29]  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Flajolet and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Sedgewick.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Analytic Combinatorics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' 1st ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' USA:  Cambridge University Press, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' isbn: 0521898064.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  [30]  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Fusy and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' Tanasa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' “Asymptotic expansion of the multi-orientable  random tensor model”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' In: (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='48550/ARXIV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='1408.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='5725.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
+page_content='  33' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9A0T4oBgHgl3EQfJv8c/content/2301.02093v1.pdf'}
diff --git a/m9E3T4oBgHgl3EQf6wsw/content/tmp_files/2301.04792v1.pdf.txt b/m9E3T4oBgHgl3EQf6wsw/content/tmp_files/2301.04792v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a04f0e815142bb28731e3bafc4d62e66e83a97d6
--- /dev/null
+++ b/m9E3T4oBgHgl3EQf6wsw/content/tmp_files/2301.04792v1.pdf.txt
@@ -0,0 +1,1485 @@
+A Programming Model for GPU Load Balancing
+Muhammad Osama
+mosama@ucdavis.edu
+University of California, Davis
+Davis, California, USA
+Serban D. Porumbescu
+sdporumbescu@ucdavis.edu
+University of California, Davis
+Davis, California, USA
+John D. Owens
+jowens@ucdavis.edu
+University of California, Davis
+Davis, California, USA
+Abstract
+We propose a GPU fine-grained load-balancing abstraction
+that decouples load balancing from work processing and
+aims to support both static and dynamic schedules with a
+programmable interface to implement new load-balancing
+schedules. Prior to our work, the only way to unleash the
+GPU’s potential on irregular problems has been to workload-
+balance through application-specific, tightly coupled load-
+balancing techniques.
+With our open-source framework for load-balancing, we
+hope to improve programmers’ productivity when devel-
+oping irregular-parallel algorithms on the GPU, and also
+improve the overall performance characteristics for such
+applications by allowing a quick path to experimentation
+with a variety of existing load-balancing techniques. Con-
+sequently, we also hope that by separating the concerns of
+load-balancing from work processing within our abstraction,
+managing and extending existing code to future architectures
+becomes easier.
+CCS Concepts: • Computing methodologies → Shared
+memory algorithms.
+Keywords: load balancing, sparse computation, GPU, sched-
+uling
+1
+Introduction
+Graphical Processing Units (GPUs) excel at and are often
+designed for regular fine-grained parallel problems, such as
+General Matrix Multiplication (GEMM). In regular problems
+like GEMM, neighboring threads have similar or identical
+workloads and often achieve nearly 100% of peak GPU theo-
+retical performance. What is much more challenging is an
+application with ample fine-grained parallelism but irregu-
+lar parallelism. In such applications, neighboring threads
+Distribution Statement “A” (Approved for Public Release, Distribution Un-
+limited).
+Permission to make digital or hard copies of part or all of this work for
+personal or classroom use is granted without fee provided that copies are
+not made or distributed for profit or commercial advantage and that copies
+bear this notice and the full citation on the first page. Copyrights for third-
+party components of this work must be honored. For all other uses, contact
+the owner/author(s).
+PPoPP ’23, February 25-March 1, 2023, Montreal, QC, Canada
+© 2023 Copyright held by the owner/author(s).
+ACM ISBN 979-8-4007-0015-6/23/02.
+https://doi.org/10.1145/3572848.3577434
+running in a lockstep fashion will have different workloads—
+perhaps different amounts of work—making an efficient im-
+plementation on a highly parallel machine like a GPU a
+significant challenge.
+Consider Sparse-Matrix Vector Multiplication (SpMV),
+with a sparse matrix A and a dense vector 𝑥 as inputs. SpMV
+computes the output vector 𝑦 = A𝑥 and is an example of ir-
+regular fine-grained parallelism. Unlike in GEMM, the sparse
+matrix in SpMV can contain irregularity within the rows of
+the matrix: the rows of the matrix can have different numbers
+of non-zero entries. A simple mapping of one row to each
+GPU thread can expose this irregularity, where neighboring
+threads may be assigned different amounts of non-zeros to
+process, causing threads within the same warp1 to wait on
+threads with large amounts of non-zeros. The imbalance cre-
+ated due to this irregularity—specifically, when the work is
+not equally distributed among the parallel actors, and conse-
+quently, some actors are idle while others do more work—is
+defined as the load-imbalance problem.
+Current implementations solve this load-imbalance prob-
+lem on GPUs using application-specific load-balancing tech-
+niques that aim to evenly distribute the work such that each
+thread gets the same number of work items to achieve maxi-
+mum performance (for instance, Merrill and Garland’s load-
+balanced SpMV implementation [20]). These load-balancing
+techniques are often tightly coupled with the application
+itself. The load-balancing components within these imple-
+mentations are both complex and often collectively the most
+significant contributor to the performance of an applica-
+tion. Our work here generalizes today’s application-specific
+load-balancing algorithms into a clean, modular, powerful
+abstraction that can be applied to many complex irregular
+workloads.
+In the process of building our abstraction, we identified
+common load-balancing approaches currently deployed with-
+in sparse, irregular applications on GPUs: application-specific
+frameworks such as GraphIt [5], Gunrock [29], and Graph-
+BLAST [31]; techniques from low-level CUDA libraries such
+as ModernGPU [3] and CUB [24]; and other hand-coded
+implementations of load-balancing algorithms within ap-
+plications such as SpMV/SpMM [10, 14, 20], triangle count-
+ing [13, 16], and breadth-first search [6, 21]. We show that
+1A CUDA warp is a collection of 32 threads that execute instructions in lock-
+step. Threads in a warp are divergent-free, and run in a Single Instruction
+Multiple Thread (SIMT) fashion.
+arXiv:2301.04792v1  [cs.DC]  12 Jan 2023
+
+PPoPP ’23, February 25-March 1, 2023, Montreal, QC, Canada
+M. Osama, S. D. Porumbescu, and J. D. Owens
+with a simple, intuitive, powerful abstraction, these load-
+balancing schedules can be extended to support irregular
+workloads that are more general than the specific problem
+for which they were designed. We demonstrate this by using
+sparse-linear-algebra-based load balancing for data-centric
+graph traversal kernels.
+Writing high-performance load-balancing code is com-
+plex, in large part because this code must perform many
+roles. Among other tasks, it must ingest data from a specific
+data structure, perform user-defined computation on that
+data, and schedule that computation in a load-balanced way.
+The key insight in our abstraction is to separate the concerns
+between workload mapping (the load-balance task) and work
+execution (the user-defined computation), where we map
+sparse formats (such as Compressed Sparse Row (CSR)) to
+simple abstraction components called work atoms, tiles,
+and sets. These fundamental components are expressed as
+composable C++ ranges and range-based for loops, and are
+used to build load-balancing schedules. Programmers can
+then use these APIs to build load-balanced, high-performance
+applications and primitives. Expressed in this way, we can
+reconstruct existing application-dependent load-balancing
+techniques that address irregularity to be more general, port-
+able, and programmable. The contributions of our work are
+as follows:
+1. We present a novel abstraction for irregular-parallel
+workloads on GPUs. Our abstraction at a high level al-
+lows programmers to develop sparse, irregular-parallel
+algorithms with minimal code while delivering high
+performance.
+2. We design and implement a set of intuitive APIs, avail-
+able in our open-source GPU load-balancing frame-
+work, built on the proposed abstraction using CUDA-
+C++ ranges and range-based for loops.
+3. We show the ease of implementing new load-balancing
+schedules by implementing a novel cooperative groups-
+based load-balancing schedule, described in Section 5.2,
+which is a generalization of previous thread-, warp-,
+and block-level load-balancing schedules [30].
+4. We provide state-of-the-art SpMV performance as a
+benchmark with a geomean of speedup of 2.7× for
+the SuiteSparse Matrix Collection [11] over cuSparse’s
+state-of-the-art implementation using simple heuris-
+tics and 3 GPU load-balancing schedules.
+2
+Design Goals
+Our programming model focuses on the broad category of
+fine-grained nested data parallelism. Load-balancing task-
+level parallelism requires a different approach and is beyond
+the scope of this work. This section highlights the design
+goals of our load-balancing abstraction:
+Achieve high performance. First and foremost, the goal
+of our work is to achieve the high performance of existing-
+load balancing algorithms for irregular applications. Our ab-
+straction cannot come at the cost of significant overhead or
+performance degradation. We measure our success in achiev-
+ing high performance by comparing the performance of our
+abstraction against the performance of existing hardwired
+implementations.
+A composable and programmable interface. Importan-
+tly, we do not want to restrict the user to a library interface
+that takes control of the larger system. Programmers strongly
+prefer to adopt new software components that fit into their
+control structures rather than require them to adopt a new
+control structure. We want to allow the users to (1) maintain
+control of GPU kernel boundaries (kernel launches), (2) be
+able to add new load-balancing algorithms, and (3) compose
+new load-balanced primitives from existing load-balancing
+APIs. We measure the programmability of our work by com-
+paring the Lines of Code (LOC) of our abstraction against
+existing implementations and show composability by im-
+plementing a new load-balancing algorithm in terms of our
+existing APIs.
+Extensible to new applications. We aim to decouple and
+extend application-specific load-balancing techniques to new
+irregular-parallel domains. Our abstraction seeks to promote
+the reuse of existing load-balancing techniques for new ap-
+plications. We use SpMV as a benchmark application im-
+plemented using three different load-balancing techniques,
+some of which were previously used to implement parallel
+graph analytics kernels [5, 6, 10, 29].
+Facilitate the exploration of optimizations. A key goal
+of our abstraction is to facilitate the exploration of optimiza-
+tions for a given application by switching the underlying
+load-balancing algorithms used to balance the work. We
+want to encourage our users to experiment with heuristics
+and new load-balancing techniques to discover what works
+best for their application needs. We measure the success of
+this goal by optimizing SpMV’s performance response for
+a large corpus of sparse matrices across several different
+load-balancing techniques.
+Non-Goals
+In addition to the above design goals, we also define our
+non-goals:
+Targeting other parallel architectures. Although we
+believe the lessons learned should apply to other parallel
+architectures, we explicitly target NVIDIA’s CUDA architec-
+ture and programming model [23]. Many components of our
+abstraction leverage CUDA’s compute hierarchy of threads,
+warps and blocks mapped onto the physical streaming mul-
+tiprocessors, the oversubscription model of assigning more
+work than the number of processors to fully saturate the
+
+A Programming Model for GPU Load Balancing
+PPoPP ’23, February 25-March 1, 2023, Montreal, QC, Canada
+underlying hardware, and CUDA’s Cooperative Groups pro-
+gramming model [18], described in Section 5.2, to achieve
+high performance.
+Multi-GPU support. This work focuses on load-imbalance
+issues for a single GPU and does not consider multi-GPU
+single-node or multi-node systems, although these are inter-
+esting directions for future work.
+3
+Our Load-Balancing Abstraction
+The key insight behind our GPU load balancing abstraction is
+the separation of concerns between the mapping of the work
+items to processing units and work execution. We divide our
+abstraction into three key concepts (illustrated in Figure 1),
+each of which describes a different aspect of an implementa-
+tion: (1) defining the work; (2) defining the workload balance
+across GPU threads, warps or blocks; and (3) defining the
+work execution and computation per thread on the balanced
+work. This separation allows us to cleanly divide the work be-
+tween an application developer and a load-balanced-library
+developer and facilitates the exploration of optimizations
+by mixing different load-balancing techniques and sparse-
+irregular algorithms. Sidebar 1 presents a practical example
+of the motivation for our load balancing abstraction.
+3.1
+Input from Sparse Data Structures
+We begin with our input data expressed in some form of
+sparse data structure. Examples of such data structures in-
+clude, but are not limited to, Compressed Sparse Row (CSR)
+and Coordinate (COO) formats. The goal of the first stage of
+our abstraction is to map the input data format to a common
+data framework and vocabulary that is the input to the next
+stage. This vocabulary has three simple components that
+together express the input data:
+1. A work atom, a single unit of work that is to be sched-
+uled onto the processors (for example, a non-zero el-
+ement of a sparse matrix). We assume that all work
+atoms have an equal cost during execution.
+2. A work tile, a logical entity represented as a set of
+work atoms (for example, a row of a sparse matrix).
+Work tiles may have different costs during execution.
+As we highlighted in the introduction, work is most
+logically parallelized over work tiles but is often most
+efficiently parallelized over work atoms, and mapping
+between work tiles and work atoms may be expensive
+and complex.
+3. A tile set, a set of work tiles that together comprise
+the entire working problem (for example, a sparse ma-
+trix). In our abstraction, the tiles within a tile set must
+be independent (and thus can run in parallel across
+multiple processors).
+This mapping between sparse formats and atoms/tiles/tile
+sets is defined by the user. Though we have not implemented
+Sidebar 1 A practical example of the existing, predominant
+approach to load-balancing sparse-irregular workloads.
+Consider an SpMV implementation on the GPU provided in
+the open-source CUDA CUB library [24]. CUB implements
+and maintains the SpMV algorithm presented in the paper by
+Merrill and Garland [20]. Merge-based SpMV, explained in
+detail in Section 5.2.1, is a CSR-based, perfectly load-balanced
+SpMV, where each thread gets an even share of work, and
+the amount of work is defined by the total number of matrix
+rows and the total number of non-zeros, summed. In the
+reference, this highly efficient, state-of-the-art implemen-
+tation took 1,100 lines of code (LoC) (or 503 LoC of kernel
+code) across 3 files (not including a 4th file required for a
+segmented fixup step of an additional 234 LoC). In contrast,
+the actual computation of SpMV within this reference imple-
+mentation is expressed within a single for-loop and 4–5 LoC!
+This disparity between the LoC required to map the work
+items to processing units in a load-balanced way and the
+LoC required to express the desired computation is the key
+motivation behind our work. Additionally, the CUB imple-
+mentation is specifically dedicated to the SpMV algorithm
+and would require a significant rewrite to apply it to other al-
+gorithms, even within the same computing domain. One such
+example of this exact rewrite is by Yang et al., who extend
+merge-path load balancing from SpMV to a Sparse-Matrix
+Dense-Matrix Multiplication (SpMM) implementation [30].
+The load-balancing algorithm in both works is the same but
+applied to different computations, which motivates the need
+for reuse.
+all of them, we believe our mapping abstraction here is flexi-
+ble enough to express a wide variety of existing sparse data
+formats in the literature [12] in such a way that they are
+suitable for load balancing in our abstraction’s next stage.
+As well, we have already included several common sparse
+formats (CSR, CSC, COO) in our load-balancing library im-
+plementation so that users can simply select and use them
+without having to implement them. Given a mapping to
+atoms/tiles/tile sets, we can next implement a load-balancing
+algorithm that can parallelize over work atoms or tiles trans-
+parently from the computation’s perspective.
+3.2
+Defining Load Balancing
+By expressing workloads through an abstraction that cap-
+tures work at differing levels of granularity (i.e., tile set,
+atoms, and tiles), we can more easily distribute computa-
+tion evenly across the GPU’s available resources. Given a
+user-defined input tile set and associated sequences of atoms
+and tiles, along with a user-selected partitioning algorithm,
+our load-balancing stage outputs subsequences of atoms and
+tiles assigned to processor ids (i.e., where atoms or tiles will
+be processed).
+
+PPoPP ’23, February 25-March 1, 2023, Montreal, QC, Canada
+M. Osama, S. D. Porumbescu, and J. D. Owens
+Load balance scheduler
+2
+1
+3
+6
+Sparse Data Structure
+Iterator Representation
+Load Balancing
+User-defined
+Computation 
+(kernel)
+User-defined
+Computation 
+(kernel)
+Work Execution
+Thread0
+Work Atoms and Tiles
+Thread1
+atoms iter = 0,1,2,3
+tile iter = 0,1,2,3 
+atoms/tile = 0,1,3,0
+values = 1,3,6,2
+Thread0
+Thread1
+Figure 1. Load balancing as a simple pipeline of the three key concepts of our abstraction: (1) sparse data structures represented
+as iterators, (2) load-balancing algorithm that partitions the work onto threads, and (3) user-defined computation consuming
+the balanced work and executing on each thread.
+The resulting assignment of subsequences to processor ids
+is critical to effectively balancing workloads across process-
+ing elements and is generally problem- and dataset-specific.
+The user must specify the necessary sequences. Ideally, an or-
+acle would take these sequences and select the most optimal
+subsequences for every processing element. Finding such an
+oracle is an open problem and thus we provide the next best
+thing: the ability for users to choose and experiment from
+a set of predefined schedules and the ability to implement
+their own schedules. In general, load-balancing algorithm
+designers must balance between the cost of scheduling and
+the benefits from better scheduling. A schedule could be as
+straightforward as assigning processing elements to tiles
+with arbitrary numbers of atoms (e.g., rows with an arbi-
+trary number of non-zeros in a sparse matrix) to something
+more complicated/expensive that takes on a more holistic ap-
+proach to work (e.g., considering work across multiple rows
+with a varying number of non-zeros in a sparse matrix).
+3.3
+Defining Work Execution
+The final component of our load-balancing abstraction ex-
+presses the irregular-parallel computation itself. The previ-
+ous stage inputs load-imbalanced work and load-balances
+it; this stage then consumes that load-balanced work by
+performing computation on it. The scope of what compu-
+tation can be expressed is extensive, and is only limited by
+how the load-balanced work, represented as sequences, can
+be consumed within a CUDA kernel. Since the framework
+does not assume control of the kernel, anything you can
+write in a CUDA kernel will also work in our framework.
+For instance, programmers can express a mathematical op-
+eration performed on each atom or each tile of the work,
+or build cooperative algorithms that not only consume the
+work assigned to each thread but also combine the results
+with neighboring threads to implement more complex algo-
+rithms such as parallel reduce or scan. Practical examples
+that we have implemented in our framework (see Section 4.3
+and 5.3) using this abstraction include, but are not limited
+to, sparse-linear algebra kernels, such as Sparse-Matrix and
+Sparse-Tensor contractions, and data-centric parallel graph
+algorithms, such as Single-Source Shortest Path (SSSP) and
+Breadth-First Search (BFS) built on a neighborhood traversal
+kernel.
+We expect typical users of our library will only write their
+own code for this stage of the abstraction and use standard
+data structures and load-balancing schedules that are already
+part of our library. However, those users can also implement
+custom data formats and load-balancing schedules.
+4
+High-Level Framework Implementation
+Our GPU load-balancing framework implements the abstrac-
+tion described in Section 3 using C++17 and CUDA. In our
+system, programmers use CUDA/C++ to develop irregular-
+parallel algorithms and implement new load-balancing sched-
+ules. Per our design goals of composable APIs, extensibil-
+ity, and reuse, this and the following section introduce the
+implementation details of our API, and how it is used to
+develop new applications that promote the reuse of high-
+performance load-balancing techniques available within the
+framework. We also explore a new load-balancing method
+(Section 5.2) built on CUDA’s Cooperative Groups model.
+Furthermore, we identify how our work can be used to facil-
+itate the exploration of optimizations for a given application
+such as SpMV.
+4.1
+Implementing Sparse Data Structures
+Our framework translates sparse data structures (e.g., COO,
+CSR, CSC) into work atoms, work tiles, and tile sets (Sec-
+tion 3.1) using simple C++ iterators. C++ iterators are objects
+that point to some element in a range of elements and en-
+able iteration through the elements of that range using a
+set of operators. For example, a counting_iterator is an
+iterator that represents a pointer into a range of sequen-
+tial values [1]. Our framework requires the user to define
+three important iterators using C++: (1) an iterator over all
+work atoms; (2) an iterator over the work tiles; and (3) an
+iterator over the number of atoms in each work tile. (Our
+library already supports several common sparse data struc-
+tures.) Using these iterators, the load-balancing schedule can
+then determine and distribute load-balanced work across the
+
+A Programming Model for GPU Load Balancing
+PPoPP ’23, February 25-March 1, 2023, Montreal, QC, Canada
+1
+// Simple iterators for atoms and tiles.
+2
+counting_iterator<int> atoms_iter(0, nnz);
+3
+counting_iterator<int> tile_iter(0, rows);
+4
+// Iterator over the atoms within tile i.
+5
+auto atoms_per_tile = make_transform_iterator(
+6
+tile_iter,
+7
+[tile_iter, row_offsets]
+8
+__host__ __device__(const int& i) {
+9
+return (row_offsets[tile_iter[i + 1]] -
+10
+row_offsets[tile_iter[i]]);
+11
+});
+Listing 1. Compressed-Sparse Row (CSR) format expressed
+within our framework using C++17. The CSR format de-
+scribes a matrix using three arrays: (1) column indices of
+nonzero values; (2) the extent of rows (row offsets); and
+(3) the nonzero values. Since the CSR data structure does
+not contain arrays that point to indices of atoms and tiles
+(nonzeros and rows), in the listing above we define atom
+and tile iterators as simple counting iterators from 0 to the
+total number of nonzeros (nnz) and from 0 to the total rows
+in the matrix (rows), respectively (Lines 2–3). The iterator
+over the atoms-per-work-tile is expressed using a transform
+iterator, which computes the expression within a provided
+function for each tile id. For CSR, this is simply the row offset
+of the current tile subtracted from the offset of the next tile
+(Lines 5–11).
+underlying hardware. Listing 1 shows how our abstraction
+expresses the commonly used CSR format as a tile set within
+our framework.
+4.2
+Implementing Load-Balancing Schedules
+Perhaps the most straightforward schedule is scheduling
+each work tile onto one GPU thread. This approach is com-
+mon in the literature and practice [3, 10, 21, 26, 30]; although
+this strategy is ineffective in the presence of significant load
+imbalance across tiles, we use it here as an example to illus-
+trate how load balancing is defined within our framework.
+The inputs are the three iterators from the last stage
+plus an atom and tile count. The load-balance algorithm
+developer, then, implements tiles() and atoms() proce-
+dure calls, which return the C++ range of tiles and atoms
+to be processed by the current thread, effectively creating
+a map between assigned processor ids and segments of the
+workload. Listing 2 shows a complete example of the thread-
+mapped schedule. Although a simple algorithm, it can de-
+liver high performance for well-balanced workloads with
+coarse-grained parallelism (a small number of atoms per
+tile), such as multiplying a sparse vector by a dense vector.
+Furthermore, our abstraction is not limited to only simple
+scheduling algorithms, as Section 5.2 provides examples of
+more complex load-balancing algorithms.
+1
+class schedule_t {
+2
+// Construct a thread-mapped schedule.
+3
+__host__ __device__
+4
+schedule_t(atoms_it_t atoms_it,
+5
+tiles_it_t tiles_it,
+6
+atoms_it_t atoms_per_tile_it,
+7
+size_t num_atoms, size_t num_tiles) :
+8
+m_atoms_it(atoms_it), m_tiles_it(tiles_it),
+9
+m_atoms_per_tile_it(atoms_per_tile_it),
+10
+m_num_atoms(num_atoms),
+11
+m_num_tiles(num_tiles) {}
+12
+// Range of tiles to process in "this" thread.
+13
+// Stride by grid dimension.
+14
+__host__ __device__ auto tiles() {
+15
+auto begin = m_tiles_it(blockDim.x * blockIdx.x
+16
++ threadIdx.x);
+17
+auto end = m_tiles_it(m_num_tiles);
+18
+return range(begin, end)
+19
+.step(gridDim.x * blockDim.x);
+20
+}
+21
+// Range of atoms to process in "this" thread.
+22
+__host__ __device__ auto atoms(
+23
+const std::size_t& tile) {
+24
+auto begin = m_atoms_per_tile_it[tile];
+25
+auto end = m_atoms_per_tile_it[tile + 1];
+26
+return range(begin, end).step(1);
+27
+}
+28
+};
+29
+using schedule_t = thread_mapped_schedule_t;
+Listing 2. A thread-mapped load-balancing algorithm ex-
+pressed as C++ ranges, incorporating the atoms and tiles
+defined as iterators from Listing 1. Each tile is mapped to a
+thread, where the thread id corresponds to the index of the
+tile in the tile set. All atoms within a tile are sequentially
+processed by the thread. After a tile is processed, a thread
+is mapped to the next tile, obtained by striding the index by
+the grid size of the kernel.
+4.3
+Implementing Work Execution
+Our framework is designed to explicitly let the user own the
+kernel launch boundary. Owning a CUDA kernel boundary
+means that the user is responsible for maintaining and con-
+figuring launch parameters and implementing the CUDA
+kernel used to define the application. Although this design
+decision comes at a cost of convenience and simplicity, it of-
+fers significant flexibility in what users can express through
+our abstraction. This design decision is motivated by the fol-
+lowing reasons. (1) Users are not required to add a complex
+dependency to their existing workflow/libraries, therefore
+making code maintenance simpler and more scalable as they
+do not have to rely on our framework to incorporate new
+CUDA constructs and features. (2) Users are free to express
+anything and everything CUDA allows within their kernels
+while consuming our load-balanced C++ ranges. This allows
+
+PPoPP ’23, February 25-March 1, 2023, Montreal, QC, Canada
+M. Osama, S. D. Porumbescu, and J. D. Owens
+for versatility in what can be expressed, as the users can
+now specify multiple load-balanced work domains, range-
+based for loops, and even fusing multiple computations to
+build more complex algorithms within a single kernel. (3)
+Higher-level APIs can be used to build simpler higher-level
+abstractions that do own the kernel boundary and provide
+simpler APIs at the cost of flexibility.
+As an input to this stage, users consume the load-balanced
+C++ ranges to implement their computation. This can be
+done in multiple ways, but one of the most common pat-
+terns is a nested range-based for loop that loops over all
+the assigned tiles and atoms ranges. Listing 3 shows a sim-
+ple example of a CUDA kernel that implements the SpMV
+algorithm the using CSR format and thread-mapped load-
+balancing algorithm described in Listings 1 and 2. In this
+example, the outer for loop within each thread iterates over
+the assigned rows of the sparse matrix (tiles), and the inner
+loop sequentially processes the assigned nonzeros (atoms)
+within each row. In Section 5.3 we implement and discuss
+more complex kernels and computations.
+5
+Implementation Details
+5.1
+Flexible, Composable CUDA-enabled Ranges
+The composability of load-balanced primitives and applica-
+tions using our API is a conscious design choice within our
+framework supported through the use of CUDA-enabled C++
+ranges. Our framework does not own the kernel boundary
+(kernel launch), which forces our APIs to be focused and
+contained within the kernels. This allows programmers to
+build and maintain their own kernels while still benefiting
+from our framework’s load-balancing capabilities. This is
+largely implemented using device-wide C++ functions and
+classes tagged with CUDA’s __device__ keyword.2 We im-
+plemented and expose several different types of specialized
+ranges that were particularly useful in implementing load-
+balanced schedules:
+• step_range: A range that iterates from begin to end
+in steps of step. Useful for defining load balancing
+schedules that require a custom stepping range or
+process a constant number of work items per thread
+(which can be defined using step).
+• infinite_range: A range that iterates from begin to
+infinity. Useful for defining load balancing schedules
+in persistent kernel mode [32], where the kernel persis-
+tently runs until all work is consumed or an algorithm
+has converged.
+• grid_stride_range: A specialized case of step range
+that iterates from begin to end in steps of step using
+the CUDA kernel’s grid size. Also supports block and
+2A method decorated with the __device__ keyword allows the CUDA
+compiler to generate a device-callable entry point. This allows the code to
+be called from within kernels [23].
+1
+// Implements load-balanced SpMV kernel.
+2
+__global__ void spmv(const size_t rows,
+3
+const size_t cols, const size_t nnz,
+4
+const int* offsets, const int* indices,
+5
+const float* values, const float* x,
+6
+float* y) {
+7
+// Configure load-balancing.
+8
+// Input: iterators defined for CSR format.
+9
+schedule_t config(
+10
+atoms_iter, tile_iter,
+11
+atoms_per_tile_it,
+12
+nnz, rows);
+13
+// Consume rows using a range-based for loop.
+14
+for (auto row : config.tiles()) {
+15
+type_t sum = 0;
+16
+// Consume atoms using a range-based for loop.
+17
+for (auto nz : config.atoms(row))
+18
+sum += values[nz] * x[indices[nz]];
+19
+y[row] = sum;
+20
+}
+21
+}
+22
+// Launches SpMV kernel.
+23
+constexpr size_t blocks = 256;
+24
+size_t grid = (rows + blocks - 1) / blocks;
+25
+spmv<<<grid, blocks>>>(rows, cols, nnz,
+26
+offsets, indices, values, x, y);
+Listing 3. Sparse-Vector Matrix Multiplication (SpMV) im-
+plemented within our load-balancing abstraction using
+range-based nested for loops. The sparse matrix is repre-
+sented using a CSR-based format, where 𝑥 is the dense input
+vector and 𝑦 is the dense output vector (𝑦 = 𝐴𝑥). Lines 9–12
+use the load-balancing schedule implemented in Listing 2
+and the iterators defined in Listing 1 to construct the load-
+balanced work to be processed. Lines 14 and 17 show the for
+loops within each thread, which iterate over the assigned
+rows of the sparse matrix and sequentially process the as-
+signed atoms within each row. Line 18 shows the actual
+computation performed on each work atom (nonzero), and
+Line 19 writes the result to the dense output vector 𝑦.
+warp stride variants that iterate in steps of the block
+or warp size, respectively.
+5.2
+Implementing Non-Trivial Load-Balancing
+As we describe in Section 5.1, we can decouple and express
+existing load-balancing techniques as a set of C++ ranges.
+To illustrate the potential of this abstraction, we begin by
+decoupling and expressing a state-of-the-art load-balancing
+algorithm known as merge-path [17] previously used for bal-
+ancing CSR-based SpMV and SpMM [20, 30], and implement
+three additional load balancing algorithms (warp-, block-
+and group-mapped), all of which are available in our library
+for programmers to use. Our new group-mapped algorithm
+is a tile-per-group-based schedule, where a group is defined
+
+A Programming Model for GPU Load Balancing
+PPoPP ’23, February 25-March 1, 2023, Montreal, QC, Canada
+as a collection of threads of any arbitrary size (not limited
+to a warp or block size). Our group-mapped schedule is a
+generalization of the tile-per-thread, -warp or -block sched-
+ules [5, 21] using CUDA’s Cooperative Groups programming
+model [18].
+5.2.1
+Merge-path load balancing. In the language of a
+sparse matrix, merge-path assumes that each non-zero in
+the matrix and each new row in the matrix are an equivalent
+amount of work, then evenly divides nnzs+rows work across
+the set of worker threads. Each thread then performs a 2-D
+binary search within the nonzero indices and row offsets
+of a CSR matrix to find the starting position of the row
+and nonzero it needs to process. Threads then sequentially
+process the rows and nonzeros from the starting position
+until they reach the end of their assigned work [20].
+We implement this algorithm as a load-balancing schedule
+in our abstraction by expressing it in two steps: (1) Setup:
+The initialization step of the C++ schedule class computes
+the number of work units per thread, conducts a binary
+search as described above, and stores the starting position
+of each tile and atom in a thread-local variable. (2) Ranges:
+The second step of the algorithm builds the ranges for each
+thread to process as “complete” tiles and “partial” tiles [20].
+If a thread’s atom range lies entirely within one tile, it is
+“complete”, and is processed in a simple nested loop. If a
+thread’s range crosses a tile boundary, the thread processes
+its work in a separate nested loop.
+Because we decouple the load-balancing method (Sec-
+tion 4.2, and above) from work execution (Section 4.3), we
+can use this merge-path implementation to implement not
+only SpMV but also any other algorithm whose work can
+be divided into tiles and atoms, e.g., a graph neighborhood-
+traversal algorithm used to implement breadth-first search [29].
+Just as importantly, the merge-path schedule is now no
+longer limited to a CSR-based sparse format. Supporting
+other formats only requires building the necessary slightly
+more complex iterators that are able to count atoms per tile
+(the computation that the CSR implementation achieves with
+the row offsets array in Listing 1).
+5.2.2
+Warp- and block-level load balancing. The goal
+of a warp- or block-level load-balancing schedule is to assign
+an equal share of tiles to each warp or block, which are then
+sequentially processed. The work atoms within each tile will
+be processed in parallel by the available threads within a
+warp or a block. Each thread strides by the size of the warp
+or block to process a new work atom until the end of work
+is reached.
+The imbalance across different processing units is left for
+the hardware scheduler to handle. This scheduler depends on
+the oversubscription model of CUDA, where the programmer
+can launch a larger number of warps or blocks than the GPU
+can physically schedule at any given time. As the processing
+units finish processing their work, new ones are scheduled
+from the oversubscribed pool [5, 21].
+5.2.3
+Group-level load balancing. Group-level load bal-
+ancing generalizes warp- and block-level schedules. Instead
+of requiring that group sizes are the size of a warp or block,
+as above, this method leverages CUDA’s Cooperative Groups
+(CG) programming model [18] to allow programmer-specified
+dynamically sized groups of arbitrary size. Within these
+groups, the CG model permits detailed control of the group’s
+synchronization behaviors as well as simple parallel group-
+level collectives such as reduce or scan. We leverage this
+powerful tool to implement a generalized group-level load
+balancing schedule, effectively giving us the warp- and block-
+level schedules above for free when the group size equals
+that of a warp or a block.
+Our schedule assigns work tiles to a group, and each group
+looks at its equal share of tiles and computes the number
+of atoms for each tile and stores it in a scratchpad memory
+(CUDA’s shared memory). The group then performs a paral-
+lel prefix-sum, a widely used parallel algorithm that inputs
+an array and produces a new array where the element at
+any position is a sum of all previous elements [4]. We use
+this prefix-sum array for two purposes: (1) the last element
+of a prefix-sum array indicates the aggregated number of
+work atoms that a group has to process, and (2) the posi-
+tion of each sum in the prefix-sum array corresponds to the
+work tile to which those atoms belong. The setup phase of
+the schedule builds the prefix-sum arrays per group in the
+scratchpad memory, and the ranged-loop of the schedule re-
+turns the atom to process in each thread. The corresponding
+tile, if needed, is obtained by a simple get_tile(atom_id)
+operation, which executes a binary search within the prefix-
+sum array to find the tile corresponding to the atom being
+processed.
+Relying on the CG model for this load-balancing sched-
+ule has a unique advantage of configuring the group size
+(effectively software constructs that directly map onto the
+hardware) per the shape of the problem and the underlying
+hardware architecture. For example, targeting GPUs where
+the warp size is not 32 threads (AMD’s GPU architecture
+supports a warp size of 64 [2]) is now possible with a sim-
+ple compile-time constant, or configuring the group size to
+perfectly align with the structure of the problem.
+5.3
+Application Space
+Our work definition (Section 3.1), composable APIs (Sec-
+tion 5.1), and multiple sophisticated, high-performance load-
+balancing schedules (Section 5.2) together provide for a ver-
+satile and extensible framework with plenty of room for
+application-specific optimizations. In Listing 3 we already
+demonstrated how to implement the SpMV algorithm using
+
+PPoPP ’23, February 25-March 1, 2023, Montreal, QC, Canada
+M. Osama, S. D. Porumbescu, and J. D. Owens
+1
+// ... Inside the CUDA kernel.
+2
+// Loop over all the assigned rows.
+3
+for (auto row : config.tiles()) {
+4
+// Loop over all the columns of Matrix B.
+5
+for (auto col : range(size_t(0), B.cols)
+6
+.stride(size_t(1))) { /// < New Loop
+7
+float sum = 0;
+8
+// Loop over all the assigned nonzeros.
+9
+for (auto nz : config.atoms(row))
+10
+sum += values[nz] * B(nz, col);
+11
+// Output the sum to Matrix-C.
+12
+C(row, col) = sum;
+13
+}
+14
+}
+Listing 4. A simple loop wrapped around SpMV introduced
+in Listing 3 allows us to represent the slightly more complex
+SpMM load-balanced computation.
+our framework. A simple and natural extension is to im-
+plement Sparse-Matrix Matrix Multiplication (SpMM). List-
+ing 4 shows the minor change necessary, which adds another
+loop over the columns of the B matrix around the existing
+code from Listing 3 to implement SpMM. This implementa-
+tion could also be extended to support Gustavson’s General
+Sparse Matrix-Matrix Multiplication (SpGEMM), using two
+kernels and an allocation stage; the first kernel would com-
+pute the size of the output rows used to allocate the memory
+for the output sparse matrix and the second kernel would
+perform the multiply-accumulation.
+Beyond sparse linear algebra, we can use our framework to
+address applications in other domains. Listing 5 implements
+the graph primitive Single-Source Shortest Path (SSSP) using
+our group-level load-balancing schedule. SSSP’s performance
+on GPUs is largely gated by good load balancing [5, 29],
+but if the programmer chooses a load-balancing schedule
+from our library, the details of load balancing are completely
+hidden. Moreover, the same schedules that were used in one
+application domain (e.g., sparse linear algebra) are easily
+reusable in this different application domain.
+6
+Evaluation
+We aim to show that our framework, built on our load balanc-
+ing abstraction, enables both high performance and better
+programmability for sparse-irregular problems. Our evalua-
+tion below uses our SpMV implementation as a benchmark
+against state-of-the-art implementations provided within
+NVIDIA’s (open-source) CUB library and production (closed-
+source) cuSparse library. We considered (and implemented)
+several additional applications for evaluation, including SSSP,
+BFS, and SpMM. We found they led to similar high-level con-
+clusions. Thus our evaluation here focuses on SpMV. Our
+test corpus consists of approximately the entire SuiteSparse
+Matrix Collection [11] with a broad scope of sparse matrices
+1
+// ... Inside the CUDA kernel.
+2
+// Loop over all the assigned edges to process.
+3
+for (auto edge : config.atoms()) {
+4
+auto source = config.get_tile(edge);
+5
+// G is the graph data structure
+6
+auto neighbor = G.get_neighbor(source, edge);
+7
+auto weight = G.get_edge_weight(edge);
+8
+float source_dist = dist[source];
+9
+float neighbor_dist = source_dist + weight;
+10
+// Check if the destination node has been
+11
+// claimed as someone's child.
+12
+float recover_distance =
+13
+atomicMin(&(dist[neighbor]), neighbor_dist);
+14
+// Add the neighbor to the frontier.
+15
+if (neighbor_dist < recover_distance)
+16
+out_frontier[neighbor] = true;
+17
+}
+18
+19
+// ... Outside the CUDA kernel.
+20
+// Loop until the frontier is empty.
+Listing 5. The parallel single-source shortest path (SSSP)
+graph primitive expressed using our load-balanced schedule.
+1
+10
+100
+1,000
+10,000
+100,000
+1,000,000
+10,000,000
+100,000,000
+Number of Nonzeros
+0.001
+0.002
+0.01
+0.02
+0.1
+0.2
+1
+2
+10
+20
+100
+Runtime (ms)
+cub
+merge-path
+Kernel
+Figure 2. SpMV runtime comparison: our merge-path SpMV
+implementation vs. CUB across all SuiteSparse datasets. Our
+runtimes almost perfectly match CUB’s for all datasets. The
+small number of datasets where CUB is faster is due to a
+simple heuristic that CUB uses for single-column sparse
+matrices (i.e., a sparse vector).
+from many different high-performance computing domains.
+We ran all experiments on a Ubuntu 20.04 LTS-based work-
+station with an NVIDIA Tesla V100 GPU and CUDA 11.7.
+6.1
+Performance Overhead
+Our first and foremost goal is to ensure that the elements
+within our abstraction do not add any additional perfor-
+mance overhead to the existing load balancing techniques
+and algorithms developed using them. To verify this, we
+
+A Programming Model for GPU Load Balancing
+PPoPP ’23, February 25-March 1, 2023, Montreal, QC, Canada
+compare the runtime performance of our SpMV implemen-
+tation using the merge-path schedule to the implementation
+provided by NVIDIA’s CUB library [24] (also used for Merrill
+and Garland’s merge-path SpMV paper [20]) on the Suite-
+Sparse collection. As previously mentioned, and in contrast
+to our design, CUB contains a hardwired implementation of
+the merge-path scheduling algorithms and does not decou-
+ple workload balancing from the actual SpMV computation.
+CUB’s approach is not reusable for any other irregular par-
+allel problem without significant changes to the implemen-
+tation.
+Figure 2 plots the number of nonzeros (i.e., the total work)
+vs. runtime for our work vs. CUB’s implementation. Our
+implementation has minimal performance overhead when
+using our abstraction: a geomean slowdown of 2.5% vs. CUB,
+with 92% of datasets achieving at least 90% of CUB’s perfor-
+mance. Figure 2 shows our implementation almost perfectly
+matches CUB for all datasets, except for some datasets with
+fewer than 100,000 nonzeros. Upon further investigation,
+we identify that CUB uses a simple heuristic to launch a
+thread-mapped SpMV kernel where the number of columns
+of a given input matrix equals 1 (i.e., a sparse vector). Unlike
+our more general implementation, CUB’s simple (but spe-
+cialized) thread-mapped SpMV kernel has no load-balancing
+overhead for a perfectly balanced workload such as SpVV
+computation.
+6.2
+Improved Performance Response
+We also compare our work to NVIDIA’s vendor library for
+sparse computations, cuSparse. Figure 3 shows the perfor-
+mance response of our SpMV implementation using each of
+our scheduling algorithms individually vs. cuSparse’s state-
+of-the-art implementation. Switching between any of our im-
+plementations requires very little code change; in the case of
+merge-path and thread-mapped, we need only update a sin-
+gle C++ enum (identifier) to select the desired load-balancing
+schedule.
+We then combine our scheduling algorithms into one im-
+plementation for SpMV (Figure 4), demonstrating noticeable
+performance improvements over cuSparse. This is primar-
+ily possible due to our ability to quickly experiment with
+different heuristic schemes with a variety of available load-
+balancing schedules. Here, we use merge-path unless either
+the number of rows or columns are less than the threshold
+𝛼 and the nonzeros of a given matrix are less than thresh-
+old 𝛽 (we choose 𝛼 = 500 and 𝛽 = 10000 for SuiteSparse).
+In this case, we use thread-mapped or group-mapped load
+balancing instead of merge-path. Our system shows a peak
+performance speedup of 39× and a geomean performance
+speedup of 2.7× vs. cuSparse.
+Our framework not only allows programmers to express
+computations efficiently and simply (i.e., without worry-
+ing about the load-balancing algorithms), but also quickly
+Load Balancing Algorithm
+NVIDIA/CUB
+Our Work
+Merge-Path
+503
+36
+Thread-Mapped
+22
+21
+Group-Mapped
+N/A
+30
+Warp-Mapped
+N/A
+30 (free)
+Block-Mapped
+N/A
+30 (free)
+Table 1. Lines of code (LoC) comparison for NVIDIA’s
+CUB library versus our work for SpMV application im-
+plemented using merge-path, thread-mapped and group-
+mapped (warp- and block-mapped use the exact same code
+for group-mapped) load balancing algorithms. We report
+only non-commented lines of code, formatted using the
+clang-format tool with the Chromium style guide [15], that
+contributes to the kernel implementation.
+optimize a given application using a range of scheduling
+algorithms, both with minor code changes.
+6.3
+Lines of Code (LOC)
+We are able to achieve these performance gains with mini-
+mal code complexity. Table 1 shows lines of code (LOC) for
+our framework when compared to the state-of-the-art open-
+source implementation of merge-path and thread-mapped
+within NVIDIA’s CUB library. We deliver the same per-
+formance results as highlighted in the previous sections
+with 14× and 1× fewer lines of code for merge-path and
+thread-mapped scheduling algorithms, respectively. Using
+our merge-path implementation only requires ∼15 additional
+LoC to the trivial thread-mapped schedule.
+Furthermore, we extend the same SpMV computation to
+our novel group-mapped load balancing schedule (that can
+also be specialized to perform block- and warp-mapped load
+balancing) within the same 30 LoC.
+7
+Related Work
+Load balancing is the key to achieving high performance on
+GPUs for sparse, irregular parallel problems. Several high-
+performance computing applications deploy sophisticated
+load balancing algorithms on the GPUs. For instance, high-
+performance sparse-matrix vector multiplication (SpMV)
+leverages merge-path [20] (discussed in detail in this pa-
+per) or a nonzero splitting algorithm, which partitions the
+number of non-zeros in a sparse-matrix evenly across the
+number of threads [3, 9, 26]. Sparse-matrix matrix multipli-
+cation (SpMM) and sparse matricized tensor times Khatri-
+Rao product (SpMTTKRP) use binning and bundling algo-
+rithms [14, 22, 30], which attempt to bin like-length work
+together such that they are processed together.
+While some applications actively perform work to load-
+balance a given input, others store the input in more ef-
+ficient, already-load-balanced/-partitioned formats. These
+include the F-COO format (a variant of coordinate format)
+
+PPoPP ’23, February 25-March 1, 2023, Montreal, QC, Canada
+M. Osama, S. D. Porumbescu, and J. D. Owens
+0.001
+0.002
+0.01
+0.02
+0.1
+0.2
+1
+2
+10
+20
+100
+Runtime (ms)
+0.001
+0.002
+0.01
+0.02
+0.1
+0.2
+1
+2
+10
+20
+100
+Runtime (ms)
+1
+10
+100
+1,000
+10,000
+100,0001,000,000
+100,000,000
+Number of Nonzeros
+1
+10
+100
+1,000
+10,000
+100,0001,000,000
+100,000,000
+Number of Nonzeros
+cusparse
+group-mapped
+merge-path
+thread-mapped
+Kernel
+Figure 3. Complete performance landscape of SpMV across all SuiteSparse datasets using 3 load balancing schedules vs.
+NVIDIA’s cuSparse library. This performance comparison highlights the impact of different approaches to load-balancing
+SpMV for a given dataset and number of nonzero entries within each dataset. Later in Figure 4 we use this insight to select the
+fastest schedule for an improved overall performance. Additionally, our 3 different SpMV implementations are made possible
+with very little code change.
+used for SpMTTKRP and Sparse-Tensor Tensor Multiplica-
+tion (SpTTM), where each thread gets the same number of
+nonzeros to process [19].
+Many of the above GPU load-balancing algorithms, along
+with other novel techniques, were first described in the graph
+analytics domain. Davidson et al. and Merrill and Garland
+were the first to present Warp, Block-level and Thread-Warp-
+CTA dynamic load balancing techniques for Single-Source
+
+A Programming Model for GPU Load Balancing
+PPoPP ’23, February 25-March 1, 2023, Montreal, QC, Canada
+1
+10
+100
+1,000
+10,000
+100,000
+1,000,000
+10,000,000
+100,000,000
+Number of Nonzeros
+0.1
+0.2
+0.3
+1
+2
+3
+10
+20
+30
+100
+Speedup w.r.t cuSparse
+group-mapped
+merge-path
+thread-mapped
+Kernel
+Figure 4. Speedup of our framework’s SpMV vs. cuSparse’s
+SpMV across SuiteSparse using a heuristic (Section 6.2) to
+choose the appropriate load-balancing schedule.
+Shortest Path (SSSP) and Breadth-First Search (BFS) respec-
+tively [10, 21]. Logarithmic Radix Binning (LRB) is a par-
+ticularly effective technique for binning work based on a
+logarithmic work estimate, used for the Triangle Counting
+graph algorithm and more [13, 16]. Gunrock, GraphIT, and
+GraphBLAST are graph analytics libraries that implement
+several different graph algorithms such as BFS, SSSP, Page-
+Rank, Graph Coloring, and more, built on these previously
+mentioned load-balancing techniques [5, 29, 31]. Although
+many of these are effective load balancing techniques with
+high-performance implementations, they all tightly couple
+workload scheduling with the application itself. Our frame-
+work is designed to separate these two concerns, allowing
+the application to be independent of the load-balancing algo-
+rithm, and therefore be expressed simply. Our approach also
+allows these previously proposed techniques to be imple-
+mented within our framework, and be used for applications
+beyond those originally targeted.
+Relatively few GPU works target generalized load balanc-
+ing for irregular workloads. Most of these are focused on pro-
+viding a singular, dynamic load-balancing solution centered
+on task parallelism, often using a GPU queue-based data
+structure. Cederman and Tsigas proposed a task-based ap-
+proach to load balancing an octree partitioning workload us-
+ing lock-free and lock-based methods [7]. Two Tzeng works
+provide task-management frameworks that implement load
+balancing of tasks using a single monolithic task queue and
+distributed queues with task stealing and donation [27, 28].
+CUIRRE, a framework for load balancing and characteriz-
+ing irregular applications on GPUs, also uses a task-pool
+approach [33], and more recently, Atos, a task-parallel GPU
+dynamic scheduling framework, targets asynchronous algo-
+rithms [8]. All of these works deploy either a centralized
+or a distributed queue-like data structure on the GPUs, each
+making design decisions on how the queue is to be parti-
+tioned and updated. Except for the most recent Atos work,
+most earlier works focus on a coarse-grained parallelism ap-
+proach of effectively distributing tasks to the GPU. Our work
+takes advantage of more modern GPU architectures, which
+are more effectively utilized by a fine-grained parallelism
+approach (parallelizing over work atoms instead of work
+tiles). Unlike our abstraction, these aforementioned works
+also rely on a singular load-balancing solution, whereas our
+abstraction flexibly adapts to many different load-balancing
+techniques, static and dynamic, and allows for new schedules
+to be implemented within our framework.
+8
+Conclusion
+In this paper, we present a programming model for GPU load
+balancing for sparse irregular parallel problems. Our model is
+built on the idea of separation of concerns between workload
+mapping and work execution. In the future, we are interested
+in expanding our model to a multi-GPU environment, and
+implementing load-balancing schedules that span across the
+GPU boundary covering multiple devices and nodes for mas-
+sive parallel problems. Our current work focuses solely on
+load balancing, but we also identify locality to be another key
+factor for high performance. We are interested in identifying
+an orthogonal model that builds an abstraction for caching
+and locality into our existing load-balancing framework.
+Acknowledgments
+This material is based upon work supported by Defense Ad-
+vanced Research Projects Agency (DARPA) under Contract
+No. HR0011-18-3-0007 and the National Science Foundation
+under Contract No. OAC-1740333. Any opinions, findings
+and conclusions or recommendations expressed in this mate-
+rial are those of the author(s) and do not necessarily reflect
+the views of the U.S. Government. Distribution Statement
+“A” (Approved for Public Release, Distribution Unlimited).
+We would like to acknowledge Michael Garland and Du-
+ane Merrill from NVIDIA for their guidance on the frame-
+work. We would also like to acknowledge Toluwanimi Ode-
+muyiwa, Jonathan Wapman, Matthew Drescher and Muham-
+mad Awad for research discussions and feedback on the
+work. We also acknowledge the support of AMD, Inc. (Jalal
+Mahmud and AMD Research) in the form of travel funding,
+which enables us to attend the conference to present this
+work.
+References
+[1] 2017. ISO International Standard ISO/IEC 14882:2017(E) - Program-
+ming Language C++. Technical Report. International Organization for
+Standardization (ISO). https://isocpp.org/std/the-standard.
+[2] Advanced Micro Devices, Inc. 2022. HIP Programming Guide v5.2.
+(June 2022). https://docs.amd.com/bundle/HIP-Programming-Guide-
+v5.2/page/Introduction.html
+
+PPoPP ’23, February 25-March 1, 2023, Montreal, QC, Canada
+M. Osama, S. D. Porumbescu, and J. D. Owens
+[3] Sean Baxter. 2013–2016. Moderngpu: Patterns and Behaviors for GPU
+Computing. (2013–2016). http://moderngpu.github.io/moderngpu.
+[4] Guy E. Blelloch. 1990. Prefix Sums and Their Applications. Technical
+Report CMU-CS-90-190. School of Computer Science, Carnegie Mellon
+University.
+[5] Ajay Brahmakshatriya, Yunming Zhang, Changwan Hong, Shoaib
+Kamil, Julian Shun, and Saman Amarasinghe. 2021. Compiling Graph
+Applications for GPUs with GraphIt. In IEEE/ACM International Sym-
+posium on Code Generation and Optimization (CGO 2021). 248–261.
+https://doi.org/10.1109/CGO51591.2021.9370321
+[6] F. Busato and N. Bombieri. 2015. BFS-4K: An Efficient Implementation
+of BFS for Kepler GPU Architectures. IEEE Transactions on Parallel
+and Distributed Systems 26, 7 (July 2015), 1826–1838. https://doi.org/
+10.1109/TPDS.2014.2330597
+[7] Daniel Cederman and Philippas Tsigas. 2008. On Dynamic Load-
+Balancing on Graphics Processors. In Graphics Hardware (GH ’08).
+57–64. https://doi.org/10.2312/EGGH/EGGH08/057-064
+[8] Yuxin Chen, Benjamin Brock, Serban Porumbescu, Aydın Buluç,
+Katherine Yelick, and John D. Owens. 2022. Atos: A Task-Parallel
+GPU Scheduler for Graph Analytics. In Proceedings of the International
+Conference on Parallel Processing (ICPP 2022). https://doi.org/10.1145/
+3545008.3545056 arXiv:2112.00132
+[9] Steven Dalton, Sean Baxter, Duane Merrill, Luke Olson, and Michael
+Garland. 2015. Optimizing Sparse Matrix Operations on GPUs Using
+Merge Path. In IEEE International Parallel and Distributed Processing
+Symposium. 407–416. https://doi.org/10.1109/IPDPS.2015.98
+[10] Andrew Davidson, Sean Baxter, Michael Garland, and John D. Owens.
+2014. Work-Efficient Parallel GPU Methods for Single-Source Short-
+est Paths. In Proceedings of the 28th IEEE International Parallel and
+Distributed Processing Symposium (IPDPS 2014). 349–359.
+https:
+//doi.org/10.1109/IPDPS.2014.45
+[11] Timothy A. Davis and Yifan Hu. 2011. The University of Florida Sparse
+Matrix Collection. ACM Trans. Math. Softw. 38, 1, Article 1 (Dec. 2011),
+25 pages. https://doi.org/10.1145/2049662.2049663
+[12] Salvatore Filippone, Valeria Cardellini, Davide Barbieri, and Alessan-
+dro Fanfarillo. 2017. Sparse Matrix-Vector Multiplication on GPG-
+PUs. ACM Trans. Math. Softw. 43, 4, Article 30 (Jan. 2017), 49 pages.
+https://doi.org/10.1145/3017994
+[13] James Fox, Alok Tripathy, and Oded Green. 2019. Improving Schedul-
+ing for Irregular Applications with Logarithmic Radix Binning. 2019
+IEEE High Performance Extreme Computing Conference (2019), 1–7.
+https://doi.org/10.1109/HPEC.2019.8916333
+[14] Trevor Gale, Matei Zaharia, Cliff Young, and Erich Elsen. 2020. Sparse
+GPU Kernels for Deep Learning. In Proceedings of the International
+Conference for High Performance Computing, Networking, Storage and
+Analysis (SC ’20). Article 17, 14 pages. https://doi.org/10.1109/SC41405.
+2020.00021
+[15] Google. 2023. Chromium C++ style guide. (2023). https://chromium.
+googlesource.com/chromium/src/+/HEAD/styleguide/c++/c++.md
+[16] Oded Green, James Fox, Alex Watkins, Alok Tripathy, Kasimir Gabert,
+Euna Kim, Xiaojing An, Kumar Aatish, and David A. Bader. 2018.
+Logarithmic Radix Binning and Vectorized Triangle Counting. In IEEE
+High Performance Extreme Computing Conference (HPEC 2018). 1–7.
+https://doi.org/10.1109/HPEC.2018.8547581
+[17] Oded Green, Robert McColl, and David A. Bader. 2012. GPU Merge
+Path: A GPU Merging Algorithm. In Proceedings of the 26th ACM
+International Conference on Supercomputing (ICS ’12). 331–340. https:
+//doi.org/10.1145/2304576.2304621
+[18] Mark Harris and Kyrylo Perelygin. 2017. Cooperative Groups: Flexible
+CUDA Thread Programming. (2017). https://developer.nvidia.com/
+blog/cooperative-groups/
+[19] Bangtian Liu, Chengyao Wen, Anand D. Sarwate, and Maryam Mehri
+Dehnavi. 2017. A Unified Optimization Approach for Sparse Tensor
+Operations on GPUs. IEEE International Conference on Cluster Com-
+puting (Sept. 2017), 47–57. https://doi.org/10.1109/CLUSTER.2017.75
+[20] Duane Merrill and Michael Garland. 2016. Merge-Based Parallel Sparse
+Matrix-Vector Multiplication. In International Conference for High Per-
+formance Computing, Networking, Storage and Analysis (SC ’16). 678–
+689. https://doi.org/10.1109/SC.2016.57
+[21] Duane Merrill, Michael Garland, and Andrew Grimshaw. 2012. Scal-
+able GPU Graph Traversal. In Proceedings of the 17th ACM SIGPLAN
+Symposium on Principles and Practice of Parallel Programming (PPoPP
+’12). 117–128. https://doi.org/10.1145/2145816.2145832
+[22] Israt Nisa, Jiajia Li, Aravind Sukumaran-Rajam, Richard Vuduc, and P.
+Sadayappan. 2019. Load-Balanced Sparse MTTKRP on GPUs. In IEEE
+International Parallel and Distributed Processing Symposium (IPDPS
+2019). 123–133. https://doi.org/10.1109/IPDPS.2019.00023
+[23] NVIDIA Corporation. 2007–2022. CUDA C++ Programming Guide.
+(Dec. 2007–2022). https://docs.nvidia.com/cuda/ PG-02829-001_v12.0.
+[24] NVIDIA Corporation. 2023. CUB: Cooperative primitives for CUDA
+C++. (2023). https://nvlabs.github.io/cub/.
+[25] Muhammad Osama, Serban D. Porumbescu, and John D. Owens. 2022.
+A Programming Model for GPU Load Balancing. (Dec. 2022). https:
+//doi.org/10.5281/zenodo.7465053
+[26] Markus Steinberger, Rhaleb Zayer, and Hans-Peter Seidel. 2017. Glob-
+ally homogeneous, locally adaptive sparse matrix-vector multiplication
+on the GPU. In Proceedings of the International Conference on Supercom-
+puting (ICS 2017). ACM, 13:1–13:11. https://doi.org/10.1145/3079079.
+3079086
+[27] Stanley Tzeng, Brandon Lloyd, and John D. Owens. 2012. A GPU
+Task-Parallel Model with Dependency Resolution. IEEE Computer 45,
+8 (Aug. 2012), 34–41. https://doi.org/10.1109/MC.2012.255
+[28] Stanley Tzeng, Anjul Patney, and John D. Owens. 2010. Task Manage-
+ment for Irregular-Parallel Workloads on the GPU. In Proceedings of
+High Performance Graphics (HPG ’10). 29–37. https://doi.org/10.2312/
+EGGH/HPG10/029-037
+[29] Yangzihao Wang, Yuechao Pan, Andrew Davidson, Yuduo Wu, Carl
+Yang, Leyuan Wang, Muhammad Osama, Chenshan Yuan, Weitang
+Liu, Andy T. Riffel, and John D. Owens. 2017. Gunrock: GPU Graph
+Analytics. ACM Transactions on Parallel Computing 4, 1 (Aug. 2017),
+3:1–3:49. https://doi.org/10.1145/3108140
+[30] Carl Yang, Aydın Buluç, and John D. Owens. 2018. Design Principles for
+Sparse Matrix Multiplication on the GPU. In Euro-Par 2018: Proceedings
+of the 24th International European Conference on Parallel and Distributed
+Computing, Marco Aldinucci, Luca Padovani, and Massimo Torquati
+(Eds.). 672–687. https://doi.org/10.1007/978-3-319-96983-1_48
+[31] Carl Yang, Aydın Buluç, and John D. Owens. 2022. GraphBLAST: A
+High-Performance Linear Algebra-based Graph Framework on the
+GPU. ACM Trans. Math. Software 48, 1, Article 1 (Feb. 2022), 51 pages.
+https://doi.org/10.1145/3466795
+[32] Lingqi Zhang, Mohamed Wahib, Peng Chen, Jintao Meng, Xiao Wang,
+and Satoshi Matsuoka. 2022. Persistent Kernels for Iterative Memory-
+bound GPU Applications. CoRR (April 2022). arXiv:2204.02064
+[33] Tao Zhang, Wei Shu, and Min-You Wu. 2014. CUIRRE: An open-source
+library for load balancing and characterizing irregular applications on
+GPUs. J. Parallel and Distrib. Comput. 74, 10 (Oct. 2014), 2951–2966.
+https://doi.org/10.1016/j.jpdc.2014.07.004
+
+A Programming Model for GPU Load Balancing
+PPoPP ’23, February 25-March 1, 2023, Montreal, QC, Canada
+A
+Artifact Description
+We provide the source code of our load-balancing frame-
+work called loops and our testing harness for evaluating the
+results provided within this paper.
+A.1
+Requirements
+1. Operating System Ubuntu 18.04, 20.04, Windows.
+2. Hardware NVIDIA GPU (Volta microarchitecture or
+newer).
+3. Software CUDA 11.7 or above and cmake 3.20.1 or
+newer.
+4. Compilation NVCC (comes with CUDA), g++ and
+gcc, msvc with support for C++14 standard.
+5. Output Comma-separated values (CSV) files that are
+used to generate the graphs in Section 6.
+6. Disk space 886 GB to store the entire SuiteSparse
+Matrix Collection [11] compressed and uncompressed.
+Can be reduced significantly by running the tests on
+only a subset of the dataset.
+7. Code License Apache 2.0.
+A.2
+How to Access
+The main repository is hosted on GitHub: https://github.
+com/gunrock/loops. Our framework is also available as a
+Zenodo archive: https://doi.org/10.5281/zenodo.7465053 [25].
+Detailed and well-formatted instructions are available within
+the README markdown file in the repositories, and a sum-
+mary is available below.
+A.3
+Getting Started
+Before building loops, make sure you have the CUDA Toolkit
+and cmake installed on your system, and exported in PATH of
+your system. Other external dependencies such as thrust,
+cub, etc. are automatically fetched using cmake.
+cd loops
+mkdir build && cd build
+cmake -DCMAKE_CUDA_ARCHITECTURES =70 ..
+make -j$(nproc)
+A.3.1
+Sanity Check. Run the following command in the
+cmake’s build directory:
+bin/loops.spmv.merge_path \
+-m ../ datasets/chesapeake/chesapeake.mtx \
+--validate -v
+# Expected Output
+# Elapsed (ms):
+0.063328
+# Matrix:
+chesapeake.mtx
+# Dimensions:
+39 x 39 (340)
+# Errors:
+0
+A.4
+Reproducing Results
+We provide the following instructions to regenerate the re-
+sults presented in this paper.
+1. In the run script, update DATASET_DIR to point to the
+path of all the downloaded datasets (set to the path
+of the directory containing the MM directory; inside MM
+are subdirectories with .mtx files): scripts/run.sh.
+• You may change the path to DATASET_FILES_NAME
+containing the list of all the datasets (default points
+to suitesparse.txt file in the datasets directory).
+2. Fire up the complete run using run.sh found in the
+scripts directory, cd scripts && ./run.sh. Note one
+complete run can take up to 3 days (the run goes over
+the entire SuiteSparse matrix collection dataset four
+times with four different algorithms; the main bottle-
+neck is loading files from disk).
+• Warning: Some runs on the matrices are expected to
+fail as they are not in proper MatrixMarket Format
+although labeled as .mtx. These matrices and the
+ones that do not fit on the GPU will result in run-
+time exceptions or type overflow and can be safely
+ignored.
+3. To run N number of datasets, simply adjust the stop
+condition here (default set to 10): run.sh#L22, or re-
+move this if-condition entirely to run on all available
+.mtx files: run.sh#L22-L26.
+Additionally, we provide pre-generated results (in the form
+of CSV files) to create the plots from Section 6 without need-
+ing to run all the experiments. These pre-generated results
+are available under the docs directory of the repository.
+A.5
+Expected Output and Plots
+The expected output from the above runs are csv files in
+the same directory as the run.sh. These can replace the
+existing csv files within docs/data, and a python jupyter
+notebook can be used to evaluate the results. The python
+notebook includes instructions on generating plots. See a
+sample output of one of the csv files below:
+kernel ,dataset ,rows ,cols ,nnzs ,elapsed
+merge -path ,144 ,144649 ,144649 ,2148786 ,0.07202
+merge -path ,08 blocks ,300 ,300 ,592 ,0.0170898
+merge -path ,1138 _bus ,1138 ,1138 ,4054 ,0.0200195
+
diff --git a/m9E3T4oBgHgl3EQf6wsw/content/tmp_files/load_file.txt b/m9E3T4oBgHgl3EQf6wsw/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..468ee7baa52f8889d52362495815ff522008d5ad
--- /dev/null
+++ b/m9E3T4oBgHgl3EQf6wsw/content/tmp_files/load_file.txt
@@ -0,0 +1,899 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf,len=898
+page_content='A Programming Model for GPU Load Balancing  Muhammad Osama  mosama@ucdavis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='edu  University of California, Davis  Davis, California, USA  Serban D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Porumbescu  sdporumbescu@ucdavis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='edu  University of California, Davis  Davis, California, USA  John D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Owens  jowens@ucdavis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='edu  University of California, Davis  Davis, California, USA  Abstract  We propose a GPU fine-grained load-balancing abstraction  that decouples load balancing from work processing and  aims to support both static and dynamic schedules with a  programmable interface to implement new load-balancing  schedules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Prior to our work, the only way to unleash the  GPU’s potential on irregular problems has been to workload-  balance through application-specific, tightly coupled load-  balancing techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  With our open-source framework for load-balancing, we  hope to improve programmers’ productivity when devel-  oping irregular-parallel algorithms on the GPU, and also  improve the overall performance characteristics for such  applications by allowing a quick path to experimentation  with a variety of existing load-balancing techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Con-  sequently, we also hope that by separating the concerns of  load-balancing from work processing within our abstraction,  managing and extending existing code to future architectures  becomes easier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  CCS Concepts: • Computing methodologies → Shared  memory algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  Keywords: load balancing, sparse computation, GPU, sched-  uling  1  Introduction  Graphical Processing Units (GPUs) excel at and are often  designed for regular fine-grained parallel problems, such as  General Matrix Multiplication (GEMM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' In regular problems  like GEMM, neighboring threads have similar or identical  workloads and often achieve nearly 100% of peak GPU theo-  retical performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' What is much more challenging is an  application with ample fine-grained parallelism but irregu-  lar parallelism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' In such applications, neighboring threads  Distribution Statement “A” (Approved for Public Release, Distribution Un-  limited).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  Permission to make digital or hard copies of part or all of this work for  personal or classroom use is granted without fee provided that copies are  not made or distributed for profit or commercial advantage and that copies  bear this notice and the full citation on the first page.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Copyrights for third-  party components of this work must be honored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' For all other uses, contact  the owner/author(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  PPoPP ’23, February 25-March 1, 2023, Montreal, QC, Canada  © 2023 Copyright held by the owner/author(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  ACM ISBN 979-8-4007-0015-6/23/02.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1145/3572848.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='3577434  running in a lockstep fashion will have different workloads—  perhaps different amounts of work—making an efficient im-  plementation on a highly parallel machine like a GPU a  significant challenge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  Consider Sparse-Matrix Vector Multiplication (SpMV),  with a sparse matrix A and a dense vector 𝑥 as inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' SpMV  computes the output vector 𝑦 = A𝑥 and is an example of ir-  regular fine-grained parallelism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Unlike in GEMM, the sparse  matrix in SpMV can contain irregularity within the rows of  the matrix: the rows of the matrix can have different numbers  of non-zero entries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' A simple mapping of one row to each  GPU thread can expose this irregularity, where neighboring  threads may be assigned different amounts of non-zeros to  process, causing threads within the same warp1 to wait on  threads with large amounts of non-zeros.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' The imbalance cre-  ated due to this irregularity—specifically, when the work is  not equally distributed among the parallel actors, and conse-  quently, some actors are idle while others do more work—is  defined as the load-imbalance problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  Current implementations solve this load-imbalance prob-  lem on GPUs using application-specific load-balancing tech-  niques that aim to evenly distribute the work such that each  thread gets the same number of work items to achieve maxi-  mum performance (for instance, Merrill and Garland’s load-  balanced SpMV implementation [20]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' These load-balancing  techniques are often tightly coupled with the application  itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' The load-balancing components within these imple-  mentations are both complex and often collectively the most  significant contributor to the performance of an applica-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Our work here generalizes today’s application-specific  load-balancing algorithms into a clean, modular, powerful  abstraction that can be applied to many complex irregular  workloads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  In the process of building our abstraction, we identified  common load-balancing approaches currently deployed with-  in sparse, irregular applications on GPUs: application-specific  frameworks such as GraphIt [5], Gunrock [29], and Graph-  BLAST [31];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' techniques from low-level CUDA libraries such  as ModernGPU [3] and CUB [24];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' and other hand-coded  implementations of load-balancing algorithms within ap-  plications such as SpMV/SpMM [10, 14, 20], triangle count-  ing [13, 16], and breadth-first search [6, 21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' We show that  1A CUDA warp is a collection of 32 threads that execute instructions in lock-  step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Threads in a warp are divergent-free, and run in a Single Instruction  Multiple Thread (SIMT) fashion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='04792v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='DC]  12 Jan 2023  PPoPP ’23, February 25-March 1, 2023, Montreal, QC, Canada  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Osama, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Porumbescu, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Owens  with a simple, intuitive, powerful abstraction, these load-  balancing schedules can be extended to support irregular  workloads that are more general than the specific problem  for which they were designed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' We demonstrate this by using  sparse-linear-algebra-based load balancing for data-centric  graph traversal kernels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  Writing high-performance load-balancing code is com-  plex, in large part because this code must perform many  roles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Among other tasks, it must ingest data from a specific  data structure, perform user-defined computation on that  data, and schedule that computation in a load-balanced way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  The key insight in our abstraction is to separate the concerns  between workload mapping (the load-balance task) and work  execution (the user-defined computation), where we map  sparse formats (such as Compressed Sparse Row (CSR)) to  simple abstraction components called work atoms, tiles,  and sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' These fundamental components are expressed as  composable C++ ranges and range-based for loops, and are  used to build load-balancing schedules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Programmers can  then use these APIs to build load-balanced, high-performance  applications and primitives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Expressed in this way, we can  reconstruct existing application-dependent load-balancing  techniques that address irregularity to be more general, port-  able, and programmable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' The contributions of our work are  as follows:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' We present a novel abstraction for irregular-parallel  workloads on GPUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Our abstraction at a high level al-  lows programmers to develop sparse, irregular-parallel  algorithms with minimal code while delivering high  performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' We design and implement a set of intuitive APIs, avail-  able in our open-source GPU load-balancing frame-  work, built on the proposed abstraction using CUDA-  C++ ranges and range-based for loops.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' We show the ease of implementing new load-balancing  schedules by implementing a novel cooperative groups-  based load-balancing schedule, described in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2,  which is a generalization of previous thread-, warp-,  and block-level load-balancing schedules [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' We provide state-of-the-art SpMV performance as a  benchmark with a geomean of speedup of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='7× for  the SuiteSparse Matrix Collection [11] over cuSparse’s  state-of-the-art implementation using simple heuris-  tics and 3 GPU load-balancing schedules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  2  Design Goals  Our programming model focuses on the broad category of  fine-grained nested data parallelism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Load-balancing task-  level parallelism requires a different approach and is beyond  the scope of this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' This section highlights the design  goals of our load-balancing abstraction:  Achieve high performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' First and foremost, the goal  of our work is to achieve the high performance of existing-  load balancing algorithms for irregular applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Our ab-  straction cannot come at the cost of significant overhead or  performance degradation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' We measure our success in achiev-  ing high performance by comparing the performance of our  abstraction against the performance of existing hardwired  implementations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  A composable and programmable interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Importan-  tly, we do not want to restrict the user to a library interface  that takes control of the larger system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Programmers strongly  prefer to adopt new software components that fit into their  control structures rather than require them to adopt a new  control structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' We want to allow the users to (1) maintain  control of GPU kernel boundaries (kernel launches), (2) be  able to add new load-balancing algorithms, and (3) compose  new load-balanced primitives from existing load-balancing  APIs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' We measure the programmability of our work by com-  paring the Lines of Code (LOC) of our abstraction against  existing implementations and show composability by im-  plementing a new load-balancing algorithm in terms of our  existing APIs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  Extensible to new applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' We aim to decouple and  extend application-specific load-balancing techniques to new  irregular-parallel domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Our abstraction seeks to promote  the reuse of existing load-balancing techniques for new ap-  plications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' We use SpMV as a benchmark application im-  plemented using three different load-balancing techniques,  some of which were previously used to implement parallel  graph analytics kernels [5, 6, 10, 29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  Facilitate the exploration of optimizations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' A key goal  of our abstraction is to facilitate the exploration of optimiza-  tions for a given application by switching the underlying  load-balancing algorithms used to balance the work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' We  want to encourage our users to experiment with heuristics  and new load-balancing techniques to discover what works  best for their application needs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' We measure the success of  this goal by optimizing SpMV’s performance response for  a large corpus of sparse matrices across several different  load-balancing techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  Non-Goals  In addition to the above design goals, we also define our  non-goals:  Targeting other parallel architectures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Although we  believe the lessons learned should apply to other parallel  architectures, we explicitly target NVIDIA’s CUDA architec-  ture and programming model [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Many components of our  abstraction leverage CUDA’s compute hierarchy of threads,  warps and blocks mapped onto the physical streaming mul-  tiprocessors, the oversubscription model of assigning more  work than the number of processors to fully saturate the  A Programming Model for GPU Load Balancing  PPoPP ’23, February 25-March 1, 2023, Montreal, QC, Canada  underlying hardware, and CUDA’s Cooperative Groups pro-  gramming model [18], described in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2, to achieve  high performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  Multi-GPU support.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' This work focuses on load-imbalance  issues for a single GPU and does not consider multi-GPU  single-node or multi-node systems, although these are inter-  esting directions for future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  3  Our Load-Balancing Abstraction  The key insight behind our GPU load balancing abstraction is  the separation of concerns between the mapping of the work  items to processing units and work execution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' We divide our  abstraction into three key concepts (illustrated in Figure 1),  each of which describes a different aspect of an implementa-  tion: (1) defining the work;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' (2) defining the workload balance  across GPU threads, warps or blocks;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' and (3) defining the  work execution and computation per thread on the balanced  work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' This separation allows us to cleanly divide the work be-  tween an application developer and a load-balanced-library  developer and facilitates the exploration of optimizations  by mixing different load-balancing techniques and sparse-  irregular algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Sidebar 1 presents a practical example  of the motivation for our load balancing abstraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1  Input from Sparse Data Structures  We begin with our input data expressed in some form of  sparse data structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Examples of such data structures in-  clude, but are not limited to, Compressed Sparse Row (CSR)  and Coordinate (COO) formats.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' The goal of the first stage of  our abstraction is to map the input data format to a common  data framework and vocabulary that is the input to the next  stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' This vocabulary has three simple components that  together express the input data:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' A work atom, a single unit of work that is to be sched-  uled onto the processors (for example, a non-zero el-  ement of a sparse matrix).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' We assume that all work  atoms have an equal cost during execution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' A work tile, a logical entity represented as a set of  work atoms (for example, a row of a sparse matrix).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  Work tiles may have different costs during execution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  As we highlighted in the introduction, work is most  logically parallelized over work tiles but is often most  efficiently parallelized over work atoms, and mapping  between work tiles and work atoms may be expensive  and complex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' A tile set, a set of work tiles that together comprise  the entire working problem (for example, a sparse ma-  trix).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' In our abstraction, the tiles within a tile set must  be independent (and thus can run in parallel across  multiple processors).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  This mapping between sparse formats and atoms/tiles/tile  sets is defined by the user.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Though we have not implemented  Sidebar 1 A practical example of the existing, predominant  approach to load-balancing sparse-irregular workloads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  Consider an SpMV implementation on the GPU provided in  the open-source CUDA CUB library [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' CUB implements  and maintains the SpMV algorithm presented in the paper by  Merrill and Garland [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Merge-based SpMV, explained in  detail in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1, is a CSR-based, perfectly load-balanced  SpMV, where each thread gets an even share of work, and  the amount of work is defined by the total number of matrix  rows and the total number of non-zeros, summed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' In the  reference, this highly efficient, state-of-the-art implemen-  tation took 1,100 lines of code (LoC) (or 503 LoC of kernel  code) across 3 files (not including a 4th file required for a  segmented fixup step of an additional 234 LoC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' In contrast,  the actual computation of SpMV within this reference imple-  mentation is expressed within a single for-loop and 4–5 LoC!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  This disparity between the LoC required to map the work  items to processing units in a load-balanced way and the  LoC required to express the desired computation is the key  motivation behind our work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Additionally, the CUB imple-  mentation is specifically dedicated to the SpMV algorithm  and would require a significant rewrite to apply it to other al-  gorithms, even within the same computing domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' One such  example of this exact rewrite is by Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=', who extend  merge-path load balancing from SpMV to a Sparse-Matrix  Dense-Matrix Multiplication (SpMM) implementation [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  The load-balancing algorithm in both works is the same but  applied to different computations, which motivates the need  for reuse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  all of them, we believe our mapping abstraction here is flexi-  ble enough to express a wide variety of existing sparse data  formats in the literature [12] in such a way that they are  suitable for load balancing in our abstraction’s next stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  As well, we have already included several common sparse  formats (CSR, CSC, COO) in our load-balancing library im-  plementation so that users can simply select and use them  without having to implement them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Given a mapping to  atoms/tiles/tile sets, we can next implement a load-balancing  algorithm that can parallelize over work atoms or tiles trans-  parently from the computation’s perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2  Defining Load Balancing  By expressing workloads through an abstraction that cap-  tures work at differing levels of granularity (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=', tile set,  atoms, and tiles), we can more easily distribute computa-  tion evenly across the GPU’s available resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Given a  user-defined input tile set and associated sequences of atoms  and tiles, along with a user-selected partitioning algorithm,  our load-balancing stage outputs subsequences of atoms and  tiles assigned to processor ids (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=', where atoms or tiles will  be processed).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  PPoPP ’23, February 25-March 1, 2023, Montreal, QC, Canada  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Osama, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Porumbescu, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Owens  Load balance scheduler  2  1  3  6  Sparse Data Structure  Iterator Representation  Load Balancing  User-defined  Computation  (kernel)  User-defined  Computation  (kernel)  Work Execution  Thread0  Work Atoms and Tiles  Thread1  atoms iter = 0,1,2,3  tile iter = 0,1,2,3  atoms/tile = 0,1,3,0  values = 1,3,6,2  Thread0  Thread1  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Load balancing as a simple pipeline of the three key concepts of our abstraction: (1) sparse data structures represented  as iterators, (2) load-balancing algorithm that partitions the work onto threads, and (3) user-defined computation consuming  the balanced work and executing on each thread.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  The resulting assignment of subsequences to processor ids  is critical to effectively balancing workloads across process-  ing elements and is generally problem- and dataset-specific.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  The user must specify the necessary sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Ideally, an or-  acle would take these sequences and select the most optimal  subsequences for every processing element.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Finding such an  oracle is an open problem and thus we provide the next best  thing: the ability for users to choose and experiment from  a set of predefined schedules and the ability to implement  their own schedules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' In general, load-balancing algorithm  designers must balance between the cost of scheduling and  the benefits from better scheduling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' A schedule could be as  straightforward as assigning processing elements to tiles  with arbitrary numbers of atoms (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=', rows with an arbi-  trary number of non-zeros in a sparse matrix) to something  more complicated/expensive that takes on a more holistic ap-  proach to work (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=', considering work across multiple rows  with a varying number of non-zeros in a sparse matrix).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='3  Defining Work Execution  The final component of our load-balancing abstraction ex-  presses the irregular-parallel computation itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' The previ-  ous stage inputs load-imbalanced work and load-balances  it;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' this stage then consumes that load-balanced work by  performing computation on it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' The scope of what compu-  tation can be expressed is extensive, and is only limited by  how the load-balanced work, represented as sequences, can  be consumed within a CUDA kernel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Since the framework  does not assume control of the kernel, anything you can  write in a CUDA kernel will also work in our framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  For instance, programmers can express a mathematical op-  eration performed on each atom or each tile of the work,  or build cooperative algorithms that not only consume the  work assigned to each thread but also combine the results  with neighboring threads to implement more complex algo-  rithms such as parallel reduce or scan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Practical examples  that we have implemented in our framework (see Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='3  and 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='3) using this abstraction include, but are not limited  to, sparse-linear algebra kernels, such as Sparse-Matrix and  Sparse-Tensor contractions, and data-centric parallel graph  algorithms, such as Single-Source Shortest Path (SSSP) and  Breadth-First Search (BFS) built on a neighborhood traversal  kernel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  We expect typical users of our library will only write their  own code for this stage of the abstraction and use standard  data structures and load-balancing schedules that are already  part of our library.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' However, those users can also implement  custom data formats and load-balancing schedules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  4  High-Level Framework Implementation  Our GPU load-balancing framework implements the abstrac-  tion described in Section 3 using C++17 and CUDA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' In our  system, programmers use CUDA/C++ to develop irregular-  parallel algorithms and implement new load-balancing sched-  ules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Per our design goals of composable APIs, extensibil-  ity, and reuse, this and the following section introduce the  implementation details of our API, and how it is used to  develop new applications that promote the reuse of high-  performance load-balancing techniques available within the  framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' We also explore a new load-balancing method  (Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2) built on CUDA’s Cooperative Groups model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  Furthermore, we identify how our work can be used to facil-  itate the exploration of optimizations for a given application  such as SpMV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1  Implementing Sparse Data Structures  Our framework translates sparse data structures (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=', COO,  CSR, CSC) into work atoms, work tiles, and tile sets (Sec-  tion 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1) using simple C++ iterators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' C++ iterators are objects  that point to some element in a range of elements and en-  able iteration through the elements of that range using a  set of operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' For example, a counting_iterator is an  iterator that represents a pointer into a range of sequen-  tial values [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Our framework requires the user to define  three important iterators using C++: (1) an iterator over all  work atoms;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' (2) an iterator over the work tiles;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' and (3) an  iterator over the number of atoms in each work tile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' (Our  library already supports several common sparse data struc-  tures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=') Using these iterators, the load-balancing schedule can  then determine and distribute load-balanced work across the  A Programming Model for GPU Load Balancing  PPoPP ’23, February 25-March 1, 2023, Montreal, QC, Canada  1  // Simple iterators for atoms and tiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  2  counting_iterator<int> atoms_iter(0, nnz);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  3  counting_iterator<int> tile_iter(0, rows);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  4  // Iterator over the atoms within tile i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  5  auto atoms_per_tile = make_transform_iterator(  6  tile_iter,  7  [tile_iter, row_offsets]  8  __host__ __device__(const int& i) {  9  return (row_offsets[tile_iter[i + 1]] -  10  row_offsets[tile_iter[i]]);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  11  });' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  Listing 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Compressed-Sparse Row (CSR) format expressed  within our framework using C++17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' The CSR format de-  scribes a matrix using three arrays: (1) column indices of  nonzero values;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' (2) the extent of rows (row offsets);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' and  (3) the nonzero values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Since the CSR data structure does  not contain arrays that point to indices of atoms and tiles  (nonzeros and rows), in the listing above we define atom  and tile iterators as simple counting iterators from 0 to the  total number of nonzeros (nnz) and from 0 to the total rows  in the matrix (rows), respectively (Lines 2–3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' The iterator  over the atoms-per-work-tile is expressed using a transform  iterator, which computes the expression within a provided  function for each tile id.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' For CSR, this is simply the row offset  of the current tile subtracted from the offset of the next tile  (Lines 5–11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  underlying hardware.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Listing 1 shows how our abstraction  expresses the commonly used CSR format as a tile set within  our framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2  Implementing Load-Balancing Schedules  Perhaps the most straightforward schedule is scheduling  each work tile onto one GPU thread.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' This approach is com-  mon in the literature and practice [3, 10, 21, 26, 30];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' although  this strategy is ineffective in the presence of significant load  imbalance across tiles, we use it here as an example to illus-  trate how load balancing is defined within our framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  The inputs are the three iterators from the last stage  plus an atom and tile count.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' The load-balance algorithm  developer, then, implements tiles() and atoms() proce-  dure calls, which return the C++ range of tiles and atoms  to be processed by the current thread, effectively creating  a map between assigned processor ids and segments of the  workload.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Listing 2 shows a complete example of the thread-  mapped schedule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Although a simple algorithm, it can de-  liver high performance for well-balanced workloads with  coarse-grained parallelism (a small number of atoms per  tile), such as multiplying a sparse vector by a dense vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  Furthermore, our abstraction is not limited to only simple  scheduling algorithms, as Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2 provides examples of  more complex load-balancing algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  1  class schedule_t {  2  // Construct a thread-mapped schedule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  3  __host__ __device__  4  schedule_t(atoms_it_t atoms_it,  5  tiles_it_t tiles_it,  6  atoms_it_t atoms_per_tile_it,  7  size_t num_atoms, size_t num_tiles) :  8  m_atoms_it(atoms_it), m_tiles_it(tiles_it),  9  m_atoms_per_tile_it(atoms_per_tile_it),  10  m_num_atoms(num_atoms),  11  m_num_tiles(num_tiles) {}  12  // Range of tiles to process in "this" thread.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  13  // Stride by grid dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  14  __host__ __device__ auto tiles() {  15  auto begin = m_tiles_it(blockDim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='x * blockIdx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='x  16  + threadIdx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='x);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  17  auto end = m_tiles_it(m_num_tiles);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  18  return range(begin, end)  19  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='step(gridDim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='x * blockDim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='x);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  20  }  21  // Range of atoms to process in "this" thread.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  22  __host__ __device__ auto atoms(  23  const std::size_t& tile) {  24  auto begin = m_atoms_per_tile_it[tile];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  25  auto end = m_atoms_per_tile_it[tile + 1];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  26  return range(begin, end).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='step(1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  27  }  28  };' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  29  using schedule_t = thread_mapped_schedule_t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  Listing 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' A thread-mapped load-balancing algorithm ex-  pressed as C++ ranges, incorporating the atoms and tiles  defined as iterators from Listing 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Each tile is mapped to a  thread, where the thread id corresponds to the index of the  tile in the tile set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' All atoms within a tile are sequentially  processed by the thread.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' After a tile is processed, a thread  is mapped to the next tile, obtained by striding the index by  the grid size of the kernel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='3  Implementing Work Execution  Our framework is designed to explicitly let the user own the  kernel launch boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Owning a CUDA kernel boundary  means that the user is responsible for maintaining and con-  figuring launch parameters and implementing the CUDA  kernel used to define the application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Although this design  decision comes at a cost of convenience and simplicity, it of-  fers significant flexibility in what users can express through  our abstraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' This design decision is motivated by the fol-  lowing reasons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' (1) Users are not required to add a complex  dependency to their existing workflow/libraries, therefore  making code maintenance simpler and more scalable as they  do not have to rely on our framework to incorporate new  CUDA constructs and features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' (2) Users are free to express  anything and everything CUDA allows within their kernels  while consuming our load-balanced C++ ranges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' This allows  PPoPP ’23, February 25-March 1, 2023, Montreal, QC, Canada  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Osama, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Porumbescu, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Owens  for versatility in what can be expressed, as the users can  now specify multiple load-balanced work domains, range-  based for loops, and even fusing multiple computations to  build more complex algorithms within a single kernel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' (3)  Higher-level APIs can be used to build simpler higher-level  abstractions that do own the kernel boundary and provide  simpler APIs at the cost of flexibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  As an input to this stage, users consume the load-balanced  C++ ranges to implement their computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' This can be  done in multiple ways, but one of the most common pat-  terns is a nested range-based for loop that loops over all  the assigned tiles and atoms ranges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Listing 3 shows a sim-  ple example of a CUDA kernel that implements the SpMV  algorithm the using CSR format and thread-mapped load-  balancing algorithm described in Listings 1 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' In this  example, the outer for loop within each thread iterates over  the assigned rows of the sparse matrix (tiles), and the inner  loop sequentially processes the assigned nonzeros (atoms)  within each row.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' In Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='3 we implement and discuss  more complex kernels and computations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  5  Implementation Details  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1  Flexible, Composable CUDA-enabled Ranges  The composability of load-balanced primitives and applica-  tions using our API is a conscious design choice within our  framework supported through the use of CUDA-enabled C++  ranges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Our framework does not own the kernel boundary  (kernel launch), which forces our APIs to be focused and  contained within the kernels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' This allows programmers to  build and maintain their own kernels while still benefiting  from our framework’s load-balancing capabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' This is  largely implemented using device-wide C++ functions and  classes tagged with CUDA’s __device__ keyword.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2 We im-  plemented and expose several different types of specialized  ranges that were particularly useful in implementing load-  balanced schedules:  step_range: A range that iterates from begin to end  in steps of step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Useful for defining load balancing  schedules that require a custom stepping range or  process a constant number of work items per thread  (which can be defined using step).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  infinite_range: A range that iterates from begin to  infinity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Useful for defining load balancing schedules  in persistent kernel mode [32], where the kernel persis-  tently runs until all work is consumed or an algorithm  has converged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  grid_stride_range: A specialized case of step range  that iterates from begin to end in steps of step using  the CUDA kernel’s grid size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Also supports block and  2A method decorated with the __device__ keyword allows the CUDA  compiler to generate a device-callable entry point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' This allows the code to  be called from within kernels [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  1  // Implements load-balanced SpMV kernel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  2  __global__ void spmv(const size_t rows,  3  const size_t cols, const size_t nnz,  4  const int* offsets, const int* indices,  5  const float* values, const float* x,  6  float* y) {  7  // Configure load-balancing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  8  // Input: iterators defined for CSR format.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  9  schedule_t config(  10  atoms_iter, tile_iter,  11  atoms_per_tile_it,  12  nnz, rows);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  13  // Consume rows using a range-based for loop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  14  for (auto row : config.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='tiles()) {  15  type_t sum = 0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  16  // Consume atoms using a range-based for loop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  17  for (auto nz : config.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='atoms(row))  18  sum += values[nz] * x[indices[nz]];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  19  y[row] = sum;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  20  }  21  }  22  // Launches SpMV kernel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  23  constexpr size_t blocks = 256;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  24  size_t grid = (rows + blocks - 1) / blocks;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  25  spmv<<<grid, blocks>>>(rows, cols, nnz,  26  offsets, indices, values, x, y);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  Listing 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Sparse-Vector Matrix Multiplication (SpMV) im-  plemented within our load-balancing abstraction using  range-based nested for loops.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' The sparse matrix is repre-  sented using a CSR-based format, where 𝑥 is the dense input  vector and 𝑦 is the dense output vector (𝑦 = 𝐴𝑥).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Lines 9–12  use the load-balancing schedule implemented in Listing 2  and the iterators defined in Listing 1 to construct the load-  balanced work to be processed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Lines 14 and 17 show the for  loops within each thread, which iterate over the assigned  rows of the sparse matrix and sequentially process the as-  signed atoms within each row.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Line 18 shows the actual  computation performed on each work atom (nonzero), and  Line 19 writes the result to the dense output vector 𝑦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  warp stride variants that iterate in steps of the block  or warp size, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2  Implementing Non-Trivial Load-Balancing  As we describe in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1, we can decouple and express  existing load-balancing techniques as a set of C++ ranges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  To illustrate the potential of this abstraction, we begin by  decoupling and expressing a state-of-the-art load-balancing  algorithm known as merge-path [17] previously used for bal-  ancing CSR-based SpMV and SpMM [20, 30], and implement  three additional load balancing algorithms (warp-, block-  and group-mapped), all of which are available in our library  for programmers to use.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Our new group-mapped algorithm  is a tile-per-group-based schedule, where a group is defined  A Programming Model for GPU Load Balancing  PPoPP ’23, February 25-March 1, 2023, Montreal, QC, Canada  as a collection of threads of any arbitrary size (not limited  to a warp or block size).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Our group-mapped schedule is a  generalization of the tile-per-thread, -warp or -block sched-  ules [5, 21] using CUDA’s Cooperative Groups programming  model [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1  Merge-path load balancing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' In the language of a  sparse matrix, merge-path assumes that each non-zero in  the matrix and each new row in the matrix are an equivalent  amount of work, then evenly divides nnzs+rows work across  the set of worker threads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Each thread then performs a 2-D  binary search within the nonzero indices and row offsets  of a CSR matrix to find the starting position of the row  and nonzero it needs to process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Threads then sequentially  process the rows and nonzeros from the starting position  until they reach the end of their assigned work [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  We implement this algorithm as a load-balancing schedule  in our abstraction by expressing it in two steps: (1) Setup:  The initialization step of the C++ schedule class computes  the number of work units per thread, conducts a binary  search as described above, and stores the starting position  of each tile and atom in a thread-local variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' (2) Ranges:  The second step of the algorithm builds the ranges for each  thread to process as “complete” tiles and “partial” tiles [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  If a thread’s atom range lies entirely within one tile, it is  “complete”, and is processed in a simple nested loop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' If a  thread’s range crosses a tile boundary, the thread processes  its work in a separate nested loop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  Because we decouple the load-balancing method (Sec-  tion 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2, and above) from work execution (Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='3), we  can use this merge-path implementation to implement not  only SpMV but also any other algorithm whose work can  be divided into tiles and atoms, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=', a graph neighborhood-  traversal algorithm used to implement breadth-first search [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  Just as importantly, the merge-path schedule is now no  longer limited to a CSR-based sparse format.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Supporting  other formats only requires building the necessary slightly  more complex iterators that are able to count atoms per tile  (the computation that the CSR implementation achieves with  the row offsets array in Listing 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2  Warp- and block-level load balancing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' The goal  of a warp- or block-level load-balancing schedule is to assign  an equal share of tiles to each warp or block, which are then  sequentially processed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' The work atoms within each tile will  be processed in parallel by the available threads within a  warp or a block.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Each thread strides by the size of the warp  or block to process a new work atom until the end of work  is reached.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  The imbalance across different processing units is left for  the hardware scheduler to handle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' This scheduler depends on  the oversubscription model of CUDA, where the programmer  can launch a larger number of warps or blocks than the GPU  can physically schedule at any given time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' As the processing  units finish processing their work, new ones are scheduled  from the oversubscribed pool [5, 21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='3  Group-level load balancing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Group-level load bal-  ancing generalizes warp- and block-level schedules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Instead  of requiring that group sizes are the size of a warp or block,  as above, this method leverages CUDA’s Cooperative Groups  (CG) programming model [18] to allow programmer-specified  dynamically sized groups of arbitrary size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Within these  groups, the CG model permits detailed control of the group’s  synchronization behaviors as well as simple parallel group-  level collectives such as reduce or scan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' We leverage this  powerful tool to implement a generalized group-level load  balancing schedule, effectively giving us the warp- and block-  level schedules above for free when the group size equals  that of a warp or a block.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  Our schedule assigns work tiles to a group, and each group  looks at its equal share of tiles and computes the number  of atoms for each tile and stores it in a scratchpad memory  (CUDA’s shared memory).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' The group then performs a paral-  lel prefix-sum, a widely used parallel algorithm that inputs  an array and produces a new array where the element at  any position is a sum of all previous elements [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' We use  this prefix-sum array for two purposes: (1) the last element  of a prefix-sum array indicates the aggregated number of  work atoms that a group has to process, and (2) the posi-  tion of each sum in the prefix-sum array corresponds to the  work tile to which those atoms belong.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' The setup phase of  the schedule builds the prefix-sum arrays per group in the  scratchpad memory, and the ranged-loop of the schedule re-  turns the atom to process in each thread.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' The corresponding  tile, if needed, is obtained by a simple get_tile(atom_id)  operation, which executes a binary search within the prefix-  sum array to find the tile corresponding to the atom being  processed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  Relying on the CG model for this load-balancing sched-  ule has a unique advantage of configuring the group size  (effectively software constructs that directly map onto the  hardware) per the shape of the problem and the underlying  hardware architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' For example, targeting GPUs where  the warp size is not 32 threads (AMD’s GPU architecture  supports a warp size of 64 [2]) is now possible with a sim-  ple compile-time constant, or configuring the group size to  perfectly align with the structure of the problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='3  Application Space  Our work definition (Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1), composable APIs (Sec-  tion 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1), and multiple sophisticated, high-performance load-  balancing schedules (Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2) together provide for a ver-  satile and extensible framework with plenty of room for  application-specific optimizations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' In Listing 3 we already  demonstrated how to implement the SpMV algorithm using  PPoPP ’23, February 25-March 1, 2023, Montreal, QC, Canada  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Osama, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Porumbescu, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Owens  1  // .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Inside the CUDA kernel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  2  // Loop over all the assigned rows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  3  for (auto row : config.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='tiles()) {  4  // Loop over all the columns of Matrix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  5  for (auto col : range(size_t(0), B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='cols)  6  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='stride(size_t(1))) { /// < New Loop  7  float sum = 0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  8  // Loop over all the assigned nonzeros.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  9  for (auto nz : config.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='atoms(row))  10  sum += values[nz] * B(nz, col);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  11  // Output the sum to Matrix-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  12  C(row, col) = sum;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  13  }  14  }  Listing 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' A simple loop wrapped around SpMV introduced  in Listing 3 allows us to represent the slightly more complex  SpMM load-balanced computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  our framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' A simple and natural extension is to im-  plement Sparse-Matrix Matrix Multiplication (SpMM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' List-  ing 4 shows the minor change necessary, which adds another  loop over the columns of the B matrix around the existing  code from Listing 3 to implement SpMM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' This implementa-  tion could also be extended to support Gustavson’s General  Sparse Matrix-Matrix Multiplication (SpGEMM), using two  kernels and an allocation stage;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' the first kernel would com-  pute the size of the output rows used to allocate the memory  for the output sparse matrix and the second kernel would  perform the multiply-accumulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  Beyond sparse linear algebra, we can use our framework to  address applications in other domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Listing 5 implements  the graph primitive Single-Source Shortest Path (SSSP) using  our group-level load-balancing schedule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' SSSP’s performance  on GPUs is largely gated by good load balancing [5, 29],  but if the programmer chooses a load-balancing schedule  from our library, the details of load balancing are completely  hidden.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Moreover, the same schedules that were used in one  application domain (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=', sparse linear algebra) are easily  reusable in this different application domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  6  Evaluation  We aim to show that our framework, built on our load balanc-  ing abstraction, enables both high performance and better  programmability for sparse-irregular problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Our evalua-  tion below uses our SpMV implementation as a benchmark  against state-of-the-art implementations provided within  NVIDIA’s (open-source) CUB library and production (closed-  source) cuSparse library.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' We considered (and implemented)  several additional applications for evaluation, including SSSP,  BFS, and SpMM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' We found they led to similar high-level con-  clusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Thus our evaluation here focuses on SpMV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Our  test corpus consists of approximately the entire SuiteSparse  Matrix Collection [11] with a broad scope of sparse matrices  1  // .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Inside the CUDA kernel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  2  // Loop over all the assigned edges to process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  3  for (auto edge : config.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='atoms()) {  4  auto source = config.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='get_tile(edge);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  5  // G is the graph data structure  6  auto neighbor = G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='get_neighbor(source, edge);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  7  auto weight = G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='get_edge_weight(edge);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  8  float source_dist = dist[source];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  9  float neighbor_dist = source_dist + weight;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content="  10  // Check if the destination node has been  11  // claimed as someone's child." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  12  float recover_distance =  13  atomicMin(&(dist[neighbor]), neighbor_dist);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  14  // Add the neighbor to the frontier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  15  if (neighbor_dist < recover_distance)  16  out_frontier[neighbor] = true;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  17  }  18  19  // .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Outside the CUDA kernel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  20  // Loop until the frontier is empty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  Listing 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' The parallel single-source shortest path (SSSP)  graph primitive expressed using our load-balanced schedule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  1  10  100  1,000  10,000  100,000  1,000,000  10,000,000  100,000,000  Number of Nonzeros  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='001  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='002  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2  1  2  10  20  100  Runtime (ms)  cub  merge-path  Kernel  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' SpMV runtime comparison: our merge-path SpMV  implementation vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' CUB across all SuiteSparse datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Our  runtimes almost perfectly match CUB’s for all datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' The  small number of datasets where CUB is faster is due to a  simple heuristic that CUB uses for single-column sparse  matrices (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=', a sparse vector).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  from many different high-performance computing domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  We ran all experiments on a Ubuntu 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='04 LTS-based work-  station with an NVIDIA Tesla V100 GPU and CUDA 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1  Performance Overhead  Our first and foremost goal is to ensure that the elements  within our abstraction do not add any additional perfor-  mance overhead to the existing load balancing techniques  and algorithms developed using them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' To verify this, we  A Programming Model for GPU Load Balancing  PPoPP ’23, February 25-March 1, 2023, Montreal, QC, Canada  compare the runtime performance of our SpMV implemen-  tation using the merge-path schedule to the implementation  provided by NVIDIA’s CUB library [24] (also used for Merrill  and Garland’s merge-path SpMV paper [20]) on the Suite-  Sparse collection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' As previously mentioned, and in contrast  to our design, CUB contains a hardwired implementation of  the merge-path scheduling algorithms and does not decou-  ple workload balancing from the actual SpMV computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  CUB’s approach is not reusable for any other irregular par-  allel problem without significant changes to the implemen-  tation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  Figure 2 plots the number of nonzeros (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=', the total work)  vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' runtime for our work vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' CUB’s implementation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Our  implementation has minimal performance overhead when  using our abstraction: a geomean slowdown of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='5% vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' CUB,  with 92% of datasets achieving at least 90% of CUB’s perfor-  mance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Figure 2 shows our implementation almost perfectly  matches CUB for all datasets, except for some datasets with  fewer than 100,000 nonzeros.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Upon further investigation,  we identify that CUB uses a simple heuristic to launch a  thread-mapped SpMV kernel where the number of columns  of a given input matrix equals 1 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=', a sparse vector).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Unlike  our more general implementation, CUB’s simple (but spe-  cialized) thread-mapped SpMV kernel has no load-balancing  overhead for a perfectly balanced workload such as SpVV  computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2  Improved Performance Response  We also compare our work to NVIDIA’s vendor library for  sparse computations, cuSparse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Figure 3 shows the perfor-  mance response of our SpMV implementation using each of  our scheduling algorithms individually vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' cuSparse’s state-  of-the-art implementation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Switching between any of our im-  plementations requires very little code change;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' in the case of  merge-path and thread-mapped, we need only update a sin-  gle C++ enum (identifier) to select the desired load-balancing  schedule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  We then combine our scheduling algorithms into one im-  plementation for SpMV (Figure 4), demonstrating noticeable  performance improvements over cuSparse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' This is primar-  ily possible due to our ability to quickly experiment with  different heuristic schemes with a variety of available load-  balancing schedules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Here, we use merge-path unless either  the number of rows or columns are less than the threshold  𝛼 and the nonzeros of a given matrix are less than thresh-  old 𝛽 (we choose 𝛼 = 500 and 𝛽 = 10000 for SuiteSparse).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  In this case, we use thread-mapped or group-mapped load  balancing instead of merge-path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Our system shows a peak  performance speedup of 39× and a geomean performance  speedup of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='7× vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' cuSparse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  Our framework not only allows programmers to express  computations efficiently and simply (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=', without worry-  ing about the load-balancing algorithms), but also quickly  Load Balancing Algorithm  NVIDIA/CUB  Our Work  Merge-Path  503  36  Thread-Mapped  22  21  Group-Mapped  N/A  30  Warp-Mapped  N/A  30 (free)  Block-Mapped  N/A  30 (free)  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Lines of code (LoC) comparison for NVIDIA’s  CUB library versus our work for SpMV application im-  plemented using merge-path, thread-mapped and group-  mapped (warp- and block-mapped use the exact same code  for group-mapped) load balancing algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' We report  only non-commented lines of code, formatted using the  clang-format tool with the Chromium style guide [15], that  contributes to the kernel implementation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  optimize a given application using a range of scheduling  algorithms, both with minor code changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='3  Lines of Code (LOC)  We are able to achieve these performance gains with mini-  mal code complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Table 1 shows lines of code (LOC) for  our framework when compared to the state-of-the-art open-  source implementation of merge-path and thread-mapped  within NVIDIA’s CUB library.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' We deliver the same per-  formance results as highlighted in the previous sections  with 14× and 1× fewer lines of code for merge-path and  thread-mapped scheduling algorithms, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Using  our merge-path implementation only requires ∼15 additional  LoC to the trivial thread-mapped schedule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  Furthermore, we extend the same SpMV computation to  our novel group-mapped load balancing schedule (that can  also be specialized to perform block- and warp-mapped load  balancing) within the same 30 LoC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  7  Related Work  Load balancing is the key to achieving high performance on  GPUs for sparse, irregular parallel problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Several high-  performance computing applications deploy sophisticated  load balancing algorithms on the GPUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' For instance, high-  performance sparse-matrix vector multiplication (SpMV)  leverages merge-path [20] (discussed in detail in this pa-  per) or a nonzero splitting algorithm, which partitions the  number of non-zeros in a sparse-matrix evenly across the  number of threads [3, 9, 26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Sparse-matrix matrix multipli-  cation (SpMM) and sparse matricized tensor times Khatri-  Rao product (SpMTTKRP) use binning and bundling algo-  rithms [14, 22, 30], which attempt to bin like-length work  together such that they are processed together.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  While some applications actively perform work to load-  balance a given input, others store the input in more ef-  ficient, already-load-balanced/-partitioned formats.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' These  include the F-COO format (a variant of coordinate format)  PPoPP ’23, February 25-March 1, 2023, Montreal, QC, Canada  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Osama, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Porumbescu, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Owens  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='001  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='002  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2  1  2  10  20  100  Runtime (ms)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='001  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='002  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2  1  2  10  20  100  Runtime (ms)  1  10  100  1,000  10,000  100,0001,000,000  100,000,000  Number of Nonzeros  1  10  100  1,000  10,000  100,0001,000,000  100,000,000  Number of Nonzeros  cusparse  group-mapped  merge-path  thread-mapped  Kernel  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Complete performance landscape of SpMV across all SuiteSparse datasets using 3 load balancing schedules vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  NVIDIA’s cuSparse library.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' This performance comparison highlights the impact of different approaches to load-balancing  SpMV for a given dataset and number of nonzero entries within each dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Later in Figure 4 we use this insight to select the  fastest schedule for an improved overall performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Additionally, our 3 different SpMV implementations are made possible  with very little code change.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  used for SpMTTKRP and Sparse-Tensor Tensor Multiplica-  tion (SpTTM), where each thread gets the same number of  nonzeros to process [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  Many of the above GPU load-balancing algorithms, along  with other novel techniques, were first described in the graph  analytics domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Davidson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' and Merrill and Garland  were the first to present Warp, Block-level and Thread-Warp-  CTA dynamic load balancing techniques for Single-Source  A Programming Model for GPU Load Balancing  PPoPP ’23, February 25-March 1, 2023, Montreal, QC, Canada  1  10  100  1,000  10,000  100,000  1,000,000  10,000,000  100,000,000  Number of Nonzeros  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='3  1  2  3  10  20  30  100  Speedup w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='t cuSparse  group-mapped  merge-path  thread-mapped  Kernel  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Speedup of our framework’s SpMV vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' cuSparse’s  SpMV across SuiteSparse using a heuristic (Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2) to  choose the appropriate load-balancing schedule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  Shortest Path (SSSP) and Breadth-First Search (BFS) respec-  tively [10, 21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Logarithmic Radix Binning (LRB) is a par-  ticularly effective technique for binning work based on a  logarithmic work estimate, used for the Triangle Counting  graph algorithm and more [13, 16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Gunrock, GraphIT, and  GraphBLAST are graph analytics libraries that implement  several different graph algorithms such as BFS, SSSP, Page-  Rank, Graph Coloring, and more, built on these previously  mentioned load-balancing techniques [5, 29, 31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Although  many of these are effective load balancing techniques with  high-performance implementations, they all tightly couple  workload scheduling with the application itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Our frame-  work is designed to separate these two concerns, allowing  the application to be independent of the load-balancing algo-  rithm, and therefore be expressed simply.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Our approach also  allows these previously proposed techniques to be imple-  mented within our framework, and be used for applications  beyond those originally targeted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  Relatively few GPU works target generalized load balanc-  ing for irregular workloads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Most of these are focused on pro-  viding a singular, dynamic load-balancing solution centered  on task parallelism, often using a GPU queue-based data  structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Cederman and Tsigas proposed a task-based ap-  proach to load balancing an octree partitioning workload us-  ing lock-free and lock-based methods [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Two Tzeng works  provide task-management frameworks that implement load  balancing of tasks using a single monolithic task queue and  distributed queues with task stealing and donation [27, 28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  CUIRRE, a framework for load balancing and characteriz-  ing irregular applications on GPUs, also uses a task-pool  approach [33], and more recently, Atos, a task-parallel GPU  dynamic scheduling framework, targets asynchronous algo-  rithms [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' All of these works deploy either a centralized  or a distributed queue-like data structure on the GPUs, each  making design decisions on how the queue is to be parti-  tioned and updated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Except for the most recent Atos work,  most earlier works focus on a coarse-grained parallelism ap-  proach of effectively distributing tasks to the GPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Our work  takes advantage of more modern GPU architectures, which  are more effectively utilized by a fine-grained parallelism  approach (parallelizing over work atoms instead of work  tiles).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Unlike our abstraction, these aforementioned works  also rely on a singular load-balancing solution, whereas our  abstraction flexibly adapts to many different load-balancing  techniques, static and dynamic, and allows for new schedules  to be implemented within our framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  8  Conclusion  In this paper, we present a programming model for GPU load  balancing for sparse irregular parallel problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Our model is  built on the idea of separation of concerns between workload  mapping and work execution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' In the future, we are interested  in expanding our model to a multi-GPU environment, and  implementing load-balancing schedules that span across the  GPU boundary covering multiple devices and nodes for mas-  sive parallel problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Our current work focuses solely on  load balancing, but we also identify locality to be another key  factor for high performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' We are interested in identifying  an orthogonal model that builds an abstraction for caching  and locality into our existing load-balancing framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  Acknowledgments  This material is based upon work supported by Defense Ad-  vanced Research Projects Agency (DARPA) under Contract  No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' HR0011-18-3-0007 and the National Science Foundation  under Contract No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' OAC-1740333.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Any opinions, findings  and conclusions or recommendations expressed in this mate-  rial are those of the author(s) and do not necessarily reflect  the views of the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Government.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Distribution Statement  “A” (Approved for Public Release, Distribution Unlimited).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  We would like to acknowledge Michael Garland and Du-  ane Merrill from NVIDIA for their guidance on the frame-  work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' We would also like to acknowledge Toluwanimi Ode-  muyiwa, Jonathan Wapman, Matthew Drescher and Muham-  mad Awad for research discussions and feedback on the  work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' We also acknowledge the support of AMD, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' (Jalal  Mahmud and AMD Research) in the form of travel funding,  which enables us to attend the conference to present this  work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  References  [1] 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' ISO International Standard ISO/IEC 14882:2017(E) - Program-  ming Language C++.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Technical Report.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' International Organization for  Standardization (ISO).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' https://isocpp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='org/std/the-standard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  [2] Advanced Micro Devices, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' HIP Programming Guide v5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  (June 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' https://docs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='amd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='com/bundle/HIP-Programming-Guide-  v5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2/page/Introduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='html  PPoPP ’23, February 25-March 1, 2023, Montreal, QC, Canada  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Osama, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Porumbescu, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Owens  [3] Sean Baxter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2013–2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Moderngpu: Patterns and Behaviors for GPU  Computing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' (2013–2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' http://moderngpu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='io/moderngpu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  [4] Guy E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Blelloch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 1990.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Prefix Sums and Their Applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Technical  Report CMU-CS-90-190.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' School of Computer Science, Carnegie Mellon  University.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  [5] Ajay Brahmakshatriya, Yunming Zhang, Changwan Hong, Shoaib  Kamil, Julian Shun, and Saman Amarasinghe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Compiling Graph  Applications for GPUs with GraphIt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' In IEEE/ACM International Sym-  posium on Code Generation and Optimization (CGO 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 248–261.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1109/CGO51591.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='9370321  [6] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Busato and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Bombieri.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' BFS-4K: An Efficient Implementation  of BFS for Kepler GPU Architectures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' IEEE Transactions on Parallel  and Distributed Systems 26, 7 (July 2015), 1826–1838.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='org/  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1109/TPDS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2330597  [7] Daniel Cederman and Philippas Tsigas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' On Dynamic Load-  Balancing on Graphics Processors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' In Graphics Hardware (GH ’08).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  57–64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2312/EGGH/EGGH08/057-064  [8] Yuxin Chen, Benjamin Brock, Serban Porumbescu, Aydın Buluç,  Katherine Yelick, and John D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Owens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Atos: A Task-Parallel  GPU Scheduler for Graph Analytics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' In Proceedings of the International  Conference on Parallel Processing (ICPP 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1145/  3545008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='3545056 arXiv:2112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='00132  [9] Steven Dalton, Sean Baxter, Duane Merrill, Luke Olson, and Michael  Garland.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Optimizing Sparse Matrix Operations on GPUs Using  Merge Path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' In IEEE International Parallel and Distributed Processing  Symposium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 407–416.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1109/IPDPS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='98  [10] Andrew Davidson, Sean Baxter, Michael Garland, and John D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Owens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Work-Efficient Parallel GPU Methods for Single-Source Short-  est Paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' In Proceedings of the 28th IEEE International Parallel and  Distributed Processing Symposium (IPDPS 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 349–359.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  https:  //doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1109/IPDPS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='45  [11] Timothy A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Davis and Yifan Hu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' The University of Florida Sparse  Matrix Collection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' ACM Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Softw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 38, 1, Article 1 (Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2011),  25 pages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1145/2049662.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2049663  [12] Salvatore Filippone, Valeria Cardellini, Davide Barbieri, and Alessan-  dro Fanfarillo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Sparse Matrix-Vector Multiplication on GPG-  PUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' ACM Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Softw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 43, 4, Article 30 (Jan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2017), 49 pages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1145/3017994  [13] James Fox, Alok Tripathy, and Oded Green.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Improving Schedul-  ing for Irregular Applications with Logarithmic Radix Binning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2019  IEEE High Performance Extreme Computing Conference (2019), 1–7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1109/HPEC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='8916333  [14] Trevor Gale, Matei Zaharia, Cliff Young, and Erich Elsen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Sparse  GPU Kernels for Deep Learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' In Proceedings of the International  Conference for High Performance Computing, Networking, Storage and  Analysis (SC ’20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Article 17, 14 pages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1109/SC41405.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='00021  [15] Google.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Chromium C++ style guide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' (2023).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' https://chromium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  googlesource.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='com/chromium/src/+/HEAD/styleguide/c++/c++.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='md  [16] Oded Green, James Fox, Alex Watkins, Alok Tripathy, Kasimir Gabert,  Euna Kim, Xiaojing An, Kumar Aatish, and David A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Bader.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  Logarithmic Radix Binning and Vectorized Triangle Counting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' In IEEE  High Performance Extreme Computing Conference (HPEC 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 1–7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1109/HPEC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='8547581  [17] Oded Green, Robert McColl, and David A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Bader.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' GPU Merge  Path: A GPU Merging Algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' In Proceedings of the 26th ACM  International Conference on Supercomputing (ICS ’12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 331–340.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' https:  //doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1145/2304576.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2304621  [18] Mark Harris and Kyrylo Perelygin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Cooperative Groups: Flexible  CUDA Thread Programming.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' https://developer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='nvidia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='com/  blog/cooperative-groups/  [19] Bangtian Liu, Chengyao Wen, Anand D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Sarwate, and Maryam Mehri  Dehnavi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' A Unified Optimization Approach for Sparse Tensor  Operations on GPUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' IEEE International Conference on Cluster Com-  puting (Sept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2017), 47–57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1109/CLUSTER.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='75  [20] Duane Merrill and Michael Garland.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Merge-Based Parallel Sparse  Matrix-Vector Multiplication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' In International Conference for High Per-  formance Computing, Networking, Storage and Analysis (SC ’16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 678–  689.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1109/SC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='57  [21] Duane Merrill, Michael Garland, and Andrew Grimshaw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Scal-  able GPU Graph Traversal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' In Proceedings of the 17th ACM SIGPLAN  Symposium on Principles and Practice of Parallel Programming (PPoPP  ’12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 117–128.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1145/2145816.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2145832  [22] Israt Nisa, Jiajia Li, Aravind Sukumaran-Rajam, Richard Vuduc, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  Sadayappan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Load-Balanced Sparse MTTKRP on GPUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' In IEEE  International Parallel and Distributed Processing Symposium (IPDPS  2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 123–133.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1109/IPDPS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='00023  [23] NVIDIA Corporation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2007–2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' CUDA C++ Programming Guide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  (Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2007–2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' https://docs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='nvidia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='com/cuda/ PG-02829-001_v12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  [24] NVIDIA Corporation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' CUB: Cooperative primitives for CUDA  C++.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' (2023).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' https://nvlabs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='io/cub/.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  [25] Muhammad Osama, Serban D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Porumbescu, and John D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Owens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  A Programming Model for GPU Load Balancing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' (Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' https:  //doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='5281/zenodo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='7465053  [26] Markus Steinberger, Rhaleb Zayer, and Hans-Peter Seidel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Glob-  ally homogeneous, locally adaptive sparse matrix-vector multiplication  on the GPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' In Proceedings of the International Conference on Supercom-  puting (ICS 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' ACM, 13:1–13:11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1145/3079079.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  3079086  [27] Stanley Tzeng, Brandon Lloyd, and John D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Owens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' A GPU  Task-Parallel Model with Dependency Resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' IEEE Computer 45,  8 (Aug.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2012), 34–41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1109/MC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='255  [28] Stanley Tzeng, Anjul Patney, and John D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Owens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Task Manage-  ment for Irregular-Parallel Workloads on the GPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' In Proceedings of  High Performance Graphics (HPG ’10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 29–37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2312/  EGGH/HPG10/029-037  [29] Yangzihao Wang, Yuechao Pan, Andrew Davidson, Yuduo Wu, Carl  Yang, Leyuan Wang, Muhammad Osama, Chenshan Yuan, Weitang  Liu, Andy T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Riffel, and John D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Owens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Gunrock: GPU Graph  Analytics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' ACM Transactions on Parallel Computing 4, 1 (Aug.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2017),  3:1–3:49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1145/3108140  [30] Carl Yang, Aydın Buluç, and John D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Owens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Design Principles for  Sparse Matrix Multiplication on the GPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' In Euro-Par 2018: Proceedings  of the 24th International European Conference on Parallel and Distributed  Computing, Marco Aldinucci, Luca Padovani, and Massimo Torquati  (Eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 672–687.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1007/978-3-319-96983-1_48  [31] Carl Yang, Aydın Buluç, and John D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Owens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' GraphBLAST: A  High-Performance Linear Algebra-based Graph Framework on the  GPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' ACM Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Software 48, 1, Article 1 (Feb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2022), 51 pages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1145/3466795  [32] Lingqi Zhang, Mohamed Wahib, Peng Chen, Jintao Meng, Xiao Wang,  and Satoshi Matsuoka.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Persistent Kernels for Iterative Memory-  bound GPU Applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' CoRR (April 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' arXiv:2204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='02064  [33] Tao Zhang, Wei Shu, and Min-You Wu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' CUIRRE: An open-source  library for load balancing and characterizing irregular applications on  GPUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Parallel and Distrib.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 74, 10 (Oct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' 2014), 2951–2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='jpdc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='004  A Programming Model for GPU Load Balancing  PPoPP ’23, February 25-March 1, 2023, Montreal, QC, Canada  A  Artifact Description  We provide the source code of our load-balancing frame-  work called loops and our testing harness for evaluating the  results provided within this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1  Requirements  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Operating System Ubuntu 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='04, 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='04, Windows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Hardware NVIDIA GPU (Volta microarchitecture or  newer).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Software CUDA 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='7 or above and cmake 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1 or  newer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Compilation NVCC (comes with CUDA), g++ and  gcc, msvc with support for C++14 standard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Output Comma-separated values (CSV) files that are  used to generate the graphs in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Disk space 886 GB to store the entire SuiteSparse  Matrix Collection [11] compressed and uncompressed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  Can be reduced significantly by running the tests on  only a subset of the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Code License Apache 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='2  How to Access  The main repository is hosted on GitHub: https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  com/gunrock/loops.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Our framework is also available as a  Zenodo archive: https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='5281/zenodo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='7465053 [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  Detailed and well-formatted instructions are available within  the README markdown file in the repositories, and a sum-  mary is available below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='3  Getting Started  Before building loops, make sure you have the CUDA Toolkit  and cmake installed on your system, and exported in PATH of  your system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Other external dependencies such as thrust,  cub, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' are automatically fetched using cmake.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  cd loops  mkdir build && cd build  cmake -DCMAKE_CUDA_ARCHITECTURES =70 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='.  make -j$(nproc)  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='1  Sanity Check.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Run the following command in the  cmake’s build directory:  bin/loops.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='spmv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='merge_path \\  m .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='./ datasets/chesapeake/chesapeake.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='mtx \\  --validate -v  # Expected Output  # Elapsed (ms):  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='063328  # Matrix:  chesapeake.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='mtx  # Dimensions:  39 x 39 (340)  # Errors:  0  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='4  Reproducing Results  We provide the following instructions to regenerate the re-  sults presented in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' In the run script, update DATASET_DIR to point to the  path of all the downloaded datasets (set to the path  of the directory containing the MM directory;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' inside MM  are subdirectories with .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='mtx files): scripts/run.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='sh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  You may change the path to DATASET_FILES_NAME  containing the list of all the datasets (default points  to suitesparse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='txt file in the datasets directory).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Fire up the complete run using run.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='sh found in the  scripts directory, cd scripts && .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='/run.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='sh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' Note one  complete run can take up to 3 days (the run goes over  the entire SuiteSparse matrix collection dataset four  times with four different algorithms;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' the main bottle-  neck is loading files from disk).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  Warning: Some runs on the matrices are expected to  fail as they are not in proper MatrixMarket Format  although labeled as .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='mtx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' These matrices and the  ones that do not fit on the GPU will result in run-  time exceptions or type overflow and can be safely  ignored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' To run N number of datasets, simply adjust the stop  condition here (default set to 10): run.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='sh#L22, or re-  move this if-condition entirely to run on all available  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='mtx files: run.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='sh#L22-L26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  Additionally, we provide pre-generated results (in the form  of CSV files) to create the plots from Section 6 without need-  ing to run all the experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' These pre-generated results  are available under the docs directory of the repository.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='5  Expected Output and Plots  The expected output from the above runs are csv files in  the same directory as the run.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='sh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' These can replace the  existing csv files within docs/data, and a python jupyter  notebook can be used to evaluate the results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' The python  notebook includes instructions on generating plots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content=' See a  sample output of one of the csv files below:  kernel ,dataset ,rows ,cols ,nnzs ,elapsed  merge -path ,144 ,144649 ,144649 ,2148786 ,0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='07202  merge -path ,08 blocks ,300 ,300 ,592 ,0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='0170898  merge -path ,1138 _bus ,1138 ,1138 ,4054 ,0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
+page_content='0200195' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E3T4oBgHgl3EQf6wsw/content/2301.04792v1.pdf'}
diff --git a/mNE1T4oBgHgl3EQfOAOw/content/2301.03010v1.pdf b/mNE1T4oBgHgl3EQfOAOw/content/2301.03010v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..ef2c5da17a091eedaceba243fbdcd2c18ee76df3
--- /dev/null
+++ b/mNE1T4oBgHgl3EQfOAOw/content/2301.03010v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1c9e123e8212bf7f0920b408fbcc6db11bfd66ed8170fb8a32570c783e4e93f0
+size 454193
diff --git a/mNE1T4oBgHgl3EQfOAOw/vector_store/index.pkl b/mNE1T4oBgHgl3EQfOAOw/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..6b0ebc1ea64aecfb00ac07628a75531a3f881140
--- /dev/null
+++ b/mNE1T4oBgHgl3EQfOAOw/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3cffe106a7e0d091f7313c41975adc1fce66238ce0aa618c7ec8b86777ec1ad2
+size 86638
diff --git a/o9E2T4oBgHgl3EQf0Aih/vector_store/index.pkl b/o9E2T4oBgHgl3EQf0Aih/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..63cd10e52fce540c681c26d0df47386ec21d9512
--- /dev/null
+++ b/o9E2T4oBgHgl3EQf0Aih/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0ffae806ca474749077351bbd213eaceb4daa4860e0c3af194f6bd53504ee477
+size 30022
diff --git a/oNE0T4oBgHgl3EQfqQFw/content/2301.02550v1.pdf b/oNE0T4oBgHgl3EQfqQFw/content/2301.02550v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..2782e6e95e152f7d00144f141e9e0b7a2a945d35
--- /dev/null
+++ b/oNE0T4oBgHgl3EQfqQFw/content/2301.02550v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8657d88a98c45ebf81486505a91b075562aeab6477394b6d4f0c082105dd5874
+size 124955
diff --git a/oNE0T4oBgHgl3EQfqQFw/vector_store/index.faiss b/oNE0T4oBgHgl3EQfqQFw/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..9732ba1e1165f23784bc7f4f70e8598db09ac965
--- /dev/null
+++ b/oNE0T4oBgHgl3EQfqQFw/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:fa3d4938d27d611555f2de3e21ca4c1184a7a0b249142a7d0d401362f4546330
+size 1310765
diff --git a/oNE0T4oBgHgl3EQfqQFw/vector_store/index.pkl b/oNE0T4oBgHgl3EQfqQFw/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..e3695efaea8dedf7c5af1a224f8e7afc10cb0949
--- /dev/null
+++ b/oNE0T4oBgHgl3EQfqQFw/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0ba682a9cc5a3fb43da86457fd2184ee72a4b8426b4d63d954a733ad0e042da6
+size 50807
diff --git a/oNE1T4oBgHgl3EQf1wUI/content/tmp_files/2301.03470v1.pdf.txt b/oNE1T4oBgHgl3EQf1wUI/content/tmp_files/2301.03470v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4f309ceaf9a8f29171c55f3a26fc26dd3932022e
--- /dev/null
+++ b/oNE1T4oBgHgl3EQf1wUI/content/tmp_files/2301.03470v1.pdf.txt
@@ -0,0 +1,1169 @@
+Unsupervised Multivariate Time-Series
+Transformers for Seizure Identification on EEG
+˙Ilkay Yıldız Potter
+BioSensics LLC
+Newton, MA, USA
+ilkay.yildiz@biosensics.com
+George Zerveas
+Dept. of Computer Science
+Brown University
+Providence, RI, USA
+george_zerveas@brown.edu
+Carsten Eickhoff
+Dept. of Computer Science
+Brown University
+Providence, RI, USA
+carsten@brown.edu
+Dominique Duncan
+Keck School of Medicine
+University of Southern California
+Los Angeles, CA, USA
+Dominique.Duncan@loni.usc.edu
+Abstract—Epilepsy is one of the most common neurologi-
+cal disorders, typically observed via seizure episodes. Epileptic
+seizures are commonly monitored through electroencephalogram
+(EEG) recordings due to their routine and low expense collection.
+The stochastic nature of EEG makes seizure identification via
+manual inspections performed by highly-trained experts a tedious
+endeavor, motivating the use of automated identification. The lit-
+erature on automated identification focuses mostly on supervised
+learning methods requiring expert labels of EEG segments that
+contain seizures, which are difficult to obtain. Motivated by these
+observations, we pose seizure identification as an unsupervised
+anomaly detection problem. To this end, we employ the first
+unsupervised transformer-based model for seizure identification
+on raw EEG. We train an autoencoder involving a transformer
+encoder via an unsupervised loss function, incorporating a novel
+masking strategy uniquely designed for multivariate time-series
+data such as EEG. Training employs EEG recordings that do not
+contain any seizures, while seizures are identified with respect
+to reconstruction errors at inference time. We evaluate our
+method on three publicly available benchmark EEG datasets
+for distinguishing seizure vs. non-seizure windows. Our method
+leads to significantly better seizure identification performance
+than supervised learning counterparts, by up to 16% recall, 9%
+accuracy, and 9% Area under the Receiver Operating Charac-
+teristics Curve (AUC), establishing particular benefits on highly
+imbalanced data. Through accurate seizure identification, our
+method could facilitate widely accessible and early detection of
+epilepsy development, without needing expensive label collection
+or manual feature extraction.
+Index Terms—Epilepsy, Seizure, EEG, Unsupervised Learning,
+Time-series Transformer
+I. INTRODUCTION
+Epilepsy is one of the most common neurological disorders,
+affecting over 70 million people worldwide [35]. Epilepsy
+patients typically suffer from seizures, involving uncontrolled
+jerking movements or momentary losses of awareness due to
+abnormal excessive or synchronous activities in the brain [39].
+The degraded quality of life for patients strongly motivates
+early seizure identification, as early seizures have been shown
+This is a pre-print version of the article: I. Yıldız Potter, G. Zerveas, C.
+Eickhoff, D. Duncan, “Unsupervised Multivariate Time-Series Transformers
+for Seizure Identification on EEG”, IEEE Conference on Machine Learning
+and Applications (ICMLA) 2022, DOI 10.1109/ICMLA55696.2022.00208.
+Work was performed at University of Southern California and supported by
+the National Institutes of Health (NIH) National Institute of Neurological Dis-
+orders and Stroke (NINDS) grant R01NS111744. Code is publicly available
+at https://github.com/ilkyyldz95/EEG_MVTS.
+to be prognostic markers for later epileptogenic develop-
+ment. Successful identification of early seizures can initiate
+antiepileptogenic intervention and therapies that can remark-
+ably improve the quality of life for patients and their care-
+givers. To this end, electroencephalogram (EEG) recordings
+received particular attention for seizure identification [33], due
+to their routine and low expense collection compared to, e.g.,
+neuroimaging. Seizures on EEG are defined as generalized
+spike-wave discharges at three per second or faster, and clearly
+evolving discharges of any type that reach a frequency of four
+per second or faster.
+Despite their volume and rich information content, EEG
+recordings are known to contain many artifacts due to move-
+ment, physiological activity such as perspiration, and measure-
+ment hardware [13], [30]. The stochastic nature of clinically-
+acquired EEG makes seizure identification via manual inspec-
+tion laborious and difficult, leading to significant variability
+across clinical labels of different experts [43]. This challenge
+motivated the recent literature to focus on automated identi-
+fication of epileptic seizures on EEG as a promising comple-
+ment to manual inspection. The literature on automated EEG
+seizure identification is extensive (c.f. Section II), focusing
+mostly on supervised machine learning methods using both
+manual feature extraction [1], [26], [29], [46], as well as deep
+neural networks (DNNs) without manual feature extraction
+[16], [25], [44].
+Despite their success, supervised methods require expert
+labels indicating EEG segments that contain seizures, while
+obtaining large and consistently-labeled EEG datasets is un-
+favourable due to the stochastic nature of EEG [43]. Diffi-
+culty of label collection also leads to severely imbalanced
+EEG datasets, in which the number of non-seizure recordings
+significantly exceeds the number of seizure recordings; this
+poses a further challenge for supervised learning that is prone
+to overfitting towards dominant class predictions [23].
+Unsupervised machine learning methods, which do not rely
+on labeled data have not yet been widely explored. A few
+methods employed traditional shallow models for unsuper-
+vised seizure identification on both raw EEG [7], as well as
+spatio-temporal features extracted from EEG [2], [3], [10].
+To the best of our knowledge, unsupervised DNN methods
+for EEG seizure identification have been limited to a couple
+arXiv:2301.03470v1  [eess.SP]  3 Jan 2023
+
+of recent works, requiring feature extraction prior to training
+[40] or employing convolutional DNN architectures that are
+not tailored for multivariate time-series data such as EEG [41].
+We propose a fully-unsupervised deep learning approach
+that can identify seizures on raw EEG recordings. To this end,
+we make the following contributions:
+• We employ the first unsupervised transformer-based
+model for seizure identification on raw EEG, inspired by
+recent advances in multivariate time-series analysis [42].
+• We pose seizure identification as an anomaly detection
+problem. To this end, we train an autoencoder involving
+a transformer encoder via an unsupervised loss function,
+incorporating a novel masking strategy uniquely designed
+for modeling multivariate time-series data such as EEG.
+As training employs EEG recordings that do not contain
+seizures, seizures are identified via mean reconstruction
+errors at inference time.
+• We extensively validate the seizure identification per-
+formance of our method on three publicly available
+benchmark EEG datasets. Our method can successfully
+distinguish between non-seizure vs. seizure windows,
+with up to 0.94 Area under the Receiver Operating Char-
+acteristics Curve (AUC). Moreover, our unsupervised
+anomaly detection approach leads to significantly better
+seizure identification performance than the supervised
+learning counterparts, by up to 16% recall, 9% accuracy,
+and 9% AUC, establishing a particular benefit for learning
+from highly imbalanced data.
+II. RELATED WORK
+The literature on automated seizure identification on EEG
+is vast; we refer the reader to the review by [5] for more
+details. A significant body of works focus on extracting spatio-
+temporal features from EEG via, e.g., wavelet transformations
+[1], [28], local mean decomposition [43], Fourier transfor-
+mations [26], [29], and power spectra [46]. Extracted fea-
+tures are used to train supervised machine learning methods,
+including support vector machines and neural networks, to
+identify whether a given EEG contains a seizure in a binary
+classification setting.
+Deep neural network (DNN)-based supervised seizure iden-
+tification methods have lately dominated the literature [45]
+and obviated the need for manual feature extraction. DNN
+methods further improved in combination with recurrent neural
+networks to aid time-series modeling [6], adversarial training
+to generalize identification across patients [44], autoencoder-
+based feature extraction [34], and attention mechanisms to
+improve predictions and interpretability [25].
+In recent years, self-attention modules have become an in-
+tegral part of DNN methods employed in machine vision [15],
+natural language processing [14], and time-series modeling
+[42]; the resulting DNN architectures are termed as trans-
+formers. Transformer architectures have been very recently
+applied for various identification tasks on EEG, including,
+e.g., sleep-stage classification , human-computer interface-
+based action recognition, and seizure identification [16], [24].
+These methods employ unsupervised pre-training prior to
+supervised training on ground-truth expert labels pertaining to
+the identification task. The unsupervised pre-training objective
+involves different augmentations of the same EEG segment
+and trains the transformer by maximizing (minimizing) the
+similarity of different augmentations (segments).
+All in all, the literature on automated seizure identifica-
+tion often focuses on supervised machine learning methods.
+Despite their success, these methods require expert labels
+indicating EEG segments that contain seizures, which are
+difficult to obtain due to the stochastic nature of EEG [43].
+Meanwhile, unsupervised machine learning methods that do
+not rely on labeled data have not yet been widely explored. A
+few methods applied shallow models for unsupervised seizure
+identification, including K-means, hierarchical clustering, and
+Gaussian mixture models, on both raw EEG [7], as well as
+spatio-temporal features extracted from EEG [2], [3].
+Recently, a couple of unsupervised DNN methods for
+seizure identification on EEG have been proposed. You et
+al. (2020) preprocess EEGs to extract time-frequency spectro-
+gram images and train a generative adversarial network (GAN)
+[40] on the spectrograms that do not contain seizures. For each
+spectrogram at testing time, they have to search for the latent
+GAN input that leads to the smallest loss value and use the cor-
+responding generated spectrogram for seizure identification.
+As training involves non-seizure activity, test spectrograms
+that significantly differ from the spectrograms generated by the
+GAN are successfully identified to contain seizures. Yıldız et
+al. (2022) train a convolutional variational autoencoder (VAE)
+over raw EEG, employing an objective tailored for suppressing
+EEG artifacts. Unlike You et al. (2020), they identify seizures
+with respect to the reconstruction errors at inference time.
+We differ from the existing works by applying the first
+fully-unsupervised transformer-based model on raw EEG. Our
+architecture and training objective are particularly designed
+for multivariate time-series analysis and do not require a
+sophisticated minimax optimization such as GAN training.
+The fundamental benefit of a transformer encoder over other
+DNN architectures is that self-attention can selectively high-
+light important input features and sequence segments, without
+relying on sequence-aligned convolutions or slow recurrent
+modules [38]; we also experimentally demonstrate this advan-
+tage against unsupervised VAE-based seizure identification in
+Section IV-E.
+III. PROBLEM FORMULATION
+We consider a dataset of N EEG recordings, each collected
+from M electrode channels and consisting of T time points.
+Formally, we denote each EEG recording by X(i) ∈ RT ×M,
+for i ∈ [1, . . . , N]. Our aim is to design an unsupervised
+method that does not rely on ground-truth expert labels during
+learning and can identify the existence of seizures in a given
+EEG recording. To this end, we employ an autoencoder
+architecture involving a transformer network encoder that is
+uniquely designed for multivariate time-series data [42], such
+as EEG. We note that our method naturally generalizes to
+
+EEG recordings comprising different numbers of time points
+and channels (see our preprocessing setup in Section IV-B).
+A. Multivariate Time-Series Transformer
+Our autoencoder architecture is based on a transformer
+encoder and is depicted in Figure 1: the model learns to
+extract and transform latent features from a given EEG
+recording in order to reconstruct the stochastically-masked
+input [42]. Formally, the transformer encoder network receives
+a recording X(i) ∈ RT ×M, i ∈ [1, . . . , N], and extracts
+latent features Z(i) ∈ RT ×D. The output layer applies an
+affine transformation on Z(i) to reconstruct the recording as
+ˆ
+X(i) ∈ RT ×M.
+1) Transformer Encoder: Transformer encoder operations
+begin with projecting a recording X(i) from M dimensions
+to D dimensions via a trainable affine transformation P ∈
+RM×D. To preserve the ordering information of the input
+sequence, a fully-trainable positional encoding E ∈ RT ×D
+is added for each input. The resulting latent features extracted
+from each recording are thus: Z(i) = X(i)P + E.
+Dimensional projection and positional encoding are fol-
+lowed by the successive application of several transformer
+layers. Each transformer layer consists of a multi-headed
+self-attention (MSA) module, a stochastic dropout operation
+˜d [32], batch normalization (Norm) [22], and a fully-connected
+network (FCN) consisting of two linear layers separated by a
+GELU [21] activation, a non-linearity designed to be used in
+combination with dropout and batch normalization. Formally,
+latent features are updated by each transformer layer via:
+Z(i) ← Norm
+�
+˜d
+�
+MSA(Z(i))
+�
++ Z(i)�
+,
+Z(i) ← Norm
+�
+˜d
+�
+FCN(Z(i))
+�
++ Z(i)�
+.
+(1)
+The summation of each latent feature with its transformation
+is a skip connection that aids generalization [20], along with
+batch normalization that has been shown improvement against
+layer normalization for multivariate time-series analysis [42].
+2) Multi-headed Self-attention Module: An MSA module
+is designed to assign selective importance to latent features
+extracted for each time point by the preceding layers of the
+encoder [38]. Particularly, MSA contains trainable parameters
+that capture the similarity between input features at different
+time points via their query, key, and value representations.
+Multiple attention heads enable adaptations to long-term de-
+pendencies and capture relevance between segments of multi-
+variate data, without prior bias based on position [42].
+Formally, at each time point t, the output representation is
+computed via a weighted sum over the value vectors z(i)
+v,t′ ∈
+RDv, t′ ∈ [1, . . . , T], where the importance weight assigned
+to the value vector at time t′ is computed as a dot-product
+similarity between its corresponding key vector z(i)
+k,t′ ∈ RDq
+and a query vector z(i)
+q,t ∈ RDq at time t. As a result, given a
+latent feature Z(i), a query Z(i)
+q
+= [z(i)
+q,1; . . . ; z(i)
+q,T ] ∈ RT ×Dq,
+a key Z(i)
+k
+=
+[z(i)
+k,1; . . . ; z(i)
+k,T ]
+∈
+RT ×Dq, and a value
+Z(i)
+v
+= [z(i)
+v,1; . . . ; z(i)
+v,T ] ∈ RT ×Dv are computed by applying
+three different trainable affine transformations on Z(i). The
+self-attention output for a single attention head (SA) is then
+computed via a scaled dot-product:
+SA(Z(i)) = softmax
+�
+Z(i)
+q Z(i)⊤
+k
+�
+Dq
+�
+Z(i)
+v ,
+(2)
+where softmax converts the similarity scores to a probability
+distribution over the input sequence of length T. This opera-
+tion is performed in parallel for each of the H attention heads
+(each with its own trainable transformations). The resulting
+outputs SAh ∈ RT ×Dv, h ∈ [1, . . . , H] are first concatenated
+and finally aggregated into a single representation through a
+trainable linear transformation WA ∈ RHDv×D:
+MSA(Z(i))=[SA1(Z(i)) SA2(Z(i)). . .SAH(Z(i))]WA. (3)
+B. Reconstruction-Based Loss Function
+We aim for the transformer model to extract discriminative
+latent features that govern the generation of EEG recordings,
+i.e., to model the input data distribution. To this end, we
+corrupt each input sample by a novel masking strategy that
+is uniquely designed for modeling multivariate time-series
+data such as EEG [42]. We train the transformer model
+via a loss function that minimizes the error between the
+original (unmasked) recording X(i) and the corresponding
+reconstruction ˆ
+X(i).
+Formally, a proportion r ∈ (0, 1) of each channel m ∈
+{1, . . . , M} in each EEG recording X(i) is dynamically
+masked at the beginning of each training step by setting
+the encoder input values at chosen time points to 0. The
+values at each channel alternate between consecutive masked
+and unmasked sequences. The number of masked time points
+follows a geometric distribution with mean lm, while the num-
+ber of unmasked time points follows a geometric distribution
+with mean lu =
+1−r
+r lm. This transition paradigm is also
+known as an M/M/1 queue, in which the number of customers
+in a system is geometrically distributed [18]. The resulting
+masking strategy encourages the transformer to attend on time
+points preceding and following the masked segments both in
+individual channels, as well as across the aligned time points
+in other channels to capture inter-channel dependencies, and
+has been found more effective than other denoising strategies
+for downstream tasks, including Bernoulli masking (c.f. Table
+II & [42]).
+Finally, the reconstruction loss for end-to-end training of our
+model is the mean-squared reconstruction error. Crucially, the
+loss is computer over only the set of masked time points M =
+{(t, m) | masked X(i)
+t,m, t ∈ {1, . . . , T}, m ∈ {1, . . . , M}}:
+1
+|M|
+�
+(t,m)∈M
+(X(i)
+t,m − ˆX(i)
+t,m)2.
+(4)
+C. Seizure Identification
+We aim to employ the trained transformer to distinguish
+between EEG recordings that contain seizures and those
+which do not; this motivates us to pose unsupervised seizure
+
+Transformer Encoder
+Output 
+Layer
+Time
+Channels
+Affine 
+Dimension 
+Reduction
+Positional 
+Encoding
+Multi-head 
+self-attention
+Batch 
+normalization
+Fully-connected 
+Neural Network
+Batch 
+normalization
+Affine 
+Transform
+Transformer layers repeated
+Multivariate Input 
+Reconstruction               
+Latent features 
+Fig. 1: Our autoencoder architecture. The transformer encoder network receives a recording X(i), and extracts latent features
+Z(i). The output layer applies an affine transformation on Z(i) to reconstruct the recording as ˆ
+X(i) ∈ RT ×M. During training,
+a proportion of each channel is masked by setting the input values at masked time points (shaded in gray) to 0.
+identification as an anomaly detection problem. Thus, we train
+the transformer architecture on recordings that do not contain
+seizures. This allows for the learned latent features to capture
+non-seizure activity [40]. As the transformer is trained to
+model non-seizure activity, recordings with no seizures are
+expected to be reconstructed with low error in inference time.
+In contrast, EEG recordings including seizure activity come
+from a different distribution, and thus, the model naturally
+reconstructs such input recordings with a relatively larger
+error; we use this observation as an indicator for a seizure
+(c.f. Section IV-D).
+We note that the exclusion of seizure recordings from the
+training set does not constitute supervision or require any
+special annotation, as the default states of patients and healthy
+individuals alike are non-seizure, whose recordings can be
+collected and kept separate from the recordings of seizure
+episodes (which we only use for evaluating our method). In
+real-life applications, EEG data with no seizure activity can
+be easily augmented with recordings from healthy individuals,
+which are trivially accessible compared to the ones from
+patients experiencing seizures.
+IV. EXPERIMENTS
+A. Datasets
+We evaluate our method on three publicly available EEG
+datasets collected at the: (i) Massachusetts Institute of Tech-
+nology (MIT) and Boston Children’s Hospital [31] (ii) Uni-
+versity of Pennsylvania (UPenn) and Mayo Clinic [36], and
+(iii) Temple University Hospital of Philadelphia (TUH) [27].
+The MIT dataset contains EEG recordings acquired on the
+scalp with 256 Hz sampling rate from a maximum of M = 38
+channels. 198 seizure recordings were labeled w.r.t. their start
+and end times. The total duration of non-seizure recordings is
+40, 800 seconds and seizure recordings is 2889 seconds.
+The UPenn dataset contains 1-second long EEG recordings
+acquired intracranially at 500 − 5000 Hz from a maximum of
+M = 72 channels. The total duration of non-seizure recordings
+is 7164 seconds and seizure recordings is 653 seconds.
+The TUH dataset contains EEG recordings acquired on the
+scalp with 250 Hz sampling rate from a maximum of M = 38
+channels. 1229 seizure recordings were labeled w.r.t. their start
+and end times. The total duration of non-seizure recordings is
+49, 922 seconds and seizure recordings is 2600 seconds.
+B. Preprocessing
+EEG recordings are typically preprocessed to eliminate the
+powerline noise at 60 Hz [40]. We first unify the sampling rates
+in each dataset by downsampling to the smallest sampling rate
+across all recordings. Then, we filter the recordings via a 4-th
+order Butterworth bandpass filter with range 0.5-50 Hz.
+To construct samples with the same size, we extract sliding
+windows over each recording, where each window contains
+T time points and overlaps with its consecutive window by
+50%. We choose T based on the shortest seizure segment
+in each dataset. In doing so, T = 1536 for MIT, T = 500
+for UPenn, and T = 462 for TUH. This process results in
+13, 600 windows with non-seizure activity and 963 windows
+with seizure activity for MIT, 14, 329 windows with non-
+seizure activity and 1307 windows with seizure activity for
+UPenn, and 54, 264 windows with non-seizure activity and
+2826 windows with seizure activity for TUH. In real-life appli-
+cations, a minimum seizure window length can be decided by
+clinical experts, as in UPenn that directly provides 1 second-
+long seizure recordings.
+Moreover, we aim to consistently form T ×M size windows,
+while not disregarding any channels with potential seizure ac-
+tivity. Thus, to construct samples with the same number of M
+channels, we reuse data from other channels for the recordings
+that have missing data at certain channels, compared to the
+recording with the largest number of channels in each dataset.
+Again, in real-life applications, clinical experts can determine
+which channels to employ or discard for seizure identification.
+Finally, we normalize windows by subtracting the mean and
+dividing by the standard deviation across all windows to aid
+the convergence of training [22].
+
+X()x()Z(i)Dataset
+Method
+Precision
+Recall
+Accuracy
+AUC
+MIT
+Unsupervised Transformer
+0.98 ± 0.003
+0.9 ± 0.006
+0.87 ± 0.006
+0.94 ± 0.023
+Unsupervised K-means
+0.33 ± 0.008
+0.5 ± 0.009
+0.5 ± 0.009
+0.59 ± 0.041
+Unsupervised VAE
+0.97 ± 0.003
+0.75 ± 0.008
+0.61 ± 0.009
+0.61 ± 0.041
+Supervised XGBoost
+0.98 ± 0.003
+0.8 ± 0.007
+0.8 ± 0.007
+0.88 ± 0.031
+Supervised ROCKET
+0.98 ± 0.003
+0.74 ± 0.008
+0.78 ± 0.008
+0.86 ± 0.032
+Supervised Transformer
+0.98 ± 0.003
+0.83 ± 0.007
+0.83 ± 0.007
+0.88 ± 0.031
+Pre-trained 50% Supervised Transformer
+0.97 ± 0.003
+0.72 ± 0.008
+0.63 ± 0.009
+0.66 ± 0.021
+Pre-trained 100% Supervised Transformer
+0.99 ± 0.002
+0.98 ± 0.003
+0.94 ± 0.005
+0.97 ± 0.017
+UPenn
+Unsupervised Transformer
+0.88 ± 0.01
+0.76 ± 0.013
+0.68 ± 0.014
+0.73 ± 0.027
+Unsupervised K-means
+0.33 ± 0.014
+0.5 ± 0.015
+0.5 ± 0.015
+0.56 ± 0.028
+Unsupervised VAE
+0.8 ± 0.012
+0.5 ± 0.015
+0.49 ± 0.015
+0.47 ± 0.027
+Supervised XGBoost
+0.87 ± 0.01
+0.62 ± 0.015
+0.6 ± 0.015
+0.65 ± 0.028
+Supervised ROCKET
+0.87 ± 0.01
+0.67 ± 0.014
+0.62 ± 0.015
+0.67 ± 0.028
+Supervised Transformer
+0.87 ± 0.01
+0.69 ± 0.014
+0.62 ± 0.015
+0.64 ± 0.028
+Pre-trained 50% Supervised Transformer
+0.86 ± 0.011
+0.77 ± 0.013
+0.63 ± 0.015
+0.64 ± 0.032
+Pre-trained 100% Supervised Transformer
+0.92 ± 0.008
+0.85 ± 0.011
+0.82 ± 0.012
+0.89 ± 0.02
+TUH
+Unsupervised Transformer
+0.92 ± 0.005
+0.57 ± 0.009
+0.61 ± 0.009
+0.57 ± 0.013
+Unsupervised K-means
+0.17 ± 0.007
+0.5 ± 0.009
+0.35 ± 0.008
+0.57 ± 0.013
+Unsupervised VAE
+0.93 ± 0.005
+0.86 ± 0.006
+0.83 ± 0.007
+0.86 ± 0.009
+Supervised XGBoost
+0.93 ± 0.005
+0.73 ± 0.008
+0.71 ± 0.008
+0.78 ± 0.011
+Supervised ROCKET
+0.93 ± 0.005
+0.7 ± 0.008
+0.66 ± 0.008
+0.74 ± 0.012
+Supervised Transformer
+0.92 ± 0.005
+0.37 ± 0.009
+0.54 ± 0.009
+0.52 ± 0.012
+Pre-trained 50% Supervised Transformer
+0.94 ± 0.005
+0.61 ± 0.009
+0.75 ± 0.008
+0.71 ± 0.025
+Pre-trained 100% Supervised Transformer
+0.93 ± 0.005
+0.66 ± 0.008
+0.7 ± 0.008
+0.72 ± 0.012
+TABLE I: Seizure identification performance metrics and confidence intervals on UPenn, MIT and TUH. We compare our
+transformer-based unsupervised identification method (in bold) with unsupervised methods comprising VAE and t-SNE followed
+by K-means clustering, as well as supervised methods comprising XGBoost, ROCKET, and the same transformer architecture
+trained via supervised and pre-trained supervised learning. Best performance for each dataset are in italics.
+C. Experiment Setup and Competing Methods
+We partition all windows containing non-seizure and seizure
+activity into training, validation, and test sets in a stratified
+manner, allocating 60% for training, 20% for validation, and
+the remaining 20% for testing. As baseline methods, we im-
+plement shallow and deep learning models for both supervised
+and unsupervised settings.
+1) Unsupervised Learning Methods: For our method, we
+employ the transformer encoder architecture proposed by
+Vaswani et al. (2017), with the modifications of fully-trainable
+positional encoding, batch normalization and the same hyper-
+parameters suggested by Zerveas et al. (2021). We train the
+autoencoder over only non-seizure training windows using the
+unsupervised loss given by Eq. (4). We monitor the loss value
+computed over the non-seizure windows in the validation set
+and use the model that attains the lowest validation loss.
+Following the literature on shallow unsupervised methods
+[8], we reduce the dimension of all EEG windows in the test
+set to 3 using the t-Distributed Stochastic Neighbor Embed-
+ding (t-SNE) [37] algorithm, and apply K-means clustering
+[4] on the resulting windows with two clusters indicating
+non-seizure and seizure. Moreover, as an unsupervised deep
+learning baseline, we train a state-of-the-art convolutional VAE
+[41].
+2) Supervised Learning Methods: First, we employ the
+same transformer encoder architecture described in Section
+III-A and map the latent features learned from each window
+to a binary prediction. In doing so, we concatenate all latent
+features corresponding to all time points of each window
+into a single vector and apply a fully-connected layer com-
+prising a scalar output with sigmoid activation. We train the
+resulting architecture via cross-entropy loss over all training
+windows, employing the same hyperparameters found optimal
+by Zerveas et al. (2021). To combat overfitting due to class
+imbalance in supervised learning, we oversample and augment
+the seizure windows in training via random reversing and
+drifting. We monitor the F1-score computed over the validation
+set and use the model that attains the best validation score.
+Moreover, we train state-of-the-art shallow models XGBoost
+[11] and ROCKET [12] over the supervised training set.
+XGBoost is a decision-tree classifier using gradient boosting
+for ensembling. ROCKET transforms time-series using 500
+random convolutional kernels and uses the extracted features
+to train a ridge regression classifier. Ridge regression hyper-
+
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Time (s)
+200000
+100000
+0
+100000
+200000
+300000
+V
+Patient_8_ictal_2869
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Time (s)
+200000
+150000
+100000
+50000
+0
+50000
+Patient_8_ictal_2870
+(a) Correctly Identified Seizure Windows (True Positive)
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Time (s)
+60
+40
+20
+0
+20
+40
+V
+Patient_2_interictal_1658
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Time (s)
+20
+0
+20
+40
+60
+Patient_2_interictal_1566
+(b) Correctly Identified Non-seizure Windows (True Negative)
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Time (s)
+60
+40
+20
+0
+20
+40
+V
+Patient_2_ictal_3983
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Time (s)
+40
+20
+0
+20
+Patient_2_ictal_3984
+(c) Falsely Identified Seizure Windows (False Negative)
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Time (s)
+1000
+500
+0
+500
+1000
+V
+Patient_2_interictal_31
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Time (s)
+1500
+1000
+500
+0
+500
+1000
+1500
+2000
+2500
+Patient_2_interictal_602
+(d) Falsely Identified Non-seizure Windows (False Positive)
+Fig. 2: Example EEG windows, corresponding seizure identifications and self-attention weights on UPenn. First and third rows
+contain example windows of true positive, true negative, false negative, and false positive identifications, respectively. Second
+and fourth rows contain the corresponding self-attention weight heatmaps computed by the transformer architecture, where
+darker colors indicate higher importance. For each window, we visualize the channel with the largest reconstruction error.
+parameter is varied in [10−3, 103] and best hyperparameter is
+determined w.r.t. the accuracy over the validation set.
+3) Pre-trained Supervised Learning: Finally, we combine
+the transformer-based seizure identification methods via unsu-
+pervised pre-training and supervised fine-tuning [42]. Follow-
+ing the unsupervised approach described in Section IV-C1, we
+first pre-train the transformer encoder over non-seizure training
+windows. Having initialized its weights accordingly, we then
+fine-tune the model via both non-seizure and seizure training
+windows, using the same setup described in Section IV-C2.
+D. Evaluation Metrics
+To evaluate the seizure identification performance of our
+approach, as well as the VAE baseline, we use the mean ab-
+solute error over the time points and electrode channels in each
+EEG window from the test set as the corresponding seizure
+prediction score. For all supervised competing methods, we
+use the traditional prediction score for inference.
+For all competing methods described in Section IV-C, we
+report AUC for distinguishing seizure vs. non-seizure windows
+in the test set. To compute binary decision metrics, we thresh-
+old the prediction score of each window at the value for which
+the geometric mean of recall and true negative rate is maxi-
+mal [17]. Using the respective threshold, we calculate class-
+weighted precision and recall, as well as balanced accuracy
+for binary identification of seizure vs. non-seizure windows in
+the test set, considering the imbalanced distribution between
+the two. In real-life applications, decision thresholds may be
+determined by clinical experts with respect to the desired
+trade-off between false positives and negatives [9].
+We report all metrics along with the 95% confidence in-
+tervals, which are computed as 1.96 × σA, where σ2
+A is the
+variance for metric A. Variance for AUC is computed by:
+σ2
+A= 1
+mn
+�
+A(1−A)+(m−1)(Px−A2)+(n−1)(Py−A2)
+�
+,
+(5)
+where Px = A/(2 − A), Py = 2A2/(1 + A), and m, n are
+the number of seizure and non-seizure windows, respectively
+[19]. Variance for other metrics are computed by:
+σ2
+A = A(1 − A)/(m + n).
+(6)
+E. Results and Discussion
+1) Seizure Identification Performance: Table I shows the
+seizure identification performance of our transformer-based
+
+unsupervised method vs. supervised and pre-trained super-
+vised transformers, XGBoost, ROCKET, VAE, and t-SNE
+followed by K-means clustering over all datasets. Our novel
+transformer-based anomaly detection method establishes a
+dramatic improvement among all unsupervised methods, by
+successfully distinguishing between non-seizure vs. seizure
+windows with up to 0.94 AUC and outperforming its state-
+of-the-art deep learning counterpart VAE by up to 33% AUC
+on MIT. Clustering on raw EEG windows cannot capture the
+complex evolution of EEG and predicts all windows as non-
+seizure. These observations demonstrate the benefit of the
+transformer architecture for unsupervised anomaly detection
+in our setting.
+Crucially, despite the lack of seizure labels during training,
+our unsupervised anomaly detection approach leads to signif-
+icantly better seizure identification than all purely supervised
+learning baselines and the pre-trained transformer fine-tuned
+with 50% of the training labels over UPenn and MIT, by
+up to 16% recall, 9% accuracy, and 9% AUC. Moreover,
+unlike supervised learning, class imbalance strongly biases
+supervised models towards non-seizure predictions and hinders
+generalization over the distribution of held-out test samples.
+As a result, unsupervised anomaly detection via transformers
+establishes a consistently better balance between precision and
+recall than supervised learning and further demonstrates its
+benefit in learning from imbalanced datasets such as ours.
+The TUH dataset is particularly challenging by being a
+compilation of several EEG databases collected over years
+from patients with vast variations in demographic and medical
+backgrounds [27], compared to self-contained UPenn and MIT
+datasets collected from only 8 and 24 patients, respectively. In
+this case, our unsupervised transformer still fares significantly
+better than the purely supervised transformer, while unsuper-
+vised VAE outperforms all supervised learning baselines, in-
+cluding the pre-trained transformer. These observations further
+motivate unsupervised learning for our task.
+As expected, the computationally expensive transformer
+model, which has first undergone unsupervised pre-training
+and then supervised fine-tuning with all training labels, outper-
+forms both purely supervised as well as purely unsupervised
+transformer models (the latter by a smaller margin). However,
+our unsupervised anomaly detection method does not require
+ground-truth seizure labels during training as a crucial advan-
+tage, while still leading to successful seizure identification.
+2) Seizure Identification Examples: We visualize example
+EEG windows from UPenn and the corresponding seizure
+identifications of the unsupervised transformer in the first and
+third rows of Figure 2, selecting the channel with the largest
+mean reconstruction error for each window. Agreeing with
+the clinical description of seizures, true seizure windows in
+Figure 2a contain high-frequency waves with large amplitudes
+[39]. Meanwhile, true non-seizure windows in Fig. 2b attain
+significantly less amplitude changes and spikes compared to
+true positive windows. Note that the seizure patterns cannot
+be identified w.r.t. only large amplitude or high frequency,
+motivating a more sophisticated approach such as ours. For
+Dataset
+Method
+Precision Recall Accuracy AUC
+MIT
+Geometric (Ours)
+0.98
+0.9
+0.87
+0.94
+Bernoulli
+0.98
+0.85
+0.85
+0.9
+UPenn Geometric (Ours)
+0.88
+0.76
+0.68
+0.73
+Bernoulli
+0.86
+0.72
+0.65
+0.72
+TUH
+Geometric (Ours)
+0.92
+0.57
+0.61
+0.57
+Bernoulli
+0.93
+0.4
+0.59
+0.54
+TABLE II: Effect of masking strategy on seizure identification.
+instance, non-seizure windows in Fig. 2d have a larger ampli-
+tude range than the seizure windows in Figure 2c, while the
+seizure windows in Fig. 2c contain similar spikes to the non-
+seizure windows in Figure 2b w.r.t. amplitude and frequency.
+3) Benefit of Self-Attention: We visualize the self-attention
+weights computed by the last encoder layer of the unsuper-
+vised transformer on example EEG windows from UPenn as
+2D heatmaps in the second and fourth rows of Figure 2. For
+each time point along the horizontal axis of each heatmap, self-
+attention weights (c.f. Equation (3)) from other time points
+are indicated along the vertical axis. Darker heatmap colors
+correspond to larger weights and, thus, higher importance.
+It appears that the transformer model within our unsu-
+pervised identification method can successfully learn to pay
+more attention to seizure patterns including high-frequency
+spikes and waves evolving with large amplitudes [39]. More-
+over, when the model predicts the existence of seizures, it
+shows patterns of focused attention, containing only few time
+points with large weights (Figures 2a and 2d), while windows
+identified as non-seizure (Figures 2b and 2c) lead to much
+more evenly distributed attention. These observations indicate
+that employing a transformer architecture with self-attention
+can improve both performance, as well as explainability of
+seizure identification decisions, by underlining, e.g., spike-
+wave discharges that are indicative of seizures [39].
+4) Effect of Masking Strategy: Table II shows the seizure
+identification performance of training with our geometric
+masking strategy against masking each time point indepen-
+dently at random with a Bernoulli distribution. Our approach
+of unsupervised training with geometric masking consistently
+leads to better performance than Bernoulli masking, demon-
+strating its benefit in modeling multivariate data such as EEG.
+V. CONCLUSION
+We propose a fully-unsupervised transformer-based method
+for seizure identification on raw EEG. Our method can suc-
+cessfully distinguish between non-seizure and seizure windows
+and can even achieve significantly better seizure identifica-
+tion performance than state-of-the-art supervised time-series
+methods, including its purely supervised transformer-based
+counterpart. Generalizing our method to other applications
+involving anomalous activity detection on multivariate time-
+series data is a promising future direction.
+Our unsupervised approach can significantly alleviate the
+burden on clinical experts regarding laborious and difficult
+EEG inspections to provide labels indicating segments that
+contain seizures. Furthermore, if automated identification per-
+formance meets clinical requirements, our method can aid
+
+availability of seizure diagnoses for the wider public, espe-
+cially in areas where access to well-trained healthcare profes-
+sionals is limited.
+REFERENCES
+[1] Hafeez Ullah Amin, Mohd Zuki Yusoff, and Rana Fayyaz Ahmad. A
+novel approach based on wavelet analysis and arithmetic coding for
+automated detection and diagnosis of epileptic seizure in EEG signals
+using machine learning techniques. Biomedical Signal Processing and
+Control, 56, 2020.
+[2] Sabrina Belhadj, Abdelouahab Attia, Ahmed Bachir Adnane, Zoubir
+Ahmed-Foitih, and Abdelmalik Ahmed Taleb.
+Whole brain epileptic
+seizure detection using unsupervised classification. In 2016 8th Inter-
+national Conference on Modelling, Identification and Control (ICMIC),
+pages 977–982. IEEE, 2016.
+[3] Javad Birjandtalab, Maziyar Baran Pouyan, and Mehrdad Nourani.
+Unsupervised EEG analysis for automated epileptic seizure detection.
+In First International Workshop on Pattern Recognition, volume 10011,
+page 100110M. International Society for Optics and Photonics, 2016.
+[4] Christopher M Bishop. Pattern recognition. Machine learning, 128(9),
+2006.
+[5] Poomipat Boonyakitanont, Apiwat Lek-Uthai, Krisnachai Chomtho, and
+Jitkomut Songsiri.
+A review of feature extraction and performance
+evaluation in epileptic seizure detection using EEG. Biomedical Signal
+Processing and Control, 57:101702, 2020.
+[6] Satarupa Chakrabarti, Aleena Swetapadma, and Prasant Kumar Pat-
+tnaik.
+A channel independent generalized seizure detection method
+for pediatric epileptic seizures. Computer Methods and Programs in
+Biomedicine, 209, 2021.
+[7] Satarupa Chakrabarti, Aleena Swetapadma, Prasant Kumar Pattnaik, and
+Tina Samajdar. Pediatric seizure prediction from EEG signals based on
+unsupervised learning techniques using various distance measures. In
+2017 1st International Conference on Electronics, Materials Engineer-
+ing and Nano-Technology (IEMENTech), 2017.
+[8] Satarupa Chakrabarti, Aleena Swetapadma, Prasant Kumar Pattnaik, and
+Tina Samajdar. Pediatric seizure prediction from EEG signals based on
+unsupervised learning techniques using various distance measures. In
+2017 1st International Conference on Electronics, Materials Engineer-
+ing and Nano-Technology, pages 1–5, 2017.
+[9] Raghavendra Chalapathy and Sanjay Chawla. Deep learning for anomaly
+detection: A survey. CoRR, abs/1901.03407, 2019.
+[10] Krit Charupanit, Indranil Sen-Gupta, Jack J Lin, and Beth A Lopour.
+Detection of anomalous high-frequency events in human intracranial
+EEG. Epilepsia Open, 5(2):263–273, 2020.
+[11] Tianqi Chen and Carlos Guestrin. Xgboost: A scalable tree boosting
+system. In Proceedings of the 22nd SIGKDD International Conference
+on Knowledge Discovery and Data Mining, pages 785–794, 2016.
+[12] Angus Dempster, François Petitjean, and Geoffrey I Webb. ROCKET:
+Exceptionally fast and accurate time series classification using random
+convolutional kernels. Data Mining and Knowledge Discovery, 34(5),
+2020.
+[13] Zhaohong Deng, Peng Xu, Lixiao Xie, Kup-Sze Choi, and Shitong
+Wang. Transductive joint-knowledge-transfer TSK-FS for recognition
+of epileptic EEG signals. Transactions on Neural Systems and Rehabil-
+itation Engineering, 26(8):1481–1494, 2018.
+[14] Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova.
+BERT: Pre-training of deep bidirectional transformers for language
+understanding.
+In Proceedings of the 2019 Conference of the North
+American Chapter of the Association for Computational Linguistics:
+Human Language Technologies, Volume 1 (Long and Short Papers),
+pages 4171–4186, 2019.
+[15] Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weis-
+senborn,
+Xiaohua
+Zhai,
+Thomas
+Unterthiner,
+Mostafa
+Dehghani,
+Matthias Minderer, Georg Heigold, Sylvain Gelly, et al. An image is
+worth 16x16 words: Transformers for image recognition at scale. arXiv
+preprint arXiv:2010.11929, 2020.
+[16] Emadeldeen Eldele, Mohamed Ragab, Zhenghua Chen, Min Wu,
+Chee Keong Kwoh, Xiaoli Li, and Cuntai Guan. Time-series represen-
+tation learning via temporal and contextual contrasting. arXiv preprint
+arXiv:2106.14112, 2021.
+[17] Tom Fawcett. An introduction to ROC analysis. Pattern Recognition
+Letters, 27(8):861–874, 2006.
+[18] Robert G Gallager.
+Stochastic Processes: Theory for Applications.
+Cambridge University Press, 2013.
+[19] James A Hanley and Barbara J McNeil. The meaning and use of the
+area under a receiver operating characteristic (ROC) curve. Radiology,
+143(1):29–36, 1982.
+[20] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun.
+Deep
+residual learning for image recognition. In Proceedings of the IEEE
+Conference on Computer Vision and Pattern Recognition, pages 770–
+778, 2016.
+[21] Dan Hendrycks and Kevin Gimpel. Bridging nonlinearities and stochas-
+tic regularizers with gaussian error linear units. CoRR, abs/1606.08415,
+2016.
+[22] Sergey Ioffe and Christian Szegedy. Batch normalization: Accelerating
+deep network training by reducing internal covariate shift. In Interna-
+tional Conference on Machine Learning, pages 448–456. PMLR, 2015.
+[23] Nizar Islah, Jamie Koerner, Roman Genov, Taufik A Valiante, and
+Gerard O’Leary. Machine learning with imbalanced EEG datasets using
+outlier-based sampling. In 2020 42nd Annual International Conference
+of the IEEE Engineering in Medicine & Biology Society, pages 112–115.
+IEEE, 2020.
+[24] Demetres Kostas, Stéphane Aroca-Ouellette, and Frank Rudzicz.
+BENDR: Using transformers and a contrastive self-supervised learning
+task to learn from massive amounts of EEG data. Frontiers in Human
+Neuroscience, 15:253, 2021.
+[25] Yang Li, Yu Liu, Wei-Gang Cui, Yu-Zhu Guo, Hui Huang, and Zhong-Yi
+Hu. Epileptic seizure detection in EEG signals using a unified temporal-
+spectral squeeze-and-excitation network. IEEE Transactions on Neural
+Systems and Rehabilitation Engineering, 28(4):782–794, 2020.
+[26] Virender Kumar Mehla, Amit Singhal, Pushpendra Singh, and Ram Bilas
+Pachori. An efficient method for identification of epileptic seizures from
+EEG signals using fourier analysis. Physical and Engineering Sciences
+in Medicine, 2021.
+[27] Iyad Obeid and Joseph Picone. The temple university hospital EEG data
+corpus. Frontiers in Neuroscience, 10:196, 2016.
+[28] Moein Radman, Milad Moradi, Ali Chaibakhsh, Mojtaba Kordestani,
+and Mehrdad Saif. Multi-feature fusion approach for epileptic seizure
+detection from EEG signals. IEEE Sensors Journal, 21(3):3533–3543,
+2020.
+[29] Ricardo Ramos-Aguilar, J Arturo Olvera-López, Ivan Olmos-Pineda, and
+Susana Sánchez-Urrieta. Feature extraction from EEG spectrograms for
+epileptic seizure detection. Pattern Recognition Letters, 133:202–209,
+2020.
+[30] Sari Saba-Sadiya, Eric Chantland, Tuka Alhanai, Taosheng Liu, and
+Mohammad M Ghassemi.
+Unsupervised EEG artifact detection and
+correction. Frontiers in Digital Health, 2:57, 2021.
+[31] Ali Hossam Shoeb. Application of machine learning to epileptic seizure
+onset detection and treatment. PhD thesis, Massachusetts Institute of
+Technology, 2009.
+[32] Nitish Srivastava, Geoffrey Hinton, Alex Krizhevsky, Ilya Sutskever,
+and Ruslan Salakhutdinov. Dropout: A simple way to prevent neural
+networks from overfitting.
+Journal of Machine Learning Research,
+15(56), 2014.
+[33] Richard J Staba, Matt Stead, and Gregory A Worrell. Electrophysiolog-
+ical biomarkers of epilepsy. Neurotherapeutics, 11(2), 2014.
+[34] Leilei Sun, Bo Jin, Haoyu Yang, Jianing Tong, Chuanren Liu, and
+Hui Xiong. Unsupervised EEG feature extraction based on echo state
+network. Information Sciences, 475:1–17, 2019.
+[35] Roland D Thijs, Rainer Surges, Terence J O’Brien, and Josemir W
+Sander. Epilepsy in adults. The Lancet, 393(10172):689–701, 2019.
+[36] UPenn and MayoClinic. Upenn and Mayo Clinic’s seizure detection
+challenge, 2014.
+[37] Laurens Van der Maaten and Geoffrey Hinton. Visualizing data using
+t-SNE. Journal of Machine Learning Research, 9(11), 2008.
+[38] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion
+Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin. Attention
+is all you need. In Advances in Neural Information Processing Systems,
+pages 5998–6008, 2017.
+[39] Paul M Vespa, Vikesh Shrestha, Nicholas Abend, Denes Agoston, Alicia
+Au, Michael J Bell, Thomas P Bleck, Manuel Buitrago Blanco, Jan
+Claassen, Ramon Diaz-Arrastia, et al. The epilepsy bioinformatics study
+for anti-epileptogenic therapy (EpiBioS4Rx) clinical biomarker: study
+design and protocol. Neurobiology of Disease, 123:110–114, 2019.
+[40] Sungmin You, Baek Hwan Cho, Soonhyun Yook, Joo Young Kim,
+Young-Min Shon, Dae-Won Seo, and In Young Kim. Unsupervised au-
+
+tomatic seizure detection for focal-onset seizures recorded with behind-
+the-ear EEG using an anomaly-detecting generative adversarial network.
+Computer Methods and Programs in Biomedicine, 193:105472, 2020.
+[41] ˙Ilkay Yıldız, Rachael Garner, Matthew Lai, and Dominique Duncan.
+Unsupervised seizure identification on EEG. Computer Methods and
+Programs in Biomedicine, 215:106604, 2022.
+[42] George
+Zerveas,
+Srideepika
+Jayaraman,
+Dhaval
+Patel,
+Anuradha
+Bhamidipaty, and Carsten Eickhoff.
+A transformer-based framework
+for multivariate time series representation learning. In Proceedings of
+the 27th ACM SIGKDD Conference on Knowledge Discovery & Data
+Mining, pages 2114–2124, 2021.
+[43] Tao Zhang and Wanzhong Chen. LMD based features for the automatic
+seizure detection of EEG signals using SVM. IEEE Transactions on
+Neural Systems and Rehabilitation Engineering, 25(8), 2016.
+[44] Xiang Zhang, Lina Yao, Manqing Dong, Zhe Liu, Yu Zhang, and Yong
+Li. Adversarial representation learning for robust patient-independent
+epileptic seizure detection.
+IEEE Journal of Biomedical and Health
+Informatics, 24(10):2852–2859, 2020.
+[45] Wei Zhao, Wenbing Zhao, Wenfeng Wang, Xiaolu Jiang, Xiaodong
+Zhang, Yonghong Peng, Baocan Zhang, and Guokai Zhang. A novel
+deep neural network for robust detection of seizures using EEG signals.
+Computational and Mathematical Methods in Medicine, 2020, 2020.
+[46] Bingzhao Zhu and Mahsa Shoaran. Unsupervised domain adaptation for
+cross-subject few-shot neurological symptom detection. In 2021 10th
+International IEEE/EMBS Conference on Neural Engineering (NER),
+2021.
+
diff --git a/oNE1T4oBgHgl3EQf1wUI/content/tmp_files/load_file.txt b/oNE1T4oBgHgl3EQf1wUI/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f3a1b07179c3db896a98d3e073dfdcf79b741353
--- /dev/null
+++ b/oNE1T4oBgHgl3EQf1wUI/content/tmp_files/load_file.txt
@@ -0,0 +1,732 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf,len=731
+page_content='Unsupervised Multivariate Time-Series  Transformers for Seizure Identification on EEG  ˙Ilkay Yıldız Potter  BioSensics LLC  Newton, MA, USA  ilkay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='yildiz@biosensics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='com  George Zerveas  Dept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' of Computer Science  Brown University  Providence, RI, USA  george_zerveas@brown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='edu  Carsten Eickhoff  Dept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' of Computer Science  Brown University  Providence, RI, USA  carsten@brown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='edu  Dominique Duncan  Keck School of Medicine  University of Southern California  Los Angeles, CA, USA  Dominique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='Duncan@loni.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='usc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='edu  Abstract—Epilepsy is one of the most common neurologi-  cal disorders, typically observed via seizure episodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Epileptic  seizures are commonly monitored through electroencephalogram  (EEG) recordings due to their routine and low expense collection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  The stochastic nature of EEG makes seizure identification via  manual inspections performed by highly-trained experts a tedious  endeavor, motivating the use of automated identification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' The lit-  erature on automated identification focuses mostly on supervised  learning methods requiring expert labels of EEG segments that  contain seizures, which are difficult to obtain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Motivated by these  observations, we pose seizure identification as an unsupervised  anomaly detection problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' To this end, we employ the first  unsupervised transformer-based model for seizure identification  on raw EEG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' We train an autoencoder involving a transformer  encoder via an unsupervised loss function, incorporating a novel  masking strategy uniquely designed for multivariate time-series  data such as EEG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Training employs EEG recordings that do not  contain any seizures, while seizures are identified with respect  to reconstruction errors at inference time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' We evaluate our  method on three publicly available benchmark EEG datasets  for distinguishing seizure vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' non-seizure windows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Our method  leads to significantly better seizure identification performance  than supervised learning counterparts, by up to 16% recall, 9%  accuracy, and 9% Area under the Receiver Operating Charac-  teristics Curve (AUC), establishing particular benefits on highly  imbalanced data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Through accurate seizure identification, our  method could facilitate widely accessible and early detection of  epilepsy development, without needing expensive label collection  or manual feature extraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  Index Terms—Epilepsy, Seizure, EEG, Unsupervised Learning,  Time-series Transformer  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' INTRODUCTION  Epilepsy is one of the most common neurological disorders,  affecting over 70 million people worldwide [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Epilepsy  patients typically suffer from seizures, involving uncontrolled  jerking movements or momentary losses of awareness due to  abnormal excessive or synchronous activities in the brain [39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  The degraded quality of life for patients strongly motivates  early seizure identification, as early seizures have been shown  This is a pre-print version of the article: I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Yıldız Potter, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Zerveas, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  Eickhoff, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Duncan, “Unsupervised Multivariate Time-Series Transformers  for Seizure Identification on EEG”, IEEE Conference on Machine Learning  and Applications (ICMLA) 2022, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='1109/ICMLA55696.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='00208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  Work was performed at University of Southern California and supported by  the National Institutes of Health (NIH) National Institute of Neurological Dis-  orders and Stroke (NINDS) grant R01NS111744.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Code is publicly available  at https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='com/ilkyyldz95/EEG_MVTS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  to be prognostic markers for later epileptogenic develop-  ment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Successful identification of early seizures can initiate  antiepileptogenic intervention and therapies that can remark-  ably improve the quality of life for patients and their care-  givers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' To this end, electroencephalogram (EEG) recordings  received particular attention for seizure identification [33], due  to their routine and low expense collection compared to, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=',  neuroimaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Seizures on EEG are defined as generalized  spike-wave discharges at three per second or faster, and clearly  evolving discharges of any type that reach a frequency of four  per second or faster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  Despite their volume and rich information content, EEG  recordings are known to contain many artifacts due to move-  ment, physiological activity such as perspiration, and measure-  ment hardware [13], [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' The stochastic nature of clinically-  acquired EEG makes seizure identification via manual inspec-  tion laborious and difficult, leading to significant variability  across clinical labels of different experts [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' This challenge  motivated the recent literature to focus on automated identi-  fication of epileptic seizures on EEG as a promising comple-  ment to manual inspection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' The literature on automated EEG  seizure identification is extensive (c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Section II), focusing  mostly on supervised machine learning methods using both  manual feature extraction [1], [26], [29], [46], as well as deep  neural networks (DNNs) without manual feature extraction  [16], [25], [44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  Despite their success, supervised methods require expert  labels indicating EEG segments that contain seizures, while  obtaining large and consistently-labeled EEG datasets is un-  favourable due to the stochastic nature of EEG [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Diffi-  culty of label collection also leads to severely imbalanced  EEG datasets, in which the number of non-seizure recordings  significantly exceeds the number of seizure recordings;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' this  poses a further challenge for supervised learning that is prone  to overfitting towards dominant class predictions [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  Unsupervised machine learning methods, which do not rely  on labeled data have not yet been widely explored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' A few  methods employed traditional shallow models for unsuper-  vised seizure identification on both raw EEG [7], as well as  spatio-temporal features extracted from EEG [2], [3], [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  To the best of our knowledge, unsupervised DNN methods  for EEG seizure identification have been limited to a couple  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='03470v1  [eess.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='SP]  3 Jan 2023  of recent works, requiring feature extraction prior to training  [40] or employing convolutional DNN architectures that are  not tailored for multivariate time-series data such as EEG [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  We propose a fully-unsupervised deep learning approach  that can identify seizures on raw EEG recordings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' To this end,  we make the following contributions:  We employ the first unsupervised transformer-based  model for seizure identification on raw EEG, inspired by  recent advances in multivariate time-series analysis [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  We pose seizure identification as an anomaly detection  problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' To this end, we train an autoencoder involving  a transformer encoder via an unsupervised loss function,  incorporating a novel masking strategy uniquely designed  for modeling multivariate time-series data such as EEG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  As training employs EEG recordings that do not contain  seizures, seizures are identified via mean reconstruction  errors at inference time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  We extensively validate the seizure identification per-  formance of our method on three publicly available  benchmark EEG datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Our method can successfully  distinguish between non-seizure vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' seizure windows,  with up to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='94 Area under the Receiver Operating Char-  acteristics Curve (AUC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Moreover, our unsupervised  anomaly detection approach leads to significantly better  seizure identification performance than the supervised  learning counterparts, by up to 16% recall, 9% accuracy,  and 9% AUC, establishing a particular benefit for learning  from highly imbalanced data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' RELATED WORK  The literature on automated seizure identification on EEG  is vast;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' we refer the reader to the review by [5] for more  details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' A significant body of works focus on extracting spatio-  temporal features from EEG via, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=', wavelet transformations  [1], [28], local mean decomposition [43], Fourier transfor-  mations [26], [29], and power spectra [46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Extracted fea-  tures are used to train supervised machine learning methods,  including support vector machines and neural networks, to  identify whether a given EEG contains a seizure in a binary  classification setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  Deep neural network (DNN)-based supervised seizure iden-  tification methods have lately dominated the literature [45]  and obviated the need for manual feature extraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' DNN  methods further improved in combination with recurrent neural  networks to aid time-series modeling [6], adversarial training  to generalize identification across patients [44], autoencoder-  based feature extraction [34], and attention mechanisms to  improve predictions and interpretability [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  In recent years, self-attention modules have become an in-  tegral part of DNN methods employed in machine vision [15],  natural language processing [14], and time-series modeling  [42];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' the resulting DNN architectures are termed as trans-  formers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Transformer architectures have been very recently  applied for various identification tasks on EEG, including,  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=', sleep-stage classification , human-computer interface-  based action recognition, and seizure identification [16], [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  These methods employ unsupervised pre-training prior to  supervised training on ground-truth expert labels pertaining to  the identification task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' The unsupervised pre-training objective  involves different augmentations of the same EEG segment  and trains the transformer by maximizing (minimizing) the  similarity of different augmentations (segments).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  All in all, the literature on automated seizure identifica-  tion often focuses on supervised machine learning methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  Despite their success, these methods require expert labels  indicating EEG segments that contain seizures, which are  difficult to obtain due to the stochastic nature of EEG [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  Meanwhile, unsupervised machine learning methods that do  not rely on labeled data have not yet been widely explored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' A  few methods applied shallow models for unsupervised seizure  identification, including K-means, hierarchical clustering, and  Gaussian mixture models, on both raw EEG [7], as well as  spatio-temporal features extracted from EEG [2], [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  Recently, a couple of unsupervised DNN methods for  seizure identification on EEG have been proposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' You et  al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' (2020) preprocess EEGs to extract time-frequency spectro-  gram images and train a generative adversarial network (GAN)  [40] on the spectrograms that do not contain seizures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' For each  spectrogram at testing time, they have to search for the latent  GAN input that leads to the smallest loss value and use the cor-  responding generated spectrogram for seizure identification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  As training involves non-seizure activity, test spectrograms  that significantly differ from the spectrograms generated by the  GAN are successfully identified to contain seizures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Yıldız et  al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' (2022) train a convolutional variational autoencoder (VAE)  over raw EEG, employing an objective tailored for suppressing  EEG artifacts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Unlike You et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' (2020), they identify seizures  with respect to the reconstruction errors at inference time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  We differ from the existing works by applying the first  fully-unsupervised transformer-based model on raw EEG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Our  architecture and training objective are particularly designed  for multivariate time-series analysis and do not require a  sophisticated minimax optimization such as GAN training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  The fundamental benefit of a transformer encoder over other  DNN architectures is that self-attention can selectively high-  light important input features and sequence segments, without  relying on sequence-aligned convolutions or slow recurrent  modules [38];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' we also experimentally demonstrate this advan-  tage against unsupervised VAE-based seizure identification in  Section IV-E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' PROBLEM FORMULATION  We consider a dataset of N EEG recordings, each collected  from M electrode channels and consisting of T time points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  Formally, we denote each EEG recording by X(i) ∈ RT ×M,  for i ∈ [1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' , N].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Our aim is to design an unsupervised  method that does not rely on ground-truth expert labels during  learning and can identify the existence of seizures in a given  EEG recording.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' To this end, we employ an autoencoder  architecture involving a transformer network encoder that is  uniquely designed for multivariate time-series data [42], such  as EEG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' We note that our method naturally generalizes to  EEG recordings comprising different numbers of time points  and channels (see our preprocessing setup in Section IV-B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Multivariate Time-Series Transformer  Our autoencoder architecture is based on a transformer  encoder and is depicted in Figure 1: the model learns to  extract and transform latent features from a given EEG  recording in order to reconstruct the stochastically-masked  input [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Formally, the transformer encoder network receives  a recording X(i) ∈ RT ×M, i ∈ [1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' , N], and extracts  latent features Z(i) ∈ RT ×D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' The output layer applies an  affine transformation on Z(i) to reconstruct the recording as  ˆ  X(i) ∈ RT ×M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  1) Transformer Encoder: Transformer encoder operations  begin with projecting a recording X(i) from M dimensions  to D dimensions via a trainable affine transformation P ∈  RM×D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' To preserve the ordering information of the input  sequence, a fully-trainable positional encoding E ∈ RT ×D  is added for each input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' The resulting latent features extracted  from each recording are thus: Z(i) = X(i)P + E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  Dimensional projection and positional encoding are fol-  lowed by the successive application of several transformer  layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Each transformer layer consists of a multi-headed  self-attention (MSA) module, a stochastic dropout operation  ˜d [32], batch normalization (Norm) [22], and a fully-connected  network (FCN) consisting of two linear layers separated by a  GELU [21] activation, a non-linearity designed to be used in  combination with dropout and batch normalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Formally,  latent features are updated by each transformer layer via:  Z(i) ← Norm  �  ˜d  �  MSA(Z(i))  �  + Z(i)�  ,  Z(i) ← Norm  �  ˜d  �  FCN(Z(i))  �  + Z(i)�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  (1)  The summation of each latent feature with its transformation  is a skip connection that aids generalization [20], along with  batch normalization that has been shown improvement against  layer normalization for multivariate time-series analysis [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  2) Multi-headed Self-attention Module: An MSA module  is designed to assign selective importance to latent features  extracted for each time point by the preceding layers of the  encoder [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Particularly, MSA contains trainable parameters  that capture the similarity between input features at different  time points via their query, key, and value representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  Multiple attention heads enable adaptations to long-term de-  pendencies and capture relevance between segments of multi-  variate data, without prior bias based on position [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  Formally, at each time point t, the output representation is  computed via a weighted sum over the value vectors z(i)  v,t′ ∈  RDv, t′ ∈ [1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' , T], where the importance weight assigned  to the value vector at time t′ is computed as a dot-product  similarity between its corresponding key vector z(i)  k,t′ ∈ RDq  and a query vector z(i)  q,t ∈ RDq at time t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' As a result, given a  latent feature Z(i), a query Z(i)  q  = [z(i)  q,1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' z(i)  q,T ] ∈ RT ×Dq,  a key Z(i)  k  =  [z(i)  k,1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' z(i)  k,T ]  ∈  RT ×Dq, and a value  Z(i)  v  = [z(i)  v,1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' z(i)  v,T ] ∈ RT ×Dv are computed by applying  three different trainable affine transformations on Z(i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' The  self-attention output for a single attention head (SA) is then  computed via a scaled dot-product:  SA(Z(i)) = softmax  �  Z(i)  q Z(i)⊤  k  �  Dq  �  Z(i)  v ,  (2)  where softmax converts the similarity scores to a probability  distribution over the input sequence of length T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' This opera-  tion is performed in parallel for each of the H attention heads  (each with its own trainable transformations).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' The resulting  outputs SAh ∈ RT ×Dv, h ∈ [1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' , H] are first concatenated  and finally aggregated into a single representation through a  trainable linear transformation WA ∈ RHDv×D:  MSA(Z(i))=[SA1(Z(i)) SA2(Z(i)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='SAH(Z(i))]WA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' (3)  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Reconstruction-Based Loss Function  We aim for the transformer model to extract discriminative  latent features that govern the generation of EEG recordings,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=', to model the input data distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' To this end, we  corrupt each input sample by a novel masking strategy that  is uniquely designed for modeling multivariate time-series  data such as EEG [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' We train the transformer model  via a loss function that minimizes the error between the  original (unmasked) recording X(i) and the corresponding  reconstruction ˆ  X(i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  Formally, a proportion r ∈ (0, 1) of each channel m ∈  {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' , M} in each EEG recording X(i) is dynamically  masked at the beginning of each training step by setting  the encoder input values at chosen time points to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' The  values at each channel alternate between consecutive masked  and unmasked sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' The number of masked time points  follows a geometric distribution with mean lm, while the num-  ber of unmasked time points follows a geometric distribution  with mean lu =  1−r  r lm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' This transition paradigm is also  known as an M/M/1 queue, in which the number of customers  in a system is geometrically distributed [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' The resulting  masking strategy encourages the transformer to attend on time  points preceding and following the masked segments both in  individual channels, as well as across the aligned time points  in other channels to capture inter-channel dependencies, and  has been found more effective than other denoising strategies  for downstream tasks, including Bernoulli masking (c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Table  II & [42]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  Finally, the reconstruction loss for end-to-end training of our  model is the mean-squared reconstruction error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Crucially, the  loss is computer over only the set of masked time points M =  {(t, m) | masked X(i)  t,m, t ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' , T}, m ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' , M}}:  1  |M|  �  (t,m)∈M  (X(i)  t,m − ˆX(i)  t,m)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  (4)  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Seizure Identification  We aim to employ the trained transformer to distinguish  between EEG recordings that contain seizures and those  which do not;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' this motivates us to pose unsupervised seizure  Transformer Encoder  Output  Layer  Time  Channels  Affine  Dimension  Reduction  Positional  Encoding  Multi-head  self-attention  Batch  normalization  Fully-connected  Neural Network  Batch  normalization  Affine  Transform  Transformer layers repeated  Multivariate Input  Reconstruction  Latent features  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' 1: Our autoencoder architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' The transformer encoder network receives a recording X(i), and extracts latent features  Z(i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' The output layer applies an affine transformation on Z(i) to reconstruct the recording as ˆ  X(i) ∈ RT ×M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' During training,  a proportion of each channel is masked by setting the input values at masked time points (shaded in gray) to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  identification as an anomaly detection problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Thus, we train  the transformer architecture on recordings that do not contain  seizures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' This allows for the learned latent features to capture  non-seizure activity [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' As the transformer is trained to  model non-seizure activity, recordings with no seizures are  expected to be reconstructed with low error in inference time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  In contrast, EEG recordings including seizure activity come  from a different distribution, and thus, the model naturally  reconstructs such input recordings with a relatively larger  error;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' we use this observation as an indicator for a seizure  (c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Section IV-D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  We note that the exclusion of seizure recordings from the  training set does not constitute supervision or require any  special annotation, as the default states of patients and healthy  individuals alike are non-seizure, whose recordings can be  collected and kept separate from the recordings of seizure  episodes (which we only use for evaluating our method).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' In  real-life applications, EEG data with no seizure activity can  be easily augmented with recordings from healthy individuals,  which are trivially accessible compared to the ones from  patients experiencing seizures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' EXPERIMENTS  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Datasets  We evaluate our method on three publicly available EEG  datasets collected at the: (i) Massachusetts Institute of Tech-  nology (MIT) and Boston Children’s Hospital [31] (ii) Uni-  versity of Pennsylvania (UPenn) and Mayo Clinic [36], and  (iii) Temple University Hospital of Philadelphia (TUH) [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  The MIT dataset contains EEG recordings acquired on the  scalp with 256 Hz sampling rate from a maximum of M = 38  channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' 198 seizure recordings were labeled w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' their start  and end times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' The total duration of non-seizure recordings is  40, 800 seconds and seizure recordings is 2889 seconds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  The UPenn dataset contains 1-second long EEG recordings  acquired intracranially at 500 − 5000 Hz from a maximum of  M = 72 channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' The total duration of non-seizure recordings  is 7164 seconds and seizure recordings is 653 seconds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  The TUH dataset contains EEG recordings acquired on the  scalp with 250 Hz sampling rate from a maximum of M = 38  channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' 1229 seizure recordings were labeled w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' their start  and end times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' The total duration of non-seizure recordings is  49, 922 seconds and seizure recordings is 2600 seconds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Preprocessing  EEG recordings are typically preprocessed to eliminate the  powerline noise at 60 Hz [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' We first unify the sampling rates  in each dataset by downsampling to the smallest sampling rate  across all recordings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Then, we filter the recordings via a 4-th  order Butterworth bandpass filter with range 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='5-50 Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  To construct samples with the same size, we extract sliding  windows over each recording, where each window contains  T time points and overlaps with its consecutive window by  50%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' We choose T based on the shortest seizure segment  in each dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' In doing so, T = 1536 for MIT, T = 500  for UPenn, and T = 462 for TUH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' This process results in  13, 600 windows with non-seizure activity and 963 windows  with seizure activity for MIT, 14, 329 windows with non-  seizure activity and 1307 windows with seizure activity for  UPenn, and 54, 264 windows with non-seizure activity and  2826 windows with seizure activity for TUH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' In real-life appli-  cations, a minimum seizure window length can be decided by  clinical experts, as in UPenn that directly provides 1 second-  long seizure recordings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  Moreover, we aim to consistently form T ×M size windows,  while not disregarding any channels with potential seizure ac-  tivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Thus, to construct samples with the same number of M  channels, we reuse data from other channels for the recordings  that have missing data at certain channels, compared to the  recording with the largest number of channels in each dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  Again, in real-life applications, clinical experts can determine  which channels to employ or discard for seizure identification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  Finally, we normalize windows by subtracting the mean and  dividing by the standard deviation across all windows to aid  the convergence of training [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  X()x()Z(i)Dataset  Method  Precision  Recall  Accuracy  AUC  MIT  Unsupervised Transformer  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='98 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='003  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='9 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='006  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='87 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='006  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='94 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='023  Unsupervised K-means  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='33 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='008  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='5 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='009  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='5 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='009  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='59 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='041  Unsupervised VAE  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='97 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='003  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='75 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='008  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='61 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='009  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='61 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='041  Supervised XGBoost  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='98 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='003  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='8 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='007  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='8 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='007  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='88 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='031  Supervised ROCKET  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='98 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='003  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='74 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='008  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='78 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='008  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='86 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='032  Supervised Transformer  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='98 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='003  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='83 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='007  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='83 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='007  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='88 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='031  Pre-trained 50% Supervised Transformer  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='97 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='003  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='72 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='008  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='63 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='009  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='66 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='021  Pre-trained 100% Supervised Transformer  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='99 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='002  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='98 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='003  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='94 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='97 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='017  UPenn  Unsupervised Transformer  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='88 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='76 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='013  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='68 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='014  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='73 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='027  Unsupervised K-means  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='33 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='014  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='5 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='015  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='5 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='015  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='56 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='028  Unsupervised VAE  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='8 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='012  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='5 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='015  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='49 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='015  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='47 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='027  Supervised XGBoost  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='87 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='62 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='015  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='6 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='015  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='65 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='028  Supervised ROCKET  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='87 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='67 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='014  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='62 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='015  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='67 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='028  Supervised Transformer  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='87 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='69 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='014  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='62 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='015  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='64 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='028  Pre-trained 50% Supervised Transformer  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='86 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='011  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='77 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='013  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='63 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='015  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='64 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='032  Pre-trained 100% Supervised Transformer  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='92 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='008  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='85 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='011  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='82 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='012  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='89 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='02  TUH  Unsupervised Transformer  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='92 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='57 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='009  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='61 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='009  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='57 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='013  Unsupervised K-means  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='17 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='007  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='5 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='009  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='35 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='008  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='57 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='013  Unsupervised VAE  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='93 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='86 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='006  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='83 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='007  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='86 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='009  Supervised XGBoost  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='93 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='73 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='008  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='71 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='008  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='78 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='011  Supervised ROCKET  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='93 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='7 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='008  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='66 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='008  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='74 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='012  Supervised Transformer  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='92 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='37 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='009  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='54 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='009  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='52 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='012  Pre-trained 50% Supervised Transformer  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='94 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='61 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='009  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='75 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='008  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='71 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='025  Pre-trained 100% Supervised Transformer  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='93 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='66 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='008  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='7 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='008  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='72 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='012  TABLE I: Seizure identification performance metrics and confidence intervals on UPenn, MIT and TUH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' We compare our  transformer-based unsupervised identification method (in bold) with unsupervised methods comprising VAE and t-SNE followed  by K-means clustering, as well as supervised methods comprising XGBoost, ROCKET, and the same transformer architecture  trained via supervised and pre-trained supervised learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Best performance for each dataset are in italics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Experiment Setup and Competing Methods  We partition all windows containing non-seizure and seizure  activity into training, validation, and test sets in a stratified  manner, allocating 60% for training, 20% for validation, and  the remaining 20% for testing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' As baseline methods, we im-  plement shallow and deep learning models for both supervised  and unsupervised settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  1) Unsupervised Learning Methods: For our method, we  employ the transformer encoder architecture proposed by  Vaswani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' (2017), with the modifications of fully-trainable  positional encoding, batch normalization and the same hyper-  parameters suggested by Zerveas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' We train the  autoencoder over only non-seizure training windows using the  unsupervised loss given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' We monitor the loss value  computed over the non-seizure windows in the validation set  and use the model that attains the lowest validation loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  Following the literature on shallow unsupervised methods  [8], we reduce the dimension of all EEG windows in the test  set to 3 using the t-Distributed Stochastic Neighbor Embed-  ding (t-SNE) [37] algorithm, and apply K-means clustering  [4] on the resulting windows with two clusters indicating  non-seizure and seizure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Moreover, as an unsupervised deep  learning baseline, we train a state-of-the-art convolutional VAE  [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  2) Supervised Learning Methods: First, we employ the  same transformer encoder architecture described in Section  III-A and map the latent features learned from each window  to a binary prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' In doing so, we concatenate all latent  features corresponding to all time points of each window  into a single vector and apply a fully-connected layer com-  prising a scalar output with sigmoid activation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' We train the  resulting architecture via cross-entropy loss over all training  windows, employing the same hyperparameters found optimal  by Zerveas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' To combat overfitting due to class  imbalance in supervised learning, we oversample and augment  the seizure windows in training via random reversing and  drifting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' We monitor the F1-score computed over the validation  set and use the model that attains the best validation score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  Moreover, we train state-of-the-art shallow models XGBoost  [11] and ROCKET [12] over the supervised training set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  XGBoost is a decision-tree classifier using gradient boosting  for ensembling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' ROCKET transforms time-series using 500  random convolutional kernels and uses the extracted features  to train a ridge regression classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Ridge regression hyper-  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='0  Time (s)  200000  100000  0  100000  200000  300000  V  Patient_8_ictal_2869  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='0  Time (s)  200000  150000  100000  50000  0  50000  Patient_8_ictal_2870  (a) Correctly Identified Seizure Windows (True Positive)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='0  Time (s)  60  40  20  0  20  40  V  Patient_2_interictal_1658  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='0  Time (s)  20  0  20  40  60  Patient_2_interictal_1566  (b) Correctly Identified Non-seizure Windows (True Negative)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='0  Time (s)  60  40  20  0  20  40  V  Patient_2_ictal_3983  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='0  Time (s)  40  20  0  20  Patient_2_ictal_3984  (c) Falsely Identified Seizure Windows (False Negative)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='0  Time (s)  1000  500  0  500  1000  V  Patient_2_interictal_31  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='0  Time (s)  1500  1000  500  0  500  1000  1500  2000  2500  Patient_2_interictal_602  (d) Falsely Identified Non-seizure Windows (False Positive)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' 2: Example EEG windows, corresponding seizure identifications and self-attention weights on UPenn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' First and third rows  contain example windows of true positive, true negative, false negative, and false positive identifications, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Second  and fourth rows contain the corresponding self-attention weight heatmaps computed by the transformer architecture, where  darker colors indicate higher importance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' For each window, we visualize the channel with the largest reconstruction error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  parameter is varied in [10−3, 103] and best hyperparameter is  determined w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' the accuracy over the validation set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  3) Pre-trained Supervised Learning: Finally, we combine  the transformer-based seizure identification methods via unsu-  pervised pre-training and supervised fine-tuning [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Follow-  ing the unsupervised approach described in Section IV-C1, we  first pre-train the transformer encoder over non-seizure training  windows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Having initialized its weights accordingly, we then  fine-tune the model via both non-seizure and seizure training  windows, using the same setup described in Section IV-C2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Evaluation Metrics  To evaluate the seizure identification performance of our  approach, as well as the VAE baseline, we use the mean ab-  solute error over the time points and electrode channels in each  EEG window from the test set as the corresponding seizure  prediction score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' For all supervised competing methods, we  use the traditional prediction score for inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  For all competing methods described in Section IV-C, we  report AUC for distinguishing seizure vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' non-seizure windows  in the test set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' To compute binary decision metrics, we thresh-  old the prediction score of each window at the value for which  the geometric mean of recall and true negative rate is maxi-  mal [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Using the respective threshold, we calculate class-  weighted precision and recall, as well as balanced accuracy  for binary identification of seizure vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' non-seizure windows in  the test set, considering the imbalanced distribution between  the two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' In real-life applications, decision thresholds may be  determined by clinical experts with respect to the desired  trade-off between false positives and negatives [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  We report all metrics along with the 95% confidence in-  tervals, which are computed as 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='96 × σA, where σ2  A is the  variance for metric A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Variance for AUC is computed by:  σ2  A= 1  mn  �  A(1−A)+(m−1)(Px−A2)+(n−1)(Py−A2)  �  ,  (5)  where Px = A/(2 − A), Py = 2A2/(1 + A), and m, n are  the number of seizure and non-seizure windows, respectively  [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Variance for other metrics are computed by:  σ2  A = A(1 − A)/(m + n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  (6)  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Results and Discussion  1) Seizure Identification Performance: Table I shows the  seizure identification performance of our transformer-based  unsupervised method vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' supervised and pre-trained super-  vised transformers, XGBoost, ROCKET, VAE, and t-SNE  followed by K-means clustering over all datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Our novel  transformer-based anomaly detection method establishes a  dramatic improvement among all unsupervised methods, by  successfully distinguishing between non-seizure vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' seizure  windows with up to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='94 AUC and outperforming its state-  of-the-art deep learning counterpart VAE by up to 33% AUC  on MIT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Clustering on raw EEG windows cannot capture the  complex evolution of EEG and predicts all windows as non-  seizure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' These observations demonstrate the benefit of the  transformer architecture for unsupervised anomaly detection  in our setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  Crucially, despite the lack of seizure labels during training,  our unsupervised anomaly detection approach leads to signif-  icantly better seizure identification than all purely supervised  learning baselines and the pre-trained transformer fine-tuned  with 50% of the training labels over UPenn and MIT, by  up to 16% recall, 9% accuracy, and 9% AUC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Moreover,  unlike supervised learning, class imbalance strongly biases  supervised models towards non-seizure predictions and hinders  generalization over the distribution of held-out test samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  As a result, unsupervised anomaly detection via transformers  establishes a consistently better balance between precision and  recall than supervised learning and further demonstrates its  benefit in learning from imbalanced datasets such as ours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  The TUH dataset is particularly challenging by being a  compilation of several EEG databases collected over years  from patients with vast variations in demographic and medical  backgrounds [27], compared to self-contained UPenn and MIT  datasets collected from only 8 and 24 patients, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' In  this case, our unsupervised transformer still fares significantly  better than the purely supervised transformer, while unsuper-  vised VAE outperforms all supervised learning baselines, in-  cluding the pre-trained transformer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' These observations further  motivate unsupervised learning for our task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  As expected, the computationally expensive transformer  model, which has first undergone unsupervised pre-training  and then supervised fine-tuning with all training labels, outper-  forms both purely supervised as well as purely unsupervised  transformer models (the latter by a smaller margin).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' However,  our unsupervised anomaly detection method does not require  ground-truth seizure labels during training as a crucial advan-  tage, while still leading to successful seizure identification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  2) Seizure Identification Examples: We visualize example  EEG windows from UPenn and the corresponding seizure  identifications of the unsupervised transformer in the first and  third rows of Figure 2, selecting the channel with the largest  mean reconstruction error for each window.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Agreeing with  the clinical description of seizures, true seizure windows in  Figure 2a contain high-frequency waves with large amplitudes  [39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Meanwhile, true non-seizure windows in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' 2b attain  significantly less amplitude changes and spikes compared to  true positive windows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Note that the seizure patterns cannot  be identified w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' only large amplitude or high frequency,  motivating a more sophisticated approach such as ours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' For  Dataset  Method  Precision Recall Accuracy AUC  MIT  Geometric (Ours)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='98  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='87  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='94  Bernoulli  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='98  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='85  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='85  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='9  UPenn Geometric (Ours)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='88  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='76  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='68  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='73  Bernoulli  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='86  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='72  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='65  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='72  TUH  Geometric (Ours)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='92  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='57  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='61  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='57  Bernoulli  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='93  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='59  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='54  TABLE II: Effect of masking strategy on seizure identification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  instance, non-seizure windows in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' 2d have a larger ampli-  tude range than the seizure windows in Figure 2c, while the  seizure windows in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' 2c contain similar spikes to the non-  seizure windows in Figure 2b w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' amplitude and frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  3) Benefit of Self-Attention: We visualize the self-attention  weights computed by the last encoder layer of the unsuper-  vised transformer on example EEG windows from UPenn as  2D heatmaps in the second and fourth rows of Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' For  each time point along the horizontal axis of each heatmap, self-  attention weights (c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Equation (3)) from other time points  are indicated along the vertical axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Darker heatmap colors  correspond to larger weights and, thus, higher importance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  It appears that the transformer model within our unsu-  pervised identification method can successfully learn to pay  more attention to seizure patterns including high-frequency  spikes and waves evolving with large amplitudes [39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' More-  over, when the model predicts the existence of seizures, it  shows patterns of focused attention, containing only few time  points with large weights (Figures 2a and 2d), while windows  identified as non-seizure (Figures 2b and 2c) lead to much  more evenly distributed attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' These observations indicate  that employing a transformer architecture with self-attention  can improve both performance, as well as explainability of  seizure identification decisions, by underlining, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=', spike-  wave discharges that are indicative of seizures [39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  4) Effect of Masking Strategy: Table II shows the seizure  identification performance of training with our geometric  masking strategy against masking each time point indepen-  dently at random with a Bernoulli distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Our approach  of unsupervised training with geometric masking consistently  leads to better performance than Bernoulli masking, demon-  strating its benefit in modeling multivariate data such as EEG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' CONCLUSION  We propose a fully-unsupervised transformer-based method  for seizure identification on raw EEG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Our method can suc-  cessfully distinguish between non-seizure and seizure windows  and can even achieve significantly better seizure identifica-  tion performance than state-of-the-art supervised time-series  methods, including its purely supervised transformer-based  counterpart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Generalizing our method to other applications  involving anomalous activity detection on multivariate time-  series data is a promising future direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  Our unsupervised approach can significantly alleviate the  burden on clinical experts regarding laborious and difficult  EEG inspections to provide labels indicating segments that  contain seizures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Furthermore, if automated identification per-  formance meets clinical requirements, our method can aid  availability of seizure diagnoses for the wider public, espe-  cially in areas where access to well-trained healthcare profes-  sionals is limited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  REFERENCES  [1] Hafeez Ullah Amin, Mohd Zuki Yusoff, and Rana Fayyaz Ahmad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' A  novel approach based on wavelet analysis and arithmetic coding for  automated detection and diagnosis of epileptic seizure in EEG signals  using machine learning techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Biomedical Signal Processing and  Control, 56, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [2] Sabrina Belhadj, Abdelouahab Attia, Ahmed Bachir Adnane, Zoubir  Ahmed-Foitih, and Abdelmalik Ahmed Taleb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  Whole brain epileptic  seizure detection using unsupervised classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' In 2016 8th Inter-  national Conference on Modelling, Identification and Control (ICMIC),  pages 977–982.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' IEEE, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [3] Javad Birjandtalab, Maziyar Baran Pouyan, and Mehrdad Nourani.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  Unsupervised EEG analysis for automated epileptic seizure detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  In First International Workshop on Pattern Recognition, volume 10011,  page 100110M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' International Society for Optics and Photonics, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [4] Christopher M Bishop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Pattern recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Machine learning, 128(9),  2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [5] Poomipat Boonyakitanont, Apiwat Lek-Uthai, Krisnachai Chomtho, and  Jitkomut Songsiri.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  A review of feature extraction and performance  evaluation in epileptic seizure detection using EEG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Biomedical Signal  Processing and Control, 57:101702, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [6] Satarupa Chakrabarti, Aleena Swetapadma, and Prasant Kumar Pat-  tnaik.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  A channel independent generalized seizure detection method  for pediatric epileptic seizures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Computer Methods and Programs in  Biomedicine, 209, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [7] Satarupa Chakrabarti, Aleena Swetapadma, Prasant Kumar Pattnaik, and  Tina Samajdar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Pediatric seizure prediction from EEG signals based on  unsupervised learning techniques using various distance measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' In  2017 1st International Conference on Electronics, Materials Engineer-  ing and Nano-Technology (IEMENTech), 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [8] Satarupa Chakrabarti, Aleena Swetapadma, Prasant Kumar Pattnaik, and  Tina Samajdar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Pediatric seizure prediction from EEG signals based on  unsupervised learning techniques using various distance measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' In  2017 1st International Conference on Electronics, Materials Engineer-  ing and Nano-Technology, pages 1–5, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [9] Raghavendra Chalapathy and Sanjay Chawla.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Deep learning for anomaly  detection: A survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' CoRR, abs/1901.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='03407, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [10] Krit Charupanit, Indranil Sen-Gupta, Jack J Lin, and Beth A Lopour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  Detection of anomalous high-frequency events in human intracranial  EEG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Epilepsia Open, 5(2):263–273, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [11] Tianqi Chen and Carlos Guestrin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Xgboost: A scalable tree boosting  system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' In Proceedings of the 22nd SIGKDD International Conference  on Knowledge Discovery and Data Mining, pages 785–794, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [12] Angus Dempster, François Petitjean, and Geoffrey I Webb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' ROCKET:  Exceptionally fast and accurate time series classification using random  convolutional kernels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Data Mining and Knowledge Discovery, 34(5),  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [13] Zhaohong Deng, Peng Xu, Lixiao Xie, Kup-Sze Choi, and Shitong  Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Transductive joint-knowledge-transfer TSK-FS for recognition  of epileptic EEG signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Transactions on Neural Systems and Rehabil-  itation Engineering, 26(8):1481–1494, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [14] Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  BERT: Pre-training of deep bidirectional transformers for language  understanding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  In Proceedings of the 2019 Conference of the North  American Chapter of the Association for Computational Linguistics:  Human Language Technologies, Volume 1 (Long and Short Papers),  pages 4171–4186, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [15] Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weis-  senborn,  Xiaohua  Zhai,  Thomas  Unterthiner,  Mostafa  Dehghani,  Matthias Minderer, Georg Heigold, Sylvain Gelly, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' An image is  worth 16x16 words: Transformers for image recognition at scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' arXiv  preprint arXiv:2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='11929, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [16] Emadeldeen Eldele, Mohamed Ragab, Zhenghua Chen, Min Wu,  Chee Keong Kwoh, Xiaoli Li, and Cuntai Guan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Time-series represen-  tation learning via temporal and contextual contrasting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' arXiv preprint  arXiv:2106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='14112, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [17] Tom Fawcett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' An introduction to ROC analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Pattern Recognition  Letters, 27(8):861–874, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [18] Robert G Gallager.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  Stochastic Processes: Theory for Applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  Cambridge University Press, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [19] James A Hanley and Barbara J McNeil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' The meaning and use of the  area under a receiver operating characteristic (ROC) curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Radiology,  143(1):29–36, 1982.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [20] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  Deep  residual learning for image recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' In Proceedings of the IEEE  Conference on Computer Vision and Pattern Recognition, pages 770–  778, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [21] Dan Hendrycks and Kevin Gimpel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Bridging nonlinearities and stochas-  tic regularizers with gaussian error linear units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' CoRR, abs/1606.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='08415,  2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [22] Sergey Ioffe and Christian Szegedy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Batch normalization: Accelerating  deep network training by reducing internal covariate shift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' In Interna-  tional Conference on Machine Learning, pages 448–456.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' PMLR, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [23] Nizar Islah, Jamie Koerner, Roman Genov, Taufik A Valiante, and  Gerard O’Leary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Machine learning with imbalanced EEG datasets using  outlier-based sampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' In 2020 42nd Annual International Conference  of the IEEE Engineering in Medicine & Biology Society, pages 112–115.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  IEEE, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [24] Demetres Kostas, Stéphane Aroca-Ouellette, and Frank Rudzicz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  BENDR: Using transformers and a contrastive self-supervised learning  task to learn from massive amounts of EEG data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Frontiers in Human  Neuroscience, 15:253, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [25] Yang Li, Yu Liu, Wei-Gang Cui, Yu-Zhu Guo, Hui Huang, and Zhong-Yi  Hu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Epileptic seizure detection in EEG signals using a unified temporal-  spectral squeeze-and-excitation network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' IEEE Transactions on Neural  Systems and Rehabilitation Engineering, 28(4):782–794, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [26] Virender Kumar Mehla, Amit Singhal, Pushpendra Singh, and Ram Bilas  Pachori.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' An efficient method for identification of epileptic seizures from  EEG signals using fourier analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Physical and Engineering Sciences  in Medicine, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [27] Iyad Obeid and Joseph Picone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' The temple university hospital EEG data  corpus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Frontiers in Neuroscience, 10:196, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [28] Moein Radman, Milad Moradi, Ali Chaibakhsh, Mojtaba Kordestani,  and Mehrdad Saif.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Multi-feature fusion approach for epileptic seizure  detection from EEG signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' IEEE Sensors Journal, 21(3):3533–3543,  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [29] Ricardo Ramos-Aguilar, J Arturo Olvera-López, Ivan Olmos-Pineda, and  Susana Sánchez-Urrieta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Feature extraction from EEG spectrograms for  epileptic seizure detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Pattern Recognition Letters, 133:202–209,  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [30] Sari Saba-Sadiya, Eric Chantland, Tuka Alhanai, Taosheng Liu, and  Mohammad M Ghassemi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  Unsupervised EEG artifact detection and  correction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Frontiers in Digital Health, 2:57, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [31] Ali Hossam Shoeb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Application of machine learning to epileptic seizure  onset detection and treatment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' PhD thesis, Massachusetts Institute of  Technology, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [32] Nitish Srivastava, Geoffrey Hinton, Alex Krizhevsky, Ilya Sutskever,  and Ruslan Salakhutdinov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Dropout: A simple way to prevent neural  networks from overfitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  Journal of Machine Learning Research,  15(56), 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [33] Richard J Staba, Matt Stead, and Gregory A Worrell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Electrophysiolog-  ical biomarkers of epilepsy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Neurotherapeutics, 11(2), 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [34] Leilei Sun, Bo Jin, Haoyu Yang, Jianing Tong, Chuanren Liu, and  Hui Xiong.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Unsupervised EEG feature extraction based on echo state  network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Information Sciences, 475:1–17, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [35] Roland D Thijs, Rainer Surges, Terence J O’Brien, and Josemir W  Sander.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Epilepsy in adults.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' The Lancet, 393(10172):689–701, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [36] UPenn and MayoClinic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Upenn and Mayo Clinic’s seizure detection  challenge, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [37] Laurens Van der Maaten and Geoffrey Hinton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Visualizing data using  t-SNE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Journal of Machine Learning Research, 9(11), 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [38] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion  Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Attention  is all you need.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' In Advances in Neural Information Processing Systems,  pages 5998–6008, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [39] Paul M Vespa, Vikesh Shrestha, Nicholas Abend, Denes Agoston, Alicia  Au, Michael J Bell, Thomas P Bleck, Manuel Buitrago Blanco, Jan  Claassen, Ramon Diaz-Arrastia, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' The epilepsy bioinformatics study  for anti-epileptogenic therapy (EpiBioS4Rx) clinical biomarker: study  design and protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Neurobiology of Disease, 123:110–114, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [40] Sungmin You, Baek Hwan Cho, Soonhyun Yook, Joo Young Kim,  Young-Min Shon, Dae-Won Seo, and In Young Kim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Unsupervised au-  tomatic seizure detection for focal-onset seizures recorded with behind-  the-ear EEG using an anomaly-detecting generative adversarial network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  Computer Methods and Programs in Biomedicine, 193:105472, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [41] ˙Ilkay Yıldız, Rachael Garner, Matthew Lai, and Dominique Duncan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  Unsupervised seizure identification on EEG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Computer Methods and  Programs in Biomedicine, 215:106604, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [42] George  Zerveas,  Srideepika  Jayaraman,  Dhaval  Patel,  Anuradha  Bhamidipaty, and Carsten Eickhoff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  A transformer-based framework  for multivariate time series representation learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' In Proceedings of  the 27th ACM SIGKDD Conference on Knowledge Discovery & Data  Mining, pages 2114–2124, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [43] Tao Zhang and Wanzhong Chen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' LMD based features for the automatic  seizure detection of EEG signals using SVM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' IEEE Transactions on  Neural Systems and Rehabilitation Engineering, 25(8), 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [44] Xiang Zhang, Lina Yao, Manqing Dong, Zhe Liu, Yu Zhang, and Yong  Li.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Adversarial representation learning for robust patient-independent  epileptic seizure detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  IEEE Journal of Biomedical and Health  Informatics, 24(10):2852–2859, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [45] Wei Zhao, Wenbing Zhao, Wenfeng Wang, Xiaolu Jiang, Xiaodong  Zhang, Yonghong Peng, Baocan Zhang, and Guokai Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' A novel  deep neural network for robust detection of seizures using EEG signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  Computational and Mathematical Methods in Medicine, 2020, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content='  [46] Bingzhao Zhu and Mahsa Shoaran.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' Unsupervised domain adaptation for  cross-subject few-shot neurological symptom detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
+page_content=' In 2021 10th  International IEEE/EMBS Conference on Neural Engineering (NER),  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/oNE1T4oBgHgl3EQf1wUI/content/2301.03470v1.pdf'}
diff --git a/odAzT4oBgHgl3EQfOfsX/content/tmp_files/2301.01165v1.pdf.txt b/odAzT4oBgHgl3EQfOfsX/content/tmp_files/2301.01165v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..562d213cfecbde80536fd5c67bd2c897d8481f42
--- /dev/null
+++ b/odAzT4oBgHgl3EQfOfsX/content/tmp_files/2301.01165v1.pdf.txt
@@ -0,0 +1,9515 @@
+Noname manuscript No.
+(will be inserted by the editor)
+Herbig Stars
+A Quarter Century of Progress
+Sean D. Brittain · Inga Kamp · Gwendolyn Meeus · Ren´e D.
+Oudmaijer · L. B. F. M. Waters
+Received: date / Accepted: date
+Abstract Herbig Ae/Be stars are young contracting
+stars on the radiative track in the HR diagram on their
+way to the Main Sequence. These stars provide a valu-
+able link between high and low mass stars. Here we
+review the progress that has been made in our under-
+standing of these fascinating objects and their disks
+since the last major review on this topic published in
+1998. We begin with a general overview of these stars
+and their properties. We then discuss the accretion of
+circumstellar material onto these stars. Next we dis-
+cuss the dust and gas properties of the circumstellar
+S. Brittain
+Department of Physics and Astronomy, Clemson University,
+Clemson, SC, 29634-0978, USA
+Tel.: +1-864-633-8265
+E-mail: sbritt@clemson.edu
+I. Kamp
+Kapteyn Astronomical Institute, University of Groningen,
+Groningen, The Netherlands, Postal code
+G. Meeus
+Dpto. F´ısica Te´orica, Universidad Aut´onoma de Madrid,
+28049 Madrid, Spain
+Centro de Investigaci´on Avanzada en F´ısica Fundamental
+(CIAFF), Facultad de Ciencias, UAM, 28049 Madrid, Spain
+R. D. Oudmaijer
+School of Physics and Astronomy, University of Leeds, Leeds,
+LS2 9JT, UK
+L. B. F. M. Waters
+Institute for Mathematics, Astrophysics & Particle Physics,
+Department of Astrophysics, Radboud University, P.O. Box
+9010, NL-6500 GL Nijmegen, The Netherlands
+SRON Netherlands Institute for Space Research, Sorbon-
+nelaan 2, 3584, CA Utrecht, The Netherlands
+disk before exploring the evidence for planet formation
+in these disks. We conclude with a brief discussion of fu-
+ture prospects for deepening our understanding of these
+sources and propose a new working definition of Herbig
+Ae/Be stars.
+Keywords Herbig Ae/Be Stars · Star Formation ·
+Stellar Accretion Disks · Circumstellar dust · Circum-
+stellar gas · Protoplanetary Disks
+1 INTRODUCTION
+Understanding the formation and early evolution of stars
+and planetary systems is one of the key questions in
+astrophysics, closely linked to the origin of the solar
+system. Stars form in dense molecular clouds in which
+gravity overtakes gas pressure, resulting in the forma-
+tion of a core. Conservation of angular momentum causes
+the formation of an accretion disk through which gas
+and dust is transported to the accreting star. When the
+molecular cloud disperses (typically after 0.5-1 Myrs)
+the accretion slows down and a slower phase (typi-
+cally 5-15 Myrs) of pre-main-sequence evolution ensues,
+which ends when the star ignites hydrogen in its core
+(see Palla and Stahler, 1993, Lada, 2005, McKee and
+Ostriker, 2007, Li et al., 2014, for reviews).
+Planet formation takes place in the (remnant) ac-
+cretion disk; there is growing evidence that this pro-
+cess begins very early when accretion onto the star is
+still strong (ALMA Partnership et al., 2015, Segura-
+Cox et al., 2020, Kenyon et al., 2016, Tsukamoto et al.,
+2017). Most studies favor the core accretion growth
+model for the formation of gas giant exoplanets, in
+which dust in the disk settles to the mid-plane to form
+large, millimeter to centimeter sized grains, planetesi-
+mals, and a rocky core (e.g., Lissauer, 1993, Drazkowska
+arXiv:2301.01165v1  [astro-ph.SR]  3 Jan 2023
+
+2
+Sean D. Brittain et al.
+et al., 2022). When above a critical mass of 10-20 M⊕,
+the rapid accretion of a H/He envelope follows (e.g. Pol-
+lack et al. 1996). Planet formation may also proceed via
+gravitational instability in massive disks (Boss, 1997),
+explaining the presence of very massive planets in wide
+orbits found in some intermediate mass stars.
+This general scenario for star- and planet formation
+is believed to hold for solar type stars (0.3M⊙ ≲ M⋆ ≲
+1.5M⊙), and there is growing evidence that it also ap-
+plies to lower mass stars and brown dwarfs (M⋆ ≲
+0.3M⊙; Luhman, 2012). For higher mass stars, this is
+likely to break down for M⋆ ≳ 4−5M⊙ as disk lifetimes
+grow too short. Because the timescale for star formation
+decreases rapidly with increasing mass, high mass stars
+do not experience a visible pre-main-sequence phase.
+Their much higher luminosity strongly affects the phys-
+ical and chemical properties of the accretion disk (e.g.,
+Gorti et al., 2009). Models suggest a rapid evapora-
+tion of the outer disk and no reservoir of large dust
+grains is able to form, inhibiting the formation of plan-
+ets through core growth. However, planets may still
+form around massive young stars through gravitational
+instability. So far, observations indicate there is no evi-
+dence for close-in planets orbiting stars with mass above
+4-5 M⊙, while campaigns for planets at larger separa-
+tions are underway (Janson et al. 2021).
+The Herbig Ae/Be stars are intermediate mass ob-
+jects and as such bridge the gap between the lower mass,
+solar type stars (M⋆ ≲ 1.5 M⊙) and the most massive
+stars (M⋆ ≳ 10′s M⊙). They were first discussed as a
+group in the seminal paper of Herbig (1960). In this
+paper, George Herbig sought to identify more massive
+stars (aiming at 3-20 M⊙) by selecting a sample of 26
+A and B stars with emission lines in the spectrum (in
+particular Hα) that were associated with (reflection)
+nebulosity. These stars have since been studied in great
+detail and indeed many of them turned out to be inter-
+mediate mass pre-main-sequence (PMS) stars. In later
+literature, intermediate mass PMS stars were given his
+name Herbig Ae/Be stars. In the context of star forma-
+tion studies, these stars form the higher mass counter-
+parts to the solar mass T Tau stars, named after the
+prototype T Tau. Herbig also immediately noted the
+difficulty in disentangling these stars from other classes
+of B and A stars with circumstellar matter, such as the
+classical Be stars (Rivinius et al., 2013) and the B[e]
+stars (Kraus, 2019). Herbig continued to work on these
+objects throughout his career, as evidenced by his ex-
+tensive bibliography.
+Previous reviews dedicated to Herbig Ae/Be stars
+can be found in the conference proceedings Th´e et al.
+(1994b), and in Perez and Grady (1997) and Waters
+and Waelkens (1998a). In addition, there have been
+numerous reviews on disks around young stars that
+are relevant to Herbig Ae/Be stars. Examples include
+Dullemond and Monnier (2010), Williams and Cieza
+(2011), Andrews (2020). For recent reviews dedicated
+to aspects of Herbig Ae/Be stars please see the Topical
+Collection on Herbig Ae/Be stars published in 2015 in
+Astrophysics and Space Science1.
+In recent years a wealth of new observational and
+theoretical studies have shed light on the nature and
+evolutionary status of Herbig Ae/Be stars and their cir-
+cumstellar environment. As we will summarize in this
+review, Herbig Ae/Be stars are at an exciting cross-
+roads between low- and high-mass star formation. The
+high stellar luminosity, disk mass, and often large disks
+allow easier access to the relevant spatial scales to study
+planet formation processes when compared to lower
+mass objects. Indeed, the gas and dust in their cir-
+cumstellar disks has been spatially resolved with un-
+precedented detail, revealing Keplerian disks that show
+convincing evidence for the presence of forming plan-
+ets. As samples of known exoplanets rapidly increase,
+we can begin to make the link between the diversity
+of exoplanetary systems in intermediate mass stars and
+their birth sites. Herbig Ae/Be stars also mark the up-
+per mass limit of stars with habitable zones in which life
+on a planet could develop. The main sequence lifetime
+of 2.5M⊙ stars is ∼600Myr (Ekstr¨om et al., 2012) the
+lower bound for which life is thought to have evolved on
+Earth (Lopez et al., 2005, Danchi and Lopez, 2013). For
+more massive stars, the main sequence lifetime becomes
+prohibitively short.
+1.1 Definition of Herbig stars
+Evidence that the objects presented in Herbig (1960)
+were indeed intermediate mass PMS stars was provided
+by placing these stars on an HR diagram (Strom et al.,
+1972) and were consistent with stellar masses span-
+ning ∼ 2 − 15M⊙(see also Hillenbrand et al., 1992).
+Subsequent studies found emission above what is ex-
+pected from the stellar photosphere at wavelengths with
+λ ≳ 1µm (e.g., Cohen, 1973, 1980, Hillenbrand et al.,
+1992, Malfait et al., 1998), caused by a dusty enve-
+lope. Several papers presented criteria to observation-
+ally define the class of Herbig Ae/Be stars (e.g., Th´e
+et al., 1994a, Malfait et al., 1998, Waters and Waelkens,
+1998b, Vieira et al., 2003) leading to a general consensus
+that Herbig Ae/Be stars have a spectral type B, A, or
+F, H i emission lines, and an infrared excess. Most pa-
+pers identify the stellar mass range represented by such
+objects to range from ∼1.5 - 10M⊙. The lower mass
+1 https://link.springer.com/collections/hbggjficdi
+
+Herbig Stars
+3
+limit was set by the spectral type of the coolest star
+that was thought to reach the zero age main sequence
+(ZAMS) as an A9 star. The upper mass limit is set by
+the maximum mass a star is expected to experience a
+pre-main-sequence phase while it is not enshrouded in
+its protostellar envelope, however, this upper mass limit
+is not sharply defined as many stars typically included
+in catalogs of Herbig Ae/Be stars have higher masses
+(e.g., Vioque et al., 2018).
+In this review, we will refer to the Herbig Ae/Be
+stars as Herbig stars, and predominately limit ourselves
+to stars with the following properties: young A or B
+type stars that are evolving towards the main sequence,
+with Hα emission, often associated with a nebulosity,
+and an infrared (IR) excess due to warm (∼1000 K)
+and/or cold (∼100 K) circumstellar dust. Herbig stars
+in principle do not include objects cooler than about
+7000 K (i.e., stars with spectral types later than A9),
+but some F-type stars such as HD 142527, CQ Tau and
+HD 135344B have also been discussed in the literature
+in the context of Herbig star samples, because of their
+high luminosity and associated mass. We will include
+these in this review. Most if not all of these stars are not
+yet core-hydrogen burning PMS stars; however, for the
+most luminous objects in the sample this is not easy to
+establish. We do not consider the A and B stars with de-
+bris disks, that have lost their primordial gas and have
+secondary dust produced by collisions between larger
+bodies (Hughes et al., 2018). Nor do we discuss young
+PMS A and B stars that show no evidence for circum-
+stellar material any more (and would be the equivalent
+to the naked T Tauri stars; e.g., Walter 1986). Catalogs
+of (candidate) Herbig stars were published by Finken-
+zeller and Mundt (1984), Herbig and Bell (1988), Th´e
+et al. (1994a), Vieira et al. (2003), and more recently
+by Vioque et al. (2018). HArchiBe, an on-line archive
+of known Herbig Ae/Be stars and their properties is
+described in Guzm´an-D´ıaz et al. (2021) 2. From this
+catalog, we identify 31 Herbig stars (including spectral
+type F) within 225 pc and 87 Herbig stars within 450
+pc.
+1.2 Connection to Intermediate Mass T Tauri stars
+Late F, G, and K type intermediate mass PMS stars
+are classified as T Tauri stars. They are the evolution-
+ary predecessors of the Herbig stars. Since young inter-
+mediate mass stars evolve from the birth line towards
+the main sequence, they will have properties that clas-
+sify them as T Tauri stars when still cool and shift to
+earlier spectral types as their temperature increases as
+2 http://svo2.cab.inta-csic.es/projects/harchibe/main/
+they evolve along the radiative track on their way to the
+ZAMS (Figure 1). In fact, T Tau itself has been shown
+to be of intermediate mass (Duchˆene et al., 2006). Her-
+big and Bell (1988) defined a special group called “su”
+stars with properties similar to that of the intermediate
+mass T Tauri star SU Aur. Herbst et al. (1994) intro-
+duced the class of Early Type T Tau stars, that con-
+tains both T Tauri and Herbig stars. Calvet et al. (2004)
+used the term intermediate mass T Tauri (IMTT) stars,
+which has been adopted in subsequent literature to de-
+note the low temperature progenitors of the Herbig
+stars.
+In a recent study, Valeg˚ard et al. (2021) compiled a
+list of about 50 IMTT stars from the T Tau literature
+(i.e. stars classified as T Tau stars) and, based on Gaia
+DR2 distances (Gaia Collaboration et al., 2016, 2018)
+to these stars, derived basic properties such as tem-
+perature, luminosity, and IR excess. Stars with mass
+above 1.5 M⊙ were selected, based on their position
+in the HR diagram and using PMS evolutionary tracks.
+This study shows that the circumstellar environment of
+IMTT stars is qualitatively similar to that of the Her-
+big stars. A full view on how intermediate mass stars
+and their environment evolve from the birth line to-
+wards the main sequence ideally includes IMTT stars.
+We will return to this point in Section 7. In this review,
+we will not consider the IMTT stars any further.
+1.3 Link between low mass and high mass star
+formation
+Herbig stars can be found in low- and high mass star
+forming regions (e.g., Chamaeleon and Orion respec-
+tively). However, early type Herbig Be stars tend to be
+surrounded by a dense clustering of stars, while this is
+not the case for Herbig Ae stars (Hillenbrand et al.,
+1995, Testi et al., 1999). There is a smooth transition
+in clustering between these two ranges. This points to
+a qualitative difference in the mode of star formation
+that leads to massive (M⋆ ≳ 10 − 20 M⊙) and lower
+mass stars. Models for star formation also distinguish
+between two modes: isolated, low mass star formation
+in clouds of modest mass, and clustered, high mass star
+formation in giant molecular clouds (Motte et al., 2018).
+An important difference between these modes is that
+in high mass star forming regions massive stars, that
+evolve quickly, provide a strong feedback on their en-
+vironment. Their stellar winds and UV radiation fields
+are important already during the main accretion phase.
+Stars with mass above 8-10 M⊙ do not/are not expected
+to go through a visible PMS phase; although, this has
+not yet been revisited incorporating the latest insights
+
+4
+Sean D. Brittain et al.
+Fig. 1
+HR diagram containing 218 Herbig stars with high quality DR2 Gaia parallaxes (adapted from Vioque et al. (2018),
+their Figure 2). The solid lines represent PMS tracks (Bressan et al., 2012), with the final masses indicated on the Main
+Sequence. The dashed lines represent isochrones taken from Marigo et al. (2017). The Zero Age Main Sequence is the region
+marked by the end of the PMS tracks.
+Figure kindly provided by M. Vioque.
+relating to the modelling of the spectral energy distri-
+bution (SED) of Herbig stars. Radiation pressure on
+dust grains for instance inhibits the formation of very
+massive stars via the core accretion model (Wolfire and
+Cassinelli, 1987), although non-spherical accretion can
+circumvent this difficulty (Yorke and Sonnhalter, 2002).
+Feedback is believed to become relevant for masses above
+10-20 M⊙ (e.g., Hosokawa and Omukai, 2009).
+Observations and models suggest that the core ac-
+cretion model for star formation, developed for low mass
+stars, is also applicable to more massive stars, up to
+masses of 10-20 M⊙. Young massive YSOs in M17 have
+been found to have disks with properties consistent with
+a remnant accretion disk (e.g. Hoffmeister et al. 2008,
+Ochsendorf et al. 2011, Ilee et al. 2013). Beyond a mass
+of about 20 M⊙, it is unclear which mechanism dom-
+inates: core accretion and competitive accretion (Bon-
+nell et al., 2001) have been suggested (Krumholz and
+Bonnell, 2009).
+Intermediate mass stars are at the crossroads be-
+tween low- and high mass star formation. As stellar
+mass and luminosity increase, the shortening stellar
+evolutionary timescales, the increased strength of the
+stellar UV radiation field, and the denser cluster envi-
+ronment that occurs for more massive stars will strongly
+influence the physical and chemical properties of Herbig
+star disks and the way they dissipate. Therefore these
+disks are of interest to understand how stellar mass af-
+fects the early evolution of stars and planetary systems.
+This is one of the main motivations to study young in-
+termediate mass stars.
+In the quarter century since the last major review of
+Herbig stars (Waters and Waelkens, 1998b), there has
+been enormous progress in our understanding of these
+systems. Here we review this progress. First we discuss
+the stellar properties of Herbig stars - namely their mul-
+tiplicity fraction, X-ray properties, and variability (Sec.
+2). We then move to the star-disk interface and discuss
+the stellar accretion properties of these stars (Sec. 3).
+Moving further out, we discuss the dust (Sec. 4) and gas
+(Sec. 5) properties of the disks orbiting Herbig stars.
+We then discuss the advances in our understanding of
+planet formation in these disks (Sec. 6) and conclude
+with summary of key future lines of investigations that
+arise from the topics we cover in the review (Sec. 7) and
+a modest proposal for a new definition of Herbig stars
+(Sec. 8).
+
+6
+5 
+4
+5
+log(L) [Lo]
+3
+2
+1
+0 
+Herbig stars
+4.8
+4.6
+4.4
+4.2
+4.0
+3.8
+3.6
+log(Teff) [K]Herbig Stars
+5
+2 STELLAR PROPERTIES
+Over the past quarter century, millimeter (mm) inter-
+ferometry of gas emission from disks around young stars
+have enabled the measurement of dynamical masses of
+young stars (Simon et al., 2000, Schaefer et al., 2009,
+Guilloteau et al., 2014, Simon et al., 2017, Braun et al.,
+2021, Law et al., 2022). The spatial resolution and sensi-
+tivity provided by the Atacama Large Millimeter Array
+(ALMA) has opened the door to measuring ever larger
+samples of dynamical masses that provide a valuable
+measure for testing stellar evolution models and thus
+the ages and masses inferred from them. Braun et al.
+(2021) compiles the largest such sample to date and
+finds that stars with masses of stars ranging from 1.3-
+3.0M⊙ inferred from stellar evolution models predict
+masses ranging from -5% to -14% of the mass inferred
+dynamically.
+It may be useful to see the Herbig stars in the con-
+text of their position in the HR diagram. Vioque et al.
+(2018) placed the 218 then known and proposed Herbig
+stars with high quality Gaia DR2 parallaxes (Gaia Col-
+laboration et al., 2018) in the HR diagram, a version
+of which is reproduced in Figure 1. To guide the eye,
+several evolutionary tracks and isochrones are overplot-
+ted. As expected, most Herbig objects fall at or above
+the ZAMS indicating that intermediate stars cease ac-
+creting prior to or just after reaching the ZAMS. The
+more massive Herbig Be stars are sparser than the Her-
+big Ae stars which can be explained by the Initial Mass
+Function, as well as the shorter evolutionary time scales
+that are associated with their evolution towards the
+Main Sequence. Higher mass Herbig stars are invariably
+younger than their lower mass counterparts (Figure 2).
+The ages of the lower mass Herbig stars typically range
+from several millions of years up to 10 Myr. The latter
+high values have implications for the disks, their evo-
+lution and survival which will be discussed after the
+overview of the stellar properties. We will proceed with
+the binary properties of the objects in the following
+sub-section.
+2.1 Binaries among Herbig stars
+The multiplicity of Herbig stars bears on models of their
+formation, the origin of X-ray emission observed toward
+Herbig stars (cf. Sec. 2.2), and can affect the appear-
+ance of the disk (cf. Sec 4.9). Herbig stars are predom-
+inately found in binary systems, and many of these are
+found at arcsecond scales. However, not all separations
+have been equally well sampled (Duchˆene 2015). The
+last dedicated binary studies using large samples are
+the spectro-astrometric surveys of Baines et al. (2006)
+and Wheelwright et al. (2010) who observed 31 and 45
+objects respectively, totalling 62 unique targets. The
+separations probed were in the 0.1 − 2′′ range while a
+flux difference of 6 magnitudes could be reached. Their
+data were tested against the (slightly less deep) survey
+AO data of Leinert et al. (1997) and imaging of Pirzkal
+et al. (1997), and found to be in agreement where there
+was overlap.
+Both studies yielded a multiplicity of order 70% for
+this parameter range, with a hint that the Herbig Be
+stars are more likely to be found in binaries. Wheel-
+wright et al. (2010) could disentangle the spectra of
+some of the otherwise unresolved binaries and deter-
+mined that the mass ratios are close to one. This value is
+inconsistent with a random sampling of the IMF, which
+would be expected if stellar capture was the main bi-
+nary formation mechanism. The same team reported in
+Wheelwright et al. (2011) that the alignment between
+the binary objects and the disks surrounding the pri-
+maries was consistent with disk fragmentation. Similar
+conclusions on fragmentation being the cause of Herbig
+binaries were put forward by Arun et al. (2021) who
+reported the discovery of a wide (6.6′′) Herbig Ae - M
+star binary. Given the wide separation, fragmentation
+at an earlier stage was favored.
+The surveys with the Very Large Telescope Inter-
+ferometer (VLTI) of Lazareff et al. (2017, H-band, 51
+objects) and Gravity Collaboration et al. (2019, K band,
+27 objects) probed smaller separations and similar con-
+trasts to the above studies. These studies report few
+detections of binary companions. However, the surveys
+were designed to study disks, so the targets were se-
+lected against the presence of radial velocity binaries.
+Milli-arcsecond Herbig Be binaries, corresponding to
+sub-500 au separations, have been observed using VLTI
+data however (Kraus et al., 2017, Koumpia et al., 2019).
+Finally, the smallest separations can be probed us-
+ing spectroscopy, where a binary system can be revealed
+through radial velocity variations or directly in a dou-
+ble lined binary. Not much work has been done in this
+field, with the spectroscopic survey by Corporon and
+Lagrange (1999) of 42 Herbig stars still the largest ded-
+icated such study. The latter category includes spatially
+resolved objects with known separations of order 0.5′′,
+so the observed close binary fraction based on radial
+velocity variations alone is 17%.
+Summary: The majority of Herbig stars are in binaries
+(≳ 70%). The mass ratios of the binary Herbig stars in-
+dicates that the binaries form from disk fragmentation.
+Given that many of these are unresolved at arcsecond
+resolution, this also has important implications for in-
+
+6
+Sean D. Brittain et al.
+Fig. 2 The distribution of ages of the 218 Herbig stars as
+determined from the position in Figure 1 (Vioque et al. 2018).
+The highest mass stars have the smallest ages. Most Herbig
+Ae stars, and thus their disks, have ages in excess of several
+Myr. Figure kindly provided by M. Vioque.
+Properties
+O-early B
+Herbig
+T Tauri
+Plasma T
+< 12 MK
+12-60MK
+5-30 MK
+kT
+< 1 keV
+1-5 keV
+0.4-2.6keV
+logLX (erg/s)
+29-33
+29-31.5
+28-30
+log(LX/Lbol)
+-7
+[-6,-4]
+up to -3
+Origin
+radiative
+companion?
+αω dynamo
+wind
+shear dynamo?
+Detection rate
+65%
+35%
+100%
+Table 1 Typical properties for the X-ray emission of MS
+OB-type, Herbig and T Tauri stars
+terpreting the X-ray properties of Herbig stars – the
+topic of our next section.
+2.2 X-ray emission
+The more massive young objects, with spectral types
+O to B1, are often detected in X-rays. Their emission
+is soft (kT < 1 keV) with fractional luminosities, log
+(LX/Lbol) ∼ -7, attributed to shocks that originate in
+line-driven winds. At the other end of the mass distribu-
+tion, solar-mass T Tauri stars have a magnetic dynamo
+that can persist due to their convective motion, giving
+rise to hard X-ray emission (0.4 ≲ kT ≲ 3 keV) from
+the magnetically heated corona, and log (LX/Lbol) sat-
+urating around -3 (see Table 1). Herbig stars, on the
+other hand, are thought to be fully radiative so that
+they cannot support a dynamo by convection, nor are
+they hot enough for a radiation driven wind; therefore,
+the detection of X-ray emission from Herbig stars was
+unexpected (Zinnecker and Preibisch, 1994, Damiani
+et al., 1994). If the stars are indeed fully radiative, this
+would suggest that Herbigs should not generate strong
+well-ordered magnetic fields as observed in their cooler,
+convective counterparts. However, some do have strong
+magnetic fields (cf., Sect. 3.1).
+Hamaguchi et al. (2005) detected 30% of the Herbig
+stars observed with the Advanced Satellite for Cosmol-
+ogy and Astrophysics (ASCA), and determined an X-
+ray luminosity higher than for T Tauri stars (Table 1).
+The fractional X-ray luminosity is slightly lower than
+that of TTS, but higher than for MS B-type stars: log
+(LX/Lbol) = [-6,-4]. They found no evidence for a cor-
+relation between v sin i (an indication of rotational ve-
+locity) and X-ray luminosity, unlike what is observed in
+TTS where a strong correlation was found, supporting
+the αω dynamo scenario (Pallavicini et al., 1981).
+The plasma temperatures of Herbig stars are be-
+tween 1 and 5 keV which is too high to be produced in
+wind-driven shocks (Hamaguchi et al., 2005). Also flares
+were observed, which also cannot be explained by stellar
+winds. Since Herbig stars evolve from fully convective
+IMTT stars, some of these may possess a fossil magnetic
+field (see section 3.1). Activity parameters such as Hα
+and radio emission do not correlate with LX, but the
+amplitude of optical variability, ∆V, does (Stelzer et al.,
+2006). Also, magnetospheric accretion can be ruled out
+as the origin of the X-ray emission because the free-fall
+velocities are too low. Hamaguchi et al. (2005) propose
+that the X-ray emission stems from magnetic activity,
+where the fossil magnetic fields of the stars reconnect
+with the disk (a star-disk magnetosphere).
+With the better spatial resolution of Chandra (∼1′′),
+Stelzer et al. (2006) observed 17 Herbig stars to study
+the companion hypothesis. They detected X-ray emis-
+sion from 76% of their sample. After correcting for the
+presence of known lower-mass companions, they derived
+an occurrence rate of 35% which was consistent with
+previous work by Hamaguchi et al. (2005). Interestingly,
+the detection rate of X-rays from Herbig stars is com-
+parable to the binary rate of Herbig stars (see section
+2.1). Further study of the binarity of X-ray emitting
+Herbig stars will clarify the extent to which unresolved
+companions can account for the X-ray emission.
+In a follow-up paper, Stelzer et al. (2009) distin-
+guishes between late B to A-type Herbig stars and early
+B-type PMS stars. They propose that the early B-type
+PMS stars behave like the B-type MS stars, while the
+X-ray emission in the later-type Herbig stars is con-
+nected to magnetic fields, which have only been firmly
+detected in ∼ 20 Herbig stars (e.g. J¨arvinen et al. 2019,
+3.1).
+Summary: The origin of the X-ray emission detected
+towards Herbig stars remains an unsolved mystery. An
+origin in a stellar wind can be excluded due to the high
+
+45
+M>10 Mo
+40
+5<M<10 Mo
+35
+0<M<5 Mo
+Number of sources
+30
+25
+20
+15
+10
+5
+0
+10
+10
+10
+10
+Age [Myr]Herbig Stars
+7
+plasma temperatures observed. It is possible that the
+X-rays could come from an unseen companion or by
+remnant magnetic fields. A dedicated study including
+precise magnetic field measurements, high spatial res-
+olution X-ray observations, and sensitive searches for
+companions for a large sample of Herbig stars is needed
+to test these hypotheses.
+2.3 Variability
+Herbig stars have long been known to show both photo-
+metric and spectroscopic variations. The variability can
+be traced back to changes in the circumstellar disks, the
+accretion regions, and the structure of the stars them-
+selves. We discuss the photometric and spectroscopic
+behaviours separately below.
+2.3.1 Photometric variability
+Some Herbig stars show non-periodic brightness vari-
+ations as large as ∆V ∼ 3 mag (Herbst et al., 1994).
+Important clues about the nature of the variations and
+the (inner) disk regions came from studying the bright-
+ness variations of the star UX Ori: when the star fades
+in brightness, its color becomes redder. However, when
+fading even more, this color change turns around, and
+the star becomes bluer, the so-called ‘blueing effect’
+(Bibo and The, 1990). In tandem with the fading of
+the star, its radiation was found to become more po-
+larized, hinting at starlight being scattered off circum-
+stellar dust. These effects, referred to as the UXor phe-
+nomenon in later literature, were further studied with
+simultaneous photometric, polarimetric and spectroscopic
+observations (Grinin, 1992, Grinin et al., 1994), sup-
+porting the hypothesis that the blueing effect is caused
+by an opaque dust cloud in the disk, intersecting in the
+line of sight towards the star. In Sect. 4.9.3 we focus on
+the properties of the inner disks that were revealed by
+the UXor phenomenon.
+In the near infrared (NIR), the variability of Her-
+big stars is far more modest than in the optical. Eiroa
+et al. (2002) observed a sample of T Tauri and Her-
+big Ae stars using quasi-simultaneous optical and near-
+infrared photometric observations, taken typically less
+than 1 hour and at most 2 hours apart. The peak-
+to-peak variations at optical wavelengths could be as
+high as 0.5 magnitudes during their period of observa-
+tions, while the NIR photometry varied mostly at the
+0.1 magnitude level. Out of the 12 Herbig Ae objects
+observed, only 3 were reported as non-variable, while
+8 of the remaining nine showed a correlation between
+the optical and NIR photometric variations. Given that
+the NIR emission is most likely re-radiated by the hot
+circumstellar dust that absorbed the optical light, the
+location of the near-infrared variability can be traced
+to the inner circumstellar disks (see also Sect. 4.9.3).
+The remaining one object, UX Ori, did not show a cor-
+relation between the photometric variations, which was
+interpreted as possibly being due to rotational modu-
+lation of star spots on the stellar photosphere. Vioque
+et al. (2018) later determined that roughly 25% of Her-
+big stars can be classified as having such UXor varia-
+tions, while Herbig Be stars are markedly less variable
+than the Herbig Ae stars.
+Finally, variability at milli-magnitude amplitudes
+has been positively detected towards a small sample
+of Herbig Ae stars (Zwintz et al. (2014); see also the
+compilation by Steindl et al. 2021). Such observations
+are challenging as any signatures at the milli-magnitude
+level not only require space-based photometry (Zwintz
+et al., 2009, Casey et al., 2013) but need a careful disen-
+tangling of such data with the non-periodic variations
+described above. The Herbig Ae stars appear to show δ
+Scuti type variability (Marconi and Ripepi, 2017). This
+variability arises among stars whose temperature and
+mass lead to an ionization structure that leads to ra-
+dial oscillations resulting in variability with a period on
+the order of a few hours. Such stars fall in a well de-
+fined region of the HR diagram known as the instability
+strip. Herbig stars in this region are no exception. The
+milli-magnitude photometric data have the prospect of
+probing into these pre-Main Sequence stars using as-
+teroseismology. An interesting example is the case of
+HD 139614, whose age was estimated from asteroseis-
+mology to be about 11 Myrs (Murphy et al., 2021). This
+old age confirms the results of other studies, and shows
+that gas-rich disks can survive for a substantial period
+of time. We will return to this in Sect. 5.1.
+2.3.2 Spectroscopic variability
+In addition to photometric variability, the emission lines
+observed towards Herbig stars have long been known to
+vary (for a review, see Catala 1994). Spectroscopic vari-
+ability studies of individual objects have revealed vari-
+ations in the emission lines and their profiles which can
+be traced back to rotational modulation of the accretion
+regions (Garcia Lopez et al., 2016, Sch¨oller et al., 2016).
+It would appear that the variations are less extreme
+than those observed for T Tauri stars whose variations
+are connected to the magnetically controlled accretion
+(Kurosawa et al., 2011).
+Dedicated studies of larger samples of Herbig ob-
+jects have been sparse. Costigan et al. (2014) investi-
+gated the Hα line variability for a sample of, mostly,
+Herbig Ae and T Tauri stars. The amplitude of the
+
+8
+Sean D. Brittain et al.
+variability increases from minute timescales to level off
+at the days-weeks timescales, even over periods as long
+as years. This indicates that the variability occurs in a
+small volume around the star and Costigan et al. (2014)
+attribute the variability mainly to changes in the accre-
+tion rate. Overall, it would appear that the variability
+of the emission lines is connected to the accretion pro-
+cesses occurring in Herbig stars, the topic of the next
+section.
+Lastly, another type of spectral variability has been
+observed towards Herbig stars which was first found
+towards β Pic. Multi-epoch spectroscopy revealed that
+metallic absorption lines would change on timescales
+of hours to months. In particular, lines could suddenly
+appear in absorption and the absorption itself would
+become more red-shifted in matters of hours. This be-
+haviour was interpreted as evidence of infalling material
+from cometary bodies (Ferlet et al., 1987). Grady et al.
+(1996) presented spectra of 41 Herbig stars and found
+that 22 of them showed variability consistent with the
+presence of gas released from infall of evaporative bod-
+ies. We will return to this issue in Sec. 6.2.2, where this
+phenomenom is discussed as an indirect tracer for the
+presence of planets in the disks of Herbig stars.
+Summary: Herbig stars display photometric and spec-
+troscopic changes on timescales ranging from hours to
+months and longer. The larger amplitude photometric
+changes can be traced back to variable dust obscura-
+tion from an orbiting disk, while variability at smaller,
+milli-magnitude, amplitudes can be analysed with as-
+teroseismology. Spectroscopically, variable line emission
+is mostly associated with the accretion process, while
+variable absorption lines can be due to changes in the
+accretion process itself, but can also be caused by in-
+falling rocky material such as exo-comets.
+3 ACCRETION ONTO HERBIG STARS
+In this section we discuss the accretion and accretion
+mechanisms of Herbig stars. Given that the intermedi-
+ate mass Herbig stars are, for all intents and purposes,
+the high mass counterpart of the solar mass T Tauri
+stars, let us begin with a description of the paradigm
+for understanding accretion onto T Tauri stars. Dedi-
+cated reviews of these objects can be found in Bertout
+(1989) and Bouvier et al. (2007), recent reviews on the
+accretion process in pre-Main Sequence stars in general
+can be found in Beltr´an and de Wit (2016), Hartmann
+et al. (2016) respectively, while Mendigut´ıa (2020) fo-
+cuses on accretion onto Herbig stars.
+T Tauri stars are well known to sustain a magnetic
+field due to their internal dynamo and exhibit both evi-
+dence for accretion onto the stars and bi-polar outflows
+powered by the accretion. The accretion itself is mag-
+netically mediated. The stellar magnetic field truncates
+the disk where the ram pressure from accretion balances
+the opposing pressure from the stellar magnetic field.
+Material from the disk free-falls along the magnetic field
+lines through accretion funnels onto the star. With typ-
+ical disk-truncation radii of 2-3 stellar radii, the free-fall
+velocities are very high, of order 100s km s−1. The grav-
+itation potential energy of the material released when
+it crashes onto the photosphere is therefore substan-
+tial. The resulting shock produces X-ray radiation that
+is absorbed by surrounding particles. Then, these par-
+ticles heat up and re-radiate at ultraviolet wavelengths,
+producing a UV-excess that can be observed. A cartoon
+of the situation is provided in Fig. 3 (see e.g. Bouvier
+et al. 2007 for more details).
+The relatively cool T Tauri stars radiate most of
+their photospheric energy at optical and longer wave-
+lengths, so the observed UV emission can be used as
+a proxy for the accretion luminosity, which reflects the
+potential energy released by the infalling matter. As-
+suming the material is falling from infinity, the mass
+accretion rate is given by,
+˙Macc = LaccR∗
+GM∗
+,
+(1)
+where Lacc is the accretion luminosity, R∗ is the stellar
+radius, M∗ is the stellar mass, and G is the gravitational
+constant.
+It may be clear that a proper characterisation of
+the stellar parameters is important. As will be discussed
+later, the Gaia satellite, which provides parallaxes, from
+which distances are determined, for more than a billion
+stars has had an important impact on the field.
+The magnetospheric accretion (MA) paradigm has
+been applied extensively over the past years to deter-
+mine the accretion rates of Herbig stars. In the follow-
+ing we give not only an overview of the results, but also
+critically analyse the assumptions made in this endeav-
+our. We will demonstrate that while the MA paradigm
+seems to be applicable to most Herbig stars, there is
+compelling evidence that it cannot act for some extreme
+cases, and that there is strong evidence for a change in
+accretion mechanism at higher masses.
+3.1 Magnetic properties of Herbig stars
+Let us first discuss an immediate potential critique that
+can be fielded against the use of the MA paradigm to
+Herbig stars. Conventional wisdom is that no magnetic
+
+Herbig Stars
+9
+Fig. 3 Cartoon of the immediate circumstellar environment of a HAe star. Initially designed to illustrate the magnetospheric
+accretion paradigm for CTTSs, this cartoon also applies to HAe stars. The dust in the disk is sublimated when it reaches a
+temperature of ∼1500 K. Interior to this region the disk is gaseous and heavily ionized. The disk is truncated by the magnetic
+field where the pressure from accreting gas is balanced by magnetic pressure. The accreting gas then falls into the star along
+field lines from which hydrogen recombination emission emerges and creates an accretion shock near the surface of the star.
+Figure based on Gravity Collaboration et al. (2020).
+field is expected to be generated in Herbig stars be-
+cause the envelopes of A and B stars are radiative. The
+B-field is typically generated in a dynamo which usu-
+ally occurs by convection in cooler stars. Indeed, mag-
+netic fields have only fairly recently been detected to-
+wards a limited number of objects (e.g., Alecian et al.,
+2013). Based on the compilation of Hubrig et al. (2015),
+Mendigut´ıa (2020) presents all reported magnetic field
+detections of Herbig stars and their stellar parameters.
+The list contains a total of 18 objects with measured
+B-fields, which constitutes roughly 10% of all known
+and proposed Herbig stars (viz. Vioque et al. 2018).
+Intriguingly, this fraction is similar to a 10% detection
+rate in field A stars (Landstreet, 1992). Most of these B-
+fields have strengths of order 100 G, while a few Herbig
+stars have magnetic field strengths that are significantly
+higher (e.g., V380 Ori (2kG), and Z CMa (1.2 kG)). As
+already alluded to in Sec. 2.2, rather than being gener-
+ated, the magnetic field in these magnetic objects could
+be fossil in nature, either from the original collapsing
+parental cloud or the remnant field of an earlier IMTT
+star phase.
+Whatever the cause of the magnetic fields, it should
+be noted that most B-field determinations concern the
+global integrated magnetic field, a non-detection is there-
+fore not necessarily evidence for the absence of it; a
+complex geometry would inevitably result in a lower
+observed strength. Villebrun et al. (2019) mapped the
+B-fields of the IMTT stars, and find that the fields be-
+come weaker, but also more complex and at higher tem-
+peratures (see also Fig. 4). The possibility that higher
+temperature pre-Main Sequence stars harbour strong
+magnetic fields is therefore a realistic prospect. As a
+consequence, the MA scenario which is well established
+for T Tauri stars (e.g. Bouvier et al. 2007), may also be
+applicable to hotter objects.
+In the next section, we will go into more detail on
+similarities between T Tauri stars and Herbig objects
+with emphasis on their accretion properties. We then
+consider the determination of the accretion rates of Her-
+big stars and provide global inferences resulting from
+these.
+Summary: About 10% of Herbig stars have measur-
+able magnetic fields. While most of these are of order
+100 G, a few have magnetic field strengths about an or-
+der of magnitude larger. These B-field determinations
+are measurements of the global integrated field. If the
+magnetic fields of Herbigs tend to have a complex ge-
+ometry, it is possible that the surface magnetic field
+strength of the typical Herbig star is much higher than
+these measurements suggest.
+3.2 Accretion Geometry - similarity with T Tauri stars
+The earliest investigation into MA onto Herbig stars
+was carried out by Muzerolle et al. (2004). They ap-
+plied their MA models to the Herbig Ae star UX Ori,
+
+Brackett 
+emission
+inner
+gas disk
+accreting
+material
+truncation
+accretionshock
+radius
+magnetic field lines
+dust sublimation radius10
+Sean D. Brittain et al.
+and found that the computed emission line profiles were
+in qualitative agreement with the observed emission line
+profiles. In parallel, they also concluded that the mag-
+netic field strength would be weaker and its geometry
+should be more complex than the usual dipole field in
+T Tauri stars, just as was later shown to be the case
+by Villebrun et al. (2019). Further supporting evidence
+that Herbig Ae stars may be accreting in a similar fash-
+ion as T Tauri stars comes from various observational
+studies. These often stem from comparative investiga-
+tions into the accretion-related properties of T Tauri
+stars on the one hand and Herbig Ae and Herbig Be
+stars on the other hand. An additional result from these
+studies is that Herbig Be stars often have very different
+properties than their Ae counterparts.
+Early suggestions that the accretion processes of
+Herbig Ae stars and T Tauri stars are similar were re-
+ported based on results from linear spectropolarime-
+try. Although the accretion funnels are still too small
+to be directly imaged, indirect linear spectropolarimet-
+ric methods are able to probe these regions at scales
+of order stellar radii (e.g. Vink, 2015, Ababakr et al.,
+2016, 2017). The similarity of the linear spectropolar-
+metric properties of the Hα line for Herbig Ae stars
+and T Tauri stars was reported by Vink et al. (2002,
+2005a). The observations were explained with line emis-
+sion from accretion hot spots scattering off truncated
+disks. Indeed, the inferred sizes of order stellar radii of
+the inner holes (Vink et al., 2005b) are consistent with
+those expected for a magnetically truncated disk. In
+contrast, the very different effects observed towards the
+Herbig Be stars are more consistent with disks reaching
+onto the central star - hinting at a different accretion
+mechanism in those. Ababakr et al. (2017) presented
+the largest sample of Herbig stars observed with lin-
+ear spectropolarimetry around Hα, which allowed them
+to identify the transition from truncated disks to disks
+reaching into the stellar surface around spectral type
+B7/8.
+Other studies related to accretion diagnostics are
+broadly consistent with these findings. Cauley and Johns-
+Krull (2014) studied the He i 1.083 µm line profiles of
+a large sample of Herbig stars. Due to its high excita-
+tion energy, this transition is particularly sensitive to
+accretion. These authors found that both T Tauri stars
+(observed by Edwards et al., 2006) and Herbig Ae stars
+had similar line profiles and comparable fractions of
+red-shifted absorption lines, tracing infall, all of which
+could be explained in the context of MA, while the Her-
+big Be stars did not. Furthermore, they inferred that
+the Herbig Ae stars could have smaller magnetospheres
+than their T Tauri counterparts.
+As mentioned earlier, Herbig stars display spectro-
+scopic variability. Costigan et al. (2014) found that both
+the timescales and amplitude of the variability were
+similar for T Tauri and Herbig Ae stars, which led these
+authors to suggest that the mode of accretion of Her-
+big Ae stars is also similar to that of T Tauri stars.
+Although less extensive in time coverage, the Hα vari-
+ability study of Mendigut´ıa et al. (2011b) extends to
+the more massive Herbig Be stars. These objects were
+found to have different Hα variability properties than
+the Herbig Ae stars. Of note is that these authors not
+only considered the Hα line strength variations, but
+also those of the line width, which, given the high free-
+fall velocities involved may be more effective in tracing
+the accretion flows. Its variability was found to be con-
+siderably smaller for the Herbig Be stars than for the
+Herbig Ae stars, which, in turn, is smaller than for T
+Tauri stars (Fang et al., 2013).
+Kreplin et al. (2018) find from modelling their high
+resolution infrared spectro-interferometry, that the in-
+ner radii of the disk-winds are consistent with the Alfv´en
+radii computed using the low B-field strengths observed
+for a few Herbig Ae stars. Guimar˜aes et al. (2006) ob-
+served 15 Herbig Ae stars (some with spectral type
+B9Ve) and found four that showed red-shifted absorp-
+tion in the Balmer lines. The authors demonstrated
+that this absorption can be qualitatively explained with
+magnetospheric accretion if the disk were truncated rel-
+atively close to the star.
+Detailed studies on individual targets have reached
+similar conclusions as above. Grady et al. (2010) found
+the location of the accretion footprint on a Herbig Ae
+star to be very like those on T Tauri stars. The in-
+depth spectroscopic variability study of a Herbig Ae
+star showed it is undergoing magnetospheric accretion
+in the same manner as classical T Tauri stars (Sch¨oller
+et al., 2016). From their modelling of spectra, Moura
+et al. (2020) find evidence that Herbig Ae stars undergo
+MA, while they do not find this to be the case for a
+Herbig Be star. On the hotter side, Patel et al. (2017)
+model the inner gaseous disks of several Herbig Be stars,
+and find they do not need magnetospheres to reproduce
+the emission line spectra.
+Summary: It has been empirically shown that Herbig
+Ae stars exhibit many similar accretion-related char-
+acteristics as T Tauri stars. This provides indirect ev-
+idence for magnetically controlled accretion operating
+for these objects as well. In turn, it validates the use
+of MA shock modelling to derive accretion rates for at
+least the later-type Herbig stars.
+
+Herbig Stars
+11
+2 M¤
+0.5 M¤
+4 M¤
+1 Myr
+10 Myr
+-5 Myr
+Fig. 4 The B-fields of T Tauri stars and Herbig Ae stars according to Villebrun et al. (2019). The black and gray symbols are
+stars with non-detections, while the red and blue symbols represent objects with detections with symbol sizes proportional to
+the B-field strengths. The orange zone indicates the area where stars are fully convective, the blue zone where they are fully
+radiative, while the other colors represent a mix; green (radiative core and convective envelope); pink (convective core and
+radiative envelope). The various evolutionary tracks (black lines) and isochrones (white lines) are from Behrend and Maeder
+(2001). Figure kindly provided by E. Alecian.
+3.3 Measurement of mass accretion rates
+Let us now turn to the determination of the accretion
+rates of Herbig stars using the MA paradigm. As a word
+of caution, we stress that it is used for all Herbig stars,
+regardless of their spectral type. However, as will be
+discussed later, this approach serves as an additional
+means to identify where a change in accretion properties
+may be present.
+3.3.1 Direct determination of the accretion luminosity
+As can be seen from Eq.1, once we know the stellar mass
+and radius, the mass accretion rate can be derived from
+the accretion luminosity. For the cool T Tauri stars, this
+emission is most readily identified by UV-excess emis-
+sion over and above the stars’ photospheric radiation.
+In addition, it can also be seen at optical wavelengths,
+where the excess emission due to accretion fills in the
+underlying absorption lines. In the absence of UV obser-
+vations, a value for the excess emission can be obtained
+by determining the extent of this “veiling”.
+In contrast to the T Tauri stars, the determination
+of the contribution of the accretion shock to the to-
+tal blue/UV emission is less straightforward for Herbig
+objects. By virtue of their higher temperatures, these
+stars are more luminous at UV wavelengths. Thus the
+contrast between the accretion shock and the photo-
+
+12
+Sean D. Brittain et al.
+Normalized Flux
+Wavelength (Å)
+Fig. 5 Figure from Donehew and Brittain (2011). The spec-
+trum of V350 Ori (black line) is compared to a template
+of a non-accreting A star (red line). While there is a good
+match between V350 Ori and the template long-ward of
+3800˚A V350 Ori is brighter than the template at shorter
+wavelengths. This excess Balmer continuum radiation is due
+to the accretion shock over and above that of a normal star
+with the same spectral type.
+sphere at UV wavelengths is much smaller for Herbigs
+than for CTTSs. Because of this smaller contrast, dis-
+entangling the contributions from the stellar and ac-
+cretion properties to the UV emission is challenging.
+Veiling measurements also prove problematic. The ac-
+cretion luminosity can exceed the stellar luminosity of
+T Tauri stars, allowing a comparatively straightforward
+determination of the veiling. However Herbig stars are
+brighter and the photosphere dominates the light out-
+put at optical wavelengths hampering the identification
+and measurement of the veiling. Despite these chal-
+lenges and the rather labor-intensive methodologies of
+determining the UV-excess in these objects, the num-
+ber of Herbig stars with directly determined accretion
+luminosities is surprisingly large; Donehew and Brit-
+tain (2011, 33 objects) and Fairlamb et al. (2015, 91
+stars) obtained blue spectra for Herbig stars and de-
+termined the accretion luminosities for most targets by
+carefully comparing their Balmer continuum (excess)
+emission with spectra of standard stars (see Fig. 5).
+Mendigut´ıa et al. (2011a, 38 objects) used broadband
+UBV photometry to determine the Balmer excess emis-
+sion and accretion luminosity. One advantage of using
+the Balmer continuum emission to measure the accre-
+tion luminosity is that this property is minimally af-
+fected by reddening (Garrison, 1978, Muzerolle et al.,
+2004).
+The lowest accretion luminosities that could be mea-
+sured are of order 1 L⊙ and the corresponding accre-
+tion rates are of order 10−8 M⊙yr−1. The lower limits
+are due to the sensitivity of the observations and the
+ability to determine the excess emission. This sensitiv-
+ity descreases for the higher temperature objects. It is
+interesting to see that more than 70% of all the Her-
+big stars investigated in this manner exhibit Balmer
+continuum excess emission. As it is non-trivial to find
+alternative explanations for this excess, this observa-
+tion constitutes independent supporting evidence that
+these objects are accreting matter.
+3.3.2 Indirect determinations of accretion luminosity
+It turns out that it is not strictly necessary to obtain
+dedicated UV or Balmer continuum observations to ar-
+rive at estimates of the accretion rates. A correlation
+between the brightness of emission lines and the accre-
+tion luminosity exists for IMTT stars (Calvet et al.,
+2004). Indeed, by using (ideally) simultaneous UV and
+line observations, this correlation can be used to cali-
+brate the line luminosity to arrive at the accretion rate
+(e.g. Ingleby et al. 2013). Garcia Lopez et al. (2006) ex-
+trapolated this finding to Herbig stars and determined
+their mass accretion rates using the Brγ line luminos-
+ity. Their approach was validated when Donehew and
+Brittain (2011) and Mendigut´ıa et al. (2011a) confirmed
+that this correlation between accretion luminosity (as
+derived from the UV and Balmer excess) and the lumi-
+nosity of emission lines also extends to Herbig stars.
+Fairlamb et al. (2017) demonstrated that the strength
+of most, if not all, emission lines in the spectra of Herbig
+stars correlate with the Balmer-excess based accretion
+luminosity. They provided best-fit parameters for many
+lines, which cover the wavelength range from the UV to
+the NIR, allowing accretion luminosities to be worked
+out when observations of only limited parts of the spec-
+trum are available.
+The relationship between accretion luminosity and
+line luminosity goes as (cf. e.g. Mendigut´ıa et al. 2011a):
+log
+�Lacc
+L⊙
+�
+= A + B × log
+�Lline
+L⊙
+�
+,
+(2)
+where A and B correspond to the intercept and the gra-
+dient of the (straight-line) relation between log(Lacc/L⊙)
+and log(Lline/L⊙) respectively. As example, Fairlamb
+et al. (2017) determined the constants to A = 2.09 ±
+0.06 and B = 1.00 ± 0.05 in the case of Hα.
+Summary: Because Herbig stars are much more lumi-
+nous than their cooler counterparts, measurement of
+excess UV emission is challenging. For stellar accretion
+rates exceeding 10−8M⊙yr−1, the accretion luminosity
+can be inferred from measurement of the excess Balmer
+continuum. There luminosity of emission lines has been
+shown to scale with this excess enabling a simpler mea-
+surement of the accretion luminosity.
+
+Herbig Stars
+13
+Fig. 6 HR diagram containing the 163 Herbig stars with good Gaia DR2 parallaxes and their accretion rates. The solid
+lines represent PMS tracks (Bressan et al., 2012, Tang et al., 2014), with the final masses indicared on the Main Sequence.
+The dashed lines are isochrones of 0.01, 0.1, 1, and 10 Myr (Marigo et al., 2017). The color map denotes the mass accretion
+rate. While it is evident that the younger stars are accreting at higher rates, the younger stars are also much more massive.
+Characterization of the evolution of the stellar accretion rate requires disentangling stellar mass and age. Figure based on
+Wichittanakom et al. (2020)
+3.4 Mass accretion rates of Herbig stars
+As outlined above, in order to compute the mass ac-
+cretion rate of a Herbig star, it is important to have
+well-determined stellar parameters (mass, luminosity,
+or radius and temperature, as well as extinction). In ad-
+dition, we need a value of the accretion luminosity such
+as derived from the UV excess, which is the only direct
+observational measure of accretion, while an emission
+line luminosity provides an indirect value via Eq. 2. As
+noted in Section 2, significant progress was made in the
+determination of Herbig stellar parameters through the
+Gaia astrometric study by Vioque et al. (2018).
+Arun et al. (2019) used these data and Hα Equiv-
+alent Widths reported in the literature to determine
+accretion rates for many of the objects. Wichittanakom
+et al. (2020) used a slightly larger sample to expand
+the spectroscopically determined temperatures of Fair-
+lamb et al. (2015) with an additional 30 objects. They
+rederived the line-of-sight extinction to the objects, as
+well as measured the Hα emission line strength from the
+same spectra, yielding a large sample to be analysed in
+a homogeneous way. These were supplemented by ob-
+jects from Vioque et al. (2018), resulting in a sample
+of 163 Herbig Ae/Be stars with well-determined stel-
+
+6
+40Mo
+-3
+5
+20Mo
+10Mo
+4
+4
+5Mo
+log(L*) [Lo]
+3
+2Mo
+5
+1Mo
+2
+6
+0.01 Myr
+1
+0.1 Myr
+-7
+Myr
+0
+10 Myr
+8
+4.8
+3.6
+4.6
+4.4
+4.2
+4.0
+3.8
+log(Teff)[K]14
+Sean D. Brittain et al.
+lar parameters and as homogeneously derived accretion
+rates as possible.
+An illustration of the results is provided in Fig. 6.
+It can be seen that the higher mass objects have larger
+accretion rates. Fig. 7 shows the accretion luminosities
+of the Herbig stars and several samples of T Tauri stars
+taken from the literature (Hartmann et al., 1998, White
+and Basri, 2003, Calvet et al., 2004, Natta et al., 2006),
+as a function of stellar luminosity. The T Tauri data are
+not based on Gaia parallaxes, so although not directly
+comparable to the Herbig star measurements, these ob-
+jects are mostly selected to be members of clusters and
+at similar distances. The dependencies of the accretion
+luminosity on the total luminosity should therefore, at
+least to first order, be similar.
+As was already known, the accretion luminosity in-
+creases with stellar luminosity. However, a striking fea-
+ture in this graph is that the Herbig Ae stars follow the
+T Tauri stars closely; the best-fitting slopes of the re-
+spective Lacc − L∗ relations for both groups of objects
+are similar to within the error bars, while both slope
+and scatter are significantly different for the higher mass
+Herbig Be stars. As was described earlier, the Herbig
+Ae stars share many accretion-related properties with
+T Tauri stars, and the dependence of the accretion lu-
+minosity on the stellar luminosity proves no exception.
+The MA accretion paradigm should thus be applicable
+to the Herbig Ae star regime.
+The Herbig Be stars again differ in properties from
+their lower mass counterparts. To this we add that Fair-
+lamb et al. (2015) noted that a number of Herbig Be
+stars required very large surface covering factors of the
+accretion shocks in their MA models, with values ap-
+proaching 100% and higher. As such, these solutions
+are unphysical and their UV/blue excess cannot be ex-
+plained within the MA framework. It would appear that
+the accretion rates as derived in the MA paradigm fur-
+ther support the notion that Herbig Be stars accrete
+their material in a different manner than the T Tauri
+and Herbig Ae stars. The break as seen in Fig. 7, is also
+present in
+˙Macc − M∗ space, and occurs around 4 M⊙
+(Wichittanakom et al., 2020), in agreement with the in-
+dependent study of Ababakr et al. (2017), who found a
+marked change in linear spectropolarimetric properties
+around spectral type B7/8.
+This break at 4 M⊙ is also seen in the high spec-
+tral resolution study of Brγ by Grant et al. (2022). They
+found that the accretion rate increases with stellar mass
+following a trend similar to that of T Tauri stars for
+stellar masses ≤ 4 M⊙. They also found that the distri-
+bution of line shapes of Brγ was consistent across stellar
+mass and spectral type, though they caution that incli-
+nation affects may obscure any underlying systematic
+differences.
+Summary: The relationship between the stellar lumi-
+nosity and the accretion luminosity is consistent be-
+tween T Tauri stars and Herbig Ae stars. There is a
+break in this relationship around 4M⊙. A similar break
+is seen in the mass dependence of the stellar accre-
+tion rate, and is consistent with the marked change in
+the linear spectropolarimetric properties aound spec-
+tral type B7/B8. The mean accretion rate of Herbig Ae
+stars is 10−7M⊙yr−1.
+3.5 Mass accretion rate as a function of stellar age,
+disk dispersal times
+We continue this discussion with a word of caution. In
+order to understand the evolution of pre-Main Sequence
+stars and the disk dispersion timescales, it has been
+common to study the mass accretion rate as a function
+of age of the stars (e.g. Hartmann et al., 1998). Due
+to the comparatively small mass range and large sam-
+ples of objects from clusters with well-defined ages, it is
+feasible to determine this relationship empirically for T
+Tauri stars. Several attempts to do so have been made
+for Herbig stars, and, indeed, it has been found that
+the mass accretion rate decreases with the stellar age
+(e.g. Fairlamb et al., 2015, Arun et al., 2019). However,
+one should be extremely careful in deriving conclusions
+from this result.
+As can be seen from the isochrones in Fig. 6, the
+PMS evolution across the HR diagram is much faster
+for high mass stars than for low mass stars. As a re-
+sult, a higher mass Herbig star inevitably has a younger
+age than a lower mass object. This in turn means that
+when investigating relationships of various parameters
+with “stellar age”, the age essentially acts as proxy for
+the stellar mass. Given that, as mentioned earlier, the
+higher mass Herbig stars have larger mass accretion
+rates, we can expect this effect to dominate any age-
+related correlations. In order to disentangle these ef-
+fects, and study the mass accretion rate as a function
+of age, one needs to select a very narrow mass range to
+remove or minimize this effect.
+Wichittanakom et al. (2020) struggled finding a sta-
+tistical sample of stars within a mass range narrow
+enough to isolate the time dependence of the mass ac-
+cretion rate. The best subsample (having a mass range
+2-2.5M⊙) hinted at a decrease, but with generous error
+bars, ˙Macc ∝ Age−1.95±0.49. Improved mass determina-
+tions, which are still dominated by uncertainties in the
+parallax and extinction, and larger samples of Herbig
+stars are needed to make progress in this area.
+
+Herbig Stars
+15
+Fig. 7 Accretion luminosity versus stellar luminosity for 163 Herbig stars from Wichittanakom et al. (2020) and classical T
+Tauri stars from the literature. Note the similarity between T Tauri and Herbig Ae stars, while the Herbig Be stars behave
+differently. Figure based on Wichittanakom et al. (2020).
+A second caveat to keep in mind is that Herbig stars
+are selected on the basis of possessing emission lines.
+Once these stars cease to accrete, it is very difficult to
+identify PMS stars in this mass range. Thus it is likely
+that as these stars age, the sample of PMS intermediate
+mass stars becomes less complete such that the Herbig
+stars represent the tip of a distribution of sources with
+long-lived accretion disks. If this is true, measurement
+of the time dependence of mass accretion from this bi-
+ased sample is an upper limit. Next to the identification
+of non-accreting PMS intermediate mass stars, consid-
+eration of accretion rates of the direct progenitors of
+the Herbig stars, the IMTT stars, will help clarify our
+understanding on the time dependence of the stellar
+accretion rate.
+Summary: Inferring the time dependence of the stellar
+accretion rate for Herbig stars is challenging because
+of the strong mass dependence of this relationship. For
+a narrow mass range (2.0-2.5M⊙), the mass accretion
+rate scales as t−1.95±0.49.
+3.6 Accretion onto Herbig Be stars
+The MA paradigm is shown not to work for the higher
+mass Herbig Be stars, while evidence has been pre-
+sented that these massive objects accrete matter in a
+different manner than for T Tauri and Herbig Ae stars.
+The natural next question is how material is deliv-
+ered to the massive Herbig Be stars. Understanding ac-
+cretion onto Herbig Be stars and their formation also
+
+CTTs
+Best fit for CTTs
+Best fit for low-mass HAeBes
+Best fit for high-mass HAeBes
+Wichittanakom et al. (2020)
+[0] (387)60]
+2
+0
+1.03 ± 0.08
+-2
+-2
+0
+2
+4
+6
+log(L*)[Lo]16
+Sean D. Brittain et al.
+addresses a wider issue. The intermediate mass Her-
+big stars connect the low mass T Tauri stars and the
+most massive stars whose formation is a topic of intense
+debate (Krumholz and Bonnell, 2009). Observational
+studies have not yet reached the same level of detail as
+for lower mass objects, as massive pre-Main Sequence
+stars are often optically invisible; due to their rapid col-
+lapse, they are still enshrouded by dust from their natal
+clouds (Zhang et al., 2018, Frost et al., 2019). The Her-
+big stars therefore may offer valuable insights into the
+formation of the most massive stars.
+Regarding the disk-to-star accretion on Herbig Be
+stars, we should bear in mind a crucial piece of evidence
+provided by the linear spectropolarimetric studies. The
+data for the higher mass Herbig Be stars is remark-
+ably similar to those of the classical Be stars, which are
+readily explained with disks that reach onto the stellar
+surface (e.g. Poeckert and Marlborough, 1976, 1977).
+Hence, it would appear that the Herbig Be stars ac-
+crete material from a disk that is in contact with the
+stellar photosphere. This situation is reminiscent of the
+so-called Boundary Layer (BL) accretion that is a natu-
+ral consequence of a viscous circumstellar disk (Lynden-
+Bell and Pringle, 1974). The BL is a thin annulus close
+to the star in which matter slows down from its (Kep-
+lerian) rotation velocity to the slower stellar rotation.
+In this region, kinetic energy will be dissipated. This
+model considers how material is transferred from a Ke-
+plerian rotating disk to the, more slowly rotating, stellar
+surface. The region where the disk material slows down
+and releases its kinetic energy is the boundary layer.
+The BL paradigm is being applied to many accret-
+ing astrophysical systems such as White Dwarfs and
+neutron stars in binary systems (e.g. Tylenda, 1977,
+Romanova et al., 2012). It had even been explored for
+T Tauri stars before the MA scenario prevailed (Bertout
+et al., 1988). Blondel and Djie (2006) applied this sce-
+nario to a sample of mainly later type Herbig stars. The
+models could mostly reproduce the UV emission and
+the authors derived accretion rates using this approach.
+The UV excess, and its associated effective tempera-
+ture, can be controlled by the projected size of the BL
+on the sky, while the accretion luminosity depends on
+the amount of matter accreted. The BL model requires
+higher accretion rates than the MA model to repro-
+duce similar accretion luminosities. This is because the
+kinetic energy from Keplerian rotating material is half
+that of the gravitational potential energy. We would ex-
+pect, therefore, that - all other things, such as radiating
+area being equal - when applied to the higher mass Her-
+big stars, the BL derived accretion rates would need to
+be higher. This could well result in a steeper slope of the
+Macc−M∗ relation at the high end, yielding a universal
+accretion behaviour across the PMS mass range.
+Although the BL accretion has been suggested to
+apply in the case of the more massive Herbig stars
+(e.g. Mendigut´ıa et al., 2011a, Cauley and Johns-Krull,
+2014), it has never been tested nor investigated in de-
+tail. The time is ripe for dedicated magneto-hydrodyna-
+mic models to be applied to the full Herbig star mass
+range to investigate the viability of the, surprisingly un-
+derinvestigated, BL model and provide predictions of
+the resulting covering factors and mass accretion rates
+to compare with observations.
+Summary: The magnetospheric paradigm for inferring
+the accretion properties of Herbig Ae stars does not
+apply to their more massive counterparts. It is possible
+that these more massive stars accrete via a boundary
+layer, but more this has not yet been modeled in detail.
+3.7 Probing the accretion regions
+To directly observe the accretion region we need to
+reach as close to the stellar surface as possible. With
+the exception of the UV excess, we have thus far dis-
+cussed indirect probes of the accretion. With regards to
+spatially resolved diagnostics, the smallest scales that
+can be probed directly are through milli-arcsecond op-
+tical and NIR interferometry of the Hα and Brγ lines.
+Over the years, such studies have been conducted using
+facilities such as the VLTI, aimed at the Brγ line (Kraus
+et al., 2008, Mendigut´ıa et al., 2015, Tambovtseva et al.,
+2016, Kreplin et al., 2018) and CHARA, whose obser-
+vations target Hα (Benisty et al., 2013, Perraut et al.,
+2016, Mendigut´ıa et al., 2017).
+The picture that has emerged essentially confirmed
+the original findings from a small sub-sample by Kraus
+et al. (2008); there is a diversity in line properties, emis-
+sion region sizes and line origins. Perhaps most relevant
+to note here is that these milli-arcsecond resolution in-
+terferometric optical and NIR studies of the hydrogen
+line emission do not necessarily identify the line emit-
+ting regions of Herbig stars with the magnetospheric
+accretion channels.
+For example Kraus et al. (2008), Mendigut´ıa et al.
+(2015), Tambovtseva et al. (2016), Kreplin et al. (2018)
+and Mendigut´ıa et al. (2017) report the line emission to
+be sometimes consistent with compact accretion chan-
+nels and sometimes larger than that, making them more
+likely to be due to winds and outflows. When applying
+models to the data, it appears that, generally speaking,
+the line emission regions and properties are consistent
+with a disk-wind, and compatible with MHD driven
+winds (Garcia Lopez et al., 2015, Tambovtseva et al.,
+
+Herbig Stars
+17
+MIR
+Scattered Light
+(sub-)mm
+1
+100
+Distance in au
+10
+1
+2
+3
+4
+a
+b
+c
+d
+1 Turbulent mixing (radial or vertical) 
+Vertical Settling
+Radial Drift
+b) Bouncing
+2
+3
+4
+c) Fragmentation with mass transfer
+d) Fragmentation 
+a) Sticking
+10 μm
+Fig. 8 Schematic of a disks around young star adapted from Testi et al. (2014). This schematic highlights the principal
+processes that drive the evolution of dust (left) and the regions of the disk probed by various wavelengths (right).
+2016, Caratti o Garatti et al., 2015). Although the lines
+themselves may not probe the accretion itself, the natu-
+ral question as to how the emission line strengths allow
+us to determine the accretion rates can be answered
+fairly straightfowardly. As outflows in young stars are
+accretion powered (e.g. Hartmann et al., 2016), a corre-
+lation between line luminosity and accretion luminosity
+may therefore not be surprising after all. Indeed, it also
+explains why we can use the line luminosities for ac-
+cretion rate determinations, and explains the observa-
+tion that the line luminosities do not vary at the same
+timescales or amplitudes as the UV excess (Mendigut´ıa
+et al., 2013).
+Summary: There is compelling evidence that Herbig
+stars with spectral types later than ∼B7 accrete mag-
+netosphericaly, and their Hi and other atomic emission
+lines scale with the accretion luminosity though the
+origin of this relationship remains uncertain. The ac-
+cretion rates of Herbig stars with masses ≲ 4 M⊙ are
+10−8 M⊙ yr−1 ≲
+˙M ≲ 10−6 M⊙ yr−1. The relation-
+ship between the stellar luminosity and the accretion
+luminosity is consistent −2 ≲ log(L∗/L⊙) ≲ 2. There is
+a break in this relationship for stars with higher lumi-
+nosities (corresponding to ∼ 4 M⊙). A study comparing
+the accretion rate of IMTT stars to Herbig stars will
+clarify how the stellar accretion rate evolves over time.
+4 DUST DISKS AROUND HERBIG STARS
+Our understanding of the properties and evolution of
+disks around young stars has advanced dramatically
+over the last 20 years. For a review about the evolu-
+tion of dust in disks, we point the reader to a chapter
+from Protostars & Planets VI by Testi et al. (2014)
+and the review by Andrews (2020). At the time of this
+writing, updated reviews are being prepared for Proto-
+stars & Planets VII and should be available in 2023. In
+Fig. 8, we present a schematic that highlights the domi-
+nant processes thought to drive the evolution of dust in
+disks. In this section, we will summarize the advances
+in our understanding of dust in Herbig disks, while gas
+will be discussed in Sect. 5.
+That the SEDs of Herbig stars show an excess at in-
+frared wavelengths was established in the early 1970’s
+(e.g. Strom, 1972, and references therein). Both disks
+and envelopes - some with a cavity carved by an outflow
+- were invoked to explain this excess (e.g. Gillett and
+Stein, 1971, Strom et al., 1972, Hillenbrand et al., 1992,
+Berrilli et al., 1992, Hartmann et al., 1993, Mannings,
+1994). Unfortunately, due to the low spatial resolution
+of the observations (typically ∼20′′ at millimeter wave-
+lengths, corresponding to 3000 au at 150 pc), it was
+not possible to distinguish which of the proposed mor-
+phologies fitting the SED was the correct one.
+
+18
+Sean D. Brittain et al.
+The first spatially resolved observation of contin-
+uum emission around a Herbig star was obtained by
+Mannings and Sargent (1997) using mm interferometry
+with the Owens Radio Valley Telescope (OVRO); they
+found extended emission up to 110 au for HD 163296,
+using beam sizes of 4-5′′. These authors also detected
+Keplerian velocities of the CO gas, providing the first
+observational confirmation of a disk around a Herbig
+star (see Sect. 5). The Hubble Space Telescope provided
+the first resolved scattered light images of Herbig disks
+(e.g., Weinberger et al., 1999, Grady et al., 1999), and
+in the last years, high contrast imagery with 8m class
+telescopes provide even greater detail of dust structures
+in the disk (e.g. Garufi et al., 2017a). With the avail-
+ability of the ALMA, disk emission can now routinely
+be spatially resolved for many Herbig stars thanks to
+the dramatically improved spatial resolution: typically
+0.05-0.1′′ (7-15 au at a distance of 150 pc; Andrews
+et al. 2018a).
+Before we look more into the detailed properties of
+the dust disks around Herbig stars, it is worth to con-
+sider the differences that are related to the spectral type
+of the central star.
+4.1 Herbig Be and Herbig Ae disks
+Due to their rapid evolution towards the ZAMS, Herbig
+Be stars are typically surrounded by the cloud material
+from which they were formed, and this cold envelope
+will contribute to their continuum emission at longer
+wavelengths. For instance, a significant fraction of the
+Polycyclic Aromatic Hydrocarbon (PAH) emission is
+thought to originate from the surrounding envelope, in-
+stead of from the disk, as is the case in Herbig Ae stars
+(Boersma et al., 2009, Verhoeff et al., 2012).
+Herbig Be stars have a much stronger UV radia-
+tion field than the cooler Herbig Ae stars: from 3450
+L⊙ for a B2V, 50 L⊙ for a B8V and 7 L⊙ for an A0V
+type star (Jim´enez-Donaire et al., 2017). This translates
+to important observational differences, mainly in terms
+of gas emission lines (see Sect. 5.7) and disk proper-
+ties. Alonso-Albi et al. (2009) compared the mm emis-
+sion of Herbig Ae stars to Herbig Be stars, and found
+that, in general, the flux of the Herbig Be stars is 5-10
+times lower, pointing to smaller disk masses. This can
+be attributed to photo-evaporation of the outer disk
+by UV photons on short timescales (∼ 105 yr; Gorti
+et al., 2009). This is further supported by mid-infrared
+(MIR) observations, showing that the disks around Her-
+big Be stars are typically vertically flatter and smaller
+in size than those around Herbig Ae stars (Verhoeff
+et al., 2012).
+Furthermore, Vioque et al. (2018) derived the excess
+in the NIR (1.24-3.4 µm) and MIR (3.4-22 µm) for a
+large sample of Herbig stars. They found that the total
+infrared excess for objects more massive than 7 M⊙ is
+typically smaller than that of the lower mass objects.
+This again points to important differences in disk prop-
+erties depending on the stellar mass, and hence the stel-
+lar radiation field, although external evaporation due to
+nearby massive stars cannot be excluded.
+Another important difference between Herbig Ae
+and Herbig Be stars is the typical distance to the ob-
+jects. Herbig Be stars are typically located at d ≥ 1000
+pc, while the best studied Herbig Ae stars are at dis-
+tances of 100-200 pc, implying that the spatial resolu-
+tion that can be achieved will differ by a factor of 5-10.
+Due to the complications caused by the presence of
+envelope emission, in combination with the low spatial
+resolution when observing Herbig Be stars, we will now
+concentrate on the cooler Herbig Ae stars, thereby in-
+cluding objects from spectral type B9.5 up to ∼ F5.
+Summary: Herbig Be stars evolve toward the main se-
+quence much faster than Herbig Ae stars, thus they
+tend to still be enshrouded in remnant cloud material.
+The NIR, MIR, and mm emission of Herbig Be stars is
+substantially lower than that of Herbig Ae stars. The
+faster disk dissipation timescale of Herbig Be stars is
+likely due to their higher UV luminosity and thus faster
+photoevaporation of the disk.
+4.2 Early disk models: SED classification into group I
+and II
+One of the first efforts to classify the SED of young
+stars were provided by Lada and Wilking (1984) and
+Lada (1987). These authors divided the SEDs of young
+stars into three classes, based on the slope of the SED
+between 2µm and 25µm given by,
+a = dlog(λFλ)
+dlog(λ) .
+(3)
+Objects whose SED had a slope 0 ≤ a ≲ 3 where la-
+beled Class I. Similarly, objects with −2 ≲ a ≲ 0 where
+labeled Class II, and objects with −3 ≲ a ≲ −2 were
+labeled Class III. Eventually this classification scheme
+was expanded to include Class 0 objects that were only
+detected at λ ≳ 10µm (Andre et al., 1993). Most of the
+objects discussed in this review belong to class II.
+The earliest disk models of Herbig stars required ex-
+tremely high accretion rates (> 10−6 M⊙/yr) and large
+optically thin inner holes to fit the SED near 3 µm (Hil-
+lenbrand et al., 1992). However, Hartmann et al. (1993)
+pointed out that, at the accretion rates necessary to fit
+
+Herbig Stars
+19
+100
+101
+102
+Wavelength [ m]
+F
+HD97048
+100
+101
+102
+Wavelength [ m]
+F
+HD104237
+Fig. 9 IR SED of a group I (top) and a group II star (bot-
+tom). Blue dots: photometry, grey line: Spitzer IRS spectrum,
+orange line: Kurucz atmosphere model. After Pascual et al.
+(2016).
+the observed 3 µm excess, the inner region of the disk
+would be optically thick and thus emit too much ra-
+diation at short wavelengths to agree with the obser-
+vations. Instead, they suggest that most Herbig stars
+do not harbor disks but envelopes. However, as noted
+above, mm interferometry and scattered light imagery
+established the presence of disks around Herbig stars
+just a few years later.
+Chiang and Goldreich (1997) modelled the excess
+emission observed in the SEDs of the lower-mass T
+Tauri stars with passive disks in hydrostatic radiative
+equilibrium. In those disks, the surface density goes
+as Σ(r) ∝ r−3/2. They distinguished between flat and
+flared disks: in a flat disk, the opening angle of the disk
+is constant, while in a flared disk it increases with dis-
+tance. The optically thick disk is surrounded by an opti-
+cally thin layer, the disk surface, that is directly heated
+by the star, and where the temperature is higher than
+that of the midplane. This surface layer will also heat
+the interior of the disk. Such 2-layered models can also
+be used for Herbig disks, with some modifications, as
+will be discussed in Sect.4.3.
+For a sample of 45 Herbig stars, the SED could
+be well-characterised in the infrared thanks to obser-
+vations with IRAS (Malfait et al., 1998). These authors
+proposed an evolutionary sequence where the initially
+continuous disk would evolve into a disk with a gap (a
+pre-transitional disk), after which the NIR excess would
+disappear (a transition disk), and finally a gas-poor de-
+bris disk would remain. A few years later, Meeus et al.
+(2001) proposed a classification scheme based upon the
+shape of the IR SED3: Meeus group I (GI) objects have
+an SED where the continuum of the IR to sub-mm re-
+gion can be reconstructed by the sum of a power-law
+and a black body, while Meeus group II (GII) objects
+have an SED where the continuum can be reconstructed
+by a power-law alone (see Fig. 9). Possible locations for
+these components are an optically thick, geometrically
+thin disk (power-law component) and an optically thin
+flared region (black body).
+To facilitate the observational classification into GI
+and GII, van Boekel et al. (2005) introduced a cri-
+terion based on the NIR to total IR luminosity ra-
+tios and the IRAS 12−60 µm color: GI sources have
+LNIR/LIR ≤ (m12 −m60) + 1.5, while GII sources have
+LNIR/LIR > (m12 − m60) + 1.5. A more recent (and
+equivalent) criterion, based on an IR flux ratio that is
+easier to use was proposed by Khalafinejad et al. (2016):
+sources with flux ratio F30µm/F13.5µm < 2.1 are GII,
+while those with a larger ratio belong to GI.
+Summary: The disk of Herbig stars can be classified
+based upon the shape of their SED: to fit their excess,
+GI disks need a power-law + black body component,
+while GII disks only need a power-law. Criteria based
+on infrared photometry can be used to classify the disks.
+4.3 Improvements to the early disk models
+For a long time, the structure of the disk remained a
+topic of debate due to the lack of spatial resolution,
+with both models of accretion disks with an optically
+thin hole and spherically symmetric envelopes matching
+the observed SEDs. However, Tuthill et al. (2001) were
+the first to spatially resolve the inner disk of a Herbig
+star, LkHα 101, using interferometric data of Keck in
+the H and K band. They found a central cavity that was
+much larger (up to 10 times) than previously assumed
+from theoretical accretion disk models, and connected
+3 This classification scheme should not be confused with
+the one proposed by Hillenbrand et al. (1992) where group I
+sources have an infrared excess that scales as λ−4/3 longward
+of 2 µm, group II sources have an SED with a positive slope
+in the infrared, and group III sources have a minimal infrared
+excess.
+
+20
+Sean D. Brittain et al.
+the location of the hot inner disk edge with the radius
+at which dust grains sublimate due to the stellar irra-
+diation.
+Disk models that could properly account for the
+NIR structure of the SED were developed by Natta
+et al. (2001). They proposed a model where the ma-
+terial inside the dust evaporation radius is optically
+thin gas and introduced the concept of a hot puffed-
+up inner wall of optically thick dust grains at the dust
+evaporation radius that could explain the NIR excess.
+Dullemond et al. (2001) gave an expression for the black
+body temperature of the rim,
+Trim =
+�
+L∗
+4πR2
+rimσ
+�1/4 �
+1 + Hrim
+Rrim
+�1/4
+(4)
+They further developed this idea with a semi-ana-
+lytical model in which the hot puffed-up inner wall casts
+a shadow, obscuring parts of the flared disk. In some
+stars, even the entire disk might be shadowed.
+Following this work, Dominik et al. (2003) modelled
+the observations with a disk model in hydrostatic equi-
+librium where the GI sources were modelled with a disk
+with varying surface densities, for some stars even in-
+creasing with radius. In this case most of the material
+is located in the outer regions of the disk, while the
+inner region is depleted. The GII sources, on the other
+hand, could more easily be modelled with a compact
+disk and/or a flattened outer region. However, the pres-
+ence of the silicate feature in GII disks indicates that at
+least a small part of the disk intercepts stellar radiation
+(Dominik et al., 2003).
+Dullemond and Dominik (2004a) used 2-D radiative
+transfer to model GI and GII disks and found that disks
+with a higher optical depth are flaring, while disks with
+a lower optical depth become self-shadowed. Building
+on this work, Dullemond and Dominik (2004b) showed
+that the growth and subsequent settling of dust grains
+towards the midplane could enhance self-shadowing.
+This work provided a successful framework for in-
+terpreting the SEDs of Herbig stars in the evolutionary
+scheme proposed by Malfait et al. (1998) that is intu-
+itively compelling. Qualitatively the idea is that disks
+start out in a flared geometry (with envelopes). As small
+grains agglomerate to form larger grains, they settle
+toward the midplane resulting in flat, shadowed disks.
+However, more recent work has challenged this picture,
+as we will discuss in the following section.
+Summary: The disks around Herbig stars can be de-
+scribed with an optically thick midplane surrounded by
+an optically thin surface layer. The inner disk edge is
+puffed-up, and the innermost region is depleted in dust.
+GI sources emit stronger in the far-IR than GII sources.
+4.4 Group I: disks with a cavity, Group II:
+self-shadowed disks
+The paradigm of GI and GII being understood as an
+evolutionary sequence from young flared disks to set-
+tled flat disks stood for more than a decade until it was
+challenged by mid-IR spatially resolved studies. Honda
+et al. (2012, 2015) and Maaskant et al. (2013) used
+MIR observations to conclude that several GI sources
+have large gaps in their disks, more specifically, a dust-
+depleted region between the inner and outer disk. Disks
+with gaps are called pre-transitional disks, based on the
+assumption that as such disks further evolve and the in-
+ner disk dissipates, the SED would lack a near-IR excess
+(and become a transitional disk, see Sect. 4.8). These
+authors suggested that GI disks could in fact be more
+evolved than GII disks, and proposed two distinct evo-
+lutionary pathways for disks.
+Fig. 10 Accretion rates for group I and II Herbigs, based on
+the HArchiBe catalogue (Guzm´an-D´ıaz et al., 2021).
+When comparing the accretion rate (determined from
+a variety of accretion tracers) in function of the stellar
+luminosity, no difference between GI and GII sources is
+observed (see Fig. 10). A similar behavior was found by
+Grant et al. (2022) who compared the accretion rate,
+derived from the Brγ line, for Group I and Group II
+sources and found a similar distribution, indicating that
+the accretion properties of the star is largely indepen-
+dent of the dust geometry.
+In Table 2, we summarize the main differences ob-
+served between GI and GII objects: selection criteria
+based on IR colors and fluxes, the mm flux scaled to
+a distance of 140 pc (‘mm flux’), the slope αmm mea-
+sured in the mm regions (‘mm slope’), the extent of the
+dust continuum as observed at mm wavelengths (‘mm
+disk size’), the gap size in the mm dust continuum (‘gap
+
+group I
+group II
+logMacc (Mo/yr)
+-5
+<logacc[Gl]>=-5.989
+-9
+<log acc[Gl]>=-5.987
+N
+3
+4
+5
+6
+logL(LO)Herbig Stars
+21
+Diagnostic
+Group I
+Group II
+LNIR/LIR − 1.5
+≤ m12 − m60
+> m12 − m60
+F30µm/F13.5µm
+> 2.2
+< 2.2
+<mm flux>
+750 mJy
+220 mJy
+<mm slope>
+-3.41
+-3.05
+mm disk size
+40-250 au
+<150 au
+mm gap size
+large, 5-140 au
+small, <5 au
+mm structure
+cavity, rings
+barely resolved
+scattered light
+100-600 au
+elusive, < 100 au
+scattered
+light structure
+cavity, rings, spirals
+barely resolved
+CO disk size
+100-650 au
+80-200 au
+CO inner radius
+5-18 au
+3 au
+CO transition
+J=36-35
+J=13-12
+silicate feature
+sometimes absent
+typically present
+PAHs
+strong features
+weak/absent
+Table 2 Main observed differences between group I and II
+disks. References: mm disk size: Stapper et al. (2022); mm
+flux at 140pc, calculated from Stapper et al. (2022), mm
+slope: Pascual et al. (2016); scattered light, gap size, disk
+structure: Garufi et al. (2017b) and references therein; CO
+disk size: Taun, MSc 2020; CO inner radius: Banzatti et al.
+(2018); highest CO level detected: Meeus et al. (2012), van
+der Wiel et al. (2014); silicate feature: Juh´asz et al. (2010);
+PAHs: Acke et al. (2010).
+size’), the disk substructure observed in mm continuum,
+the extent of the small dust grains (‘scattered light’),
+the appearance of the disk in scattered light, the extent
+of the disk seen in CO emission (‘CO disk size’), the
+inner radius where CO ro-vib lines are detected (‘CO
+inner radius’), the emission transition from the highest
+rotational level in the ground vibrational state of CO
+observed (‘CO transition’), the 10 µm silicate feature
+and finally the PAH strength.
+Recently, Banzatti et al. (2018) noted a dichotomy
+in the NIR excess of group I sources: it is either low
+(< 10%) or high (> 25%), while the group II sources
+have intermediate values. Furthermore, they found a
+connection between the strength of the NIR excess and
+the radius at which CO emission is detected: sources
+with a low NIR excess have CO emission starting at
+larger radii indicating that the inner regions are more
+depleted in these sources. We depict the morphologies
+of those 3 different disk types in Fig. 11. In a recent
+paper, Garufi et al. (2022) studied GII disks in scat-
+tered light. They found an anti-correlation between the
+disk brightness in scattered light and the NIR excess,
+supporting the scenario where the inner wall casts a
+shadow on the disk behind it, as was proposed earlier
+by Dullemond and Dominik (2004a).
+Summary: GI disks have a large cavity, depleted in dust,
+that can explain the observed differences in flaring. GII
+disks, on the other hand, have either no cavity or a
+very small one and are self-shadowed, so they are fainter
+both at FIR wavelengths and in scattered light.
+4.5 Dust properties in Herbig disks
+The disk material from which planets eventually form
+originates in the interstellar medium (ISM). There, dust
+particles are either oxygen- (mainly silicates) or carbon-
+rich (mainly Polycyclic Aromatic Hydrocarbons - PAHs).
+Silicates can be divided into olivines (Mg2xFe2−2xSiO4)
+and pyroxenes (MgxFe1−xSiO3). In the ISM, silicates
+are small (< 0.1 µm) and amorphous, with a crystalline
+mass fraction < 2.2% (Kemper et al., 2004), so that the
+detection of larger and/or crystalline silicates in Herbig
+disks would indicate dust processing. Dust grains can
+grow when the density is high and the collision velocity
+low enough (e.g. Windmark et al., 2012). Crystalliza-
+tion of grains can occur either through thermal anneal-
+ing of amorphous dust or condensation from the gas
+phase, both of which occur at high temperatures (T >
+1000 K; Fabian et al., 2000). Our knowledge about dust
+in protoplanetary disks is limited by the fact that the
+bulk of the mass resides in the (partially) optically thick
+mid-plane, and that the emitting surface per unit mass
+decreases as grains grow. However, there are 3 portions
+of the dust population that can be observed through
+different methods:
+1) submicron-sized dust grains in the disksurface scat-
+ter optical and near-IR light;
+2) micron-sized dust grains, also located in the disksur-
+face, emit thermally in the mid-IR when at the right
+temperature (T ≲ few hundreds of K), hence at a cer-
+tain distance from the star. It is here that we can iden-
+tify their main solid-state features;
+3) mm-sized dust grains, located near the midplane at
+larger distances from the star, with T ≲ few tens of K,
+will emit thermally in the mm range, where the optical
+depth is lower.
+We will now look at each of these methods and dis-
+cuss the main results derived from them, with a focus
+on what we have learned from IR spectroscopy, reveal-
+ing the properties of the dust grains.
+4.5.1 Scattering by micron-sized dust grains
+Small grains or aggregates located in the surface layer
+of the disk can be traced through the light they scatter.
+If the disk is inclined, it is possible to measure the scat-
+tering efficiency at different angles (the phase function)
+of the dust grains. The more inclined the disk is, the
+larger the phase angle range that can be observed (see
+Fig. 2 in Benisty et al. 2022). However, Stolker et al.
+(2016) showed that it is important to take the flaring
+of the disk into account when deriving the phase func-
+tion and interpreting the scattered light images, due to
+projection effects in the image plane. Several dust prop-
+
+22
+Sean D. Brittain et al.
+Fig. 11 The different disk structures proposed by Banzatti et al. (2018) for Herbig disks. Top: A schematic of a disk with
+an inner cavity and a flared outer disk. This geometry results in a GI SED with little to no excess NIR emission. Middle: A
+schematic of a disk with a gap that separates the inner and outer disk. This geometry also results in a GI SED, however, there
+is a substantial excess NIR emission. Bottom: A schematic of a continuous disk. This geometry results in a GII SED. Figure
+based on Bosman et al. (2019).
+erties can be derived from the degree and intensity of
+polarization of the scattered light, as well as from the
+way these depend on the scattering angle.
+The phase function of a dust grain depends mainly
+on its size (but also on its shape, structure, and re-
+fractive index), with smaller dust grains (a < λobs)
+having a more isotropic phase function, while the po-
+larization by larger dust grains (a > λobs) tends to
+peak towards small angles (0◦, or forward scattering).
+Therefore, when comparing the ratio of forward and
+backward (180◦) scattering intensity, the size of the ag-
+gregates can be estimated (e.g. Tazaki et al., 2019).
+Furthermore, for larger aggregates, the amount of po-
+larization is related to the porosity of the material. Also
+the color of the aggregates can further reveal the poros-
+ity of the dust (Mulders et al., 2013). In Herbig stars,
+polarized phase functions of both small and large aggre-
+gates have been observed in several objects (e.g. Stolker
+et al., 2016, Ginski et al., 2016). However, as these ob-
+servations are very time consuming, due to the sensi-
+tivity and spatial resolution required, more progress in
+this field is expected to be made in the future (see also
+Benisty et al., 2022).
+4.5.2 Thermal emission of warm small dust grains
+The largest advances so far in deriving detailed dust
+properties was done based on infrared spectroscopy.
+By comparing optical constants obtained in the lab,
+the dust responsible for the observed spectral features
+can be characterised in terms of its composition, de-
+gree of crystallisation, and grain size (e.g. Henning and
+Meeus, 2011). Ground-based observations of silicates
+have mainly concentrated on the 10 µm window, where
+both amorphous and crystalline silicates can have strong
+features. However, for a more detailed study, space based
+observatories were necessary to obtain more sensitive
+and longer wavelength data.
+Observations with ISO were crucial to make a first
+inventory of the IR spectral features in Herbig disks.
+A key result was the discovery of crystalline silicate
+features in the spectrum of HD 100546, reminiscent of
+features found in the Solar System comet Hale-Bopp
+(see Fig 12; Malfait et al., 1998). Furthermore, a study
+of 14 Herbig stars showed a wide variety in dust prop-
+erties: from unprocessed silicates (mainly amorphous
+and small as in the ISM) to highly processed silicates
+(crystalline and large); with no relation to any of their
+stellar parameters (Bouwman et al., 2001). Surprisingly,
+several GI sources do not show silicate emission, even
+though their SEDs were similar to other GI sources that
+did. This can be attributed to either a lack of warm
+and/or small silicates, what can be modelled by 1) re-
+moving the small grains and 2) increasing the height of
+the inner wall (Meeus et al., 2002, Dominik et al., 2003).
+
+group I, low NiR
+opt. thin surface layer
+cavity
+puffed-up wall
+group I, high NiR
+puffed-upwall
+opt.thin surface layer
+disk gap
+opt.thin surface layer
+group Il
+puffed-upwallHerbig Stars
+23
+Fig. 12 The spectra of Herbig star HD 100546 and Solar
+System comet Hale-Bopp. With the vertical marks the po-
+sitions of forsterite features are indicated. Figure based on
+Malfait et al. (1998).
+However, both model options cannot explain the ob-
+servations. Therefore, Dominik et al. (2003) speculated
+that the absence of the silicate feature could be caused
+by a gap, removing those dust grains in the tempera-
+ture range (∼ 200-400 K) needed to emit in the MIR.
+Indeed, a decade later Maaskant et al. (2013) showed
+with spatially resolved mid-IR observations that the ab-
+sence of the 10 µm silicate feature in GI disks can be
+explained by certain gaps in the disk.
+Fig. 13 The 11.3/9.8 µm ratio versus the peak to continuum
+ratio of the 10µm silicate feature for GI and GII sources,
+Fnorm = 1 + (Fobs - Fcont)/Fcont. After Juh´asz et al. (2010).
+To study the grain size, van Boekel et al. (2003)
+introduced an intuitive method, based on the change
+in strength and shape of the 10 µm silicate feature as
+grains grow: comparison of the 11.3/9.8 µm ratio of
+the silicate feature to its peak-to-continuum ratio. They
+showed that the observed band strength and shape are
+correlated, so that a weaker feature provides evidence
+for larger grains in the inner surface layers and cannot
+be attributed to a mere contrast effect. This method in-
+dicates that there is no difference between GI disks and
+GII disks in terms of silicate grain growth (see Fig. 13).
+Studies of large samples with higher S/N spectra (taken
+with Spitzer) that were fit with a two-layer temperature
+distribution model confirm a variety of dust properties
+(dominated by amorphous olivines; Juh´asz et al. 2010).
+These authors found that the crystallinity fraction of
+small dust graints in disks around Herbig stars ranged
+from 1% to 30 % and did not correlate with stellar or
+other disk properties.
+The wavelength and band shape of the 69 µm fea-
+ture emitted by forsterite at temperatures below 300 K
+are very sensitive tracers of the Fe content and tem-
+perature of the grains. This feature became accessible
+with Herschel/PACS (e.g. Sturm et al., 2010, Maaskant
+et al., 2015). The analysis of 7 Herbig stars showed that
+most of the forsterite grains responsible for the 69 µm
+band have rather high temperatures of 100-200 K, and
+that the Fe content is less than 2% (Sturm et al., 2013).
+It is important to keep in mind that the emission
+features seen in the IR spectra trace dust grains that
+are in the optically thin surface layer of the disk, while
+the bulk of the mass resides in the disk mid-plane. Also,
+those grains need to be at the right radial distance in
+order to be warm enough to emit at IR wavelengths
+(Kessler-Silacci et al., 2007). It is, therefore, uncertain
+how representative these dust grains are of the bulk
+of the disk. This will naturally depend on the amount
+of (vertical) turbulence in the disk, and the dynamical
+coupling between the gas and dust grains, which also
+depends on the grain size.
+4.5.3 Spatial distribution of silicates in disks
+The spatial distribution of silicates (in particular the
+crystalline silicates) can be measured with MIR inter-
+ferometry, and indirectly in spatially unresolved spec-
+tra that cover a wide wavelength range and hence tem-
+perature range of the emitting dust. The MID-infrared
+Interferometer at the VLTI (Leinert et al., 2003) was
+the first instrument that provided the angular resolu-
+tion necessary to spatially resolve the silicate emission.
+It was shown that the abundance of crystalline silicates
+increases in the inner few au of Herbig disks (see Fig. 14;
+van Boekel et al., 2004). Subsequent studies confirmed
+this result for other Herbig stars (e.g. Menu et al., 2015)
+and T Tauri stars (Varga et al., 2018).
+While more indirect, Juh´asz et al. (2010) used the
+wide wavelength range (5-38 µm) of Spitzer/IRS to in-
+fer the radial distribution of the crystalline silicates
+
+250
+200
+HD100546
+Flux
+150
+100
+50
+Hale-Bopp
+0
+5
+10
+15
+20
+25
+30
+35
+40
+45
+Wavelength[um]1.2
+GI
+GII
+1.1
+1.0
+3
+0.9
+11.
+0.8
+largergrains
+0.7
+0.6
+1.5
+2.0
+2.5
+3.0
+3.524
+Sean D. Brittain et al.
+Fig. 14 The 10 µm spectra of HD 144432 taken with 3 differ-
+ent baselines, covering different radial distances in the disk.
+The dust in the innermost region is clearly more processed
+than that of the entire disk. Figure from van Boekel et al.
+(2006).
+in the disk. They split the spectra in 2 parts repre-
+senting the warmer material in the inner disk and the
+colder material in the outer disk. They found forsterite
+at a wide range of radial distances, including regions
+far below the annealing temperature of silicates, sug-
+gesting they were formed through eruptive processes.
+In contrast, enstatite was preferentially (but not exclu-
+sively) found in the inner disk, so that the enstatite-
+to-forsterite mass ratio declines with distance from the
+star. For a discussion on possible formation scenarios,
+we refer to Juh´asz et al. (2010).
+The abundance of forsterite can be locally enhanced
+under certain conditions. This is the case in HD 100546,
+a GI Herbig star with a bright disk wall at 13 au. Mul-
+ders et al. (2011) found that most of the forsterite emis-
+sion originates from the inner wall (at 13-20 au), with a
+dust temperature of 150 to 200 K. While there is a high
+forsterite abundance (40-60%) in the wall, the observa-
+tions are consistent with the absence of fosterite in the
+outer disk. Thus an observed strong feature does not
+necessarily mean a high average abundance in the disk,
+but can reflect a locally enhanced abundance in small
+crystalline silicate grains. Such local enhancements may
+be related to planet formation. Indeed, in the case of
+HD 100546, several planetary candidates have been pro-
+posed (see Sect. 6). If present, such a massive planet
+may stir up a local population of larger bodies or peb-
+bles in the exposed inner regions of the outer disk,
+and/or cause shocks that produce crystalline silicates.
+Hence, a direct relation between the planet formation
+process and the occurrence of crystalline silicates could
+explain the observed global lack of correlations with
+stellar or disk parameters.
+4.5.4 Thermal emission of cold large dust grains: grain
+size and disk mass
+The thermal emission of mm-sized dust grains located
+closer to the mid-plane of the disk is expected to be
+optically thin at a distance > 5-10 au. As their mm
+emission is in the Rayleigh-Jeans (R-J) limit, their flux
+is proportional to the dust opacity: Fν ∝ κνν2. Un-
+fortunately, the optical properties of the dust are not
+known a priori. However, at mm wavelengths, κν can
+be approximated by νβ, with β the dust opacity in-
+dex, such that: Fν ∝ ν2+β. The dust opacity index β
+is dependent on the dust properties, with dust grain
+size thought to be the most important - besides com-
+position, shape and porosity. In the ISM, the value of
+β is typically 1.7-2.0, and declines as the grains grow.
+Therefore, the observed spectral index, α, of the SED
+(Fν ∝ να) can be used as a proxy for grain growth
+deeper in the disk, assuming optically thin emission in
+the R-J limit, so that α = β + 2.
+Acke et al. (2004) found that β was lower for GII
+disks than for GI disks, suggesting enhanced grain growth
+in GII disks (see also Pascual et al. 2016). However,
+these observations provide the radial average of β, while
+a radial dependency of the spectral indices was found
+in several disks (e.g. HD 163296 (Guidi et al., 2016),
+HD 141569A (White and Boley, 2018), and HD 100546
+(Miley et al., 2019)), with a lower spectral index in the
+inner regions than the outer regions, pointing to en-
+hanced grain growth in the inner disk.
+Pinilla et al. (2014) found that β is higher in sources
+with dust-depleted cavities (where grain growth is not
+favorable), and showed that β can even be related to the
+cavity size. Therefore, the radially integrated value of
+β can provide a misleading measure of the overall grain
+growth throughout the disk. Furthermore, Woitke et al.
+(2019a) showed that while β is thought to be dominated
+by the size of the grains, variation in the composition
+of the grains can lead to deviations in β ranging from
+∼ 0.2 − 0.7 in the warm Herbig disks while cooler disks
+- such as around TTS - have even larger deviations.
+The dust disk mass can be estimated from the ob-
+served flux at mm wavelengths, assuming that the emis-
+sion is optically thin and that the dust opacity and tem-
+perature are known (e.g., Beckwith et al., 1990, Hen-
+ning et al., 1994):
+Mdust =
+c2d2Fν
+2ν2k < Tdust > κabs
+ν
+(5)
+with c the speed of light, d the distance, Fν the flux, ν
+the frequency, k the Boltzmann constant, < Tdust > the
+mass-averaged dust temperature and κabs
+ν
+the absorp-
+tion coefficient per unit dust mass (cm2g−1). Pascual
+
+o m
+100%flux
+46m
+40%flux
+102 m
+20% flux
+8
+6
+10
+11
+12
+13
+入[μm]Herbig Stars
+25
+Fig. 15 The 1.3mm flux, scaled to 140pc and divided by M∗
+versus M∗, a proxy for Mdust/M∗, for stars with d < 500pc.
+The largest fluxes are seen in GI sources, but many GI sources
+have similar values as GII. Based on data from Stapper et al.
+(2022).
+et al. (2016) found that, on average, GI sources have
+larger mm luminosities than GII sources; a similar re-
+sult was found by Stapper et al. (2022); see Fig. 15.
+Assuming that the temperature and dust opacity is the
+same in every disk, this would imply that GI disks have
+larger dust masses than GII disks. However, there is ev-
+idence that the disk temperatures and dust opacity of
+GI and GII sources are not the same (Woitke et al.,
+2019a); also, the size of the largest dust grains that we
+can trace is similar to the longest wavelength we ob-
+serve, thus large rocks etc. remain unaccounted for.
+Woitke et al. (2019a) compared dust masses derived
+with 3 different methods: 1) the classical way, with a
+fixed dust opacity and dust temperature, 2) the classi-
+cal way but with dust opacities and temperatures de-
+rived from SED modelling, and 3) dust mass directly
+derived from SED modelling. They point out that, 1)
+typically, the dust opacities are larger than the ‘canon-
+ical value of 3.5 cm2g−1, so that the actual dust masses
+are lower; 2) not all disks are optically thin at (sub)mm
+wavelengths; 3) the dust temperature can be higher in
+the case of a small disk, or lower in the case of an ex-
+tended disk, leading to actual lower/higher dust masses
+for smaller/larger disk then when derived in the clas-
+sical way. However, when comparing the results from
+method 1) and 3), Woitke et al. (2019a) found that
+these effects tend to cancel out, so that only an uncer-
+tainty of 0.5 dex in dust mass remains. Additionally,
+as we will discuss in Sect. 5.1, the gas to dust ratio in
+disks is poorly constrained. While the use of the mm
+luminosity to estimate the disk mass is convenient, the
+poor characterization of the required parameters sug-
+gests that this approach should be taken with some
+caution.
+Summary: Evidence for dust processing in terms of
+crystallization and grain growth has been found in the
+IR spectra of Herbig disks, but no connection between
+the amount of the dust processing and stellar or disk
+properties was found. However, the dust grains observed
+in the MIR represent only a small fraction of the dust
+present in the disk.
+The absence of the 10 µm silicate feature in GI disks
+can be explained by dust cavities at a distance where
+dust grains would obtain a temperature of 200-400K.
+The decrease in enstatite/forsterite ratio with dis-
+tance from the star suggests that (long-lasting) erup-
+tive processes are the dominant source of cold forsterite
+in the outer disk regions. On the other hand, the low
+Fe content observed in the 69 µm forsterite feature
+is consistent with silicate formation in chemical equi-
+librium at high temperatures. More detailed modeling
+of crystallization processes, taking into account radial
+transport, shock heating, and stellar eruptions is clearly
+needed.
+Under the (somewhat simplistic) assumption that
+the Herbig disks have similar temperatures and dust
+opacities, GI disks have, on average, larger dust masses
+than GII disks, as derived from their mm fluxes assum-
+ing optically thin emission. However, when ignoring ra-
+dial variations of β, GI disks have, on average, higher β
+values than GII, pointing to smaller grains, thus result-
+ing in stronger emission for a similar mass. In addition,
+different dust compositions will result in different val-
+ues of β. It is clear that, when deriving and comparing
+dust disk masses, more attention needs to be paid to
+dust opacities and temperatures.
+4.6 PAHs in Herbig disks
+While silicates are oxygen-rich materials, Polycyclic Aro-
+matic Hydrocarbons (PAHs) are carbon-rich. They are
+actually large molecules rather than dust particles, so
+they are suspended in the disk atmosphere. Since PAHs
+emit by reprocessing UV photons, they trace the sur-
+face of the disk exposed to the radiation field of the
+star, and can thus be detected at larger distances from
+the star than silicates, which are thermally excited.
+Meeus et al. (2001) found that in GII sources, PAHs
+are absent or weak, while GI sources show stronger PAH
+emission features. This result was confirmed by Acke
+et al. (2010) for a sample of 53 Herbig Ae stars: the
+PAH-to-stellar luminosity ratio is higher in targets with
+a flared disk (GI). The observation that the PAH lumi-
+nosity is stronger in GI than in GII disks, for a given
+stellar temperature, can be related to a larger amount of
+PAHs that are exposed to UV photons. Indeed, when a
+
+1750
+V12470ri
+group I
+1500
+group II
+(M)
+1250
+1000
+750
+HD135344B
+HD142527
+500
+HD97048
+250
+0
+1.5
+2.0
+2.5
+3.0
+3.5
+4.0
+M*(M。)26
+Sean D. Brittain et al.
+gap opens in the disk, a larger part of the disk is exposed
+to stellar photons that warm the disk and thus increase
+the flaring. The few GII sources where PAHs were de-
+tected (e.g. HD 142666, Meeus et al., 2001) might have
+small gaps (Menu et al., 2015). Alternatively, for some
+sources the gas in the disk could be flared, even when
+the dust has settled (Acke et al., 2010).
+The variations seen in the positions of the features
+are mainly due to chemical differences of the PAHs in-
+duced by the stellar UV field (Acke et al., 2010): the C-
+C bonds at 6.2 and 7.8 µm shift to longer wavelengths
+with decreasing stellar effective temperature and is a
+measure for the aliphatic/aromatic content ratio of the
+hydrocarbon mixture. Furthermore, Maaskant et al. (2014)
+found that the ionization state of the PAHs (that can
+be deduced from the I6.2/I11.3 band ratio) critically de-
+pends on the optical thickness of the disk, with a higher
+ionization fraction in optically thinner disks. These au-
+thors also propose that PAHs are not only located in
+the disk surface as is generally assumed, but that they
+are also present in the more optically thin disk gaps.
+Summary: PAHs trace the disk surface out to large dis-
+tances. Their emission is stronger in flared disks where
+they can intercept more stellar photons. The observed
+chemical differences (aliphatic vs. aromatic) are due to
+differences in the stellar UV radiation, while the ion-
+ization state depends on the optical thickness of the
+disk.
+4.7 Ices in Herbig disks
+Ices are thought to be an important component in the
+framework of planet formation, due to 1) their higher
+sticking coefficient, making it easier for icy grains to
+grow 4, and 2) the increase of the density in solids when
+dust grains are covered in ice. Therefore, the location
+of the ice line (where a particular molecule freezes out
+in a disk) determines the region where the growth of
+planetesimals could occur more easily.
+Unfortunately, the spatial distribution of ices in Her-
+big disks is not well known, mainly due to a lack of
+spatial resolution at far-IR wavelengths, as well as due
+to the fact that most ices are located deeper in the
+disk, where the optical depth is too high for them to
+be seen. However, at 3.1 µm, water ice can be observed
+through scattered light spectra. With this method, a
+decrease in surface brightness at 3.1 µm was observed
+in HD 142527, beyond the cavity and inner wall of the
+4 However, experimental work by Gundlach et al. (2018)
+did not confirm the theoretical prediction that ices have
+higher tensile strengths than silicates.
+outer disk (Honda et al., 2009). Furthermore, a crude
+spatial distribution of water ice was derived by Honda
+et al. (2016) for HD 100546 from the radial profile of
+the 3.1 µm opacity, but the results are inconclusive.
+Fig. 16 The ISO SWS and LWS spectra of HD 142527, and
+the imaginary part of the refractive index of water ice at 50
+K in blue. Indicated are water ice emission peaks at 43 and
+62 µm. After Min et al. (2016a).
+In the far-IR, the water ice feature at 43 µm can
+be strong, but that wavelength unfortunately lies out
+of the wavelength covered by Spitzer and Herschel, but
+it was detected for a few sources with ISO/SWS (Mal-
+fait et al., 1999). Another ice feature at 62 µm has a
+large width (see Fig. 16) that hinders straightforward
+identification as it is rather weak. Both features were
+identified in HD 142527 (note that HD 142527 has a
+large dust gap (> 140 au) with likely low gas density;
+Casassus et al., 2015). Min et al. (2016a) modelled the
+far-IR spectra and determined that the emitting water
+ice resides in the outer disk of HD 142527 where the
+ratio of water ice to silicates is 1.6, showing that the
+density of solids clearly increases due to ice. They also
+concluded that 80% of the oxygen in the outer regions
+resides in water ice, a similar amount as what is found in
+the outer solar system and in dense interstellar clouds.
+Min et al. (2016a) found the water ice in HD 142527
+to be mainly crystalline, even though it is located in
+regions with temperatures for which the crystallisation
+timescale is too long to have occurred. Therefore, they
+considered various scenarios to form crystalline ice: 1)
+heating by a strong accretion burst, 2) formation in the
+inner disk and subsequent transport to the outer regions
+by radiation pressure, or alternatively, and 3) the break-
+up of larger icy bodies through collisions in which crys-
+talline ice is preserved, again with subsequent transport
+outwards by radiation pressure. These authors consid-
+ered the third scenario the most likely.
+
+3.0
+140
+HD142527
+120
+2.5
+ex
+100
+2.0
+inde
+(Jy)
+80
+Im(refractive 
+Flux 
+1.5
+60
+1.0
+40
+WatericeT=50K
+0.5
+20
+0
+0.0
+40
+50
+60
+70
+80
+90
+Wavelength [μm]Herbig Stars
+27
+The temperature at which water and CO freezes out
+under typical disk conditions is 128-155 K and 23-28 K,
+respectively (Zhang et al., 2015). By deriving the disk
+temperature profile, the location of the ice line thus can
+be determined, as Isella et al. (2016) did for HD 163296
+based on ALMA observations: for the midplane, Tm(r)
+= 24K (r/100au)−0.5 and for the surface, Ts(r, z) =
+68K(
+√
+r2 + z2/100au)−0.6. This would place the water
+snow line at ∼ 3-4 au, too small to be resolved with
+ALMA, and the CO ice line at ∼ 75-110 au, well within
+reach with ALMA.
+Summary: Water ice has been detected at 3.1 µm in
+scattered light in a few Herbig stars. Despite water ice
+having strong features at 43 and 62 µm, the paucity
+of observations and detections at those wavelengths re-
+sults in a poor understanding of water ice in Herbig
+disks. To detect the snow line, very high spatial resolu-
+tion is required; so far water has not been detected in
+a disk around a Herbig star with ALMA. Soon, JWST
+will provide more sensitive measurements of water emis-
+sion from disks, as MIRI (5-29 µm) covers the mid-IR
+lines of water with excitation temperatures of a few
+1000 K with a spectral resolution of 3000, so water lines
+in Herbigs are expected to be detected.
+4.8 Transition Disks to Debris disks
+Disk type
+Planet
+Transitional
+Debris
+forming
+Onset IR excess
+NIR
+MIR
+FIR
+Gas content
+gas-rich
+intermediate
+gas-poor
+˙Macc (M⊙/yr)
+7 ×10−7
+2 ×10−8
+–
+LIR−mm/L∗
+0.5
+0.01
+< 0.008(b)
+F1.3mm (mJy)
+500
+1.7-7(a)
+0.1-3(c)
+CO 2-1 (Jy km/s)
+2-50
+6.3(a)
+0.05-3(b)
+Prototype
+AB Aur
+HD 141569A
+Vega
+Table 3 Comparison of the properties of circumstellar disks
+at different evolutionary stages. Listed are typical values, for
+detected sources - many are not detected, especially the debris
+disks in CO. References: Meeus et al. (2012) and (a)Di Folco
+et al. (2020); (b)Hughes et al. (2018), (c)Mo´or et al. (2017).
+CO and mm fluxes are normalised to a distance of 140 pc.
+Disks evolve from a massive primordial gas-rich disk
+into a gas-poor debris disk, after passing through the
+transition disk phase. The definition of a “transition”
+disk is varied in the literature. This term is variously
+used to define disks whose near-IR excess is smaller
+than the median among disks in Taurus (Calvet et al.,
+2005), disks possessing a cavity (Espaillat et al., 2014),
+and disks whose SED reveals no NIR excess and a signif-
+icant excess at wavelengths beyond 10µm (Strom et al.,
+1989). In this review, we adopt the latter definition. The
+lack of a NIR excess can be attributed to the depletion
+of small grains in the inner disk (e.g., Strom et al.,
+1989), creating a cavity in the disk. This can be caused
+by clearing by a giant planet, but other scenarios, such
+as grain growth or photo-evaporation might also con-
+tribute (e.g. Armitage, 2019). In Table 3, we compare
+the main properties of planet forming, transitional and
+debris disks.
+Fig. 17 SED of the transition disk HD 141569A. The excess
+in the NIR is absent, and only starts beyond 5 µm.
+A survey of sub-mm emission for debris disks in
+combination with a literature compilation shows that
+the dust mass in debris disks is lower by about two
+orders of magnitude (adopting a constant dust opac-
+ity and representative dust temperatures, Pani´c et al.,
+2013). However, there is some overlap between primor-
+dial disks and debris disks in the age range of a few Myr
+to 20 Myr.
+A prime example of a transition disk is the 9 ± 4.5
+Myr A0 star HD 141569A. The infrared excess emerges
+near 5 µm (Fig. 17), and its fractional IR luminosity is
+at least a factor 10 smaller than that of a typical Herbig
+Ae star (Pascual et al., 2016). The Hα emission line is
+double peaked and the accretion rate is 2×10−8M⊙yr−1
+(Fairlamb et al., 2015). The presence of warm molecu-
+lar gas was identified from ro-vibrational CO emission
+(Brittain and Rettig, 2002) and the presence of cool
+molecular gas was identified from rotational CO emis-
+sion (Zuckerman et al., 1995). The presence of gas in
+the disk is further confirmed through emission lines of
+[OI] and [CII] in the far-IR (Thi, 2014).
+Di Folco et al. (2020) compared spatially resolved
+images of CO emission and mm continuum acquired
+with ALMA with resolved scattered light imagery ac-
+quired with the Spectro-Polarimetric High-contrast Ex-
+oplanet REsearch (SPHERE) on the VLT. They found
+
+28
+Sean D. Brittain et al.
+large differences in the radial distribution of the ma-
+terial probed by these observations. The mm thermal
+continuum extends to ∼250 au while the disk is de-
+tected out to ∼400 au in scattered light, where several
+rings are seen. The CO gas was only detected out to
+the distance of the mm continuum (250 au). The flux
+of these pure rotational lines can be converted to a total
+gas mass of ∼ 70M⊕ (∼2×10−4 M⊙), on the lower end
+for Herbig stars, but 10 times higher than the most gas-
+rich debris disk known to date (Mo´or et al., 2017). Cu-
+riously, with the disk mass inferred from the CO lines,
+the stellar accretion rate could only be sustained for
+a few thousand years, suggesting that either the CO is
+severely depleted or the inference of the stellar accretion
+rate inferred from the veiling of the Balmer continuum
+is overestimated (see Sect. 5.1).
+Summary: A transition disk is a disk that is in transi-
+tion between the protoplanetary and debris phase. In
+those disks, the infrared excess starts in the MIR. Gas
+is still present in these disks and the stars accrete. The
+total IR luminosity, CO luminosity and mm flux is in
+between that of Herbigs and debris disks.
+4.9 Detailed disk morphology
+The MIR image of HD 97048 taken by Lagage et al.
+(2006) revealed for the first time a strongly flaring disk
+surface through the emission of PAHs located in the
+disk surface where they are transiently heated by stel-
+lar UV photons. This flaring surface was later confirmed
+with NIR scattered light observations (Ginski et al.,
+2016). On the other hand, under the assumption of
+optically thin emission, the surface density profile of
+the large grains can be derived from mm observations.
+ALMA is perfectly suited for this purpose, as it traces
+the thermal emission of cold mm-sized dust grains with
+high spatial resolution. ALMA uncovered several large
+(> 10 au) cavities in the dust continuum, the largest
+-140 au- seen in HD 142527 (Perez et al., 2015), and
+80 au in HD 34282 (van der Plas et al., 2017a). Sub-
+sequent progress in observational techniques at both
+shorter and longer wavelengths (increased sensitivity
+and spatial resolution) led to the discovery of substruc-
+tures in the disks, as will be discussed below. But first
+we will summarize what is expected from theoretical
+disk models.
+4.9.1 Theoretical predictions for disk substructure
+In a continuous disk, large mm-sized grains are ex-
+pected to spiral inwards as they experience a headwind
+due to the surrounding gas, making them lose angular
+momentum, a process called radial drift. The smaller
+micron-sized dust grains, on the other hand, are cou-
+pled to the gas and do not experience such a headwind.
+Grains can also spread outwards to redistribute the an-
+gular momentum in the presence of (turbulent) viscos-
+ity (e.g. Birnstiel et al., 2010).
+Models predict that an embedded planet, brown
+dwarf, or low-mass stellar companion can dynamically
+clear its orbit and open a gap in a disk (Lin and Pa-
+paloizou, 1979). When a planet opens a gap in the disk,
+a local enhancement in gas pressure is created - a pos-
+itive pressure gradient, trapping dust grains and thus
+creating a region with low collisional velocities in which
+the dust grains can grow more rapidly, as is illustrated
+in Fig. 18 (Pinilla et al., 2012, 2016). Another scenario
+to create a gap is a dead zone, a region with a low
+ionization fraction, and by consequence a low turbu-
+lence level. At the edge of such a dead zone a pile-up
+of material is expected, creating a gap in the disk (e.g.
+Reg´aly et al., 2012). For both scenarios, the viscosity is
+an important parameter.
+!"#$%&'()#"*(
+Fig. 18 Gas surface density in function of distance, illustrat-
+ing particle trapping in a disk, the result of pressure bumps
+caused by a massive planet located at 10 au (Pinilla, private
+communication).
+The efficiency of dust trapping depends on the grain
+size: larger grains are trapped in the pressure bump
+while smaller grains migrate inward - a process referred
+to as dust filtration (Rice et al., 2006, Zhu et al., 2012).
+This can be verified with high spatial resolution obser-
+vations: at mm wavelengths, tracing the larger grains,
+one would observe a ring-like structure with a large gap,
+while in the NIR scattered light, tracing smaller grains,
+this gap would either be smaller or even non-existent
+(e.g. de Juan Ovelar et al., 2013). The width of the
+ring that is induced by a massive planet through pres-
+
+1.0
+Gap opened by
+a massive planet
+0.8
+negative
+pressure
+0.6
+gradient
+M
+positive
+0.4
+pressure
+gradient
+0.2
+0.0
+1.0
+1.5
+2.0
+2.5
+3.0Herbig Stars
+29
+sure bumps will depend on the disk and stellar mass,
+as well as the location of the planet and the viscosity
+parameter α (Pinilla et al., 2018).
+This process of dust filtration was confirmed by ob-
+servations: the cavity size seen in NIR scattered light
+is often smaller than that in the mm, for instance for
+HD 135344B ∼ 28 au in the NIR versus ∼ 46 au at mm
+wavelengths (Garufi et al., 2013, Muto et al., 2012). To
+match the observations, Dong et al. (2012) used a disk
+model where inside the cavity, the surface density pro-
+file of the small grains is flat and can reproduce the
+observed NIR excess, while the larger dust grains are
+depleted.
+Zhu et al. (2012) find that in the presence of a giant
+planet, grains ≳ 10−100 µm are trapped in the pressure
+bump and this accounts for roughly 99% of the dust
+mass (assuming a grain size distribution n(a) ∝ a−3 in
+the outer disk, where grains have already grown to mm
+sizes, only 1% of the dust mass is in small micron-sized
+grains). Thus the material that moves inward is heavily
+depleted in solids. Therefore, the relative abundance of
+refractory elements accreting onto the star should also
+be depleted relative to volatile elements. In the case of
+Herbig stars with radiative exteriors, this could result in
+a photospheric abundance pattern where refractory ele-
+ments are depleted relative to volatile elements (i.e., the
+λ Bo¨o phenomenon, Kama et al., 2015, see Sect. 6.2.1).
+Another feature that can be induced by a planet in
+a disk are spiral arms (e.g., Kley and Nelson, 2012).
+If the planet is sufficiently massive, spiral arms can be
+observed in scattered light (planet to stellar mass ratio
+q ≳ a few × 10−3; Dong et al. 2015). This is a kine-
+matic effect that results in increasing the scale height
+of the disk above the spiral arm such that the disk in-
+tercepts more light. Furthermore, Dong et al. (2016)
+used hydrodynamical and radiative transfer simulations
+to determine how the disk appearance depends on its
+inclination and position angle. To summarize, a giant
+planet cannot only create a cavity but, with he right
+parameters (α, h/r, Mplanet) also rings or spiral arms,
+or simply cause asymmetries.
+Turning to the inner disk, we find a puffed-up inner
+wall at the dust evaporation radius located behind an
+optically thin gas-rich region (Sect. 4.3, Natta et al.
+2001). This model was further refined by Isella and
+Natta (2005), who realised that, as the dust evapora-
+tion temperature is density dependent, and there is a
+vertical density gradient in the disk, the inner wall will
+be curved, rather than have a sharp edge. Due to this
+curvature, the NIR excess will weakly depend on the
+inclination, while the observed shape will strongly de-
+pend on the inclination. Face-on disks will reveal rims
+that appear axisymmetric, while inclined disks will re-
+veal rims that appear elliptic, with one side brighter
+than the other one. Furthermore, Kama et al. (2009)
+showed that the rim morphology depends on the dust
+grain size, composition and the inner disk surface den-
+sity.
+In the following sections we will discuss how obser-
+vations compare with these predictions. We will first
+look at the outer regions of the disk and then continue
+with the inner disk, before discussing the different sub-
+structures seen in the disk.
+4.9.2 Observations of the outer disk region
+As we mentioned in Sect. 4, the first time a disk was re-
+solved was through mm interferometry (Mannings and
+Sargent, 1997). In a recent study, Stapper et al. (2022)
+analyzed archival ALMA data of 36 Herbig stars within
+450 pc. For the disks with d < 225 pc, 15/25 ‘nearby’
+disks are resolved, but this sample was likely biased to-
+wards the brightest objects. However, given that there
+are only 31 Herbig stars within 225 pc, we can conclude
+that at least 50% of them are resolved, all of which show
+substructure.
+Another way to obtain high spatial resolution is to
+move to shorter wavelengths. Optical and NIR images
+trace light that is scattered off the disk surface by small,
+submicron-sized dust grains, but the stellar brightness
+limits how close to the star one can get (inner working
+angle). Instruments such as SPHERE and the Gemini
+Planet Imager (GPI) use polarimetric differential imag-
+ing (PDI) techniques to remove the light of the central
+star and reveal the scattered light of the disk. What re-
+mains is light polarized by the dust grains in the disk.
+The inner working angle of PDI on 8m class telescopes
+is typically 0.1′′, or 15 au at a distance of 150 pc.
+A comparison between ALMA and SPHERE obser-
+vations of the outer disk has shown that the large and
+small grains are not always co-spatial, with the larger
+grains being more radially confined than the smaller
+ones (e.g. the GI star HD 97048, large grains seen up
+to 350 au, small grains up to 640 au; Walsh et al., 2016).
+On the other hand, the small grains are more or less co-
+spatial with the gas, indicating that they are dynami-
+cally coupled.
+Another important result is that the extent of the
+disk in the mm continuum is often much smaller than
+that of the gas, derived from low-J pure rotational CO
+transitions: e.g. 350 vs. 750 au in HD 97048 (Walsh
+et al., 2016), and 375 vs. 1000 au for HD 34282 (van
+der Plas et al., 2017a). These results were confirmed in
+a larger study (Taun, MSc 2020; see Sect. 5.5).
+The differences in disk sizes do not only depend on
+the material being traced (large or small dust grains,
+
+30
+Sean D. Brittain et al.
+or gas), but also on the disk group considered. Based
+on SED modeling, Dominik et al. (2003) proposed that
+GII disks are smaller than GI disks, an idea that now
+can be tested as we can often obtain high enough spa-
+tial resolution. Early on, GI sources were routinely re-
+solved with ALMA, while the few GII sources observed
+were either unresolved or small (< 100 au; e.g. Walsh
+et al. 2016, van der Marel et al. 2021). Stapper et al.
+(2022) further showed that, on average, GII disks are
+more compact than GI disks, although this trend is
+mainly caused by 3 outliers (AB Aur, HD 97048 and
+HD 142527; see Fig. 19), and bright disks such as the
+GI source HD100546 (68% radius of 35 au) have similar
+sizes as the GII disks.
+Fig. 19 The dust radius at 68% of the light (ALMA band 6
+or 7) versus stellar mass for stars with d < 225pc. The error
+bars are indicated as well as the upper limits. The largest radii
+are seen in GI sources, but many GI sources have similar sizes
+as GII. Based on Stapper et al. (2022).
+In a study of Herbig disks with SPHERE, Garufi
+et al. (2017b) found that GII disks, when detected in
+scattered light, are much fainter than GI disks which
+are commonly detected. Also their spatial extent is dif-
+ferent: disks around GI sources are detected out to dis-
+tances of 100-600 au, while disks around GII sources
+are usually smaller than 100 au. Indeed, several nearby
+(d≲ 200 pc) GII disks are not resolved at all, such
+as HD 150193A (Garufi et al., 2014), which is a bi-
+nary with a nearby companion (a=1.1′′; Bouvier and
+Corporon 2001) that likely has truncated the disk to
+give it its compact appearance. However, the disk of
+HD 100453, a GI star, is also truncated by a companion
+at 1.1′′ but here the companion is thought to give rise
+to the observed spiral arms reaching out to 42 au (Wag-
+ner et al., 2018). Similar behavior has been observed in
+the MIR with 8m telescopes (e.g. Honda et al., 2015).
+These differences can be attributed to larger gaps (> 5
+au) and/or larger flaring angles in GI disks, while GII
+disks are either small or self-shadowed (Garufi et al.,
+2017b).
+However, from a systematic comparison between ALMA
+and SPHERE data, Garufi et al. (2022) found that the
+extent of GII disks in scattered light is much smaller
+than that at mm wavelengths, due to the outer disk
+only being partially illuminated. This is in stark con-
+trast with the observations of GI disks, where the ex-
+tent in scattered light is larger than that in the mm,
+as seen in e.g. HD 97048 (Walsh et al., 2016). This is
+because GII disks are flat and/or self-shadowed, while
+GI disks are flared, so that their disk surfaces can be
+traced much further out.
+4.9.3 Observations of the inner disk region
+In a pioneering study of TTSs and Herbig stars with
+the IOTA interferometer, Monnier and Millan-Gabet
+(2002) found a correlation between the ‘size of the in-
+ner disk’, measured in the H- or K-band, and the stellar
+luminosity. They explained this finding with an inner
+rim at the dust evaporation radius, located behind an
+optically thin inner region. Later, Monnier et al. (2005)
+measured more Herbig disks in the K-band with the
+Keck Interferometer and found sizes between 0.02 and
+4 au, in agreement with emission at the dust evapora-
+tion radius, and showed that, for spectral types A to
+late B, the inner disk size can be related to the stellar
+luminosity as R ∝ √L∗.
+Another important clue about the inner disk region
+came from studying the brightness variations of UXors
+that show the blueing effect due to obscuration by dust
+in the line of sight (see Sect. 2.3.2). Dullemond et al.
+(2003) realized that the variability timescale of weeks
+to months means that the obscuring cloud must be in
+the inner disk, at the location of a puffed-up inner rim.
+They also showed that this effect would only be seen
+in GII disks, where the line of sight towards the inner
+rim remains largely undisturbed. The blueing effect in
+UXors is thus caused by the clumpy nature of the inner
+disk.
+Lazareff et al. (2017) observed 51 Herbig stars with
+PIONIER, a NIR interferometric instrument that com-
+bines the 4 VLT telescopes. They found that the in-
+ner rims are smooth, radially extended, and consistent
+with axisymmetry. However, Kluska et al. (2020) fur-
+ther studied the inner disk rim morphology with PI-
+ONIER, reaching a spatial resolution of a few milli-
+arcseconds, and found evidence for a non-axisymmetric
+structure in 27% of the objects. This could be due to
+warping of the inner disk or instabilities at the inner
+rim, potentially linked to the presence of a compan-
+
+group I
+HD142527
+200
+group II
+ABAur
+HD97048
+150
+100
+50
+1.50
+1.75
+2.00
+2.25
+2.50
+2.75
+3.00
+3.25
+M*(M。)Herbig Stars
+31
+ion. MATISSE, also combining 4 telescopes but now
+in the L, M and N band (Lopez et al., 2022), uncov-
+ered L′-band variable brightness asymmetries in the
+disk of HD 163296 at scales < 0.3 au (Varga et al.,
+2021). Such variations are also detected in the H and
+K band, and persist over several years (GRAVITY Col-
+laboration et al., 2021). They reflect an orbiting, in-
+homogeneous dust distribution in the innermost disk
+regions, similar to what was already predicted from the
+UX Ori-like brightness and color variations.
+4.9.4 Disk substructures
+More detailed ALMA observations of disks with a cav-
+ity reveal substructures (for an overview see Andrews,
+2020, van der Marel et al., 2021), some of which are
+shown in Fig. 20. Multiple rings were found in e.g.
+HD 169142 (Fedele et al., 2017) and HD 97048 (Walsh
+et al., 2016, van der Plas et al., 2017b). Other objects,
+such as HD 142527, show asymmetries and/or shadows,
+which are referred to as horseshoes (Casassus et al.,
+2013). Finally, some objects show spiral arms: e.g. AB
+Aur (Tang et al., 2017).
+Fig. 20 ALMA continuum images illustrating the variety
+in structure present in the Herbig disks. The beam size is
+indicated in the lower left. The tickmarks go from -1.5′′ to
++1.5′′for HD 169142, HD 163296 and MWC758, and from -
+3′′ to +3′′for HD 142527. Figure from van der Marel, private
+communication, after van der Marel et al. (2021)
+.
+Zhang et al. (2018) created a 2-D hydrodynamical
+gas + dust model grid to study the effect the disk pa-
+rameters viscosity, scale height and planet mass have
+on the presence of gaps in the disk. From a compari-
+son with the DSHARP ALMA survey (Andrews et al.,
+2018b), they deduced that the observed disk gaps could
+be caused by planets located beyond 10 au with masses
+between that of Neptune and Jupiter. More massive
+planets, the super-Jupiters, are capable of carving out
+larger (> 20 au) cavities in a disk, as shown by hydro-
+dynamical modelling of PDS 70 (Muley et al., 2019).
+With more and more objects being observed with
+ALMA, a reflection on the methods used for interpreta-
+tion is needed. Kim et al. (2019) performed a synthetic
+analysis to determine the best set of ALMA bands to
+derive the dust properties of the T Tauri star TW Hya
+and concluded that, in order to constrain the tempera-
+ture profile properly, several ALMA bands are needed,
+preferably with the largest frequency intervals possi-
+ble, and covering both optically thin and optically thick
+emission. Such an analysis likely also applies to Herbig
+stars, meaning that the ALMA bands with which the
+disk is observed should be carefully selected to include
+frequencies that trace both optically thin and optically
+thick emission.
+2
+2.1
+2.3
+2.6
+3.3
+4.7
+7.6
+13
+24
+47
+9
+100
+150
+200
+250
+300
+260
+240
+220
+200
+180
+160
+140
+50
+0
+50
+100
+150
+140
+120
+100
+80
+60
+40
+20
+-200
+0
+200
+400
+600
+800
+1000
+800
+700
+600
+500
+400
+300
+200
+100
+0
+300
+350
+400
+450
+500
+550
+600
+650
+650
+600
+550
+500
+450
+400
+2
+2.1
+2.3
+2.6
+3.3
+4.7
+7.6
+13
+24
+47
+9
+100
+150
+200
+250
+300
+260
+240
+220
+200
+180
+160
+140
+50
+0
+50
+100
+150
+140
+120
+100
+80
+60
+40
+20
+-200
+0
+200
+400
+600
+800
+1000
+800
+700
+600
+500
+400
+300
+200
+100
+0
+300
+350
+400
+450
+500
+550
+600
+650
+650
+600
+550
+500
+450
+400
+2
+2.1
+2.3
+2.6
+3.3
+4.7
+7.6
+13
+24
+47
+9
+100
+150
+200
+250
+300
+260
+240
+220
+200
+180
+160
+140
+50
+0
+50
+100
+150
+140
+120
+100
+80
+60
+40
+20
+-200
+0
+200
+400
+600
+800
+1000
+800
+700
+600
+500
+400
+300
+200
+100
+0
+300
+350
+400
+450
+500
+550
+600
+650
+650
+600
+550
+500
+450
+400
+2
+2.1
+2.3
+2.6
+3.3
+4.7
+7.6
+13
+24
+47
+9
+100
+150
+200
+250
+300
+260
+240
+220
+200
+180
+160
+140
+50
+0
+50
+100
+150
+140
+120
+100
+80
+60
+40
+20
+-200
+0
+200
+400
+600
+800
+1000
+800
+700
+600
+500
+400
+300
+200
+100
+0
+300
+350
+400
+450
+500
+550
+600
+650
+650
+600
+550
+500
+450
+400
+HD135344B
+HD100453
+HD142527
+HD97048
+20 au
+20 au
+20 au
+20 au
+Fig. 21 Key examples of disks observed with SPHERE in
+PDI: spiral arms (HD 135344B and HD 100453), a large cav-
+ity (HD 142527) and rings (HD 97048). Note the large dif-
+ferences in scale between the different panels: HD 100453 is
+much smaller than HD 142527 and would fit 3-4 times in-
+side its cavity. A. Garufi, private communication, after Garufi
+et al. (2017a).
+Scattered-light observations probe small grains and
+thus can be used to constrain the flaring surface of
+a disk as was done for HD 100546 (Avenhaus et al.,
+
+HD169142
+HD163296
++
+HD142527
+MWC75832
+Sean D. Brittain et al.
+2014, Stolker et al., 2016) and HD 97048 (Ginski et al.,
+2016). Large scattered light surveys of protoplanetary
+disks were made with GPI on Gemini South (Macintosh
+et al., 2008), High-Contrast Coronographic Imager for
+Adaptive Optics (HiCiAO) on Subaru (Tamura, 2009)
+and SPHERE on the VLT (Garufi et al., 2017b), uncov-
+ering a wide variety in disk substructures (see Fig. 21).
+Spirals were seen in e.g. HD 135344B (Muto et al.,
+2012, Garufi et al., 2013) and HD 36112 (MWC758;
+Grady et al., 2013, Benisty et al., 2015), while rings
+were found in e.g. HD 169142 (Quanz et al., 2013b)
+and HD 97048 (Ginski et al., 2016). Other disks, such
+as those around AB Aur (Hashimoto et al., 2011) and
+HD 142527 (Avenhaus et al., 2014) show large, asym-
+metric structures that could be seen as parts of spiral
+arms or even rings. Indeed, Dong et al. (2016) studied
+the effect the inclination and position angle (PA) of the
+disk has on its observed appearance, and found that a
+disk with 2 spiral arms might be masked as an asym-
+metric structure with either only one trailing arm, or
+two arms on the same side of the star, possibly wind-
+ing in different directions. The interpretation of inclined
+disks should, therefore, take into account this masking
+effect.
+Garufi et al. (2018) organized the disks according
+to their appearance in scattered light and found that
+bright GI disks show spirals, rings, and bright rims at
+the edge of a cavity, while other disks (mainly GII)
+are faint and/or compact and show no such features.
+They related the disk features with the NIR excess, and
+found that sources with spirals or shadows have a high
+NIR excess, while sources with rings show a low NIR
+excess. Sources with a GII disk have an intermediate
+NIR excess. The high NIR excess could be attributed to
+the presence of a massive (≥ 1MJup) planet perturbing
+the orientation and scale height of the inner disk and
+finally causing spiral waves.
+Bohn et al. (2022) compared the inclination of the
+inner (< 1 au) and outer (> 10 au) disks as derived from
+VLTI/GRAVITY and ALMA (CO) observations. When
+the inner and outer disks are misaligned, it is expected
+that the inner disk will cast a shadow on the outer
+disk. For those 3 GI sources where misalignment was
+observed, Bohn et al. (2022) predicted the location of
+the shadow, and found this to agree well with scattered
+light observations.
+It is surprising to see that the substructures derived
+from scattered light and thermal emission do not al-
+ways coincide. For instance, HD 100453 shows spirals in
+scattered light, but only a ring disk in thermal emission
+(Wagner et al., 2015, van der Plas et al., 2019). In gen-
+eral, spirals are more often detected in scattered light
+than in thermal emission, indicating that the micron-
+sized grains experience more the effect of density waves
+in the disk. For example, HD 163296 has an SED that
+places it at the boundary of GI and GII disks. Muro-
+Arena et al. (2018) found that, while the mm contin-
+uum data show several rings, scattered light images
+only trace the innermost ring, leading the authors to
+conclude that the outer disk is either more depleted of
+small grains or more settled. However, in multi-epoch
+HST/STIS images, four rings were detected (Rich et al.,
+2020), with the fourth ring located at 330 au. Similarly,
+Tang et al. (2017) found 2 CO spirals inside the large
+mm cavity of AB Aur, that were confirmed in scattered
+light (Boccaletti et al., 2020). However, the spiral arms
+that were detected in CO in the outer disk are not seen
+in scattered light.
+Summary: The preferred scenario to form a gap in the
+disk is a pressure bump, either caused by a planet or
+a dead zone. While the large particles are trapped, the
+smaller particles can move inwards with the gas as they
+are dynamically coupled. Dust filtration might lead to
+selective accretion of gas rich in volatiles, so that the
+stellar photosphere is depleted in refractory elements.
+The inner rim is located at the dust evaporation
+radius and has a puffed-up curved inner wall whose
+properties depend on the grain size distribution and
+inclination. Once a disk is resolved, it often shows some
+substructure like rings, spirals or asymmetries. Small
+micron-sized grains are found both closer to and further
+from the star than the large mm-sized grains. These
+distinct locations can be explained by a combination
+of radial drift (large grains) and dust filtration (small
+grains). At mm wavelengths, some GI disks are very
+large, while many other GI and GII disks overlap in size;
+however, not that many GII sources have been observed
+with sufficient spatial resolution. In scattered light (op-
+tical/NIR), GI disks are routinely resolved while GII
+are either faint or undetected. Contrary to GI disks,
+GII disks are smaller in scattered light than in mm
+emission, due to self-shadowing.
+To conclude this dust section, the combination of
+improved spectral coverage in the IR with space-based
+observatories and sub-arcsecond resolution imaging at
+optical/NIR and mm wavelengths on the ground has
+revolutionized our understanding of the dust disks sur-
+rounding Herbig stars. It is clear that the IR-mm ex-
+cess of Herbig stars arises from disks with remarkable
+structures including gaps, rings, and spiral arms. These
+disks also have a rich mineralogy indicative of signifi-
+cant dust processing and grain growth. There is strong
+evidence that the differences between GI and GII disks
+are tied to the presence of gaps in the disk. GI disks
+are flaring and have large gaps, while GII disks appear
+
+Herbig Stars
+33
+to be compact and/or shadowed. The old evolution-
+ary scenario where disks evolve from GI to GII is not
+consistent with later studies. Instead, a large GII disk
+where no or only a small gap is present might open
+up a larger gap and become a GI disk while small GII
+disks may stay small and gradually lose their content as
+they evolve into debris disks. Alternative, GI and GII
+disks may follow independent evolutionary paths. The
+extent to which these differences reflect differences in
+the early evolution of the circumstellar disk and enve-
+lope or interactions with massive companions remains
+unclear. Even though the gaps in GI disks are com-
+monly attributed to planets, the influence that stellar
+and planetary companions have on the evolution of the
+disk remains an important open question.
+5 GAS IN DISKS AROUND HERBIG STARS
+Early interferometric observations with OVRO of 12CO
+J = 2 − 1 revealed a rotating disk of gas around the
+star MWC 480 (Mannings et al., 1997). Several pioneer-
+ing surveys have since then systematically targeted the
+intrinsically strong CO (sub-)mm lines as key tracers
+for the disk bulk gas content (e.g. Zuckerman et al.,
+1995, Dent et al., 2005, Hales et al., 2014) and find
+that disks around many young Herbig stars contain
+traceable amounts of cold (a few 10 K) gas. Due to
+the large range of temperatures present — a couple of
+1000 K in the inner disk (< few au) to a few 10 K
+in the outer disk (≳ 100 au) — the emission of gas
+is traced over a wide range of wavelengths. The cold
+outer disk is mostly traced at far-IR to mm wavelengths
+(e.g. low rotational lines of CO), while the inner disk
+is traced by near- to MIR wavelengths. Due to their
+brightness and warm temperatures (stellar luminosities
+heating the disk range from a few to a few 10 L⊙),
+Herbig disks are generally easier to detect and to spa-
+tially resolve compared to T Tauri disks. This enables
+studying many processes related to disk evolution and
+planet formation in more detail. The main drawback
+here is the often small sample sizes and less well con-
+strained ages of these objects (Sect.2). In the follow-
+ing, we summarize our current understanding of the
+physics, chemistry and physical processes pertaining to
+the gas inside these disks that we obtained based on
+multi-wavelengths observations.
+5.1 How and when do Herbig disks lose their gas?
+As summarized in section 4, the classification scheme of
+Herbigs is largely based on the distribution of dust in
+the disk, however, gas comprises 99% of the disk mass.
+Ideally, the evolutionary state of Herbig disks would be
+informed by the evolution of the gas mass of the disk
+as they evolve from gas rich accretion disks to dusty
+debris disks.
+Several methods using far-IR and sub-mm line emis-
+sion have been proposed to study disk gas masses di-
+rectly: (1) The CO sub-mm line emission (Thi et al.,
+2001), (2) the [O i] 63 µm line together with the CO
+sub-mm line (Kamp et al., 2011), (3) HD lines (Bergin
+et al., 2013), and (4) the CO isotopologue sub-mm lines
+(Williams and Best, 2014, Miotello et al., 2016). Below,
+we present an overview of the results from such obser-
+vational attempts.
+Dent et al. (2005) conducted a northern survey of
+the 12CO J = 3−2 line in bright Herbig disks using the
+JCMT. Following this up, Hales et al. (2014) carried
+out an APEX/ASTE survey targeting the 12CO J =
+3 − 2 line in 52 southern Herbig disks. They report
+that ∼ 45 % of the IR bright disks (LIR/L∗ ≥ 0.01) —
+21 out of 46 in the combined sample — are not de-
+tected in CO, the pre-ALMA, sensitivity limit being
+∼ 104 Jy km/s pc2. At the faint end of IR excesses this
+has been continued using ALMA by Mo´or et al. (2017)
+to detect the 12CO J = 2 − 1 line in young A-type
+debris disks (10 − 50 Myr); they find that CO emission
+does not correlate with IR excess (104−106 Jy km/s pc2
+for objects with LIR/L∗ <0.01). P´ericaud et al. (2017)
+did a similar study focusing on debris disks around
+A-type stars younger than 100 Myr using APEX and
+IRAM, targeting the 12CO J = 2 − 1 and 3 − 2 lines.
+Folding in literature data on T Tauri and Herbig disks,
+they identify a general correlation between CO line flux
+and mm(sub-mm) continuum flux; however, this corre-
+lation is strongly driven by the T Tauri disks. They also
+find a subclass of disks around A-type stars which have
+CO line fluxes brighter than the above correlation pre-
+dicts based on their sub-mm continuum flux and termed
+them “hybrid” disks (HIP 76310, HIP 84881, HD 21997,
+HD 131835, 49 Cet, HD 141569). Some of these sources
+show indications of inner dust cavities (a few to several
+10 au) (HIP 76310, HIP 84881, HD 21997, HD 131835,
+Lieman-Sifry et al., 2016, K´osp´al et al., 2013, Hung
+et al., 2015) and/or rings (HD 141569, 49 Cet, Augereau
+et al., 1999, Wahhaj et al., 2007, Biller et al., 2015).
+This places them into the category of transitional disks
+(see Sect. 4.8), but the two classifications (based on ei-
+ther dust or gas observables) do not necessarily agree
+for all objects.
+Williams and Best (2014) proposed to combine the
+two less abundant isotopologues 13CO and C18O to es-
+timate disk gas masses. This method has been refined
+using thermo-chemical disk models by Miotello et al.
+(2016) including isotope selective photodissociation for
+
+34
+Sean D. Brittain et al.
+the regime of TTauri and Herbig disks. This technique
+produces in general gas-to-dust mass ratios in disks
+that are well below the canonical one of 100 (e.g. Ans-
+dell et al., 2016, Miotello et al., 2017). Since this result
+is hard to reconcile with the estimated mass accretion
+rates, carbon element depletion is often invoked as an
+explanation.
+Thermo-chemical disk models have shown that the
+[O i] 63 µm emission requires excitation temperatures of
+several 10 K and typically originates from inside 300 au
+(Kamp et al., 2010). The [O i]/CO line ratio serves
+here as a temperature proxy and the [O i] 63 µm line
+emitting region shifts with disk mass, indicating that
+the combination of the line ratio and the [O i] 63 µm
+line flux could be a reliable tool to estimate the total
+disk gas mass. Meeus et al. (2012) applied this method
+to the GASPS5 sample of Herbig disks deriving disk
+gas mass estimates in the range 2.4 × 10−4 (HD 36112)
+to 2.5 × 10−2 M⊙ (HD 163296), spanning two orders
+of magnitude. However, using the ages recently deter-
+mined from Gaia DR2 (Vioque et al., 2018), there is no
+clear trend of gas mass with age between 5 and 15 Myr.
+Likely other disk parameters, such as size play a more
+dominant role. We will come back to this in Sect. 5.5.
+The lowest rotational lines of HD (J = 1 − 0 at
+112 µm and J = 2 − 1 at 56 µm) have not been de-
+tected with Herschel in the disks around Herbig stars
+(Kama et al., 2020). Upper limits on the HD J =1 − 0
+line at this stage can only rule out very massive disks
+(10−1 − 10−2 M⊙) around most sources. Interestingly,
+HD 163296 yields an HD upper gas mass limit of 6.7 ×
+10−2 M⊙, compatible with the estimate based on [OI].
+For HD 163296, many alternative techniques have
+been more recently applied to estimate the gas mass
+(full thermo-chemical disk modeling, dust radial drift,
+the very rare isotopologue 13C17O, Rab et al., 2020,
+Woitke et al., 2019a, Powell et al., 2019, Booth et al.,
+2019), all of them now converging on a fairly high disk
+gas mass of ∼0.2 M⊙. Kamp et al. (2011) have shown
+from thermo-chemical modeling that optical depth ef-
+fects turn disk gas mass estimates via the [O i]/CO
+method into lower limits for gas masses larger than
+10−3 M⊙. So, the [O i]/CO disk gas mass lower esti-
+mate is consistent with the more recent studies. The
+HD upper gas mass limit is lower than many of the esti-
+mates derived using other techniques. Since the method
+of Powell et al. (2019) using dust radial drift6 is inde-
+5 GASPS (Gas Survey of Protoplanetary Systems has been
+an Open Time Herschel Key Program led by Bill Dent (Dent
+et al., 2013)
+6 This method uses dust radial drift in a gas-rich disk to
+estimate gas masses. To first order, the spatial extent of the
+dust emission at different sub-mm wavelength is affected by
+the efficiency of dust drift and hence amount of gas in the
+pendent of element abundances, the most probable rea-
+son for this gas mass discrepancy could be in the gas
+temperatures underlying the HD estimate. The conver-
+sion from line flux to gas mass is very sensitive to the
+gas temperature (Bergin et al., 2013) and if 2D thermo-
+chemical disk models are used, the model gas temper-
+ature depends strongly on the properties of the dust
+(e.g., grain size distribution, composition, and settling).
+The masses of disks are in tension with the stel-
+lar accretion rates around Herbig stars (Sect. 3.4). The
+typical accretion rate of Herbig stars is ∼ a few ×10−7
+M⊙yr−1. For such rates to be sustained for ∼1 Myr
+would require disk masses approaching 0.1M⋆ - much
+higher than the typical disk masses inferred from the
+techniques described above.
+Summary: Gas masses in Herbig disks (5 − 15 Myr)
+span about three orders of magnitude with no clear
+trend with age. There is a clear correlation between the
+strength of sub-mm gas emission and sub-mm contin-
+uum emission. This correlation becomes less clear for
+older objects (≫ 10 Myr), where in several objects sig-
+nificant levels of CO gas are detected while the dust
+is clearly of secondary (debris) origin (termed “hybrid”
+disks or “gas-rich” debris disks). So, while continuum
+observations seem to indicate a clear dichotomy be-
+tween primordial and debris dust masses around ∼ 5−
+20 Myr (see Sect. 4.8), it is not clear that the gas follows
+a similar evolution.
+5.2 Turbulence in Herbig disks
+The exquisite sensitivity and spectral resolution of ALMA
+allows now the precise measurement of the width of
+spectral lines. If the gas probed by ALMA is turbulent,
+then the lines should be broader than predicted by the
+sound speed of the gas. Early pre-ALMA estimates of
+gas turbulence were limited by spatial and spectral res-
+olution as well as the S/N of the channel maps (Dartois
+et al., 2003, Pi´etu et al., 2003, 2005, 2007, Hughes et al.,
+2011). ALMA has significantly improved our ability to
+estimate the gas turbulence in the outer disk since its
+high quality data sets (bright sources) allow the sepa-
+ration of the front and back side of the disk and so a
+better disentangling of gas temperature and turbulence.
+Early measurements were strictly applicable only to the
+outer disk (100 au scale), while ALMA can now also
+probe regions closer to the star. Rosenfeld et al. (2013)
+used ALMA science verification data to demonstrate
+the high potential of the gain in spatial and spectral
+disk; strictly, this works only for disks that do not show sub-
+structure.
+
+Herbig Stars
+35
+resolution; they demonstrate the presence of a vertical
+temperature and radial pressure gradient for the disk
+around HD 163296. Estimates of gas turbulence in disks
+keep pushing its upper limits to smaller values, typically
+less than 5-10% of the sound speed at 30-few 100 au (see
+Table 4 and references therein). This has strong impli-
+cations for the process of angular momentum transport
+in these disk, since it implies very low α viscosity values
+for the outer disk (α<10−2, Flaherty et al., 2020).
+Another method for inferring supra-thermal line broad-
+ening of gas is through spectral synthesis of the CO
+overtone bandheads (Carr et al., 2004). The rotational-
+vibrational transitions of the R-branch grow closer to-
+gether with increasing rotational level and eventually
+pile-up at the blue-end of the spectrum before turn-
+ing around moving to redder wavelengths. This pile-up
+is referred to as the bandhead. Because the transitions
+near the bandhead are very closely spaced, the instrinsic
+width of the lines affects the opacity of the bandhead
+(i.e., the shape of the lines determines the opacity of
+the pseudo continuum). Thus even without spectrally
+resolving the individual lines comprising the bandhead,
+the intrinsic line broadening of the lines can be inferred
+from the emergent flux. Because of the large number
+of transitions involved, the temperature of the gas is
+well constrained. Further, the shape of the bandhead
+is determined by the bulk motion of the gas allowing
+for the determination of the radial extent of the emis-
+sion if the stellar mass and disk inclination are known.
+This method has been used to measure the turbulent
+velocity of gas in the disk atmosphere within the inner
+∼1 au of intermediate mass stars such as WL 16 (where
+the turbulent broadening is twice the sound speed; Na-
+jita et al. 1996), SVS 13 (1.5-3 times the sound speed;
+Carr et al. 2004), V1331 Cyg (∼ the sound speed; Na-
+jita et al. 2009, Doppmann et al. 2011), and HD 101412
+(≲ the sound speed; Adams et al. 2019). However, there
+is no direct tension with the (sub)mm measurements
+that probe the turbulence in the disk at much larger
+distances from the star.
+There are alternative methods suggested to esti-
+mate the gas turbulence in disks around Herbig stars
+and to understand the underlying driving mechanism:
+smoothed out snow lines (concentration gradients, Owen,
+2014), dust settling (mm-dust grains confined to a geo-
+metrically thin midplane, Pinte et al., 2016), vortices in
+disks (stability, Zhu and Stone, 2014), planet induced
+structures (morphology, de Juan Ovelar et al., 2016),
+and outer gas disk shape (sharpness, Facchini et al.,
+2017). SED shapes contain information on dust settling,
+though the problem of fitting them is highly degener-
+ate. Mulders and Dominik (2012) show that the median
+SED shapes of brown dwarf, T Tauri and Herbig disks
+are consistent with a low turbulent α value, not depend-
+ing on the (sub-)stellar mass. Comparing ALMA dust
+and gas observations with 2D hydrodynamical mod-
+els shows that the turbulence affects the sharpness of
+planet-induced gaps, ring-gap separation, and the gas-
+to-dust mass ratio inside (Lin and Papaloizou, 1993,
+Long et al., 2018, Liu et al., 2018). For HD 163296,
+Liu et al. (2018) deduce a smaller α in the inner disk
+(∼60 au) compared to the outer disk (>100 au); how-
+ever, α stays well below 10−2.
+Given the observed mass accretion rates (Sect. 3.4),
+it remains unclear what the underlying driving mecha-
+nism is and if the turbulence depends strongly on radial
+distance from the star. Non-ideal MHD effects causing
+disk winds could offer a solution here (Bai, 2013, Ri-
+ols and Lesur, 2018). In their review, Hartmann et al.
+(2016) suggested that different mechanisms might cause
+turbulence in the different disk regions (thermally and
+non-thermally activated MRI, winds, non-ideal MHD
+effects).
+Summary: ALMA has enabled the measurements on
+non-thermal broadening of gas lines which place upper
+limits on the turbulence of the gas in the outer disk at
+≲ 5−10% of the sound speed. For a hand full of objects
+with CO bandhead emission, high resolution NIR spec-
+troscopy has been used to measure non-thermal broad-
+ening of the gas in the innermost disk that is compa-
+rable to the sound speed. Other observational evidence
+points to minimal turbulence in the outer disk includ-
+ing smoothed out snow lines, dust settling, vorticies in
+disks, planet induced structures, and the sharpness of
+the boundary of the outer disk.
+5.3 Are Herbig disk surfaces flaring or flat?
+Scattered light observations of small dust grains can
+trace the shape of the disk surface (see Sect. 4.9). Direct
+observations of gas emission can also reveal how the
+stellar luminosity is reprocessed by the disk and hence
+provide indirect evidence of the degree to which the disk
+surface is flaring.
+An example is the Herschel survey of the [O i] 63 µm
+line (Open Time Key Program GASPS, Dent et al.,
+2013). Comparing the data with a large grid of thermo-
+chemical disk models (Woitke et al., 2010, Kamp et al.,
+2011), Pinte et al. (2010) show that the brightness of
+this cooling line agrees with a stellar UV heating mech-
+anism. Meeus et al. (2012) confirm this by demonstrat-
+ing a clear correlation between the UV stellar flux and
+the line luminosity for the GASPS sample of 20 Herbig
+disks. However, they do not find a correlation between
+the SED slope (IR-mm) and the strength of the [O i]
+
+36
+Sean D. Brittain et al.
+Table 4 Overview of turbulence measurements for Herbig Ae disks.
+object
+tracer
+method
+vturb [cs]
+reference
+inner disk (few au)
+V1331 Cyg
+NIR CO bandhead and water
+spectrum
+∼ 1
+Najita et al. (2009)
+HD 101412
+NIR CO bandhead and water
+spectrum
+∼ 1
+Adams et al. (2019)
+outer disk
+HD 34282
+CO sub-mm isotopologues
+visibilities
+< 1
+Pi´etu et al. (2003, 2005, 2007)
+AB Aur
+MWC 480
+HD 163296
+CO sub-mm
+channel maps
+∼ 0.4
+Hughes et al. (2011)
+HD 163296
+CO sub-mm isotopologues
+channel maps
+< 0.03
+Flaherty et al. (2015)
+HD 163296
+DCO+
+channel maps
+< 0.04
+Flaherty et al. (2017)
+MWC 480
+CO sub-mm
+channel maps
+< 0.08
+Flaherty et al. (2020)
+cooling line. In contrast, the CO high-J rotational lines
+are only detected in disks that show a shallower SED
+slope (group I, Meeus et al., 2013). However, Sect. 4
+clarifies that the SED slope is not necessarily a direct
+reflection of the amount of disk flaring. The CO ladders
+for the few GI Herbig disks that show line detections
+with sufficient coverage in J stay flat between J = 10
+and 20 (see Fig. 22). According to thermo-chemical
+models, this is a trend seen in moderate to strongly
+flaring disks such that β ≥ 1.15, where β is the power
+law exponent of the radial dependence of the gas scale
+height (i.e., H(r) ∝ rβ; Woitke et al., 2010).
+The [O i] fine structure lines react strongly to the
+amount of disk flaring (Woitke et al., 2010), but sev-
+eral other parameters play an important role as well
+such as inner gaps, dust settling and the stellar heating.
+The CO ladder also reacts to flaring (Bruderer et al.,
+2012, Fedele et al., 2016) — the ladder drops steeply
+beyond J = 10 for flat disks due to the altered gas
+temperature profile — and here the gas-to-dust mass
+ratio is the most cofounding other variable. The Her-
+big disks differ substantially in their geometry, making
+a simple ”grid” approach for the interpretation of ob-
+servational data rather difficult. Recently, the DIANA
+project (DIsc ANAlysis; Woitke et al., 2019a) mod-
+eled six of these Herbig disks consistently using multi-
+wavelength dust and gas observations with a unified
+thermo-chemical modeling approach. The observational
+data includes the far-IR [O i] and CO rotational lines.
+For all except one of the disks (AB Aur), they find the
+need for a flared outer gas disk 1.19≥β ≥1.07, a range
+that is well below the maximum Chiang and Goldreich
+solution (β =9/7, Chiang and Goldreich, 1997).
+The geometry of the upper tenuous layers of the in-
+ner disk is much better probed using lines that predom-
+inantly originate there, i.e. the forbidden [O i] 6300 ˚A
+line (Finkenzeller, 1985, Acke et al., 2005, van der Plas
+et al., 2008). The excitation mechanism for the line can
+be thermal (gas temperature of a few 1000 K or non-
+thermal (photodissociation of OH, St¨orzer and Hollen-
+Fig. 22 Compiled CO ladders for six Herbig disks. Over-
+plotted are the normalized modelled CO ladders for a typical
+Herbig disk by Fedele et al. (2016). The three lines repre-
+sent disks with different flaring angles, β = 1.05 (red), 1.15
+(green), 1.25 (blue).
+The models have been normalized to the observed J=10 − 9
+line flux; for IRS48 we used the first detected J line.
+bach, 2000). Due to the limited spectral resolution in
+earlier work, the origin of this line emission remained
+disputed: infall, wind or disk origin. Acke et al. (2005)
+found that the majority of Herbig disks show narrow
+symmetric profiles (FWHM∼ 50 km/s), with the line
+profiles observed towards GII sources being on average
+∼ 20 km/s broader than the line profiles observed to-
+
+2
+2
+0
+AB Aur
+HD97048
+1
+0
+10
+20
+30
+40
+0
+10
+20
+30
+40
+Jup
+Jup
+2
+2
+1
+0
+0
+HD100546
+HD163296
+0
+10
+20
+30
+40
+0
+10
+20
+30
+40
+Jup
+2
+2
+山
+0
+0
+HD169142
+IRS48
+1
+0
+10
+20
+30
+40
+0
+10
+20
+30
+40
+Jup
+JupHerbig Stars
+37
+−40
+−20
+0
+20
+40
+1.0
+1.1
+1.2
+1.3
+−40
+−20
+0
+20
+40
+Velocity (km s−1)
+1.0
+1.1
+1.2
+1.3
+Normalized Flux
+Fig. 23 Comparison of the [O i] 6300 ˚A(black), v = 1−0 OH
+P4.5 (blue) and the v = 1 − 0 P26 CO (red) line profiles from
+the disk around HD 100546.
+ward GI sources. Also, the detection rate of this line is
+much lower in GII disks than in GI disks. Several of the
+line profiles display the characteristic double peak sug-
+gesting an origin within a rotating disk. van der Plas
+et al. (2008) investigate the radial intensity profiles of
+the [O i] line and find that it can be related to the in-
+ner disk geometry (puffed up regions casting shadows
+on regions further out). Interestingly, HD 101412 shows
+two emission peaks, possibly indicating that there is a
+second ’puffed’ up region at larger distances (few au);
+this is a feature seen in hydrostatic disk models (e.g.
+Woitke et al., 2009, Min et al., 2009, Meijerink et al.,
+2012, a second shadow for the tenuous surface layers).
+In some cases (e.g. the Herbig Be star MWC 147, Bag-
+noli et al., 2010), the line emission could even originate
+from inside the dust sublimation radius.
+The OH P4.5 doublet (2.934 µm) was been detected
+in 4/5 GI disks and 0/6 GII disks by Fedele et al.
+(2011), sometimes showing very complex profiles sug-
+gesting multiple radial emission zones. Brittain et al.
+(2016) detected the OH P4.5 doublet in about 50% of
+the Herbig disks in their sample; again, the detection
+rate is much higher for the GI disks (61%) than GII
+disks (25%). The line profile of the high J CO line and
+the OH doublet are consistent (see Fig. 23). The fact
+that OH is more readily observed among GI disks indi-
+cates that that OH photodissociation could contribute
+to the excitation of the [O i] 6300 ˚A line (Fedele et al.,
+2011).
+Also [Ne ii] emission at 12.81 µm is often used to
+probe jets, outflows and disk winds. Baldovin-Saavedra
+et al. (2012) detected this line for the first time in a
+disk around a Herbig Be star (V892 Tau); its centrally
+peaked narrow line profile is consistent with a photo-
+evaporative wind. Since this line requires the presence
+of X-rays, most of the work so far has been focused
+on T Tauri disks (e.g. Pascucci et al., 2011, Baldovin-
+Saavedra et al., 2012, Sacco et al., 2012). A more sys-
+tematic study combining high spectral resolution (3 −
+10 km/s) optical ([O i] 6300 ˚A) and IR spectra (OH and
+CO ro-vib, like shown in Fig. 23) with dust interferom-
+etry could allow a detailed study of the inner disk gas
+and dust geometry and the potential existence of weak
+disk winds, something that has been piloted by Fedele
+et al. (2008) for three sources.
+Summary: Gas studies suggest that the outer disks of
+Herbigs are moderately flaring (below the theoretical
+maximum of 9/7). However, the inner disks show more
+complex geometries required to interpret gas line pro-
+files, such as shadows and disk winds. A systematic
+study of combined near-IR dust and gas observations
+for a large sample of Herbig disks would help here to
+disentangle the processes shaping the inner disks.
+5.4 Gas temperatures and the position of icelines
+The thermal structure of the disks is a key element
+in understanding planet formation as it determines the
+stability of disks (Toomre Q parameter7) as well as the
+composition of the material that is forming the plan-
+ets (icelines). The midplane of Herbig disks is typically
+optically thick, in the inner disk (<30 au) often up to
+sub-mm wavelengths. Figure 24 illustrates how we can
+either use gas emission lines to infer radial and vertical
+temperature profiles of disks or revert to indirect tracers
+such as the spatial distribution of molecules associated
+with specific icelines (e.g. N2H+, DCO+, water).
+The temperature profiles for the gas can be de-
+rived from molecular emission line studies in several
+ways: (1) interferometric gas line observation (spatial
+and spectral resolution), (2) from a suite of gas line
+profiles (spectral resolution), (3) from a suite of un-
+resolved emission line fluxes from lines with different
+excitation temperatures (e.g. CO ladder). We discuss
+each of these in the following and discuss to which ex-
+tent the conclusions from them agree and also how they
+compare to the dust temperature studies. However, as
+a matter of fact, the continuum optical depth at any
+wavelength limits the vertical depth down to which we
+can probe. For the inner disk (< 30 au), this limits the
+7 This parameter depends on distance from the star r and
+is defined as Q(r) = cs(r)Ω/πGΣg(r), with cs the sound
+speed, Ω the angular velocity, G the gravitational constant
+and Σg the disks gas mass surface density.
+
+38
+Sean D. Brittain et al.
+Fig. 24 Schematic of various methods to assess the disk gas
+temperature profiles and icelines (radially and vertically). In-
+dicated are the key molecular tracers used to derive the tem-
+perature profiles. Arrows indicate how the line emission re-
+gion shifts with increasing rotational quantum number J or
+decreasing Einstein coefficient Aij.
+information we can get since these regions are often op-
+tically thick even at sub-mm wavelengths. Exceptions
+are disks where this region has been partly cleared.
+Interferometric gas line observations Pi´etu et al. (2007)
+derived gas temperature profiles using IRAM/PdB in-
+terferometric data for a suite of CO and HCO+ lines.
+Fitting visibilities with simple power law disk models
+(T ∝rq) for MWC 480, they find gas temperature pro-
+files of the molecular emitting region with power law
+exponents of q = 0.65 for 12CO and shallower (q =
+0.37 − 0.28) for 13CO. They also note a clear vertical
+temperature gradient of several 10 K based on 12CO
+J = 2 − 1, 13CO J = 2 − 1 and J = 1 − 0 lines which
+originate from different heights in the disk. Such values
+agree quite well with typical thermo-chemical disk mod-
+els (Fig. 25, showing extracted radial temperature pro-
+files from the MWC 480 model, Woitke et al., 2019a).
+Flaherty et al. (2015) follow a similar approach but
+use a full 2D power-law disk model. They find fairly
+shallow temperature gradients for all CO isotopologues
+(q=0.216−0.278) in the disk around HD 163296, while
+Isella et al. (2016) find a steeper profile (q=0.6) for the
+molecular layer. However, these results depend to some
+extent on the assumed model parametrization; for ex-
+ample Flaherty et al. (2015) assume the same power law
+exponent for the molecular layer and midplane temper-
+atures and we know that the dust distribution in this
+disk shows prominent rings inside 200 au and thus devi-
+ates from a simple power law. So, there is a strong push
+to develop methods that are independent of model as-
+sumptions.
+Channel maps with high spatial and spectral resolu-
+tion provide a promising alternative. They can be used
+to reconstruct the temperature profile directly from the
+CO brightness temperature if the dust is optically thin
+Fig. 25 Gas temperature profile in a typical Herbig disk
+model extracted at three different heights in the disk (solid
+lines). Dashed lines show the corresponding dust temperature
+profiles. Black dotted lines show two typical power laws with
+exponents -0.6 and -0.4.
+(assuming optically thick line emission, Pinte et al.,
+2018a, Dullemond et al., 2020). If substantial CO freeze-
+out occurs, this method measures the temperature of
+the CO ice surface, otherwise, it can be used to estimate
+the midplane temperature. For HD 163296, this method
+finds a very shallow temperature gradient (q = 0.14).
+There is considerable agreement for the midplane tem-
+perature profiles for HD 163296 with different methods
+(e.g. estimated temperatures at 100-150 au differ by less
+than 3 K), but the underlying assumptions need to be
+evaluated on a case-by-case basis. For example, detailed
+thermo-chemical models matching the DSHARP data
+(dust and gas) of HD 163296 show significant freeze-out
+of CO in the midplane at 100-150 au (Rab et al., 2020).
+Gas line profiles Fedele et al. (2013) use HD 100546 to
+show that the CO line profiles of CO J =16−15, 10−9
+(Herschel/HIFI) and 3−2 (APEX) become successively
+narrower, thus confirming the shift of their radial ori-
+gin to increasingly larger distance from the star. This
+method had already been suggested by Bruderer et al.
+(2012) based on thermo-chemical disk modeling. The
+resulting best fit temperature profile from simple disk
+power law models has a radial slope of 0.85 ± 0.1 (be-
+tween ∼ 30 and 300 au), steeper than that found for
+MWC 480 and also steeper than what is typically found
+for the dust (Sect. 4.2 and 4.3).
+Emission line flux ladder In the case of spectrally and
+spatially unresolved lines, we use the fact that molec-
+ular emission lines trace the gas temperature in the
+
+C0. H20
+C0. H20
+Aij
+isotopologues
+ices
+N2H+
+HCO+
+150 K
+20 K2.8
+z/r= 0.30
+2.6
+z/r= 0.20
+z/r= 0.15
+2.4
+0.6
+2.2
+人
+2.0
+--0.4
+1.8
+1.6
+1.4
+0.0
+0.5
+1.0
+1.5
+2.0
+log r [au]Herbig Stars
+39
+vertical layer and radial regime over which they emit.
+Interesting tracers in that context are molecules that
+possess a suite of lines with a large range in excita-
+tion energy and Einstein A coefficients. The CO lad-
+der, where the excitation energy (Tex) increases with
+the rotational quantum number (Tex(J = 4) = 55.3 K
+to Tex(J = 36) = 3669 K), scans the disk surface with
+higher rotational lines originating ever closer to the star
+(van der Wiel et al., 2014, Fedele et al., 2016). The
+same holds for the series of OH doublets (Tex rang-
+ing between 120 and 875 K). Also water lines span
+a huge range of excitation conditions. The second di-
+mension, the vertical depth, is probed by studying iso-
+topologues (e.g. 13CO, C17O, C18O, 13C17O), and/or
+by choosing lines with low Einstein A coefficients (e.g.
+water; Notsu et al., 2017). This method to extract radial
+temperature profiles works particularly well at mid- to
+far-IR wavelengths and has been discussed by Brud-
+erer et al. (2012), van der Wiel et al. (2014) based
+on Herschel/PACS and SPIRE CO ladders. Bruderer
+et al. (2012) demonstrate that the gas temperature in
+the disk surface (atmosphere) has to be larger than
+that of the dust in order to explain the CO ladder.
+This is confirmation of earlier work, both theory (Kamp
+and Dullemond, 2004, Jonkheid et al., 2004) and obser-
+vations (Carmona et al., 2008, e.g. H2 MIR observa-
+tions). Fedele et al. (2016) applied simple power law
+and thermo-chemical disk models to FIR data of four
+Herbig disks. The power law temperature gradients de-
+rived from simple models fall in the range 0.5−1.0. The
+observed CO ladders stay flat in many cases out to high
+rotational quantum numbers (J ∼16−20) (Meeus et al.,
+2012, 2013, van der Wiel et al., 2014, see Fig. 22), a be-
+havior that requires a steep temperature gradient in the
+power law disk models, something that can be achieved
+with a high flaring angle in the thermo-chemical disk
+models (Fedele et al., 2016).
+Icelines More indirectly, specific molecules are associ-
+ated with specific phase transitions in the disk, i.e. ice-
+lines. Even though they are pressure dependent, they
+serve as important calibration points for the gas tem-
+perature profiles. Water at the high pressure condi-
+tions in the midplane freezes out at temperatures below
+∼150 K, and CO typically freezes out at around 20 K.
+The term ‘iceline’ can be misleading because the phase
+transition of a molecule does not occur at a single dis-
+tance from the star. Rather it bends towards larger radii
+as the density decreases towards the disk surface. In ad-
+dition, non-thermal desorption processes such as photo-
+desorption and cosmic ray (CR) desorption cause the
+iceline to eventually bend back towards the midplane
+at larger radii where disks become more optically thin
+to UV radiation (stellar and interstellar).
+Icelines can be traced directly using the molecule
+in question and spatially and/or spectrally resolving
+its emission in optically thin lines. Examples of this
+are 13CO observations of HD 163296 (Qi et al., 2011)
+putting the CO iceline at 155 au and low Einstein A
+water lines constraining the snowline in HD 163296 to
+between 8 and 20 au (Notsu et al., 2019). This lat-
+ter work modeled the water line emission to determine
+which isotopes and transitions are most suited to deter-
+mine the location of the water snowline. Unfortunately,
+ALMA did not detect any of those selected transitions
+in HD 163296, with 3σ upper limits for ortho-H16
+2 O at
+321 Ghz < 5.3 × 10−21 W m−2, and for para-H18
+2 O at
+322 GHz < 8.5 × 10−21 W m−2. So the water snow
+line position remains difficult to measure even in the
+brightest Herbig disks.
+The water snowline can also be traced indirectly by
+molecules that correlate with its location. Leemker et al.
+(2021) studied the use of HCO+ as a chemical tracer of
+the water snow line. The abundance of HCO+ and H2O
+are anti-correlated due to the reaction HCO+ + H2O
+→ CO + H3O+. However, they concluded that, due to
+degeneracies complicating the interpretation, HCO+ is
+not a good tracer of the snowline in Herbig disks.
+Similarly, N2H+ and DCO+ trace the CO iceline
+indirectly because both of these molecules are tightly
+connected to the gas phase CO. If CO is present, it will
+compete with N2 in reactions with H+
+3 , diminishing the
+production of N2H+; at the same time, N2H+ is also
+destroyed in reactions with CO, leading to the forma-
+tion of HCO+ (for a detailed discussion see van ’t Hoff
+et al., 2017). A consequence of this is that HCO+ will
+be abundant just above the CO iceline. The low tem-
+peratures there (∼20 K) are conducive to deuteration,
+which could result in DCO+ to peak in abundance just
+above/inside of the CO iceline — a method that has
+been applied earlier to pre-stellar cores (Caselli et al.,
+1999, Pagani et al., 2012). Observing DCO+, Math-
+ews et al. (2013) confirm the CO iceline location in
+HD 163296 found by Qi et al. (2011).
+Summary: There is convincing evidence that the gas
+temperatures in the disk atmosphere are higher than
+the dust temperatures. However, our understanding of
+the 2D temperature structure in Herbig disks remains
+incomplete. The resulting temperature profiles depend
+strongly on which tracer and method is chosen to ex-
+tract them. HD 163296 is one of the disks that has been
+studied using almost every available method. A trend
+emerges from the observations that shows a very steep
+radial temperature gradient for the uppermost layers
+
+40
+Sean D. Brittain et al.
+close to the central star (CO high rotational lines) and
+a flattening of that gradient as one moves to tracers
+that probe layers closer to the midplane and further
+out (CO isotopologues). This agrees qualitatively well
+with 2D thermo-chemical disk models. The CO iceline
+estimate from CO and DCO+ suggest a temperature of
+∼20 K at 155 au, which agrees very well with the mid-
+plane temperature profiles derived from interferometric
+data. The snowline estimate from the ALMA water line
+data suggests ∼150 K at 8-20 au, which is a higher tem-
+perature than what is inferred from the extrapolation
+of the midplane power law temperature profiles from
+interferometry. Given the intricate dust substructure
+seen inside 50 au (Andrews et al., 2018b), such a sim-
+ple extrapolation is however questionable. The presence
+of gaps and rings will alter the midplane temperature
+profile (e.g. Pinte et al., 2016, Rab et al., 2020).
+5.5 The radial distribution of gas
+In the context of planet formation, it is of immediate in-
+terest how the gas mass is distributed within the disk,
+especially in the planet forming regions inside 50 au.
+For the understanding of the mechanisms creating gaps
+and rings observed in mm-sized dust, it is crucial to
+know whether gas and dust are spatially related (i.e.,
+whether dust gaps also imply gas gaps). A key ques-
+tion is how the gas in the inner disk evolves during the
+planet formation era. Does it follow the dust behavior
+(gap/hole formation) or does it decouple from the dust?
+Also, the outer edge of the gas potentially carries an im-
+print of either viscous spreading or dynamic encounters
+truncating the disk.
+Studies of the CO ro-vibrational lines profiles show
+that in many cases, the onset of CO emission coincides
+with the dust inner radius (Goto et al., 2006, Brittain
+et al., 2007, Salyk et al., 2009, Hein Bertelsen et al.,
+2014, van der Plas et al., 2015, Hein Bertelsen et al.,
+2016). However, in some cases the authors find evi-
+dence for wide CO ro-vib line profiles in GI disks which
+host dust cavities. For example, Salyk et al. (2009)
+modeled the CO ro-vib inner emission radius assuming
+a power law intensity profile and found for LkHα330
+(IMTTS) that the CO gas resides inside the dust cav-
+ity (50 au). Several more cases are shown by Hein Ber-
+telsen et al. (2016). In those cases, gas and dust could be
+spatially de-coupled. Banzatti and Pontoppidan (2015)
+show that the CO gas in systems with large inner cav-
+ities (as deduced from the CO line profile) is vibra-
+tionally ‘hot’. One explanation of this could be UV flu-
+orescence reaching the outer disk because the inner disk
+is also devoid of dust. Following up on the powerful CO
+ro-vib line diagnostic, Banzatti et al. (2017a) showed
+Fig. 26 Compiled CO surface density profiles from the liter-
+ature (Zhang et al., 2021, Fedele et al., 2017, Carmona et al.,
+2014, 2017, Carmona, 2021, van der Marel et al., 2016). We
+used a constant CO abundance of 10−4 if required to convert
+from total gas surface densities. The solid lines are derived
+from ALMA data, while the dashed lines are from CRIRES
+data. The black dotted line shows the Minimum Mass Solar
+Nebula. The blue/green colors indicate normal class ii disks,
+while the yellow/orange/red colors indicate transitional disks.
+that water line detections in T Tauri disks (2.9-33 µm)
+correlate with gas gap sizes deduced from the CO lines.
+In disks with small gaps, the highest water excitation
+lines are no longer detected and with increasing gap
+size, these non-detections expand to lower excitation
+water lines. Antonellini et al. (2015) showed that wa-
+ter lines with lower excitation temperatures tend to
+originate from increasingly larger distances from the
+star. Detailed thermo-chemical disk modeling of CO
+ro-vibrational lines by Bosman et al. (2019) and An-
+tonellini et al. (2020) shows that the observations of
+Herbig disks may point to a more complex inner disk
+structure, possibly de-coupling of dust and gas and pos-
+sibly positive density gradients consistent with gaps
+carved by giant planets (e.g. Bryden et al., 1999, Lubow
+and D’Angelo, 2006). Carmona et al. (2014) used the
+CO ro-vib line profiles combined with a large set of
+multi-wavelength data (photometry, line fluxes, and im-
+ages) for the disk around HD 135344B to deduce the
+shape of the gas surface density profile inside ∼50 au.
+From the CO v=1-0 line profile they find a positive
+surface density profile and also evidence for dust deple-
+tion with respect to the canonical gas-to-dust ratio of
+100 inside the gap of this pre-transitional disk (GI, see
+Fig. 26). Also fitting three CO isotopologues in the pre-
+transitional disk around HD 139614 indicates a positive
+surface density profile inside 6 au, and even possibly
+a deep narrow gap that could point to a giant planet
+around 4 au (Carmona et al., 2017). Using the same
+
+HD163296
+22
+MWC480
+HD169142
+20
+HD 139614
+HD135344B
+IRS48
+18
+16
+0.5
+1.0
+1.5
+2.0
+2.5
+log r [au]Herbig Stars
+41
+method, the CO isotopologue lines in HD 169142 are
+consistent with a flat or increasing gas surface density
+profile inside ∼20 au (Carmona et al. 2021; Fig. 26).
+Given the high spatial resolution that ALMA offers
+now, the CO pure rotational lines can also be used to
+probe the inner disk regions. The caveat here is that
+the typical gas temperatures inside 10 au are above a
+few 100 K and so the low rotational levels are not max-
+imally populated. In a pioneering survey of disks with
+inner dust gaps (pre-transitional disks8), van der Marel
+et al. (2016) characterized the depth and shape of such
+gaps for HD 135344B and IRS 48. They find that the
+sizes of gas gaps are typically smaller by a factor two
+compared to the dust gaps and that for HD 135344B
+the data at this stage cannot yet distinguish between a
+smooth gas surface density profile with a negative gradi-
+ent and a step-like positive one (different gas depletion
+levels); notably the CO ro-vib data is more constrain-
+ing for this object (see above). IRS48 requires a sharp
+edge in the gas surface density profile at ∼ 25 au (see
+Fig. 26). The DIANA models (Woitke et al., 2019b)
+show that the observational data are consistent with
+an outer gas surface density gradient smaller than −1.5
+(Minimum Mass Solar Nebula, Weidenschilling, 1977),
+a result previously also reported by Williams and Cieza
+(2011).
+Concerning the outer disk, the DSHARP program
+(Andrews et al., 2018b) obtained high spatial resolu-
+tion ALMA data (30-60 mas) for a few Herbig Ae disks,
+HD 163296, HD 142666 and the IMTTS HD 143006. From
+this program, only one source, HD 163296, has a high
+quality dataset that allows the determination of a de-
+tailed gas surface density profile (see Fig. 26). Since the
+dust rings are not optically thin, derivation of the gas
+surface density profile requires simultaneous modeling
+of dust and gas. While Isella et al. (2016) inferred the
+presence of gas gaps for the inner two dust gaps at 60
+and 100 au from power law (plus gaps) disk model-
+ing of ALMA CO data, more detailed thermo-chemical
+dust+gas modeling using the DSHARP data does not
+confirm this (Rab et al., 2020). The observations of the
+high S/N high spatial resolution 12CO data (DSHARP)
+are still consistent with no gas depletion inside the dust
+gaps.
+In a sample of 22 disks from a pre-ALMA northern
+survey of the 12CO J = 3 − 2 line (Dent et al., 2005),
+Pani´c and Hogerheijde (2009) find from disk modeling
+(power-law disk models without chemistry) that 75 % of
+this Herbig sample are smaller than 200 au; of course,
+pre-ALMA data is likely biased towards large/bright
+8 Note that the term transitional disk is here reserved to
+disks that have no near-IR excess; HD135344B and IRS48 do
+have such an excess.
+disks and could underestimate this percentage. Unfor-
+tunately, in the epoch of ALMA, there does not exist a
+homogeneous large survey for disk sizes at the time of
+this writing. Taun et al. (MSc thesis, paper in prepa-
+ration) collected archival data of Herbig disks in band
+6 (all three CO isotopologues) with spatial resolution
+of 20-100 au (e.g. data from Miley et al., 2019). They
+added Herbig disks observed only in band 7 (13CO and
+C18O) to enhance the sample. This led to 17 Herbig
+disks, ten GI, five GII and two intermediate disks (Fig.
+27). The dust and gas radii were derived using the cu-
+mulative fluxes (from elliptical apertures) and defining
+the outer radius when 90% of the total flux was reached
+(see Trapman et al., 2019, for details of the method).
+In general, GI disks span a large range in dust (90∼370
+AU) and gas (180∼850 AU) outer disk radii while the
+five GII disks are small, with four unresolved dust disks
+and three unresolved gas disks (13CO). The GI/II disks
+have similar sub-mm properties (gas outer radii, con-
+tinuum and CO fluxes) to GI disks. Like in the case of
+the lower mass counterparts (T Tauri disks), the aver-
+age ratio between gas and dust outer radii is ∼ 2 with
+a large spread (e.g. Ansdell et al., 2018). Facchini et al.
+(2017) and Trapman et al. (2019) find that radial drift
+of dust grains has a profound effect on the outer disk
+thermal gas structure and the ratio between inferred
+dust and gas radii; specifically, radial differences of a
+factor four or more are clear signatures of dust evolu-
+tion and radial drift.
+Individual disks have been investigated using high
+spatial resolution ALMA data and find similar results:
+a factor 2.4 for HD 97048 (van der Plas et al., 2017b),
+more than a factor 2 for HD 163296, (de Gregorio-Monsalvo
+et al., 2013), and more than a factor 5.8 for HD 100546
+(Pineda et al., 2014). For the disks around HD 163296
+and HD 100546, the authors claim that the dust disk
+has a sharper cut-off compared to the gas, possibly in-
+dicating signatures of grain growth and radial dust mi-
+gration. The DIANA disk modeling results show that
+for five Herbig disks, the outer disk edge is consistent
+with a soft edge (γ = 0.5 − 1.0 9 ), and only for one
+object, the sharp edge previously reported is recov-
+ered (HD 163296, γ = 0.2 Woitke et al., 2019a). Pani´c
+et al. (2021) investigated two binaries of intermedi-
+ate separation (HD 144668 and KK Oph) where both
+components are surrounded by dust-rich (gas-to-dust
+mass ratio ⩽ 2.4) planet forming disks. The respec-
+tive disk sizes are consistent with tidal truncation in
+these systems and they appear to have lower gas masses
+9 The
+surface
+density
+is
+here
+assumed
+as
+Σ(r)
+∝
+r−ϵ exp
+�
+−
+�
+r
+Rtap
+�2−γ�
+with the radius r and the taper ra-
+dius Rtap.
+
+42
+Sean D. Brittain et al.
+Fig. 27 Gas outer radii of Herbig disks derived from ALMA 13CO archival data versus dust outer radii (Taun, MSc thesis).
+The right panel zooms in excluding the three largest disks.
+(< 0.1 MJupiter) than the average single Herbig disks;
+so it is unlikely that gas giant planets can still form
+around these two stars.
+Summary Based on NIR gas observations of Herbig
+disks with dust cavities (up to several 10 au), there
+is evidence for positive surface density gradients inside
+those cavities. In some cases, the gas clearly extends in-
+side the dust cavity and in most cases, the gas-to-dust
+ratio is high inside the cavities. Broadly speaking, this
+is consistent with giant planet formation models. The
+gas surface density gradient in the outer disk (beyond
+several 10 au) is often more shallow than the minimum
+mass solar nebula (-1.5, see Fig. 26). We have in a few
+cases high spatial resolution ALMA observations indi-
+cating that growth and radial migration of dust affect
+the outer edges of disks around Herbig Ae stars. In-
+termediate separation binaries also suggest that tidal
+truncation operates, maybe in tandem with promoting
+more efficient dust evolution.
+5.6 Chemistry in Herbig disks
+To understand what type of planetary systems can emerge
+from the disks around Herbig stars, we also need to ad-
+dress the question of how chemically rich these disks
+are. (1) Which level of molecular complexity do we find
+compared to disks around low mass stars? (2) Are the
+differences primarily due to differences in the physical
+and thermal disk structure (e.g. level of UV and X-ray
+irradiation) or do they reflect true differences in the
+gas chemistry? And, most fundamentally, (3) do Her-
+big disks contain significant amounts of water, a tracer
+often invoked to assess the possibility of forming habit-
+able planets. (4) What is the C/O ratio in Herbig disks?
+Level of molecular complexity: A systematic SMA sur-
+vey by ¨Oberg et al. (2010, 2011) finds a lack of cold
+chemistry tracers in Herbig disks, i.e. N2H+, DCO+,
+DCN, H2CO, compared to T Tauri disks. These early
+studies focused on the brightest (and so largest) disks
+in each category. With ALMA’s increasing spatial reso-
+lution and sensitivity, the studies of the chemical com-
+position of Herbig disks has gained momentum. ¨Oberg
+et al. (2015) showed that the bright Herbig disk around
+MWC 480 hosts a number of complex nitriles (HC3N
+and CH3CN) next to the commonly detected HCN and
+its isotopologue. Overall, the number of Herbig disks
+in which ALMA has searched for molecules is still too
+small and the data is too inhomogeneous (spatial reso-
+lution, transitions) to have conclusive answers as to how
+different Herbig disks are amongst themselves (see Ta-
+ble 5 for sources that have molecular detections beyond
+the CO molecule); this is not changing with the MAPS
+survey (¨Oberg et al., 2021), since it includes only two of
+the already well characterized Herbig disks MWC 480
+and HD 163296. In the inner disk, Spitzer surveys have
+shown that Herbig disks also lack the richness in molec-
+ular lines typically found in T Tauri disks (Pontoppi-
+dan et al., 2010, Salyk et al., 2011). The Herbig disks
+show for example no detections of HCN, C2H2, CO2 and
+OH; only HD 101412 is detected in CO2. Warm water
+(∼300 − 700 K) is only detected at longer wavelengths
+(e.g. 29.85 µm, Pontoppidan et al. 2010) among several
+Herbig disks (4/25). HD 163296 is also clearly detected
+at 33 µm (Banzatti et al., 2017a). Given the low spec-
+tral resolution of Spitzer, this can be a result of limited
+
+006
+HD31648
+400
+800
+350
+HD163296
+700
+HD34282
+600
+300
+(AU)
+(AU)
+HD97048
+500
+250
+HD100546
+13CO
+THD142527
+HD169142
+HD3Y648
+400
+200
+HD104237
+HD135344
+AD163296
+Rg = 3Rd
+150
+HD139614
+300
+H100546
+Rg =2Rd
+KKOph
+AKSCO
+200
+Rg= Rd
+100
+THD14266.6
+Group I
+100
+Group I/ll
+50
+Group Il
+0
+0
+0
+100
+200
+300
+400
+500
+600
+0
+25
+50
+75
+100 125 150
+175200
+Rout Dust (AU)
+Rout Dust (AU)Herbig Stars
+43
+Table 5 Detected molecules (transitions) in Herbig disks with ALMA beyond CO. References: Bosman et al. (2019, Bo19),
+van der Plas et al. (2017b, vdP17), Aikawa et al. (2021, A21), Booth et al. (2019, B19), Bergner et al. (2021, B21), Carney
+et al. (2018, C18), Cataldi et al. (2021, C21), Fedele et al. (2017, F17), Guzm´an-D´ıaz et al. (2021, G21), Huang et al. (2017,
+H17), Ilee et al. (2021, I21), Loomis et al. (2020, L20), Le Gal et al. (2021, LG21), Mathews et al. (2013, M13), Mac´ıas et al.
+(2017, M17), ¨Oberg et al. (2015, O15), Pegues et al. (2020, P20), Qi et al. (2015, Q15), Zhang et al. (2021, Z21).
+line
+ident
+HD 97048
+MWC 480
+HD 163296
+HD 143006
+HD 169142
+12CO
+J=1-0
+vdP17
+13CO
+J=1-0
+Z21
+Z21
+C18O
+J=1-0
+Z21
+Z21
+C17O
+J=1-0
+Z21
+Z21
+12CO
+J=2-1
+Z21
+Z21
+F17
+13CO
+J=2-1
+Z21
+Z21
+F17
+C18O
+J=2-1
+B19,Z21
+Q15,B19,Z21
+B19
+F17
+12CO
+J=3-2
+vdP17,Bo19
+HCO+
+J=1-0
+A21
+A21
+HCO+
+J=4-3
+vdP17,Bo19
+M13
+DCO+
+J=3-2
+M17,C18
+DCO+
+J=5-4
+M13
+M17,C18
+H13CO+
+J=1-0
+A21
+A21
+H13CO+
+J=3-2
+H17
+H17
+H13CO+
+J=4-3
+Bo19
+M13
+H2CO
+J=3-2
+P20,G21
+P20,G21
+P20
+H2CO
+J=4-3
+P20
+P20
+HCN
+J=1-0
+G21
+G21
+HCN
+J=3-2
+B19,G21
+B19,G21
+B19
+H13CN
+J=3-2
+O15,H17
+H17
+HC15N
+J=4-3
+Bo19
+DCN
+J=3-2
+C21
+C21
+CN
+N=1-0
+B21
+B21
+CN
+N=2-1
+B21
+N2H+
+J=3-2
+L20
+Q15
+N2D+
+J=3-2
+C21
+C21
+HC3N
+29-28
+I21
+I21
+CH3CN
+120-110
+I21
+I21
+C2H
+N=3-2
+B19,G21
+B19,G21
+C2H
+N=1-0
+G21
+G21
+c-C3H2
+707-616
+I21
+I21
+SO2
+LG21
+12CS
+J=2-1
+LG21
+LG21
+12CS
+J=5-4
+LG21
+12CS
+J=6-5
+L20
+C34S
+J=5-4
+LG21
+H2CS
+L20,LG21
+sensitivity since models predict that the line flux scales
+weaker than linear with the central star luminosity (An-
+tonellini, 2016).
+Origin of differences between T Tauri and Herbig disks:
+Single dish sub-mm observations focused initially on de-
+tecting molecules in the cold outer disk and analysing
+integrated line ratios. Thi et al. (2004) presented a first
+comparative study of the sub-mm lines of CO, HCO+,
+CN, HCN, and H2CO in T Tauri stars (LkCa 15 and
+TW Hya) and Herbig stars (HD 163296 and MWC 480);
+they found that the CN/HCN ratio is higher in Herbig
+disks than in T Tauri disks and attributed this to ei-
+ther differences in the radiation field (Ly α or X-rays)
+or a thermal effect (the two molecules have different
+freeze-out temperatures). Using the PdB Interferome-
+ter, Henning et al. (2010) found that C2H emission is
+lower in the Herbig disk around MWC 480 than in the
+T Tauri disks around DM Tau and LkCa 15; again, they
+explained this by the presence of strong UV and lack
+of X-rays in the case of the Herbig disk. The SMA sur-
+vey by ¨Oberg et al. (2010, 2011) shows no clear differ-
+ence in the CN/HCN ratio between T Tauri and Her-
+big disks. Subsequent large surveys of T Tauri and Her-
+big disks using IRAM also show no systematic differ-
+ence in CN emission between the two type of sources
+(Chapillon et al., 2012, Guilloteau et al., 2013). How-
+ever, MWC 480 and HD 163296 show strong CN emis-
+sion, while AB Aur, MWC 758, CQ Tau and SU Aur show
+only upper limits or weak emission. Notably the strong
+CN disks are both intermediate GI/GII disks; also Ta-
+ble 5 shows that these are also to-date the two best
+
+44
+Sean D. Brittain et al.
+studied disks. Contrary to the above studies, Chapillon
+et al. (2012) find that the CN/HCN line ratio is higher
+in Herbig disks compared to T Tauri disks — however,
+the sample for which both lines have been observed with
+IRAM is small.
+A comprehensive ALMA line survey of LkCa 15 (a
+T Tauri star) and MWC 480 finds clear differences in
+the cold chemistry tracers N2H+, and DCN, and the
+nitriles HC3N, CH3CN. The latter are brighter in the
+Herbig disk, maybe due to its instrinsically higher tem-
+peratures (Loomis et al., 2020). Le Gal et al. (2019)
+focused on the sulphur bearing molecules in disks in-
+cluding again MWC 480. They find no difference in CS
+between T Tauris and this Herbig disk. On the other
+hand, a much larger sample studied by Pegues et al.
+(2020) shows that H2CO (formaldehyde) is less abun-
+dant in Herbig disks compared to T Tauri disks. The
+observations suggest that both chemical channels, gas-
+phase and grain-surface, likely operate to explain the
+formaldehyde observations in disks; hydrogenation of
+CO ice can lead to efficient H2CO formation in cold
+T Tauri disks. The general idea is that formaldehyde
+can be further hydrogenated to methanol (e.g. Hiraoka
+et al., 1994, Watanabe and Kouchi, 2002) and simu-
+lations support that this works under the conditions
+found in cold dense cores or cold YSO envelopes (Cup-
+pen et al., 2009). Carney et al. (2019) carried out a deep
+search for methanol in HD 163296 with no detection.
+Compared to TW Hya, the methanol to formaldehyde
+ratio is much lower. However, still multiple explanations
+are possible given that we still have an incomplete pic-
+ture of the role of surface chemistry versus gas phase
+chemistry and also given uncertainties in the desorption
+efficiencies of these two molecules.
+The cold chemistry in the outer disk also drives
+deuteration of molecules. Huang et al. (2017) find no
+significant difference in the deuteration between the
+T Tauri and Herbig disks (MWC 480 and HD 163296).
+This is surprising given the earlier finding of a compar-
+ative lack/lower emission level of cold chemistry tracers
+in the outer disk of Herbig stars.
+Disk modeling studies (van Zadelhoff et al., 2003,
+Cazzoletti et al., 2018) indeed suggest that higher FUV
+irradiation enhances the CN emission. Walsh et al. (2015),
+Antonellini (2016), Ag´undez et al. (2018) used thermo-
+chemical models to investigate the difference in chemi-
+cal composition between disks of various spectral types.
+Using the same generic disk structure and exchanging
+the central star, Ag´undez et al. (2018) do not find strik-
+ing differences in the outer disk molecular reservoir be-
+tween T Tauri and Herbig disks. Walsh et al. (2015) use
+the same approach and focus on the inner 10 au. They
+do not find significant differences between Herbig and
+T Tauri disks in key molecules such as HCN and C2H2;
+if at all, the Herbig disks have higher column densities.
+It is important to note that these works assumed high
+abundances of relatively small grains in the disk sur-
+face (up to 1 µm size). This causes the H/H2 transition
+to reside very high in the disk at warm temperatures
+(several 100 K), thus promoting a very efficient neutral
+chemistry (Walsh et al., 2015). This is not the case in
+disk models that assume a wider grain size distribution
+(up to mm-size) and dust settling; the small grains are
+then indeed left in the disk surface, but their fractional
+mass is much smaller, preventing high abundances of
+H2O and C2H2 above τ ∼1 in the disk surface (Woitke
+et al., 2019b, Greenwood et al., 2019).
+Water in Herbig disks: The lowest excitation water lines
+from the outer disk have been detected with Herschel/HIFI
+in one out of four Herbig stars (HD 100546 detection
+versus HD 163296, MWC 758, MWC 480 non detections
+van Dishoeck et al., 2021). Also, water ice has been
+unambigiously detected in the Herbig disks HD 142527
+(Min et al., 2016b) and HD 100546 (Honda et al., 2016),
+see Sect. 4.7.
+Moving slowly to warmer disk regions closer to the
+star, warm water (∼200 − 300 K) has been detected in
+the far-IR with Herschel in HD 163296 (Meeus et al.,
+2012), and through line stacking also in HD 104237 and
+HD 142527 (Fedele et al., 2013). Contrary to the funda-
+mental water lines, HD 100546 is not detected in warm
+water with PACS; the original claim by Sturm et al.
+(2010) has been retracted (Meeus et al., 2012). Also
+warm OH (∼100 − 500 K) has been detected in disks,
+both in GI and GII (Meeus et al., 2012, Fedele et al.,
+2012, 2013). Higher OH/H2O abundance ratios are found
+in Herbig disks compared to T Tauri disks based on slab
+models that assume the same spatial origin for both
+molecules. However, thermo-chemical models of T Tauri
+disks show that these lines originate from very differ-
+ent radial and vertical disk layers (Woitke et al., 2019b,
+Greenwood et al., 2019).
+At NIR wavelengths, ground based studies have been
+used to search for hot water (few 1000 K) and OH in
+the inner disks around Herbig stars (Fedele et al., 2011,
+Brittain et al., 2016, Adams et al., 2019). The NIR
+detections of OH are more common among GI disks
+(Brittain et al., 2016) in contrast to the far-IR OH de-
+tections. This could relate to the inner disk architec-
+ture where dust cavities/gaps (more common among
+GI disks) create better excitation conditions, e.g. at the
+inner edge of the outer disk. Brittain et al. (2016) find
+that the high J CO and OH P4.5 doublet line ratio is
+roughly constant (∼10) in Herbig disks; T Tauri disks
+show a lower ratio between the CO P10 line and the
+
+Herbig Stars
+45
+OH doublet at 2.9 µm (Banzatti et al., 2017a). Subse-
+quently, Adams et al. (2019) found that the H2O to
+OH line ratio in Herbig disks (based on HD 101412 and
+upper limits from Fedele et al., 2011) is systematically
+lower than for T Tauri disks (Banzatti et al., 2017a).
+The C/O ratio in Herbig disks: A key controversy at
+this stage is the global C/O ratio in disks, because it re-
+lates very closely to the composition of gas giant planets
+and planetary atmospheres forming within these disks.
+Bruderer et al. (2012), Kama et al. (2016a,b) use a
+combination of atomic fine structure lines ([O i)], [C i],
+[C ii]) and CO sub-mm lines to investigate the carbon
+depletion in the upper layers of the outer disk; the [C i]
+data originates from APEX surveys. They find that the
+volatile carbon abundance could be a factor 5−20 lower
+than the solar one (2.7×10−4 relative to hydrogen, As-
+plund et al., 2009); however to derive robust conclu-
+sions, [C i] detections are essential, thus warranting the
+sensitivity of ALMA. The recent MAPS project found
+no difference in the amount of CO depletion in three
+T Tauri and two Herbig disks (Zhang et al., 2021). Sub-
+sequent 2D thermo-chemical disk modeling of the five
+disks (Bosman et al., 2021) shows that the C/O ratio
+varies strongly within each disk, irrespective of spectral
+type.
+Summary: Surveys of Herbig disks have shown less chem-
+ical richness compared to their lower mass counterparts,
+the T Tauri disks. The to-date richest Herbig disks are
+the two GI/GII disks HD 163296 and MWC 480; how-
+ever, this could be a selection bias since few comprehen-
+sive Herbig line surveys have been done with ALMA.
+Despite thermo-chemical modeling, it remains unclear
+the extent to which this is due to differences in disk
+structure or chemistry. A systematic survey of OH, wa-
+ter and CO would again be key (see also Sect. 5.3) in
+disentangling the excitation and abundance question
+for these molecules and understanding the differences
+between T Tauri and Herbig disks. If elemental carbon
+depletion is invoked to explain the weak CO lines in the
+submm, factors of up to several 10 (relative to solar) are
+found in Herbig disks; the C/O ratio could be as high
+as 2.
+5.7 Differences between Herbig Ae and Be disks
+Most of the discussion above pertains to disks around
+Herbig Ae stars. Their B-type counterparts have much
+higher luminosities and they often reside in more dis-
+tant star forming regions (see also Sect. 4.1). The larger
+distance and their embedded nature makes them diffi-
+cult targets for directly resolving their disks. However,
+they have been studied spectroscopically from optical
+to far-IR wavelengths.
+Bik and Thi (2004) detected the CO bandhead emis-
+sion in a young B-type star (IRAS08576-4334, M∗ =
+6 M⊙) and showed that it is fully consistent with orig-
+inating from a small (few au sized) disk in Keplerian ro-
+tation. Subsequent X-shooter and SINFONI data (Eller-
+broek et al., 2011) suggest that the system also features
+a jet and would thus be still accreting with rates of the
+order of 10−5 − 10−6 M⊙/yr. Ram´ırez-Tannus et al.
+(2017) classified and investigated young stellar objects
+in M17 (d=1.98 kpc) and found five of them having a
+spectral type B (B243, B268, B275, B331, B337) and at
+least two of the attributes: NIR excess, CO bandhead
+emission, double-peaked emission lines of hydrogen, the
+Ca triplet, [O i] 6300˚A; B275 had been previously con-
+firmed to be a young pre-main sequence B-type star
+by Ochsendorf et al. (2011). A detailed analysis of the
+line profiles shows that the gaseous disks are again very
+small (0.5-5 au scale) and that the hydrogen emission
+originates from further out compared to [O i] and the
+Ca triplet. Ilee et al. (2013, 2014) detected the CO over-
+tone emission at 2.3 µm with CRIRES and X-shooter in
+a sample of 6 out of 91 Herbig disks (4 Be disks and 2 Ae
+disks); the detection rate is higher among the Be disks.
+Fitting the CO overtone line profile again suggests an
+origin within a small gaseous disk (< few au). For the
+B-type stars, the CO emitting region is well inside the
+estimated dust sublimation radius, but well beyond the
+corotation radius. So, the picture that emerges is that
+these Be-type stars have a NIR excess and host small
+gaseous disks, likely inside the dust sublimation radius.
+At far-IR wavelength, Jim´enez-Donaire et al. (2017)
+compared the Herschel far-IR spectra of two Herbig
+Be stars (R Mon with spectral type B8, 0.8 kpc, and
+PDS 27 with spectral type B2, 1.25 kpc). While the
+spectrum of the B8 type star is rich in emission lines
+of [O i], H2O, OH and CO up to J = 34 − 33, the B2
+star barely shows any emission lines, besides CO up to
+J = 11 − 10. However, due to the limited spatial and
+spectral resolution, the disk and outflow (shock) con-
+tribution to these lines cannot be disentangled. Further
+observations at far-IR and sub-mm wavelengths (either
+with high spatial or spectral resolution), are required to
+find out whether the more massive HBe stars possess
+outer gaseous disks similar to the Herbig Ae stars or
+not.
+Summary: Over the past 25 years it has become clear
+that Herbig stars possess rotationally supported gas
+disks. Spectroscopic capabilities across the electromag-
+netic spectrum have revealed the presence of many molecules
+in these disks. Thermo-chemical models of disks can re-
+
+46
+Sean D. Brittain et al.
+produce the main trends. The mass of disks remains
+highly uncertain and model dependent. There is a dis-
+crepancy between the masses of disks inferred from var-
+ious indirect tracers and the stellar accretion rate that
+points to either missing physics in our interpretation
+of stellar accretion rates and/or the interpretations of
+tracers used to infer the mass of disks. While there is
+evidence that Herbig Be stars possess disks, these are
+much smaller and less chemically rich than their Herbig
+Ae counterparts.
+5.8 The relative radial distribution of gas and dust in
+disks around Herbig stars
+At large spatial scales (few 10’s of au), the substruc-
+tures frequently seen in the dust do not always have a
+corresponding gas structure and vice versa. For exam-
+ple, the clear dust gaps in HD 163296 have a correspon-
+dence in the gas (Isella et al., 2016), but this can be a
+pure temperature and/or opacity effect (van der Marel
+et al., 2018, Rab et al., 2020). The pre-transitional disk
+around HD 142527 shows a clear dust trap in 1.3 mm
+emission, but the CO emission is smoother and extends
+much further inwards (Boehler et al., 2017). HCN and
+CS emission in this source is offset from the dust trap
+by almost 180◦ (van der Plas et al., 2014); again, the
+explanation could be either a temperature or an opac-
+ity effect. AB Aur shows two prominent 12CO gas spiral
+arms inside the mm dust cavity (Tang et al., 2017).
+A radial dependence on the vertical dust settling has
+been measured in the disk around HD 163296. At the
+inner dust ring (∼70 au), dust and gas remain vertically
+well mixed. At the outer dust ring (∼100 au), the scale
+height of the dust is roughly ten times smaller than the
+scale height of the gas (Doi and Kataoka, 2021). This
+is consistent with only the inner ring being detected in
+scattered light (Muro-Arena et al., 2018).
+At the spatial scales of the inner disk, interferomet-
+ric studies of the dust and optical and near-IR spec-
+troscopy of the [OI] and CO ro-vibrational lines can
+reveal whether or not gas and dust are co-spatial. van
+der Plas et al. (2009) inferred that CO is absent in the
+dust gaps (<10 au) of HD 97048 and HD 100546; how-
+ever, [OI] 6300 ˚A emission extends well inside the dust
+gaps, thus showing the presence of gas. van der Plas
+et al. (2015) then compared the inner radius derived
+from CO emission with that of the dust and other inner
+disk gas tracers ([OI], PAHs) for a larger sample of Her-
+big stars. The GI disks show systematically larger CO
+inner radii than GII disks; in both cases, the [OI] emis-
+sion extends further inward than the CO. Banzatti and
+Pontoppidan (2015), Banzatti et al. (2017b) compared
+the CO and water emission lines to measurements of
+the dust inner holes. They confirm that inner dust gaps
+are indeed depleted in molecular line emission (water
+and CO). Hein Bertelsen et al. (2016) added to the CO
+diagnostic by introducing the line FWHM as function
+of upper level quantum number J as a new diagnostic:
+(1) a constant FWHM versus J can be used to infer the
+presence of a dust gap, (2) the presence of line wings
+can indicate the presence of gas inside a dust gap, and
+(3) a strongly decreasing line flux versus J behaviour
+can indicate a gas depleted region (Hein Bertelsen 2015,
+PhD thesis). Carmona et al. (2014, 2017) studied two
+pre-transitional disks (HD 135344B, HD 139614) with
+very deep CRIRES observations and find that for these
+two disks, the dust gaps (30 and 6 au respectively) are
+partially filled with molecular gas emission. This agrees
+with the findings from ALMA CO submm observations
+by van der Marel et al. (2016).
+Summary: The structures observed in gas lines and in
+the continuum do not necessarily correspond. This may
+be due to either temperature or opacity effects. The
+vertical mixing of the gas and dust has been shown to
+vary for at least one source which may explain differ-
+ences in what is observed in the mm continuum and
+in scattered light. In the inner disk, the inward extent
+of the molecular gas tends to follow the inward extent
+of the dust, though there are exceptions. Atomic gas
+(as traced by [OI] for example) generally extends in-
+ward of the molecular gas. Thermo-chemical disk mod-
+eling work (Bruderer, 2013, Bosman et al., 2019, van
+der Marel et al., 2018, Hein Bertelsen 2015, PhD the-
+sis) has revealed the complex interplay between gas and
+dust in the inner disk. The local gas-to-dust ratio, dust
+opacities, disk scale height, presence of dust traps and
+gas excitation mechanism all play a role in interpreting
+the observations.
+6 PLANET FORMATION AROUND
+HERBIG STARS
+6.1 Planet occurrence rates among intermediate mass
+stars
+The occurrence rate of super-Earths within ∼1 au of
+their host star peaks at 0.5M⊙ (Mulders et al. 2021, see
+also Howard et al. 2012, Mulders et al. 2015). On the
+other hand, the occurrence rate of supra-Jovian mass
+planets with periods ≤4 years increases with stellar
+mass reaching a maximum at ∼2 M⊙and then rapidly
+declines (Reffert et al. 2015, see also Luhn et al. 2019,
+Johnson et al. 2010). The most massive star around
+which a planet has been detected thus far is a binary
+with a system mass of 6-10M⊙(Janson et al., 2021).
+
+Herbig Stars
+47
+The planet was detected by direct imaging and has a
+semi-major axis of 560 au. Thus it is clear that planets
+can form even around fairly massive Herbig stars.
+Transit searches for planets find systematically lower
+occurrence rates for planets than radial velocity searches
+that is largely driven by selection effects of the sur-
+veys (Moe and Kratter, 2021). These authors note that
+this driven by the fact that binaries with intermedi-
+ate separations (a=0.5 – 200 au) suppress planet for-
+mation and that radial velocity searches systematically
+exclude binaries while transit searches do not. Moe and
+Kratter (2021) argue that half of the dependence of the
+superEarth occurrence rate on stellar mass can be ac-
+counted for by the effect of binaries. The occurrence
+rate of supra-Jovian mass planets within 1 au around
+single AF stars is 8.6 ± 2.3% (Moe and Kratter, 2021)
+- consistent with the estimate by Reffert et al. (2015)
+for solar metalicity stars with masses ranging from 1.8-
+2.6M⊙. It is not clear how the occurrence rate of supra-
+Jovian mass planets scales with orbital separation.
+Indeed, direct images of planets around intermedi-
+ate mass stars are rare. Bowler (2016) find that high
+mass planets (5–13 MJ) are detected at 30–300 au or-
+bital separation in only a small fraction of young A-
+stars (2.8%). Similarly, the Gemini Planet Imager Ex-
+oplanet Survey (GPIES) reports a modestly higher oc-
+currence rate for the same mass range of supra-Jovian
+planets (9+5
+−4%) from 10–100 au (Figure 28; Nielsen et al.
+2019). Assuming that this reflects the actual occurrence
+rate of massive companions orbiting intermediate mass
+stars (i.e., the planets haven’t migrated inward of ∼10-
+30 au), one might conclude that only a few percent of
+Herbig stars should reveal signatures of ongoing supra-
+Jovian gas giant planet formation at distances ≳ 10 au.
+However, that does not appear to be the case. Here we
+summarize the evidence for ongoing planet formation
+in Herbig disks and discuss the challenges to detecting
+forming planets in these systems.
+6.2 Sign-posts of planets in disks
+There are several indirect signatures of the presence of
+planets in disks: the λ Bo¨o phenomenon, falling evapo-
+rative bodies, gaps/rings in disks, kinematic signatures
+in the orbital motion of the gas in the vicinity of the
+orbit of a gas giant planet, and spiral arms. Here we
+describe what each of these signposts tell us about the
+presence of planets in disks around Herbig stars.
+6.2.1 The λ Bo¨otis phenomenon
+The identification of the λ Bo¨otis phenomenon among
+Herbig stars has been interpreted as a signpost of a gap-
+Fig. 28 Depth of search for the intermediate mass stars in
+the GPIES sample (Nielsen et al., 2019). Of the 123 interme-
+diate mass stars observed thus far, four reveal planets: β Pic,
+51 Eri, HD 95806, and HR 8799. Three of the six imaged
+companions orbit HR 8799.
+opening planet in the disk (e.g., Acke and Waelkens,
+2004, Folsom et al., 2012, Kama et al., 2015, Jermyn
+and Kama, 2018). The λ Bo¨otis phenomenon was first
+identified by Morgan et al. (1943) who noted a depletion
+of Mg and Ca in the photosphere of λ Bo¨otis. The def-
+inition of the class of λ Bo¨o stars has been refined and
+is now understood to comprise late-B through early-F
+stars (10,500 K ≤ Teff ≤ 6,500 K) that possess a deple-
+tion of refractory elements and near solar abundance
+of volatile species (Paunzen et al., 2002). Such stars
+comprise about 2% of main-sequence field stars in this
+spectral type range.
+There are two related leading hypotheses to account
+for this anomalous abundance pattern. Waters et al.
+(1992) propose that λ Bo¨o stars continue to accrete
+residual material from the circumstellar environment.
+The refractory elements are disproportionately found
+in dust that is blown away more efficiently than gas re-
+sulting in this abundance pattern. Kamp et al. (2002)
+note that there is no correlation between the λ Bo¨o phe-
+nomenon with stellar age spanning several billion years
+leading them to suggest that the anomalous abundance
+pattern arises from the passage of these stars through
+the diffuse ISM. In this scenario gas is accreted selec-
+tively relative to the dust as the dust is blown away by
+the radiation pressure of the star.
+The λ Bo¨o abundance pattern observed among main
+sequence B-F stars has also been observed among Her-
+big stars (Acke and Waelkens, 2004, Bruderer et al.,
+2012, Folsom et al., 2012). In contrast to ∼2% of field
+stars that show this abundance pattern, Folsom et al.
+
+100
+4Stars
+Stars
+Stars
+Mass (MJup)
+4Stars
+10
+S
+1
+1
+10
+100
+Semi-Major Axis (AU)48
+Sean D. Brittain et al.
+(2012) found that at least 33% of Herbig stars show
+this effect. Building on this work, Kama et al. (2015)
+examined the relationship between the abundance of GI
+Herbig stars and GII Herbig stars (see also Kama et al.
+2016a,b, Jermyn and Kama 2018, Kama et al. 2019,
+Castelli et al. 2020). Kama et al. (2015) find that while
+the abundance of volatiles among GI and GII Herbig
+stars are equivalent, GI Herbig stars are depleted in re-
+fractory elements by ∼0.5 dex. These authors note that
+all known disks with cavities among Herbig stars are
+GI sources. They note that pressure bumps in the disk
+at the boundary of gaps (perhaps due to planet-disk
+tidal interactions) trap and hold back grains (cf. Sect.
+4.9.1), leading to accretion onto the star from an inner
+gas rich disk depleted in refractory elements. Based on
+their analysis they conclude that ∼1/3 of Herbig stars
+could possess a planet with sufficient mass to open a
+gap that results in a dust filtration.
+6.2.2 Falling Evaporative Bodies
+As mentioned in Sec. 2.3.2, the narrow, intermittent
+components of metallic absorption lines in the spectra
+of Herbig stars have been interpreted as due to infalling,
+evaporating material such as exo-comets.
+In fact, the presence of these infalling comets is an-
+other indirect signpost of planets in disks around Her-
+big stars. These were first observed towards the young
+debris disk β Pic by Ferlet et al. (1987). Beust et al.
+(1991) suggest that the presence of these infalling solid
+bodies result from stirring by a planetary mass body.
+Grady et al. (1996) observed similar behaviour towards
+a large sample of Herbig stars and suggest that this phe-
+nomenon is evidence that planets have already formed
+in the disk and thus perturb planetesimals onto eccen-
+tric orbits that bring them close to the star. However,
+the gas in the inner disk of Herbig stars should damp
+the eccentricity of these orbits. Further study of the
+association between the occurrence rate of red shifted
+absorption features and clearing of the inner disk (or
+perhaps the accretion rate) may clarify whether this
+mechanism is plausible.
+In the largest survey of this phenomenon to date,
+Rebollido et al. (2020) studied a sample of 117 main
+sequence stars with spectral types spanning G8 - B8.
+Their sample was selected on the basis of having either
+1) previous evidence of β Pic like phenomena, 2) an
+edge-on debris disk, 3) a debris disk with cold gas, 4)
+an infrared excess, 5) membership in a young associa-
+tion, 6) shell stars, or 6) a λ Bo¨o abundance pattern.
+Among this sample, 16 of the stars showed variable red
+or blue shifted features that could be attributed to in-
+falling evaporative bodies (i.e., exocomets) all of which
+were earlier than A9. They note that this could be due
+to the difficulty of detecting these signatures against
+the structure in the cooler photospheres. An unbiased
+survey of young A and B stars may shed additional
+light on the presence of planets around these stars nec-
+essary for stirring exocomets and thus the occurrence
+of planets in disks around Herbig stars.
+6.2.3 Rings and gaps in disks
+The presence of a planet in a disk also has other ef-
+fects on its structure, as we saw in section 4.9.1. To
+summarize, the radial drift that would naturally occur
+in disks can only be halted by strong enough pressure
+bumps, that in turn are caused by objects of certain
+mass. Pressure bumps due to massive planets will lead
+to disk structures like cavities or rings, while the ab-
+sence of strong pressure bumps will not be able to halt
+radial drift of the dust grains efficiently, making the
+disk more compact over time. In these disks, less mas-
+sive planets such as super-earths could still form. There-
+fore, for a 1.5 M⊙ star, disks with large cavities have
+massive planets (> 200 M�, while ring-like disks host
+somewhat lighter planets (M ∼ 70-200 M�), and lastly
+compact disks have planets with a mass < 10 M� (van
+der Marel and Mulders, 2021).
+From a comparison of exoplanet statistics with a
+large ALMA disk survey, not only including Herbig
+stars but also lower-mass T Tauri stars, van der Marel
+and Mulders (2021) show that the occurrence rate of
+exoplanets inferred from radial velocity and transit sur-
+veys among stars in different mass bins is in agreement
+with occurrence rate of disk structures (cavity, rings).
+The authors also conclude that the mass of a planet
+present in the disk is crucial in determining the disk
+structure and size.
+6.2.4 Kinematic Planetary Signatures
+When planets in a disk open a gap (cf. Sect. 4.9.1), the
+resulting pressure gradient will affect the orbital veloc-
+ity of the gas (Perez et al., 2015, P´erez et al., 2018, Pinte
+et al., 2019, Disk Dynamics Collaboration et al., 2020).
+The gas exterior to the gap will experience a boost and
+the gas interior to the orbit of the planet will be slowed
+(see for example Armitage, 2007). In the spiral struc-
+tures emanating from the planet, the deviation from
+a Keplerian orbit reaches a maximum. This results in
+a ‘Doppler flip’ (for a review of this phenomenon see
+Disk Dynamics Collaboration et al., 2020, and refer-
+ences therein). These authors propose a set of criteria
+for confirming that such kinematic signatures of planets
+
+Herbig Stars
+49
+(KSPs) are not artefacts due to processing and discuss
+other effects that can mimic this phenomenon.
+With the unparalleled sensitivity, spatial resolution,
+and spectral resolution of ALMA, several authors have
+presented evidence of KSPs in disks around Herbig stars:
+AB Aur (Tang et al., 2017), HD 163296 (Pinte et al.,
+2018b, Teague et al., 2018, 2021), HD 100546 (Walsh
+et al., 2017, Casassus and Perez, 2019, P´erez et al.,
+2020), HD 97048 (Pinte et al., 2019), and MWC 480
+(Teague et al., 2021). While these observations are too
+expensive to have conducted an unbiased survey of nearby
+Herbig stars, the results are suggestive. Application of
+this technique to more sources will elucidate the fre-
+quency of gas giant planet formation in disks.
+6.2.5 Spiral arms in disks
+High-resolution, high-contrast observations of Herbig
+disks with 8m class telescopes have produced exquisite
+images. Indeed, Dong et al. (2018a) noted that of the
+10 Herbig stars within 200 pc that had been imaged
+and lack a stellar companion from 0.3′′-5′′ that could
+drive spiral arms in the outer disk, five show spiral
+structure (Fig. 29). Since then additional sources have
+been imaged such as HD 139614 (Muro-Arena et al.,
+2020) which shows multiple rings and significant shad-
+owing indicative of warped disk. There are at least two
+mechanisms that can give rise to spiral structure: grav-
+itational instabilities or planet-disk interactions with a
+supra-Jovian mass planet. A gravitationally unstable
+disk will form spiral structures (e.g., Hall et al. 2019).
+While disk masses of order MD ∼ 0.5M⋆ are necessary
+to drive two-armed spirals and only last for thousands
+of years, multi-armed spirals can form with disk masses
+as low as 0.1M⋆ and persist for Myrs. Are such masses
+representative of disks around Herbig stars?
+Typical dust masses in GI Herbig stars are around
+1−3×10−4 M⊙(Garufi et al., 2018), so assuming d/g =
+0.01, disk masses would be typically 1 − 3 × 10−2 M⊙.
+However, measuring disk mass is fraught with uncer-
+tainty. Estimates of disk mass from CO isotopologues,
+mm-continuum, and disk accretion rates span roughly
+two orders of magnitude (Sect. 5.1). As disk mass es-
+timates from stellar accretion rates are often consis-
+tent with Mdisk ∼ 0.1M⋆, multi-armed spirals observed
+around Herbig stars could be the consequence of moder-
+ately gravitationally unstable disks. On the other hand,
+models of the upper limits on flux of HD suggest that
+most Herbig stars’ disks may not be gravitationally un-
+stable (Kama et al., 2020). Whatever the case, two-
+armed spirals require much higher disk masses and sur-
+vive in that state for very short periods of time, so
+it is unlikely that gravitational instability accounts for
+these.
+Alternatively, a massive planet can account for the
+spiral structure observed in these disks (e.g., Fung et al.,
+2015, Dong and Fung, 2017, Dong et al., 2018a). Thus it
+appears that the population of supra-Jovian mass plan-
+ets in the outer disk (≳ 30 au) of young intermediate
+mass stars could be ∼20-50% which is consistent with
+the occurrence rate inferred from Kama et al. (2015)
+from the abundance patterns of Herbig stars. However,
+at this time there has only been one confirmed detec-
+tion of a gas giant planet orbiting a Herbig star (AB Aur
+b; Currie et al. 2022; see also Zhou et al. 2022). While
+the direct detection of young massive companions orbit-
+ing intermediate mass stars remains quite low (Bowler,
+2016, Nielsen et al., 2019), indirect signposts of forming
+massive companions are quite common. The disparity
+between the detection rate of supra-Jovian mass planets
+beyond ∼30 au and the frequency of indirect signatures
+of planet formation in this range is a puzzle.
+Summary: There are a number of indirect pieces of
+evidence that point to the ubiquity of planet forma-
+tion in the disks of Herbig stars including the λ Bo¨o
+phenomenon, the presence of falling evaporative bod-
+ies, rings and gaps in disks, KPSs, and spiral structure.
+While the exoplanet statistics and occurrence rate of
+gaps/rings in disks are fairly consistent (van der Marel
+et al., 2021), there is tension between the detection
+rate of supra-Jovian mass planets from 30-300au and
+the occurrence rate of spiral structures pointing to the
+presence of supraJovian gas giant planets in this region
+(Dong et al., 2018a). Validation of these indirect sig-
+natures by connecting them to detections of planets is
+crucial.
+6.3 Detecting forming planets in disks
+The detectability of gas giant planets depends on their
+formation pathway. The two limits are the hot start
+and cold start births (e.g., Marley et al., 2007, Fortney
+et al., 2008, Spiegel and Burrows, 2012). In the case
+of the hot start, the accreting material goes into heat-
+ing the planet making it more luminous. In the case of
+the cold start, the accreting material radiates its en-
+ergy away resulting in a colder, less luminous young
+planet. For the first 100 Myr of the planet’s life, this
+makes a significant difference in the luminosity of the
+planet. In the case of the young MS stars HR 8799 and
+β Pic, it appears that the orbiting companions began
+their life as hot start planets (Brandt et al., 2021a,b).
+If this is the typical formation pathway for Jovian mass
+planets, then it sharpens the discrepancy between the
+
+50
+Sean D. Brittain et al.
+Fig. 29 10 single Herbig stars within 200pc that have been imaged with high contrast imagery (based on figures from Ginski
+et al., 2016, Kusakabe et al., 2012, Pohl et al., 2017, van der Marel et al., 2021, Muro-Arena et al., 2018, Benisty et al., 2015,
+Garufi et al., 2013, Hashimoto et al., 2011, Avenhaus et al., 2017, Follette et al., 2017). Of these 10 Herbig stars, five show
+spiral structure indicative of the presence of a supra-Jovian mass planet (Dong et al., 2018b).
+evident signposts of forming massive companions and
+the direct detection of such companions orbiting young
+intermediate mass stars.
+One possibility is that the initial conditions of form-
+ing planets span the whole cold start – hot start contin-
+uum (Spiegel and Burrows, 2012). If there is a signifi-
+cant number of planets that begin their life as cold start
+objects, then the escaping accretion energy from the cir-
+cumplanetary disk should be readily detectable (Brit-
+tain et al., 2020). Several complementary techniques
+have been employed to detect the presence of form-
+ing planets in disks such as sparse aperture masking
+(e.g., Hu´elamo et al. 2011), angular differential imag-
+ing (ADI; e.g., Marois et al. 2006), Hα imaging (e.g.,
+Close et al. 2014), and deep searches with ALMA (e.g.,
+Andrews et al., 2021). There have been several intrigu-
+ing hints of planets imaged in disks around Herbig stars
+(e.g., HD 100546-Quanz et al. 2013a, Currie et al. 2014,
+Quanz et al. 2015, Currie et al. 2015, Follette et al.
+2017, Rameau et al. 2017, Currie et al. 2017, MWC
+758-Reggiani et al. 2018, Wagner et al. 2019, Boccaletti
+et al. 2021, HD 169142-Reggiani et al. 2014, Ligi et al.
+2018, Gratton et al. 2019, and AB Aur Currie et al.
+2022); however, AB Aur is the only Herbig star with a
+confirmed planet detected in the disk thus far. This low
+detection rate is similar to that of T Tauri stars where
+PDS 70 is the only one for which forming planets have
+been imaged (Keppler et al., 2018, M¨uller et al., 2018,
+Haffert et al., 2019, Isella et al., 2019, Zurlo et al., 2020,
+Benisty et al., 2021).
+It could be that planets in disks accrete episodically,
+and our sample is too small to have detected a forming
+planet in its accretion outburst phase (Brittain et al.,
+2020). Another possibility is that emission from circum-
+planetary disks peaks in the MIR and current NIR sur-
+veys for forming planets lack the requisite sensitivity
+to detect a forming planet (e.g., Szul´agyi et al. 2019).
+An alternative approach to direct imaging of a forming
+planet is spectroscopic monitoring of warm gas emission
+lines arising from the circumplanetary disk.
+Rab and Kamp (2019) used the thermochemical code,
+ProDiMo (Woitke et al., 2009), to calculate the gas and
+dust temperature of a circumplanetary disk. They find
+that the gas is much hotter than the dust. In their ref-
+erence model, gas at a temperature of ≳1500 K extends
+to 0.3 au before dropping to 500 K at 0.5 au and 150 K
+at 1 au. The temperature depends on the interstellar
+background radiation, the accretion luminosity of the
+planet, and shock heating as gas enters the circumplan-
+etary disk. They showed that it is plausible to detect
+rotational lines of CO from a circumplanetary disk with
+ALMA. The spatial and spectral resolution of ALMA
+will provide useful insight to the circumplanetary struc-
+ture of material accreting onto forming planets.
+While the circumplanetary disk is not resolvable
+with 8m class telescopes, high-resolution spectroscopy
+serves as a surrogate for spatial resolution. This tech-
+nique was pioneered in the study of classical T Tauri
+stars and has been applied extensively to the study of
+warm CO and OH emission in disks around Herbig stars
+5. Such observations may also provide the means to de-
+tect circumplanetary disks (Brittain et al., 2019).
+Circumplanetary envelopes have complex structures
+that likely include a rotationally supported circumplan-
+
+HD 97048
+MWC 480o
+HD 169142
+HD 163296
+IRS 48
+=134 au
+:185.au
+1"=137 au
+=114 au
+1"=101 au
+SAO 206462
+AB Aur
+HD 142527
+HD 100546
+MWC
+=160 au
+1"=136 au
+1'=163 au
+1"=157 au
+"=110 auHerbig Stars
+51
+etary disk whose outer extent may range from one-third
+to the full extent of the Hill sphere (e.g., Quillen et al.,
+2004, Ayliffe and Bate, 2009b,a, Martin and Lubow,
+2011, Tanigawa et al., 2012, Ayliffe and Bate, 2012,
+Gressel et al., 2013, Szul´agyi et al., 2014, 2016, 2017).
+Models indicate that the temperature in the circum-
+planetary disk is ≳ 1000 K in steady state (Szul´agyi,
+2017) and perhaps much higher during an outburst
+(Zhu, 2015). At these sizes and temperatures, ro-vibrational
+emission of CO in the NIR is also detectable (e.g., Na-
+jita et al., 2003).
+The ro-vibrational CO emission from the Herbig
+star with a pre-transition disk, HD 100546, may arise
+from such a scenario. The presence of an inner compan-
+ion has been inferred from a component of the v = 1−0
+ro-vibrational CO emission that varies relative to the
+stable hot band (i.e., v′ ≥ 2) emission (Brittain et al.
+2019). The profile of the v = 1 − 0 ro-vibrational line
+varied relative to the lines with v′ ≥ 2 (i.e., the hot
+band lines). In 2003 the line profile of the v = 1 − 0
+lines matched the profile of the hot band lines. In 2006
+the red side of the v = 1 − 0 line brightened. In 2010,
+the v = 1 − 0 line remained elevated relative to 2003,
+but the Doppler shift of the emission was -1 km s−1. In
+2013, the blue side of the v = 1 − 0 line was brighter
+than in 2003. By 2017, the line profile returned to the
+profile of the gas in 2003 (Brittain et al., 2019). The
+Doppler shift and time between observations is consis-
+tent with a source of warm gas orbiting at 11.6 – 12.3
+au. In the case of HD 100546, the CO flux is consis-
+tent with emission from gas in a circumplanetary disk
+with a radius of ∼ 0.3 au (Brittain et al., 2013). Py-
+erin et al. (2021) model the 0.9mm ALMA images of
+this HD 100546 and find that an 8MJup planet best re-
+produces the ring structure that is observed. The Hill
+sphere of an object with this mass 12au from HD 100546
+is ∼1au, so a circumplanetary disk that fills one-third
+of the Hill sphere is comparable to the size of the emit-
+ting region inferred from the CO emission. Oberg et al.
+(2022) applied thermochemical modeling of such a cir-
+cumplanetary disk and found that the luminosity of the
+emission of the CO rovibrational emission inferred from
+their modeling is consistent with the observed luminos-
+ity.
+The source of the CO emission is now behind the
+near side of the disk. When it emerges in 2031, the
+source of emission can be studied with 30 m class tele-
+scopes. In the meantime, ongoing monitoring of CO
+emission from similar transition disks around Herbig
+stars may provide additional candidate sources (Ban-
+zatti et al., 2022). Expansion of this sample will open
+the door to more detailed studies of this important en-
+vironment.
+Summary: There has only been one robust detection
+of a planet in a disk around a Herbig star at the time
+of this writing (Currie et al., 2022). Improvements in
+instrumentation and the commissioning of 30m class
+telescopes will likely enable further detections. A com-
+plimentary approach to detecting the presence of the
+planet is to observe gas lines from the circumplanetary
+disk. Rab and Kamp (2019) show that rotational lines
+of CO from circumstellar disks should be observable for
+wide-orbit systems. Brittain et al. (2019) provide evi-
+dence of ro-vibrational CO emission arising from a cir-
+cumplanetary disk that is consistent with expectations
+from models (Oberg et al., 2022).
+7 FUTURE PROSPECTS
+Immense progress has been made since the last ded-
+icated review of Herbig stars (Waters and Waelkens,
+1998b), and there are several exciting lines of inquiry
+available to astronomers that promise to advance our
+understanding of these important objects even more
+over the next 25 years. Here we summarize a few of
+the key areas of investigation that we believe will be
+particularly fruitful.
+Since George Herbig first proposed a class of in-
+termediate mass pre-main sequence stars, identifying
+objects of this class has been a challenge. Over the
+years, catalogs of Herbig stars have included contro-
+versial candidates. As the number of objects in these
+catalogs has been limited, the study of intermediate
+mass pre-main sequence stars has necessarily been lim-
+ited. Furthermore, once pre-main sequence intermedi-
+ate mass stars shed their disk, they are difficult to iden-
+tify due to a lack of activity signatures (the so-called
+“Naked Herbigs” that are analogs to weak lined T Tauri
+stars). Large scale surveys such as from telescopes such
+as Spitzer, WISE, and Gaia have improved this situa-
+tion. For example, Mooley et al. (2013) used Spitzer and
+Wise data to identify young A stars in Taurus. Using
+the Gaia database, Vioque et al. (2020) used Machine
+Learning to increase the number of Herbig-candidates
+by an order of magnitude. Upcoming large scale surveys
+enabled by instrumentation such as WEAVE and facil-
+ities such as Pan-STARRS and the Vera Rubin Obser-
+vatory promise to enable further such advances in our
+identification of Herbig stars.
+The source of the X-ray emission observed from Her-
+big stars is still not well understood. Roughly 70% of
+Herbig stars are binaries (Sec. 2.1) and roughly 70% of
+Herbig stars are detected in X-rays (Sec. 2.2). However,
+there is little overlap among these samples. A dedicated
+study of multiplicity among Herbig stars for which X-
+ray observations exist will clarify the extent to which
+
+52
+Sean D. Brittain et al.
+lower mass companions can account for the X-ray prop-
+erties of Herbigs.
+Related to this is the structure of the stellar mag-
+netic field. There is compelling evidence that Herbig
+stars with masses ≲4 M⊙ accrete magnetospherically,
+but the geometry of these fields has not been estab-
+lished. The more massive Herbig stars appear to be
+accreting by some other process, with boundary layer
+accretion being the leading contender. Modeling this for
+Herbig stars will clarify the situation and perhaps pro-
+vide a more accurate means of converting accretion lu-
+minosity to accretion rate. There is some evidence that
+the accretion rate of 2-2.5M⊙ Herbig stars declines as
+t−2
+age from ∼3-10Myr. However, this may underestimate
+the rate of decline as non-accreting A stars in this age
+bin are not included in this sample. Combining data
+from the evolutionary precursors to Herbig stars (inter-
+mediate mass T Tauri stars) and non-accreting A-stars
+in this age bin will shed light on how the accretion rate
+of intermediate mass stars evolves.
+As the UV excess that veils the Balmer discontinu-
+ity is difficult to measure for accretion rates less than
+10−8M⊙ yr−1, we must rely on proxies such as Hi emis-
+sion lines. However, the underlying physics that drives
+this correlation is not known. Optical and NIR inter-
+ferometry at longer baselines is necessary to determine
+the origin of these lines - particularly for very low ac-
+creting sources. As it stands, the accretion rates in-
+ferred for Herbig stars imply much higher disk masses
+than typically observed by other indirect tracers such as
+(sub)mm CO lines (and their isotopologues), (sub)mm
+dust emission, and HD emission.
+Excellent progress has been made on understanding
+the distribution of dust in disks and the resultant SED.
+The evolutionary pathways that lead to GI and GII
+disks and the metamorphosis of pre-transitional disks
+to transition disks to debris disks remains an open ques-
+tion. New instrumentation such as MATISSE on the
+VLT will provide unparalleled interferometric imaging
+in the thermal IR (L′−, M−, and N−) bands. This will
+clarify the radial structure of the inner disks around GI
+and GII Herbig stars. The James Webb Space Tele-
+scope, with its dramatic increase in sensitivity, will en-
+able the study of solid state features for a much larger
+sample of Herbig stars allowing better characterization
+of the role of environment on the dust properties of
+these stars, and to detect weak emission from gas in
+the inner disk. Such studies will also enable studies of
+the role stellar multiplicity plays in the development of
+GI and GII disks. ALMA has revolutionized our under-
+standing of mm grains in disks, and now the Square
+Kilometer Array (SKA) promises to do the same for
+cm-sized grains (Ilee et al., 2020). Looking even fur-
+ther ahead the Next Generation Very Long Array will
+provide unprecedented resolution and sensitivity at fre-
+quencies bridging SKA and ALMA.
+Our knowledge of the gas content of Herbig disks
+has increased remarkably over the past 25yrs. Thermo-
+chemical modeling of disks is able to reproduce many
+of the trends observed among various gas emission lines
+spanning the NIR to the mm. JWST, with its enhanced
+resolution and sensitivity, promises to open new win-
+dows into the gas content of disks albeit many known
+Herbig stars being too bright to be studied. Under-
+standing how the gas content and excitation varies among
+stars with different effective temperatures, degrees of
+flaring, and dust properties will improve the charac-
+terization of the initial chemical conditions of forming
+planets; especially in the inner disk (<10 au) the syn-
+ergy between continuum and emission line studies can
+provide unique insights. We note that ALMA observa-
+tions have only scratched the surface of understanding
+the chemistry in disks (MWC 480 and HD 163296 the
+only two disks being studied in detail) and more efforts
+are required to push beyond the commonly used tracer
+CO. Perhaps the most direct tracer of disk mass is HD,
+but the conversion of line flux from this molecule into
+disk masses requires careful characterization of the disk
+temperature which in turn depends sensitively on the
+dust properties of the disk. The mass of disks around
+Herbig stars remains an ongoing puzzle.
+Finally, the detection of planets around Herbig stars
+remains a challenge. The advent of 30m class telescopes
+in the coming decade will enhance our sensitivity to the
+presence of forming planets and move the inner working
+angle closer to the star. The detection of a significant
+sample of forming planets will provide the means to
+probe the early evolution of forming planets and clar-
+ify the range of initial conditions (bounded by the cold
+start and hot start scenarios) are reflected in the pop-
+ulation of planets and thus clarify the status of direct
+imaging surveys of gas giant planets around young main
+sequence stars in the solar neighborhood.
+8 A NEW DEFINITION OF HERBIG STARS
+While the empirical classification criteria that defined
+the classes of Herbig and T Tauri stars have been, and
+still are, very useful for many studies of star- and planet
+formation, we already noted in Sect. 1.1 that a full view
+on the evolution of intermediate mass stars should ide-
+ally be based on the mass of the star (more difficult
+to derive directly from observations) and not directly
+on its temperature (evident from spectral type). This
+thought motivates the definition of a new, stellar mass-
+based definition of the group of Herbig stars, i.e. leaving
+
+Herbig Stars
+53
+out the spectral type limitation of the Herbig star or T
+Tauri star definitions. As a lower mass boundary we
+propose to use the criterion that the atmosphere has
+to be radiative at the ZAMS. We propose to define the
+Herbig stars as the class of intermediate mass young
+stars that are evolving towards the main sequence, with
+mass ≳1.5 M⊙, that are surrounded by a remnant accre-
+tion disk, as evidenced by the detection of circumstellar
+gas at optical and/or longer wavelengths, and an IR ex-
+cess caused by circumstellar dust. Herbig stars can be
+subdivided into warmer Herbig Ae/Be stars and cooler
+IMTT stars. The upper mass boundary is more diffi-
+cult establish. The stars with masses ≳ 8-10M⊙ likely
+reach the main sequence prior to the dissipation of the
+surrounding envelope and are all but impossible to de-
+tect on a pre-main sequence track. However there are
+well established pre-main sequence B stars that exceed
+this mass (e.g., MWC 297). This definition carves out a
+general area in the HR diagram whose boundaries are
+set by the birth line, the ZAMS line, and evolutionary
+tracks of stars with mass ≳1.5M⊙.
+Acknowledgements IK acknowledges funding from the Eu-
+ropean Union H2020-MSCA-ITN-2019 under Grant Agree-
+ment no. 860470 (CHAMELEON). GM acknowledges fund-
+ing from the Spanish project ”On the Rocks II” (PGC2018-
+101950-B-100). RDO acknowledges funding for the STARRY
+project which received funding from the European Union’s
+Horizon 2020 research and innovation programme under MSCA
+ITN-EID grant agreement No 676036.
+Conflict of interest
+The authors declare that they have no conflict of inter-
+est.
+References
+Ababakr KM, Oudmaijer RD, Vink JS (2016) Linear
+spectropolarimetry across the optical spectrum of
+Herbig Ae/Be stars. MNRAS461(3):3089–3110, DOI
+10.1093/mnras/stw1534, 1607.02440
+Ababakr KM, Oudmaijer RD, Vink JS (2017) A sta-
+tistical spectropolarimetric study of Herbig Ae/Be
+stars.
+MNRAS472:854–868,
+DOI
+10.1093/mnras/
+stx1891, 1707.08408
+Acke B, Waelkens C (2004) Chemical analysis of
+24 dusty (pre-)main-sequence stars. A&A427:1009–
+1017, DOI 10.1051/0004-6361:20041460, astro-ph/
+0408221
+Acke B, van den Ancker ME, Dullemond CP, van
+Boekel R, Waters LBFM (2004) Correlation between
+grain growth and disk geometry in Herbig Ae/Be
+systems. A&A422:621–626, DOI 10.1051/0004-6361:
+20040197, astro-ph/0404553
+Acke B, van den Ancker ME, Dullemond CP (2005)
+[O I] 6300 ˚A emission in Herbig Ae/Be systems:
+Signature of Keplerian rotation. A&A436(1):209–
+230, DOI 10.1051/0004-6361:20042484, astro-ph/
+0502504
+Acke B, Bouwman J, Juh´asz A, Henning T, van
+den Ancker ME, Meeus G, Tielens AGGM, Wa-
+ters LBFM (2010) Spitzer’s View on Aromatic and
+Aliphatic Hydrocarbon Emission in Herbig Ae Stars.
+ApJ718(1):558–574, DOI 10.1088/0004-637X/718/
+1/558, 1006.1130
+Adams SC, ´Ad´amkovics M, Carr JS, Najita JR, Brit-
+tain SD (2019) Water and OH Emission from the
+Inner Disk of a Herbig Ae/Be Star. ApJ871(2):173,
+DOI 10.3847/1538-4357/aaf9a4, 1812.07094
+Ag´undez M, Roueff E, Le Petit F, Le Bourlot J (2018)
+The chemistry of disks around T Tauri and Herbig
+Ae/Be stars. A&A616:A19, DOI 10.1051/0004-6361/
+201732518, 1803.09450
+Aikawa Y, Cataldi G, Yamato Y, Zhang K, Booth AS,
+Furuya K, Andrews SM, Bae J, Bergin EA, Bergner
+JB, Bosman AD, Cleeves LI, Czekala I, Guzm´an VV,
+Huang J, Ilee JD, Law CJ, Le Gal R, Loomis RA,
+M´enard F, Nomura H, ¨Oberg KI, Qi C, Schwarz
+KR, Teague R, Tsukagoshi T, Walsh C, Wilner
+DJ (2021) Molecules with ALMA at Planet-forming
+Scales (MAPS). XIII. HCO+ and Disk Ionization
+Structure. ApJS257(1):13, DOI 10.3847/1538-4365/
+ac143c, 2109.06419
+Alecian E, Wade GA, Catala C, Grunhut JH, Land-
+street JD, Bagnulo S, B¨ohm T, Folsom CP, Mars-
+den S, Waite I (2013) A high-resolution spectropo-
+larimetric survey of Herbig Ae/Be stars - I. Obser-
+vations and measurements. MNRAS429:1001–1026,
+DOI 10.1093/mnras/sts383, 1211.2907
+ALMA Partnership, Brogan CL, P´erez LM, Hunter
+TR, Dent WRF, Hales AS, Hills RE, Corder S, Fo-
+malont EB, Vlahakis C, Asaki Y, Barkats D, Hi-
+rota A, Hodge JA, Impellizzeri CMV, Kneissl R, Li-
+uzzo E, Lucas R, Marcelino N, Matsushita S, Nakan-
+ishi K, Phillips N, Richards AMS, Toledo I, Aladro
+R, Broguiere D, Cortes JR, Cortes PC, Espada D,
+Galarza F, Garcia-Appadoo D, Guzman-Ramirez L,
+Humphreys EM, Jung T, Kameno S, Laing RA, Leon
+S, Marconi G, Mignano A, Nikolic B, Nyman LA,
+Radiszcz M, Remijan A, Rod´on JA, Sawada T, Taka-
+hashi S, Tilanus RPJ, Vila Vilaro B, Watson LC,
+Wiklind T, Akiyama E, Chapillon E, de Gregorio-
+Monsalvo I, Di Francesco J, Gueth F, Kawamura A,
+Lee CF, Nguyen Luong Q, Mangum J, Pietu V, San-
+hueza P, Saigo K, Takakuwa S, Ubach C, van Kem-
+
+54
+Sean D. Brittain et al.
+pen T, Wootten A, Castro-Carrizo A, Francke H,
+Gallardo J, Garcia J, Gonzalez S, Hill T, Kamin-
+ski T, Kurono Y, Liu HY, Lopez C, Morales F,
+Plarre K, Schieven G, Testi L, Videla L, Villard
+E, Andreani P, Hibbard JE, Tatematsu K (2015)
+The 2014 ALMA Long Baseline Campaign: First
+Results from High Angular Resolution Observations
+toward the HL Tau Region. ApJ808(1):L3, DOI
+10.1088/2041-8205/808/1/L3, 1503.02649
+Alonso-Albi T, Fuente A, Bachiller R, Neri R, Plane-
+sas P, Testi L, Bern´e O, Joblin C (2009) Circumstel-
+lar disks around Herbig Be stars. A&A497:117–136,
+DOI 10.1051/0004-6361/200810401, 0812.1636
+Andre P, Ward-Thompson D, Barsony M (1993) Sub-
+millimeter Continuum Observations of rho Ophiuchi
+A: The Candidate Protostar VLA 1623 and Prestel-
+lar Clumps. ApJ406:122, DOI 10.1086/172425
+Andrews SM (2020) Observations of Protoplanetary
+Disk Structures. ARA&A58:483–528, DOI 10.1146/
+annurev-astro-031220-010302, 2001.05007
+Andrews SM, Huang J, P´erez LM, Isella A, Dulle-
+mond CP, Kurtovic NT, Guzm´an VV, Carpenter
+JM, Wilner DJ, Zhang S, Zhu Z, Birnstiel T, Bai
+XN, Benisty M, Hughes AM, ¨Oberg KI, Ricci L
+(2018a) The Disk Substructures at High Angular
+Resolution Project (DSHARP). I. Motivation, Sam-
+ple, Calibration, and Overview. ApJ869:L41, DOI
+10.3847/2041-8213/aaf741, 1812.04040
+Andrews SM, Huang J, P´erez LM, Isella A, Dulle-
+mond CP, Kurtovic NT, Guzm´an VV, Carpenter
+JM, Wilner DJ, Zhang S, Zhu Z, Birnstiel T, Bai
+XN, Benisty M, Hughes AM, ¨Oberg KI, Ricci L
+(2018b) The Disk Substructures at High Angular
+Resolution Project (DSHARP). I. Motivation, Sam-
+ple, Calibration, and Overview. ApJ869(2):L41, DOI
+10.3847/2041-8213/aaf741, 1812.04040
+Andrews SM, Elder W, Zhang S, Huang J, Benisty
+M,
+Kurtovic
+NT,
+Wilner
+DJ,
+Zhu
+Z,
+Car-
+penter
+JM,
+P´erez
+LM,
+Teague
+R,
+Isella
+A,
+Ricci
+L
+(2021)
+Limits
+on
+Millimeter
+Contin-
+uum Emission from Circumplanetary Material in
+the DSHARP Disks. ApJ916(1):51, DOI 10.3847/
+1538-4357/ac00b9, 2105.08821
+Ansdell M, Williams JP, van der Marel N, Carpenter
+JM, Guidi G, Hogerheijde M, Mathews GS, Manara
+CF, Miotello A, Natta A, Oliveira I, Tazzari M, Testi
+L, van Dishoeck EF, van Terwisga SE (2016) ALMA
+Survey of Lupus Protoplanetary Disks. I. Dust and
+Gas Masses. ApJ828(1):46, DOI 10.3847/0004-637X/
+828/1/46, 1604.05719
+Ansdell M, Williams JP, Trapman L, van Terwisga SE,
+Facchini S, Manara CF, van der Marel N, Miotello
+A, Tazzari M, Hogerheijde M, Guidi G, Testi L, van
+Dishoeck EF (2018) ALMA Survey of Lupus Proto-
+planetary Disks. II. Gas Disk Radii. ApJ859(1):21,
+DOI 10.3847/1538-4357/aab890, 1803.05923
+Antonellini
+S
+(2016)
+Water
+in
+protoplanetary
+disks
+-
+Line
+flux
+modeling
+and
+disk
+struc-
+ture.
+PhD
+thesis,
+Kapteyn
+Astronomical
+In-
+stitute,
+University
+of
+Groningen,
+Landleven
+12,
+9700
+AV
+Groningen,
+The
+Netherlands
+¡EMAIL¿antonellini@astro.rug.nl¡/EMAIL¿
+Antonellini S, Kamp I, Riviere-Marichalar P, Meijerink
+R, Woitke P, Thi WF, Spaans M, Aresu G, Lee
+G (2015) Understanding the water emission in the
+mid- and far-IR from protoplanetary disks around T
+Tauri stars. A&A582:A105, DOI 10.1051/0004-6361/
+201525724, 1510.01482
+Antonellini S, Banzatti A, Kamp I, Thi WF, Woitke
+P (2020) Model exploration of near-IR ro-vibrational
+CO emission as a tracer of inner cavities in protoplan-
+etary disks. A&A637:A29, DOI 10.1051/0004-6361/
+201834077, 2003.11788
+Armitage PJ (2007) Lecture notes on the formation and
+early evolution of planetary systems. arXiv e-prints
+astro-ph/0701485, astro-ph/0701485
+Armitage PJ (2019) Physical Processes in Protoplan-
+etary Disks. Saas-Fee Advanced Course 45:1, DOI
+10.1007/978-3-662-58687-7 1
+Arun R, Mathew B, Manoj P, Ujjwal K, Kartha
+SS, Viswanath G, Narang M, Paul KT (2019) On
+the Mass Accretion Rate and Infrared Excess in
+Herbig Ae/Be Stars. AJ157(4):159, DOI 10.3847/
+1538-3881/ab0ca1, 1903.01070
+Arun R, Mathew B, Rengaswamy S, Manoj P, Narang
+M, Kartha SS, Maheshwar G (2021) Discovery of
+an M-type companion to the Herbig Ae Star V1787
+Ori. MNRAS501(1):1243–1252, DOI 10.1093/mnras/
+staa3652, 2011.10222
+Asplund
+M,
+Grevesse
+N,
+Sauval
+AJ,
+Scott
+P
+(2009) The Chemical Composition of the Sun.
+ARA&A47(1):481–522, DOI 10.1146/annurev.astro.
+46.060407.145222, 0909.0948
+Augereau JC, Lagrange AM, Mouillet D, Papaloizou
+JCB, Grorod PA (1999) On the HR 4796 A circum-
+stellar disk. A&A348:557–569, astro-ph/9906429
+Avenhaus H, Quanz SP, Meyer MR, Brittain SD,
+Carr JS, Najita JR (2014) HD100546 Multi-epoch
+Scattered Light Observations. ApJ790(1):56, DOI
+10.1088/0004-637X/790/1/56, 1405.6120
+Avenhaus H, Quanz SP, Schmid HM, Dominik C,
+Stolker T, Ginski C, de Boer J, Szul´agyi J, Garufi
+A, Zurlo A, Hagelberg J, Benisty M, Henning T,
+M´enard F, Meyer MR, Baruffolo A, Bazzon A,
+Beuzit JL, Costille A, Dohlen K, Girard JH, Gisler
+D, Kasper M, Mouillet D, Pragt J, Roelfsema R,
+
+Herbig Stars
+55
+Salasnich B, Sauvage JF (2017) Exploring Dust
+around HD 142527 down to 0.”025 (4 au) Us-
+ing SPHERE/ZIMPOL. AJ154(1):33, DOI 10.3847/
+1538-3881/aa7560, 1705.09680
+Ayliffe BA, Bate MR (2009a) Circumplanetary disc
+properties obtained from radiation hydrodynam-
+ical simulations of gas accretion by protoplan-
+ets. MNRAS397:657–665, DOI 10.1111/j.1365-2966.
+2009.15002.x, 0904.4884
+Ayliffe BA, Bate MR (2009b) Gas accretion on to plan-
+etary cores: three-dimensional self-gravitating radi-
+ation hydrodynamical calculations. MNRAS393:49–
+64, DOI 10.1111/j.1365-2966.2008.14184.x, 0811.
+1259
+Ayliffe BA, Bate MR (2012) The growth and hy-
+drodynamic collapse of a protoplanet envelope.
+MNRAS427:2597–2612,
+DOI
+10.1111/j.1365-2966.
+2012.21979.x, 1208.5513
+Bagnoli T, van Lieshout R, Waters LBFM, van der Plas
+G, Acke B, van Winckel H, Raskin G, Meerburg PD
+(2010) An Inner Gaseous Disk Around the Herbig
+Be Star MWC 147. ApJ724(1):L5–L8, DOI 10.1088/
+2041-8205/724/1/L5, 1010.1414
+Bai XN (2013) Wind-driven Accretion in Protoplane-
+tary Disks. II. Radial Dependence and Global Pic-
+ture. ApJ772(2):96, DOI 10.1088/0004-637X/772/2/
+96, 1305.7232
+Baines
+D,
+Oudmaijer
+RD,
+Porter
+JM,
+Pozzo
+M
+(2006) On the binarity of Herbig Ae/Be stars.
+MNRAS367:737–753,
+DOI
+10.1111/j.1365-2966.
+2006.10006.x, astro-ph/0512534
+Baldovin-Saavedra C, Audard M, Carmona A, G¨udel
+M, Briggs K, Rebull LM, Skinner SL, Ercolano B
+(2012) On the origin of [Ne II] emission in young
+stars: mid-infrared and optical observations with the
+Very Large Telescope. A&A543:A30, DOI 10.1051/
+0004-6361/201118329, 1205.2182
+Banzatti A, Pontoppidan KM (2015) An Empirical
+Sequence of Disk Gap Opening Revealed by Rovi-
+brational CO. ApJ809:167, DOI 10.1088/0004-637X/
+809/2/167, 1507.06650
+Banzatti A, Pontoppidan KM, Salyk C, Herczeg GJ,
+van Dishoeck EF, Blake GA (2017a) The Depletion of
+Water During Dispersal of Planet-forming Disk Re-
+gions. ApJ834(2):152, DOI 10.3847/1538-4357/834/
+2/152, 1611.06230
+Banzatti A, Pontoppidan KM, Salyk C, Herczeg GJ,
+van Dishoeck EF, Blake GA (2017b) The Depletion
+of Water During Dispersal of Planet-forming Disk
+Regions. ApJ834:152, DOI 10.3847/1538-4357/834/
+2/152, 1611.06230
+Banzatti A, Garufi A, Kama M, Benisty M, Brittain
+S, Pontoppidan KM, Rayner J (2018) Observing the
+linked depletion of dust and CO gas at 0.1-10 au in
+disks of intermediate-mass stars. A&A609:L2, DOI
+10.1051/0004-6361/201732034, 1711.09095
+Banzatti A, Abernathy KM, Brittain S, Bosman AD,
+Pontoppidan KM, Boogert A, Jensen S, Carr J, Na-
+jita J, Grant S, Sigler RM, Sanchez MA, Kern J,
+Rayner JT (2022) Scanning Disk Rings and Winds in
+CO at 0.01-10 au: A High-resolution M-band Spec-
+troscopy Survey with IRTF-iSHELL. AJ163(4):174,
+DOI 10.3847/1538-3881/ac52f0, 2202.03438
+Beckwith SVW, Sargent AI, Chini RS, Guesten R
+(1990) A survey for circumstellar disks around young
+stellar objects. AJ99:924–945, DOI 10.1086/115385
+Behrend R, Maeder A (2001) Formation of mas-
+sive stars by growing accretion rate. A&A373:190–
+198, DOI 10.1051/0004-6361:20010585, astro-ph/
+0105054
+Beltr´an MT, de Wit WJ (2016) Accretion disks in
+luminous young stellar objects. A&ARv24:6, DOI
+10.1007/s00159-015-0089-z, 1509.08335
+Benisty M, Perraut K, Mourard D, Stee P, Lima
+GHRA, Le Bouquin JB, Borges Fernandes M, Ches-
+neau O, Nardetto N, Tallon-Bosc I, McAlister H,
+Ten Brummelaar T, Ridgway S, Sturmann J, Stur-
+mann L, Turner N, Farrington C, Goldfinger PJ
+(2013) Enhanced Hα activity at periastron in the
+young and massive spectroscopic binary HD 200775.
+A&A555:A113, DOI 10.1051/0004-6361/201219893,
+1306.0390
+Benisty M, Juhasz A, Boccaletti A, Avenhaus H, Milli
+J, Thalmann C, Dominik C, Pinilla P, Buenzli E,
+Pohl A, Beuzit JL, Birnstiel T, de Boer J, Bon-
+nefoy M, Chauvin G, Christiaens V, Garufi A, Grady
+C, Henning T, Huelamo N, Isella A, Langlois M,
+M´enard F, Mouillet D, Olofsson J, Pantin E, Pinte
+C, Pueyo L (2015) Asymmetric features in the proto-
+planetary disk MWC 758. A&A578:L6, DOI 10.1051/
+0004-6361/201526011, 1505.05325
+Benisty M, Bae J, Facchini S, Keppler M, Teague R,
+Isella A, Kurtovic NT, P´erez LM, Sierra A, Andrews
+SM, Carpenter J, Czekala I, Dominik C, Henning
+T, Menard F, Pinilla P, Zurlo A (2021) A Circum-
+planetary Disk around PDS70c. ApJ916(1):L2, DOI
+10.3847/2041-8213/ac0f83, 2108.07123
+Benisty M, Dominik C, Follette K, Garufi A, Gin-
+ski C, Hashimoto J, Keppler M, Kley W, Mon-
+nier J (2022) Optical and Near-infrared View of
+Planet-forming Disks and Protoplanets. arXiv e-
+prints arXiv:2203.09991, 2203.09991
+Bergin EA, Cleeves LI, Gorti U, Zhang K, Blake
+GA, Green JD, Andrews SM, Evans NJ II, Hen-
+ning T, ¨Oberg K, Pontoppidan K, Qi C, Salyk C,
+van Dishoeck EF (2013) An old disk still capable
+
+56
+Sean D. Brittain et al.
+of forming a planetary system. Nature493:644–646,
+DOI 10.1038/nature11805, 1303.1107
+Bergner JB, ¨Oberg KI, Guzm´an VV, Law CJ, Loomis
+RA, Cataldi G, Bosman AD, Aikawa Y, Andrews
+SM, Bergin EA, Booth AS, Cleeves LI, Czekala I,
+Huang J, Ilee JD, Le Gal R, Long F, Nomura H,
+M´enard F, Qi C, Schwarz KR, Teague R, Tsuk-
+agoshi T, Walsh C, Wilner DJ, Yamato Y (2021)
+Molecules with ALMA at Planet-forming Scales
+(MAPS). XI. CN and HCN as Tracers of Photo-
+chemistry in Disks. ApJS257(1):11, DOI 10.3847/
+1538-4365/ac143a, 2109.06694
+Berrilli F, Corciulo G, Ingrosso G, Lorenzetti D,
+Nisini B, Strafella F (1992) Infrared Emission from
+Dust Structures Surrounding Herbig Ae/Be Stars.
+ApJ398:254, DOI 10.1086/171853
+Bertout C (1989) T Tauri stars - Wild as dust.
+ARA&A27:351–395,
+DOI
+10.1146/annurev.aa.27.
+090189.002031
+Bertout C, Basri G, Bouvier J (1988) Accretion disks
+around T Tauri stars. ApJ330:350–373, DOI 10.1086/
+166476
+Beust H, Vidal-Madjar A, Ferlet R (1991) The beta
+Pectoris protoplanetary system. XII. Planetary per-
+turbations in the disk and star-grazing bodies.
+A&A247:505
+Bibo EA, The PS (1990) A study of the Herbig Ae-
+type star UX Orionis : its remarkable behaviour in
+the colour-magnitude diagram, and the properties of
+its dust shell. A&A236:155
+Bik
+A,
+Thi
+WF
+(2004)
+Evidence
+for
+an
+inner
+molecular disk around massive Young Stellar Ob-
+jects. A&A427:L13–L16, DOI 10.1051/0004-6361:
+200400088, astro-ph/0410098
+Biller BA, Liu MC, Rice K, Wahhaj Z, Nielsen
+E, Hayward T, Kuchner MJ, Close LM, Chun
+M, Ftaclas C, Toomey DW (2015) The Gemini
+NICI Planet-Finding Campaign: asymmetries in the
+HD 141569 disc. MNRAS450(4):4446–4457, DOI
+10.1093/mnras/stv870, 1504.05224
+Birnstiel T, Dullemond CP, Brauer F (2010) Gas- and
+dust evolution in protoplanetary disks. A&A513:A79,
+DOI 10.1051/0004-6361/200913731, 1002.0335
+Blondel PFC, Djie HRETA (2006) Modeling of PMS
+Ae/Fe stars using UV spectra. A&A456(3):1045–
+1068, DOI 10.1051/0004-6361:20040269
+Boccaletti A, Di Folco E, Pantin E, Dutrey A, Guil-
+loteau S, Tang YW, Pi´etu V, Habart E, Milli J,
+Beck TL, Maire AL (2020) Possible evidence of on-
+going planet formation in AB Aurigae. A showcase
+of the SPHERE/ALMA synergy. A&A637:L5, DOI
+10.1051/0004-6361/202038008, 2005.09064
+Boccaletti A, Pantin E, M´enard F, Galicher R, Lan-
+glois M, Benisty M, Gratton R, Chauvin G, Ginski C,
+Lagrange AM, Zurlo A, Biller B, Bonavita M, Bon-
+nefoy M, Brown-Sevilla S, Cantalloube F, Desidera S,
+D’Orazi V, Feldt M, Hagelberg J, Lazzoni C, Mesa
+D, Meyer M, Perrot C, Vigan A, Sauvage JF, Ramos
+J, Rousset G, Magnard Y (2021) Investigating point
+sources in MWC 758 with SPHERE. A&A652:L8,
+DOI 10.1051/0004-6361/202141177, 2107.07850
+Boehler Y, Weaver E, Isella A, Ricci L, Grady C, Car-
+penter J, Perez L (2017) A Close-up View of the
+Young Circumbinary Disk HD 142527. ApJ840(1):60,
+DOI 10.3847/1538-4357/aa696c, 1704.00787
+Boersma C, Peeters E, Mart´ın-Hern´andez NL, van
+der Wolk G, Verhoeff AP, Tielens AGGM, Wa-
+ters LBFM, Pel JW (2009) A spatial study of
+the mid-IR emission features in four Herbig Ae/Be
+stars. A&A502(1):175–187, DOI 10.1051/0004-6361/
+200911820
+Bohn AJ, Benisty M, Perraut K, van der Marel N,
+W¨olfer L, van Dishoeck EF, Facchini S, Manara
+CF, Teague R, Francis L, Berger JP, Garcia-Lopez
+R, Ginski C, Henning T, Kenworthy M, Kraus S,
+M´enard F, M´erand A, P´erez LM (2022) Probing in-
+ner and outer disk misalignments in transition disks.
+Constraints from VLTI/GRAVITY and ALMA ob-
+servations. A&A658:A183, DOI 10.1051/0004-6361/
+202142070, 2112.00123
+Bonnell IA, Bate MR, Clarke CJ, Pringle JE (2001)
+Competitive accretion in embedded stellar clusters.
+MNRAS323(4):785–794, DOI 10.1046/j.1365-8711.
+2001.04270.x, astro-ph/0102074
+Booth AS, Walsh C, Ilee JD, Notsu S, Qi C, Nomura
+H, Akiyama E (2019) The First Detection of 13C17O
+in a Protoplanetary Disk: A Robust Tracer of Disk
+Gas Mass. ApJ882(2):L31, DOI 10.3847/2041-8213/
+ab3645, 1908.05045
+Bosman AD, Banzatti A, Bruderer S, Tielens AGGM,
+Blake GA, van Dishoeck EF (2019) Probing planet
+formation and disk substructures in the inner disk
+of Herbig Ae stars with CO rovibrational emission.
+A&A631:A133, DOI 10.1051/0004-6361/201935910,
+1909.02031
+Bosman AD, Alarc´on F, Bergin EA, Zhang K, van’t
+Hoff MLR, ¨Oberg KI, Guzm´an VV, Walsh C, Aikawa
+Y, Andrews SM, Bergner JB, Booth AS, Cataldi G,
+Cleeves LI, Czekala I, Furuya K, Huang J, Ilee JD,
+Law CJ, Le Gal R, Liu Y, Long F, Loomis RA,
+M´enard F, Nomura H, Qi C, Schwarz KR, Teague
+R, Tsukagoshi T, Yamato Y, Wilner DJ (2021)
+Molecules with ALMA at Planet-forming Scales
+(MAPS). VII. Substellar O/H and C/H and Su-
+perstellar C/O in Planet-feeding Gas. ApJS257(1):7,
+DOI 10.3847/1538-4365/ac1435, 2109.06221
+
+Herbig Stars
+57
+Boss AP (1997) Giant planet formation by gravita-
+tional instability. Science 276:1836–1839, DOI 10.
+1126/science.276.5320.1836
+Bouvier J, Corporon P (2001) Herbig Ae/Be Visual Bi-
+naries. In: Zinnecker H, Mathieu R (eds) The Forma-
+tion of Binary Stars, vol 200, p 155
+Bouvier J, Alencar SHP, Harries TJ, Johns-Krull CM,
+Romanova MM (2007) Magnetospheric Accretion in
+Classical T Tauri Stars. Protostars and Planets V pp
+479–494, astro-ph/0603498
+Bouwman J, Meeus G, de Koter A, Hony S, Dominik
+C, Waters LBFM (2001) Processing of silicate dust
+grains in Herbig Ae/Be systems. A&A375:950–962,
+DOI 10.1051/0004-6361:20010878
+Bowler BP (2016) Imaging Extrasolar Giant Planets.
+PASP128(10):102001, DOI 10.1088/1538-3873/128/
+968/102001, 1605.02731
+Brandt GM, Brandt TD, Dupuy TJ, Li Y, Michalik D
+(2021a) Precise Dynamical Masses and Orbital Fits
+for beta Pic β and β Pic c. AJ161(4):179, DOI 10.
+3847/1538-3881/abdc2e, 2011.06215
+Brandt GM, Brandt TD, Dupuy TJ, Michalik D, Mar-
+leau GD (2021b) The First Dynamical Mass Mea-
+surement in the HR 8799 System. ApJ915(1):L16,
+DOI 10.3847/2041-8213/ac0540, 2105.12820
+Braun TAM, Yen HW, Koch PM, Manara CF, Miotello
+A, Testi L (2021) Dynamical Stellar Masses of Pre-
+main-sequence Stars in Lupus and Taurus Obtained
+with ALMA Surveys in Comparison with Stellar
+Evolutionary Models. ApJ908(1):46, DOI 10.3847/
+1538-4357/abd24f, 2012.07441
+Bressan A, Marigo P, Girardi L, Salasnich B, Dal Cero
+C, Rubele S, Nanni A (2012) PARSEC: stellar tracks
+and isochrones with the PAdova and TRieste Stellar
+Evolution Code. MNRAS427:127–145, DOI 10.1111/
+j.1365-2966.2012.21948.x, 1208.4498
+Brittain SD, Rettig TW (2002) CO and H+
+3 in the
+protoplanetary disk around the star HD141569.
+Nature418:57–59, DOI 10.1038/nature800
+Brittain SD, Simon T, Najita JR, Rettig TW (2007)
+Warm
+Gas
+in
+the
+Inner
+Disks
+around
+Young
+Intermediate-Mass Stars. ApJ659:685–704, DOI 10.
+1086/511255, astro-ph/0612201
+Brittain SD, Najita JR, Carr JS, Liskowsky J, Trout-
+man MR, Doppmann GW (2013) High-resolution
+Near-infrared
+Spectroscopy
+of
+HD
+100546.
+II.
+Analysis of Variable Rovibrational CO Emission
+Lines. ApJ767:159, DOI 10.1088/0004-637X/767/2/
+159, 1311.5647
+Brittain SD, Najita JR, Carr JS, ´Ad´amkovics M,
+Reynolds N (2016) A Study of Ro-vibrational OH
+Emission from Herbig Ae/Be Stars. ApJ830(2):112,
+DOI 10.3847/0004-637X/830/2/112, 1608.00986
+Brittain
+SD,
+Najita
+JR,
+Carr
+JS
+(2019)
+High-
+resolution Near-infrared Spectroscopy of HD 100546.
+IV.
+Orbiting
+Companion
+Disappears
+on
+Sched-
+ule. ApJ883(1):37, DOI 10.3847/1538-4357/ab380b,
+1908.00132
+Brittain SD, Najita JR, Dong R, Zhu Z (2020) The
+Planetary Luminosity Problem: “Missing Planets”
+and the Observational Consequences of Episodic
+Accretion. ApJ895(1):48, DOI 10.3847/1538-4357/
+ab8388, 2003.11980
+Bruderer S (2013) Survival of molecular gas in cavi-
+ties of transition disks. I. CO. A&A559:A46, DOI
+10.1051/0004-6361/201321171, 1308.2966
+Bruderer S, van Dishoeck EF, Doty SD, Herczeg
+GJ (2012) The warm gas atmosphere of the HD
+100546 disk seen by Herschel. Evidence of a gas-
+rich, carbon-poor atmosphere? A&A541:A91, DOI
+10.1051/0004-6361/201118218, 1201.4860
+Bryden G, Chen X, Lin DNC, Nelson RP, Papaloizou
+JCB (1999) Tidally Induced Gap Formation in Pro-
+tostellar Disks: Gap Clearing and Suppression of
+Protoplanetary Growth. ApJ514(1):344–367, DOI
+10.1086/306917
+Calvet N, Muzerolle J, Brice˜no C, Hern´andez J, Hart-
+mann L, Saucedo JL, Gordon KD (2004) The Mass
+Accretion Rates of Intermediate-Mass T Tauri Stars.
+AJ128:1294–1318, DOI 10.1086/422733
+Calvet N, D’Alessio P, Watson DM, Franco-Hern´andez
+R, Furlan E, Green J, Sutter PM, Forrest WJ, Hart-
+mann L, Uchida KI, Keller LD, Sargent B, Najita J,
+Herter TL, Barry DJ, Hall P (2005) Disks in Tran-
+sition in the Taurus Population: Spitzer IRS Spectra
+of GM Aurigae and DM Tauri. ApJ630:L185–L188,
+DOI 10.1086/491652
+Caratti o Garatti A, Tambovtseva LV, Garcia Lopez
+R, Kraus S, Schertl D, Grinin VP, Weigelt G, Hof-
+mann KH, Massi F, Lagarde S, Vannier M, Mal-
+bet F (2015) AMBER/VLTI high spectral resolu-
+tion observations of the Brγ emitting region in HD
+98922. A compact disc wind launched from the inner
+disc region. A&A582:A44, DOI 10.1051/0004-6361/
+201526002, 1508.00798
+Carmona
+A
+(2021)
+HD169142
+with
+CRIRES.
+A&Asubmitted
+Carmona
+A,
+van
+den
+Ancker
+ME,
+Henning
+T,
+Pavlyuchenkov Y, Dullemond CP, Goto M, Thi WF,
+Bouwman J, Waters LBFM (2008) A search for mid-
+infrared molecular hydrogen emission from proto-
+planetary disks. A&A477(3):839–852, DOI 10.1051/
+0004-6361:20077846, 0710.2813
+Carmona A, Pinte C, Thi WF, Benisty M, M´enard F,
+Grady C, Kamp I, Woitke P, Olofsson J, Roberge
+A, Brittain S, Duchˆene G, Meeus G, Martin-Za¨ıdi C,
+
+58
+Sean D. Brittain et al.
+Dent B, Le Bouquin JB, Berger JP (2014) Constrain-
+ing the structure of the transition disk HD 135344B
+(SAO 206462) by simultaneous modeling of multi-
+wavelength gas and dust observations. A&A567:A51,
+DOI 10.1051/0004-6361/201322534, 1403.6193
+Carmona A, Thi WF, Kamp I, Baruteau C, Matter A,
+van den Ancker M, Pinte C, K´osp´al A, Audard M,
+Liebhart A, Sicilia-Aguilar A, Pinilla P, Reg´aly Z,
+G¨udel M, Henning T, Cieza LA, Baldovin-Saavedra
+C, Meeus G, Eiroa C (2017) A gas density drop in the
+inner 6 AU of the transition disk around the Herbig
+Ae star HD 139614 . Further evidence for a giant
+planet inside the disk? A&A598:A118, DOI 10.1051/
+0004-6361/201628472, 1609.06708
+Carney MT, Fedele D, Hogerheijde MR, Favre C, Walsh
+C, Bruderer S, Miotello A, Murillo NM, Klaassen
+PD, Henning T, van Dishoeck EF (2018) Probing
+midplane CO abundance and gas temperature with
+DCO+ in the protoplanetary disk around HD 169142.
+A&A614:A106, DOI 10.1051/0004-6361/201732384,
+1802.09280
+Carney MT, Hogerheijde MR, Guzm´an VV, Walsh C,
+¨Oberg KI, Fayolle EC, Cleeves LI, Carpenter JM,
+Qi C (2019) Upper limits on CH3OH in the HD
+163296 protoplanetary disk. Evidence for a low gas-
+phase CH3OH-to-H2CO ratio. A&A623:A124, DOI
+10.1051/0004-6361/201834353, 1901.02689
+Carr JS, Tokunaga AT, Najita J (2004) Hot H2O Emis-
+sion and Evidence for Turbulence in the Disk of a
+Young Star. ApJ603:213–220, DOI 10.1086/381356,
+astro-ph/0312125
+Casassus S, Perez S (2019) Kinematic detections of pro-
+toplanets: a Doppler-flip in the disk of HD100546.
+arXiv e-prints arXiv:1906.06302, 1906.06302
+Casassus S, van der Plas G, M SP, Dent WRF, Fo-
+malont E, Hagelberg J, Hales A, Jord´an A, Mawet
+D, M´enard F, Wootten A, Wilner D, Hughes AM,
+Schreiber MR, Girard JH, Ercolano B, Canovas H,
+Rom´an PE, Salinas V (2013) Flows of gas through a
+protoplanetary gap. Nature493(7431):191–194, DOI
+10.1038/nature11769, 1305.6062
+Casassus S, Wright CM, Marino S, Maddison ST, Woot-
+ten A, Roman P, P´erez S, Pinilla P, Wyatt M,
+Moral V, M´enard F, Christiaens V, Cieza L, van der
+Plas G (2015) A Compact Concentration of Large
+Grains in the HD 142527 Protoplanetary Dust Trap.
+ApJ812(2):126, DOI 10.1088/0004-637X/812/2/126,
+1505.07743
+Caselli P, Walmsley CM, Tafalla M, Dore L, Myers
+PC (1999) CO Depletion in the Starless Cloud Core
+L1544. ApJ523(2):L165–L169, DOI 10.1086/312280
+Casey MP, Zwintz K, Guenther DB, Weiss WW,
+Amado PJ, D´ıaz-Fraile D, Rodriguez E, Kuschnig R,
+Matthews JM, Moffat AFJ, Rowe JF, Rucinski SM,
+Sasselov D (2013) MOST observations of the Herbig
+Ae δ-Scuti star HD 34282. MNRAS428(3):2596–2604,
+DOI 10.1093/mnras/sts241, 1210.4828
+Castelli F, Hubrig S, J¨arvinen SP, Sch¨oller M (2020)
+The chemical composition of the Herbig Ae SB2
+system AK Sco (HD 152404). MNRAS491(2):2010–
+2024, DOI 10.1093/mnras/stz3015, 1910.09372
+Catala C (1994) The spectroscopic variability of the
+Herbig Ae/Be stars. In: The PS, Perez MR, van den
+Heuvel EPJ (eds) The Nature and Evolutionary Sta-
+tus of Herbig Ae/Be Stars, Astronomical Society of
+the Pacific Conference Series, vol 62, p 91
+Cataldi G, Yamato Y, Aikawa Y, Bergner JB, Fu-
+ruya K, Guzm´an VV, Huang J, Loomis RA, Qi C,
+Andrews SM, Bergin EA, Booth AS, Bosman AD,
+Cleeves LI, Czekala I, Ilee JD, Law CJ, Le Gal R,
+Liu Y, Long F, M´enard F, Nomura H, ¨Oberg KI,
+Schwarz KR, Teague R, Tsukagoshi T, Walsh C,
+Wilner DJ, Zhang K (2021) Molecules with ALMA at
+Planet-forming Scales (MAPS). X. Studying Deuter-
+ation at High Angular Resolution toward Protoplane-
+tary Disks. ApJS257(1):10, DOI 10.3847/1538-4365/
+ac143d, 2109.06462
+Cauley PW, Johns-Krull CM (2014) Diagnosing Mass
+Flows around Herbig Ae/Be Stars Using the He I
+λ10830 Line. ApJ797:112, DOI 10.1088/0004-637X/
+797/2/112, 1410.6964
+Cazzoletti P, van Dishoeck EF, Visser R, Facchini
+S, Bruderer S (2018) CN rings in full protoplan-
+etary disks around young stars as probes of disk
+structure. A&A609:A93, DOI 10.1051/0004-6361/
+201731457, 1709.01463
+Chapillon E, Guilloteau S, Dutrey A, Pi´etu V, Gu´elin
+M (2012) Chemistry in disks. VI. CN and HCN in
+protoplanetary disks. A&A537:A60, DOI 10.1051/
+0004-6361/201116762, 1109.5595
+Chiang EI, Goldreich P (1997) Spectral Energy Dis-
+tributions of T Tauri Stars with Passive Circum-
+stellar Disks. ApJ490:368–376, DOI 10.1086/304869,
+astro-ph/9706042
+Close LM, Follette KB, Males JR, Puglisi A, Xom-
+pero M, Apai D, Najita J, Weinberger AJ, Morzin-
+ski K, Rodigas TJ, Hinz P, Bailey V, Briguglio R
+(2014) Discovery of Hα Emission from the Close
+Companion inside the Gap of Transitional Disk HD
+142527. ApJ781:L30, DOI 10.1088/2041-8205/781/
+2/L30, 1401.1273
+Cohen M (1973) Infra-red observations of young stars
+- II. T Tauri stars and the Orion population. MN-
+RAS161:97, DOI 10.1093/mnras/161.1.97
+Cohen
+M
+(1980)
+Infrared
+observations
+of
+young
+stars.
+VIII.
+Spectra
+in
+the
+ten-micronregion.
+
+Herbig Stars
+59
+MNRAS191:499–509, DOI 10.1093/mnras/191.3.499
+Corporon
+P,
+Lagrange
+AM
+(1999)
+A
+search
+for
+spectroscopic binaries among Herbig Ae/Be stars.
+A&AS136:429–444, DOI 10.1051/aas:1999225
+Costigan G, Vink JS, Scholz A, Ray T, Testi L (2014)
+Temperaments of young stars: rapid mass accre-
+tion rate changes in T Tauri and Herbig Ae stars.
+MNRAS440:3444–3461, DOI 10.1093/mnras/stu529,
+1403.4088
+Cuppen HM, van Dishoeck EF, Herbst E, Tielens
+AGGM (2009) Microscopic simulation of methanol
+and
+formaldehyde
+ice
+formation
+in
+cold
+dense
+cores. A&A508(1):275–287, DOI 10.1051/0004-6361/
+200913119, 0911.0283
+Currie T, Muto T, Kudo T, Honda M, Brandt TD,
+Grady C, Fukagawa M, Burrows A, Janson M,
+Kuzuhara M, McElwain MW, Follette K, Hashimoto
+J, Henning T, Kandori R, Kusakabe N, Kwon J,
+Mede K, Morino Ji, Nishikawa J, Pyo TS, Ser-
+abyn G, Suenaga T, Takahashi Y, Wisniewski J,
+Tamura M (2014) Recovery of the Candidate Pro-
+toplanet HD 100546 b with Gemini/NICI and De-
+tection of Additional (Planet-induced?) Disk Struc-
+ture at Small Separations. ApJ796(2):L30, DOI
+10.1088/2041-8205/796/2/L30, 1411.0315
+Currie T, Cloutier R, Brittain S, Grady C, Burrows
+A, Muto T, Kenyon SJ, Kuchner MJ (2015) Re-
+solving the HD 100546 Protoplanetary System with
+the Gemini Planet Imager: Evidence for Multiple
+Forming, Accreting Planets. ApJ814(2):L27, DOI
+10.1088/2041-8205/814/2/L27, 1511.02526
+Currie T, Brittain S, Grady CA, Kenyon SJ, Muto T
+(2017) Clarifying the Status of HD 100546 as Ob-
+served by the Gemini Planet Imager. Research Notes
+of the American Astronomical Society 1(1):40, DOI
+10.3847/2515-5172/aaa022, 1712.02819
+Currie T, Lawson K, Schneider G, Lyra W, Wisniewski
+J, Grady C, Guyon O, Tamura M, Kotani T, Kawa-
+hara H, Brandt T, Uyama T, Muto T, Dong R,
+Kudo T, Hashimoto J, Fukagawa M, Wagner K, Lozi
+J, Chilcote J, Tobin T, Groff T, Ward-Duong K,
+Januszewski W, Norris B, Tuthill P, van der Marel
+N, Sitko M, Deo V, Vievard S, Jovanovic N, Mar-
+tinache F, Skaf N (2022) Images of embedded Jo-
+vian planet formation at a wide separation around
+AB Aurigae. Nature Astronomy 6:751–759, DOI
+10.1038/s41550-022-01634-x, 2204.00633
+Damiani F, Micela G, Sciortino S, Harnden J F R
+(1994) Einstein X-Ray Observations of Herbig Ae/Be
+Stars. ApJ436:807, DOI 10.1086/174957
+Danchi WC, Lopez B (2013) Effect of Metallicity on
+the Evolution of the Habitable Zone from the Pre-
+main Sequence to the Asymptotic Giant Branch and
+the Search for Life. ApJ769(1):27, DOI 10.1088/
+0004-637X/769/1/27, 1304.1464
+Dartois E, Dutrey A, Guilloteau S (2003) Structure of
+the DM Tau Outer Disk: Probing the vertical ki-
+netic temperature gradient. A&A399:773–787, DOI
+10.1051/0004-6361:20021638
+de Gregorio-Monsalvo I, M´enard F, Dent W, Pinte C,
+L´opez C, Klaassen P, Hales A, Cort´es P, Rawlings
+MG, Tachihara K, Testi L, Takahashi S, Chapillon E,
+Mathews G, Juhasz A, Akiyama E, Higuchi AE, Saito
+M, Nyman L˚A, Phillips N, Rod´on J, Corder S, Van
+Kempen T (2013) Unveiling the gas-and-dust disk
+structure in HD 163296 using ALMA observations.
+A&A557:A133, DOI 10.1051/0004-6361/201321603,
+1307.1357
+de Juan Ovelar M, Min M, Dominik C, Thalmann C,
+Pinilla P, Benisty M, Birnstiel T (2013) Imaging di-
+agnostics for transitional discs. A&A560:A111, DOI
+10.1051/0004-6361/201322218, 1309.1039
+de Juan Ovelar M, Pinilla P, Min M, Dominik C,
+Birnstiel T (2016) Constraining turbulence mixing
+strength in transitional discs with planets using
+SPHERE and ALMA. MNRAS459(1):L85–L89, DOI
+10.1093/mnrasl/slw051, 1603.09357
+Dent WRF, Greaves JS, Coulson IM (2005) CO emis-
+sion from discs around isolated HAeBe and Vega-
+excess stars. MNRAS359:663–676, DOI 10.1111/j.
+1365-2966.2005.08938.x, astro-ph/0502544
+Dent WRF, Thi WF, Kamp I, Williams JP, Menard F,
+Andrews S, Ardila D, Aresu G, Augereau JC, Bar-
+rado y Navascues D, Brittain S, Carmona A, Ciardi
+D, Danchi W, Donaldson J, Duchene G, Eiroa C,
+Fedele D, Grady C, de Gregorio-Molsalvo I, Howard
+C, Hu´elamo N, Krivov A, Lebreton J, Liseau R,
+Martin-Zaidi C, Mathews G, Meeus G, Mendigut´ıa
+I, Montesinos B, Morales-Calderon M, Mora A, No-
+mura H, Pantin E, Pascucci I, Phillips N, Pinte C,
+Podio L, Ramsay SK, Riaz B, Riviere-Marichalar P,
+Roberge A, Sandell G, Solano E, Tilling I, Torrelles
+JM, Vandenbusche B, Vicente S, White GJ, Woitke
+P (2013) GASPS—A Herschel Survey of Gas and
+Dust in Protoplanetary Disks: Summary and Initial
+Statistics. PASP125:477–505, DOI 10.1086/670826,
+1306.0275
+Di Folco E, P´ericaud J, Dutrey A, Augereau JC,
+Chapillon E, Guilloteau S, Pi´etu V, Boccaletti A
+(2020) An ALMA/NOEMA study of gas dissipation
+and dust evolution in the 5 Myr-old HD 141569A
+hybrid disc. A&A635:A94, DOI 10.1051/0004-6361/
+201732243
+Disk Dynamics Collaboration, Armitage PJ, Bae J,
+Benisty M, Bergin EA, Casassus S, Czekala I, Fac-
+chini S, Fung J, Hall C, Ilee JD, Keppler M,
+
+60
+Sean D. Brittain et al.
+Kuznetsova A, Le Gal R, Loomis RA, Lyra W,
+Manger N, Perez S, Pinte C, Price DJ, Rosotti G,
+Szulagyi J, Schwarz K, Simon JB, Teague R, Zhang K
+(2020) Visualizing the Kinematics of Planet Forma-
+tion. arXiv e-prints arXiv:2009.04345, 2009.04345
+Doi K, Kataoka A (2021) Estimate on Dust Scale
+Height from the ALMA Dust Continuum Image of
+the HD 163296 Protoplanetary Disk. ApJ912(2):164,
+DOI 10.3847/1538-4357/abe5a6, 2102.06209
+Dominik C, Dullemond CP, Waters LBFM, Walch
+S (2003) Understanding the spectra of isolated
+Herbig
+stars
+in
+the
+frame
+of
+a
+passive
+disk
+model. A&A398:607–619, DOI 10.1051/0004-6361:
+20021629, astro-ph/0212032
+Donehew B, Brittain S (2011) Measuring the Stellar
+Accretion Rates of Herbig Ae/Be Stars. AJ141:46,
+DOI 10.1088/0004-6256/141/2/46
+Dong R, Fung J (2017) How Bright are Planet-induced
+Spiral Arms in Scattered Light? ApJ835(1):38, DOI
+10.3847/1538-4357/835/1/38, 1612.00446
+Dong R, Rafikov R, Zhu Z, Hartmann L, Whitney B,
+Brandt T, Muto T, Hashimoto J, Grady C, Follette
+K, Kuzuhara M, Tanii R, Itoh Y, Thalmann C, Wis-
+niewski J, Mayama S, Janson M, Abe L, Brandner
+W, Carson J, Egner S, Feldt M, Goto M, Guyon O,
+Hayano Y, Hayashi M, Hayashi S, Henning T, Ho-
+dapp KW, Honda M, Inutsuka S, Ishii M, Iye M,
+Kandori R, Knapp GR, Kudo T, Kusakabe N, Mat-
+suo T, McElwain MW, Miyama S, Morino JI, Moro-
+Martin A, Nishimura T, Pyo TS, Suto H, Suzuki R,
+Takami M, Takato N, Terada H, Tomono D, Turner
+EL, Watanabe M, Yamada T, Takami H, Usuda
+T, Tamura M (2012) The Missing Cavities in the
+SEEDS Polarized Scattered Light Images of Transi-
+tional Protoplanetary Disks: A Generic Disk Model.
+ApJ750(2):161, DOI 10.1088/0004-637X/750/2/161,
+1203.1612
+Dong R, Zhu Z, Rafikov RR, Stone JM (2015) Observa-
+tional Signatures of Planets in Protoplanetary Disks:
+Spiral Arms Observed in Scattered Light Imaging
+Can be Induced by Planets. ApJ809:L5, DOI 10.
+1088/2041-8205/809/1/L5, 1507.03596
+Dong R, Fung J, Chiang E (2016) How Spirals and Gaps
+Driven by Companions in Protoplanetary Disks Ap-
+pear in Scattered Light at Arbitrary Viewing An-
+gles. ApJ826(1):75, DOI 10.3847/0004-637X/826/1/
+75, 1602.04814
+Dong R, Liu Sy, Eisner J, Andrews S, Fung J, Zhu
+Z, Chiang E, Hashimoto J, Liu HB, Casassus S,
+Esposito T, Hasegawa Y, Muto T, Pavlyuchenkov
+Y, Wilner D, Akiyama E, Tamura M, Wisniewski
+J (2018a) The Eccentric Cavity, Triple Rings, Two-
+armed Spirals, and Double Clumps of the MWC
+758 Disk. ApJ860(2):124, DOI 10.3847/1538-4357/
+aac6cb, 1805.12141
+Dong R, Najita JR, Brittain S (2018b) Spiral Arms
+in
+Disks:
+Planets
+or
+Gravitational
+Instability?
+ApJ862:103, DOI 10.3847/1538-4357/aaccfc, 1806.
+05183
+Doppmann GW, Najita JR, Carr JS, Graham JR
+(2011) Warm H2O and OH Disk Emission in V1331
+Cyg. ApJ738(1):112, DOI 10.1088/0004-637X/738/
+1/112, 1106.5173
+Drazkowska J, Bitsch B, Lambrechts M, Mulders GD,
+Harsono D, Vazan A, Liu B, Ormel CW, Kretke K,
+Morbidelli A (2022) Planet Formation Theory in the
+Era of ALMA and Kepler: from Pebbles to Exoplan-
+ets. arXiv e-prints arXiv:2203.09759, 2203.09759
+Duchˆene G (2015) Herbig AeBe stars: multiplicity and
+consequences. Ap&SS355(2):291–301, DOI 10.1007/
+s10509-014-2173-7, 1410.5883
+Duchˆene G, Beust H, Adjali F, Konopacky QM, Ghez
+AM (2006) Accurate stellar masses in the multiple
+system T Tauri. A&A457(1):L9–L12, DOI 10.1051/
+0004-6361:20065917, astro-ph/0608018
+Dullemond
+CP,
+Dominik
+C
+(2004a)
+Flaring
+vs.
+self-shadowed disks: The SEDs of Herbig Ae/Be
+stars. A&A417:159–168, DOI 10.1051/0004-6361:
+20031768, astro-ph/0401495
+Dullemond CP, Dominik C (2004b) The effect of
+dust settling on the appearance of protoplanetary
+disks. A&A421:1075–1086, DOI 10.1051/0004-6361:
+20040284, astro-ph/0405226
+Dullemond CP, Monnier JD (2010) The Inner Regions
+of Protoplanetary Disks. ARA&A48:205–239, DOI
+10.1146/annurev-astro-081309-130932, 1006.3485
+Dullemond CP, Dominik C, Natta A (2001) Pas-
+sive Irradiated Circumstellar Disks with an In-
+ner Hole. ApJ560(2):957–969, DOI 10.1086/323057,
+astro-ph/0106470
+Dullemond CP, van den Ancker ME, Acke B, van
+Boekel R (2003) Explaining UX Orionis Star Vari-
+ability with Self-shadowed Disks. ApJ594(1):L47–
+L50, DOI 10.1086/378400, astro-ph/0306113
+Dullemond CP, Isella A, Andrews SM, Skobleva I,
+Dzyurkevich N (2020) Midplane temperature and
+outer edge of the protoplanetary disk around HD
+163296.
+A&A633:A137,
+DOI
+10.1051/0004-6361/
+201936438, 1911.12434
+Edwards S, Fischer W, Hillenbrand L, Kwan J (2006)
+Probing T Tauri Accretion and Outflow with 1
+Micron Spectroscopy. ApJ646(1):319–341, DOI 10.
+1086/504832, astro-ph/0604006
+Eiroa C, Oudmaijer RD, Davies JK, de Winter D,
+Garz´on F, Palacios J, Alberdi A, Ferlet R, Grady
+CA, Collier Cameron A, Deeg HJ, Harris AW, Horne
+
+Herbig Stars
+61
+K, Mer´ın B, Miranda LF, Montesinos B, Mora A,
+Penny A, Quirrenbach A, Rauer H, Schneider J,
+Solano E, Tsapras Y, Wesselius PR (2002) On the
+simultaneous optical and near-infrared variability of
+pre-main sequence stars. A&A384:1038–1049, DOI
+10.1051/0004-6361:20020096
+Ekstr¨om S, Georgy C, Eggenberger P, Meynet G,
+Mowlavi N, Wyttenbach A, Granada A, Decressin
+T, Hirschi R, Frischknecht U, Charbonnel C, Maeder
+A (2012) Grids of stellar models with rotation. I.
+Models from 0.8 to 120 M⊙ at solar metallicity (Z
+= 0.014). A&A537:A146, DOI 10.1051/0004-6361/
+201117751, 1110.5049
+Ellerbroek LE, Kaper L, Bik A, de Koter A, Hor-
+robin M, Puga E, Sana H, Waters LBFM (2011) The
+Intermediate-mass Young Stellar Object 08576nr292:
+Discovery of A Disk-Jet System. ApJ732(1):L9, DOI
+10.1088/2041-8205/732/1/L9, 1103.4611
+Espaillat
+C,
+Muzerolle
+J,
+Najita
+J,
+Andrews
+S,
+Zhu Z, Calvet N, Kraus S, Hashimoto J, Kraus
+A, D’Alessio P (2014) An Observational Perspec-
+tive of Transitional Disks. In: Beuther H, Klessen
+RS, Dullemond CP, Henning T (eds) Protostars
+and Planets VI, p 497, DOI 10.2458/azu uapress
+9780816531240-ch022, 1402.7103
+Fabian D, J¨ager C, Henning T, Dorschner J, Mutschke
+H (2000) Steps toward interstellar silicate mineral-
+ogy. V. Thermal Evolution of Amorphous Magnesium
+Silicates and Silica. A&A364:282–292
+Facchini S, Birnstiel T, Bruderer S, van Dishoeck
+EF (2017) Different dust and gas radial extents
+in protoplanetary disks: consistent models of grain
+growth and CO emission. A&A605:A16, DOI 10.
+1051/0004-6361/201630329, 1705.06235
+Fairlamb JR, Oudmaijer RD, Mendigut´ıa I, Ilee JD,
+van den Ancker ME (2015) A spectroscopic survey
+of Herbig Ae/Be stars with X-shooter - I. Stellar pa-
+rameters and accretion rates. MNRAS453:976–1001,
+DOI 10.1093/mnras/stv1576, 1507.05967
+Fairlamb JR, Oudmaijer RD, Mendigutia I, Ilee JD,
+van den Ancker ME (2017) A spectroscopic survey
+of Herbig Ae/Be stars with X-Shooter - II. Accre-
+tion diagnostic lines. MNRAS464:4721–4735, DOI
+10.1093/mnras/stw2643, 1610.09636
+Fang M, Kim JS, van Boekel R, Sicilia-Aguilar A, Hen-
+ning T, Flaherty K (2013) Young Stellar Objects in
+Lynds 1641: Disks, Accretion, and Star Formation
+History. ApJS207:5, DOI 10.1088/0067-0049/207/1/
+5, 1304.7777
+Fedele D, van den Ancker ME, Acke B, van der Plas
+G, van Boekel R, Wittkowski M, Henning T, Bouw-
+man J, Meeus G, Rafanelli P (2008) The struc-
+ture of the protoplanetary disk surrounding three
+young intermediate mass stars. II. Spatially resolved
+dust and gas distribution. A&A491(3):809–820, DOI
+10.1051/0004-6361:200810126, 0809.3947
+Fedele D, Pascucci I, Brittain S, Kamp I, Woitke P,
+Williams JP, Dent WRF, Thi WF (2011) Water De-
+pletion in the Disk Atmosphere of Herbig AeBe Stars.
+ApJ732(2):106, DOI 10.1088/0004-637X/732/2/106,
+1103.6039
+Fedele D, Bruderer S, van Dishoeck EF, Herczeg GJ,
+Evans NJ, Bouwman J, Henning T, Green J (2012)
+Warm H2O and OH in the disk around the Her-
+big star HD 163296. A&A544:L9, DOI 10.1051/
+0004-6361/201219615, 1207.3969
+Fedele D, Bruderer S, van Dishoeck EF, Carr J, Herczeg
+GJ, Salyk C, Evans NJ, Bouwman J, Meeus G, Hen-
+ning T, Green J, Najita JR, G¨udel M (2013) DIGIT
+survey of far-infrared lines from protoplanetary disks.
+I. [O i], [C ii], OH, H2O, and CH+. A&A559:A77,
+DOI 10.1051/0004-6361/201321118, 1308.1578
+Fedele D, van Dishoeck EF, Kama M, Bruderer S,
+Hogerheijde MR (2016) Probing the 2D temperature
+structure of protoplanetary disks with Herschel ob-
+servations of high-J CO lines. A&A591:A95, DOI
+10.1051/0004-6361/201526948, 1604.02055
+Fedele D, Carney M, Hogerheijde MR, Walsh C,
+Miotello A, Klaassen P, Bruderer S, Henning T,
+van Dishoeck EF (2017) ALMA unveils rings and
+gaps in the protoplanetary system ¡ASTROBJ¿HD
+169142¡/ASTROBJ¿: signatures of two giant pro-
+toplanets. A&A600:A72, DOI 10.1051/0004-6361/
+201629860, 1702.02844
+Ferlet R, Hobbs LM, Vidal-Madjar A (1987) The beta
+Pictoris circumstellar disk. V. Time variations of the
+Ca II-K line. A&A185:267–270
+Finkenzeller U (1985) Rotational velocities, spectral
+types and forbidden lines of Herbig Ae/Be stars.
+A&A151:340–348
+Finkenzeller U, Mundt R (1984) The Herbig Ae/Be
+stars associated with nebulosity. A&AS55:109–141
+Flaherty K, Hughes AM, Simon JB, Qi C, Bai
+XN, Bulatek A, Andrews SM, Wilner DJ, K´osp´al
+´A (2020) Measuring Turbulent Motion in Planet-
+forming Disks with ALMA: A Detection around DM
+Tau and Nondetections around MWC 480 and V4046
+Sgr. ApJ895(2):109, DOI 10.3847/1538-4357/ab8cc5,
+2004.12176
+Flaherty KM, Hughes AM, Rosenfeld KA, Andrews
+SM, Chiang E, Simon JB, Kerzner S, Wilner DJ
+(2015) Weak Turbulence in the HD 163296 Proto-
+planetary Disk Revealed by ALMA CO Observa-
+tions. ApJ813(2):99, DOI 10.1088/0004-637X/813/
+2/99, 1510.01375
+Flaherty KM, Hughes AM, Rose SC, Simon JB, Qi
+
+62
+Sean D. Brittain et al.
+C, Andrews SM, K´osp´al ´A, Wilner DJ, Chiang E,
+Armitage PJ, Bai Xn (2017) A Three-dimensional
+View of Turbulence: Constraints on Turbulent Mo-
+tions in the HD 163296 Protoplanetary Disk Us-
+ing DCO+. ApJ843(2):150, DOI 10.3847/1538-4357/
+aa79f9, 1706.04504
+Follette KB, Rameau J, Dong R, Pueyo L, Close LM,
+Duchˆene G, Fung J, Leonard C, Macintosh B, Males
+JR, Marois C, Millar-Blanchaer MA, Morzinski KM,
+Mullen W, Perrin M, Spiro E, Wang J, Ammons SM,
+Bailey VP, Barman T, Bulger J, Chilcote J, Cot-
+ten T, De Rosa RJ, Doyon R, Fitzgerald MP, Good-
+sell SJ, Graham JR, Greenbaum AZ, Hibon P, Hung
+LW, Ingraham P, Kalas P, Konopacky Q, Larkin JE,
+Maire J, Marchis F, Metchev S, Nielsen EL, Oppen-
+heimer R, Palmer D, Patience J, Poyneer L, Rajan A,
+Rantakyr¨o FT, Savransky D, Schneider AC, Sivara-
+makrishnan A, Song I, Soummer R, Thomas S, Vega
+D, Wallace JK, Ward-Duong K, Wiktorowicz S, Wolff
+S (2017) Complex Spiral Structure in the HD 100546
+Transitional Disk as Revealed by GPI and MagAO.
+AJ153:264, DOI 10.3847/1538-3881/aa6d85, 1704.
+06260
+Folsom CP, Bagnulo S, Wade GA, Alecian E, Land-
+street JD, Marsden SC, Waite IA (2012) Chemical
+abundances of magnetic and non-magnetic Herbig
+Ae/Be stars. MNRAS422:2072–2101, DOI 10.1111/
+j.1365-2966.2012.20718.x, 1202.1845
+Fortney JJ, Marley MS, Saumon D, Lodders K (2008)
+Synthetic Spectra and Colors of Young Giant Planet
+Atmospheres: Effects of Initial Conditions and At-
+mospheric Metallicity. ApJ683(2):1104–1116, DOI
+10.1086/589942, 0805.1066
+Frost
+AJ,
+Oudmaijer
+RD,
+de
+Wit
+WJ,
+Lums-
+den
+SL
+(2019)
+A
+multi-scale
+exploration
+of
+a
+massive young stellar object. A transition disk
+around G305.20+0.21? A&A625:A44, DOI 10.1051/
+0004-6361/201834583, 1903.04393
+Fung J, Artymowicz P, Wu Y (2015) The 3D Flow Field
+Around an Embedded Planet. ApJ811(2):101, DOI
+10.1088/0004-637X/811/2/101, 1505.03152
+Gaia Collaboration, Brown AGA, Vallenari A, Prusti T,
+de Bruijne JHJ, Mignard F, Drimmel R, Babusiaux
+C, Bailer-Jones CAL, Bastian U, et al (2016) Gaia
+Data Release 1. Summary of the astrometric, pho-
+tometric, and survey properties. A&A595:A2, DOI
+10.1051/0004-6361/201629512, 1609.04172
+Gaia Collaboration, Brown AGA, Vallenari A, Prusti
+T, de Bruijne JHJ, Babusiaux C, Bailer-Jones CAL,
+Biermann M, Evans DW, Eyer L, et al (2018) Gaia
+Data Release 2. Summary of the contents and survey
+properties. A&A616:A1, DOI 10.1051/0004-6361/
+201833051, 1804.09365
+Garcia Lopez R, Natta A, Testi L, Habart E (2006)
+Accretion rates in Herbig Ae stars. A&A459:837–
+842, DOI 10.1051/0004-6361:20065575, astro-ph/
+0609032
+Garcia Lopez R, Tambovtseva LV, Schertl D, Grinin
+VP, Hofmann KH, Weigelt G, Caratti o Garatti
+A (2015) Probing the accretion-ejection connec-
+tion with VLTI/AMBER. High spectral resolution
+observations of the Herbig Ae star HD 163296.
+A&A576:A84, DOI 10.1051/0004-6361/201424778,
+1502.03027
+Garcia Lopez R, Kurosawa R, Caratti o Garatti A,
+Kreplin A, Weigelt G, Tambovtseva LV, Grinin VP,
+Ray TP (2016) Investigating the origin and spectro-
+scopic variability of the near-infrared H I lines in the
+Herbig star VV Ser. MNRAS456(1):156–170, DOI
+10.1093/mnras/stv2664, 1511.03181
+Garrison J L M (1978) Observational studies of
+the Herbig Ae/Be stars. III. Spectrophotometry.
+ApJ224:535–545, DOI 10.1086/156401
+Garufi A, Quanz SP, Avenhaus H, Buenzli E, Do-
+minik C, Meru F, Meyer MR, Pinilla P, Schmid
+HM, Wolf S (2013) Small vs. large dust grains in
+transitional disks: do different cavity sizes indicate
+a planet?. SAO 206462 (HD 135344B) in polar-
+ized light with VLT/NACO. A&A560:A105, DOI
+10.1051/0004-6361/201322429, 1311.4195
+Garufi A, Podio L, Kamp I, M´enard F, Brittain S,
+Eiroa C, Montesinos B, Alonso-Mart´ınez M, Thi WF,
+Woitke P (2014) The protoplanetary disk of FT
+Tauri: multiwavelength data analysis and modeling.
+A&A567:A141, DOI 10.1051/0004-6361/201321987,
+1405.7692
+Garufi A, Benisty M, Stolker T, Avenhaus H, de Boer
+J, Pohl A, Quanz SP, Dominik C, Ginski C, Thal-
+mann C, van Boekel R, Boccaletti A, Henning T,
+Janson M, Salter G, Schmid HM, Sissa E, Langlois
+M, Beuzit JL, Chauvin G, Mouillet D, Augereau
+JC, Bazzon A, Biller B, Bonnefoy M, Buenzli E,
+Cheetham A, Daemgen S, Desidera S, Engler N,
+Feldt M, Girard J, Gratton R, Hagelberg J, Keller
+C, Keppler M, Kenworthy M, Kral Q, Lopez B,
+Maire AL, Menard F, Mesa D, Messina S, Meyer
+MR, Milli J, Min M, Muller A, Olofsson J, Pawellek
+N, Pinte C, Szulagyi J, Vigan A, Wahhaj Z, Wa-
+ters R, Zurlo A (2017a) Three Years of SPHERE:
+The Latest View of the Morphology and Evolution
+of Protoplanetary Discs. The Messenger 169:32–37,
+DOI 10.18727/0722-6691/5036, 1710.02795
+Garufi A, Meeus G, Benisty M, Quanz SP, Banzatti A,
+Kama M, Canovas H, Eiroa C, Schmid HM, Stolker
+T, Pohl A, Rigliaco E, M´enard F, Meyer MR, van
+Boekel R, Dominik C (2017b) Evolution of proto-
+
+Herbig Stars
+63
+planetary disks from their taxonomy in scattered
+light: Group I vs. Group II. A&A603:A21, DOI
+10.1051/0004-6361/201630320, 1703.01512
+Garufi A, Benisty M, Pinilla P, Tazzari M, Dominik C,
+Ginski C, Henning T, Kral Q, Langlois M, M´enard
+F, Stolker T, Szulagyi J, Villenave M, van der Plas
+G (2018) Evolution of protoplanetary disks from
+their taxonomy in scattered light: spirals, rings,
+cavities, and shadows. A&A620:A94, DOI 10.1051/
+0004-6361/201833872, 1810.04564
+Garufi A, Dominik C, Ginski C, Benisty M, van Hol-
+stein RG, Henning T, Pawellek N, Pinte C, Aven-
+haus H, Facchini S, Galicher R, Gratton R, M´enard
+F, Muro-Arena G, Milli J, Stolker T, Vigan A, Vil-
+lenave M, Moulin T, Origne A, Rigal F, Sauvage
+JF, Weber L (2022) A SPHERE survey of self-
+shadowed planet-forming disks. A&A658:A137, DOI
+10.1051/0004-6361/202141692, 2111.07856
+Gillett FC, Stein WA (1971) Infrared Studies of Galac-
+tic Nebulae. II. B Stars Associated with Nebulosity.
+ApJ164:77, DOI 10.1086/150817
+Ginski C, Stolker T, Pinilla P, Dominik C, Boccaletti
+A, de Boer J, Benisty M, Biller B, Feldt M, Garufi
+A, Keller CU, Kenworthy M, Maire AL, M´enard F,
+Mesa D, Milli J, Min M, Pinte C, Quanz SP, van
+Boekel R, Bonnefoy M, Chauvin G, Desidera S, Grat-
+ton R, Girard JHV, Keppler M, Kopytova T, La-
+grange AM, Langlois M, Rouan D, Vigan A (2016)
+Direct detection of scattered light gaps in the tran-
+sitional disk around HD 97048 with VLT/SPHERE.
+A&A595:A112, DOI 10.1051/0004-6361/201629265,
+1609.04027
+Gorti U, Dullemond CP, Hollenbach D (2009) Time
+Evolution
+of
+Viscous
+Circumstellar
+Disks
+due
+to Photoevaporation by Far-Ultraviolet, Extreme-
+Ultraviolet, and X-ray Radiation from the Cen-
+tral
+Star.
+ApJ705(2):1237–1251,
+DOI
+10.1088/
+0004-637X/705/2/1237, 0909.1836
+Goto M, Usuda T, Dullemond CP, Henning T, Linz H,
+Stecklum B, Suto H (2006) Inner Rim of a Molec-
+ular Disk Spatially Resolved in Infrared CO Emis-
+sion Lines. ApJ652:758–762, DOI 10.1086/506582,
+astro-ph/0606362
+Grady CA, Perez MR, Talavera A, Bjorkman KS, de
+Winter D, The PS, Molster FJ, van den Ancker ME,
+Sitko ML, Morrison ND, Beaver ML, McCollum B,
+Castelaz MW (1996) The β Pictoris phenomenon
+among Herbig Ae/Be stars. UV and optical high dis-
+persion spectra. Astronomy and Astrophysics Sup-
+plement Series 120:157–177
+Grady CA, Woodgate B, Bruhweiler FC, Boggess A,
+Plait P, Lindler DJ, Clampin M, Kalas P (1999)
+Hubble Space Telescope Space Telescope Imaging
+Spectrograph Coronagraphic Imaging of the Herbig
+AE Star AB Aurigae. ApJ523(2):L151–L154, DOI
+10.1086/312270
+Grady CA, Hamaguchi K, Schneider G, Stecklum B,
+Woodgate BE, McCleary JE, Williger GM, Sitko ML,
+M´enard F, Henning T, Brittain S, Troutmann M,
+Donehew B, Hines D, Wisniewski JP, Lynch DK,
+Russell RW, Rudy RJ, Day AN, Shenoy A, Wilner
+D, Silverstone M, Bouret JC, Meusinger H, Clampin
+M, Kim S, Petre R, Sahu M, Endres M, Collins KA
+(2010) Locating the Accretion Footprint on a Her-
+big Ae Star: MWC 480. ApJ719(2):1565–1581, DOI
+10.1088/0004-637X/719/2/1565
+Grady CA, Muto T, Hashimoto J, Fukagawa M, Cur-
+rie T, Biller B, Thalmann C, Sitko ML, Russell R,
+Wisniewski J, Dong R, Kwon J, Sai S, Hornbeck
+J, Schneider G, Hines D, Moro Mart´ın A, Feldt
+M, Henning T, Pott JU, Bonnefoy M, Bouwman
+J, Lacour S, Mueller A, Juh´asz A, Crida A, Chau-
+vin G, Andrews S, Wilner D, Kraus A, Dahm S,
+Robitaille T, Jang-Condell H, Abe L, Akiyama E,
+Brandner W, Brandt T, Carson J, Egner S, Fol-
+lette KB, Goto M, Guyon O, Hayano Y, Hayashi
+M, Hayashi S, Hodapp K, Ishii M, Iye M, Janson
+M, Kandori R, Knapp G, Kudo T, Kusakabe N,
+Kuzuhara M, Mayama S, McElwain M, Matsuo T,
+Miyama S, Morino JI, Nishimura T, Pyo TS, Serabyn
+G, Suto H, Suzuki R, Takami M, Takato N, Terada
+H, Tomono D, Turner E, Watanabe M, Yamada T,
+Takami H, Usuda T, Tamura M (2013) Spiral Arms
+in the Asymmetrically Illuminated Disk of MWC
+758 and Constraints on Giant Planets. ApJ762(1):48,
+DOI 10.1088/0004-637X/762/1/48, 1212.1466
+Grant SL, Espaillat CC, Brittain S, Scott-Joseph C,
+Calvet N (2022) Tracing Accretion onto Herbig
+Ae/Be Stars Using the Brγ Line. ApJ926(2):229,
+DOI 10.3847/1538-4357/ac450a, 2112.10428
+Gratton R, Ligi R, Sissa E, Desidera S, Mesa D, Bon-
+nefoy M, Chauvin G, Cheetham A, Feldt M, La-
+grange AM, Langlois M, Meyer M, Vigan A, Boc-
+caletti A, Janson M, Lazzoni C, Zurlo A, De Boer
+J, Henning T, D’Orazi V, Gluck L, Madec F, Jaquet
+M, Baudoz P, Fantinel D, Pavlov A, Wildi F (2019)
+Blobs, spiral arms, and a possible planet around
+HD 169142. A&A623:A140, DOI 10.1051/0004-6361/
+201834760, 1901.06555
+Gravity Collaboration, Perraut K, Labadie L, Lazareff
+B, Klarmann L, Segura-Cox D, Benisty M, Bou-
+vier J, Brandner W, Caratti O Garatti A, Caselli
+P, Dougados C, Garcia P, Garcia-Lopez R, Kendrew
+S, Koutoulaki M, Kervella P, Lin CC, Pineda J,
+Sanchez-Bermudez J, van Dishoeck E, Abuter R,
+Amorim A, Berger JP, Bonnet H, Buron A, Can-
+
+64
+Sean D. Brittain et al.
+talloube F, Cl´enet Y, Coud´e Du Foresto V, Dexter
+J, de Zeeuw PT, Duvert G, Eckart A, Eisenhauer F,
+Eupen F, Gao F, Gendron E, Genzel R, Gillessen S,
+Gordo P, Grellmann R, Haubois X, Haussmann F,
+Henning T, Hippler S, Horrobin M, Hubert Z, Jocou
+L, Lacour S, Le Bouquin JB, L´ena P, M´erand A, Ott
+T, Paumard T, Perrin G, Pfuhl O, Rabien S, Ray T,
+Rau C, Rousset G, Scheithauer S, Straub O, Straub-
+meier C, Sturm E, Vincent F, Waisberg I, Wank I,
+Widmann F, Wieprecht E, Wiest M, Wiezorrek E,
+Woillez J, Yazici S (2019) The GRAVITY Young
+Stellar Object survey. I. Probing the disks of Her-
+big Ae/Be stars in terrestrial orbits. A&A632:A53,
+DOI 10.1051/0004-6361/201936403, 1911.00611
+Gravity Collaboration, Garcia Lopez R, Natta A,
+Caratti o Garatti A, Ray TP, Fedriani R, Koutoulaki
+M, Klarmann L, Perraut K, Sanchez-Bermudez J,
+Benisty M, Dougados C, Labadie L, Brandner W,
+Garcia PJV, Henning T, Caselli P, Duvert G, de
+Zeeuw T, Grellmann R, Abuter R, Amorim A,
+Baub¨ock M, Berger JP, Bonnet H, Buron A, Cl´enet
+Y, Coud´e Du Foresto V, de Wit W, Eckart A, Eisen-
+hauer F, Filho M, Gao F, Garcia Dabo CE, Gen-
+dron E, Genzel R, Gillessen S, Habibi M, Haubois
+X, Haussmann F, Hippler S, Hubert Z, Horrobin M,
+Jimenez Rosales A, Jocou L, Kervella P, Kolb J, La-
+cour S, Le Bouquin JB, L´ena P, Ott T, Paumard
+T, Perrin G, Pfuhl O, Ramirez A, Rau C, Rousset
+G, Scheithauer S, Shangguan J, Stadler J, Straub O,
+Straubmeier C, Sturm E, van Dishoeck E, Vincent F,
+von Fellenberg S, Widmann F, Wieprecht E, Wiest
+M, Wiezorrek E, Woillez J, Yazici S, Zins G (2020)
+A measure of the size of the magnetospheric ac-
+cretion region in TW Hydrae. Nature584(7822):547–
+550, DOI 10.1038/s41586-020-2613-1, 2104.06441
+GRAVITY
+Collaboration,
+Sanchez-Bermudez
+J,
+Caratti O Garatti A, Garcia Lopez R, Perraut K,
+Labadie L, Benisty M, Brandner W, Dougados C,
+Garcia PJV, Henning T, Klarmann L, Amorim A,
+Baub¨ock M, Berger JP, Le Bouquin JB, Caselli
+P, Cl´enet Y, Coud´e Du Foresto V, de Zeeuw PT,
+Drescher A, Duvert G, Eckart A, Eisenhauer F,
+Filho M, Gao F, Gendron E, Genzel R, Gillessen
+S, Grellmann R, Heissel G, Horrobin M, Hubert Z,
+Jim´enez-Rosales A, Jocou L, Kervella P, Lacour S,
+Lapeyr`ere V, L´ena P, Ott T, Paumard T, Perrin
+G, Pineda JE, Rodr´ıguez-Coira G, Rousset G,
+Segura-Cox DM, Shangguan J, Shimizu T, Stadler
+J, Straub O, Straubmeier C, Sturm E, van Dishoeck
+E, Vincent F, von Fellenberg SD, Widmann F,
+Woillez J (2021) The GRAVITY young stellar
+object
+survey.
+VI.
+Mapping
+the
+variable
+inner
+disk of HD 163296 at sub-au scales. A&A654:A97,
+DOI 10.1051/0004-6361/202039600, 2107.02391
+Greenwood AJ, Kamp I, Waters LBFM, Woitke P, Thi
+WF (2019) Effects of dust evolution on protoplan-
+etary disks in the mid-infrared. A&A626:A6, DOI
+10.1051/0004-6361/201834365
+Gressel O, Nelson RP, Turner NJ, Ziegler U (2013)
+Global Hydromagnetic Simulations of a Planet Em-
+bedded in a Dead Zone: Gap Opening, Gas Accretion,
+and Formation of a Protoplanetary Jet. ApJ779:59,
+DOI 10.1088/0004-637X/779/1/59, 1309.2871
+Grinin VP (1992) Young stars with non-periodic algol-
+type minima. Astronomical and Astrophysical Trans-
+actions 3(1):17–32, DOI 10.1080/10556799208230535
+Grinin VP, The PS, de Winter D, Giampapa M, Ros-
+topchina AN, Tambovtseva LV, van den Ancker ME
+(1994) The β Pictoris phenomenon among young
+stars. I. The case of the Herbig AE star UX Orio-
+nis. A&A292:165–174
+Guidi G, Tazzari M, Testi L, de Gregorio-Monsalvo
+I, Chandler CJ, P´erez L, Isella A, Natta A, Or-
+tolani S, Henning T, Corder S, Linz H, Andrews S,
+Wilner D, Ricci L, Carpenter J, Sargent A, Mundy
+L, Storm S, Calvet N, Dullemond C, Greaves J,
+Lazio J, Deller A, Kwon W (2016) Dust properties
+across the CO snowline in the HD 163296 disk from
+ALMA and VLA observations. A&A588:A112, DOI
+10.1051/0004-6361/201527516, 1601.07542
+Guilloteau S, Di Folco E, Dutrey A, Simon M, Grosso
+N, Pi´etu V (2013) A sensitive survey for 13CO, CN,
+H2CO, and SO in the disks of T Tauri and Her-
+big Ae stars. A&A549:A92, DOI 10.1051/0004-6361/
+201220298, 1211.4776
+Guilloteau S, Simon M, Pi´etu V, Di Folco E, Dutrey
+A, Prato L, Chapillon E (2014) The masses of
+young stars: CN as a probe of dynamical masses.
+A&A567:A117, DOI 10.1051/0004-6361/201423765,
+1406.3805
+Guimar˜aes MM, Alencar SHP, Corradi WJB, Vieira
+SLA (2006) Stellar parameters and evidence of cir-
+cumstellar activity for a sample of Herbig Ae/Be
+stars. A&A457(2):581–589, DOI 10.1051/0004-6361:
+20065005
+Gundlach B, Schmidt KP, Kreuzig C, Bischoff D,
+Rezaei F, Kothe S, Blum J, Grzesik B, Stoll E
+(2018) The tensile strength of ice and dust ag-
+gregates and its dependence on particle proper-
+ties. MNRAS479(1):1273–1277, DOI 10.1093/mnras/
+sty1550
+Guzm´an-D´ıaz J, Mendigut´ıa I, Montesinos B, Oud-
+maijer RD, Vioque M, Rodrigo C, Solano E, Meeus
+G, Marcos-Arenal P (2021) Homogeneous study of
+Herbig Ae/Be stars from spectral energy distribu-
+tions and Gaia EDR3. A&A650:A182, DOI 10.1051/
+
+Herbig Stars
+65
+0004-6361/202039519, 2104.11759
+Haffert SY, Bohn AJ, de Boer J, Snellen IAG, Brinch-
+mann J, Girard JH, Keller CU, Bacon R (2019)
+Two accreting protoplanets around the young star
+PDS 70. Nature Astronomy p 329, DOI 10.1038/
+s41550-019-0780-5, 1906.01486
+Hales AS, De Gregorio-Monsalvo I, Montesinos B,
+Casassus S, Dent WFR, Dougados C, Eiroa C,
+Hughes AM, Garay G, Mardones D, M´enard F, Palau
+A, P´erez S, Phillips N, Torrelles JM, Wilner D (2014)
+A CO Survey in Planet-forming Disks: Character-
+izing the Gas Content in the Epoch of Planet For-
+mation. AJ148(3):47, DOI 10.1088/0004-6256/148/
+3/47, 1405.6966
+Hall C, Dong R, Rice K, Harries TJ, Najita J, Alexan-
+der R, Brittain S (2019) The Temporal Requirements
+of Directly Observing Self-gravitating Spiral Waves
+in Protoplanetary Disks with ALMA. ApJ871(2):228,
+DOI 10.3847/1538-4357/aafac2, 1901.02407
+Hamaguchi K, Yamauchi S, Koyama K (2005) X-Ray
+Study of Herbig Ae/Be Stars. ApJ618(1):360–384,
+DOI 10.1086/423192, astro-ph/0406489
+Hartmann L, Kenyon SJ, Calvet N (1993) The Excess
+Infrared Emission of Herbig Ae/Be Stars: Disks or
+Envelopes? ApJ407:219, DOI 10.1086/172507
+Hartmann L, Calvet N, Gullbring E, D’Alessio P
+(1998) Accretion and the Evolution of T Tauri Disks.
+ApJ495:385–400, DOI 10.1086/305277
+Hartmann L, Herczeg G, Calvet N (2016) Accretion
+onto Pre-Main-Sequence Stars. ARA&A54:135–180,
+DOI 10.1146/annurev-astro-081915-023347
+Hashimoto J, Tamura M, Muto T, Kudo T, Fuka-
+gawa M, Fukue T, Goto M, Grady CA, Henning
+T, Hodapp K, Honda M, Inutsuka S, Kokubo E,
+Knapp G, McElwain MW, Momose M, Ohashi N,
+Okamoto YK, Takami M, Turner EL, Wisniewski J,
+Janson M, Abe L, Brandner W, Carson J, Egner S,
+Feldt M, Golota T, Guyon O, Hayano Y, Hayashi M,
+Hayashi S, Ishii M, Kandori R, Kusakabe N, Matsuo
+T, Mayama S, Miyama S, Morino JI, Moro-Martin
+A, Nishimura T, Pyo TS, Suto H, Suzuki R, Takato
+N, Terada H, Thalmann C, Tomono D, Watanabe
+M, Yamada T, Takami H, Usuda T (2011) Direct
+Imaging of Fine Structures in Giant Planet-forming
+Regions of the Protoplanetary Disk Around AB Au-
+rigae. ApJ729(2):L17, DOI 10.1088/2041-8205/729/
+2/L17, 1102.4408
+Hein Bertelsen RP, Kamp I, Goto M, van der Plas G,
+Thi WF, Waters LBFM, van den Ancker ME, Woitke
+P (2014) CO ro-vibrational lines in HD 100546.
+A search for disc asymmetries and the role of flu-
+orescence. A&A561:A102, DOI 10.1051/0004-6361/
+201322574, 1311.5353
+Hein Bertelsen RP, Kamp I, van der Plas G, van
+den Ancker ME, Waters LBFM, Thi WF, Woitke P
+(2016) A proposed new diagnostic for Herbig disc ge-
+ometry. FWHM versus J of CO ro-vibrational lines.
+A&A590:A98, DOI 10.1051/0004-6361/201527652,
+1603.03546
+Henning T, Meeus G (2011) Dust Processing and Min-
+eralogy in Protoplanetary Accretion Disks, pp 114–
+148
+Henning T, Launhardt R, Steinacker J, Thamm E
+(1994) Cold dust around southern Herbig Ae/Be
+stars. A&A291:546–556
+Henning T, Semenov D, Guilloteau S, Dutrey A, Her-
+sant F, Wakelam V, Chapillon E, Launhardt R, Pi´etu
+V, Schreyer K (2010) Chemistry in Disks. III. Pho-
+tochemistry and X-ray Driven Chemistry Probed by
+the Ethynyl Radical (CCH) in DM Tau, LkCa 15,
+and MWC 480. ApJ714(2):1511–1520, DOI 10.1088/
+0004-637X/714/2/1511, 1003.5793
+Herbig GH (1960) The Spectra of Be- and Ae-Type
+Stars Associated with Nebulosity. ApJS4:337, DOI
+10.1086/190050
+Herbig GH, Bell KR (1988) Third Catalog of Emission-
+Line Stars of the Orion Population : 3 : 1988
+Herbst W, Herbst DK, Grossman EJ, Weinstein D
+(1994) Catalogue of UBVRI Photometry of T Tauri
+Stars and Analysis of the Causes of Their Variability.
+AJ108:1906, DOI 10.1086/117204
+Hillenbrand LA, Strom SE, Vrba FJ, Keene J (1992)
+Herbig Ae/Be Stars: Intermediate-Mass Stars Sur-
+rounded by Massive Circumstellar Accretion Disks.
+ApJ397:613, DOI 10.1086/171819
+Hillenbrand LA, Meyer MR, Strom SE, Skrutskie MF
+(1995) Isolated Star-Forming Regions Containing
+Herbig AE/BE Stars. I. The Young Stellar Aggregate
+Associated With BD +40 degrees 4124. AJ109:280,
+DOI 10.1086/117272
+Hiraoka K, Ohashi N, Kihara Y, Yamamoto K, Sato T,
+Yamashita A (1994) Formation of formaldehyde and
+methanol from the reactions of H atoms with solid
+CO at 10-20 K. Chemical Physics Letters 229(4):408–
+414, DOI 10.1016/0009-2614(94)01066-8
+Hoffmeister VH, Chini R, Scheyda CM, Schulze D,
+Watermann R, N¨urnberger D, Vogt N (2008) The
+Stellar Population of M17. ApJ686(1):310–324, DOI
+10.1086/591070
+Honda M, Inoue AK, Fukagawa M, Oka A, Nakamoto
+T, Ishii M, Terada H, Takato N, Kawakita H,
+Okamoto YK, Shibai H, Tamura M, Kudo T,
+Itoh
+Y
+(2009)
+Detection
+of
+Water
+Ice
+Grains
+on the Surface of the Circumstellar Disk Around
+HD 142527. ApJ690(2):L110–L113, DOI 10.1088/
+0004-637X/690/2/L110
+
+66
+Sean D. Brittain et al.
+Honda M, Maaskant K, Okamoto YK, Kataza H, Fuka-
+gawa M, Waters LBFM, Dominik C, Tielens AGGM,
+Mulders GD, Min M, Yamashita T, Fujiyoshi T,
+Miyata T, Sako S, Sakon I, Fujiwara H, Onaka
+T (2012) Mid-infrared Imaging of the Transitional
+Disk of HD 169142: Measuring the Size of the Gap.
+ApJ752(2):143, DOI 10.1088/0004-637X/752/2/143,
+1204.5364
+Honda M, Maaskant K, Okamoto YK, Kataza H, Ya-
+mashita T, Miyata T, Sako S, Fujiyoshi T, Sakon
+I, Fujiwara H, Kamizuka T, Mulders GD, Lopez-
+Rodriguez E, Packham C, Onaka T (2015) High-
+resolution 25 µm Imaging of the Disks around
+Herbig Ae/Be Stars. ApJ804(2):143, DOI 10.1088/
+0004-637X/804/2/143, 1504.00096
+Honda M, Kudo T, Takatsuki S, Inoue AK, Nakamoto
+T, Fukagawa M, Tamura M, Terada H, Takato N
+(2016) Water Ice at the Surface of the HD 100546
+Disk. ApJ821(1):2, DOI 10.3847/0004-637X/821/1/
+2, 1603.09512
+Hosokawa T, Omukai K (2009) Evolution of Mas-
+sive
+Protostars
+with
+High
+Accretion
+Rates.
+ApJ691(1):823–846,
+DOI
+10.1088/0004-637X/
+691/1/823, 0806.4122
+Howard AW, Marcy GW, Bryson ST, Jenkins JM,
+Rowe JF, Batalha NM, Borucki WJ, Koch DG,
+Dunham EW, Gautier I Thomas N, Van Cleve J,
+Cochran WD, Latham DW, Lissauer JJ, Torres G,
+Brown TM, Gilliland RL, Buchhave LA, Caldwell
+DA, Christensen-Dalsgaard J, Ciardi D, Fressin F,
+Haas MR, Howell SB, Kjeldsen H, Seager S, Rogers
+L, Sasselov DD, Steffen JH, Basri GS, Charbonneau
+D, Christiansen J, Clarke B, Dupree A, Fabrycky
+DC, Fischer DA, Ford EB, Fortney JJ, Tarter J,
+Girouard FR, Holman MJ, Johnson JA, Klaus TC,
+Machalek P, Moorhead AV, Morehead RC, Ragozzine
+D, Tenenbaum P, Twicken JD, Quinn SN, Isaacson
+H, Shporer A, Lucas PW, Walkowicz LM, Welsh WF,
+Boss A, Devore E, Gould A, Smith JC, Morris RL,
+Prsa A, Morton TD, Still M, Thompson SE, Mul-
+lally F, Endl M, MacQueen PJ (2012) Planet Occur-
+rence within 0.25 AU of Solar-type Stars from Ke-
+pler. ApJS201(2):15, DOI 10.1088/0067-0049/201/2/
+15, 1103.2541
+Huang J,
+¨Oberg KI, Qi C, Aikawa Y, Andrews
+SM, Furuya K, Guzm´an VV, Loomis RA, van
+Dishoeck EF, Wilner DJ (2017) An ALMA Survey
+of DCN/H13CN and DCO+/H13CO+ in Protoplane-
+tary Disks. ApJ835(2):231, DOI 10.3847/1538-4357/
+835/2/231, 1701.01735
+Hubrig S, Carroll TA, Scholler M, Ilyin I (2015) The
+prevalence of weak magnetic fields in Herbig Ae stars:
+the case of PDS 2. MNRAS449:L118–L122, DOI 10.
+1093/mnrasl/slv034, 1502.05498
+Hu´elamo
+N,
+Lacour
+S,
+Tuthill
+P,
+Ireland
+M,
+Kraus A, Chauvin G (2011) A companion candi-
+date in the gap of the T Chamaeleontis transi-
+tional disk. A&A528:L7, DOI 10.1051/0004-6361/
+201016395, 1102.4982
+Hughes AM, Wilner DJ, Andrews SM, Qi C, Hogerhei-
+jde MR (2011) Empirical Constraints on Turbulence
+in Protoplanetary Accretion Disks. ApJ727(2):85,
+DOI 10.1088/0004-637X/727/2/85, 1011.3826
+Hughes
+AM,
+Duchˆene
+G,
+Matthews
+BC
+(2018)
+Debris
+Disks:
+Structure,
+Composition,
+and
+Variability.
+ARA&A56:541–591,
+DOI
+10.1146/annurev-astro-081817-052035, 1802.04313
+Hung LW, Fitzgerald MP, Chen CH, Mittal T, Kalas
+PG, Graham JR (2015) Discovery of Resolved De-
+bris Disk around HD 131835. ApJ802(2):138, DOI
+10.1088/0004-637X/802/2/138, 1502.02035
+Ilee JD, Wheelwright HE, Oudmaijer RD, de Wit WJ,
+Maud LT, Hoare MG, Lumsden SL, Moore TJT,
+Urquhart JS, Mottram JC (2013) CO bandhead
+emission of massive young stellar objects: determin-
+ing disc properties. MNRAS429(4):2960–2973, DOI
+10.1093/mnras/sts537, 1212.0554
+Ilee JD, Fairlamb J, Oudmaijer RD, Mendigut´ıa
+I, van den Ancker ME, Kraus S, Wheelwright
+HE (2014) Investigating the inner discs of Her-
+big
+Ae/Be
+stars
+with
+CO
+bandhead
+and
+Brγ
+emission. MNRAS445(4):3723–3736, DOI 10.1093/
+mnras/stu1942, 1409.4897
+Ilee JD, Hall C, Walsh C, Jim´enez-Serra I, Pinte C,
+Terry J, Bourke TL, Hoare M (2020) Observing
+protoplanetary discs with the Square Kilometre Ar-
+ray - I. Characterizing pebble substructure caused
+by forming planets. MNRAS498(4):5116–5127, DOI
+10.1093/mnras/staa2699, 2009.00562
+Ilee JD, Walsh C, Booth AS, Aikawa Y, Andrews SM,
+Bae J, Bergin EA, Bergner JB, Bosman AD, Cataldi
+G, Cleeves LI, Czekala I, Guzm´an VV, Huang J,
+Law CJ, Le Gal R, Loomis RA, M´enard F, No-
+mura H, ¨Oberg KI, Qi C, Schwarz KR, Teague
+R, Tsukagoshi T, Wilner DJ, Yamato Y, Zhang
+K (2021) Molecules with ALMA at Planet-forming
+Scales (MAPS). IX. Distribution and Properties
+of the Large Organic Molecules HC3N, CH3CN,
+and c-C3H2. ApJS257(1):9, DOI 10.3847/1538-4365/
+ac1441, 2109.06319
+Ingleby L, Calvet N, Herczeg G, Blaty A, Walter F,
+Ardila D, Alexand er R, Edwards S, Espaillat C,
+Gregory SG, Hillenbrand L, Brown A (2013) Accre-
+tion Rates for T Tauri Stars Using Nearly Simultane-
+ous Ultraviolet and Optical Spectra. ApJ767(2):112,
+DOI 10.1088/0004-637X/767/2/112, 1303.0769
+
+Herbig Stars
+67
+Isella A, Natta A (2005) The shape of the inner rim
+in proto-planetary disks. A&A438(3):899–907, DOI
+10.1051/0004-6361:20052773, astro-ph/0503635
+Isella A, Guidi G, Testi L, Liu S, Li H, Li S, Weaver
+E, Boehler Y, Carperter JM, De Gregorio-Monsalvo
+I, Manara CF, Natta A, P´erez LM, Ricci L, Sar-
+gent A, Tazzari M, Turner N (2016) Ringed Struc-
+tures of the HD 163296 Protoplanetary Disk Re-
+vealed by ALMA. Phys. Rev. Lett.117(25):251101,
+DOI 10.1103/PhysRevLett.117.251101
+Isella A, Benisty M, Teague R, Bae J, Keppler M, Fac-
+chini S, P´erez L (2019) Detection of Continuum Sub-
+millimeter Emission Associated with Candidate Pro-
+toplanets. ApJ879(2):L25, DOI 10.3847/2041-8213/
+ab2a12, 1906.06308
+Janson M, Squicciarini V, Delorme P, Gratton R, Bon-
+nefoy M, Reffert S, Mamajek EE, Eriksson SC, Vi-
+gan A, Langlois M, Engler N, Chauvin G, Desidera
+S, Mayer L, Marleau GD, Bohn AJ, Samland M,
+Meyer M, d’Orazi V, Henning T, Quanz S, Ken-
+worthy M, Carson JC (2021) BEAST begins: sample
+characteristics and survey performance of the B-star
+Exoplanet Abundance Study. A&A646:A164, DOI
+10.1051/0004-6361/202039683, 2101.02043
+J¨arvinen SP, Carroll TA, Hubrig S, Ilyin I, Sch¨oller
+M (2019) New evidence for weak magnetic fields in
+Herbig Ae/Be stars. MNRAS489(1):886–890, DOI
+10.1093/mnras/stz2190, 1908.02093
+Jermyn AS, Kama M (2018) Stellar photospheric
+abundances
+as
+a
+probe
+of
+discs
+and
+plan-
+ets. MNRAS476(4):4418–4434, DOI 10.1093/mnras/
+sty429, 1804.06414
+Jim´enez-Donaire MJ, Meeus G, Karska A, Montesinos
+B, Bouwman J, Eiroa C, Henning T (2017) Herschel
+observations of the circumstellar environments of the
+Herbig Be stars R Mon and PDS 27. A&A605:A62,
+DOI 10.1051/0004-6361/201629053, 1705.05860
+Johnson JA, Howard AW, Bowler BP, Henry GW,
+Marcy GW, Wright JT, Fischer DA, Isaacson H
+(2010) Retired A Stars and Their Companions. IV.
+Seven Jovian Exoplanets from Keck Observatory.
+PASP122:701, DOI 10.1086/653809, 1003.3445
+Jonkheid
+B,
+Faas
+FGA,
+van
+Zadelhoff
+GJ,
+van
+Dishoeck EF (2004) The gas temperature in flaring
+disks around pre-main sequence stars. A&A428:511–
+521, DOI 10.1051/0004-6361:20048013, astro-ph/
+0408503
+Juh´asz A, Bouwman J, Henning T, Acke B, van den
+Ancker ME, Meeus G, Dominik C, Min M, Tie-
+lens AGGM, Waters LBFM (2010) Dust Evolu-
+tion in Protoplanetary Disks Around Herbig Ae/Be
+Stars—the Spitzer View. ApJ721:431–455, DOI 10.
+1088/0004-637X/721/1/431, 1008.0083
+Kama M, Min M, Dominik C (2009) The inner rim
+structures of protoplanetary discs. A&A506(3):1199–
+1213,
+DOI
+10.1051/0004-6361/200912068,
+0908.
+1692
+Kama M, Folsom CP, Pinilla P (2015) Fingerprints of
+giant planets in the photospheres of Herbig stars.
+A&A582:L10, DOI 10.1051/0004-6361/201527094,
+1509.02741
+Kama M, Bruderer S, Carney M, Hogerheijde M, van
+Dishoeck EF, Fedele D, Baryshev A, Boland W,
+G¨usten R, Aikutalp A, Choi Y, Endo A, Frieswijk
+W, Karska A, Klaassen P, Koumpia E, Kristensen L,
+Leurini S, Nagy Z, Perez Beaupuits JP, Risacher C,
+van der Marel N, van Kempen TA, van Weeren RJ,
+Wyrowski F, Yıldız UA (2016a) Observations and
+modelling of CO and [C I] in protoplanetary disks.
+First detections of [C I] and constraints on the carbon
+abundance. A&A588:A108, DOI 10.1051/0004-6361/
+201526791, 1601.01449
+Kama M, Bruderer S, van Dishoeck EF, Hogerhei-
+jde M, Folsom CP, Miotello A, Fedele D, Belloche
+A, G¨usten R, Wyrowski F (2016b) Volatile-carbon
+locking and release in protoplanetary disks. A study
+of TW Hya and HD 100546. A&A592:A83, DOI
+10.1051/0004-6361/201526991, 1605.05093
+Kama
+M,
+Shorttle
+O,
+Jermyn
+AS,
+Folsom
+CP,
+Furuya
+K,
+Bergin
+EA,
+Walsh
+C,
+Keller
+L
+(2019) Abundant Refractory Sulfur in Protoplane-
+tary Disks. ApJ885(2):114, DOI 10.3847/1538-4357/
+ab45f8, 1908.05169
+Kama M, Trapman L, Fedele D, Bruderer S, Hoger-
+heijde MR, Miotello A, van Dishoeck EF, Clarke
+C, Bergin EA (2020) Mass constraints for 15 pro-
+toplanetary discs from HD 1-0. A&A634:A88, DOI
+10.1051/0004-6361/201937124, 1912.11883
+Kamp I, Dullemond CP (2004) The Gas Tempera-
+ture in the Surface Layers of Protoplanetary Disks.
+ApJ615:991–999, DOI 10.1086/424703, astro-ph/
+0408501
+Kamp I, Hempel M, Holweger H (2002) Do dusty
+A stars exhibit accretion signatures in their photo-
+spheres? A&A388:978–984, DOI 10.1051/0004-6361:
+20020493, astro-ph/0204449
+Kamp I, Tilling I, Woitke P, Thi W, Hogerhei-
+jde
+M
+(2010)
+Radiation
+thermo-chemical
+mod-
+els of protoplanetary disks. II. Line diagnostics.
+A&A510(26):A260000+,
+DOI
+10.1051/0004-6361/
+200913076, 0911.1949
+Kamp I, Woitke P, Pinte C, Tilling I, Thi WF,
+Menard F, Duchene G, Augereau JC (2011) Con-
+tinuum and line modelling of discs around young
+stars. II. Line diagnostics for GASPS from the
+DENT grid. A&A532:A85, DOI 10.1051/0004-6361/
+
+68
+Sean D. Brittain et al.
+201016399, 1103.5763
+Kemper F, Vriend WJ, Tielens AGGM (2004) The Ab-
+sence of Crystalline Silicates in the Diffuse Inter-
+stellar Medium. ApJ609(2):826–837, DOI 10.1086/
+421339, astro-ph/0403609
+Kenyon SJ, Najita JR, Bromley BC (2016) Rocky
+Planet Formation: Quick and Neat. ApJ831(1):8,
+DOI 10.3847/0004-637X/831/1/8, 1608.05410
+Keppler M, Benisty M, M¨uller A, Henning T, van
+Boekel R, Cantalloube F, Ginski C, van Holstein RG,
+Maire AL, Pohl A, Samland M, Avenhaus H, Baudino
+JL, Boccaletti A, de Boer J, Bonnefoy M, Chauvin
+G, Desidera S, Langlois M, Lazzoni C, Marleau GD,
+Mordasini C, Pawellek N, Stolker T, Vigan A, Zurlo
+A, Birnstiel T, Brandner W, Feldt M, Flock M, Gi-
+rard J, Gratton R, Hagelberg J, Isella A, Janson M,
+Juhasz A, Kemmer J, Kral Q, Lagrange AM, Laun-
+hardt R, Matter A, M´enard F, Milli J, Molli`ere P,
+Olofsson J, P´erez L, Pinilla P, Pinte C, Quanz SP,
+Schmidt T, Udry S, Wahhaj Z, Williams JP, Buenzli
+E, Cudel M, Dominik C, Galicher R, Kasper M, Lan-
+nier J, Mesa D, Mouillet D, Peretti S, Perrot C, Salter
+G, Sissa E, Wildi F, Abe L, Antichi J, Augereau JC,
+Baruffolo A, Baudoz P, Bazzon A, Beuzit JL, Blan-
+chard P, Brems SS, Buey T, De Caprio V, Carbillet
+M, Carle M, Cascone E, Cheetham A, Claudi R, Cos-
+tille A, Delboulb´e A, Dohlen K, Fantinel D, Feautrier
+P, Fusco T, Giro E, Gluck L, Gry C, Hubin N, Hugot
+E, Jaquet M, Le Mignant D, Llored M, Madec F,
+Magnard Y, Martinez P, Maurel D, Meyer M, M¨oller-
+Nilsson O, Moulin T, Mugnier L, Orign´e A, Pavlov
+A, Perret D, Petit C, Pragt J, Puget P, Rabou P,
+Ramos J, Rigal F, Rochat S, Roelfsema R, Rousset G,
+Roux A, Salasnich B, Sauvage JF, Sevin A, Soenke C,
+Stadler E, Suarez M, Turatto M, Weber L (2018) Dis-
+covery of a planetary-mass companion within the gap
+of the transition disk around PDS 70. A&A617:A44,
+DOI 10.1051/0004-6361/201832957, 1806.11568
+Kessler-Silacci JE, Dullemond CP, Augereau JC, Mer´ın
+B, Geers VC, van Dishoeck EF, Evans I N J, Blake
+GA, Brown J (2007) Probing Protoplanetary Disks
+with Silicate Emission: Where Is the Silicate Emis-
+sion Zone? ApJ659(1):680–684, DOI 10.1086/511853,
+astro-ph/0612450
+Khalafinejad S, Maaskant KM, Mari˜nas N, Tielens
+AGGM (2016) Large dust gaps in the transitional
+disks of HD 100453 and HD 34282. Connecting the
+gap size to the spectral energy distribution and
+mid-infrared imaging. A&A587:A62, DOI 10.1051/
+0004-6361/201423984, 1509.06531
+Kim S, Nomura H, Tsukagoshi T, Kawabe R, Muto
+T (2019) The Synthetic ALMA Multiband Analysis
+of the Dust Properties of the TW Hya Protoplane-
+tary Disk. ApJ872(2):179, DOI 10.3847/1538-4357/
+ab0304, 1902.00168
+Kley W, Nelson RP (2012) Planet-Disk Interaction
+and Orbital Evolution. ARA&A50:211–249, DOI
+10.1146/annurev-astro-081811-125523, 1203.1184
+Kluska J, Berger JP, Malbet F, Lazareff B, Benisty
+M, Le Bouquin JB, Absil O, Baron F, Delboulb´e
+A, Duvert G, Isella A, Jocou L, Juhasz A, Kraus
+S, Lachaume R, M´enard F, Millan-Gabet R, Mon-
+nier JD, Moulin T, Perraut K, Rochat S, Pinte C,
+Soulez F, Tallon M, Thi WF, Thi´ebaut E, Traub
+W, Zins G (2020) A family portrait of disk in-
+ner rims around Herbig Ae/Be stars. Hunting for
+warps, rings, self shadowing, and misalignments in
+the inner astronomical units. A&A636:A116, DOI
+10.1051/0004-6361/201833774, 2004.01594
+K´osp´al ´A, Mo´or A, Juh´asz A, ´Abrah´am P, Apai D,
+Csengeri T, Grady CA, Henning T, Hughes AM,
+Kiss C (2013) ALMA Observations of the Molecu-
+lar Gas in the Debris Disk of the 30 Myr Old Star
+HD 21997. ApJ776(2):77, DOI 10.1088/0004-637X/
+776/2/77, 1310.5068
+Koumpia E, Ababakr KM, de Wit WJ, Oudmai-
+jer RD, Caratti o Garatti A, Boley P, Linz H,
+Kraus S, Vink JS, Le Bouquin JB (2019) Re-
+solving the MYSO binaries PDS 27 and PDS 37
+with VLTI/PIONIER. A&A623:L5, DOI 10.1051/
+0004-6361/201834624, 1903.02667
+Kraus M (2019) A Census of B[e] Supergiants. Galaxies
+7(4):83, DOI 10.3390/galaxies7040083, 1909.12199
+Kraus S, Hofmann KH, Benisty M, Berger JP, Ches-
+neau O, Isella A, Malbet F, Meilland A, Nardetto
+N, Natta A, Preibisch T, Schertl D, Smith M,
+Stee P, Tatulli E, Testi L, Weigelt G (2008) The
+origin of hydrogen line emission for five Herbig
+Ae/Be stars spatially resolved by VLTI/AMBER
+spectro-interferometry. A&A489(3):1157–1173, DOI
+10.1051/0004-6361:200809946, 0807.1119
+Kraus S, Kluska J, Kreplin A, Bate M, Harries TJ,
+Hofmann KH, Hone E, Monnier JD, Weigelt G,
+Anugu A, de Wit WJ, Wittkowski M (2017) A
+High-mass Protobinary System with Spatially Re-
+solved Circumstellar Accretion Disks and Circumbi-
+nary Disk. ApJ835(1):L5, DOI 10.3847/2041-8213/
+835/1/L5, 1612.07804
+Kreplin A, Tambovtseva L, Grinin V, Kraus S, Weigelt
+G, Wang Y (2018) On the Brγ line emission of
+the Herbig Ae/Be star MWC 120. MNRAS476:4520–
+4526, DOI 10.1093/mnras/sty567
+Krumholz MR, Bonnell IA (2009) Models for the for-
+mation of massive stars, pp 288–320
+Kurosawa R, Romanova MM, Harries TJ (2011) Mul-
+tidimensional models of hydrogen and helium emis-
+
+Herbig Stars
+69
+sion line profiles for classical T Tauri stars: method,
+tests and examples. MNRAS416(4):2623–2639, DOI
+10.1111/j.1365-2966.2011.19216.x, 1102.0828
+Kusakabe N, Grady CA, Sitko ML, Hashimoto J,
+Kudo T, Fukagawa M, Muto T, Wisniewski JP, Min
+M, Mayama S, Werren C, Day AN, Beerman LC,
+Lynch DK, Russell RW, Brafford SM, Kuzuhara M,
+Brandt TD, Abe L, Brandner W, Carson J, Eg-
+ner S, Feldt M, Goto M, Guyon O, Hayano Y,
+Hayashi M, Hayashi SS, Henning T, Hodapp KW,
+Ishii M, Iye M, Janson M, Kandori R, Knapp GR,
+Matsuo T, McElwain MW, Miyama S, Morino JI,
+Moro-Martin A, Nishimura T, Pyo TS, Suto H,
+Suzuki R, Takami M, Takato N, Terada H, Thal-
+mann C, Tomono D, Turner EL, Watanabe M, Ya-
+mada T, Takami H, Usuda T, Tamura M (2012)
+High-contrast Near-infrared Polarization Imaging of
+MWC480. ApJ753(2):153, DOI 10.1088/0004-637X/
+753/2/153, 1205.3159
+Lada CJ (1987) Star formation: from OB associations
+to protostars. In: Peimbert M, Jugaku J (eds) Star
+Forming Regions, IAU Symposium, vol 115, p 1
+Lada CJ (2005) Star Formation in the Galaxy: An Ob-
+servational Overview. Progress of Theoretical Physics
+Supplement 158:1–23, DOI 10.1143/PTPS.158.1
+Lada CJ, Wilking BA (1984) The nature of the em-
+bedded population in the rho Ophiuchi dark cloud
+: mid-infrared observations. ApJ287:610–621, DOI
+10.1086/162719
+Lagage PO, Doucet C, Pantin E, Habart E, Duchˆene
+G, M´enard F, Pinte C, Charnoz S, Pel JW (2006)
+Anatomy of a Flaring Proto-Planetary Disk Around
+a Young Intermediate-Mass Star. Science 314:621–
+623, DOI 10.1126/science.1131436
+Landstreet JD (1992) Magnetic fields at the surfaces of
+stars. A&ARv4(1):35–77, DOI 10.1007/BF00873569
+Law CJ, Crystian S, Teague R, ¨Oberg KI, Rich EA, An-
+drews SM, Bae J, Flaherty K, Guzm´an VV, Huang
+J, Ilee JD, Kastner JH, Loomis RA, Long F, P´erez
+LM, P´erez S, Qi C, Rosotti GP, Ru´ız-Rodr´ıguez D,
+Tsukagoshi T, Wilner DJ (2022) CO Line Emis-
+sion Surfaces and Vertical Structure in Midincli-
+nation Protoplanetary Disks. ApJ932(2):114, DOI
+10.3847/1538-4357/ac6c02, 2205.01776
+Lazareff B, Berger JP, Kluska J, Le Bouquin JB,
+Benisty M, Malbet F, Koen C, Pinte C, Thi WF,
+Absil O, Baron F, Delboulb´e A, Duvert G, Isella A,
+Jocou L, Juhasz A, Kraus S, Lachaume R, M´enard
+F, Millan-Gabet R, Monnier JD, Moulin T, Perraut
+K, Rochat S, Soulez F, Tallon M, Thi´ebaut E, Traub
+W, Zins G (2017) Structure of Herbig AeBe disks at
+the milliarcsecond scale . A statistical survey in the
+H band using PIONIER-VLTI. A&A599:A85, DOI
+10.1051/0004-6361/201629305, 1611.08428
+Le Gal R, ¨Oberg KI, Loomis RA, Pegues J, Bergner JB
+(2019) Sulfur Chemistry in Protoplanetary Disks: CS
+and H2CS. ApJ876(1):72, DOI 10.3847/1538-4357/
+ab1416, 1903.11105
+Le Gal R, ¨Oberg KI, Teague R, Loomis RA, Law
+CJ, Walsh C, Bergin EA, M´enard F, Wilner DJ,
+Andrews SM, Aikawa Y, Booth AS, Cataldi G,
+Bergner JB, Bosman AD, Cleeves LI, Czekala I, Fu-
+ruya K, Guzm´an VV, Huang J, Ilee JD, Nomura
+H, Qi C, Schwarz KR, Tsukagoshi T, Yamato Y,
+Zhang K (2021) Molecules with ALMA at Planet-
+forming Scales (MAPS). XII. Inferring the C/O and
+S/H Ratios in Protoplanetary Disks with Sulfur
+Molecules. ApJS257(1):12, DOI 10.3847/1538-4365/
+ac2583, 2109.06286
+Leemker
+M,
+van’t
+Hoff
+MLR,
+Trapman
+L,
+van
+Gelder ML, Hogerheijde MR, Ru´ız-Rodr´ıguez D,
+van Dishoeck EF (2021) Chemically tracing the wa-
+ter snowline in protoplanetary disks with HCO+.
+A&A646:A3,
+DOI
+10.1051/0004-6361/202039387,
+2011.12319
+Leinert C, Richichi A, Haas M (1997) Binaries among
+Herbig Ae/Be stars. A&A318:472–484
+Leinert C, Graser U, Waters LBFM, Perrin GS, Jaffe
+W, Lopez B, Przygodda F, Chesneau O, Schuller PA,
+Glazenborg-Kluttig AW, Laun W, Ligori S, Meisner
+JA, Wagner K, Bakker EJ, Cotton B, de Jong J,
+Mathar R, Neumann U, Storz C (2003) Ten-micron
+instrument MIDI: getting ready for observations on
+the VLTI. In: Traub WA (ed) Interferometry for Op-
+tical Astronomy II, Society of Photo-Optical Instru-
+mentation Engineers (SPIE) Conference Series, vol
+4838, pp 893–904, DOI 10.1117/12.457027
+Li ZY, Banerjee R, Pudritz RE, Jørgensen JK, Shang
+H, Krasnopolsky R, Maury A (2014) The Earliest
+Stages of Star and Planet Formation: Core Col-
+lapse, and the Formation of Disks and Outflows. In:
+Beuther H, Klessen RS, Dullemond CP, Henning T
+(eds) Protostars and Planets VI, p 173, DOI 10.2458/
+azu\ uapress\ 9780816531240-ch008, 1401.2219
+Lieman-Sifry J, Hughes AM, Carpenter JM, Gorti
+U, Hales A, Flaherty KM (2016) Debris Disks in
+the Scorpius-Centaurus OB Association Resolved
+by ALMA. ApJ828(1):25, DOI 10.3847/0004-637X/
+828/1/25, 1606.07068
+Ligi R, Vigan A, Gratton R, de Boer J, Benisty M,
+Boccaletti A, Quanz SP, Meyer M, Ginski C, Sissa
+E, Gry C, Henning T, Beuzit JL, Biller B, Bonnefoy
+M, Chauvin G, Cheetham AC, Cudel M, Delorme
+P, Desidera S, Feldt M, Galicher R, Girard J, Jan-
+son M, Kasper M, Kopytova T, Lagrange AM, Lan-
+glois M, Lecoroller H, Maire AL, M´enard F, Mesa
+
+70
+Sean D. Brittain et al.
+D, Peretti S, Perrot C, Pinilla P, Pohl A, Rouan D,
+Stolker T, Samland M, Wahhaj Z, Wildi F, Zurlo
+A, Buey T, Fantinel D, Fusco T, Jaquet M, Moulin
+T, Ramos J, Suarez M, Weber L (2018) Investiga-
+tion of the inner structures around HD 169142 with
+VLT/SPHERE. MNRAS473(2):1774–1783, DOI 10.
+1093/mnras/stx2318, 1709.01734
+Lin DNC, Papaloizou J (1979) On the structure of cir-
+cumbinary accretion disks and the tidal evolution of
+commensurable satellites. MNRAS188:191–201, DOI
+10.1093/mnras/188.2.191
+Lin DNC, Papaloizou JCB (1993) On the Tidal Inter-
+action Between Protostellar Disks and Companions.
+In: Levy EH, Lunine JI (eds) Protostars and Planets
+III, p 749
+Lissauer JJ (1993) Planet formation. ARA&A31:129–
+174, DOI 10.1146/annurev.aa.31.090193.001021
+Liu SF, Jin S, Li S, Isella A, Li H (2018) New Con-
+straints on Turbulence and Embedded Planet Mass in
+the HD 163296 Disk from Planet-Disk Hydrodynamic
+Simulations. ApJ857(2):87, DOI 10.3847/1538-4357/
+aab718, 1803.05437
+Long F, Pinilla P, Herczeg GJ, Harsono D, Dipierro G,
+Pascucci I, Hendler N, Tazzari M, Ragusa E, Salyk
+C, Edwards S, Lodato G, van de Plas G, Johnstone
+D, Liu Y, Boehler Y, Cabrit S, Manara CF, Menard
+F, Mulders GD, Nisini B, Fischer WJ, Rigliaco E,
+Banzatti A, Avenhaus H, Gully-Santiago M (2018)
+Gaps and Rings in an ALMA Survey of Disks in the
+Taurus Star-forming Region. ApJ869(1):17, DOI 10.
+3847/1538-4357/aae8e1, 1810.06044
+Loomis RA, ¨Oberg KI, Andrews SM, Bergin E, Bergner
+J, Blake GA, Cleeves LI, Czekala I, Huang J, Le Gal
+R, M´enard F, Pegues J, Qi C, Walsh C, Williams
+JP, Wilner DJ (2020) An Unbiased ALMA Spectral
+Survey of the LkCa 15 and MWC 480 Protoplane-
+tary Disks. ApJ893(2):101, DOI 10.3847/1538-4357/
+ab7cc8, 2006.16187
+Lopez B, Schneider J, Danchi WC (2005) Can Life
+Develop in the Expanded Habitable Zones around
+Red Giant Stars? ApJ627(2):974–985, DOI 10.1086/
+430416, astro-ph/0503520
+Lopez B, Lagarde S, Petrov RG, Jaffe W, Antonelli
+P, Allouche F, Berio P, Matter A, Meilland A, Mil-
+lour F, Robbe-Dubois S, Henning T, Weigelt G,
+Glindemann A, Agocs T, Bailet C, Beckmann U,
+Bettonvil F, van Boekel R, Bourget P, Bresson Y,
+Bristow P, Cruzal`ebes P, Eldswijk E, Fante¨ı Cau-
+jolle Y, Gonz´alez Herrera JC, Graser U, Guajardo
+P, Heininger M, Hofmann KH, Kroes G, Laun W,
+Lehmitz M, Leinert C, Meisenheimer K, Morel S,
+Neumann U, Paladini C, Percheron I, Riquelme M,
+Schoeller M, Stee P, Venema L, Woillez J, Zins G,
+´Abrah´am P, Abadie S, Abuter R, Accardo M, Adler
+T, Alonso J, Augereau JC, B¨ohm A, Bazin G, Bel-
+tran J, Bensberg A, Boland W, Brast R, Burtscher
+L, Castillo R, Chelli A, Cid C, Clausse JM, Connot
+C, Conzelmann RD, Danchi WC, Delbo M, Drevon J,
+Dominik C, van Duin A, Ebert M, Eisenhauer F, Fla-
+ment S, Frahm R, G´amez Rosas V, Gabasch A, Gal-
+lenne A, Garces E, Girard P, Glazenborg A, Gont´e
+FYJ, Guitton F, de Haan M, Hanenburg H, Haubois
+X, Hocd´e V, Hogerheijde M, ter Horst R, Hron J,
+Hummel CA, Hubin N, Huerta R, Idserda J, Isbell
+JW, Ives D, Jakob G, Jask´o A, Jochum L, Klarmann
+L, Klein R, Kragt J, Kuindersma S, Kokoulina E,
+Labadie L, Lacour S, Leftley J, Le Poole R, Lizon JL,
+Lopez M, Lykou F, M´erand A, Marcotto A, Mauclert
+N, Maurer T, Mehrgan LH, Meisner J, Meixner K,
+Mellein M, Menut JL, Mohr L, Mosoni L, Navarro
+R, Nußbaum E, Pallanca L, Pantin E, Pasquini L,
+Phan Duc T, Pott JU, Pozna E, Richichi A, Ridinger
+A, Rigal F, Rivinius T, Roelfsema R, Rohloff RR,
+Rousseau S, Salabert D, Schertl D, Schuhler N, Schuil
+M, Shabun K, Soulain A, Stephan C, Toledo P, Tris-
+tram K, Tromp N, Vakili F, Varga J, Vinther J,
+Waters LBFM, Wittkowski M, Wolf S, Wrhel F,
+Yoffe G (2022) MATISSE, the VLTI mid-infrared
+imaging spectro-interferometer. A&A659:A192, DOI
+10.1051/0004-6361/202141785, 2110.15556
+Lubow SH, D’Angelo G (2006) Gas Flow across Gaps
+in Protoplanetary Disks. ApJ641(1):526–533, DOI
+10.1086/500356, astro-ph/0512292
+Luhman
+KL
+(2012)
+The
+Formation
+and
+Early
+Evolution
+of
+Low-Mass
+Stars
+and
+Brown
+Dwarfs.
+ARA&A50:65–106,
+DOI
+10.1146/annurev-astro-081811-125528, 1208.5800
+Luhn JK, Bastien FA, Wright JT, Johnson JA,
+Howard AW, Isaacson H (2019) Retired A Stars
+and Their Companions. VIII. 15 New Planetary
+Signals around Subgiants and Transit Parameters
+for California Planet Search Planets with Sub-
+giant Hosts. AJ157(4):149, DOI 10.3847/1538-3881/
+aaf5d0, 1811.03043
+Lynden-Bell D, Pringle JE (1974) The evolution of vis-
+cous discs and the origin of the nebular variables.
+MNRAS168:603–637, DOI 10.1093/mnras/168.3.603
+Maaskant KM, Honda M, Waters LBFM, Tielens
+AGGM, Dominik C, Min M, Verhoeff A, Meeus
+G, van den Ancker ME (2013) Identifying gaps
+in flaring Herbig Ae/Be disks using spatially re-
+solved mid-infrared imaging. Are all group I disks
+transitional? A&A555:A64, DOI 10.1051/0004-6361/
+201321300, 1305.3138
+Maaskant KM, Min M, Waters LBFM, Tielens AGGM
+(2014) Polycyclic aromatic hydrocarbon ionization
+
+Herbig Stars
+71
+as a tracer of gas flows through protoplanetary
+disk gaps. A&A563:A78, DOI 10.1051/0004-6361/
+201323137, 1402.0902
+Maaskant KM, de Vries BL, Min M, Waters LBFM, Do-
+minik C, Molster F, Tielens AGGM (2015) Location
+and sizes of forsterite grains in protoplanetary disks.
+Interpretation from the Herschel DIGIT programme.
+A&A574:A140, DOI 10.1051/0004-6361/201423770,
+1406.3951
+Mac´ıas
+E,
+Anglada
+G,
+Osorio
+M,
+Torrelles
+JM,
+Carrasco-Gonz´alez C, G´omez JF, Rodr´ıguez LF,
+Sierra A (2017) Imaging a Central Ionized Compo-
+nent, a Narrow Ring, and the CO Snowline in the
+Multigapped Disk of HD 169142. ApJ838(2):97, DOI
+10.3847/1538-4357/aa6620, 1703.02957
+Macintosh BA, Graham JR, Palmer DW, Doyon R,
+Dunn J, Gavel DT, Larkin J, Oppenheimer B, Sad-
+dlemyer L, Sivaramakrishnan A, Wallace JK, Bau-
+man B, Erickson DA, Marois C, Poyneer LA, Soum-
+mer R (2008) The Gemini Planet Imager: from sci-
+ence to design to construction. In: Hubin N, Max
+CE, Wizinowich PL (eds) Adaptive Optics Systems,
+Society of Photo-Optical Instrumentation Engineers
+(SPIE) Conference Series, vol 7015, p 701518, DOI
+10.1117/12.788083
+Malfait K, Bogaert E, Waelkens C (1998) An ultravio-
+let, optical and infrared study of Herbig Ae/Be stars.
+A&A331:211–223
+Malfait K, Waelkens C, Waters LBFM, Vandenbussche
+B, Huygen E, de Graauw MS (1998) The spectrum
+of the young star HD 100546 observed with the In-
+frared Space Observatory. Astronomy & Astrophysics
+332:L25–L28
+Malfait K, Waelkens C, Bouwman J, de Koter A, Wa-
+ters LBFM (1999) The ISO spectrum of the young
+star HD 142527. A&A345:181–186
+Mannings V (1994) Submillimetre observations of Her-
+big Ae/Be systems. MNRAS271:587–600, DOI 10.
+1093/mnras/271.3.587
+Mannings V, Sargent AI (1997) A High-Resolution
+Study of Gas and Dust around Young Intermediate-
+Mass Stars: Evidence for Circumstellar Disks in Her-
+big Ae Systems. ApJ490(2):792–802, DOI 10.1086/
+304897
+Mannings V, Koerner DW, Sargent AI (1997) A rotat-
+ing disk of gas and dust around a young counter-
+part to β Pictoris. Nature388(6642):555–557, DOI
+10.1038/41505
+Marconi M, Ripepi V (2017) Pulsation in Herbig stars:
+an idea of Francesco and its realization. Mem. Soc.
+Astron. Italiana88:597
+Marigo P, Girardi L, Bressan A, Rosenfield P, Aringer
+B, Chen Y, Dussin M, Nanni A, Pastorelli G, Ro-
+drigues TS, Trabucchi M, Bladh S, Dalcanton J,
+Groenewegen MAT, Montalb´an J, Wood PR (2017)
+A New Generation of PARSEC-COLIBRI Stellar
+Isochrones Including the TP-AGB Phase. ApJ835:77,
+DOI 10.3847/1538-4357/835/1/77, 1701.08510
+Marley MS, Fortney JJ, Hubickyj O, Bodenheimer P,
+Lissauer JJ (2007) On the Luminosity of Young
+Jupiters. ApJ655(1):541–549, DOI 10.1086/509759,
+astro-ph/0609739
+Marois C, Lafreni`ere D, Doyon R, Macintosh B, Nadeau
+D (2006) Angular Differential Imaging: A Powerful
+High-Contrast Imaging Technique. ApJ641(1):556–
+564, DOI 10.1086/500401, astro-ph/0512335
+Martin RG, Lubow SH (2011) The Gravo-magneto
+Limit Cycle in Accretion Disks. ApJ740:L6, DOI
+10.1088/2041-8205/740/1/L6, 1108.4960
+Mathews GS, Klaassen PD, Juh´asz A, Harsono D,
+Chapillon E, van Dishoeck EF, Espada D, de
+Gregorio-Monsalvo I, Hales A, Hogerheijde MR,
+Mottram JC, Rawlings MG, Takahashi S, Testi L
+(2013) ALMA imaging of the CO snowline of the
+HD 163296 disk with DCO+. A&A557:A132, DOI
+10.1051/0004-6361/201321600, 1307.3420
+McKee CF, Ostriker EC (2007) Theory of Star Forma-
+tion. ARA&A45(1):565–687, DOI 10.1146/annurev.
+astro.45.051806.110602, 0707.3514
+Meeus G, Waters LBFM, Bouwman J, van den An-
+cker ME, Waelkens C, Malfait K (2001) ISO spec-
+troscopy of circumstellar dust in 14 Herbig Ae/Be
+systems: Towards an understanding of dust pro-
+cessing. A&A365:476–490, DOI 10.1051/0004-6361:
+20000144, astro-ph/0012295
+Meeus G, Bouwman J, Dominik C, Waters LBFM,
+de Koter A (2002) The absence of the 10 mu
+m silicate feature in the isolated Herbig Ae star
+HD
+100453.
+A&A392:1039–1046,
+DOI
+10.1051/
+0004-6361:20020952
+Meeus G, Montesinos B, Mendigut´ıa I, Kamp I, Thi
+WF, Eiroa C, Grady CA, Mathews G, Sandell G,
+Martin-Za¨ıdi C, Brittain S, Dent WRF, Howard
+C, M´enard F, Pinte C, Roberge A, Vand enbuss-
+che B, Williams JP (2012) Observations of Her-
+big Ae/Be stars with Herschel/PACS. The atomic
+and molecular contents of their protoplanetary discs.
+A&A544:A78, DOI 10.1051/0004-6361/201219225,
+1206.3413
+Meeus G, Salyk C, Bruderer S, Fedele D, Maaskant K,
+Evans NJ, van Dishoeck EF, Montesinos B, Herczeg
+G, Bouwman J, Green JD, Dominik C, Henning T,
+Vicente S (2013) DIGIT survey of far-infrared lines
+from protoplanetary discs. II. CO. A&A559:A84,
+DOI 10.1051/0004-6361/201321122, 1308.4160
+
+72
+Sean D. Brittain et al.
+Meijerink R, Aresu G, Kamp I, Spaans M, Thi WF,
+Woitke P (2012) Far-ultraviolet and X-ray irradiated
+protoplanetary disks: a grid of models. I. The disk
+structure. A&A547:A68, DOI 10.1051/0004-6361/
+201219863, 1208.4959
+Mendigut´ıa I (2020) On the Mass Accretion Rates of
+Herbig Ae/Be Stars. Magnetospheric Accretion or
+Boundary Layer? Galaxies 8(2):39, DOI 10.3390/
+galaxies8020039, 2005.01745
+Mendigut´ıa I, Calvet N, Montesinos B, Mora A, Muze-
+rolle J, Eiroa C, Oudmaijer RD, Mer´ın B (2011a)
+Accretion rates and accretion tracers of Herbig
+Ae/Be stars. A&A535:A99, DOI 10.1051/0004-6361/
+201117444, 1109.3288
+Mendigut´ıa I, Eiroa C, Montesinos B, Mora A, Oud-
+maijer RD, Mer´ın B, Meeus G (2011b) Optical
+spectroscopic variability of Herbig Ae/Be stars.
+A&A529:A34, DOI 10.1051/0004-6361/201015821,
+1102.5033
+Mendigut´ıa I, Brittain S, Eiroa C, Meeus G, Mon-
+tesinos B, Mora A, Muzerolle J, Oudmaijer RD,
+Rigliaco E (2013) Accretion Variability of Herbig
+Ae/Be Stars Observed by X-Shooter HD 31648 and
+HD 163296. ApJ776(1):44, DOI 10.1088/0004-637X/
+776/1/44, 1308.3248
+Mendigut´ıa I, de Wit WJ, Oudmaijer RD, Fairlamb
+JR, Carciofi AC, Ilee JD, Vieira RG (2015) High-
+resolution Br γ spectro-interferometry of the tran-
+sitional Herbig Ae/Be star HD 100546: a Keplerian
+gaseous disc inside the inner rim. MNRAS453:2126–
+2132, DOI 10.1093/mnras/stv1777, 1509.05411
+Mendigut´ıa I, Oudmaijer RD, Garufi A, Lumsden
+SL, Hu´elamo N, Cheetham A, de Wit WJ, Nor-
+ris B, Olguin FA, Tuthill P (2017) The protoplan-
+etary system HD 100546 in Hα polarized light from
+SPHERE/ZIMPOL. A bar-like structure across the
+disk gap? A&A608:A104, DOI 10.1051/0004-6361/
+201731131, 1711.00023
+Menu J, van Boekel R, Henning T, Leinert C, Waelkens
+C, Waters LBFM (2015) The structure of disks
+around intermediate-mass young stars from mid-
+infrared interferometry. Evidence for a population
+of group II disks with gaps. A&A581:A107, DOI
+10.1051/0004-6361/201525654, 1506.03274
+Miley JM, Pani´c O, Haworth TJ, Pascucci I, Wyatt M,
+Clarke C, Richards AMS, Ratzka T (2019) Asym-
+metric mid-plane gas in ALMA images of HD 100546.
+MNRAS485(1):739–752, DOI 10.1093/mnras/stz426,
+1902.07506
+Min M, Dullemond CP, Dominik C, de Koter A, Hov-
+enier JW (2009) Radiative transfer in very optically
+thick circumstellar disks. A&A497:155–166, DOI
+10.1051/0004-6361/200811470, 0902.3092
+Min M, Bouwman J, Dominik C, Waters LBFM, Pon-
+toppidan KM, Hony S, Mulders GD, Henning T, van
+Dishoeck EF, Woitke P, Evans NJ II, Digit Team
+(2016a) The abundance and thermal history of wa-
+ter ice in the disk surrounding HD 142527 from the
+DIGIT Herschel Key Program. A&A593:A11, DOI
+10.1051/0004-6361/201425432, 1606.07266
+Min M, Rab C, Woitke P, Dominik C, M´enard
+F (2016b) Multiwavelength optical properties of
+compact dust aggregates in protoplanetary disks.
+A&A585:A13, DOI 10.1051/0004-6361/201526048,
+1510.05426
+Miotello
+A,
+van
+Dishoeck
+EF,
+Kama
+M,
+Brud-
+erer S (2016) Determining protoplanetary disk gas
+masses from CO isotopologues line observations.
+A&A594:A85, DOI 10.1051/0004-6361/201628159,
+1605.07780
+Miotello A, van Dishoeck EF, Williams JP, Ansdell M,
+Guidi G, Hogerheijde M, Manara CF, Tazzari M,
+Testi L, van der Marel N, van Terwisga S (2017) Lu-
+pus disks with faint CO isotopologues: low gas/dust
+or high carbon depletion? A&A599:A113, DOI 10.
+1051/0004-6361/201629556, 1612.01538
+Moe M, Kratter KM (2021) Impact of binary stars
+on planet statistics - I. Planet occurrence rates and
+trends with stellar mass. MNRAS507(3):3593–3611,
+DOI 10.1093/mnras/stab2328
+Monnier
+JD,
+Millan-Gabet
+R
+(2002)
+On
+the
+Interferometric
+Sizes
+of
+Young
+Stellar
+Ob-
+jects.
+ApJ579(2):694–698,
+DOI
+10.1086/342917,
+astro-ph/0207292
+Monnier JD, Millan-Gabet R, Billmeier R, Akeson
+RL, Wallace D, Berger JP, Calvet N, D’Alessio P,
+Danchi WC, Hartmann L, Hillenbrand LA, Kuch-
+ner M, Rajagopal J, Traub WA, Tuthill PG, Boden
+A, Booth A, Colavita M, Gathright J, Hrynevych
+M, Le Mignant D, Ligon R, Neyman C, Swain
+M, Thompson R, Vasisht G, Wizinowich P, Be-
+ichman C, Beletic J, Creech-Eakman M, Koresko
+C, Sargent A, Shao M, van Belle G (2005) The
+Near-Infrared Size-Luminosity Relations for Her-
+big Ae/Be Disks. ApJ624(2):832–840, DOI 10.1086/
+429266, astro-ph/0502252
+Mooley K, Hillenbrand L, Rebull L, Padgett D, Knapp
+G (2013) B- and A-type Stars in the Taurus-Auriga
+Star-forming Region. ApJ771(2):110, DOI 10.1088/
+0004-637X/771/2/110, 1306.0598
+Mo´or A, Cur´e M, K´osp´al ´A, ´Abrah´am P, Csengeri
+T, Eiroa C, Gunawan D, Henning T, Hughes AM,
+Juh´asz A (2017) Molecular Gas in Debris Disks
+around Young A-type Stars. ApJ849(2):123, DOI
+10.3847/1538-4357/aa8e4e, 1709.08414
+
+Herbig Stars
+73
+Morgan WW, Keenan PC, Kellman E (1943) An atlas
+of stellar spectra, with an outline of spectral classifi-
+cation
+Motte
+F,
+Bontemps
+S,
+Louvet
+F
+(2018)
+High-
+Mass
+Star
+and
+Massive
+Cluster
+Formation
+in
+the Milky Way. ARA&A56:41–82, DOI 10.1146/
+annurev-astro-091916-055235, 1706.00118
+Moura T, Alencar SHP, Sousa AP, Alecian E, Lebreton
+Y (2020) Spectroscopic analysis of accretion/ejection
+signatures in the Herbig Ae/Be stars HD 261941 and
+V590 Mon. MNRAS494(3):3512–3535, DOI 10.1093/
+mnras/staa695
+Mulders GD, Dominik C (2012) Probing the turbu-
+lent mixing strength in protoplanetary disks across
+the stellar mass range: no significant variations.
+A&A539:A9,
+DOI
+10.1051/0004-6361/201118127,
+1201.1453
+Mulders GD, Waters LBFM, Dominik C, Sturm B,
+Bouwman J, Min M, Verhoeff AP, Acke B, Augereau
+JC, Evans NJ, Henning T, Meeus G, Olofsson J
+(2011) Low abundance, strong features: window-
+dressing crystalline forsterite in the disk wall of
+HD 100546. A&A531:A93, DOI 10.1051/0004-6361/
+201116770, 1105.4817
+Mulders GD, Paardekooper SJ, Pani´c O, Dominik
+C, van Boekel R, Ratzka T (2013) Planet or
+brown dwarf? Inferring the companion mass in HD
+100546 from the wall shape using mid-infrared inter-
+ferometry. A&A557:A68, DOI 10.1051/0004-6361/
+201220930, 1306.4264
+Mulders GD, Pascucci I, Apai D (2015) A Stellar-
+mass-dependent Drop in Planet Occurrence Rates.
+ApJ798(2):112, DOI 10.1088/0004-637X/798/2/112,
+1406.7356
+Mulders GD, Drazkowska J, van der Marel N, Ciesla
+FJ, Pascucci I (2021) Why Do M Dwarfs Have
+More Transiting Planets? ApJ920(1):L1, DOI 10.
+3847/2041-8213/ac2947, 2110.02971
+Muley
+D,
+Fung
+J,
+van
+der
+Marel
+N
+(2019)
+PDS 70: A Transition Disk Sculpted by a Sin-
+gle Planet. ApJ879(1):L2, DOI 10.3847/2041-8213/
+ab24d0, 1902.07191
+M¨uller A, Keppler M, Henning T, Samland M, Chau-
+vin G, Beust H, Maire AL, Molaverdikhani K, van
+Boekel R, Benisty M, Boccaletti A, Bonnefoy M,
+Cantalloube F, Charnay B, Baudino JL, Gennaro
+M, Long ZC, Cheetham A, Desidera S, Feldt M,
+Fusco T, Girard J, Gratton R, Hagelberg J, Jan-
+son M, Lagrange AM, Langlois M, Lazzoni C, Ligi
+R, M´enard F, Mesa D, Meyer M, Molli`ere P, Mor-
+dasini C, Moulin T, Pavlov A, Pawellek N, Quanz
+SP, Ramos J, Rouan D, Sissa E, Stadler E, Vigan A,
+Wahhaj Z, Weber L, Zurlo A (2018) Orbital and at-
+mospheric characterization of the planet within the
+gap of the PDS 70 transition disk. A&A617:L2, DOI
+10.1051/0004-6361/201833584, 1806.11567
+Muro-Arena GA, Dominik C, Waters LBFM, Min M,
+Klarmann L, Ginski C, Isella A, Benisty M, Pohl
+A, Garufi A, Hagelberg J, Langlois M, Menard F,
+Pinte C, Sezestre E, van der Plas G, Villenave M,
+Delboulb´e A, Magnard Y, M¨oller-Nilsson O, Pragt
+J, Rabou P, Roelfsema R (2018) Dust modeling of
+the combined ALMA and SPHERE datasets of HD
+163296. Is HD 163296 really a Meeus group II disk?
+A&A614:A24, DOI 10.1051/0004-6361/201732299,
+1802.03328
+Muro-Arena GA, Benisty M, Ginski C, Dominik C,
+Facchini S, Villenave M, van Boekel R, Chauvin G,
+Garufi A, Henning T, Janson M, Keppler M, Matter
+A, M´enard F, Stolker T, Zurlo A, Blanchard P, Mau-
+rel D, Moeller-Nilsson O, Petit C, Roux A, Sevin A,
+Wildi F (2020) Shadowing and multiple rings in the
+protoplanetary disk of HD 139614. A&A635:A121,
+DOI 10.1051/0004-6361/201936509, 1911.09612
+Murphy SJ, Joyce M, Bedding TR, White TR, Kama
+M (2021) A precise asteroseismic age and metal-
+licity for HD 139614: a pre-main-sequence star
+with a protoplanetary disc in Upper Centaurus-
+Lupus.
+MNRAS502(2):1633–1646,
+DOI
+10.1093/
+mnras/stab144, 2011.11821
+Muto T, Grady CA, Hashimoto J, Fukagawa M, Horn-
+beck JB, Sitko M, Russell R, Werren C, Cur´e M,
+Currie T, Ohashi N, Okamoto Y, Momose M, Honda
+M, Inutsuka S, Takeuchi T, Dong R, Abe L, Brandner
+W, Brandt T, Carson J, Egner S, Feldt M, Fukue T,
+Goto M, Guyon O, Hayano Y, Hayashi M, Hayashi
+S, Henning T, Hodapp KW, Ishii M, Iye M, Janson
+M, Kandori R, Knapp GR, Kudo T, Kusakabe N,
+Kuzuhara M, Matsuo T, Mayama S, McElwain MW,
+Miyama S, Morino JI, Moro-Martin A, Nishimura
+T, Pyo TS, Serabyn E, Suto H, Suzuki R, Takami
+M, Takato N, Terada H, Thalmann C, Tomono D,
+Turner EL, Watanabe M, Wisniewski JP, Yamada
+T, Takami H, Usuda T, Tamura M (2012) Discovery
+of Small-scale Spiral Structures in the Disk of SAO
+206462 (HD 135344B): Implications for the Physical
+State of the Disk from Spiral Density Wave Theory.
+ApJ748(2):L22, DOI 10.1088/2041-8205/748/2/L22,
+1202.6139
+Muzerolle J, D’Alessio P, Calvet N, Hartmann L
+(2004) Magnetospheres and Disk Accretion in Herbig
+Ae/Be Stars. ApJ617:406–417, DOI 10.1086/425260,
+astro-ph/0409008
+Najita J, Carr JS, Glassgold AE, Shu FH, Toku-
+naga AT (1996) Kinematic Diagnostics of Disks
+around Young Stars: CO Overtone Emission from
+
+74
+Sean D. Brittain et al.
+WL 16 and 1548C27. ApJ462:919, DOI 10.1086/
+177205, astro-ph/9512109
+Najita J, Carr JS, Mathieu RD (2003) Gas in the Ter-
+restrial Planet Region of Disks: CO Fundamental
+Emission from T Tauri Stars. ApJ589:931–952, DOI
+10.1086/374809
+Najita JR, Doppmann GW, Carr JS, Graham JR, Eis-
+ner JA (2009) High-Resolution K-Band Spectroscopy
+of MWC 480 and V1331 Cyg. ApJ691(1):738–748,
+DOI 10.1088/0004-637X/691/1/738, 0809.4267
+Natta A, Prusti T, Neri R, Wooden D, Grinin VP,
+Mannings V (2001) A reconsideration of disk prop-
+erties in Herbig Ae stars. A&A371:186–197, DOI
+10.1051/0004-6361:20010334
+Natta A, Testi L, Randich S (2006) Accretion in the ρ-
+Ophiuchi pre-main sequence stars. A&A452(1):245–
+252, DOI 10.1051/0004-6361:20054706, astro-ph/
+0602618
+Nielsen EL, De Rosa RJ, Macintosh B, Wang JJ, Ruf-
+fio JB, Chiang E, Marley MS, Saumon D, Savran-
+sky D, Ammons SM, Bailey VP, Barman T, Blain C,
+Bulger J, Burrows A, Chilcote J, Cotten T, Czekala
+I, Doyon R, Duchˆene G, Esposito TM, Fabrycky D,
+Fitzgerald MP, Follette KB, Fortney JJ, Gerard BL,
+Goodsell SJ, Graham JR, Greenbaum AZ, Hibon
+P, Hinkley S, Hirsch LA, Hom J, Hung LW, Daw-
+son RI, Ingraham P, Kalas P, Konopacky Q, Larkin
+JE, Lee EJ, Lin JW, Maire J, Marchis F, Marois
+C, Metchev S, Millar-Blanchaer MA, Morzinski KM,
+Oppenheimer R, Palmer D, Patience J, Perrin M,
+Poyneer L, Pueyo L, Rafikov RR, Rajan A, Rameau
+J, Rantakyr¨o FT, Ren B, Schneider AC, Sivaramakr-
+ishnan A, Song I, Soummer R, Tallis M, Thomas S,
+Ward-Duong K, Wolff S (2019) The Gemini Planet
+Imager Exoplanet Survey: Giant Planet and Brown
+Dwarf Demographics from 10 to 100 au. AJ158(1):13,
+DOI 10.3847/1538-3881/ab16e9, 1904.05358
+Notsu S, Nomura H, Ishimoto D, Walsh C, Honda
+M, Hirota T, Millar TJ (2017) Candidate Water
+Vapor Lines to Locate the H2O Snowline through
+High-dispersion Spectroscopic Observations. II. The
+Case of a Herbig Ae Star. ApJ836(1):118, DOI
+10.3847/1538-4357/836/1/118, 1701.04381
+Notsu S, Akiyama E, Booth A, Nomura H, Walsh
+C, Hirota T, Honda M, Tsukagoshi T, Millar TJ
+(2019) Dust Continuum Emission and the Upper
+Limit Fluxes of Submillimeter Water Lines of the
+Protoplanetary Disk around HD 163296 Observed
+by ALMA. ApJ875(2):96, DOI 10.3847/1538-4357/
+ab0ae9, 1902.09932
+¨Oberg KI, Qi C, Fogel JKJ, Bergin EA, Andrews
+SM, Espaillat C, van Kempen TA, Wilner DJ, Pas-
+cucci I (2010) The Disk Imaging Survey of Chem-
+istry with SMA. I. Taurus Protoplanetary Disk
+Data. ApJ720:480–493, DOI 10.1088/0004-637X/
+720/1/480, 1007.1476
+¨Oberg KI, Murray-Clay R, Bergin EA (2011) The Ef-
+fects of Snowlines on C/O in Planetary Atmospheres.
+ApJ743(1):L16, DOI 10.1088/2041-8205/743/1/L16,
+1110.5567
+¨Oberg KI, Guzm´an VV, Furuya K, Qi C, Aikawa
+Y, Andrews SM, Loomis R, Wilner DJ (2015) The
+comet-like composition of a protoplanetary disk as
+revealed by complex cyanides. Nature520(7546):198–
+201, DOI 10.1038/nature14276, 1505.06347
+¨Oberg KI, Guzm´an VV, Walsh C, Aikawa Y, Bergin
+EA, Law CJ, Loomis RA, Alarc´on F, Andrews SM,
+Bae J, Bergner JB, Boehler Y, Booth AS, Bosman
+AD, Calahan JK, Cataldi G, Cleeves LI, Czekala
+I, Furuya K, Huang J, Ilee JD, Kurtovic NT, Le
+Gal R, Liu Y, Long F, M´enard F, Nomura H, P´erez
+LM, Qi C, Schwarz KR, Sierra A, Teague R, Tsuk-
+agoshi T, Yamato Y, van’t Hoff MLR, Waggoner
+AR, Wilner DJ, Zhang K (2021) Molecules with
+ALMA at Planet-forming Scales (MAPS). I. Pro-
+gram Overview and Highlights. ApJS257(1):1, DOI
+10.3847/1538-4365/ac1432, 2109.06268
+Oberg N, Kamp I, Cazaux S, Woitke P, Thi WF
+(2022) Circumplanetary disk ices. I. Ice formation
+vs. viscous evolution and grain drift. arXiv e-prints
+arXiv:2208.11053, 2208.11053
+Ochsendorf BB, Ellerbroek LE, Chini R, Hartoog
+OE, Hoffmeister V, Waters LBFM, Kaper L (2011)
+First firm spectral classification of an early-B pre-
+main-sequence star: B275 in ¡ASTROBJ¿M 17¡/AS-
+TROBJ¿.
+A&A536:L1,
+DOI
+10.1051/0004-6361/
+201118089, 1110.5755
+Owen JE (2014) Snow Lines as Probes of Turbulent Dif-
+fusion in Protoplanetary Disks. ApJ790(1):L7, DOI
+10.1088/2041-8205/790/1/L7, 1406.6707
+Pagani L, Bourgoin A, Lique F (2012) A method to
+measure CO and N2 depletion profiles inside prestel-
+lar
+cores.
+A&A548:L4,
+DOI
+10.1051/0004-6361/
+201220137
+Palla F, Stahler SW (1993) The Pre-Main-Sequence
+Evolution of Intermediate-Mass Stars. ApJ418:414,
+DOI 10.1086/173402
+Pallavicini R, Golub L, Rosner R, Vaiana GS, Ayres
+T, Linsky JL (1981) Relations among stellar X-
+ray emission observed from Einstein, stellar rotation
+and bolometric luminosity. ApJ248:279–290, DOI
+10.1086/159152
+Pani´c O, Hogerheijde MR (2009) Characterising discs
+around Herbig Ae/Be stars through modelling of
+low-J 12CO lines. A&A508:707–716, DOI 10.1051/
+0004-6361/200912584
+
+Herbig Stars
+75
+Pani´c O, Holland WS, Wyatt MC, Kennedy GM,
+Matthews BC, Lestrade JF, Sibthorpe B, Greaves
+JS, Marshall JP, Phillips NM, Tottle J (2013) First
+results of the SONS survey: submillimetre detec-
+tions of debris discs. MNRAS435(2):1037–1046, DOI
+10.1093/mnras/stt1293
+Pani´c O, Haworth TJ, Petr-Gotzens MG, Miley J,
+van den Ancker M, Vioque M, Siess L, Parker R,
+Clarke CJ, Kamp I, Kennedy G, Oudmaijer RD,
+Pascucci I, Richards AMS, Ratzka T, Qi C (2021)
+Planet formation in intermediate-separation binary
+systems. MNRAS501(3):4317–4328, DOI 10.1093/
+mnras/staa3834, 2012.07901
+Pascual N, Montesinos B, Meeus G, Marshall JP,
+Mendigut´ıa I, Sandell G (2016) The far-infrared
+behaviour of Herbig Ae/Be discs: Herschel PACS
+photometry. A&A586:A6, DOI 10.1051/0004-6361/
+201526605, 1511.08356
+Pascucci I, Sterzik M, Alexander RD, Alencar SHP,
+Gorti U, Hollenbach D, Owen J, Ercolano B, Edwards
+S (2011) The Photoevaporative Wind from the Disk
+of TW Hya. ApJ736(1):13, DOI 10.1088/0004-637X/
+736/1/13, 1105.0045
+Patel P, Sigut TAA, Landstreet JD (2017) Photoion-
+ization Models for the Inner Gaseous Disks of Her-
+big Be Stars: Evidence against Magnetospheric Ac-
+cretion? ApJ836(2):214, DOI 10.3847/1538-4357/
+aa5c3f, 1701.06721
+Paunzen E, Iliev IK, Kamp I, Barzova IS (2002) The
+status of Galactic field λ Bootis stars in the post-
+Hipparcos era. MNRAS336(3):1030–1042, DOI 10.
+1046/j.1365-8711.2002.05865.x, astro-ph/0207488
+Pegues J, ¨Oberg KI, Bergner JB, Loomis RA, Qi
+C, Le Gal R, Cleeves LI, Guzm´an VV, Huang
+J, Jørgensen JK, Andrews SM, Blake GA, Car-
+penter JM, Schwarz KR, Williams JP, Wilner DJ
+(2020) An ALMA Survey of H2CO in Protoplane-
+tary Disks. ApJ890(2):142, DOI 10.3847/1538-4357/
+ab64d9, 2002.12525
+Perez MR, Grady CA (1997) Observational Overview
+of Young Intermediate-Mass Objects: Herbig Ae/Be
+Stars. Space Sci. Rev.82:407–450, DOI 10.1023/A:
+1005064108523
+Perez S, Dunhill A, Casassus S, Roman P, Szul´agyi
+J, Flores C, Marino S, Montesinos M (2015) Planet
+Formation Signposts: Observability of Circumplane-
+tary Disks via Gas Kinematics. ApJ811(1):L5, DOI
+10.1088/2041-8205/811/1/L5, 1505.06808
+P´erez S, Casassus S, Ben´ıtez-Llambay P (2018) Ob-
+servability of planet-disc interactions in CO kinemat-
+ics. MNRAS480(1):L12–L17, DOI 10.1093/mnrasl/
+sly109, 1806.05125
+P´erez S, Casassus S, Hales A, Marino S, Cheetham
+A, Zurlo A, Cieza L, Dong R, Alarc´on F, Ben´ıtez-
+Llambay P, Fomalont E, Avenhaus H (2020) Long
+Baseline Observations of the HD 100546 Protoplane-
+tary Disk with ALMA. ApJ889(1):L24, DOI 10.3847/
+2041-8213/ab6b2b, 1906.06305
+P´ericaud J, Di Folco E, Dutrey A, Guilloteau S, Pi´etu
+V (2017) The hybrid disks: a search and study to
+better understand evolution of disks. A&A600:A62,
+DOI 10.1051/0004-6361/201629371, 1612.06582
+Perraut K, Dougados C, Lima GHRA, Benisty M,
+Mourard D, Ligi R, Nardetto N, Tallon-Bosc I,
+ten Brummelaar T, Farrington C (2016) A disk
+wind in AB Aurigae traced with Hα interferometry.
+A&A596:A17, DOI 10.1051/0004-6361/201628931
+Pi´etu V, Dutrey A, Kahane C (2003) A Keplerian disk
+around the Herbig Ae star HD 34282. A&A398:565–
+569, DOI 10.1051/0004-6361:20021551, astro-ph/
+0210097
+Pi´etu V, Guilloteau S, Dutrey A (2005) Sub-arcsec
+imaging of the AB Aur molecular disk and en-
+velope at millimeter wavelengths: a non Keplerian
+disk. A&A443(3):945–954, DOI 10.1051/0004-6361:
+20042050, astro-ph/0504023
+Pi´etu V, Dutrey A, Guilloteau S (2007) Probing
+the structure of protoplanetary disks: a compar-
+ative study of DM Tau, LkCa 15, and MWC
+480. A&A467(1):163–178, DOI 10.1051/0004-6361:
+20066537, astro-ph/0701425
+Pineda JE, Quanz SP, Meru F, Mulders GD, Meyer
+MR, Pani´c O, Avenhaus H (2014) Resolved Images
+of the Protoplanetary Disk around HD 100546 with
+ALMA. ApJ788(2):L34, DOI 10.1088/2041-8205/
+788/2/L34, 1405.5773
+Pinilla P, Benisty M, Birnstiel T (2012) Ring shaped
+dust accumulation in transition disks. A&A545:A81,
+DOI 10.1051/0004-6361/201219315, 1207.6485
+Pinilla P, Benisty M, Birnstiel T, Ricci L, Isella A,
+Natta A, Dullemond CP, Quiroga-Nu˜nez LH, Hen-
+ning T, Testi L (2014) Millimetre spectral indices
+of transition disks and their relation to the cav-
+ity radius. A&A564:A51, DOI 10.1051/0004-6361/
+201323322, 1402.5778
+Pinilla P, Flock M, Ovelar MdJ, Birnstiel T (2016)
+Can dead zones create structures like a transi-
+tion disk? A&A596:A81, DOI 10.1051/0004-6361/
+201628441, 1610.02044
+Pinilla P, Tazzari M, Pascucci I, Youdin AN, Garufi
+A, Manara CF, Testi L, van der Plas G, Barenfeld
+SA, Canovas H, Cox EG, Hendler NP, P´erez LM,
+van der Marel N (2018) Homogeneous Analysis of
+the Dust Morphology of Transition Disks Observed
+with ALMA: Investigating Dust Trapping and the
+
+76
+Sean D. Brittain et al.
+Origin of the Cavities. ApJ859(1):32, DOI 10.3847/
+1538-4357/aabf94, 1804.07301
+Pinte C, Woitke P, M´enard F, Duchˆene G, Kamp I,
+Meeus G, Mathews G, Howard CD, Grady CA, Thi
+WF, Tilling I, Augereau JC, Dent WRF, Alacid JM,
+Andrews S, Ardila DR, Aresu G, Barrado D, Brit-
+tain S, Ciardi DR, Danchi W, Eiroa C, Fedele D, de
+Gregorio-Monsalvo I, Heras A, Huelamo N, Krivov
+A, Lebreton J, Liseau R, Martin-Za¨ıdi C, Mendigut´ıa
+I, Montesinos B, Mora A, Morales-Calderon M, No-
+mura H, Pantin E, Pascucci I, Phillips N, Podio L,
+Poelman DR, Ramsay S, Riaz B, Rice K, Riviere-
+Marichalar P, Roberge A, Sandell G, Solano E, Van-
+denbussche B, Walker H, Williams JP, White GJ,
+Wright G (2010) The Herschel view of GAS in Pro-
+toplanetary Systems (GASPS). First comparisons
+with a large grid of models. A&A518:L126, DOI
+10.1051/0004-6361/201014591, 1005.3826
+Pinte C, Dent WRF, M´enard F, Hales A, Hill T,
+Cortes P, de Gregorio-Monsalvo I (2016) Dust and
+Gas in the Disk of HL Tauri: Surface Density, Dust
+Settling, and Dust-to-gas Ratio. ApJ816:25, DOI
+10.3847/0004-637X/816/1/25, 1508.00584
+Pinte C, M´enard F, Duchˆene G, Hill T, Dent WRF,
+Woitke P, Maret S, van der Plas G, Hales A, Kamp
+I, Thi WF, de Gregorio-Monsalvo I, Rab C, Quanz
+SP, Avenhaus H, Carmona A, Casassus S (2018a)
+Direct mapping of the temperature and velocity
+gradients in discs. Imaging the vertical CO snow
+line around IM Lupi. A&A609:A47, DOI 10.1051/
+0004-6361/201731377, 1710.06450
+Pinte C, Price DJ, M´enard F, Duchˆene G, Dent WRF,
+Hill T, de Gregorio-Monsalvo I, Hales A, Mentiplay D
+(2018b) Kinematic Evidence for an Embedded Proto-
+planet in a Circumstellar Disk. ApJ860(1):L13, DOI
+10.3847/2041-8213/aac6dc, 1805.10293
+Pinte C, van der Plas G, M´enard F, Price DJ, Christi-
+aens V, Hill T, Mentiplay D, Ginski C, Choquet E,
+Boehler Y, Duchˆene G, Perez S, Casassus S (2019)
+Kinematic detection of a planet carving a gap in a
+protoplanetary disk. Nature Astronomy 3:1109–1114,
+DOI 10.1038/s41550-019-0852-6, 1907.02538
+Pirzkal
+N,
+Spillar
+EJ,
+Dyck
+HM
+(1997)
+A
+Search
+for
+Close
+Bright
+Companions
+to
+AeBe
+Stars.
+ApJ481(1):392–395,
+DOI
+10.1086/304055,
+astro-ph/9702101
+Poeckert R, Marlborough JM (1976) Intrinsic linear
+polarization of Be stars as a function of V sini.
+ApJ206:182–195, DOI 10.1086/154369
+Poeckert R, Marlborough JM (1977) Linear polariza-
+tion of Halpha in the Be star Gamma Cassiopeiae.
+ApJ218:220–226, DOI 10.1086/155673
+Pohl A, Benisty M, Pinilla P, Ginski C, de Boer J,
+Avenhaus H, Henning T, Zurlo A, Boccaletti A,
+Augereau JC, Birnstiel T, Dominik C, Facchini S,
+Fedele D, Janson M, Keppler M, Kral Q, Langlois
+M, Ligi R, Maire AL, M´enard F, Meyer M, Pinte
+C, Quanz SP, Sauvage JF, Sezestre ´E, Stolker T,
+Szul´agyi J, van Boekel R, van der Plas G, Villenave
+M, Baruffolo A, Baudoz P, Le Mignant D, Maurel
+D, Ramos J, Weber L (2017) The Circumstellar Disk
+HD 169142: Gas, Dust, and Planets Acting in Con-
+cert? ApJ850(1):52, DOI 10.3847/1538-4357/aa94c2,
+1710.06485
+Pollack JB, Hubickyj O, Bodenheimer P, Lissauer JJ,
+Podolak M, Greenzweig Y (1996) Formation of the
+Giant Planets by Concurrent Accretion of Solids
+and Gas. Icarus124(1):62–85, DOI 10.1006/icar.1996.
+0190
+Pontoppidan KM, Salyk C, Blake GA, Meijerink R,
+Carr JS, Najita J (2010) A Spitzer Survey of Mid-
+infrared Molecular Emission from Protoplanetary
+Disks. I. Detection Rates. ApJ720(1):887–903, DOI
+10.1088/0004-637X/720/1/887, 1006.4189
+Powell D, Murray-Clay R, P´erez LM, Schlichting
+HE, Rosenthal M (2019) New Constraints From
+Dust Lines on the Surface Densities of Protoplane-
+tary Disks. ApJ878(2):116, DOI 10.3847/1538-4357/
+ab20ce, 1905.03252
+Pyerin MA, Delage TN, Kurtovic NT, G´arate M, Hen-
+ning T, Pinilla P (2021) Constraining the properties
+of the potential embedded planets in the disk around
+HD 100546. A&A656:A150, DOI 10.1051/0004-6361/
+202141998
+Qi C, D’Alessio P, ¨Oberg KI, Wilner DJ, Hughes AM,
+Andrews SM, Ayala S (2011) Resolving the CO Snow
+Line in the Disk around HD 163296. ApJ740(2):84,
+DOI 10.1088/0004-637X/740/2/84, 1107.5061
+Qi C, ¨Oberg KI, Andrews SM, Wilner DJ, Bergin
+EA, Hughes AM, Hogherheijde M, D’Alessio P
+(2015) Chemical Imaging of the CO Snow Line in
+the HD 163296 Disk. ApJ813(2):128, DOI 10.1088/
+0004-637X/813/2/128, 1510.00968
+Quanz SP, Amara A, Meyer MR, Kenworthy MA,
+Kasper M, Girard JH (2013a) A Young Protoplanet
+Candidate Embedded in the Circumstellar Disk of
+HD 100546. ApJ766:L1, DOI 10.1088/2041-8205/
+766/1/L1, 1302.7122
+Quanz SP, Avenhaus H, Buenzli E, Garufi A, Schmid
+HM, Wolf S (2013b) Gaps in the HD 169142 Pro-
+toplanetary Disk Revealed by Polarimetric Imaging:
+Signs of Ongoing Planet Formation? ApJ766(1):L2,
+DOI 10.1088/2041-8205/766/1/L2, 1302.3029
+Quanz SP, Amara A, Meyer MR, Girard JH, Kenwor-
+thy MA, Kasper M (2015) Confirmation and Char-
+
+Herbig Stars
+77
+acterization of the Protoplanet HD 100546 b—Direct
+Evidence for Gas Giant Planet Formation at 50
+AU. ApJ807(1):64, DOI 10.1088/0004-637X/807/1/
+64, 1412.5173
+Quillen AC, Blackman EG, Frank A, Varni`ere P
+(2004) On the Planet and the Disk of COKU
+TAURI/4.
+ApJ612(2):L137–L140,
+DOI
+10.1086/
+424693, astro-ph/0406445
+Rab C, Kamp I (2019) HD163296 paper DSHARP data.
+A&Ain prep(1000):064301, DOI 10.1088/1538-3873/
+aaf4e5, 1812.02741
+Rab C, Kamp I, Dominik C, Ginski C, Muro-Arena
+GA, Thi WF, Waters LBFM, Woitke P (2020) In-
+terpreting high spatial resolution line observations of
+planet-forming disks with gaps and rings: the case of
+HD 163296. A&A642:A165, DOI 10.1051/0004-6361/
+202038712, 2008.05941
+Rameau J, Follette KB, Pueyo L, Marois C, Macintosh
+B, Millar-Blanchaer M, Wang JJ, Vega D, Doyon
+R, Lafreni`ere D, Nielsen EL, Bailey V, Chilcote
+JK, Close LM, Esposito TM, Males JR, Metchev
+S, Morzinski KM, Ruffio JB, Wolff SG, Ammons
+SM, Barman TS, Bulger J, Cotten T, De Rosa RJ,
+Duchene G, Fitzgerald MP, Goodsell S, Graham JR,
+Greenbaum AZ, Hibon P, Hung LW, Ingraham P,
+Kalas P, Konopacky Q, Larkin JE, Maire J, Marchis
+F, Oppenheimer R, Palmer D, Patience J, Perrin
+MD, Poyneer L, Rajan A, Rantakyr¨o FT, Marley MS,
+Savransky D, Schneider AC, Sivaramakrishnan A,
+Song I, Soummer R, Thomas S, Wallace JK, Ward-
+Duong K, Wiktorowicz S (2017) An Optical/Near-
+infrared Investigation of HD 100546 b with the Gem-
+ini Planet Imager and MagAO. AJ153:244, DOI
+10.3847/1538-3881/aa6cae, 1704.06317
+Ram´ırez-Tannus MC, Kaper L, de Koter A, Tramper
+F, Bik A, Ellerbroek LE, Ochsendorf BB, Ram´ırez-
+Agudelo OH, Sana H (2017) Massive pre-main-
+sequence stars in M17. A&A604:A78, DOI 10.1051/
+0004-6361/201629503, 1704.08216
+Rebollido I, Eiroa C, Montesinos B, Maldonado J,
+Villaver E, Absil O, Bayo A, Canovas H, Carmona
+A, Chen C, Ertel S, Henning T, Iglesias DP, Laun-
+hardt R, Liseau R, Meeus G, Mo´or A, Mora A, Olof-
+sson J, Rauw G, Riviere-Marichalar P (2020) Exo-
+comets: A spectroscopic survey. A&A639:A11, DOI
+10.1051/0004-6361/201936071, 2003.11084
+Reffert S, Bergmann C, Quirrenbach A, Trifonov T,
+K¨unstler A (2015) Precise radial velocities of giant
+stars. VII. Occurrence rate of giant extrasolar planets
+as a function of mass and metallicity. A&A574:A116,
+DOI 10.1051/0004-6361/201322360, 1412.4634
+Reg´aly Z, Juh´asz A, S´andor Z, Dullemond CP (2012)
+Possible planet-forming regions on submillimetre
+images. MNRAS419(2):1701–1712, DOI 10.1111/j.
+1365-2966.2011.19834.x, 1109.6177
+Reggiani M, Quanz SP, Meyer MR, Pueyo L, Absil
+O, Amara A, Anglada G, Avenhaus H, Girard JH,
+Carrasco Gonzalez C, Graham J, Mawet D, Meru F,
+Milli J, Osorio M, Wolff S, Torrelles JM (2014) Dis-
+covery of a Companion Candidate in the HD 169142
+Transition Disk and the Possibility of Multiple Planet
+Formation. ApJ792(1):L23, DOI 10.1088/2041-8205/
+792/1/L23, 1408.0813
+Reggiani M, Christiaens V, Absil O, Mawet D, Huby
+E, Choquet E, Gomez Gonzalez CA, Ruane G, Fe-
+menia B, Serabyn E, Matthews K, Barraza M, Car-
+lomagno B, Defr`ere D, Delacroix C, Habraken S, Jo-
+livet A, Karlsson M, Orban de Xivry G, Piron P,
+Surdej J, Vargas Catalan E, Wertz O (2018) Dis-
+covery of a point-like source and a third spiral arm
+in the transition disk around the Herbig Ae star
+MWC 758. A&A611:A74, DOI 10.1051/0004-6361/
+201732016, 1710.11393
+Rice WKM, Armitage PJ, Wood K, Lodato G (2006)
+Dust filtration at gap edges: implications for the
+spectral energy distributions of discs with embed-
+ded planets. MNRAS373:1619–1626, DOI 10.1111/j.
+1365-2966.2006.11113.x, astro-ph/0609808
+Rich EA, Wisniewski JP, Sitko ML, Grady CA, Tobin
+JJ, Fukagawa M (2020) Disk Illumination and Jet
+Variability of the Herbig Ae Star HD 163296 Using
+Multi-epoch HST/STIS Optical, Near-IR, and Ra-
+dio Imagery and Spectroscopy. ApJ902(1):4, DOI
+10.3847/1538-4357/abb2a3, 2008.11606
+Riols A, Lesur G (2018) Dust settling and rings in
+the outer regions of protoplanetary discs subject to
+ambipolar diffusion. A&A617:A117, DOI 10.1051/
+0004-6361/201833212, 1805.00458
+Rivinius T, Carciofi AC, Martayan C (2013) Clas-
+sical Be stars. Rapidly rotating B stars with vis-
+cous Keplerian decretion disks. A&ARv21:69, DOI
+10.1007/s00159-013-0069-0, 1310.3962
+Romanova MM, Ustyugova GV, Koldoba AV, Lovelace
+RVE (2012) MRI-driven accretion on to magnetized
+stars: global 3D MHD simulations of magnetospheric
+and boundary layer regimes. MNRAS421(1):63–77,
+DOI 10.1111/j.1365-2966.2011.20055.x, 1111.3068
+Rosenfeld KA, Andrews SM, Hughes AM, Wilner DJ,
+Qi C (2013) A Spatially Resolved Vertical Tempera-
+ture Gradient in the HD 163296 Disk. ApJ774(1):16,
+DOI 10.1088/0004-637X/774/1/16, 1306.6475
+Sacco GG, Flaccomio E, Pascucci I, Lahuis F, Ercolano
+B, Kastner JH, Micela G, Stelzer B, Sterzik M (2012)
+High-resolution Spectroscopy of Ne II Emission from
+Young Stellar Objects. ApJ747(2):142, DOI 10.1088/
+0004-637X/747/2/142, 1201.0184
+
+78
+Sean D. Brittain et al.
+Salyk C, Blake GA, Boogert ACA, Brown JM (2009)
+High-resolution 5 µm Spectroscopy of Transitional
+Disks. ApJ699:330–347, DOI 10.1088/0004-637X/
+699/1/330
+Salyk C, Pontoppidan KM, Blake GA, Najita JR, Carr
+JS (2011) A Spitzer Survey of Mid-infrared Molec-
+ular Emission from Protoplanetary Disks. II. Cor-
+relations and Local Thermal Equilibrium Models.
+ApJ731(2):130, DOI 10.1088/0004-637X/731/2/130,
+1104.0948
+Schaefer GH, Dutrey A, Guilloteau S, Simon M, White
+RJ (2009) A Millimeter-wave Interferometric Study
+of Dust and CO Disks Around Late Spectral Type
+Stars in Taurus-Auriga. ApJ701(1):698–709, DOI 10.
+1088/0004-637X/701/1/698
+Sch¨oller M, Pogodin MA, Cahuasqu´ı JA, Drake NA,
+Hubrig S, Petr-Gotzens MG, Savanov IS, Wolff B,
+Gonz´alez JF, Mysore S, Ilyin I, J¨arvinen SP, Stelzer
+B (2016) Spectroscopic signatures of magnetospheric
+accretion in Herbig Ae/Be stars. I. The case of
+HD 101412. A&A592:A50, DOI 10.1051/0004-6361/
+201628361, 1606.03817
+Segura-Cox DM, Schmiedeke A, Pineda JE, Stephens
+IW, Fern´andez-L´opez M, Looney LW, Caselli P, Li
+ZY, Mundy LG, Kwon W, Harris RJ (2020) Four
+annular structures in a protostellar disk less than
+500,000 years old. Nature586(7828):228–231, DOI
+10.1038/s41586-020-2779-6, 2010.03657
+Simon M, Dutrey A, Guilloteau S (2000) Dynamical
+Masses of T Tauri Stars and Calibration of Pre-Main-
+Sequence Evolution. ApJ545(2):1034–1043, DOI 10.
+1086/317838, astro-ph/0008370
+Simon M, Guilloteau S, Di Folco E, Dutrey A, Grosso
+N, Pi´etu V, Chapillon E, Prato L, Schaefer GH, Rice
+E, Boehler Y (2017) Dynamical Masses of Low-mass
+Stars in the Taurus and Ophiuchus Star-forming
+Regions. ApJ844(2):158, DOI 10.3847/1538-4357/
+aa78f1, 1706.03505
+Spiegel DS, Burrows A (2012) Spectral and Photo-
+metric Diagnostics of Giant Planet Formation Sce-
+narios. ApJ745:174, DOI 10.1088/0004-637X/745/2/
+174, 1108.5172
+Stapper LM, Hogerheijde MR, van Dishoeck EF,
+Mentel R (2022) The mass and size of Herbig disks
+as seen by ALMA. A&A658:A112, DOI 10.1051/
+0004-6361/202142164, 2112.03297
+Steindl
+T,
+Zwintz
+K,
+Barnes
+TG,
+M¨ullner
+M,
+Vorobyov EI (2021) Pulsational instability of pre-
+main-sequence models from accreting protostars.
+I. Constraining the input physics for accretion
+with spectroscopic parameters and stellar pulsations.
+A&A654:A36, DOI 10.1051/0004-6361/202140818,
+2107.07568
+Stelzer B, Micela G, Hamaguchi K, Schmitt JHMM
+(2006) On the origin of the X-ray emission from Her-
+big Ae/Be stars. A&A457(1):223–235, DOI 10.1051/
+0004-6361:20065006, astro-ph/0605590
+Stelzer
+B,
+Robrade
+J,
+Schmitt
+JHMM,
+Bou-
+vier
+J
+(2009)
+New
+X-ray
+detections
+of
+Herbig
+stars.
+A&A493(3):1109–1119,
+DOI
+10.1051/0004-6361:200810540, 0810.1836
+Stolker T, Dominik C, Avenhaus H, Min M, de Boer
+J, Ginski C, Schmid HM, Juhasz A, Bazzon A, Wa-
+ters LBFM, Garufi A, Augereau JC, Benisty M, Boc-
+caletti A, Henning T, Langlois M, Maire AL, M´enard
+F, Meyer MR, Pinte C, Quanz SP, Thalmann C,
+Beuzit JL, Carbillet M, Costille A, Dohlen K, Feldt
+M, Gisler D, Mouillet D, Pavlov A, Perret D, Petit C,
+Pragt J, Rochat S, Roelfsema R, Salasnich B, Soenke
+C, Wildi F (2016) Shadows cast on the transition disk
+of HD 135344B. Multiwavelength VLT/SPHERE po-
+larimetric differential imaging. A&A595:A113, DOI
+10.1051/0004-6361/201528039, 1603.00481
+St¨orzer H, Hollenbach D (2000) Optical Line Emission
+from Photodissociation Regions. ApJ539(2):751–759,
+DOI 10.1086/309251
+Strom KM, Strom SE, Edwards S, Cabrit S, Skrut-
+skie MF (1989) Circumstellar Material Associated
+with Solar-Type Pre-Main-Sequence Stars: A Possi-
+ble Constraint on the Timescale for Planet Building.
+AJ97:1451, DOI 10.1086/115085
+Strom SE (1972) Optical and Infrared Observations
+of Young Stellar Objects - an Informal Review.
+PASP84(502):745, DOI 10.1086/129375
+Strom SE, Strom KM, Yost J, Carrasco L, Grasdalen G
+(1972) The Nature of the Herbig Ae- and Be-TYPE
+Stars Associated with Nebulosity. ApJ173:353, DOI
+10.1086/151425
+Sturm B, Bouwman J, Henning T, Evans NJ, Acke
+B, Mulders GD, Waters LBFM, van Dishoeck EF,
+Meeus G, Green JD, Augereau JC, Olofsson J, Salyk
+C, Najita J, Herczeg GJ, van Kempen TA, Kris-
+tensen LE, Dominik C, Carr JS, Waelkens C, Bergin
+E, Blake GA, Brown JM, Chen JH, Cieza L, Dunham
+MM, Glassgold A, G¨udel M, Harvey PM, Hogerhei-
+jde MR, Jaffe D, Jørgensen JK, Kim HJ, Knez C,
+Lacy JH, Lee JE, Maret S, Meijerink R, Mer´ın B,
+Mundy L, Pontoppidan KM, Visser R, Yıldız UA
+(2010) First results of the Herschel key program
+“Dust, Ice and Gas In Time” (DIGIT): Dust and
+gas spectroscopy of HD 100546. A&A518:L129, DOI
+10.1051/0004-6361/201014674, 1005.3472
+Sturm B, Bouwman J, Henning T, Evans NJ, Wa-
+ters LBFM, van Dishoeck EF, Green JD, Olofsson
+J, Meeus G, Maaskant K, Dominik C, Augereau JC,
+Mulders GD, Acke B, Merin B, Herczeg GJ (2013)
+
+Herbig Stars
+79
+The 69 µm forsterite band in spectra of protoplan-
+etary disks. Results from the Herschel DIGIT pro-
+gramme. Astronomy & Astrophysics 553:5
+Szul´agyi J (2017) Effects of the Planetary Tempera-
+ture on the Circumplanetary Disk and on the Gap.
+ApJ842:103, DOI 10.3847/1538-4357/aa7515, 1705.
+08444
+Szul´agyi J, Morbidelli A, Crida A, Masset F (2014)
+Accretion of Jupiter-mass Planets in the Limit
+of Vanishing Viscosity. ApJ782:65, DOI 10.1088/
+0004-637X/782/2/65, 1312.6302
+Szul´agyi J, Masset F, Lega E, Crida A, Morbidelli A,
+Guillot T (2016) Circumplanetary disc or circum-
+planetary envelope? MNRAS460:2853–2861, DOI
+10.1093/mnras/stw1160, 1605.04586
+Szul´agyi J, Mayer L, Quinn T (2017) Circumplan-
+etary discs around young giant planets: a com-
+parison between core-accretion and disc instabil-
+ity. MNRAS464(3):3158–3168, DOI 10.1093/mnras/
+stw2617, 1610.01791
+Szul´agyi J, Dullemond CP, Pohl A, Quanz SP (2019)
+Observability of forming planets and their cir-
+cumplanetary discs II. - SEDs and near-infrared
+fluxes.
+MNRAS487(1):1248–1258,
+DOI
+10.1093/
+mnras/stz1326, 1905.03563
+Tambovtseva LV, Grinin VP, Weigelt G (2016) Brack-
+ett γ radiation from the inner gaseous accretion
+disk, magnetosphere, and disk wind region of Herbig
+AeBe stars. A&A590:A97, DOI 10.1051/0004-6361/
+201628256
+Tamura M (2009) Subaru Strategic Exploration of Ex-
+oplanets and Disks with HiCIAO/AO188 (SEEDS).
+In: Usuda T, Tamura M, Ishii M (eds) Exoplanets
+and Disks: Their Formation and Diversity, American
+Institute of Physics Conference Series, vol 1158, pp
+11–16, DOI 10.1063/1.3215811
+Tang J, Bressan A, Rosenfield P, Slemer A, Marigo
+P, Girardi L, Bianchi L (2014) New PARSEC evo-
+lutionary tracks of massive stars at low metallic-
+ity: testing canonical stellar evolution in nearby star-
+forming dwarf galaxies. MNRAS445:4287–4305, DOI
+10.1093/mnras/stu2029, 1410.1745
+Tang YW, Guilloteau S, Dutrey A, Muto T, Shen BT,
+Gu PG, Inutsuka Si, Momose M, Pietu V, Fuka-
+gawa M, Chapillon E, Ho PTP, di Folco E, Corder
+S, Ohashi N, Hashimoto J (2017) Planet Formation
+in AB Aurigae: Imaging of the Inner Gaseous Spi-
+rals Observed inside the Dust Cavity. ApJ840(1):32,
+DOI 10.3847/1538-4357/aa6af7, 1704.02699
+Tanigawa T, Ohtsuki K, Machida MN (2012) Dis-
+tribution of Accreting Gas and Angular Momen-
+tum onto Circumplanetary Disks. ApJ747:47, DOI
+10.1088/0004-637X/747/1/47, 1112.3706
+Tazaki
+R,
+Tanaka
+H,
+Muto
+T,
+Kataoka
+A,
+Okuzumi
+S
+(2019)
+Effect
+of
+dust
+size
+and
+structure
+on
+scattered-light
+images
+of
+proto-
+planetary discs. MNRAS485(4):4951–4966, DOI
+10.1093/mnras/stz662, 1903.01890
+Teague R, Bae J, Bergin EA, Birnstiel T, Foreman-
+Mackey
+D
+(2018)
+A
+Kinematical
+Detection
+of
+Two
+Embedded
+Jupiter-mass
+Planets
+in
+HD
+163296. ApJ860(1):L12, DOI 10.3847/2041-8213/
+aac6d7, 1805.10290
+Teague R, Bae J, Aikawa Y, Andrews SM, Bergin EA,
+Bergner JB, Boehler Y, Booth AS, Bosman AD,
+Cataldi G, Czekala I, Guzm´an VV, Huang J, Ilee
+JD, Law CJ, Le Gal R, Long F, Loomis RA, M´enard
+F, ¨Oberg KI, P´erez LM, Schwarz KR, Sierra A,
+Walsh C, Wilner DJ, Yamato Y, Zhang K (2021)
+Molecules with ALMA at Planet-forming Scales
+(MAPS). XVIII. Kinematic Substructures in the
+Disks of HD 163296 and MWC 480. ApJS257(1):18,
+DOI 10.3847/1538-4365/ac1438, 2109.06218
+Testi L, Palla F, Natta A (1999) The onset of cluster
+formation around Herbig Ae/Be stars. A&A342:515–
+523, astro-ph/9811210
+Testi L, Birnstiel T, Ricci L, Andrews S, Blum
+J, Carpenter J, Dominik C, Isella A, Natta A,
+Williams JP, Wilner DJ (2014) Dust Evolution
+in Protoplanetary Disks. In: Beuther H, Klessen
+RS, Dullemond CP, Henning T (eds) Protostars
+and Planets VI, p 339, DOI 10.2458/azu uapress
+9780816531240-ch015, 1402.1354
+Th´e PS, de Winter D, Perez MR (1994a) A new cata-
+logue of members and candidate members of the Her-
+big Ae/Be (HAEBE) stellar group. A&AS104:315–
+339
+Th´e PS, Perez MR, J vEP (eds) (1994b) The nature
+and evolutionary status of Herbig Ae/Be stars, As-
+tronomical Society of the Pacific Conference Series,
+vol 62
+Thi WF (2014) TBD. A&A510(26):A260000+, DOI
+10.1051/0004-6361/200913076, 0911.1949
+Thi WF, van Dishoeck EF, Blake GA, van Zadel-
+hoff GJ, Horn J, Becklin EE, Mannings V, Sar-
+gent AI, van den Ancker ME, Natta A, Kessler J
+(2001) H2 and CO Emission from Disks around T
+Tauri and Herbig Ae Pre-Main-Sequence Stars and
+from Debris Disks around Young Stars: Warm and
+Cold Circumstellar Gas. ApJ561(2):1074–1094, DOI
+10.1086/323361, astro-ph/0107006
+Thi WF, van Zadelhoff GJ, van Dishoeck EF (2004)
+Organic molecules in protoplanetary disks around T
+Tauri and Herbig Ae stars. A&A425:955–972, DOI
+10.1051/0004-6361:200400026, astro-ph/0406577
+
+80
+Sean D. Brittain et al.
+Trapman L, Facchini S, Hogerheijde MR, van Dishoeck
+EF,
+Bruderer
+S
+(2019)
+Gas
+versus
+dust
+sizes
+of protoplanetary discs: effects of dust evolution.
+A&A629:A79, DOI 10.1051/0004-6361/201834723,
+1903.06190
+Tsukamoto Y, Okuzumi S, Kataoka A (2017) Appar-
+ent Disk-mass Reduction and Planetisimal Forma-
+tion in Gravitationally Unstable Disks in Class 0/I
+Young Stellar Objects. ApJ838(2):151, DOI 10.3847/
+1538-4357/aa6081, 1608.03015
+Tuthill PG, Monnier JD, Danchi WC (2001) A dusty
+torus around the luminous young star LkHα101.
+Nature409(6823):1012–1014, DOI 10.1038/35059014,
+astro-ph/0102240
+Tylenda R (1977) The continuous radiation emitted
+by accretion discs in cataclysmic binaries: the dwarf
+nova SS Cyg during outburst and the old novae V603
+Aql and RR Pic. Acta Astron.27:235–249
+Valeg˚ard PG, Waters LBFM, Dominik C (2021) What
+happened before?. Disks around the precursors of
+young Herbig Ae/Be stars. A&A652:A133, DOI
+10.1051/0004-6361/202039802, 2104.14212
+van Boekel R, Waters LBFM, Dominik C, Bouwman J,
+de Koter A, Dullemond CP, Paresce F (2003) Grain
+growth in the inner regions of Herbig Ae/Be star
+disks. A&A400:L21–L24, DOI 10.1051/0004-6361:
+20030141
+van Boekel R, Min M, Leinert C, Waters LBFM,
+Richichi A, Chesneau O, Dominik C, Jaffe W, Dutrey
+A, Graser U, Henning T, de Jong J, K¨ohler R, de
+Koter A, Lopez B, Malbet F, Morel S, Paresce F,
+Perrin G, Preibisch T, Przygodda F, Sch¨oller M,
+Wittkowski M (2004) The building blocks of planets
+within the ‘terrestrial’ region of protoplanetary disks.
+Nature432(7016):479–482, DOI 10.1038/nature03088
+van Boekel R, Min M, Waters LBFM, de Koter A, Do-
+minik C, van den Ancker ME, Bouwman J (2005) A
+10 µm spectroscopic survey of Herbig Ae star disks:
+Grain growth and crystallization. A&A437(1):189–
+208, DOI 10.1051/0004-6361:20042339, astro-ph/
+0503507
+van Boekel R, ´Abrah´am P, Correia S, de Koter A, Do-
+minik C, Dutrey A, Henning T, K´osp´al ´A, Lachaume
+R, Leinert C, Linz H, Min M, Mosoni L, Preibisch
+T, Quanz S, Ratzka T, Schegerer A, Waters R,
+Wolf S, Zinnecker H (2006) Disks around young
+stars with VLTI/MIDI. In: Monnier JD, Sch¨oller
+M, Danchi WC (eds) Society of Photo-Optical In-
+strumentation Engineers (SPIE) Conference Series,
+Society of Photo-Optical Instrumentation Engineers
+(SPIE) Conference Series, vol 6268, p 62680D, DOI
+10.1117/12.673777, astro-ph/0607387
+van der Marel N, Mulders GD (2021) A Stellar Mass
+Dependence of Structured Disks: A Possible Link
+with Exoplanet Demographics. AJ162(1):28, DOI
+10.3847/1538-3881/ac0255, 2104.06838
+van der Marel N, Verhaar BW, van Terwisga S, Mer´ın
+B, Herczeg G, Ligterink NFW, van Dishoeck EF
+(2016) The (w)hole survey: An unbiased sample
+study of transition disk candidates based on Spitzer
+catalogs. A&A592:A126, DOI 10.1051/0004-6361/
+201628075, 1603.07255
+van der Marel N, Williams JP, Bruderer S (2018)
+Rings and Gaps in Protoplanetary Disks: Planets or
+Snowlines? ApJ867(1):L14, DOI 10.3847/2041-8213/
+aae88e, 1810.05614
+van der Marel N, Birnstiel T, Garufi A, Ragusa E,
+Christiaens V, Price DJ, Sallum S, Muley D, Francis
+L, Dong R (2021) On the Diversity of Asymmetries
+in Gapped Protoplanetary Disks. AJ161(1):33, DOI
+10.3847/1538-3881/abc3ba, 2010.10568
+van der Plas G, van den Ancker ME, Fedele D, Acke B,
+Dominik C, Waters LBFM, Bouwman J (2008) The
+structure of protoplanetary disks surrounding three
+young intermediate mass stars. I. Resolving the disk
+rotation in the [OI] 6300 ˚A line. A&A485(2):487–495,
+DOI 10.1051/0004-6361:20078867, 0802.0707
+van der Plas G, van den Ancker ME, Acke B, Carmona
+A, Dominik C, Fedele D, Waters LBFM (2009) Evi-
+dence for CO depletion in the inner regions of gas-rich
+protoplanetary disks. A&A500(3):1137–1141, DOI
+10.1051/0004-6361/200811148, 0810.3417
+van der Plas G, Casassus S, M´enard F, Perez S, Thi
+WF, Pinte C, Christiaens V (2014) Spatially Re-
+solved HCN J = 4-3 and CS J = 7-6 Emission from
+the Disk around HD 142527. ApJ792(2):L25, DOI
+10.1088/2041-8205/792/2/L25, 1407.1735
+van der Plas G, van den Ancker ME, Waters LBFM,
+Dominik C (2015) The structure of disks around
+Herbig Ae/Be stars as traced by CO ro-vibrational
+emission. A&A574:A75, DOI 10.1051/0004-6361/
+201425052, 1412.1311
+van der Plas G, M´enard F, Canovas H, Avenhaus H,
+Casassus S, Pinte C, Caceres C, Cieza L (2017a)
+An 80 au cavity in the disk around HD 34282.
+A&A607:A55, DOI 10.1051/0004-6361/201731392,
+1707.01688
+van der Plas G, Wright CM, M´enard F, Casassus S,
+Canovas H, Pinte C, Maddison ST, Maaskant K,
+Avenhaus H, Cieza L, Perez S, Ubach C (2017b) Cav-
+ity and other radial substructures in the disk around
+HD 97048. A&A597:A32, DOI 10.1051/0004-6361/
+201629523, 1609.02488
+van der Plas G, M´enard F, Gonzalez JF, Perez S,
+Rodet L, Pinte C, Cieza L, Casassus S, Benisty
+
+Herbig Stars
+81
+M (2019) ALMA study of the HD 100453 AB sys-
+tem and the tidal interaction of the companion with
+the disk. A&A624:A33, DOI 10.1051/0004-6361/
+201834134, 1902.00720
+van der Wiel MHD, Naylor DA, Kamp I, M´enard
+F, Thi WF, Woitke P, Olofsson G, Pontoppidan
+KM, Di Francesco J, Glauser AM, Greaves JS, Ivi-
+son RJ (2014) Signatures of warm carbon monox-
+ide in protoplanetary discs observed with Her-
+schel SPIRE. MNRAS444(4):3911–3925, DOI 10.
+1093/mnras/stu1462, 1408.5432
+van Dishoeck EF, Kristensen LE, Mottram JC, Benz
+AO, Bergin EA, Caselli P, Herpin F, Hogerheijde
+MR, Johnstone D, Liseau R, Nisini B, Tafalla M,
+van der Tak FFS, Wyrowski F, Baudry A, Benedet-
+tini M, Bjerkeli P, Blake GA, Braine J, Bruderer
+S, Cabrit S, Cernicharo J, Choi Y, Coutens A, de
+Graauw T, Dominik C, Fedele D, Fich M, Fuente A,
+Furuya K, Goicoechea JR, Harsono D, Helmich FP,
+Herczeg GJ, Jacq T, Karska A, Kaufman M, Keto
+E, Lamberts T, Larsson B, Leurini S, Lis DC, Mel-
+nick G, Neufeld D, Pagani L, Persson M, Shipman R,
+Taquet V, van Kempen TA, Walsh C, Wampfler SF,
+Yıldız U, WISH Team (2021) Water in star-forming
+regions: physics and chemistry from clouds to disks
+as probed by Herschel spectroscopy. A&A648:A24,
+DOI 10.1051/0004-6361/202039084, 2102.02225
+van ’t Hoff MLR, Walsh C, Kama M, Facchini S, van
+Dishoeck EF (2017) Robustness of N2H+ as tracer
+of the CO snowline. A&A599:A101, DOI 10.1051/
+0004-6361/201629452, 1610.06788
+van Zadelhoff GJ, Aikawa Y, Hogerheijde MR, van
+Dishoeck EF (2003) Axi-symmetric models of ul-
+traviolet radiative transfer with applications to cir-
+cumstellar disk chemistry. A&A397:789–802, DOI
+10.1051/0004-6361:20021592, astro-ph/0211014
+Varga J, ´Abrah´am P, Chen L, Ratzka T, Gab´anyi
+K´E, K´osp´al ´A, Matter A, van Boekel R, Henning
+T, Jaffe W, Juh´asz A, Lopez B, Menu J, Mo´or
+A, Mosoni L, Sipos N (2018) VLTI/MIDI atlas of
+disks around low- and intermediate-mass young stel-
+lar objects. A&A617:A83, DOI 10.1051/0004-6361/
+201832599, 1805.02939
+Varga J, Hogerheijde M, van Boekel R, Klarmann L,
+Petrov R, Waters LBFM, Lagarde S, Pantin E, Be-
+rio P, Weigelt G, Robbe-Dubois S, Lopez B, Mil-
+lour F, Augereau JC, Meheut H, Meilland A, Hen-
+ning T, Jaffe W, Bettonvil F, Bristow P, Hofmann
+KH, Matter A, Zins G, Wolf S, Allouche F, Donnan
+F, Schertl D, Dominik C, Heininger M, Lehmitz M,
+Cruzal`ebes P, Glindemann A, Meisenheimer K, Pal-
+adini C, Sch¨oller M, Woillez J, Venema L, Kokoulina
+E, Yoffe G, ´Abrah´am P, Abadie S, Abuter R, Ac-
+cardo M, Adler T, Ag´ocs T, Antonelli P, B¨ohm A,
+Bailet C, Bazin G, Beckmann U, Beltran J, Boland
+W, Bourget P, Brast R, Bresson Y, Burtscher L,
+Castillo R, Chelli A, Cid C, Clausse JM, Connot C,
+Conzelmann RD, Danchi WC, De Haan M, Delbo
+M, Ebert M, Elswijk E, Fantei Y, Frahm R, G´amez
+Rosas V, Gabasch A, Gallenne A, Garces E, Girard
+P, Gont´e FYJ, Gonz´alez Herrera JC, Graser U, Gua-
+jardo P, Guitton F, Haubois X, Hron J, Hubin N,
+Huerta R, Isbell JW, Ives D, Jakob G, Jask´o A,
+Jochum L, Klein R, Kragt J, Kroes G, Kuindersma
+S, Labadie L, Laun W, Le Poole R, Leinert C, Li-
+zon JL, Lopez M, M´erand A, Marcotto A, Mauclert
+N, Maurer T, Mehrgan LH, Meisner J, Meixner K,
+Mellein M, Mohr L, Morel S, Mosoni L, Navarro R,
+Neumann U, Nußbaum E, Pallanca L, Pasquini L,
+Percheron I, Pott JU, Pozna E, Ridinger A, Rigal F,
+Riquelme M, Rivinius T, Roelfsema R, Rohloff RR,
+Rousseau S, Schuhler N, Schuil M, Soulain A, Stee
+P, Stephan C, ter Horst R, Tromp N, Vakili F, van
+Duin A, Vinther J, Wittkowski M, Wrhel F (2021)
+The asymmetric inner disk of the Herbig Ae star
+HD 163296 in the eyes of VLTI/MATISSE: evidence
+for a vortex? A&A647:A56, DOI 10.1051/0004-6361/
+202039400, 2012.05697
+Verhoeff AP, Waters LBFM, van den Ancker ME, Min
+M, Stap FA, Pantin E, van Boekel R, Acke B, Tie-
+lens AGGM, de Koter A (2012) A mid-IR study of
+the circumstellar environment of Herbig Be stars.
+A&A538:A101, DOI 10.1051/0004-6361/201014916
+Vieira SLA, Corradi WJB, Alencar SHP, Mendes LTS,
+Torres CAO, Quast GR, Guimar˜aes MM, da Silva L
+(2003) Investigation of 131 Herbig Ae/Be Candidate
+Stars. AJ126(6):2971–2987, DOI 10.1086/379553
+Villebrun F, Alecian E, Hussain G, Bouvier J, Folsom
+CP, Lebreton Y, Amard L, Charbonnel C, Gallet F,
+Haemmerl´e L, B¨ohm T, Johns-Krull C, Kochukhov
+O, Marsden SC, Morin J, Petit P (2019) Magnetic
+fields of intermediate-mass T Tauri stars. I. Mag-
+netic detections and fundamental stellar parameters.
+A&A622:A72, DOI 10.1051/0004-6361/201833545
+Vink JS (2015) Linear line spectropolarimetry of Her-
+big Ae/Be stars. Ap&SS357(2):98, DOI 10.1007/
+s10509-015-2323-6, 1501.07436
+Vink
+JS,
+Drew
+JE,
+Harries
+TJ,
+Oudmaijer
+RD
+(2002) Probing the circumstellar structure of Her-
+big Ae/Be stars. MNRAS337:356–368, DOI 10.1046/
+j.1365-8711.2002.05920.x, astro-ph/0208137
+Vink JS, Drew JE, Harries TJ, Oudmaijer RD, Un-
+ruh Y (2005a) Probing the circumstellar structures
+of T Tauri stars and their relationship to those of
+Herbig stars. MNRAS359:1049–1064, DOI 10.1111/
+j.1365-2966.2005.08969.x, astro-ph/0502535
+
+82
+Sean D. Brittain et al.
+Vink
+JS,
+Harries
+TJ,
+Drew
+JE
+(2005b)
+Polari-
+metric
+line
+profiles
+for
+scattering
+off
+rotating
+disks. A&A430:213–222, DOI 10.1051/0004-6361:
+20041463, astro-ph/0409512
+Vioque M, Oudmaijer RD, Baines D, Mendigut´ıa
+I, P´erez-Mart´ınez R (2018) Gaia DR2 study of
+Herbig Ae/Be stars. A&A620:A128, DOI 10.1051/
+0004-6361/201832870, 1808.00476
+Vioque M, Oudmaijer RD, Schreiner M, Mendigut´ıa
+I, Baines D, Mowlavi N, P´erez-Mart´ınez R (2020)
+Catalogue of new Herbig Ae/Be and classical Be
+stars. A machine learning approach to Gaia DR2.
+A&A638:A21, DOI 10.1051/0004-6361/202037731,
+2005.01727
+Wagner K, Apai D, Kasper M, Robberto M (2015)
+Discovery of a Two-armed Spiral Structure in the
+Gapped Disk around Herbig Ae Star HD 100453.
+ApJ813(1):L2,
+DOI
+10.1088/2041-8205/813/1/L2,
+1510.02212
+Wagner K, Follete KB, Close LM, Apai D, Gibbs A,
+Keppler M, M¨uller A, Henning T, Kasper M, Wu
+YL, Long J, Males J, Morzinski K, McClure M (2018)
+Magellan Adaptive Optics Imaging of PDS 70: Mea-
+suring the Mass Accretion Rate of a Young Giant
+Planet within a Gapped Disk. ApJ863:L8, DOI
+10.3847/2041-8213/aad695, 1807.10766
+Wagner K, Stone JM, Spalding E, Apai D, Dong
+R, Ertel S, Leisenring J, Webster R (2019) Ther-
+mal
+Infrared
+Imaging
+of
+MWC
+758
+with
+the
+Large Binocular Telescope: Planetary-driven Spi-
+ral Arms? ApJ882(1):20, DOI 10.3847/1538-4357/
+ab32ea, 1907.06655
+Wahhaj Z, Koerner DW, Sargent AI (2007) High-
+Resolution
+Imaging
+of
+the
+Dust
+Disk
+around
+49 Ceti. ApJ661(1):368–373, DOI 10.1086/512716,
+astro-ph/0701352
+Walsh C, Nomura H, van Dishoeck E (2015) The molec-
+ular composition of the planet-forming regions of
+protoplanetary disks across the luminosity regime.
+A&A582:A88, DOI 10.1051/0004-6361/201526751,
+1507.08544
+Walsh C, Juh´asz A, Meeus G, Dent WRF, Maud LT,
+Aikawa Y, Millar TJ, Nomura H (2016) ALMA Re-
+veals the Anatomy of the mm-sized Dust and Molec-
+ular Gas in the HD 97048 Disk. ApJ831(2):200, DOI
+10.3847/0004-637X/831/2/200, 1609.02011
+Walsh C, Daley C, Facchini S, Juh´asz A (2017)
+CO emission tracing a warp or radial flow within
+≲100 au in the HD 100546 protoplanetary disk.
+A&A607:A114, DOI 10.1051/0004-6361/201731334,
+1710.00703
+Walter FM (1986) X-Ray Sources in Regions of Star
+Formation. I. The Naked T Tauri Stars. ApJ306:573,
+DOI 10.1086/164367
+Watanabe N, Kouchi A (2002) Efficient Formation
+of Formaldehyde and Methanol by the Addition of
+Hydrogen Atoms to CO in H2O-CO Ice at 10 K.
+ApJ571(2):L173–L176, DOI 10.1086/341412
+Waters LBFM, Waelkens C (1998a) Herbig Ae/Be
+Stars. ARA&A36:233–266, DOI 10.1146/annurev.
+astro.36.1.233
+Waters LBFM, Waelkens C (1998b) Herbig Ae/Be
+Stars. ARA&A36:233–266, DOI 10.1146/annurev.
+astro.36.1.233
+Waters LBFM, Trams NR, Waelkens C (1992) A sce-
+nario for the selective depletion of stellar atmo-
+spheres. A&A262:L37
+Weidenschilling SJ (1977) Aerodynamics of solid bodies
+in the solar nebula. MNRAS180:57–70, DOI 10.1093/
+mnras/180.1.57
+Weinberger AJ, Becklin EE, Schneider G, Smith BA,
+Lowrance PJ, Silverstone MD, Zuckerman B, Terrile
+RJ (1999) The Circumstellar Disk of HD 141569 Im-
+aged with NICMOS. ApJ525:L53–L56, DOI 10.1086/
+312334, astro-ph/9909097
+Wheelwright HE, Oudmaijer RD, Goodwin SP (2010)
+The mass ratio and formation mechanisms of Herbig
+Ae/Be star binary systems. MNRAS401:1199–1218,
+DOI 10.1111/j.1365-2966.2009.15708.x, 0910.1774
+Wheelwright HE, Vink JS, Oudmaijer RD, Drew JE
+(2011) On the alignment between the circumstel-
+lar disks and orbital planes of Herbig Ae/Be binary
+systems.
+A&A532:A28,
+DOI
+10.1051/0004-6361/
+201116996, 1106.3949
+White JA, Boley AC (2018) Extended Millimeter
+Emission in the HD 141569 Circumstellar Disk De-
+tected with ALMA. ApJ859(2):103, DOI 10.3847/
+1538-4357/aac088, 1804.09724
+White RJ, Basri G (2003) Very Low Mass Stars and
+Brown Dwarfs in Taurus-Auriga. ApJ582(2):1109–
+1122, DOI 10.1086/344673, astro-ph/0209164
+Wichittanakom
+C,
+Oudmaijer
+RD,
+Fairlamb
+JR,
+Mendigut´ıa I, Vioque M, Ababakr KM (2020) The
+accretion rates and mechanisms of Herbig Ae/Be
+stars. MNRAS493(1):234–249, DOI 10.1093/mnras/
+staa169, 2001.05971
+Williams JP, Best WMJ (2014) A Parametric Modeling
+Approach to Measuring the Gas Masses of Circum-
+stellar Disks. ApJ788:59, DOI 10.1088/0004-637X/
+788/1/59, 1312.0151
+Williams JP, Cieza LA (2011) Protoplanetary Disks
+and Their Evolution. ARA&A49(1):67–117, DOI
+10.1146/annurev-astro-081710-102548, 1103.0556
+Windmark F, Birnstiel T, G¨uttler C, Blum J, Dulle-
+mond CP, Henning T (2012) Planetesimal forma-
+tion by sweep-up: how the bouncing barrier can be
+
+Herbig Stars
+83
+beneficial to growth. A&A540:A73, DOI 10.1051/
+0004-6361/201118475, 1201.4282
+Woitke P, Kamp I, Thi WF (2009) Radiation thermo-
+chemical models of protoplanetary disks. I. Hydro-
+static disk structure and inner rim. A&A501:383–406,
+DOI 10.1051/0004-6361/200911821, 0904.0334
+Woitke P, Pinte C, Tilling I, M´enard F, Kamp I,
+Thi WF, Duchˆene G, Augereau JC (2010) Contin-
+uum and line modelling of discs around young stars
+- I. 300000 disc models for HERSCHEL/GASPS.
+MNRAS405(1):L26–L30, DOI 10.1111/j.1745-3933.
+2010.00852.x, 1003.2323
+Woitke P, Kamp I, Antonellini S, Anthonioz F,
+Baldovin-Saveedra C, Carmona A, Dionatos O, Do-
+minik C, Greaves J, G¨udel M, Ilee JD, Liebhardt
+A, Menard F, Min M, Pinte C, Rab C, Rigon L,
+Thi WF, Thureau N, Waters LBFM (2019a) Con-
+sistent Dust and Gas Models for Protoplanetary
+Disks. III. Models for Selected Objects from the
+FP7 DIANA Project. PASP131(1000):064301, DOI
+10.1088/1538-3873/aaf4e5, 1812.02741
+Woitke P, Kamp I, Antonellini S, Anthonioz F,
+Baldovin-Saveedra C, Carmona A, Dionatos O, Do-
+minik C, Greaves J, G¨udel M, Ilee JD, Liebhardt
+A, Menard F, Min M, Pinte C, Rab C, Rigon L,
+Thi WF, Thureau N, Waters LBFM (2019b) Con-
+sistent Dust and Gas Models for Protoplanetary
+Disks. III. Models for Selected Objects from the
+FP7 DIANA Project. PASP131(1000):064301, DOI
+10.1088/1538-3873/aaf4e5, 1812.02741
+Wolfire MG, Cassinelli JP (1987) Conditions for the
+Formation of Massive Stars. ApJ319:850, DOI 10.
+1086/165503
+Yorke HW, Sonnhalter C (2002) On the Formation
+of Massive Stars. ApJ569(2):846–862, DOI 10.1086/
+339264, astro-ph/0201041
+Zhang K, Blake GA, Bergin EA (2015) Evidence of
+Fast Pebble Growth Near Condensation Fronts in the
+HL Tau Protoplanetary Disk. ApJ806(1):L7, DOI
+10.1088/2041-8205/806/1/L7, 1505.00882
+Zhang K, Booth AS, Law CJ, Bosman AD, Schwarz
+KR, Bergin EA, ¨Oberg KI, Andrews SM, Guzm´an
+VV, Walsh C, Qi C, van’t Hoff MLR, Long F, Wilner
+DJ, Huang J, Czekala I, Ilee JD, Cataldi G, Bergner
+JB, Aikawa Y, Teague R, Bae J, Loomis RA, Calahan
+JK, Alarc´on F, M´enard F, Le Gal R, Sierra A, Yam-
+ato Y, Nomura H, Tsukagoshi T, P´erez LM, Trapman
+L, Liu Y, Furuya K (2021) Molecules with ALMA
+at Planet-forming Scales (MAPS). V. CO Gas Dis-
+tributions. ApJS257(1):5, DOI 10.3847/1538-4365/
+ac1580, 2109.06233
+Zhang
+S,
+Zhu
+Z,
+Huang
+J,
+Guzm´an
+VV,
+An-
+drews SM, Birnstiel T, Dullemond CP, Carpenter
+JM, Isella A, P´erez LM, Benisty M, Wilner DJ,
+Baruteau C, Bai XN, Ricci L (2018) The Disk
+Substructures at High Angular Resolution Project
+(DSHARP). VII. The Planet-Disk Interactions Inter-
+pretation. ApJ869(2):L47, DOI 10.3847/2041-8213/
+aaf744, 1812.04045
+Zhou Y, Sanghi A, Bowler BP, Wu YL, Close LM, Long
+F, Ward-Duong K, Zhu Z, Kraus AL, Follette KB,
+Bae J (2022) HST/WFC3 Hα Direct-imaging Detec-
+tion of a Pointlike Source in the Disk Cavity of AB
+Aur. ApJ934(1):L13, DOI 10.3847/2041-8213/ac7fef,
+2207.06525
+Zhu Z (2015) Accreting Circumplanetary Disks: Ob-
+servational Signatures. ApJ799(1):16, DOI 10.1088/
+0004-637X/799/1/16, 1408.6554
+Zhu Z, Stone JM (2014) Dust Trapping by Vortices
+in Transitional Disks: Evidence for Non-ideal Mag-
+netohydrodynamic Effects in Protoplanetary Disks.
+ApJ795(1):53,
+DOI
+10.1088/0004-637X/795/1/53,
+1405.2790
+Zhu Z, Nelson RP, Dong R, Espaillat C, Hartmann L
+(2012) Dust Filtration by Planet-induced Gap Edges:
+Implications for Transitional Disks. ApJ755(1):6,
+DOI 10.1088/0004-637X/755/1/6, 1205.5042
+Zinnecker H, Preibisch T (1994) X-ray emission from
+Herbig Ae/Be stars: a ROSAT survey. A&A292:152–
+164
+Zuckerman B, Forveille T, Kastner JH (1995) Inhibi-
+tion of giant-planet formation by rapid gas deple-
+tion around young stars. Nature373:494–496, DOI
+10.1038/373494a0
+Zurlo A, Cugno G, Montesinos M, Perez S, Canovas
+H, Casassus S, Christiaens V, Cieza L, Huelamo N
+(2020) The widest Hα survey of accreting protoplan-
+ets around nearby transition disks. A&A633:A119,
+DOI 10.1051/0004-6361/201936891, 1912.04911
+Zwintz
+K,
+Kallinger
+T,
+Guenther
+DB,
+Gruber-
+bauer M, Huber D, Rowe J, Kuschnig R, Weiss
+WW, Matthews JM, Moffat AFJ, Rucinski SM,
+Sasselov
+D,
+Walker
+GAH,
+Casey
+MP
+(2009)
+MOST photometry of the enigmatic PMS pulsator
+HD 142666. A&A494(3):1031–1040, DOI 10.1051/
+0004-6361:200811116, 0812.1960
+Zwintz K, Fossati L, Ryabchikova T, Guenther D,
+Aerts C, Barnes TG, Themeßl N, Lorenz D, Cameron
+C, Kuschnig R, Pollack-Drs S, Moravveji E, Baglin
+A, Matthews JM, Moffat AFJ, Poretti E, Rainer
+M, Rucinski SM, Sasselov D, Weiss WW (2014)
+Echography of young stars reveals their evolution.
+Science
+345(6196):550–553,
+DOI
+10.1126/science.
+1253645, 1407.4928
+
diff --git a/odAzT4oBgHgl3EQfOfsX/content/tmp_files/load_file.txt b/odAzT4oBgHgl3EQfOfsX/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8a22de685472fd592b84e9e067d95dfb8adb6699
--- /dev/null
+++ b/odAzT4oBgHgl3EQfOfsX/content/tmp_files/load_file.txt
@@ -0,0 +1,6443 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf,len=6442
+page_content='Noname manuscript No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  (will be inserted by the editor)  Herbig Stars  A Quarter Century of Progress  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain · Inga Kamp · Gwendolyn Meeus · Ren´e D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Oudmaijer · L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Waters  Received: date / Accepted: date  Abstract Herbig Ae/Be stars are young contracting  stars on the radiative track in the HR diagram on their  way to the Main Sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' These stars provide a valu-  able link between high and low mass stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Here we  review the progress that has been made in our under-  standing of these fascinating objects and their disks  since the last major review on this topic published in  1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' We begin with a general overview of these stars  and their properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' We then discuss the accretion of  circumstellar material onto these stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Next we dis-  cuss the dust and gas properties of the circumstellar  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain  Department of Physics and Astronomy, Clemson University,  Clemson, SC, 29634-0978, USA  Tel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' : +1-864-633-8265  E-mail: sbritt@clemson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='edu  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kamp  Kapteyn Astronomical Institute, University of Groningen,  Groningen, The Netherlands, Postal code  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Meeus  Dpto.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' F´ısica Te´orica, Universidad Aut´onoma de Madrid,  28049 Madrid, Spain  Centro de Investigaci´on Avanzada en F´ısica Fundamental  (CIAFF), Facultad de Ciencias, UAM, 28049 Madrid, Spain  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Oudmaijer  School of Physics and Astronomy, University of Leeds, Leeds,  LS2 9JT, UK  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Waters  Institute for Mathematics, Astrophysics & Particle Physics,  Department of Astrophysics, Radboud University, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Box  9010, NL-6500 GL Nijmegen, The Netherlands  SRON Netherlands Institute for Space Research, Sorbon-  nelaan 2, 3584, CA Utrecht, The Netherlands  disk before exploring the evidence for planet formation  in these disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' We conclude with a brief discussion of fu-  ture prospects for deepening our understanding of these  sources and propose a new working definition of Herbig  Ae/Be stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Keywords Herbig Ae/Be Stars · Star Formation ·  Stellar Accretion Disks · Circumstellar dust · Circum-  stellar gas · Protoplanetary Disks  1 INTRODUCTION  Understanding the formation and early evolution of stars  and planetary systems is one of the key questions in  astrophysics, closely linked to the origin of the solar  system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Stars form in dense molecular clouds in which  gravity overtakes gas pressure, resulting in the forma-  tion of a core.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Conservation of angular momentum causes  the formation of an accretion disk through which gas  and dust is transported to the accreting star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' When the  molecular cloud disperses (typically after 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5-1 Myrs)  the accretion slows down and a slower phase (typi-  cally 5-15 Myrs) of pre-main-sequence evolution ensues,  which ends when the star ignites hydrogen in its core  (see Palla and Stahler, 1993, Lada, 2005, McKee and  Ostriker, 2007, Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2014, for reviews).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Planet formation takes place in the (remnant) ac-  cretion disk;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' there is growing evidence that this pro-  cess begins very early when accretion onto the star is  still strong (ALMA Partnership et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2015, Segura-  Cox et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2020, Kenyon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2016, Tsukamoto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Most studies favor the core accretion growth  model for the formation of gas giant exoplanets, in  which dust in the disk settles to the mid-plane to form  large, millimeter to centimeter sized grains, planetesi-  mals, and a rocky core (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', Lissauer, 1993, Drazkowska  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='01165v1  [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='SR]  3 Jan 2023  2  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' When above a critical mass of 10-20 M⊕,  the rapid accretion of a H/He envelope follows (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pol-  lack et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Planet formation may also proceed via  gravitational instability in massive disks (Boss, 1997),  explaining the presence of very massive planets in wide  orbits found in some intermediate mass stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  This general scenario for star- and planet formation  is believed to hold for solar type stars (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3M⊙ ≲ M⋆ ≲  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5M⊙), and there is growing evidence that it also ap-  plies to lower mass stars and brown dwarfs (M⋆ ≲  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3M⊙;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Luhman, 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' For higher mass stars, this is  likely to break down for M⋆ ≳ 4−5M⊙ as disk lifetimes  grow too short.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Because the timescale for star formation  decreases rapidly with increasing mass, high mass stars  do not experience a visible pre-main-sequence phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Their much higher luminosity strongly affects the phys-  ical and chemical properties of the accretion disk (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  Gorti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Models suggest a rapid evapora-  tion of the outer disk and no reservoir of large dust  grains is able to form, inhibiting the formation of plan-  ets through core growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, planets may still  form around massive young stars through gravitational  instability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' So far, observations indicate there is no evi-  dence for close-in planets orbiting stars with mass above  4-5 M⊙, while campaigns for planets at larger separa-  tions are underway (Janson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The Herbig Ae/Be stars are intermediate mass ob-  jects and as such bridge the gap between the lower mass,  solar type stars (M⋆ ≲ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5 M⊙) and the most massive  stars (M⋆ ≳ 10′s M⊙).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They were first discussed as a  group in the seminal paper of Herbig (1960).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In this  paper, George Herbig sought to identify more massive  stars (aiming at 3-20 M⊙) by selecting a sample of 26  A and B stars with emission lines in the spectrum (in  particular Hα) that were associated with (reflection)  nebulosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' These stars have since been studied in great  detail and indeed many of them turned out to be inter-  mediate mass pre-main-sequence (PMS) stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In later  literature, intermediate mass PMS stars were given his  name Herbig Ae/Be stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In the context of star forma-  tion studies, these stars form the higher mass counter-  parts to the solar mass T Tau stars, named after the  prototype T Tau.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Herbig also immediately noted the  difficulty in disentangling these stars from other classes  of B and A stars with circumstellar matter, such as the  classical Be stars (Rivinius et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2013) and the B[e]  stars (Kraus, 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Herbig continued to work on these  objects throughout his career, as evidenced by his ex-  tensive bibliography.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Previous reviews dedicated to Herbig Ae/Be stars  can be found in the conference proceedings Th´e et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  (1994b), and in Perez and Grady (1997) and Waters  and Waelkens (1998a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In addition, there have been  numerous reviews on disks around young stars that  are relevant to Herbig Ae/Be stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Examples include  Dullemond and Monnier (2010), Williams and Cieza  (2011), Andrews (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' For recent reviews dedicated  to aspects of Herbig Ae/Be stars please see the Topical  Collection on Herbig Ae/Be stars published in 2015 in  Astrophysics and Space Science1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  In recent years a wealth of new observational and  theoretical studies have shed light on the nature and  evolutionary status of Herbig Ae/Be stars and their cir-  cumstellar environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' As we will summarize in this  review, Herbig Ae/Be stars are at an exciting cross-  roads between low- and high-mass star formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The  high stellar luminosity, disk mass, and often large disks  allow easier access to the relevant spatial scales to study  planet formation processes when compared to lower  mass objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Indeed, the gas and dust in their cir-  cumstellar disks has been spatially resolved with un-  precedented detail, revealing Keplerian disks that show  convincing evidence for the presence of forming plan-  ets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' As samples of known exoplanets rapidly increase,  we can begin to make the link between the diversity  of exoplanetary systems in intermediate mass stars and  their birth sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Herbig Ae/Be stars also mark the up-  per mass limit of stars with habitable zones in which life  on a planet could develop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The main sequence lifetime  of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5M⊙ stars is ∼600Myr (Ekstr¨om et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2012) the  lower bound for which life is thought to have evolved on  Earth (Lopez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2005, Danchi and Lopez, 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' For  more massive stars, the main sequence lifetime becomes  prohibitively short.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1 Definition of Herbig stars  Evidence that the objects presented in Herbig (1960)  were indeed intermediate mass PMS stars was provided  by placing these stars on an HR diagram (Strom et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  1972) and were consistent with stellar masses span-  ning ∼ 2 − 15M⊙(see also Hillenbrand et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Subsequent studies found emission above what is ex-  pected from the stellar photosphere at wavelengths with  λ ≳ 1µm (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', Cohen, 1973, 1980, Hillenbrand et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  1992, Malfait et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 1998), caused by a dusty enve-  lope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Several papers presented criteria to observation-  ally define the class of Herbig Ae/Be stars (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', Th´e  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 1994a, Malfait et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 1998, Waters and Waelkens,  1998b, Vieira et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2003) leading to a general consensus  that Herbig Ae/Be stars have a spectral type B, A, or  F, H i emission lines, and an infrared excess.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Most pa-  pers identify the stellar mass range represented by such  objects to range from ∼1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5 - 10M⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The lower mass  1 https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='springer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='com/collections/hbggjficdi  Herbig Stars  3  limit was set by the spectral type of the coolest star  that was thought to reach the zero age main sequence  (ZAMS) as an A9 star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The upper mass limit is set by  the maximum mass a star is expected to experience a  pre-main-sequence phase while it is not enshrouded in  its protostellar envelope, however, this upper mass limit  is not sharply defined as many stars typically included  in catalogs of Herbig Ae/Be stars have higher masses  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', Vioque et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  In this review, we will refer to the Herbig Ae/Be  stars as Herbig stars, and predominately limit ourselves  to stars with the following properties: young A or B  type stars that are evolving towards the main sequence,  with Hα emission, often associated with a nebulosity,  and an infrared (IR) excess due to warm (∼1000 K)  and/or cold (∼100 K) circumstellar dust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Herbig stars  in principle do not include objects cooler than about  7000 K (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', stars with spectral types later than A9),  but some F-type stars such as HD 142527, CQ Tau and  HD 135344B have also been discussed in the literature  in the context of Herbig star samples, because of their  high luminosity and associated mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' We will include  these in this review.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Most if not all of these stars are not  yet core-hydrogen burning PMS stars;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' however, for the  most luminous objects in the sample this is not easy to  establish.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' We do not consider the A and B stars with de-  bris disks, that have lost their primordial gas and have  secondary dust produced by collisions between larger  bodies (Hughes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Nor do we discuss young  PMS A and B stars that show no evidence for circum-  stellar material any more (and would be the equivalent  to the naked T Tauri stars;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', Walter 1986).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Catalogs  of (candidate) Herbig stars were published by Finken-  zeller and Mundt (1984), Herbig and Bell (1988), Th´e  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (1994a), Vieira et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2003), and more recently  by Vioque et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' HArchiBe, an on-line archive  of known Herbig Ae/Be stars and their properties is  described in Guzm´an-D´ıaz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2021) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' From this  catalog, we identify 31 Herbig stars (including spectral  type F) within 225 pc and 87 Herbig stars within 450  pc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2 Connection to Intermediate Mass T Tauri stars  Late F, G, and K type intermediate mass PMS stars  are classified as T Tauri stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They are the evolution-  ary predecessors of the Herbig stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Since young inter-  mediate mass stars evolve from the birth line towards  the main sequence, they will have properties that clas-  sify them as T Tauri stars when still cool and shift to  earlier spectral types as their temperature increases as  2 http://svo2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='cab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='inta-csic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='es/projects/harchibe/main/  they evolve along the radiative track on their way to the  ZAMS (Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In fact, T Tau itself has been shown  to be of intermediate mass (Duchˆene et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Her-  big and Bell (1988) defined a special group called “su”  stars with properties similar to that of the intermediate  mass T Tauri star SU Aur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Herbst et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (1994) intro-  duced the class of Early Type T Tau stars, that con-  tains both T Tauri and Herbig stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Calvet et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2004)  used the term intermediate mass T Tauri (IMTT) stars,  which has been adopted in subsequent literature to de-  note the low temperature progenitors of the Herbig  stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  In a recent study, Valeg˚ard et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2021) compiled a  list of about 50 IMTT stars from the T Tau literature  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' stars classified as T Tau stars) and, based on Gaia  DR2 distances (Gaia Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2016, 2018)  to these stars, derived basic properties such as tem-  perature, luminosity, and IR excess.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Stars with mass  above 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5 M⊙ were selected, based on their position  in the HR diagram and using PMS evolutionary tracks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  This study shows that the circumstellar environment of  IMTT stars is qualitatively similar to that of the Her-  big stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A full view on how intermediate mass stars  and their environment evolve from the birth line to-  wards the main sequence ideally includes IMTT stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  We will return to this point in Section 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In this review,  we will not consider the IMTT stars any further.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3 Link between low mass and high mass star  formation  Herbig stars can be found in low- and high mass star  forming regions (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', Chamaeleon and Orion respec-  tively).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, early type Herbig Be stars tend to be  surrounded by a dense clustering of stars, while this is  not the case for Herbig Ae stars (Hillenbrand et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  1995, Testi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' There is a smooth transition  in clustering between these two ranges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This points to  a qualitative difference in the mode of star formation  that leads to massive (M⋆ ≳ 10 − 20 M⊙) and lower  mass stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Models for star formation also distinguish  between two modes: isolated, low mass star formation  in clouds of modest mass, and clustered, high mass star  formation in giant molecular clouds (Motte et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  An important difference between these modes is that  in high mass star forming regions massive stars, that  evolve quickly, provide a strong feedback on their en-  vironment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Their stellar winds and UV radiation fields  are important already during the main accretion phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Stars with mass above 8-10 M⊙ do not/are not expected  to go through a visible PMS phase;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' although, this has  not yet been revisited incorporating the latest insights  4  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 1  HR diagram containing 218 Herbig stars with high quality DR2 Gaia parallaxes (adapted from Vioque et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2018),  their Figure 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The solid lines represent PMS tracks (Bressan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2012), with the final masses indicated on the Main  Sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The dashed lines represent isochrones taken from Marigo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The Zero Age Main Sequence is the region  marked by the end of the PMS tracks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Figure kindly provided by M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Vioque.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  relating to the modelling of the spectral energy distri-  bution (SED) of Herbig stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Radiation pressure on  dust grains for instance inhibits the formation of very  massive stars via the core accretion model (Wolfire and  Cassinelli, 1987), although non-spherical accretion can  circumvent this difficulty (Yorke and Sonnhalter, 2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Feedback is believed to become relevant for masses above  10-20 M⊙ (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', Hosokawa and Omukai, 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Observations and models suggest that the core ac-  cretion model for star formation, developed for low mass  stars, is also applicable to more massive stars, up to  masses of 10-20 M⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Young massive YSOs in M17 have  been found to have disks with properties consistent with  a remnant accretion disk (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hoffmeister et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2008,  Ochsendorf et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2011, Ilee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Beyond a mass  of about 20 M⊙, it is unclear which mechanism dom-  inates: core accretion and competitive accretion (Bon-  nell et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2001) have been suggested (Krumholz and  Bonnell, 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Intermediate mass stars are at the crossroads be-  tween low- and high mass star formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' As stellar  mass and luminosity increase, the shortening stellar  evolutionary timescales, the increased strength of the  stellar UV radiation field, and the denser cluster envi-  ronment that occurs for more massive stars will strongly  influence the physical and chemical properties of Herbig  star disks and the way they dissipate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Therefore these  disks are of interest to understand how stellar mass af-  fects the early evolution of stars and planetary systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  This is one of the main motivations to study young in-  termediate mass stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  In the quarter century since the last major review of  Herbig stars (Waters and Waelkens, 1998b), there has  been enormous progress in our understanding of these  systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Here we review this progress.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' First we discuss  the stellar properties of Herbig stars - namely their mul-  tiplicity fraction, X-ray properties, and variability (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' We then move to the star-disk interface and discuss  the stellar accretion properties of these stars (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Moving further out, we discuss the dust (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 4) and gas  (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 5) properties of the disks orbiting Herbig stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  We then discuss the advances in our understanding of  planet formation in these disks (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 6) and conclude  with summary of key future lines of investigations that  arise from the topics we cover in the review (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 7) and  a modest proposal for a new definition of Herbig stars  (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  6  5  4  5  log(L) [Lo]  3  2  1  0  Herbig stars  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='8  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='8  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6  log(Teff) [K]Herbig Stars  5  2 STELLAR PROPERTIES  Over the past quarter century, millimeter (mm) inter-  ferometry of gas emission from disks around young stars  have enabled the measurement of dynamical masses of  young stars (Simon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2000, Schaefer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2009,  Guilloteau et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2014, Simon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2017, Braun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2021, Law et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The spatial resolution and sensi-  tivity provided by the Atacama Large Millimeter Array  (ALMA) has opened the door to measuring ever larger  samples of dynamical masses that provide a valuable  measure for testing stellar evolution models and thus  the ages and masses inferred from them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Braun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  (2021) compiles the largest such sample to date and  finds that stars with masses of stars ranging from 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3-  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0M⊙ inferred from stellar evolution models predict  masses ranging from -5% to -14% of the mass inferred  dynamically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  It may be useful to see the Herbig stars in the con-  text of their position in the HR diagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Vioque et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  (2018) placed the 218 then known and proposed Herbig  stars with high quality Gaia DR2 parallaxes (Gaia Col-  laboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2018) in the HR diagram, a version  of which is reproduced in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' To guide the eye,  several evolutionary tracks and isochrones are overplot-  ted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' As expected, most Herbig objects fall at or above  the ZAMS indicating that intermediate stars cease ac-  creting prior to or just after reaching the ZAMS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The  more massive Herbig Be stars are sparser than the Her-  big Ae stars which can be explained by the Initial Mass  Function, as well as the shorter evolutionary time scales  that are associated with their evolution towards the  Main Sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Higher mass Herbig stars are invariably  younger than their lower mass counterparts (Figure 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The ages of the lower mass Herbig stars typically range  from several millions of years up to 10 Myr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The latter  high values have implications for the disks, their evo-  lution and survival which will be discussed after the  overview of the stellar properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' We will proceed with  the binary properties of the objects in the following  sub-section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1 Binaries among Herbig stars  The multiplicity of Herbig stars bears on models of their  formation, the origin of X-ray emission observed toward  Herbig stars (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2), and can affect the appear-  ance of the disk (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Sec 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Herbig stars are predom-  inately found in binary systems, and many of these are  found at arcsecond scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, not all separations  have been equally well sampled (Duchˆene 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The  last dedicated binary studies using large samples are  the spectro-astrometric surveys of Baines et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2006)  and Wheelwright et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2010) who observed 31 and 45  objects respectively, totalling 62 unique targets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The  separations probed were in the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1 − 2′′ range while a  flux difference of 6 magnitudes could be reached.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Their  data were tested against the (slightly less deep) survey  AO data of Leinert et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (1997) and imaging of Pirzkal  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (1997), and found to be in agreement where there  was overlap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Both studies yielded a multiplicity of order 70% for  this parameter range, with a hint that the Herbig Be  stars are more likely to be found in binaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wheel-  wright et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2010) could disentangle the spectra of  some of the otherwise unresolved binaries and deter-  mined that the mass ratios are close to one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This value is  inconsistent with a random sampling of the IMF, which  would be expected if stellar capture was the main bi-  nary formation mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The same team reported in  Wheelwright et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2011) that the alignment between  the binary objects and the disks surrounding the pri-  maries was consistent with disk fragmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Similar  conclusions on fragmentation being the cause of Herbig  binaries were put forward by Arun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2021) who  reported the discovery of a wide (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6′′) Herbig Ae - M  star binary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Given the wide separation, fragmentation  at an earlier stage was favored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The surveys with the Very Large Telescope Inter-  ferometer (VLTI) of Lazareff et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2017, H-band, 51  objects) and Gravity Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2019, K band,  27 objects) probed smaller separations and similar con-  trasts to the above studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' These studies report few  detections of binary companions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, the surveys  were designed to study disks, so the targets were se-  lected against the presence of radial velocity binaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Milli-arcsecond Herbig Be binaries, corresponding to  sub-500 au separations, have been observed using VLTI  data however (Kraus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2017, Koumpia et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Finally, the smallest separations can be probed us-  ing spectroscopy, where a binary system can be revealed  through radial velocity variations or directly in a dou-  ble lined binary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Not much work has been done in this  field, with the spectroscopic survey by Corporon and  Lagrange (1999) of 42 Herbig stars still the largest ded-  icated such study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The latter category includes spatially  resolved objects with known separations of order 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5′′,  so the observed close binary fraction based on radial  velocity variations alone is 17%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Summary: The majority of Herbig stars are in binaries  (≳ 70%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The mass ratios of the binary Herbig stars in-  dicates that the binaries form from disk fragmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Given that many of these are unresolved at arcsecond  resolution, this also has important implications for in-  6  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2 The distribution of ages of the 218 Herbig stars as  determined from the position in Figure 1 (Vioque et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The highest mass stars have the smallest ages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Most Herbig  Ae stars, and thus their disks, have ages in excess of several  Myr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Figure kindly provided by M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Vioque.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Properties  O-early B  Herbig  T Tauri  Plasma T  < 12 MK  12-60MK  5-30 MK  kT  < 1 keV  1-5 keV  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6keV  logLX (erg/s)  29-33  29-31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5  28-30  log(LX/Lbol)  7  [-6,-4]  up to -3  Origin  radiative  companion?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  αω dynamo  wind  shear dynamo?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Detection rate  65%  35%  100%  Table 1 Typical properties for the X-ray emission of MS  OB-type, Herbig and T Tauri stars  terpreting the X-ray properties of Herbig stars – the  topic of our next section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2 X-ray emission  The more massive young objects, with spectral types  O to B1, are often detected in X-rays.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Their emission  is soft (kT < 1 keV) with fractional luminosities, log  (LX/Lbol) ∼ -7, attributed to shocks that originate in  line-driven winds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' At the other end of the mass distribu-  tion, solar-mass T Tauri stars have a magnetic dynamo  that can persist due to their convective motion, giving  rise to hard X-ray emission (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4 ≲ kT ≲ 3 keV) from  the magnetically heated corona, and log (LX/Lbol) sat-  urating around -3 (see Table 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Herbig stars, on the  other hand, are thought to be fully radiative so that  they cannot support a dynamo by convection, nor are  they hot enough for a radiation driven wind;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' therefore,  the detection of X-ray emission from Herbig stars was  unexpected (Zinnecker and Preibisch, 1994, Damiani  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' If the stars are indeed fully radiative, this  would suggest that Herbigs should not generate strong  well-ordered magnetic fields as observed in their cooler,  convective counterparts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, some do have strong  magnetic fields (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Hamaguchi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2005) detected 30% of the Herbig  stars observed with the Advanced Satellite for Cosmol-  ogy and Astrophysics (ASCA), and determined an X-  ray luminosity higher than for T Tauri stars (Table 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The fractional X-ray luminosity is slightly lower than  that of TTS, but higher than for MS B-type stars: log  (LX/Lbol) = [-6,-4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They found no evidence for a cor-  relation between v sin i (an indication of rotational ve-  locity) and X-ray luminosity, unlike what is observed in  TTS where a strong correlation was found, supporting  the αω dynamo scenario (Pallavicini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 1981).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The plasma temperatures of Herbig stars are be-  tween 1 and 5 keV which is too high to be produced in  wind-driven shocks (Hamaguchi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Also flares  were observed, which also cannot be explained by stellar  winds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Since Herbig stars evolve from fully convective  IMTT stars, some of these may possess a fossil magnetic  field (see section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Activity parameters such as Hα  and radio emission do not correlate with LX, but the  amplitude of optical variability, ∆V, does (Stelzer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Also, magnetospheric accretion can be ruled out  as the origin of the X-ray emission because the free-fall  velocities are too low.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hamaguchi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2005) propose  that the X-ray emission stems from magnetic activity,  where the fossil magnetic fields of the stars reconnect  with the disk (a star-disk magnetosphere).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  With the better spatial resolution of Chandra (∼1′′),  Stelzer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2006) observed 17 Herbig stars to study  the companion hypothesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They detected X-ray emis-  sion from 76% of their sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' After correcting for the  presence of known lower-mass companions, they derived  an occurrence rate of 35% which was consistent with  previous work by Hamaguchi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Interestingly,  the detection rate of X-rays from Herbig stars is com-  parable to the binary rate of Herbig stars (see section  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Further study of the binarity of X-ray emitting  Herbig stars will clarify the extent to which unresolved  companions can account for the X-ray emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  In a follow-up paper, Stelzer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2009) distin-  guishes between late B to A-type Herbig stars and early  B-type PMS stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They propose that the early B-type  PMS stars behave like the B-type MS stars, while the  X-ray emission in the later-type Herbig stars is con-  nected to magnetic fields, which have only been firmly  detected in ∼ 20 Herbig stars (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' J¨arvinen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2019,  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Summary: The origin of the X-ray emission detected  towards Herbig stars remains an unsolved mystery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' An  origin in a stellar wind can be excluded due to the high  45  M>10 Mo  40  5<M<10 Mo  35  0<M<5 Mo  Number of sources  30  25  20  15  10  5  0  10  10  10  10  Age [Myr]Herbig Stars  7  plasma temperatures observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' It is possible that the  X-rays could come from an unseen companion or by  remnant magnetic fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A dedicated study including  precise magnetic field measurements, high spatial res-  olution X-ray observations, and sensitive searches for  companions for a large sample of Herbig stars is needed  to test these hypotheses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3 Variability  Herbig stars have long been known to show both photo-  metric and spectroscopic variations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The variability can  be traced back to changes in the circumstellar disks, the  accretion regions, and the structure of the stars them-  selves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' We discuss the photometric and spectroscopic  behaviours separately below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1 Photometric variability  Some Herbig stars show non-periodic brightness vari-  ations as large as ∆V ∼ 3 mag (Herbst et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Important clues about the nature of the variations and  the (inner) disk regions came from studying the bright-  ness variations of the star UX Ori: when the star fades  in brightness, its color becomes redder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, when  fading even more, this color change turns around, and  the star becomes bluer, the so-called ‘blueing effect’  (Bibo and The, 1990).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In tandem with the fading of  the star, its radiation was found to become more po-  larized, hinting at starlight being scattered off circum-  stellar dust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' These effects, referred to as the UXor phe-  nomenon in later literature, were further studied with  simultaneous photometric, polarimetric and spectroscopic  observations (Grinin, 1992, Grinin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 1994), sup-  porting the hypothesis that the blueing effect is caused  by an opaque dust cloud in the disk, intersecting in the  line of sight towards the star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3 we focus on  the properties of the inner disks that were revealed by  the UXor phenomenon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  In the near infrared (NIR), the variability of Her-  big stars is far more modest than in the optical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Eiroa  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2002) observed a sample of T Tauri and Her-  big Ae stars using quasi-simultaneous optical and near-  infrared photometric observations, taken typically less  than 1 hour and at most 2 hours apart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The peak-  to-peak variations at optical wavelengths could be as  high as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5 magnitudes during their period of observa-  tions, while the NIR photometry varied mostly at the  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1 magnitude level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Out of the 12 Herbig Ae objects  observed, only 3 were reported as non-variable, while  8 of the remaining nine showed a correlation between  the optical and NIR photometric variations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Given that  the NIR emission is most likely re-radiated by the hot  circumstellar dust that absorbed the optical light, the  location of the near-infrared variability can be traced  to the inner circumstellar disks (see also Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The remaining one object, UX Ori, did not show a cor-  relation between the photometric variations, which was  interpreted as possibly being due to rotational modu-  lation of star spots on the stellar photosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Vioque  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2018) later determined that roughly 25% of Her-  big stars can be classified as having such UXor varia-  tions, while Herbig Be stars are markedly less variable  than the Herbig Ae stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Finally, variability at milli-magnitude amplitudes  has been positively detected towards a small sample  of Herbig Ae stars (Zwintz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2014);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' see also the  compilation by Steindl et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Such observations  are challenging as any signatures at the milli-magnitude  level not only require space-based photometry (Zwintz  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2009, Casey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2013) but need a careful disen-  tangling of such data with the non-periodic variations  described above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The Herbig Ae stars appear to show δ  Scuti type variability (Marconi and Ripepi, 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This  variability arises among stars whose temperature and  mass lead to an ionization structure that leads to ra-  dial oscillations resulting in variability with a period on  the order of a few hours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Such stars fall in a well de-  fined region of the HR diagram known as the instability  strip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Herbig stars in this region are no exception.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The  milli-magnitude photometric data have the prospect of  probing into these pre-Main Sequence stars using as-  teroseismology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' An interesting example is the case of  HD 139614, whose age was estimated from asteroseis-  mology to be about 11 Myrs (Murphy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This  old age confirms the results of other studies, and shows  that gas-rich disks can survive for a substantial period  of time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' We will return to this in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2 Spectroscopic variability  In addition to photometric variability, the emission lines  observed towards Herbig stars have long been known to  vary (for a review, see Catala 1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Spectroscopic vari-  ability studies of individual objects have revealed vari-  ations in the emission lines and their profiles which can  be traced back to rotational modulation of the accretion  regions (Garcia Lopez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2016, Sch¨oller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  It would appear that the variations are less extreme  than those observed for T Tauri stars whose variations  are connected to the magnetically controlled accretion  (Kurosawa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Dedicated studies of larger samples of Herbig ob-  jects have been sparse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Costigan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2014) investi-  gated the Hα line variability for a sample of, mostly,  Herbig Ae and T Tauri stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The amplitude of the  8  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  variability increases from minute timescales to level off  at the days-weeks timescales, even over periods as long  as years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This indicates that the variability occurs in a  small volume around the star and Costigan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2014)  attribute the variability mainly to changes in the accre-  tion rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Overall, it would appear that the variability  of the emission lines is connected to the accretion pro-  cesses occurring in Herbig stars, the topic of the next  section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Lastly, another type of spectral variability has been  observed towards Herbig stars which was first found  towards β Pic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Multi-epoch spectroscopy revealed that  metallic absorption lines would change on timescales  of hours to months.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In particular, lines could suddenly  appear in absorption and the absorption itself would  become more red-shifted in matters of hours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This be-  haviour was interpreted as evidence of infalling material  from cometary bodies (Ferlet et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 1987).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Grady et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  (1996) presented spectra of 41 Herbig stars and found  that 22 of them showed variability consistent with the  presence of gas released from infall of evaporative bod-  ies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' We will return to this issue in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2, where this  phenomenom is discussed as an indirect tracer for the  presence of planets in the disks of Herbig stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Summary: Herbig stars display photometric and spec-  troscopic changes on timescales ranging from hours to  months and longer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The larger amplitude photometric  changes can be traced back to variable dust obscura-  tion from an orbiting disk, while variability at smaller,  milli-magnitude, amplitudes can be analysed with as-  teroseismology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Spectroscopically, variable line emission  is mostly associated with the accretion process, while  variable absorption lines can be due to changes in the  accretion process itself, but can also be caused by in-  falling rocky material such as exo-comets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  3 ACCRETION ONTO HERBIG STARS  In this section we discuss the accretion and accretion  mechanisms of Herbig stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Given that the intermedi-  ate mass Herbig stars are, for all intents and purposes,  the high mass counterpart of the solar mass T Tauri  stars, let us begin with a description of the paradigm  for understanding accretion onto T Tauri stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Dedi-  cated reviews of these objects can be found in Bertout  (1989) and Bouvier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2007), recent reviews on the  accretion process in pre-Main Sequence stars in general  can be found in Beltr´an and de Wit (2016), Hartmann  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2016) respectively, while Mendigut´ıa (2020) fo-  cuses on accretion onto Herbig stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  T Tauri stars are well known to sustain a magnetic  field due to their internal dynamo and exhibit both evi-  dence for accretion onto the stars and bi-polar outflows  powered by the accretion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The accretion itself is mag-  netically mediated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The stellar magnetic field truncates  the disk where the ram pressure from accretion balances  the opposing pressure from the stellar magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Material from the disk free-falls along the magnetic field  lines through accretion funnels onto the star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' With typ-  ical disk-truncation radii of 2-3 stellar radii, the free-fall  velocities are very high, of order 100s km s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The grav-  itation potential energy of the material released when  it crashes onto the photosphere is therefore substan-  tial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The resulting shock produces X-ray radiation that  is absorbed by surrounding particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Then, these par-  ticles heat up and re-radiate at ultraviolet wavelengths,  producing a UV-excess that can be observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A cartoon  of the situation is provided in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 3 (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bouvier  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2007 for more details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The relatively cool T Tauri stars radiate most of  their photospheric energy at optical and longer wave-  lengths, so the observed UV emission can be used as  a proxy for the accretion luminosity, which reflects the  potential energy released by the infalling matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' As-  suming the material is falling from infinity, the mass  accretion rate is given by,  ˙Macc = LaccR∗  GM∗  ,  (1)  where Lacc is the accretion luminosity, R∗ is the stellar  radius, M∗ is the stellar mass, and G is the gravitational  constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  It may be clear that a proper characterisation of  the stellar parameters is important.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' As will be discussed  later, the Gaia satellite, which provides parallaxes, from  which distances are determined, for more than a billion  stars has had an important impact on the field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The magnetospheric accretion (MA) paradigm has  been applied extensively over the past years to deter-  mine the accretion rates of Herbig stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In the follow-  ing we give not only an overview of the results, but also  critically analyse the assumptions made in this endeav-  our.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' We will demonstrate that while the MA paradigm  seems to be applicable to most Herbig stars, there is  compelling evidence that it cannot act for some extreme  cases, and that there is strong evidence for a change in  accretion mechanism at higher masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1 Magnetic properties of Herbig stars  Let us first discuss an immediate potential critique that  can be fielded against the use of the MA paradigm to  Herbig stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Conventional wisdom is that no magnetic  Herbig Stars  9  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 3 Cartoon of the immediate circumstellar environment of a HAe star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Initially designed to illustrate the magnetospheric  accretion paradigm for CTTSs, this cartoon also applies to HAe stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The dust in the disk is sublimated when it reaches a  temperature of ∼1500 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Interior to this region the disk is gaseous and heavily ionized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The disk is truncated by the magnetic  field where the pressure from accreting gas is balanced by magnetic pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The accreting gas then falls into the star along  field lines from which hydrogen recombination emission emerges and creates an accretion shock near the surface of the star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Figure based on Gravity Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  field is expected to be generated in Herbig stars be-  cause the envelopes of A and B stars are radiative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The  B-field is typically generated in a dynamo which usu-  ally occurs by convection in cooler stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Indeed, mag-  netic fields have only fairly recently been detected to-  wards a limited number of objects (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', Alecian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Based on the compilation of Hubrig et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2015),  Mendigut´ıa (2020) presents all reported magnetic field  detections of Herbig stars and their stellar parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The list contains a total of 18 objects with measured  B-fields, which constitutes roughly 10% of all known  and proposed Herbig stars (viz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Vioque et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Intriguingly, this fraction is similar to a 10% detection  rate in field A stars (Landstreet, 1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Most of these B-  fields have strengths of order 100 G, while a few Herbig  stars have magnetic field strengths that are significantly  higher (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', V380 Ori (2kG), and Z CMa (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2 kG)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' As  already alluded to in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2, rather than being gener-  ated, the magnetic field in these magnetic objects could  be fossil in nature, either from the original collapsing  parental cloud or the remnant field of an earlier IMTT  star phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Whatever the cause of the magnetic fields, it should  be noted that most B-field determinations concern the  global integrated magnetic field, a non-detection is there-  fore not necessarily evidence for the absence of it;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' a  complex geometry would inevitably result in a lower  observed strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Villebrun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2019) mapped the  B-fields of the IMTT stars, and find that the fields be-  come weaker, but also more complex and at higher tem-  peratures (see also Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The possibility that higher  temperature pre-Main Sequence stars harbour strong  magnetic fields is therefore a realistic prospect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' As a  consequence, the MA scenario which is well established  for T Tauri stars (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bouvier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2007), may also be  applicable to hotter objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  In the next section, we will go into more detail on  similarities between T Tauri stars and Herbig objects  with emphasis on their accretion properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' We then  consider the determination of the accretion rates of Her-  big stars and provide global inferences resulting from  these.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Summary: About 10% of Herbig stars have measur-  able magnetic fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' While most of these are of order  100 G, a few have magnetic field strengths about an or-  der of magnitude larger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' These B-field determinations  are measurements of the global integrated field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' If the  magnetic fields of Herbigs tend to have a complex ge-  ometry, it is possible that the surface magnetic field  strength of the typical Herbig star is much higher than  these measurements suggest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2 Accretion Geometry - similarity with T Tauri stars  The earliest investigation into MA onto Herbig stars  was carried out by Muzerolle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They ap-  plied their MA models to the Herbig Ae star UX Ori,  Brackett  emission  inner  gas disk  accreting  material  truncation  accretionshock  radius  magnetic field lines  dust sublimation radius10  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  and found that the computed emission line profiles were  in qualitative agreement with the observed emission line  profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In parallel, they also concluded that the mag-  netic field strength would be weaker and its geometry  should be more complex than the usual dipole field in  T Tauri stars, just as was later shown to be the case  by Villebrun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Further supporting evidence  that Herbig Ae stars may be accreting in a similar fash-  ion as T Tauri stars comes from various observational  studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' These often stem from comparative investiga-  tions into the accretion-related properties of T Tauri  stars on the one hand and Herbig Ae and Herbig Be  stars on the other hand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' An additional result from these  studies is that Herbig Be stars often have very different  properties than their Ae counterparts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Early suggestions that the accretion processes of  Herbig Ae stars and T Tauri stars are similar were re-  ported based on results from linear spectropolarime-  try.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Although the accretion funnels are still too small  to be directly imaged, indirect linear spectropolarimet-  ric methods are able to probe these regions at scales  of order stellar radii (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Vink, 2015, Ababakr et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2016, 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The similarity of the linear spectropolar-  metric properties of the Hα line for Herbig Ae stars  and T Tauri stars was reported by Vink et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2002,  2005a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The observations were explained with line emis-  sion from accretion hot spots scattering off truncated  disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Indeed, the inferred sizes of order stellar radii of  the inner holes (Vink et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2005b) are consistent with  those expected for a magnetically truncated disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In  contrast, the very different effects observed towards the  Herbig Be stars are more consistent with disks reaching  onto the central star - hinting at a different accretion  mechanism in those.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ababakr et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2017) presented  the largest sample of Herbig stars observed with lin-  ear spectropolarimetry around Hα, which allowed them  to identify the transition from truncated disks to disks  reaching into the stellar surface around spectral type  B7/8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Other studies related to accretion diagnostics are  broadly consistent with these findings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Cauley and Johns-  Krull (2014) studied the He i 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='083 µm line profiles of  a large sample of Herbig stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Due to its high excita-  tion energy, this transition is particularly sensitive to  accretion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' These authors found that both T Tauri stars  (observed by Edwards et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2006) and Herbig Ae stars  had similar line profiles and comparable fractions of  red-shifted absorption lines, tracing infall, all of which  could be explained in the context of MA, while the Her-  big Be stars did not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Furthermore, they inferred that  the Herbig Ae stars could have smaller magnetospheres  than their T Tauri counterparts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  As mentioned earlier, Herbig stars display spectro-  scopic variability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Costigan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2014) found that both  the timescales and amplitude of the variability were  similar for T Tauri and Herbig Ae stars, which led these  authors to suggest that the mode of accretion of Her-  big Ae stars is also similar to that of T Tauri stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Although less extensive in time coverage, the Hα vari-  ability study of Mendigut´ıa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2011b) extends to  the more massive Herbig Be stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' These objects were  found to have different Hα variability properties than  the Herbig Ae stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Of note is that these authors not  only considered the Hα line strength variations, but  also those of the line width, which, given the high free-  fall velocities involved may be more effective in tracing  the accretion flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Its variability was found to be con-  siderably smaller for the Herbig Be stars than for the  Herbig Ae stars, which, in turn, is smaller than for T  Tauri stars (Fang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Kreplin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2018) find from modelling their high  resolution infrared spectro-interferometry, that the in-  ner radii of the disk-winds are consistent with the Alfv´en  radii computed using the low B-field strengths observed  for a few Herbig Ae stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Guimar˜aes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2006) ob-  served 15 Herbig Ae stars (some with spectral type  B9Ve) and found four that showed red-shifted absorp-  tion in the Balmer lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The authors demonstrated  that this absorption can be qualitatively explained with  magnetospheric accretion if the disk were truncated rel-  atively close to the star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Detailed studies on individual targets have reached  similar conclusions as above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Grady et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2010) found  the location of the accretion footprint on a Herbig Ae  star to be very like those on T Tauri stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The in-  depth spectroscopic variability study of a Herbig Ae  star showed it is undergoing magnetospheric accretion  in the same manner as classical T Tauri stars (Sch¨oller  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' From their modelling of spectra, Moura  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2020) find evidence that Herbig Ae stars undergo  MA, while they do not find this to be the case for a  Herbig Be star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' On the hotter side, Patel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2017)  model the inner gaseous disks of several Herbig Be stars,  and find they do not need magnetospheres to reproduce  the emission line spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Summary: It has been empirically shown that Herbig  Ae stars exhibit many similar accretion-related char-  acteristics as T Tauri stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This provides indirect ev-  idence for magnetically controlled accretion operating  for these objects as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In turn, it validates the use  of MA shock modelling to derive accretion rates for at  least the later-type Herbig stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Herbig Stars  11  2 M¤  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5 M¤  4 M¤  1 Myr  10 Myr  5 Myr  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 4 The B-fields of T Tauri stars and Herbig Ae stars according to Villebrun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The black and gray symbols are  stars with non-detections, while the red and blue symbols represent objects with detections with symbol sizes proportional to  the B-field strengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The orange zone indicates the area where stars are fully convective, the blue zone where they are fully  radiative, while the other colors represent a mix;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' green (radiative core and convective envelope);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' pink (convective core and  radiative envelope).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The various evolutionary tracks (black lines) and isochrones (white lines) are from Behrend and Maeder  (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Figure kindly provided by E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Alecian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3 Measurement of mass accretion rates  Let us now turn to the determination of the accretion  rates of Herbig stars using the MA paradigm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' As a word  of caution, we stress that it is used for all Herbig stars,  regardless of their spectral type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, as will be  discussed later, this approach serves as an additional  means to identify where a change in accretion properties  may be present.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1 Direct determination of the accretion luminosity  As can be seen from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1, once we know the stellar mass  and radius, the mass accretion rate can be derived from  the accretion luminosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' For the cool T Tauri stars, this  emission is most readily identified by UV-excess emis-  sion over and above the stars’ photospheric radiation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  In addition, it can also be seen at optical wavelengths,  where the excess emission due to accretion fills in the  underlying absorption lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In the absence of UV obser-  vations, a value for the excess emission can be obtained  by determining the extent of this “veiling”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  In contrast to the T Tauri stars, the determination  of the contribution of the accretion shock to the to-  tal blue/UV emission is less straightforward for Herbig  objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' By virtue of their higher temperatures, these  stars are more luminous at UV wavelengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Thus the  contrast between the accretion shock and the photo-  12  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Normalized Flux  Wavelength (Å)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 5 Figure from Donehew and Brittain (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The spec-  trum of V350 Ori (black line) is compared to a template  of a non-accreting A star (red line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' While there is a good  match between V350 Ori and the template long-ward of  3800˚A V350 Ori is brighter than the template at shorter  wavelengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This excess Balmer continuum radiation is due  to the accretion shock over and above that of a normal star  with the same spectral type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  sphere at UV wavelengths is much smaller for Herbigs  than for CTTSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Because of this smaller contrast, dis-  entangling the contributions from the stellar and ac-  cretion properties to the UV emission is challenging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Veiling measurements also prove problematic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The ac-  cretion luminosity can exceed the stellar luminosity of  T Tauri stars, allowing a comparatively straightforward  determination of the veiling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However Herbig stars are  brighter and the photosphere dominates the light out-  put at optical wavelengths hampering the identification  and measurement of the veiling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Despite these chal-  lenges and the rather labor-intensive methodologies of  determining the UV-excess in these objects, the num-  ber of Herbig stars with directly determined accretion  luminosities is surprisingly large;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Donehew and Brit-  tain (2011, 33 objects) and Fairlamb et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2015, 91  stars) obtained blue spectra for Herbig stars and de-  termined the accretion luminosities for most targets by  carefully comparing their Balmer continuum (excess)  emission with spectra of standard stars (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Mendigut´ıa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2011a, 38 objects) used broadband  UBV photometry to determine the Balmer excess emis-  sion and accretion luminosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' One advantage of using  the Balmer continuum emission to measure the accre-  tion luminosity is that this property is minimally af-  fected by reddening (Garrison, 1978, Muzerolle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The lowest accretion luminosities that could be mea-  sured are of order 1 L⊙ and the corresponding accre-  tion rates are of order 10−8 M⊙yr−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The lower limits  are due to the sensitivity of the observations and the  ability to determine the excess emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This sensitiv-  ity descreases for the higher temperature objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' It is  interesting to see that more than 70% of all the Her-  big stars investigated in this manner exhibit Balmer  continuum excess emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' As it is non-trivial to find  alternative explanations for this excess, this observa-  tion constitutes independent supporting evidence that  these objects are accreting matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2 Indirect determinations of accretion luminosity  It turns out that it is not strictly necessary to obtain  dedicated UV or Balmer continuum observations to ar-  rive at estimates of the accretion rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A correlation  between the brightness of emission lines and the accre-  tion luminosity exists for IMTT stars (Calvet et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Indeed, by using (ideally) simultaneous UV and  line observations, this correlation can be used to cali-  brate the line luminosity to arrive at the accretion rate  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ingleby et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Garcia Lopez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2006) ex-  trapolated this finding to Herbig stars and determined  their mass accretion rates using the Brγ line luminos-  ity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Their approach was validated when Donehew and  Brittain (2011) and Mendigut´ıa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2011a) confirmed  that this correlation between accretion luminosity (as  derived from the UV and Balmer excess) and the lumi-  nosity of emission lines also extends to Herbig stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Fairlamb et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2017) demonstrated that the strength  of most, if not all, emission lines in the spectra of Herbig  stars correlate with the Balmer-excess based accretion  luminosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They provided best-fit parameters for many  lines, which cover the wavelength range from the UV to  the NIR, allowing accretion luminosities to be worked  out when observations of only limited parts of the spec-  trum are available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The relationship between accretion luminosity and  line luminosity goes as (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mendigut´ıa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2011a):  log  �Lacc  L⊙  �  = A + B × log  �Lline  L⊙  �  ,  (2)  where A and B correspond to the intercept and the gra-  dient of the (straight-line) relation between log(Lacc/L⊙)  and log(Lline/L⊙) respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' As example, Fairlamb  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2017) determined the constants to A = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='09 ±  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06 and B = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='00 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='05 in the case of Hα.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Summary: Because Herbig stars are much more lumi-  nous than their cooler counterparts, measurement of  excess UV emission is challenging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' For stellar accretion  rates exceeding 10−8M⊙yr−1, the accretion luminosity  can be inferred from measurement of the excess Balmer  continuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' There luminosity of emission lines has been  shown to scale with this excess enabling a simpler mea-  surement of the accretion luminosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Herbig Stars  13  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 6 HR diagram containing the 163 Herbig stars with good Gaia DR2 parallaxes and their accretion rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The solid  lines represent PMS tracks (Bressan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2012, Tang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2014), with the final masses indicared on the Main Sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The dashed lines are isochrones of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='01, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1, 1, and 10 Myr (Marigo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The color map denotes the mass accretion  rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' While it is evident that the younger stars are accreting at higher rates, the younger stars are also much more massive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Characterization of the evolution of the stellar accretion rate requires disentangling stellar mass and age.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Figure based on  Wichittanakom et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2020)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4 Mass accretion rates of Herbig stars  As outlined above, in order to compute the mass ac-  cretion rate of a Herbig star, it is important to have  well-determined stellar parameters (mass, luminosity,  or radius and temperature, as well as extinction).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In ad-  dition, we need a value of the accretion luminosity such  as derived from the UV excess, which is the only direct  observational measure of accretion, while an emission  line luminosity provides an indirect value via Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' As  noted in Section 2, significant progress was made in the  determination of Herbig stellar parameters through the  Gaia astrometric study by Vioque et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Arun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2019) used these data and Hα Equiv-  alent Widths reported in the literature to determine  accretion rates for many of the objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wichittanakom  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2020) used a slightly larger sample to expand  the spectroscopically determined temperatures of Fair-  lamb et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2015) with an additional 30 objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They  rederived the line-of-sight extinction to the objects, as  well as measured the Hα emission line strength from the  same spectra, yielding a large sample to be analysed in  a homogeneous way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' These were supplemented by ob-  jects from Vioque et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2018), resulting in a sample  of 163 Herbig Ae/Be stars with well-determined stel-  6  40Mo  3  5  20Mo  10Mo  4  4  5Mo  log(L*) [Lo]  3  2Mo  5  1Mo  2  6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='01 Myr  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1 Myr  7  Myr  0  10 Myr  8  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='8  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='8  log(Teff)[K]14  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  lar parameters and as homogeneously derived accretion  rates as possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  An illustration of the results is provided in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  It can be seen that the higher mass objects have larger  accretion rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 7 shows the accretion luminosities  of the Herbig stars and several samples of T Tauri stars  taken from the literature (Hartmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 1998, White  and Basri, 2003, Calvet et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2004, Natta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2006),  as a function of stellar luminosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The T Tauri data are  not based on Gaia parallaxes, so although not directly  comparable to the Herbig star measurements, these ob-  jects are mostly selected to be members of clusters and  at similar distances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The dependencies of the accretion  luminosity on the total luminosity should therefore, at  least to first order, be similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  As was already known, the accretion luminosity in-  creases with stellar luminosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, a striking fea-  ture in this graph is that the Herbig Ae stars follow the  T Tauri stars closely;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' the best-fitting slopes of the re-  spective Lacc − L∗ relations for both groups of objects  are similar to within the error bars, while both slope  and scatter are significantly different for the higher mass  Herbig Be stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' As was described earlier, the Herbig  Ae stars share many accretion-related properties with  T Tauri stars, and the dependence of the accretion lu-  minosity on the stellar luminosity proves no exception.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The MA accretion paradigm should thus be applicable  to the Herbig Ae star regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The Herbig Be stars again differ in properties from  their lower mass counterparts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' To this we add that Fair-  lamb et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2015) noted that a number of Herbig Be  stars required very large surface covering factors of the  accretion shocks in their MA models, with values ap-  proaching 100% and higher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' As such, these solutions  are unphysical and their UV/blue excess cannot be ex-  plained within the MA framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' It would appear that  the accretion rates as derived in the MA paradigm fur-  ther support the notion that Herbig Be stars accrete  their material in a different manner than the T Tauri  and Herbig Ae stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The break as seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 7, is also  present in  ˙Macc − M∗ space, and occurs around 4 M⊙  (Wichittanakom et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2020), in agreement with the in-  dependent study of Ababakr et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2017), who found a  marked change in linear spectropolarimetric properties  around spectral type B7/8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  This break at 4 M⊙ is also seen in the high spec-  tral resolution study of Brγ by Grant et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They  found that the accretion rate increases with stellar mass  following a trend similar to that of T Tauri stars for  stellar masses ≤ 4 M⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They also found that the distri-  bution of line shapes of Brγ was consistent across stellar  mass and spectral type, though they caution that incli-  nation affects may obscure any underlying systematic  differences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Summary: The relationship between the stellar lumi-  nosity and the accretion luminosity is consistent be-  tween T Tauri stars and Herbig Ae stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' There is a  break in this relationship around 4M⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A similar break  is seen in the mass dependence of the stellar accre-  tion rate, and is consistent with the marked change in  the linear spectropolarimetric properties aound spec-  tral type B7/B8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The mean accretion rate of Herbig Ae  stars is 10−7M⊙yr−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5 Mass accretion rate as a function of stellar age,  disk dispersal times  We continue this discussion with a word of caution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In  order to understand the evolution of pre-Main Sequence  stars and the disk dispersion timescales, it has been  common to study the mass accretion rate as a function  of age of the stars (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hartmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Due  to the comparatively small mass range and large sam-  ples of objects from clusters with well-defined ages, it is  feasible to determine this relationship empirically for T  Tauri stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Several attempts to do so have been made  for Herbig stars, and, indeed, it has been found that  the mass accretion rate decreases with the stellar age  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Fairlamb et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2015, Arun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However,  one should be extremely careful in deriving conclusions  from this result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  As can be seen from the isochrones in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 6, the  PMS evolution across the HR diagram is much faster  for high mass stars than for low mass stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' As a re-  sult, a higher mass Herbig star inevitably has a younger  age than a lower mass object.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This in turn means that  when investigating relationships of various parameters  with “stellar age”, the age essentially acts as proxy for  the stellar mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Given that, as mentioned earlier, the  higher mass Herbig stars have larger mass accretion  rates, we can expect this effect to dominate any age-  related correlations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In order to disentangle these ef-  fects, and study the mass accretion rate as a function  of age, one needs to select a very narrow mass range to  remove or minimize this effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Wichittanakom et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2020) struggled finding a sta-  tistical sample of stars within a mass range narrow  enough to isolate the time dependence of the mass ac-  cretion rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The best subsample (having a mass range  2-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5M⊙) hinted at a decrease, but with generous error  bars, ˙Macc ∝ Age−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='95±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Improved mass determina-  tions, which are still dominated by uncertainties in the  parallax and extinction, and larger samples of Herbig  stars are needed to make progress in this area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Herbig Stars  15  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 7 Accretion luminosity versus stellar luminosity for 163 Herbig stars from Wichittanakom et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2020) and classical T  Tauri stars from the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Note the similarity between T Tauri and Herbig Ae stars, while the Herbig Be stars behave  differently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Figure based on Wichittanakom et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A second caveat to keep in mind is that Herbig stars  are selected on the basis of possessing emission lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Once these stars cease to accrete, it is very difficult to  identify PMS stars in this mass range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Thus it is likely  that as these stars age, the sample of PMS intermediate  mass stars becomes less complete such that the Herbig  stars represent the tip of a distribution of sources with  long-lived accretion disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' If this is true, measurement  of the time dependence of mass accretion from this bi-  ased sample is an upper limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Next to the identification  of non-accreting PMS intermediate mass stars, consid-  eration of accretion rates of the direct progenitors of  the Herbig stars, the IMTT stars, will help clarify our  understanding on the time dependence of the stellar  accretion rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Summary: Inferring the time dependence of the stellar  accretion rate for Herbig stars is challenging because  of the strong mass dependence of this relationship.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' For  a narrow mass range (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5M⊙), the mass accretion  rate scales as t−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='95±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6 Accretion onto Herbig Be stars  The MA paradigm is shown not to work for the higher  mass Herbig Be stars, while evidence has been pre-  sented that these massive objects accrete matter in a  different manner than for T Tauri and Herbig Ae stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The natural next question is how material is deliv-  ered to the massive Herbig Be stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Understanding ac-  cretion onto Herbig Be stars and their formation also  CTTs  Best fit for CTTs  Best fit for low-mass HAeBes  Best fit for high-mass HAeBes  Wichittanakom et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2020)  [0] (387)60]  2  0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='03 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='08  2  2  0  2  4  6  log(L*)[Lo]16  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  addresses a wider issue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The intermediate mass Her-  big stars connect the low mass T Tauri stars and the  most massive stars whose formation is a topic of intense  debate (Krumholz and Bonnell, 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Observational  studies have not yet reached the same level of detail as  for lower mass objects, as massive pre-Main Sequence  stars are often optically invisible;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' due to their rapid col-  lapse, they are still enshrouded by dust from their natal  clouds (Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2018, Frost et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The Her-  big stars therefore may offer valuable insights into the  formation of the most massive stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Regarding the disk-to-star accretion on Herbig Be  stars, we should bear in mind a crucial piece of evidence  provided by the linear spectropolarimetric studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The  data for the higher mass Herbig Be stars is remark-  ably similar to those of the classical Be stars, which are  readily explained with disks that reach onto the stellar  surface (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Poeckert and Marlborough, 1976, 1977).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Hence, it would appear that the Herbig Be stars ac-  crete material from a disk that is in contact with the  stellar photosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This situation is reminiscent of the  so-called Boundary Layer (BL) accretion that is a natu-  ral consequence of a viscous circumstellar disk (Lynden-  Bell and Pringle, 1974).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The BL is a thin annulus close  to the star in which matter slows down from its (Kep-  lerian) rotation velocity to the slower stellar rotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  In this region, kinetic energy will be dissipated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This  model considers how material is transferred from a Ke-  plerian rotating disk to the, more slowly rotating, stellar  surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The region where the disk material slows down  and releases its kinetic energy is the boundary layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The BL paradigm is being applied to many accret-  ing astrophysical systems such as White Dwarfs and  neutron stars in binary systems (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Tylenda, 1977,  Romanova et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' It had even been explored for  T Tauri stars before the MA scenario prevailed (Bertout  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 1988).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Blondel and Djie (2006) applied this sce-  nario to a sample of mainly later type Herbig stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The  models could mostly reproduce the UV emission and  the authors derived accretion rates using this approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The UV excess, and its associated effective tempera-  ture, can be controlled by the projected size of the BL  on the sky, while the accretion luminosity depends on  the amount of matter accreted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The BL model requires  higher accretion rates than the MA model to repro-  duce similar accretion luminosities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This is because the  kinetic energy from Keplerian rotating material is half  that of the gravitational potential energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' We would ex-  pect, therefore, that - all other things, such as radiating  area being equal - when applied to the higher mass Her-  big stars, the BL derived accretion rates would need to  be higher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This could well result in a steeper slope of the  Macc−M∗ relation at the high end, yielding a universal  accretion behaviour across the PMS mass range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Although the BL accretion has been suggested to  apply in the case of the more massive Herbig stars  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mendigut´ıa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2011a, Cauley and Johns-Krull,  2014), it has never been tested nor investigated in de-  tail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The time is ripe for dedicated magneto-hydrodyna-  mic models to be applied to the full Herbig star mass  range to investigate the viability of the, surprisingly un-  derinvestigated, BL model and provide predictions of  the resulting covering factors and mass accretion rates  to compare with observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Summary: The magnetospheric paradigm for inferring  the accretion properties of Herbig Ae stars does not  apply to their more massive counterparts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' It is possible  that these more massive stars accrete via a boundary  layer, but more this has not yet been modeled in detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='7 Probing the accretion regions  To directly observe the accretion region we need to  reach as close to the stellar surface as possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' With  the exception of the UV excess, we have thus far dis-  cussed indirect probes of the accretion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' With regards to  spatially resolved diagnostics, the smallest scales that  can be probed directly are through milli-arcsecond op-  tical and NIR interferometry of the Hα and Brγ lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Over the years, such studies have been conducted using  facilities such as the VLTI, aimed at the Brγ line (Kraus  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2008, Mendigut´ıa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2015, Tambovtseva et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2016, Kreplin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2018) and CHARA, whose obser-  vations target Hα (Benisty et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2013, Perraut et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2016, Mendigut´ıa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The picture that has emerged essentially confirmed  the original findings from a small sub-sample by Kraus  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2008);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' there is a diversity in line properties, emis-  sion region sizes and line origins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Perhaps most relevant  to note here is that these milli-arcsecond resolution in-  terferometric optical and NIR studies of the hydrogen  line emission do not necessarily identify the line emit-  ting regions of Herbig stars with the magnetospheric  accretion channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  For example Kraus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2008), Mendigut´ıa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  (2015), Tambovtseva et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2016), Kreplin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2018)  and Mendigut´ıa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2017) report the line emission to  be sometimes consistent with compact accretion chan-  nels and sometimes larger than that, making them more  likely to be due to winds and outflows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' When applying  models to the data, it appears that, generally speaking,  the line emission regions and properties are consistent  with a disk-wind, and compatible with MHD driven  winds (Garcia Lopez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2015, Tambovtseva et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  Herbig Stars  17  MIR  Scattered Light  (sub-)mm  1  100  Distance in au  10  1  2  3  4  a  b  c  d  1 Turbulent mixing (radial or vertical)  Vertical Settling  Radial Drift  b) Bouncing  2  3  4  c) Fragmentation with mass transfer  d) Fragmentation  a) Sticking  10 μm  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 8 Schematic of a disks around young star adapted from Testi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This schematic highlights the principal  processes that drive the evolution of dust (left) and the regions of the disk probed by various wavelengths (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  2016, Caratti o Garatti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Although the lines  themselves may not probe the accretion itself, the natu-  ral question as to how the emission line strengths allow  us to determine the accretion rates can be answered  fairly straightfowardly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' As outflows in young stars are  accretion powered (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hartmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2016), a corre-  lation between line luminosity and accretion luminosity  may therefore not be surprising after all.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Indeed, it also  explains why we can use the line luminosities for ac-  cretion rate determinations, and explains the observa-  tion that the line luminosities do not vary at the same  timescales or amplitudes as the UV excess (Mendigut´ıa  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Summary: There is compelling evidence that Herbig  stars with spectral types later than ∼B7 accrete mag-  netosphericaly, and their Hi and other atomic emission  lines scale with the accretion luminosity though the  origin of this relationship remains uncertain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The ac-  cretion rates of Herbig stars with masses ≲ 4 M⊙ are  10−8 M⊙ yr−1 ≲  ˙M ≲ 10−6 M⊙ yr−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The relation-  ship between the stellar luminosity and the accretion  luminosity is consistent −2 ≲ log(L∗/L⊙) ≲ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' There is  a break in this relationship for stars with higher lumi-  nosities (corresponding to ∼ 4 M⊙).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A study comparing  the accretion rate of IMTT stars to Herbig stars will  clarify how the stellar accretion rate evolves over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  4 DUST DISKS AROUND HERBIG STARS  Our understanding of the properties and evolution of  disks around young stars has advanced dramatically  over the last 20 years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' For a review about the evolu-  tion of dust in disks, we point the reader to a chapter  from Protostars & Planets VI by Testi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2014)  and the review by Andrews (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' At the time of this  writing, updated reviews are being prepared for Proto-  stars & Planets VII and should be available in 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 8, we present a schematic that highlights the domi-  nant processes thought to drive the evolution of dust in  disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In this section, we will summarize the advances  in our understanding of dust in Herbig disks, while gas  will be discussed in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  That the SEDs of Herbig stars show an excess at in-  frared wavelengths was established in the early 1970’s  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Strom, 1972, and references therein).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Both disks  and envelopes - some with a cavity carved by an outflow  were invoked to explain this excess (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Gillett and  Stein, 1971, Strom et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 1972, Hillenbrand et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 1992,  Berrilli et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 1992, Hartmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 1993, Mannings,  1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Unfortunately, due to the low spatial resolution  of the observations (typically ∼20′′ at millimeter wave-  lengths, corresponding to 3000 au at 150 pc), it was  not possible to distinguish which of the proposed mor-  phologies fitting the SED was the correct one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  18  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The first spatially resolved observation of contin-  uum emission around a Herbig star was obtained by  Mannings and Sargent (1997) using mm interferometry  with the Owens Radio Valley Telescope (OVRO);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' they  found extended emission up to 110 au for HD 163296,  using beam sizes of 4-5′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' These authors also detected  Keplerian velocities of the CO gas, providing the first  observational confirmation of a disk around a Herbig  star (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The Hubble Space Telescope provided  the first resolved scattered light images of Herbig disks  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', Weinberger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 1999, Grady et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 1999), and  in the last years, high contrast imagery with 8m class  telescopes provide even greater detail of dust structures  in the disk (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Garufi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2017a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' With the avail-  ability of the ALMA, disk emission can now routinely  be spatially resolved for many Herbig stars thanks to  the dramatically improved spatial resolution: typically  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='05-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1′′ (7-15 au at a distance of 150 pc;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Andrews  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2018a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Before we look more into the detailed properties of  the dust disks around Herbig stars, it is worth to con-  sider the differences that are related to the spectral type  of the central star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1 Herbig Be and Herbig Ae disks  Due to their rapid evolution towards the ZAMS, Herbig  Be stars are typically surrounded by the cloud material  from which they were formed, and this cold envelope  will contribute to their continuum emission at longer  wavelengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' For instance, a significant fraction of the  Polycyclic Aromatic Hydrocarbon (PAH) emission is  thought to originate from the surrounding envelope, in-  stead of from the disk, as is the case in Herbig Ae stars  (Boersma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2009, Verhoeff et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Herbig Be stars have a much stronger UV radia-  tion field than the cooler Herbig Ae stars: from 3450  L⊙ for a B2V, 50 L⊙ for a B8V and 7 L⊙ for an A0V  type star (Jim´enez-Donaire et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This translates  to important observational differences, mainly in terms  of gas emission lines (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='7) and disk proper-  ties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Alonso-Albi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2009) compared the mm emis-  sion of Herbig Ae stars to Herbig Be stars, and found  that, in general, the flux of the Herbig Be stars is 5-10  times lower, pointing to smaller disk masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This can  be attributed to photo-evaporation of the outer disk  by UV photons on short timescales (∼ 105 yr;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Gorti  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This is further supported by mid-infrared  (MIR) observations, showing that the disks around Her-  big Be stars are typically vertically flatter and smaller  in size than those around Herbig Ae stars (Verhoeff  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Furthermore, Vioque et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2018) derived the excess  in the NIR (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='24-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4 µm) and MIR (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4-22 µm) for a  large sample of Herbig stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They found that the total  infrared excess for objects more massive than 7 M⊙ is  typically smaller than that of the lower mass objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  This again points to important differences in disk prop-  erties depending on the stellar mass, and hence the stel-  lar radiation field, although external evaporation due to  nearby massive stars cannot be excluded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Another important difference between Herbig Ae  and Herbig Be stars is the typical distance to the ob-  jects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Herbig Be stars are typically located at d ≥ 1000  pc, while the best studied Herbig Ae stars are at dis-  tances of 100-200 pc, implying that the spatial resolu-  tion that can be achieved will differ by a factor of 5-10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Due to the complications caused by the presence of  envelope emission, in combination with the low spatial  resolution when observing Herbig Be stars, we will now  concentrate on the cooler Herbig Ae stars, thereby in-  cluding objects from spectral type B9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5 up to ∼ F5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Summary: Herbig Be stars evolve toward the main se-  quence much faster than Herbig Ae stars, thus they  tend to still be enshrouded in remnant cloud material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The NIR, MIR, and mm emission of Herbig Be stars is  substantially lower than that of Herbig Ae stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The  faster disk dissipation timescale of Herbig Be stars is  likely due to their higher UV luminosity and thus faster  photoevaporation of the disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2 Early disk models: SED classification into group I  and II  One of the first efforts to classify the SED of young  stars were provided by Lada and Wilking (1984) and  Lada (1987).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' These authors divided the SEDs of young  stars into three classes, based on the slope of the SED  between 2µm and 25µm given by,  a = dlog(λFλ)  dlog(λ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  (3)  Objects whose SED had a slope 0 ≤ a ≲ 3 where la-  beled Class I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Similarly, objects with −2 ≲ a ≲ 0 where  labeled Class II, and objects with −3 ≲ a ≲ −2 were  labeled Class III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Eventually this classification scheme  was expanded to include Class 0 objects that were only  detected at λ ≳ 10µm (Andre et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 1993).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Most of the  objects discussed in this review belong to class II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The earliest disk models of Herbig stars required ex-  tremely high accretion rates (> 10−6 M⊙/yr) and large  optically thin inner holes to fit the SED near 3 µm (Hil-  lenbrand et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, Hartmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (1993)  pointed out that, at the accretion rates necessary to fit  Herbig Stars  19  100  101  102  Wavelength [ m]  F  HD97048  100  101  102  Wavelength [ m]  F  HD104237  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 9 IR SED of a group I (top) and a group II star (bot-  tom).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Blue dots: photometry, grey line: Spitzer IRS spectrum,  orange line: Kurucz atmosphere model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' After Pascual et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  the observed 3 µm excess, the inner region of the disk  would be optically thick and thus emit too much ra-  diation at short wavelengths to agree with the obser-  vations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Instead, they suggest that most Herbig stars  do not harbor disks but envelopes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, as noted  above, mm interferometry and scattered light imagery  established the presence of disks around Herbig stars  just a few years later.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Chiang and Goldreich (1997) modelled the excess  emission observed in the SEDs of the lower-mass T  Tauri stars with passive disks in hydrostatic radiative  equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In those disks, the surface density goes  as Σ(r) ∝ r−3/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They distinguished between flat and  flared disks: in a flat disk, the opening angle of the disk  is constant, while in a flared disk it increases with dis-  tance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The optically thick disk is surrounded by an opti-  cally thin layer, the disk surface, that is directly heated  by the star, and where the temperature is higher than  that of the midplane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This surface layer will also heat  the interior of the disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Such 2-layered models can also  be used for Herbig disks, with some modifications, as  will be discussed in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  For a sample of 45 Herbig stars, the SED could  be well-characterised in the infrared thanks to obser-  vations with IRAS (Malfait et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' These authors  proposed an evolutionary sequence where the initially  continuous disk would evolve into a disk with a gap (a  pre-transitional disk), after which the NIR excess would  disappear (a transition disk), and finally a gas-poor de-  bris disk would remain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A few years later, Meeus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  (2001) proposed a classification scheme based upon the  shape of the IR SED3: Meeus group I (GI) objects have  an SED where the continuum of the IR to sub-mm re-  gion can be reconstructed by the sum of a power-law  and a black body, while Meeus group II (GII) objects  have an SED where the continuum can be reconstructed  by a power-law alone (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Possible locations for  these components are an optically thick, geometrically  thin disk (power-law component) and an optically thin  flared region (black body).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  To facilitate the observational classification into GI  and GII, van Boekel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2005) introduced a cri-  terion based on the NIR to total IR luminosity ra-  tios and the IRAS 12−60 µm color: GI sources have  LNIR/LIR ≤ (m12 −m60) + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5, while GII sources have  LNIR/LIR > (m12 − m60) + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A more recent (and  equivalent) criterion, based on an IR flux ratio that is  easier to use was proposed by Khalafinejad et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2016):  sources with flux ratio F30µm/F13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5µm < 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1 are GII,  while those with a larger ratio belong to GI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Summary: The disk of Herbig stars can be classified  based upon the shape of their SED: to fit their excess,  GI disks need a power-law + black body component,  while GII disks only need a power-law.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Criteria based  on infrared photometry can be used to classify the disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3 Improvements to the early disk models  For a long time, the structure of the disk remained a  topic of debate due to the lack of spatial resolution,  with both models of accretion disks with an optically  thin hole and spherically symmetric envelopes matching  the observed SEDs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, Tuthill et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2001) were  the first to spatially resolve the inner disk of a Herbig  star, LkHα 101, using interferometric data of Keck in  the H and K band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They found a central cavity that was  much larger (up to 10 times) than previously assumed  from theoretical accretion disk models, and connected  3 This classification scheme should not be confused with  the one proposed by Hillenbrand et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (1992) where group I  sources have an infrared excess that scales as λ−4/3 longward  of 2 µm, group II sources have an SED with a positive slope  in the infrared, and group III sources have a minimal infrared  excess.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  20  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  the location of the hot inner disk edge with the radius  at which dust grains sublimate due to the stellar irra-  diation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Disk models that could properly account for the  NIR structure of the SED were developed by Natta  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They proposed a model where the ma-  terial inside the dust evaporation radius is optically  thin gas and introduced the concept of a hot puffed-  up inner wall of optically thick dust grains at the dust  evaporation radius that could explain the NIR excess.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Dullemond et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2001) gave an expression for the black  body temperature of the rim,  Trim =  �  L∗  4πR2  rimσ  �1/4 �  1 + Hrim  Rrim  �1/4  (4)  They further developed this idea with a semi-ana-  lytical model in which the hot puffed-up inner wall casts  a shadow, obscuring parts of the flared disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In some  stars, even the entire disk might be shadowed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Following this work, Dominik et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2003) modelled  the observations with a disk model in hydrostatic equi-  librium where the GI sources were modelled with a disk  with varying surface densities, for some stars even in-  creasing with radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In this case most of the material  is located in the outer regions of the disk, while the  inner region is depleted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The GII sources, on the other  hand, could more easily be modelled with a compact  disk and/or a flattened outer region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, the pres-  ence of the silicate feature in GII disks indicates that at  least a small part of the disk intercepts stellar radiation  (Dominik et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Dullemond and Dominik (2004a) used 2-D radiative  transfer to model GI and GII disks and found that disks  with a higher optical depth are flaring, while disks with  a lower optical depth become self-shadowed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Building  on this work, Dullemond and Dominik (2004b) showed  that the growth and subsequent settling of dust grains  towards the midplane could enhance self-shadowing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  This work provided a successful framework for in-  terpreting the SEDs of Herbig stars in the evolutionary  scheme proposed by Malfait et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (1998) that is intu-  itively compelling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Qualitatively the idea is that disks  start out in a flared geometry (with envelopes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' As small  grains agglomerate to form larger grains, they settle  toward the midplane resulting in flat, shadowed disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  However, more recent work has challenged this picture,  as we will discuss in the following section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Summary: The disks around Herbig stars can be de-  scribed with an optically thick midplane surrounded by  an optically thin surface layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The inner disk edge is  puffed-up, and the innermost region is depleted in dust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  GI sources emit stronger in the far-IR than GII sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4 Group I: disks with a cavity, Group II:  self-shadowed disks  The paradigm of GI and GII being understood as an  evolutionary sequence from young flared disks to set-  tled flat disks stood for more than a decade until it was  challenged by mid-IR spatially resolved studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Honda  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2012, 2015) and Maaskant et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2013) used  MIR observations to conclude that several GI sources  have large gaps in their disks, more specifically, a dust-  depleted region between the inner and outer disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Disks  with gaps are called pre-transitional disks, based on the  assumption that as such disks further evolve and the in-  ner disk dissipates, the SED would lack a near-IR excess  (and become a transitional disk, see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' These  authors suggested that GI disks could in fact be more  evolved than GII disks, and proposed two distinct evo-  lutionary pathways for disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 10 Accretion rates for group I and II Herbigs, based on  the HArchiBe catalogue (Guzm´an-D´ıaz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  When comparing the accretion rate (determined from  a variety of accretion tracers) in function of the stellar  luminosity, no difference between GI and GII sources is  observed (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A similar behavior was found by  Grant et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2022) who compared the accretion rate,  derived from the Brγ line, for Group I and Group II  sources and found a similar distribution, indicating that  the accretion properties of the star is largely indepen-  dent of the dust geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  In Table 2, we summarize the main differences ob-  served between GI and GII objects: selection criteria  based on IR colors and fluxes, the mm flux scaled to  a distance of 140 pc (‘mm flux’), the slope αmm mea-  sured in the mm regions (‘mm slope’), the extent of the  dust continuum as observed at mm wavelengths (‘mm  disk size’), the gap size in the mm dust continuum (‘gap  group I  group II  logMacc (Mo/yr)  5  <logacc[Gl]>=-5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='989  9  <log acc[Gl]>=-5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='987  N  3  4  5  6  logL(LO)Herbig Stars  21  Diagnostic  Group I  Group II  LNIR/LIR − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5  ≤ m12 − m60  > m12 − m60  F30µm/F13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5µm  > 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2  < 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2  <mm flux>  750 mJy  220 mJy  <mm slope>  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='41  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='05  mm disk size  40-250 au  <150 au  mm gap size  large,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 5-140 au  small,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' <5 au  mm structure  cavity,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' rings  barely resolved  scattered light  100-600 au  elusive,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' < 100 au  scattered  light structure  cavity,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' rings,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' spirals  barely resolved  CO disk size  100-650 au  80-200 au  CO inner radius  5-18 au  3 au  CO transition  J=36-35  J=13-12  silicate feature  sometimes absent  typically present  PAHs  strong features  weak/absent  Table 2 Main observed differences between group I and II  disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' References: mm disk size: Stapper et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2022);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' mm  flux at 140pc, calculated from Stapper et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2022), mm  slope: Pascual et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2016);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' scattered light, gap size, disk  structure: Garufi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2017b) and references therein;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' CO  disk size: Taun, MSc 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' CO inner radius: Banzatti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  (2018);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' highest CO level detected: Meeus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2012), van  der Wiel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2014);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' silicate feature: Juh´asz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2010);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  PAHs: Acke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  size’), the disk substructure observed in mm continuum,  the extent of the small dust grains (‘scattered light’),  the appearance of the disk in scattered light, the extent  of the disk seen in CO emission (‘CO disk size’), the  inner radius where CO ro-vib lines are detected (‘CO  inner radius’), the emission transition from the highest  rotational level in the ground vibrational state of CO  observed (‘CO transition’), the 10 µm silicate feature  and finally the PAH strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Recently, Banzatti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2018) noted a dichotomy  in the NIR excess of group I sources: it is either low  (< 10%) or high (> 25%), while the group II sources  have intermediate values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Furthermore, they found a  connection between the strength of the NIR excess and  the radius at which CO emission is detected: sources  with a low NIR excess have CO emission starting at  larger radii indicating that the inner regions are more  depleted in these sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' We depict the morphologies  of those 3 different disk types in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In a recent  paper, Garufi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2022) studied GII disks in scat-  tered light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They found an anti-correlation between the  disk brightness in scattered light and the NIR excess,  supporting the scenario where the inner wall casts a  shadow on the disk behind it, as was proposed earlier  by Dullemond and Dominik (2004a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Summary: GI disks have a large cavity, depleted in dust,  that can explain the observed differences in flaring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' GII  disks, on the other hand, have either no cavity or a  very small one and are self-shadowed, so they are fainter  both at FIR wavelengths and in scattered light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5 Dust properties in Herbig disks  The disk material from which planets eventually form  originates in the interstellar medium (ISM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' There, dust  particles are either oxygen- (mainly silicates) or carbon-  rich (mainly Polycyclic Aromatic Hydrocarbons - PAHs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Silicates can be divided into olivines (Mg2xFe2−2xSiO4)  and pyroxenes (MgxFe1−xSiO3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In the ISM, silicates  are small (< 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1 µm) and amorphous, with a crystalline  mass fraction < 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2% (Kemper et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2004), so that the  detection of larger and/or crystalline silicates in Herbig  disks would indicate dust processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Dust grains can  grow when the density is high and the collision velocity  low enough (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Windmark et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Crystalliza-  tion of grains can occur either through thermal anneal-  ing of amorphous dust or condensation from the gas  phase, both of which occur at high temperatures (T >  1000 K;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Fabian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Our knowledge about dust  in protoplanetary disks is limited by the fact that the  bulk of the mass resides in the (partially) optically thick  mid-plane, and that the emitting surface per unit mass  decreases as grains grow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, there are 3 portions  of the dust population that can be observed through  different methods:  1) submicron-sized dust grains in the disksurface scat-  ter optical and near-IR light;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  2) micron-sized dust grains, also located in the disksur-  face, emit thermally in the mid-IR when at the right  temperature (T ≲ few hundreds of K), hence at a cer-  tain distance from the star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' It is here that we can iden-  tify their main solid-state features;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  3) mm-sized dust grains, located near the midplane at  larger distances from the star, with T ≲ few tens of K,  will emit thermally in the mm range, where the optical  depth is lower.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  We will now look at each of these methods and dis-  cuss the main results derived from them, with a focus  on what we have learned from IR spectroscopy, reveal-  ing the properties of the dust grains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1 Scattering by micron-sized dust grains  Small grains or aggregates located in the surface layer  of the disk can be traced through the light they scatter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  If the disk is inclined, it is possible to measure the scat-  tering efficiency at different angles (the phase function)  of the dust grains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The more inclined the disk is, the  larger the phase angle range that can be observed (see  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2 in Benisty et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, Stolker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  (2016) showed that it is important to take the flaring  of the disk into account when deriving the phase func-  tion and interpreting the scattered light images, due to  projection effects in the image plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Several dust prop-  22  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 11 The different disk structures proposed by Banzatti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2018) for Herbig disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Top: A schematic of a disk with  an inner cavity and a flared outer disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This geometry results in a GI SED with little to no excess NIR emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Middle: A  schematic of a disk with a gap that separates the inner and outer disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This geometry also results in a GI SED, however, there  is a substantial excess NIR emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bottom: A schematic of a continuous disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This geometry results in a GII SED.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Figure  based on Bosman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  erties can be derived from the degree and intensity of  polarization of the scattered light, as well as from the  way these depend on the scattering angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The phase function of a dust grain depends mainly  on its size (but also on its shape, structure, and re-  fractive index), with smaller dust grains (a < λobs)  having a more isotropic phase function, while the po-  larization by larger dust grains (a > λobs) tends to  peak towards small angles (0◦, or forward scattering).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Therefore, when comparing the ratio of forward and  backward (180◦) scattering intensity, the size of the ag-  gregates can be estimated (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Tazaki et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Furthermore, for larger aggregates, the amount of po-  larization is related to the porosity of the material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Also  the color of the aggregates can further reveal the poros-  ity of the dust (Mulders et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In Herbig stars,  polarized phase functions of both small and large aggre-  gates have been observed in several objects (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Stolker  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2016, Ginski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, as these ob-  servations are very time consuming, due to the sensi-  tivity and spatial resolution required, more progress in  this field is expected to be made in the future (see also  Benisty et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2 Thermal emission of warm small dust grains  The largest advances so far in deriving detailed dust  properties was done based on infrared spectroscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  By comparing optical constants obtained in the lab,  the dust responsible for the observed spectral features  can be characterised in terms of its composition, de-  gree of crystallisation, and grain size (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Henning and  Meeus, 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ground-based observations of silicates  have mainly concentrated on the 10 µm window, where  both amorphous and crystalline silicates can have strong  features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, for a more detailed study, space based  observatories were necessary to obtain more sensitive  and longer wavelength data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Observations with ISO were crucial to make a first  inventory of the IR spectral features in Herbig disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A key result was the discovery of crystalline silicate  features in the spectrum of HD 100546, reminiscent of  features found in the Solar System comet Hale-Bopp  (see Fig 12;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Malfait et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Furthermore, a study  of 14 Herbig stars showed a wide variety in dust prop-  erties: from unprocessed silicates (mainly amorphous  and small as in the ISM) to highly processed silicates  (crystalline and large);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' with no relation to any of their  stellar parameters (Bouwman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Surprisingly,  several GI sources do not show silicate emission, even  though their SEDs were similar to other GI sources that  did.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This can be attributed to either a lack of warm  and/or small silicates, what can be modelled by 1) re-  moving the small grains and 2) increasing the height of  the inner wall (Meeus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2002, Dominik et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  group I, low NiR  opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' thin surface layer  cavity  puffed-up wall  group I, high NiR  puffed-upwall  opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='thin surface layer  disk gap  opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='thin surface layer  group Il  puffed-upwallHerbig Stars  23  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 12 The spectra of Herbig star HD 100546 and Solar  System comet Hale-Bopp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' With the vertical marks the po-  sitions of forsterite features are indicated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Figure based on  Malfait et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  However, both model options cannot explain the ob-  servations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Therefore, Dominik et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2003) speculated  that the absence of the silicate feature could be caused  by a gap, removing those dust grains in the tempera-  ture range (∼ 200-400 K) needed to emit in the MIR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Indeed, a decade later Maaskant et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2013) showed  with spatially resolved mid-IR observations that the ab-  sence of the 10 µm silicate feature in GI disks can be  explained by certain gaps in the disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 13 The 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3/9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='8 µm ratio versus the peak to continuum  ratio of the 10µm silicate feature for GI and GII sources,  Fnorm = 1 + (Fobs - Fcont)/Fcont.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' After Juh´asz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  To study the grain size, van Boekel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2003)  introduced an intuitive method, based on the change  in strength and shape of the 10 µm silicate feature as  grains grow: comparison of the 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3/9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='8 µm ratio of  the silicate feature to its peak-to-continuum ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They  showed that the observed band strength and shape are  correlated, so that a weaker feature provides evidence  for larger grains in the inner surface layers and cannot  be attributed to a mere contrast effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This method in-  dicates that there is no difference between GI disks and  GII disks in terms of silicate grain growth (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Studies of large samples with higher S/N spectra (taken  with Spitzer) that were fit with a two-layer temperature  distribution model confirm a variety of dust properties  (dominated by amorphous olivines;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Juh´asz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  These authors found that the crystallinity fraction of  small dust graints in disks around Herbig stars ranged  from 1% to 30 % and did not correlate with stellar or  other disk properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The wavelength and band shape of the 69 µm fea-  ture emitted by forsterite at temperatures below 300 K  are very sensitive tracers of the Fe content and tem-  perature of the grains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This feature became accessible  with Herschel/PACS (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Sturm et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2010, Maaskant  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The analysis of 7 Herbig stars showed that  most of the forsterite grains responsible for the 69 µm  band have rather high temperatures of 100-200 K, and  that the Fe content is less than 2% (Sturm et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  It is important to keep in mind that the emission  features seen in the IR spectra trace dust grains that  are in the optically thin surface layer of the disk, while  the bulk of the mass resides in the disk mid-plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Also,  those grains need to be at the right radial distance in  order to be warm enough to emit at IR wavelengths  (Kessler-Silacci et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' It is, therefore, uncertain  how representative these dust grains are of the bulk  of the disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This will naturally depend on the amount  of (vertical) turbulence in the disk, and the dynamical  coupling between the gas and dust grains, which also  depends on the grain size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3 Spatial distribution of silicates in disks  The spatial distribution of silicates (in particular the  crystalline silicates) can be measured with MIR inter-  ferometry, and indirectly in spatially unresolved spec-  tra that cover a wide wavelength range and hence tem-  perature range of the emitting dust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The MID-infrared  Interferometer at the VLTI (Leinert et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2003) was  the first instrument that provided the angular resolu-  tion necessary to spatially resolve the silicate emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  It was shown that the abundance of crystalline silicates  increases in the inner few au of Herbig disks (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 14;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  van Boekel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Subsequent studies confirmed  this result for other Herbig stars (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Menu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2015)  and T Tauri stars (Varga et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  While more indirect, Juh´asz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2010) used the  wide wavelength range (5-38 µm) of Spitzer/IRS to in-  fer the radial distribution of the crystalline silicates  250  200  HD100546  Flux  150  100  50  Hale-Bopp  0  5  10  15  20  25  30  35  40  45  Wavelength[um]1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2  GI  GII  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0  3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='9  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='8  largergrains  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='524  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 14 The 10 µm spectra of HD 144432 taken with 3 differ-  ent baselines, covering different radial distances in the disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The dust in the innermost region is clearly more processed  than that of the entire disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Figure from van Boekel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  in the disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They split the spectra in 2 parts repre-  senting the warmer material in the inner disk and the  colder material in the outer disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They found forsterite  at a wide range of radial distances, including regions  far below the annealing temperature of silicates, sug-  gesting they were formed through eruptive processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  In contrast, enstatite was preferentially (but not exclu-  sively) found in the inner disk, so that the enstatite-  to-forsterite mass ratio declines with distance from the  star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' For a discussion on possible formation scenarios,  we refer to Juh´asz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The abundance of forsterite can be locally enhanced  under certain conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This is the case in HD 100546,  a GI Herbig star with a bright disk wall at 13 au.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mul-  ders et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2011) found that most of the forsterite emis-  sion originates from the inner wall (at 13-20 au), with a  dust temperature of 150 to 200 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' While there is a high  forsterite abundance (40-60%) in the wall, the observa-  tions are consistent with the absence of fosterite in the  outer disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Thus an observed strong feature does not  necessarily mean a high average abundance in the disk,  but can reflect a locally enhanced abundance in small  crystalline silicate grains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Such local enhancements may  be related to planet formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Indeed, in the case of  HD 100546, several planetary candidates have been pro-  posed (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' If present, such a massive planet  may stir up a local population of larger bodies or peb-  bles in the exposed inner regions of the outer disk,  and/or cause shocks that produce crystalline silicates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Hence, a direct relation between the planet formation  process and the occurrence of crystalline silicates could  explain the observed global lack of correlations with  stellar or disk parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4 Thermal emission of cold large dust grains: grain  size and disk mass  The thermal emission of mm-sized dust grains located  closer to the mid-plane of the disk is expected to be  optically thin at a distance > 5-10 au.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' As their mm  emission is in the Rayleigh-Jeans (R-J) limit, their flux  is proportional to the dust opacity: Fν ∝ κνν2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Un-  fortunately, the optical properties of the dust are not  known a priori.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, at mm wavelengths, κν can  be approximated by νβ, with β the dust opacity in-  dex, such that: Fν ∝ ν2+β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The dust opacity index β  is dependent on the dust properties, with dust grain  size thought to be the most important - besides com-  position, shape and porosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In the ISM, the value of  β is typically 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='7-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0, and declines as the grains grow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Therefore, the observed spectral index, α, of the SED  (Fν ∝ να) can be used as a proxy for grain growth  deeper in the disk, assuming optically thin emission in  the R-J limit, so that α = β + 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Acke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2004) found that β was lower for GII  disks than for GI disks, suggesting enhanced grain growth  in GII disks (see also Pascual et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However,  these observations provide the radial average of β, while  a radial dependency of the spectral indices was found  in several disks (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' HD 163296 (Guidi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2016),  HD 141569A (White and Boley, 2018), and HD 100546  (Miley et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2019)), with a lower spectral index in the  inner regions than the outer regions, pointing to en-  hanced grain growth in the inner disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Pinilla et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2014) found that β is higher in sources  with dust-depleted cavities (where grain growth is not  favorable), and showed that β can even be related to the  cavity size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Therefore, the radially integrated value of  β can provide a misleading measure of the overall grain  growth throughout the disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Furthermore, Woitke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  (2019a) showed that while β is thought to be dominated  by the size of the grains, variation in the composition  of the grains can lead to deviations in β ranging from  ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='7 in the warm Herbig disks while cooler disks  such as around TTS - have even larger deviations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The dust disk mass can be estimated from the ob-  served flux at mm wavelengths, assuming that the emis-  sion is optically thin and that the dust opacity and tem-  perature are known (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', Beckwith et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 1990, Hen-  ning et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 1994):  Mdust =  c2d2Fν  2ν2k < Tdust > κabs  ν  (5)  with c the speed of light, d the distance, Fν the flux, ν  the frequency, k the Boltzmann constant, < Tdust > the  mass-averaged dust temperature and κabs  ν  the absorp-  tion coefficient per unit dust mass (cm2g−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pascual  o m  100%flux  46m  40%flux  102 m  20% flux  8  6  10  11  12  13  入[μm]Herbig Stars  25  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 15 The 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3mm flux, scaled to 140pc and divided by M∗  versus M∗, a proxy for Mdust/M∗, for stars with d < 500pc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The largest fluxes are seen in GI sources, but many GI sources  have similar values as GII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Based on data from Stapper et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2016) found that, on average, GI sources have  larger mm luminosities than GII sources;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' a similar re-  sult was found by Stapper et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2022);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Assuming that the temperature and dust opacity is the  same in every disk, this would imply that GI disks have  larger dust masses than GII disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, there is ev-  idence that the disk temperatures and dust opacity of  GI and GII sources are not the same (Woitke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2019a);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' also, the size of the largest dust grains that we  can trace is similar to the longest wavelength we ob-  serve, thus large rocks etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' remain unaccounted for.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Woitke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2019a) compared dust masses derived  with 3 different methods: 1) the classical way, with a  fixed dust opacity and dust temperature, 2) the classi-  cal way but with dust opacities and temperatures de-  rived from SED modelling, and 3) dust mass directly  derived from SED modelling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They point out that, 1)  typically, the dust opacities are larger than the ‘canon-  ical value of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5 cm2g−1, so that the actual dust masses  are lower;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2) not all disks are optically thin at (sub)mm  wavelengths;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 3) the dust temperature can be higher in  the case of a small disk, or lower in the case of an ex-  tended disk, leading to actual lower/higher dust masses  for smaller/larger disk then when derived in the clas-  sical way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, when comparing the results from  method 1) and 3), Woitke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2019a) found that  these effects tend to cancel out, so that only an uncer-  tainty of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5 dex in dust mass remains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Additionally,  as we will discuss in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1, the gas to dust ratio in  disks is poorly constrained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' While the use of the mm  luminosity to estimate the disk mass is convenient, the  poor characterization of the required parameters sug-  gests that this approach should be taken with some  caution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Summary: Evidence for dust processing in terms of  crystallization and grain growth has been found in the  IR spectra of Herbig disks, but no connection between  the amount of the dust processing and stellar or disk  properties was found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, the dust grains observed  in the MIR represent only a small fraction of the dust  present in the disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The absence of the 10 µm silicate feature in GI disks  can be explained by dust cavities at a distance where  dust grains would obtain a temperature of 200-400K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The decrease in enstatite/forsterite ratio with dis-  tance from the star suggests that (long-lasting) erup-  tive processes are the dominant source of cold forsterite  in the outer disk regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' On the other hand, the low  Fe content observed in the 69 µm forsterite feature  is consistent with silicate formation in chemical equi-  librium at high temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' More detailed modeling  of crystallization processes, taking into account radial  transport, shock heating, and stellar eruptions is clearly  needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Under the (somewhat simplistic) assumption that  the Herbig disks have similar temperatures and dust  opacities, GI disks have, on average, larger dust masses  than GII disks, as derived from their mm fluxes assum-  ing optically thin emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, when ignoring ra-  dial variations of β, GI disks have, on average, higher β  values than GII, pointing to smaller grains, thus result-  ing in stronger emission for a similar mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In addition,  different dust compositions will result in different val-  ues of β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' It is clear that, when deriving and comparing  dust disk masses, more attention needs to be paid to  dust opacities and temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6 PAHs in Herbig disks  While silicates are oxygen-rich materials, Polycyclic Aro-  matic Hydrocarbons (PAHs) are carbon-rich.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They are  actually large molecules rather than dust particles, so  they are suspended in the disk atmosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Since PAHs  emit by reprocessing UV photons, they trace the sur-  face of the disk exposed to the radiation field of the  star, and can thus be detected at larger distances from  the star than silicates, which are thermally excited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Meeus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2001) found that in GII sources, PAHs  are absent or weak, while GI sources show stronger PAH  emission features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This result was confirmed by Acke  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2010) for a sample of 53 Herbig Ae stars: the  PAH-to-stellar luminosity ratio is higher in targets with  a flared disk (GI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The observation that the PAH lumi-  nosity is stronger in GI than in GII disks, for a given  stellar temperature, can be related to a larger amount of  PAHs that are exposed to UV photons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Indeed, when a  1750  V12470ri  group I  1500  group II  (M)  1250  1000  750  HD135344B  HD142527  500  HD97048  250  0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0  M*(M。' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=')26  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  gap opens in the disk, a larger part of the disk is exposed  to stellar photons that warm the disk and thus increase  the flaring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The few GII sources where PAHs were de-  tected (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' HD 142666, Meeus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2001) might have  small gaps (Menu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Alternatively, for some  sources the gas in the disk could be flared, even when  the dust has settled (Acke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The variations seen in the positions of the features  are mainly due to chemical differences of the PAHs in-  duced by the stellar UV field (Acke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2010): the C-  C bonds at 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2 and 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='8 µm shift to longer wavelengths  with decreasing stellar effective temperature and is a  measure for the aliphatic/aromatic content ratio of the  hydrocarbon mixture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Furthermore, Maaskant et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2014)  found that the ionization state of the PAHs (that can  be deduced from the I6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2/I11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3 band ratio) critically de-  pends on the optical thickness of the disk, with a higher  ionization fraction in optically thinner disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' These au-  thors also propose that PAHs are not only located in  the disk surface as is generally assumed, but that they  are also present in the more optically thin disk gaps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Summary: PAHs trace the disk surface out to large dis-  tances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Their emission is stronger in flared disks where  they can intercept more stellar photons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The observed  chemical differences (aliphatic vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' aromatic) are due to  differences in the stellar UV radiation, while the ion-  ization state depends on the optical thickness of the  disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='7 Ices in Herbig disks  Ices are thought to be an important component in the  framework of planet formation, due to 1) their higher  sticking coefficient, making it easier for icy grains to  grow 4, and 2) the increase of the density in solids when  dust grains are covered in ice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Therefore, the location  of the ice line (where a particular molecule freezes out  in a disk) determines the region where the growth of  planetesimals could occur more easily.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Unfortunately, the spatial distribution of ices in Her-  big disks is not well known, mainly due to a lack of  spatial resolution at far-IR wavelengths, as well as due  to the fact that most ices are located deeper in the  disk, where the optical depth is too high for them to  be seen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, at 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1 µm, water ice can be observed  through scattered light spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' With this method, a  decrease in surface brightness at 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1 µm was observed  in HD 142527, beyond the cavity and inner wall of the  4 However, experimental work by Gundlach et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2018)  did not confirm the theoretical prediction that ices have  higher tensile strengths than silicates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  outer disk (Honda et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Furthermore, a crude  spatial distribution of water ice was derived by Honda  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2016) for HD 100546 from the radial profile of  the 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1 µm opacity, but the results are inconclusive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 16 The ISO SWS and LWS spectra of HD 142527, and  the imaginary part of the refractive index of water ice at 50  K in blue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Indicated are water ice emission peaks at 43 and  62 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' After Min et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2016a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  In the far-IR, the water ice feature at 43 µm can  be strong, but that wavelength unfortunately lies out  of the wavelength covered by Spitzer and Herschel, but  it was detected for a few sources with ISO/SWS (Mal-  fait et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Another ice feature at 62 µm has a  large width (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 16) that hinders straightforward  identification as it is rather weak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Both features were  identified in HD 142527 (note that HD 142527 has a  large dust gap (> 140 au) with likely low gas density;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Casassus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Min et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2016a) modelled the  far-IR spectra and determined that the emitting water  ice resides in the outer disk of HD 142527 where the  ratio of water ice to silicates is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6, showing that the  density of solids clearly increases due to ice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They also  concluded that 80% of the oxygen in the outer regions  resides in water ice, a similar amount as what is found in  the outer solar system and in dense interstellar clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Min et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2016a) found the water ice in HD 142527  to be mainly crystalline, even though it is located in  regions with temperatures for which the crystallisation  timescale is too long to have occurred.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Therefore, they  considered various scenarios to form crystalline ice: 1)  heating by a strong accretion burst, 2) formation in the  inner disk and subsequent transport to the outer regions  by radiation pressure, or alternatively, and 3) the break-  up of larger icy bodies through collisions in which crys-  talline ice is preserved, again with subsequent transport  outwards by radiation pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' These authors consid-  ered the third scenario the most likely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0  140  HD142527  120  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5  ex  100  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0  inde  (Jy)  80  Im(refractive  Flux  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5  60  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0  40  WatericeT=50K  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5  20  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0  40  50  60  70  80  90  Wavelength [μm]Herbig Stars  27  The temperature at which water and CO freezes out  under typical disk conditions is 128-155 K and 23-28 K,  respectively (Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' By deriving the disk  temperature profile, the location of the ice line thus can  be determined, as Isella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2016) did for HD 163296  based on ALMA observations: for the midplane, Tm(r)  = 24K (r/100au)−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5 and for the surface, Ts(r, z) =  68K(  √  r2 + z2/100au)−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This would place the water  snow line at ∼ 3-4 au, too small to be resolved with  ALMA, and the CO ice line at ∼ 75-110 au, well within  reach with ALMA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Summary: Water ice has been detected at 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1 µm in  scattered light in a few Herbig stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Despite water ice  having strong features at 43 and 62 µm, the paucity  of observations and detections at those wavelengths re-  sults in a poor understanding of water ice in Herbig  disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' To detect the snow line, very high spatial resolu-  tion is required;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' so far water has not been detected in  a disk around a Herbig star with ALMA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Soon, JWST  will provide more sensitive measurements of water emis-  sion from disks, as MIRI (5-29 µm) covers the mid-IR  lines of water with excitation temperatures of a few  1000 K with a spectral resolution of 3000, so water lines  in Herbigs are expected to be detected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='8 Transition Disks to Debris disks  Disk type  Planet  Transitional  Debris  forming  Onset IR excess  NIR  MIR  FIR  Gas content  gas-rich  intermediate  gas-poor  ˙Macc (M⊙/yr)  7 ×10−7  2 ×10−8  –  LIR−mm/L∗  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='01  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='008(b)  F1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3mm (mJy)  500  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='7-7(a)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1-3(c)  CO 2-1 (Jy km/s)  2-50  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3(a)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='05-3(b)  Prototype  AB Aur  HD 141569A  Vega  Table 3 Comparison of the properties of circumstellar disks  at different evolutionary stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Listed are typical values, for  detected sources - many are not detected, especially the debris  disks in CO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' References: Meeus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2012) and (a)Di Folco  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2020);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (b)Hughes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2018), (c)Mo´or et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  CO and mm fluxes are normalised to a distance of 140 pc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Disks evolve from a massive primordial gas-rich disk  into a gas-poor debris disk, after passing through the  transition disk phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The definition of a “transition”  disk is varied in the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This term is variously  used to define disks whose near-IR excess is smaller  than the median among disks in Taurus (Calvet et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2005), disks possessing a cavity (Espaillat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2014),  and disks whose SED reveals no NIR excess and a signif-  icant excess at wavelengths beyond 10µm (Strom et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  1989).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In this review, we adopt the latter definition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The  lack of a NIR excess can be attributed to the depletion  of small grains in the inner disk (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', Strom et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  1989), creating a cavity in the disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This can be caused  by clearing by a giant planet, but other scenarios, such  as grain growth or photo-evaporation might also con-  tribute (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Armitage, 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In Table 3, we compare  the main properties of planet forming, transitional and  debris disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 17 SED of the transition disk HD 141569A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The excess  in the NIR is absent, and only starts beyond 5 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A survey of sub-mm emission for debris disks in  combination with a literature compilation shows that  the dust mass in debris disks is lower by about two  orders of magnitude (adopting a constant dust opac-  ity and representative dust temperatures, Pani´c et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, there is some overlap between primor-  dial disks and debris disks in the age range of a few Myr  to 20 Myr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A prime example of a transition disk is the 9 ± 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5  Myr A0 star HD 141569A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The infrared excess emerges  near 5 µm (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 17), and its fractional IR luminosity is  at least a factor 10 smaller than that of a typical Herbig  Ae star (Pascual et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The Hα emission line is  double peaked and the accretion rate is 2×10−8M⊙yr−1  (Fairlamb et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The presence of warm molecu-  lar gas was identified from ro-vibrational CO emission  (Brittain and Rettig, 2002) and the presence of cool  molecular gas was identified from rotational CO emis-  sion (Zuckerman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The presence of gas in  the disk is further confirmed through emission lines of  [OI] and [CII] in the far-IR (Thi, 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Di Folco et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2020) compared spatially resolved  images of CO emission and mm continuum acquired  with ALMA with resolved scattered light imagery ac-  quired with the Spectro-Polarimetric High-contrast Ex-  oplanet REsearch (SPHERE) on the VLT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They found  28  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  large differences in the radial distribution of the ma-  terial probed by these observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The mm thermal  continuum extends to ∼250 au while the disk is de-  tected out to ∼400 au in scattered light, where several  rings are seen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The CO gas was only detected out to  the distance of the mm continuum (250 au).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The flux  of these pure rotational lines can be converted to a total  gas mass of ∼ 70M⊕ (∼2×10−4 M⊙), on the lower end  for Herbig stars, but 10 times higher than the most gas-  rich debris disk known to date (Mo´or et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Cu-  riously, with the disk mass inferred from the CO lines,  the stellar accretion rate could only be sustained for  a few thousand years, suggesting that either the CO is  severely depleted or the inference of the stellar accretion  rate inferred from the veiling of the Balmer continuum  is overestimated (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Summary: A transition disk is a disk that is in transi-  tion between the protoplanetary and debris phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In  those disks, the infrared excess starts in the MIR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Gas  is still present in these disks and the stars accrete.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The  total IR luminosity, CO luminosity and mm flux is in  between that of Herbigs and debris disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='9 Detailed disk morphology  The MIR image of HD 97048 taken by Lagage et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  (2006) revealed for the first time a strongly flaring disk  surface through the emission of PAHs located in the  disk surface where they are transiently heated by stel-  lar UV photons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This flaring surface was later confirmed  with NIR scattered light observations (Ginski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' On the other hand, under the assumption of  optically thin emission, the surface density profile of  the large grains can be derived from mm observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  ALMA is perfectly suited for this purpose, as it traces  the thermal emission of cold mm-sized dust grains with  high spatial resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ALMA uncovered several large  (> 10 au) cavities in the dust continuum, the largest  140 au- seen in HD 142527 (Perez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2015), and  80 au in HD 34282 (van der Plas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2017a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Sub-  sequent progress in observational techniques at both  shorter and longer wavelengths (increased sensitivity  and spatial resolution) led to the discovery of substruc-  tures in the disks, as will be discussed below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' But first  we will summarize what is expected from theoretical  disk models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1 Theoretical predictions for disk substructure  In a continuous disk, large mm-sized grains are ex-  pected to spiral inwards as they experience a headwind  due to the surrounding gas, making them lose angular  momentum, a process called radial drift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The smaller  micron-sized dust grains, on the other hand, are cou-  pled to the gas and do not experience such a headwind.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Grains can also spread outwards to redistribute the an-  gular momentum in the presence of (turbulent) viscos-  ity (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Birnstiel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Models predict that an embedded planet, brown  dwarf, or low-mass stellar companion can dynamically  clear its orbit and open a gap in a disk (Lin and Pa-  paloizou, 1979).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' When a planet opens a gap in the disk,  a local enhancement in gas pressure is created - a pos-  itive pressure gradient, trapping dust grains and thus  creating a region with low collisional velocities in which  the dust grains can grow more rapidly, as is illustrated  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 18 (Pinilla et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2012, 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Another scenario  to create a gap is a dead zone, a region with a low  ionization fraction, and by consequence a low turbu-  lence level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' At the edge of such a dead zone a pile-up  of material is expected, creating a gap in the disk (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Reg´aly et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' For both scenarios, the viscosity is  an important parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' "#$%&\'()#"*(  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 18 Gas surface density in function of distance, illustrat-  ing particle trapping in a disk, the result of pressure bumps  caused by a massive planet located at 10 au (Pinilla, private  communication).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The efficiency of dust trapping depends on the grain  size: larger grains are trapped in the pressure bump  while smaller grains migrate inward - a process referred  to as dust filtration (Rice et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2006, Zhu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  This can be verified with high spatial resolution obser-  vations: at mm wavelengths, tracing the larger grains,  one would observe a ring-like structure with a large gap,  while in the NIR scattered light, tracing smaller grains,  this gap would either be smaller or even non-existent  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' de Juan Ovelar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The width of the  ring that is induced by a massive planet through pres-  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0  Gap opened by  a massive planet  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='8  negative  pressure  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6  gradient  M  positive  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4  pressure  gradient  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0Herbig Stars  29  sure bumps will depend on the disk and stellar mass,  as well as the location of the planet and the viscosity  parameter α (Pinilla et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  This process of dust filtration was confirmed by ob-  servations: the cavity size seen in NIR scattered light  is often smaller than that in the mm, for instance for  HD 135344B ∼ 28 au in the NIR versus ∼ 46 au at mm  wavelengths (Garufi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2013, Muto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' To  match the observations, Dong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2012) used a disk  model where inside the cavity, the surface density pro-  file of the small grains is flat and can reproduce the  observed NIR excess, while the larger dust grains are  depleted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Zhu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2012) find that in the presence of a giant  planet, grains ≳ 10−100 µm are trapped in the pressure  bump and this accounts for roughly 99% of the dust  mass (assuming a grain size distribution n(a) ∝ a−3 in  the outer disk, where grains have already grown to mm  sizes, only 1% of the dust mass is in small micron-sized  grains).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Thus the material that moves inward is heavily  depleted in solids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Therefore, the relative abundance of  refractory elements accreting onto the star should also  be depleted relative to volatile elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In the case of  Herbig stars with radiative exteriors, this could result in  a photospheric abundance pattern where refractory ele-  ments are depleted relative to volatile elements (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', the  λ Bo¨o phenomenon, Kama et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2015, see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Another feature that can be induced by a planet in  a disk are spiral arms (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', Kley and Nelson, 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  If the planet is sufficiently massive, spiral arms can be  observed in scattered light (planet to stellar mass ratio  q ≳ a few × 10−3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Dong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This is a kine-  matic effect that results in increasing the scale height  of the disk above the spiral arm such that the disk in-  tercepts more light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Furthermore, Dong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2016)  used hydrodynamical and radiative transfer simulations  to determine how the disk appearance depends on its  inclination and position angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' To summarize, a giant  planet cannot only create a cavity but, with he right  parameters (α, h/r, Mplanet) also rings or spiral arms,  or simply cause asymmetries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Turning to the inner disk, we find a puffed-up inner  wall at the dust evaporation radius located behind an  optically thin gas-rich region (Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3, Natta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This model was further refined by Isella and  Natta (2005), who realised that, as the dust evapora-  tion temperature is density dependent, and there is a  vertical density gradient in the disk, the inner wall will  be curved, rather than have a sharp edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Due to this  curvature, the NIR excess will weakly depend on the  inclination, while the observed shape will strongly de-  pend on the inclination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Face-on disks will reveal rims  that appear axisymmetric, while inclined disks will re-  veal rims that appear elliptic, with one side brighter  than the other one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Furthermore, Kama et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2009)  showed that the rim morphology depends on the dust  grain size, composition and the inner disk surface den-  sity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  In the following sections we will discuss how obser-  vations compare with these predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' We will first  look at the outer regions of the disk and then continue  with the inner disk, before discussing the different sub-  structures seen in the disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2 Observations of the outer disk region  As we mentioned in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 4, the first time a disk was re-  solved was through mm interferometry (Mannings and  Sargent, 1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In a recent study, Stapper et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2022)  analyzed archival ALMA data of 36 Herbig stars within  450 pc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' For the disks with d < 225 pc, 15/25 ‘nearby’  disks are resolved, but this sample was likely biased to-  wards the brightest objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, given that there  are only 31 Herbig stars within 225 pc, we can conclude  that at least 50% of them are resolved, all of which show  substructure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Another way to obtain high spatial resolution is to  move to shorter wavelengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Optical and NIR images  trace light that is scattered off the disk surface by small,  submicron-sized dust grains, but the stellar brightness  limits how close to the star one can get (inner working  angle).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Instruments such as SPHERE and the Gemini  Planet Imager (GPI) use polarimetric differential imag-  ing (PDI) techniques to remove the light of the central  star and reveal the scattered light of the disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' What re-  mains is light polarized by the dust grains in the disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The inner working angle of PDI on 8m class telescopes  is typically 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1′′, or 15 au at a distance of 150 pc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A comparison between ALMA and SPHERE obser-  vations of the outer disk has shown that the large and  small grains are not always co-spatial, with the larger  grains being more radially confined than the smaller  ones (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' the GI star HD 97048, large grains seen up  to 350 au, small grains up to 640 au;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Walsh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  On the other hand, the small grains are more or less co-  spatial with the gas, indicating that they are dynami-  cally coupled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Another important result is that the extent of the  disk in the mm continuum is often much smaller than  that of the gas, derived from low-J pure rotational CO  transitions: e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 350 vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 750 au in HD 97048 (Walsh  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2016), and 375 vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 1000 au for HD 34282 (van  der Plas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2017a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' These results were confirmed in  a larger study (Taun, MSc 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The differences in disk sizes do not only depend on  the material being traced (large or small dust grains,  30  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  or gas), but also on the disk group considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Based  on SED modeling, Dominik et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2003) proposed that  GII disks are smaller than GI disks, an idea that now  can be tested as we can often obtain high enough spa-  tial resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Early on, GI sources were routinely re-  solved with ALMA, while the few GII sources observed  were either unresolved or small (< 100 au;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Walsh  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2016, van der Marel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Stapper et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  (2022) further showed that, on average, GII disks are  more compact than GI disks, although this trend is  mainly caused by 3 outliers (AB Aur, HD 97048 and  HD 142527;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 19), and bright disks such as the  GI source HD100546 (68% radius of 35 au) have similar  sizes as the GII disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 19 The dust radius at 68% of the light (ALMA band 6  or 7) versus stellar mass for stars with d < 225pc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The error  bars are indicated as well as the upper limits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The largest radii  are seen in GI sources, but many GI sources have similar sizes  as GII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Based on Stapper et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  In a study of Herbig disks with SPHERE, Garufi  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2017b) found that GII disks, when detected in  scattered light, are much fainter than GI disks which  are commonly detected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Also their spatial extent is dif-  ferent: disks around GI sources are detected out to dis-  tances of 100-600 au, while disks around GII sources  are usually smaller than 100 au.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Indeed, several nearby  (d≲ 200 pc) GII disks are not resolved at all, such  as HD 150193A (Garufi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2014), which is a bi-  nary with a nearby companion (a=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1′′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bouvier and  Corporon 2001) that likely has truncated the disk to  give it its compact appearance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, the disk of  HD 100453, a GI star, is also truncated by a companion  at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1′′ but here the companion is thought to give rise  to the observed spiral arms reaching out to 42 au (Wag-  ner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Similar behavior has been observed in  the MIR with 8m telescopes (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Honda et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  These differences can be attributed to larger gaps (> 5  au) and/or larger flaring angles in GI disks, while GII  disks are either small or self-shadowed (Garufi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2017b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  However, from a systematic comparison between ALMA  and SPHERE data, Garufi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2022) found that the  extent of GII disks in scattered light is much smaller  than that at mm wavelengths, due to the outer disk  only being partially illuminated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This is in stark con-  trast with the observations of GI disks, where the ex-  tent in scattered light is larger than that in the mm,  as seen in e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' HD 97048 (Walsh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This is  because GII disks are flat and/or self-shadowed, while  GI disks are flared, so that their disk surfaces can be  traced much further out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3 Observations of the inner disk region  In a pioneering study of TTSs and Herbig stars with  the IOTA interferometer, Monnier and Millan-Gabet  (2002) found a correlation between the ‘size of the in-  ner disk’, measured in the H- or K-band, and the stellar  luminosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They explained this finding with an inner  rim at the dust evaporation radius, located behind an  optically thin inner region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Later, Monnier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2005)  measured more Herbig disks in the K-band with the  Keck Interferometer and found sizes between 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='02 and  4 au, in agreement with emission at the dust evapora-  tion radius, and showed that, for spectral types A to  late B, the inner disk size can be related to the stellar  luminosity as R ∝ √L∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Another important clue about the inner disk region  came from studying the brightness variations of UXors  that show the blueing effect due to obscuration by dust  in the line of sight (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Dullemond et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  (2003) realized that the variability timescale of weeks  to months means that the obscuring cloud must be in  the inner disk, at the location of a puffed-up inner rim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  They also showed that this effect would only be seen  in GII disks, where the line of sight towards the inner  rim remains largely undisturbed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The blueing effect in  UXors is thus caused by the clumpy nature of the inner  disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Lazareff et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2017) observed 51 Herbig stars with  PIONIER, a NIR interferometric instrument that com-  bines the 4 VLT telescopes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They found that the in-  ner rims are smooth, radially extended, and consistent  with axisymmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, Kluska et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2020) fur-  ther studied the inner disk rim morphology with PI-  ONIER, reaching a spatial resolution of a few milli-  arcseconds, and found evidence for a non-axisymmetric  structure in 27% of the objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This could be due to  warping of the inner disk or instabilities at the inner  rim, potentially linked to the presence of a compan-  group I  HD142527  200  group II  ABAur  HD97048  150  100  50  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='50  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='75  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='00  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='25  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='50  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='75  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='00  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='25  M*(M。' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=')Herbig Stars  31  ion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MATISSE, also combining 4 telescopes but now  in the L, M and N band (Lopez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2022), uncov-  ered L′-band variable brightness asymmetries in the  disk of HD 163296 at scales < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3 au (Varga et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Such variations are also detected in the H and  K band, and persist over several years (GRAVITY Col-  laboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They reflect an orbiting, in-  homogeneous dust distribution in the innermost disk  regions, similar to what was already predicted from the  UX Ori-like brightness and color variations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4 Disk substructures  More detailed ALMA observations of disks with a cav-  ity reveal substructures (for an overview see Andrews,  2020, van der Marel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2021), some of which are  shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Multiple rings were found in e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  HD 169142 (Fedele et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2017) and HD 97048 (Walsh  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2016, van der Plas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2017b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Other objects,  such as HD 142527, show asymmetries and/or shadows,  which are referred to as horseshoes (Casassus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Finally, some objects show spiral arms: e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' AB  Aur (Tang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 20 ALMA continuum images illustrating the variety  in structure present in the Herbig disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The beam size is  indicated in the lower left.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The tickmarks go from -1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5′′ to  +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5′′for HD 169142, HD 163296 and MWC758, and from -  3′′ to +3′′for HD 142527.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Figure from van der Marel, private  communication, after van der Marel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2021)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2018) created a 2-D hydrodynamical  gas + dust model grid to study the effect the disk pa-  rameters viscosity, scale height and planet mass have  on the presence of gaps in the disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' From a compari-  son with the DSHARP ALMA survey (Andrews et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2018b), they deduced that the observed disk gaps could  be caused by planets located beyond 10 au with masses  between that of Neptune and Jupiter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' More massive  planets, the super-Jupiters, are capable of carving out  larger (> 20 au) cavities in a disk, as shown by hydro-  dynamical modelling of PDS 70 (Muley et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  With more and more objects being observed with  ALMA, a reflection on the methods used for interpreta-  tion is needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kim et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2019) performed a synthetic  analysis to determine the best set of ALMA bands to  derive the dust properties of the T Tauri star TW Hya  and concluded that, in order to constrain the tempera-  ture profile properly, several ALMA bands are needed,  preferably with the largest frequency intervals possi-  ble, and covering both optically thin and optically thick  emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Such an analysis likely also applies to Herbig  stars, meaning that the ALMA bands with which the  disk is observed should be carefully selected to include  frequencies that trace both optically thin and optically  thick emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='7  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6  13  24  47  9  100  150  200  250  300  260  240  220  200  180  160  140  50  0  50  100  150  140  120  100  80  60  40  20  200  0  200  400  600  800  1000  800  700  600  500  400  300  200  100  0  300  350  400  450  500  550  600  650  650  600  550  500  450  400  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='7  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6  13  24  47  9  100  150  200  250  300  260  240  220  200  180  160  140  50  0  50  100  150  140  120  100  80  60  40  20  200  0  200  400  600  800  1000  800  700  600  500  400  300  200  100  0  300  350  400  450  500  550  600  650  650  600  550  500  450  400  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='7  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6  13  24  47  9  100  150  200  250  300  260  240  220  200  180  160  140  50  0  50  100  150  140  120  100  80  60  40  20  200  0  200  400  600  800  1000  800  700  600  500  400  300  200  100  0  300  350  400  450  500  550  600  650  650  600  550  500  450  400  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='7  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6  13  24  47  9  100  150  200  250  300  260  240  220  200  180  160  140  50  0  50  100  150  140  120  100  80  60  40  20  200  0  200  400  600  800  1000  800  700  600  500  400  300  200  100  0  300  350  400  450  500  550  600  650  650  600  550  500  450  400  HD135344B  HD100453  HD142527  HD97048  20 au  20 au  20 au  20 au  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 21 Key examples of disks observed with SPHERE in  PDI: spiral arms (HD 135344B and HD 100453), a large cav-  ity (HD 142527) and rings (HD 97048).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Note the large dif-  ferences in scale between the different panels: HD 100453 is  much smaller than HD 142527 and would fit 3-4 times in-  side its cavity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Garufi, private communication, after Garufi  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2017a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Scattered-light observations probe small grains and  thus can be used to constrain the flaring surface of  a disk as was done for HD 100546 (Avenhaus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  HD169142  HD163296  +  HD142527  MWC75832  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  2014, Stolker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2016) and HD 97048 (Ginski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Large scattered light surveys of protoplanetary  disks were made with GPI on Gemini South (Macintosh  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2008), High-Contrast Coronographic Imager for  Adaptive Optics (HiCiAO) on Subaru (Tamura, 2009)  and SPHERE on the VLT (Garufi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2017b), uncov-  ering a wide variety in disk substructures (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 21).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Spirals were seen in e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' HD 135344B (Muto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2012, Garufi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2013) and HD 36112 (MWC758;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Grady et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2013, Benisty et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2015), while rings  were found in e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' HD 169142 (Quanz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2013b)  and HD 97048 (Ginski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Other disks, such  as those around AB Aur (Hashimoto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2011) and  HD 142527 (Avenhaus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2014) show large, asym-  metric structures that could be seen as parts of spiral  arms or even rings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Indeed, Dong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2016) studied  the effect the inclination and position angle (PA) of the  disk has on its observed appearance, and found that a  disk with 2 spiral arms might be masked as an asym-  metric structure with either only one trailing arm, or  two arms on the same side of the star, possibly wind-  ing in different directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The interpretation of inclined  disks should, therefore, take into account this masking  effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Garufi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2018) organized the disks according  to their appearance in scattered light and found that  bright GI disks show spirals, rings, and bright rims at  the edge of a cavity, while other disks (mainly GII)  are faint and/or compact and show no such features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  They related the disk features with the NIR excess, and  found that sources with spirals or shadows have a high  NIR excess, while sources with rings show a low NIR  excess.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Sources with a GII disk have an intermediate  NIR excess.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The high NIR excess could be attributed to  the presence of a massive (≥ 1MJup) planet perturbing  the orientation and scale height of the inner disk and  finally causing spiral waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Bohn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2022) compared the inclination of the  inner (< 1 au) and outer (> 10 au) disks as derived from  VLTI/GRAVITY and ALMA (CO) observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' When  the inner and outer disks are misaligned, it is expected  that the inner disk will cast a shadow on the outer  disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' For those 3 GI sources where misalignment was  observed, Bohn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2022) predicted the location of  the shadow, and found this to agree well with scattered  light observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  It is surprising to see that the substructures derived  from scattered light and thermal emission do not al-  ways coincide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' For instance, HD 100453 shows spirals in  scattered light, but only a ring disk in thermal emission  (Wagner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2015, van der Plas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In gen-  eral, spirals are more often detected in scattered light  than in thermal emission, indicating that the micron-  sized grains experience more the effect of density waves  in the disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' For example, HD 163296 has an SED that  places it at the boundary of GI and GII disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Muro-  Arena et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2018) found that, while the mm contin-  uum data show several rings, scattered light images  only trace the innermost ring, leading the authors to  conclude that the outer disk is either more depleted of  small grains or more settled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, in multi-epoch  HST/STIS images, four rings were detected (Rich et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2020), with the fourth ring located at 330 au.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Similarly,  Tang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2017) found 2 CO spirals inside the large  mm cavity of AB Aur, that were confirmed in scattered  light (Boccaletti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, the spiral arms  that were detected in CO in the outer disk are not seen  in scattered light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Summary: The preferred scenario to form a gap in the  disk is a pressure bump, either caused by a planet or  a dead zone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' While the large particles are trapped, the  smaller particles can move inwards with the gas as they  are dynamically coupled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Dust filtration might lead to  selective accretion of gas rich in volatiles, so that the  stellar photosphere is depleted in refractory elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The inner rim is located at the dust evaporation  radius and has a puffed-up curved inner wall whose  properties depend on the grain size distribution and  inclination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Once a disk is resolved, it often shows some  substructure like rings, spirals or asymmetries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Small  micron-sized grains are found both closer to and further  from the star than the large mm-sized grains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' These  distinct locations can be explained by a combination  of radial drift (large grains) and dust filtration (small  grains).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' At mm wavelengths, some GI disks are very  large, while many other GI and GII disks overlap in size;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  however, not that many GII sources have been observed  with sufficient spatial resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In scattered light (op-  tical/NIR), GI disks are routinely resolved while GII  are either faint or undetected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Contrary to GI disks,  GII disks are smaller in scattered light than in mm  emission, due to self-shadowing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  To conclude this dust section, the combination of  improved spectral coverage in the IR with space-based  observatories and sub-arcsecond resolution imaging at  optical/NIR and mm wavelengths on the ground has  revolutionized our understanding of the dust disks sur-  rounding Herbig stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' It is clear that the IR-mm ex-  cess of Herbig stars arises from disks with remarkable  structures including gaps, rings, and spiral arms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' These  disks also have a rich mineralogy indicative of signifi-  cant dust processing and grain growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' There is strong  evidence that the differences between GI and GII disks  are tied to the presence of gaps in the disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' GI disks  are flaring and have large gaps, while GII disks appear  Herbig Stars  33  to be compact and/or shadowed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The old evolution-  ary scenario where disks evolve from GI to GII is not  consistent with later studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Instead, a large GII disk  where no or only a small gap is present might open  up a larger gap and become a GI disk while small GII  disks may stay small and gradually lose their content as  they evolve into debris disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Alternative, GI and GII  disks may follow independent evolutionary paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The  extent to which these differences reflect differences in  the early evolution of the circumstellar disk and enve-  lope or interactions with massive companions remains  unclear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Even though the gaps in GI disks are com-  monly attributed to planets, the influence that stellar  and planetary companions have on the evolution of the  disk remains an important open question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  5 GAS IN DISKS AROUND HERBIG STARS  Early interferometric observations with OVRO of 12CO  J = 2 − 1 revealed a rotating disk of gas around the  star MWC 480 (Mannings et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Several pioneer-  ing surveys have since then systematically targeted the  intrinsically strong CO (sub-)mm lines as key tracers  for the disk bulk gas content (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Zuckerman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  1995, Dent et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2005, Hales et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2014) and find  that disks around many young Herbig stars contain  traceable amounts of cold (a few 10 K) gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Due to  the large range of temperatures present — a couple of  1000 K in the inner disk (< few au) to a few 10 K  in the outer disk (≳ 100 au) — the emission of gas  is traced over a wide range of wavelengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The cold  outer disk is mostly traced at far-IR to mm wavelengths  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' low rotational lines of CO), while the inner disk  is traced by near- to MIR wavelengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Due to their  brightness and warm temperatures (stellar luminosities  heating the disk range from a few to a few 10 L⊙),  Herbig disks are generally easier to detect and to spa-  tially resolve compared to T Tauri disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This enables  studying many processes related to disk evolution and  planet formation in more detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The main drawback  here is the often small sample sizes and less well con-  strained ages of these objects (Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In the follow-  ing, we summarize our current understanding of the  physics, chemistry and physical processes pertaining to  the gas inside these disks that we obtained based on  multi-wavelengths observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1 How and when do Herbig disks lose their gas?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  As summarized in section 4, the classification scheme of  Herbigs is largely based on the distribution of dust in  the disk, however, gas comprises 99% of the disk mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Ideally, the evolutionary state of Herbig disks would be  informed by the evolution of the gas mass of the disk  as they evolve from gas rich accretion disks to dusty  debris disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Several methods using far-IR and sub-mm line emis-  sion have been proposed to study disk gas masses di-  rectly: (1) The CO sub-mm line emission (Thi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2001), (2) the [O i] 63 µm line together with the CO  sub-mm line (Kamp et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2011), (3) HD lines (Bergin  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2013), and (4) the CO isotopologue sub-mm lines  (Williams and Best, 2014, Miotello et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Below,  we present an overview of the results from such obser-  vational attempts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Dent et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2005) conducted a northern survey of  the 12CO J = 3−2 line in bright Herbig disks using the  JCMT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Following this up, Hales et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2014) carried  out an APEX/ASTE survey targeting the 12CO J =  3 − 2 line in 52 southern Herbig disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They report  that ∼ 45 % of the IR bright disks (LIR/L∗ ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='01) —  21 out of 46 in the combined sample — are not de-  tected in CO, the pre-ALMA, sensitivity limit being  ∼ 104 Jy km/s pc2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' At the faint end of IR excesses this  has been continued using ALMA by Mo´or et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2017)  to detect the 12CO J = 2 − 1 line in young A-type  debris disks (10 − 50 Myr);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' they find that CO emission  does not correlate with IR excess (104−106 Jy km/s pc2  for objects with LIR/L∗ <0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='01).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' P´ericaud et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2017)  did a similar study focusing on debris disks around  A-type stars younger than 100 Myr using APEX and  IRAM, targeting the 12CO J = 2 − 1 and 3 − 2 lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Folding in literature data on T Tauri and Herbig disks,  they identify a general correlation between CO line flux  and mm(sub-mm) continuum flux;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' however, this corre-  lation is strongly driven by the T Tauri disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They also  find a subclass of disks around A-type stars which have  CO line fluxes brighter than the above correlation pre-  dicts based on their sub-mm continuum flux and termed  them “hybrid” disks (HIP 76310, HIP 84881, HD 21997,  HD 131835, 49 Cet, HD 141569).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Some of these sources  show indications of inner dust cavities (a few to several  10 au) (HIP 76310, HIP 84881, HD 21997, HD 131835,  Lieman-Sifry et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2016, K´osp´al et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2013, Hung  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2015) and/or rings (HD 141569, 49 Cet, Augereau  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 1999, Wahhaj et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2007, Biller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  This places them into the category of transitional disks  (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='8), but the two classifications (based on ei-  ther dust or gas observables) do not necessarily agree  for all objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Williams and Best (2014) proposed to combine the  two less abundant isotopologues 13CO and C18O to es-  timate disk gas masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This method has been refined  using thermo-chemical disk models by Miotello et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  (2016) including isotope selective photodissociation for  34  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  the regime of TTauri and Herbig disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This technique  produces in general gas-to-dust mass ratios in disks  that are well below the canonical one of 100 (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ans-  dell et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2016, Miotello et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Since this result  is hard to reconcile with the estimated mass accretion  rates, carbon element depletion is often invoked as an  explanation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Thermo-chemical disk models have shown that the  [O i] 63 µm emission requires excitation temperatures of  several 10 K and typically originates from inside 300 au  (Kamp et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The [O i]/CO line ratio serves  here as a temperature proxy and the [O i] 63 µm line  emitting region shifts with disk mass, indicating that  the combination of the line ratio and the [O i] 63 µm  line flux could be a reliable tool to estimate the total  disk gas mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Meeus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2012) applied this method  to the GASPS5 sample of Herbig disks deriving disk  gas mass estimates in the range 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4 × 10−4 (HD 36112)  to 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5 × 10−2 M⊙ (HD 163296), spanning two orders  of magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, using the ages recently deter-  mined from Gaia DR2 (Vioque et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2018), there is no  clear trend of gas mass with age between 5 and 15 Myr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Likely other disk parameters, such as size play a more  dominant role.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' We will come back to this in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The lowest rotational lines of HD (J = 1 − 0 at  112 µm and J = 2 − 1 at 56 µm) have not been de-  tected with Herschel in the disks around Herbig stars  (Kama et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Upper limits on the HD J =1 − 0  line at this stage can only rule out very massive disks  (10−1 − 10−2 M⊙) around most sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Interestingly,  HD 163296 yields an HD upper gas mass limit of 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='7 ×  10−2 M⊙, compatible with the estimate based on [OI].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  For HD 163296, many alternative techniques have  been more recently applied to estimate the gas mass  (full thermo-chemical disk modeling, dust radial drift,  the very rare isotopologue 13C17O, Rab et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2020,  Woitke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2019a, Powell et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2019, Booth et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2019), all of them now converging on a fairly high disk  gas mass of ∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2 M⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kamp et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2011) have shown  from thermo-chemical modeling that optical depth ef-  fects turn disk gas mass estimates via the [O i]/CO  method into lower limits for gas masses larger than  10−3 M⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' So, the [O i]/CO disk gas mass lower esti-  mate is consistent with the more recent studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The  HD upper gas mass limit is lower than many of the esti-  mates derived using other techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Since the method  of Powell et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2019) using dust radial drift6 is inde-  5 GASPS (Gas Survey of Protoplanetary Systems has been  an Open Time Herschel Key Program led by Bill Dent (Dent  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2013)  6 This method uses dust radial drift in a gas-rich disk to  estimate gas masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' To first order, the spatial extent of the  dust emission at different sub-mm wavelength is affected by  the efficiency of dust drift and hence amount of gas in the  pendent of element abundances, the most probable rea-  son for this gas mass discrepancy could be in the gas  temperatures underlying the HD estimate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The conver-  sion from line flux to gas mass is very sensitive to the  gas temperature (Bergin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2013) and if 2D thermo-  chemical disk models are used, the model gas temper-  ature depends strongly on the properties of the dust  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', grain size distribution, composition, and settling).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The masses of disks are in tension with the stel-  lar accretion rates around Herbig stars (Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The  typical accretion rate of Herbig stars is ∼ a few ×10−7  M⊙yr−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' For such rates to be sustained for ∼1 Myr  would require disk masses approaching 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1M⋆ - much  higher than the typical disk masses inferred from the  techniques described above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Summary: Gas masses in Herbig disks (5 − 15 Myr)  span about three orders of magnitude with no clear  trend with age.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' There is a clear correlation between the  strength of sub-mm gas emission and sub-mm contin-  uum emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This correlation becomes less clear for  older objects (≫ 10 Myr), where in several objects sig-  nificant levels of CO gas are detected while the dust  is clearly of secondary (debris) origin (termed “hybrid”  disks or “gas-rich” debris disks).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' So, while continuum  observations seem to indicate a clear dichotomy be-  tween primordial and debris dust masses around ∼ 5−  20 Myr (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='8), it is not clear that the gas follows  a similar evolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2 Turbulence in Herbig disks  The exquisite sensitivity and spectral resolution of ALMA  allows now the precise measurement of the width of  spectral lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' If the gas probed by ALMA is turbulent,  then the lines should be broader than predicted by the  sound speed of the gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Early pre-ALMA estimates of  gas turbulence were limited by spatial and spectral res-  olution as well as the S/N of the channel maps (Dartois  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2003, Pi´etu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2003, 2005, 2007, Hughes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ALMA has significantly improved our ability to  estimate the gas turbulence in the outer disk since its  high quality data sets (bright sources) allow the sepa-  ration of the front and back side of the disk and so a  better disentangling of gas temperature and turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Early measurements were strictly applicable only to the  outer disk (100 au scale), while ALMA can now also  probe regions closer to the star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Rosenfeld et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2013)  used ALMA science verification data to demonstrate  the high potential of the gain in spatial and spectral  disk;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' strictly, this works only for disks that do not show sub-  structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Herbig Stars  35  resolution;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' they demonstrate the presence of a vertical  temperature and radial pressure gradient for the disk  around HD 163296.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Estimates of gas turbulence in disks  keep pushing its upper limits to smaller values, typically  less than 5-10% of the sound speed at 30-few 100 au (see  Table 4 and references therein).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This has strong impli-  cations for the process of angular momentum transport  in these disk, since it implies very low α viscosity values  for the outer disk (α<10−2, Flaherty et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Another method for inferring supra-thermal line broad-  ening of gas is through spectral synthesis of the CO  overtone bandheads (Carr et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The rotational-  vibrational transitions of the R-branch grow closer to-  gether with increasing rotational level and eventually  pile-up at the blue-end of the spectrum before turn-  ing around moving to redder wavelengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This pile-up  is referred to as the bandhead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Because the transitions  near the bandhead are very closely spaced, the instrinsic  width of the lines affects the opacity of the bandhead  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', the shape of the lines determines the opacity of  the pseudo continuum).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Thus even without spectrally  resolving the individual lines comprising the bandhead,  the intrinsic line broadening of the lines can be inferred  from the emergent flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Because of the large number  of transitions involved, the temperature of the gas is  well constrained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Further, the shape of the bandhead  is determined by the bulk motion of the gas allowing  for the determination of the radial extent of the emis-  sion if the stellar mass and disk inclination are known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  This method has been used to measure the turbulent  velocity of gas in the disk atmosphere within the inner  ∼1 au of intermediate mass stars such as WL 16 (where  the turbulent broadening is twice the sound speed;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Na-  jita et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 1996), SVS 13 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5-3 times the sound speed;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Carr et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2004), V1331 Cyg (∼ the sound speed;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Na-  jita et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2009, Doppmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2011), and HD 101412  (≲ the sound speed;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Adams et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, there  is no direct tension with the (sub)mm measurements  that probe the turbulence in the disk at much larger  distances from the star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  There are alternative methods suggested to esti-  mate the gas turbulence in disks around Herbig stars  and to understand the underlying driving mechanism:  smoothed out snow lines (concentration gradients, Owen,  2014), dust settling (mm-dust grains confined to a geo-  metrically thin midplane, Pinte et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2016), vortices in  disks (stability, Zhu and Stone, 2014), planet induced  structures (morphology, de Juan Ovelar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2016),  and outer gas disk shape (sharpness, Facchini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' SED shapes contain information on dust settling,  though the problem of fitting them is highly degener-  ate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mulders and Dominik (2012) show that the median  SED shapes of brown dwarf, T Tauri and Herbig disks  are consistent with a low turbulent α value, not depend-  ing on the (sub-)stellar mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Comparing ALMA dust  and gas observations with 2D hydrodynamical mod-  els shows that the turbulence affects the sharpness of  planet-induced gaps, ring-gap separation, and the gas-  to-dust mass ratio inside (Lin and Papaloizou, 1993,  Long et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2018, Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' For HD 163296,  Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2018) deduce a smaller α in the inner disk  (∼60 au) compared to the outer disk (>100 au);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' how-  ever, α stays well below 10−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Given the observed mass accretion rates (Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4),  it remains unclear what the underlying driving mecha-  nism is and if the turbulence depends strongly on radial  distance from the star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Non-ideal MHD effects causing  disk winds could offer a solution here (Bai, 2013, Ri-  ols and Lesur, 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In their review, Hartmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  (2016) suggested that different mechanisms might cause  turbulence in the different disk regions (thermally and  non-thermally activated MRI, winds, non-ideal MHD  effects).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Summary: ALMA has enabled the measurements on  non-thermal broadening of gas lines which place upper  limits on the turbulence of the gas in the outer disk at  ≲ 5−10% of the sound speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' For a hand full of objects  with CO bandhead emission, high resolution NIR spec-  troscopy has been used to measure non-thermal broad-  ening of the gas in the innermost disk that is compa-  rable to the sound speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Other observational evidence  points to minimal turbulence in the outer disk includ-  ing smoothed out snow lines, dust settling, vorticies in  disks, planet induced structures, and the sharpness of  the boundary of the outer disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3 Are Herbig disk surfaces flaring or flat?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Scattered light observations of small dust grains can  trace the shape of the disk surface (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Direct  observations of gas emission can also reveal how the  stellar luminosity is reprocessed by the disk and hence  provide indirect evidence of the degree to which the disk  surface is flaring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  An example is the Herschel survey of the [O i] 63 µm  line (Open Time Key Program GASPS, Dent et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Comparing the data with a large grid of thermo-  chemical disk models (Woitke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2010, Kamp et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2011), Pinte et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2010) show that the brightness of  this cooling line agrees with a stellar UV heating mech-  anism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Meeus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2012) confirm this by demonstrat-  ing a clear correlation between the UV stellar flux and  the line luminosity for the GASPS sample of 20 Herbig  disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, they do not find a correlation between  the SED slope (IR-mm) and the strength of the [O i]  36  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Table 4 Overview of turbulence measurements for Herbig Ae disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  object  tracer  method  vturb [cs]  reference  inner disk (few au)  V1331 Cyg  NIR CO bandhead and water  spectrum  ∼ 1  Najita et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2009)  HD 101412  NIR CO bandhead and water  spectrum  ∼ 1  Adams et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2019)  outer disk  HD 34282  CO sub-mm isotopologues  visibilities  < 1  Pi´etu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2003, 2005, 2007)  AB Aur  MWC 480  HD 163296  CO sub-mm  channel maps  ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4  Hughes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2011)  HD 163296  CO sub-mm isotopologues  channel maps  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='03  Flaherty et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2015)  HD 163296  DCO+  channel maps  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='04  Flaherty et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2017)  MWC 480  CO sub-mm  channel maps  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='08  Flaherty et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2020)  cooling line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In contrast, the CO high-J rotational lines  are only detected in disks that show a shallower SED  slope (group I, Meeus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 4  clarifies that the SED slope is not necessarily a direct  reflection of the amount of disk flaring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The CO ladders  for the few GI Herbig disks that show line detections  with sufficient coverage in J stay flat between J = 10  and 20 (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 22).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' According to thermo-chemical  models, this is a trend seen in moderate to strongly  flaring disks such that β ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='15, where β is the power  law exponent of the radial dependence of the gas scale  height (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', H(r) ∝ rβ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Woitke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The [O i] fine structure lines react strongly to the  amount of disk flaring (Woitke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2010), but sev-  eral other parameters play an important role as well  such as inner gaps, dust settling and the stellar heating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The CO ladder also reacts to flaring (Bruderer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2012, Fedele et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2016) — the ladder drops steeply  beyond J = 10 for flat disks due to the altered gas  temperature profile — and here the gas-to-dust mass  ratio is the most cofounding other variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The Her-  big disks differ substantially in their geometry, making  a simple ”grid” approach for the interpretation of ob-  servational data rather difficult.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Recently, the DIANA  project (DIsc ANAlysis;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Woitke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2019a) mod-  eled six of these Herbig disks consistently using multi-  wavelength dust and gas observations with a unified  thermo-chemical modeling approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The observational  data includes the far-IR [O i] and CO rotational lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  For all except one of the disks (AB Aur), they find the  need for a flared outer gas disk 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='19≥β ≥1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='07, a range  that is well below the maximum Chiang and Goldreich  solution (β =9/7, Chiang and Goldreich, 1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The geometry of the upper tenuous layers of the in-  ner disk is much better probed using lines that predom-  inantly originate there, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' the forbidden [O i] 6300 ˚A  line (Finkenzeller, 1985, Acke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2005, van der Plas  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The excitation mechanism for the line can  be thermal (gas temperature of a few 1000 K or non-  thermal (photodissociation of OH, St¨orzer and Hollen-  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 22 Compiled CO ladders for six Herbig disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Over-  plotted are the normalized modelled CO ladders for a typical  Herbig disk by Fedele et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The three lines repre-  sent disks with different flaring angles, β = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='05 (red), 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='15  (green), 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='25 (blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The models have been normalized to the observed J=10 − 9  line flux;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' for IRS48 we used the first detected J line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  bach, 2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Due to the limited spectral resolution in  earlier work, the origin of this line emission remained  disputed: infall, wind or disk origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Acke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2005)  found that the majority of Herbig disks show narrow  symmetric profiles (FWHM∼ 50 km/s), with the line  profiles observed towards GII sources being on average  ∼ 20 km/s broader than the line profiles observed to-  2  2  0  AB Aur  HD97048  1  0  10  20  30  40  0  10  20  30  40  Jup  Jup  2  2  1  0  0  HD100546  HD163296  0  10  20  30  40  0  10  20  30  40  Jup  2  2  山  0  0  HD169142  IRS48  1  0  10  20  30  40  0  10  20  30  40  Jup  JupHerbig Stars  37  −40  −20  0  20  40  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3  −40  −20  0  20  40  Velocity (km s−1)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3  Normalized Flux  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 23 Comparison of the [O i] 6300 ˚A(black), v = 1−0 OH  P4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5 (blue) and the v = 1 − 0 P26 CO (red) line profiles from  the disk around HD 100546.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  ward GI sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Also, the detection rate of this line is  much lower in GII disks than in GI disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Several of the  line profiles display the characteristic double peak sug-  gesting an origin within a rotating disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' van der Plas  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2008) investigate the radial intensity profiles of  the [O i] line and find that it can be related to the in-  ner disk geometry (puffed up regions casting shadows  on regions further out).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Interestingly, HD 101412 shows  two emission peaks, possibly indicating that there is a  second ’puffed’ up region at larger distances (few au);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  this is a feature seen in hydrostatic disk models (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Woitke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2009, Min et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2009, Meijerink et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2012, a second shadow for the tenuous surface layers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  In some cases (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' the Herbig Be star MWC 147, Bag-  noli et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2010), the line emission could even originate  from inside the dust sublimation radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The OH P4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5 doublet (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='934 µm) was been detected  in 4/5 GI disks and 0/6 GII disks by Fedele et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  (2011), sometimes showing very complex profiles sug-  gesting multiple radial emission zones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  (2016) detected the OH P4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5 doublet in about 50% of  the Herbig disks in their sample;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' again, the detection  rate is much higher for the GI disks (61%) than GII  disks (25%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The line profile of the high J CO line and  the OH doublet are consistent (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 23).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The fact  that OH is more readily observed among GI disks indi-  cates that that OH photodissociation could contribute  to the excitation of the [O i] 6300 ˚A line (Fedele et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Also [Ne ii] emission at 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='81 µm is often used to  probe jets, outflows and disk winds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Baldovin-Saavedra  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2012) detected this line for the first time in a  disk around a Herbig Be star (V892 Tau);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' its centrally  peaked narrow line profile is consistent with a photo-  evaporative wind.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Since this line requires the presence  of X-rays, most of the work so far has been focused  on T Tauri disks (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pascucci et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2011, Baldovin-  Saavedra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2012, Sacco et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A more sys-  tematic study combining high spectral resolution (3 −  10 km/s) optical ([O i] 6300 ˚A) and IR spectra (OH and  CO ro-vib, like shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 23) with dust interferom-  etry could allow a detailed study of the inner disk gas  and dust geometry and the potential existence of weak  disk winds, something that has been piloted by Fedele  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2008) for three sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Summary: Gas studies suggest that the outer disks of  Herbigs are moderately flaring (below the theoretical  maximum of 9/7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, the inner disks show more  complex geometries required to interpret gas line pro-  files, such as shadows and disk winds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A systematic  study of combined near-IR dust and gas observations  for a large sample of Herbig disks would help here to  disentangle the processes shaping the inner disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4 Gas temperatures and the position of icelines  The thermal structure of the disks is a key element  in understanding planet formation as it determines the  stability of disks (Toomre Q parameter7) as well as the  composition of the material that is forming the plan-  ets (icelines).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The midplane of Herbig disks is typically  optically thick, in the inner disk (<30 au) often up to  sub-mm wavelengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Figure 24 illustrates how we can  either use gas emission lines to infer radial and vertical  temperature profiles of disks or revert to indirect tracers  such as the spatial distribution of molecules associated  with specific icelines (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' N2H+, DCO+, water).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The temperature profiles for the gas can be de-  rived from molecular emission line studies in several  ways: (1) interferometric gas line observation (spatial  and spectral resolution), (2) from a suite of gas line  profiles (spectral resolution), (3) from a suite of un-  resolved emission line fluxes from lines with different  excitation temperatures (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' CO ladder).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' We discuss  each of these in the following and discuss to which ex-  tent the conclusions from them agree and also how they  compare to the dust temperature studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, as  a matter of fact, the continuum optical depth at any  wavelength limits the vertical depth down to which we  can probe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' For the inner disk (< 30 au), this limits the  7 This parameter depends on distance from the star r and  is defined as Q(r) = cs(r)Ω/πGΣg(r), with cs the sound  speed, Ω the angular velocity, G the gravitational constant  and Σg the disks gas mass surface density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  38  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 24 Schematic of various methods to assess the disk gas  temperature profiles and icelines (radially and vertically).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In-  dicated are the key molecular tracers used to derive the tem-  perature profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Arrows indicate how the line emission re-  gion shifts with increasing rotational quantum number J or  decreasing Einstein coefficient Aij.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  information we can get since these regions are often op-  tically thick even at sub-mm wavelengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Exceptions  are disks where this region has been partly cleared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Interferometric gas line observations Pi´etu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2007)  derived gas temperature profiles using IRAM/PdB in-  terferometric data for a suite of CO and HCO+ lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Fitting visibilities with simple power law disk models  (T ∝rq) for MWC 480, they find gas temperature pro-  files of the molecular emitting region with power law  exponents of q = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='65 for 12CO and shallower (q =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='37 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='28) for 13CO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They also note a clear vertical  temperature gradient of several 10 K based on 12CO  J = 2 − 1, 13CO J = 2 − 1 and J = 1 − 0 lines which  originate from different heights in the disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Such values  agree quite well with typical thermo-chemical disk mod-  els (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 25, showing extracted radial temperature pro-  files from the MWC 480 model, Woitke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2019a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Flaherty et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2015) follow a similar approach but  use a full 2D power-law disk model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They find fairly  shallow temperature gradients for all CO isotopologues  (q=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='216−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='278) in the disk around HD 163296, while  Isella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2016) find a steeper profile (q=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6) for the  molecular layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, these results depend to some  extent on the assumed model parametrization;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' for ex-  ample Flaherty et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2015) assume the same power law  exponent for the molecular layer and midplane temper-  atures and we know that the dust distribution in this  disk shows prominent rings inside 200 au and thus devi-  ates from a simple power law.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' So, there is a strong push  to develop methods that are independent of model as-  sumptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Channel maps with high spatial and spectral resolu-  tion provide a promising alternative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They can be used  to reconstruct the temperature profile directly from the  CO brightness temperature if the dust is optically thin  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 25 Gas temperature profile in a typical Herbig disk  model extracted at three different heights in the disk (solid  lines).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Dashed lines show the corresponding dust temperature  profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Black dotted lines show two typical power laws with  exponents -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6 and -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  (assuming optically thick line emission, Pinte et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2018a, Dullemond et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' If substantial CO freeze-  out occurs, this method measures the temperature of  the CO ice surface, otherwise, it can be used to estimate  the midplane temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' For HD 163296, this method  finds a very shallow temperature gradient (q = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  There is considerable agreement for the midplane tem-  perature profiles for HD 163296 with different methods  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' estimated temperatures at 100-150 au differ by less  than 3 K), but the underlying assumptions need to be  evaluated on a case-by-case basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' For example, detailed  thermo-chemical models matching the DSHARP data  (dust and gas) of HD 163296 show significant freeze-out  of CO in the midplane at 100-150 au (Rab et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Gas line profiles Fedele et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2013) use HD 100546 to  show that the CO line profiles of CO J =16−15, 10−9  (Herschel/HIFI) and 3−2 (APEX) become successively  narrower, thus confirming the shift of their radial ori-  gin to increasingly larger distance from the star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This  method had already been suggested by Bruderer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  (2012) based on thermo-chemical disk modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The  resulting best fit temperature profile from simple disk  power law models has a radial slope of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='85 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1 (be-  tween ∼ 30 and 300 au), steeper than that found for  MWC 480 and also steeper than what is typically found  for the dust (Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Emission line flux ladder In the case of spectrally and  spatially unresolved lines, we use the fact that molec-  ular emission lines trace the gas temperature in the  C0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' H20  C0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' H20  Aij  isotopologues  ices  N2H+  HCO+  150 K  20 K2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='8  z/r= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='30  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6  z/r= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='20  z/r= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='15  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2  人  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0  --0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0  log r [au]Herbig Stars  39  vertical layer and radial regime over which they emit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Interesting tracers in that context are molecules that  possess a suite of lines with a large range in excita-  tion energy and Einstein A coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The CO lad-  der, where the excitation energy (Tex) increases with  the rotational quantum number (Tex(J = 4) = 55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3 K  to Tex(J = 36) = 3669 K), scans the disk surface with  higher rotational lines originating ever closer to the star  (van der Wiel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2014, Fedele et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The  same holds for the series of OH doublets (Tex rang-  ing between 120 and 875 K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Also water lines span  a huge range of excitation conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The second di-  mension, the vertical depth, is probed by studying iso-  topologues (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 13CO, C17O, C18O, 13C17O), and/or  by choosing lines with low Einstein A coefficients (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  water;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Notsu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This method to extract radial  temperature profiles works particularly well at mid- to  far-IR wavelengths and has been discussed by Brud-  erer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2012), van der Wiel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2014) based  on Herschel/PACS and SPIRE CO ladders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bruderer  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2012) demonstrate that the gas temperature in  the disk surface (atmosphere) has to be larger than  that of the dust in order to explain the CO ladder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  This is confirmation of earlier work, both theory (Kamp  and Dullemond, 2004, Jonkheid et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2004) and obser-  vations (Carmona et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2008, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' H2 MIR observa-  tions).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Fedele et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2016) applied simple power law  and thermo-chemical disk models to FIR data of four  Herbig disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The power law temperature gradients de-  rived from simple models fall in the range 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The  observed CO ladders stay flat in many cases out to high  rotational quantum numbers (J ∼16−20) (Meeus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2012, 2013, van der Wiel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2014, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 22), a be-  havior that requires a steep temperature gradient in the  power law disk models, something that can be achieved  with a high flaring angle in the thermo-chemical disk  models (Fedele et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Icelines More indirectly, specific molecules are associ-  ated with specific phase transitions in the disk, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ice-  lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Even though they are pressure dependent, they  serve as important calibration points for the gas tem-  perature profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Water at the high pressure condi-  tions in the midplane freezes out at temperatures below  ∼150 K, and CO typically freezes out at around 20 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The term ‘iceline’ can be misleading because the phase  transition of a molecule does not occur at a single dis-  tance from the star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Rather it bends towards larger radii  as the density decreases towards the disk surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In ad-  dition, non-thermal desorption processes such as photo-  desorption and cosmic ray (CR) desorption cause the  iceline to eventually bend back towards the midplane  at larger radii where disks become more optically thin  to UV radiation (stellar and interstellar).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Icelines can be traced directly using the molecule  in question and spatially and/or spectrally resolving  its emission in optically thin lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Examples of this  are 13CO observations of HD 163296 (Qi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2011)  putting the CO iceline at 155 au and low Einstein A  water lines constraining the snowline in HD 163296 to  between 8 and 20 au (Notsu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This lat-  ter work modeled the water line emission to determine  which isotopes and transitions are most suited to deter-  mine the location of the water snowline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Unfortunately,  ALMA did not detect any of those selected transitions  in HD 163296, with 3σ upper limits for ortho-H16  2 O at  321 Ghz < 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3 × 10−21 W m−2, and for para-H18  2 O at  322 GHz < 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5 × 10−21 W m−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' So the water snow  line position remains difficult to measure even in the  brightest Herbig disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The water snowline can also be traced indirectly by  molecules that correlate with its location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Leemker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  (2021) studied the use of HCO+ as a chemical tracer of  the water snow line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The abundance of HCO+ and H2O  are anti-correlated due to the reaction HCO+ + H2O  → CO + H3O+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, they concluded that, due to  degeneracies complicating the interpretation, HCO+ is  not a good tracer of the snowline in Herbig disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Similarly, N2H+ and DCO+ trace the CO iceline  indirectly because both of these molecules are tightly  connected to the gas phase CO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' If CO is present, it will  compete with N2 in reactions with H+  3 , diminishing the  production of N2H+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' at the same time, N2H+ is also  destroyed in reactions with CO, leading to the forma-  tion of HCO+ (for a detailed discussion see van ’t Hoff  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A consequence of this is that HCO+ will  be abundant just above the CO iceline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The low tem-  peratures there (∼20 K) are conducive to deuteration,  which could result in DCO+ to peak in abundance just  above/inside of the CO iceline — a method that has  been applied earlier to pre-stellar cores (Caselli et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  1999, Pagani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Observing DCO+, Math-  ews et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2013) confirm the CO iceline location in  HD 163296 found by Qi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Summary: There is convincing evidence that the gas  temperatures in the disk atmosphere are higher than  the dust temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, our understanding of  the 2D temperature structure in Herbig disks remains  incomplete.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The resulting temperature profiles depend  strongly on which tracer and method is chosen to ex-  tract them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' HD 163296 is one of the disks that has been  studied using almost every available method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A trend  emerges from the observations that shows a very steep  radial temperature gradient for the uppermost layers  40  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  close to the central star (CO high rotational lines) and  a flattening of that gradient as one moves to tracers  that probe layers closer to the midplane and further  out (CO isotopologues).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This agrees qualitatively well  with 2D thermo-chemical disk models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The CO iceline  estimate from CO and DCO+ suggest a temperature of  ∼20 K at 155 au, which agrees very well with the mid-  plane temperature profiles derived from interferometric  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The snowline estimate from the ALMA water line  data suggests ∼150 K at 8-20 au, which is a higher tem-  perature than what is inferred from the extrapolation  of the midplane power law temperature profiles from  interferometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Given the intricate dust substructure  seen inside 50 au (Andrews et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2018b), such a sim-  ple extrapolation is however questionable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The presence  of gaps and rings will alter the midplane temperature  profile (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pinte et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2016, Rab et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5 The radial distribution of gas  In the context of planet formation, it is of immediate in-  terest how the gas mass is distributed within the disk,  especially in the planet forming regions inside 50 au.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  For the understanding of the mechanisms creating gaps  and rings observed in mm-sized dust, it is crucial to  know whether gas and dust are spatially related (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  whether dust gaps also imply gas gaps).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A key ques-  tion is how the gas in the inner disk evolves during the  planet formation era.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Does it follow the dust behavior  (gap/hole formation) or does it decouple from the dust?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Also, the outer edge of the gas potentially carries an im-  print of either viscous spreading or dynamic encounters  truncating the disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Studies of the CO ro-vibrational lines profiles show  that in many cases, the onset of CO emission coincides  with the dust inner radius (Goto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2006, Brittain  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2007, Salyk et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2009, Hein Bertelsen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2014, van der Plas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2015, Hein Bertelsen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, in some cases the authors find evi-  dence for wide CO ro-vib line profiles in GI disks which  host dust cavities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' For example, Salyk et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2009)  modeled the CO ro-vib inner emission radius assuming  a power law intensity profile and found for LkHα330  (IMTTS) that the CO gas resides inside the dust cav-  ity (50 au).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Several more cases are shown by Hein Ber-  telsen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In those cases, gas and dust could be  spatially de-coupled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Banzatti and Pontoppidan (2015)  show that the CO gas in systems with large inner cav-  ities (as deduced from the CO line profile) is vibra-  tionally ‘hot’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' One explanation of this could be UV flu-  orescence reaching the outer disk because the inner disk  is also devoid of dust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Following up on the powerful CO  ro-vib line diagnostic, Banzatti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2017a) showed  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 26 Compiled CO surface density profiles from the liter-  ature (Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2021, Fedele et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2017, Carmona et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2014, 2017, Carmona, 2021, van der Marel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' We  used a constant CO abundance of 10−4 if required to convert  from total gas surface densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The solid lines are derived  from ALMA data, while the dashed lines are from CRIRES  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The black dotted line shows the Minimum Mass Solar  Nebula.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The blue/green colors indicate normal class ii disks,  while the yellow/orange/red colors indicate transitional disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  that water line detections in T Tauri disks (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='9-33 µm)  correlate with gas gap sizes deduced from the CO lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  In disks with small gaps, the highest water excitation  lines are no longer detected and with increasing gap  size, these non-detections expand to lower excitation  water lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Antonellini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2015) showed that wa-  ter lines with lower excitation temperatures tend to  originate from increasingly larger distances from the  star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Detailed thermo-chemical disk modeling of CO  ro-vibrational lines by Bosman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2019) and An-  tonellini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2020) shows that the observations of  Herbig disks may point to a more complex inner disk  structure, possibly de-coupling of dust and gas and pos-  sibly positive density gradients consistent with gaps  carved by giant planets (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bryden et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 1999, Lubow  and D’Angelo, 2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Carmona et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2014) used the  CO ro-vib line profiles combined with a large set of  multi-wavelength data (photometry, line fluxes, and im-  ages) for the disk around HD 135344B to deduce the  shape of the gas surface density profile inside ∼50 au.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  From the CO v=1-0 line profile they find a positive  surface density profile and also evidence for dust deple-  tion with respect to the canonical gas-to-dust ratio of  100 inside the gap of this pre-transitional disk (GI, see  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 26).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Also fitting three CO isotopologues in the pre-  transitional disk around HD 139614 indicates a positive  surface density profile inside 6 au, and even possibly  a deep narrow gap that could point to a giant planet  around 4 au (Carmona et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Using the same  HD163296  22  MWC480  HD169142  20  HD 139614  HD135344B  IRS48  18  16  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5  log r [au]Herbig Stars  41  method, the CO isotopologue lines in HD 169142 are  consistent with a flat or increasing gas surface density  profile inside ∼20 au (Carmona et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 26).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Given the high spatial resolution that ALMA offers  now, the CO pure rotational lines can also be used to  probe the inner disk regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The caveat here is that  the typical gas temperatures inside 10 au are above a  few 100 K and so the low rotational levels are not max-  imally populated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In a pioneering survey of disks with  inner dust gaps (pre-transitional disks8), van der Marel  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2016) characterized the depth and shape of such  gaps for HD 135344B and IRS 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They find that the  sizes of gas gaps are typically smaller by a factor two  compared to the dust gaps and that for HD 135344B  the data at this stage cannot yet distinguish between a  smooth gas surface density profile with a negative gradi-  ent and a step-like positive one (different gas depletion  levels);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' notably the CO ro-vib data is more constrain-  ing for this object (see above).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' IRS48 requires a sharp  edge in the gas surface density profile at ∼ 25 au (see  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 26).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The DIANA models (Woitke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2019b)  show that the observational data are consistent with  an outer gas surface density gradient smaller than −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5  (Minimum Mass Solar Nebula, Weidenschilling, 1977),  a result previously also reported by Williams and Cieza  (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Concerning the outer disk, the DSHARP program  (Andrews et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2018b) obtained high spatial resolu-  tion ALMA data (30-60 mas) for a few Herbig Ae disks,  HD 163296, HD 142666 and the IMTTS HD 143006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' From  this program, only one source, HD 163296, has a high  quality dataset that allows the determination of a de-  tailed gas surface density profile (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 26).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Since the  dust rings are not optically thin, derivation of the gas  surface density profile requires simultaneous modeling  of dust and gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' While Isella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2016) inferred the  presence of gas gaps for the inner two dust gaps at 60  and 100 au from power law (plus gaps) disk model-  ing of ALMA CO data, more detailed thermo-chemical  dust+gas modeling using the DSHARP data does not  confirm this (Rab et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The observations of the  high S/N high spatial resolution 12CO data (DSHARP)  are still consistent with no gas depletion inside the dust  gaps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  In a sample of 22 disks from a pre-ALMA northern  survey of the 12CO J = 3 − 2 line (Dent et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2005),  Pani´c and Hogerheijde (2009) find from disk modeling  (power-law disk models without chemistry) that 75 % of  this Herbig sample are smaller than 200 au;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' of course,  pre-ALMA data is likely biased towards large/bright  8 Note that the term transitional disk is here reserved to  disks that have no near-IR excess;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' HD135344B and IRS48 do  have such an excess.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  disks and could underestimate this percentage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Unfor-  tunately, in the epoch of ALMA, there does not exist a  homogeneous large survey for disk sizes at the time of  this writing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Taun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (MSc thesis, paper in prepa-  ration) collected archival data of Herbig disks in band  6 (all three CO isotopologues) with spatial resolution  of 20-100 au (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' data from Miley et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They  added Herbig disks observed only in band 7 (13CO and  C18O) to enhance the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This led to 17 Herbig  disks, ten GI, five GII and two intermediate disks (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  27).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The dust and gas radii were derived using the cu-  mulative fluxes (from elliptical apertures) and defining  the outer radius when 90% of the total flux was reached  (see Trapman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2019, for details of the method).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  In general, GI disks span a large range in dust (90∼370  AU) and gas (180∼850 AU) outer disk radii while the  five GII disks are small, with four unresolved dust disks  and three unresolved gas disks (13CO).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The GI/II disks  have similar sub-mm properties (gas outer radii, con-  tinuum and CO fluxes) to GI disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Like in the case of  the lower mass counterparts (T Tauri disks), the aver-  age ratio between gas and dust outer radii is ∼ 2 with  a large spread (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ansdell et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Facchini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  (2017) and Trapman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2019) find that radial drift  of dust grains has a profound effect on the outer disk  thermal gas structure and the ratio between inferred  dust and gas radii;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' specifically, radial differences of a  factor four or more are clear signatures of dust evolu-  tion and radial drift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Individual disks have been investigated using high  spatial resolution ALMA data and find similar results:  a factor 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4 for HD 97048 (van der Plas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2017b),  more than a factor 2 for HD 163296, (de Gregorio-Monsalvo  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2013), and more than a factor 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='8 for HD 100546  (Pineda et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' For the disks around HD 163296  and HD 100546, the authors claim that the dust disk  has a sharper cut-off compared to the gas, possibly in-  dicating signatures of grain growth and radial dust mi-  gration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The DIANA disk modeling results show that  for five Herbig disks, the outer disk edge is consistent  with a soft edge (γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5 − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0 9 ), and only for one  object, the sharp edge previously reported is recov-  ered (HD 163296, γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2 Woitke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2019a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pani´c  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2021) investigated two binaries of intermedi-  ate separation (HD 144668 and KK Oph) where both  components are surrounded by dust-rich (gas-to-dust  mass ratio ⩽ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4) planet forming disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The respec-  tive disk sizes are consistent with tidal truncation in  these systems and they appear to have lower gas masses  9 The  surface  density  is  here  assumed  as  Σ(r)  ∝  r−ϵ exp  �  −  �  r  Rtap  �2−γ�  with the radius r and the taper ra-  dius Rtap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  42  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 27 Gas outer radii of Herbig disks derived from ALMA 13CO archival data versus dust outer radii (Taun, MSc thesis).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The right panel zooms in excluding the three largest disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  (< 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1 MJupiter) than the average single Herbig disks;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  so it is unlikely that gas giant planets can still form  around these two stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Summary Based on NIR gas observations of Herbig  disks with dust cavities (up to several 10 au), there  is evidence for positive surface density gradients inside  those cavities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In some cases, the gas clearly extends in-  side the dust cavity and in most cases, the gas-to-dust  ratio is high inside the cavities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Broadly speaking, this  is consistent with giant planet formation models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The  gas surface density gradient in the outer disk (beyond  several 10 au) is often more shallow than the minimum  mass solar nebula (-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 26).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' We have in a few  cases high spatial resolution ALMA observations indi-  cating that growth and radial migration of dust affect  the outer edges of disks around Herbig Ae stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In-  termediate separation binaries also suggest that tidal  truncation operates, maybe in tandem with promoting  more efficient dust evolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6 Chemistry in Herbig disks  To understand what type of planetary systems can emerge  from the disks around Herbig stars, we also need to ad-  dress the question of how chemically rich these disks  are.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (1) Which level of molecular complexity do we find  compared to disks around low mass stars?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2) Are the  differences primarily due to differences in the physical  and thermal disk structure (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' level of UV and X-ray  irradiation) or do they reflect true differences in the  gas chemistry?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' And, most fundamentally, (3) do Her-  big disks contain significant amounts of water, a tracer  often invoked to assess the possibility of forming habit-  able planets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (4) What is the C/O ratio in Herbig disks?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Level of molecular complexity: A systematic SMA sur-  vey by ¨Oberg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2010, 2011) finds a lack of cold  chemistry tracers in Herbig disks, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' N2H+, DCO+,  DCN, H2CO, compared to T Tauri disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' These early  studies focused on the brightest (and so largest) disks  in each category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' With ALMA’s increasing spatial reso-  lution and sensitivity, the studies of the chemical com-  position of Herbig disks has gained momentum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ¨Oberg  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2015) showed that the bright Herbig disk around  MWC 480 hosts a number of complex nitriles (HC3N  and CH3CN) next to the commonly detected HCN and  its isotopologue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Overall, the number of Herbig disks  in which ALMA has searched for molecules is still too  small and the data is too inhomogeneous (spatial reso-  lution, transitions) to have conclusive answers as to how  different Herbig disks are amongst themselves (see Ta-  ble 5 for sources that have molecular detections beyond  the CO molecule);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' this is not changing with the MAPS  survey (¨Oberg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2021), since it includes only two of  the already well characterized Herbig disks MWC 480  and HD 163296.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In the inner disk, Spitzer surveys have  shown that Herbig disks also lack the richness in molec-  ular lines typically found in T Tauri disks (Pontoppi-  dan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2010, Salyk et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The Herbig disks  show for example no detections of HCN, C2H2, CO2 and  OH;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' only HD 101412 is detected in CO2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Warm water  (∼300 − 700 K) is only detected at longer wavelengths  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='85 µm, Pontoppidan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2010) among several  Herbig disks (4/25).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' HD 163296 is also clearly detected  at 33 µm (Banzatti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2017a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Given the low spec-  tral resolution of Spitzer, this can be a result of limited  006  HD31648  400  800  350  HD163296  700  HD34282  600  300  (AU)  (AU)  HD97048  500  250  HD100546  13CO  THD142527  HD169142  HD3Y648  400  200  HD104237  HD135344  AD163296  Rg = 3Rd  150  HD139614  300  H100546  Rg =2Rd  KKOph  AKSCO  200  Rg= Rd  100  THD14266.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6  Group I  100  Group I/ll  50  Group Il  0  0  0  100  200  300  400  500  600  0  25  50  75  100 125 150  175200  Rout Dust (AU)  Rout Dust (AU)Herbig Stars  43  Table 5 Detected molecules (transitions) in Herbig disks with ALMA beyond CO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' References: Bosman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2019, Bo19),  van der Plas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2017b, vdP17), Aikawa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2021, A21), Booth et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2019, B19), Bergner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2021, B21), Carney  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2018, C18), Cataldi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2021, C21), Fedele et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2017, F17), Guzm´an-D´ıaz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2021, G21), Huang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2017,  H17), Ilee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2021, I21), Loomis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2020, L20), Le Gal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2021, LG21), Mathews et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2013, M13), Mac´ıas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  (2017, M17), ¨Oberg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2015, O15), Pegues et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2020, P20), Qi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2015, Q15), Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2021, Z21).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  line  ident  HD 97048  MWC 480  HD 163296  HD 143006  HD 169142  12CO  J=1-0  vdP17  13CO  J=1-0  Z21  Z21  C18O  J=1-0  Z21  Z21  C17O  J=1-0  Z21  Z21  12CO  J=2-1  Z21  Z21  F17  13CO  J=2-1  Z21  Z21  F17  C18O  J=2-1  B19,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='Z21  Q15,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='B19,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='Z21  B19  F17  12CO  J=3-2  vdP17,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='Bo19  HCO+  J=1-0  A21  A21  HCO+  J=4-3  vdP17,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='Bo19  M13  DCO+  J=3-2  M17,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='C18  DCO+  J=5-4  M13  M17,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='C18  H13CO+  J=1-0  A21  A21  H13CO+  J=3-2  H17  H17  H13CO+  J=4-3  Bo19  M13  H2CO  J=3-2  P20,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='G21  P20,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='G21  P20  H2CO  J=4-3  P20  P20  HCN  J=1-0  G21  G21  HCN  J=3-2  B19,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='G21  B19,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='G21  B19  H13CN  J=3-2  O15,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='H17  H17  HC15N  J=4-3  Bo19  DCN  J=3-2  C21  C21  CN  N=1-0  B21  B21  CN  N=2-1  B21  N2H+  J=3-2  L20  Q15  N2D+  J=3-2  C21  C21  HC3N  29-28  I21  I21  CH3CN  120-110  I21  I21  C2H  N=3-2  B19,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='G21  B19,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='G21  C2H  N=1-0  G21  G21  c-C3H2  707-616  I21  I21  SO2  LG21  12CS  J=2-1  LG21  LG21  12CS  J=5-4  LG21  12CS  J=6-5  L20  C34S  J=5-4  LG21  H2CS  L20,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='LG21  sensitivity since models predict that the line flux scales  weaker than linear with the central star luminosity (An-  tonellini,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Origin of differences between T Tauri and Herbig disks:  Single dish sub-mm observations focused initially on de-  tecting molecules in the cold outer disk and analysing  integrated line ratios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Thi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2004) presented a first  comparative study of the sub-mm lines of CO, HCO+,  CN, HCN, and H2CO in T Tauri stars (LkCa 15 and  TW Hya) and Herbig stars (HD 163296 and MWC 480);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  they found that the CN/HCN ratio is higher in Herbig  disks than in T Tauri disks and attributed this to ei-  ther differences in the radiation field (Ly α or X-rays)  or a thermal effect (the two molecules have different  freeze-out temperatures).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Using the PdB Interferome-  ter, Henning et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2010) found that C2H emission is  lower in the Herbig disk around MWC 480 than in the  T Tauri disks around DM Tau and LkCa 15;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' again, they  explained this by the presence of strong UV and lack  of X-rays in the case of the Herbig disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The SMA sur-  vey by ¨Oberg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2010, 2011) shows no clear differ-  ence in the CN/HCN ratio between T Tauri and Her-  big disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Subsequent large surveys of T Tauri and Her-  big disks using IRAM also show no systematic differ-  ence in CN emission between the two type of sources  (Chapillon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2012, Guilloteau et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' How-  ever, MWC 480 and HD 163296 show strong CN emis-  sion, while AB Aur, MWC 758, CQ Tau and SU Aur show  only upper limits or weak emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Notably the strong  CN disks are both intermediate GI/GII disks;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' also Ta-  ble 5 shows that these are also to-date the two best  44  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  studied disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Contrary to the above studies, Chapillon  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2012) find that the CN/HCN line ratio is higher  in Herbig disks compared to T Tauri disks — however,  the sample for which both lines have been observed with  IRAM is small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A comprehensive ALMA line survey of LkCa 15 (a  T Tauri star) and MWC 480 finds clear differences in  the cold chemistry tracers N2H+, and DCN, and the  nitriles HC3N, CH3CN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The latter are brighter in the  Herbig disk, maybe due to its instrinsically higher tem-  peratures (Loomis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Le Gal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2019)  focused on the sulphur bearing molecules in disks in-  cluding again MWC 480.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They find no difference in CS  between T Tauris and this Herbig disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' On the other  hand, a much larger sample studied by Pegues et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  (2020) shows that H2CO (formaldehyde) is less abun-  dant in Herbig disks compared to T Tauri disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The  observations suggest that both chemical channels, gas-  phase and grain-surface, likely operate to explain the  formaldehyde observations in disks;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' hydrogenation of  CO ice can lead to efficient H2CO formation in cold  T Tauri disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The general idea is that formaldehyde  can be further hydrogenated to methanol (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hiraoka  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 1994, Watanabe and Kouchi, 2002) and simu-  lations support that this works under the conditions  found in cold dense cores or cold YSO envelopes (Cup-  pen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Carney et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2019) carried out a deep  search for methanol in HD 163296 with no detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Compared to TW Hya, the methanol to formaldehyde  ratio is much lower.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, still multiple explanations  are possible given that we still have an incomplete pic-  ture of the role of surface chemistry versus gas phase  chemistry and also given uncertainties in the desorption  efficiencies of these two molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The cold chemistry in the outer disk also drives  deuteration of molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Huang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2017) find no  significant difference in the deuteration between the  T Tauri and Herbig disks (MWC 480 and HD 163296).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  This is surprising given the earlier finding of a compar-  ative lack/lower emission level of cold chemistry tracers  in the outer disk of Herbig stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Disk modeling studies (van Zadelhoff et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2003,  Cazzoletti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2018) indeed suggest that higher FUV  irradiation enhances the CN emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Walsh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2015),  Antonellini (2016), Ag´undez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2018) used thermo-  chemical models to investigate the difference in chemi-  cal composition between disks of various spectral types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Using the same generic disk structure and exchanging  the central star, Ag´undez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2018) do not find strik-  ing differences in the outer disk molecular reservoir be-  tween T Tauri and Herbig disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Walsh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2015) use  the same approach and focus on the inner 10 au.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They  do not find significant differences between Herbig and  T Tauri disks in key molecules such as HCN and C2H2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  if at all, the Herbig disks have higher column densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  It is important to note that these works assumed high  abundances of relatively small grains in the disk sur-  face (up to 1 µm size).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This causes the H/H2 transition  to reside very high in the disk at warm temperatures  (several 100 K), thus promoting a very efficient neutral  chemistry (Walsh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This is not the case in  disk models that assume a wider grain size distribution  (up to mm-size) and dust settling;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' the small grains are  then indeed left in the disk surface, but their fractional  mass is much smaller, preventing high abundances of  H2O and C2H2 above τ ∼1 in the disk surface (Woitke  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2019b, Greenwood et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Water in Herbig disks: The lowest excitation water lines  from the outer disk have been detected with Herschel/HIFI  in one out of four Herbig stars (HD 100546 detection  versus HD 163296, MWC 758, MWC 480 non detections  van Dishoeck et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Also, water ice has been  unambigiously detected in the Herbig disks HD 142527  (Min et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2016b) and HD 100546 (Honda et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2016),  see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Moving slowly to warmer disk regions closer to the  star, warm water (∼200 − 300 K) has been detected in  the far-IR with Herschel in HD 163296 (Meeus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2012), and through line stacking also in HD 104237 and  HD 142527 (Fedele et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Contrary to the funda-  mental water lines, HD 100546 is not detected in warm  water with PACS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' the original claim by Sturm et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  (2010) has been retracted (Meeus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Also  warm OH (∼100 − 500 K) has been detected in disks,  both in GI and GII (Meeus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2012, Fedele et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2012, 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Higher OH/H2O abundance ratios are found  in Herbig disks compared to T Tauri disks based on slab  models that assume the same spatial origin for both  molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, thermo-chemical models of T Tauri  disks show that these lines originate from very differ-  ent radial and vertical disk layers (Woitke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2019b,  Greenwood et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  At NIR wavelengths, ground based studies have been  used to search for hot water (few 1000 K) and OH in  the inner disks around Herbig stars (Fedele et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2011,  Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2016, Adams et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The NIR  detections of OH are more common among GI disks  (Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2016) in contrast to the far-IR OH de-  tections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This could relate to the inner disk architec-  ture where dust cavities/gaps (more common among  GI disks) create better excitation conditions, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' at the  inner edge of the outer disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2016) find  that the high J CO and OH P4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5 doublet line ratio is  roughly constant (∼10) in Herbig disks;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' T Tauri disks  show a lower ratio between the CO P10 line and the  Herbig Stars  45  OH doublet at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='9 µm (Banzatti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2017a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Subse-  quently, Adams et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2019) found that the H2O to  OH line ratio in Herbig disks (based on HD 101412 and  upper limits from Fedele et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2011) is systematically  lower than for T Tauri disks (Banzatti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2017a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The C/O ratio in Herbig disks: A key controversy at  this stage is the global C/O ratio in disks, because it re-  lates very closely to the composition of gas giant planets  and planetary atmospheres forming within these disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Bruderer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2012), Kama et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2016a,b) use a  combination of atomic fine structure lines ([O i)], [C i],  [C ii]) and CO sub-mm lines to investigate the carbon  depletion in the upper layers of the outer disk;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' the [C i]  data originates from APEX surveys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They find that the  volatile carbon abundance could be a factor 5−20 lower  than the solar one (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='7×10−4 relative to hydrogen, As-  plund et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2009);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' however to derive robust conclu-  sions, [C i] detections are essential, thus warranting the  sensitivity of ALMA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The recent MAPS project found  no difference in the amount of CO depletion in three  T Tauri and two Herbig disks (Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Sub-  sequent 2D thermo-chemical disk modeling of the five  disks (Bosman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2021) shows that the C/O ratio  varies strongly within each disk, irrespective of spectral  type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Summary: Surveys of Herbig disks have shown less chem-  ical richness compared to their lower mass counterparts,  the T Tauri disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The to-date richest Herbig disks are  the two GI/GII disks HD 163296 and MWC 480;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' how-  ever, this could be a selection bias since few comprehen-  sive Herbig line surveys have been done with ALMA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Despite thermo-chemical modeling, it remains unclear  the extent to which this is due to differences in disk  structure or chemistry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A systematic survey of OH, wa-  ter and CO would again be key (see also Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3) in  disentangling the excitation and abundance question  for these molecules and understanding the differences  between T Tauri and Herbig disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' If elemental carbon  depletion is invoked to explain the weak CO lines in the  submm, factors of up to several 10 (relative to solar) are  found in Herbig disks;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' the C/O ratio could be as high  as 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='7 Differences between Herbig Ae and Be disks  Most of the discussion above pertains to disks around  Herbig Ae stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Their B-type counterparts have much  higher luminosities and they often reside in more dis-  tant star forming regions (see also Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The larger  distance and their embedded nature makes them diffi-  cult targets for directly resolving their disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However,  they have been studied spectroscopically from optical  to far-IR wavelengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Bik and Thi (2004) detected the CO bandhead emis-  sion in a young B-type star (IRAS08576-4334, M∗ =  6 M⊙) and showed that it is fully consistent with orig-  inating from a small (few au sized) disk in Keplerian ro-  tation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Subsequent X-shooter and SINFONI data (Eller-  broek et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2011) suggest that the system also features  a jet and would thus be still accreting with rates of the  order of 10−5 − 10−6 M⊙/yr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ram´ırez-Tannus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  (2017) classified and investigated young stellar objects  in M17 (d=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='98 kpc) and found five of them having a  spectral type B (B243, B268, B275, B331, B337) and at  least two of the attributes: NIR excess, CO bandhead  emission, double-peaked emission lines of hydrogen, the  Ca triplet, [O i] 6300˚A;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' B275 had been previously con-  firmed to be a young pre-main sequence B-type star  by Ochsendorf et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A detailed analysis of the  line profiles shows that the gaseous disks are again very  small (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5-5 au scale) and that the hydrogen emission  originates from further out compared to [O i] and the  Ca triplet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ilee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2013, 2014) detected the CO over-  tone emission at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3 µm with CRIRES and X-shooter in  a sample of 6 out of 91 Herbig disks (4 Be disks and 2 Ae  disks);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' the detection rate is higher among the Be disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Fitting the CO overtone line profile again suggests an  origin within a small gaseous disk (< few au).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' For the  B-type stars, the CO emitting region is well inside the  estimated dust sublimation radius, but well beyond the  corotation radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' So, the picture that emerges is that  these Be-type stars have a NIR excess and host small  gaseous disks, likely inside the dust sublimation radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  At far-IR wavelength, Jim´enez-Donaire et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2017)  compared the Herschel far-IR spectra of two Herbig  Be stars (R Mon with spectral type B8, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='8 kpc, and  PDS 27 with spectral type B2, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='25 kpc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' While the  spectrum of the B8 type star is rich in emission lines  of [O i], H2O, OH and CO up to J = 34 − 33, the B2  star barely shows any emission lines, besides CO up to  J = 11 − 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, due to the limited spatial and  spectral resolution, the disk and outflow (shock) con-  tribution to these lines cannot be disentangled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Further  observations at far-IR and sub-mm wavelengths (either  with high spatial or spectral resolution), are required to  find out whether the more massive HBe stars possess  outer gaseous disks similar to the Herbig Ae stars or  not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Summary: Over the past 25 years it has become clear  that Herbig stars possess rotationally supported gas  disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Spectroscopic capabilities across the electromag-  netic spectrum have revealed the presence of many molecules  in these disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Thermo-chemical models of disks can re-  46  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  produce the main trends.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The mass of disks remains  highly uncertain and model dependent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' There is a dis-  crepancy between the masses of disks inferred from var-  ious indirect tracers and the stellar accretion rate that  points to either missing physics in our interpretation  of stellar accretion rates and/or the interpretations of  tracers used to infer the mass of disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' While there is  evidence that Herbig Be stars possess disks, these are  much smaller and less chemically rich than their Herbig  Ae counterparts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='8 The relative radial distribution of gas and dust in  disks around Herbig stars  At large spatial scales (few 10’s of au), the substruc-  tures frequently seen in the dust do not always have a  corresponding gas structure and vice versa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' For exam-  ple, the clear dust gaps in HD 163296 have a correspon-  dence in the gas (Isella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2016), but this can be a  pure temperature and/or opacity effect (van der Marel  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2018, Rab et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The pre-transitional disk  around HD 142527 shows a clear dust trap in 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3 mm  emission, but the CO emission is smoother and extends  much further inwards (Boehler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' HCN and  CS emission in this source is offset from the dust trap  by almost 180◦ (van der Plas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2014);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' again, the  explanation could be either a temperature or an opac-  ity effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' AB Aur shows two prominent 12CO gas spiral  arms inside the mm dust cavity (Tang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A radial dependence on the vertical dust settling has  been measured in the disk around HD 163296.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' At the  inner dust ring (∼70 au), dust and gas remain vertically  well mixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' At the outer dust ring (∼100 au), the scale  height of the dust is roughly ten times smaller than the  scale height of the gas (Doi and Kataoka, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This  is consistent with only the inner ring being detected in  scattered light (Muro-Arena et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  At the spatial scales of the inner disk, interferomet-  ric studies of the dust and optical and near-IR spec-  troscopy of the [OI] and CO ro-vibrational lines can  reveal whether or not gas and dust are co-spatial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' van  der Plas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2009) inferred that CO is absent in the  dust gaps (<10 au) of HD 97048 and HD 100546;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' how-  ever, [OI] 6300 ˚A emission extends well inside the dust  gaps, thus showing the presence of gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' van der Plas  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2015) then compared the inner radius derived  from CO emission with that of the dust and other inner  disk gas tracers ([OI], PAHs) for a larger sample of Her-  big stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The GI disks show systematically larger CO  inner radii than GII disks;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' in both cases, the [OI] emis-  sion extends further inward than the CO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Banzatti and  Pontoppidan (2015), Banzatti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2017b) compared  the CO and water emission lines to measurements of  the dust inner holes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They confirm that inner dust gaps  are indeed depleted in molecular line emission (water  and CO).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hein Bertelsen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2016) added to the CO  diagnostic by introducing the line FWHM as function  of upper level quantum number J as a new diagnostic:  (1) a constant FWHM versus J can be used to infer the  presence of a dust gap, (2) the presence of line wings  can indicate the presence of gas inside a dust gap, and  (3) a strongly decreasing line flux versus J behaviour  can indicate a gas depleted region (Hein Bertelsen 2015,  PhD thesis).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Carmona et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2014, 2017) studied two  pre-transitional disks (HD 135344B, HD 139614) with  very deep CRIRES observations and find that for these  two disks, the dust gaps (30 and 6 au respectively) are  partially filled with molecular gas emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This agrees  with the findings from ALMA CO submm observations  by van der Marel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Summary: The structures observed in gas lines and in  the continuum do not necessarily correspond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This may  be due to either temperature or opacity effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The  vertical mixing of the gas and dust has been shown to  vary for at least one source which may explain differ-  ences in what is observed in the mm continuum and  in scattered light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In the inner disk, the inward extent  of the molecular gas tends to follow the inward extent  of the dust, though there are exceptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Atomic gas  (as traced by [OI] for example) generally extends in-  ward of the molecular gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Thermo-chemical disk mod-  eling work (Bruderer, 2013, Bosman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2019, van  der Marel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2018, Hein Bertelsen 2015, PhD the-  sis) has revealed the complex interplay between gas and  dust in the inner disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The local gas-to-dust ratio, dust  opacities, disk scale height, presence of dust traps and  gas excitation mechanism all play a role in interpreting  the observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  6 PLANET FORMATION AROUND  HERBIG STARS  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1 Planet occurrence rates among intermediate mass  stars  The occurrence rate of super-Earths within ∼1 au of  their host star peaks at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5M⊙ (Mulders et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2021, see  also Howard et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2012, Mulders et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' On the  other hand, the occurrence rate of supra-Jovian mass  planets with periods ≤4 years increases with stellar  mass reaching a maximum at ∼2 M⊙and then rapidly  declines (Reffert et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2015, see also Luhn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2019,  Johnson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The most massive star around  which a planet has been detected thus far is a binary  with a system mass of 6-10M⊙(Janson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Herbig Stars  47  The planet was detected by direct imaging and has a  semi-major axis of 560 au.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Thus it is clear that planets  can form even around fairly massive Herbig stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Transit searches for planets find systematically lower  occurrence rates for planets than radial velocity searches  that is largely driven by selection effects of the sur-  veys (Moe and Kratter, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' These authors note that  this driven by the fact that binaries with intermedi-  ate separations (a=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5 – 200 au) suppress planet for-  mation and that radial velocity searches systematically  exclude binaries while transit searches do not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Moe and  Kratter (2021) argue that half of the dependence of the  superEarth occurrence rate on stellar mass can be ac-  counted for by the effect of binaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The occurrence  rate of supra-Jovian mass planets within 1 au around  single AF stars is 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3% (Moe and Kratter, 2021)  consistent with the estimate by Reffert et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2015)  for solar metalicity stars with masses ranging from 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='8-  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6M⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' It is not clear how the occurrence rate of supra-  Jovian mass planets scales with orbital separation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Indeed, direct images of planets around intermedi-  ate mass stars are rare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bowler (2016) find that high  mass planets (5–13 MJ) are detected at 30–300 au or-  bital separation in only a small fraction of young A-  stars (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='8%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Similarly, the Gemini Planet Imager Ex-  oplanet Survey (GPIES) reports a modestly higher oc-  currence rate for the same mass range of supra-Jovian  planets (9+5  −4%) from 10–100 au (Figure 28;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Nielsen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Assuming that this reflects the actual occurrence  rate of massive companions orbiting intermediate mass  stars (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', the planets haven’t migrated inward of ∼10-  30 au), one might conclude that only a few percent of  Herbig stars should reveal signatures of ongoing supra-  Jovian gas giant planet formation at distances ≳ 10 au.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  However, that does not appear to be the case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Here we  summarize the evidence for ongoing planet formation  in Herbig disks and discuss the challenges to detecting  forming planets in these systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2 Sign-posts of planets in disks  There are several indirect signatures of the presence of  planets in disks: the λ Bo¨o phenomenon, falling evapo-  rative bodies, gaps/rings in disks, kinematic signatures  in the orbital motion of the gas in the vicinity of the  orbit of a gas giant planet, and spiral arms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Here we  describe what each of these signposts tell us about the  presence of planets in disks around Herbig stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1 The λ Bo¨otis phenomenon  The identification of the λ Bo¨otis phenomenon among  Herbig stars has been interpreted as a signpost of a gap-  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 28 Depth of search for the intermediate mass stars in  the GPIES sample (Nielsen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Of the 123 interme-  diate mass stars observed thus far, four reveal planets: β Pic,  51 Eri, HD 95806, and HR 8799.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Three of the six imaged  companions orbit HR 8799.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  opening planet in the disk (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', Acke and Waelkens,  2004, Folsom et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2012, Kama et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2015, Jermyn  and Kama, 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The λ Bo¨otis phenomenon was first  identified by Morgan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (1943) who noted a depletion  of Mg and Ca in the photosphere of λ Bo¨otis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The def-  inition of the class of λ Bo¨o stars has been refined and  is now understood to comprise late-B through early-F  stars (10,500 K ≤ Teff ≤ 6,500 K) that possess a deple-  tion of refractory elements and near solar abundance  of volatile species (Paunzen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Such stars  comprise about 2% of main-sequence field stars in this  spectral type range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  There are two related leading hypotheses to account  for this anomalous abundance pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Waters et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  (1992) propose that λ Bo¨o stars continue to accrete  residual material from the circumstellar environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The refractory elements are disproportionately found  in dust that is blown away more efficiently than gas re-  sulting in this abundance pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kamp et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2002)  note that there is no correlation between the λ Bo¨o phe-  nomenon with stellar age spanning several billion years  leading them to suggest that the anomalous abundance  pattern arises from the passage of these stars through  the diffuse ISM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In this scenario gas is accreted selec-  tively relative to the dust as the dust is blown away by  the radiation pressure of the star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The λ Bo¨o abundance pattern observed among main  sequence B-F stars has also been observed among Her-  big stars (Acke and Waelkens, 2004, Bruderer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2012, Folsom et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In contrast to ∼2% of field  stars that show this abundance pattern, Folsom et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  100  4Stars  Stars  Stars  Mass (MJup)  4Stars  10  S  1  1  10  100  Semi-Major Axis (AU)48  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  (2012) found that at least 33% of Herbig stars show  this effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Building on this work, Kama et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2015)  examined the relationship between the abundance of GI  Herbig stars and GII Herbig stars (see also Kama et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  2016a,b, Jermyn and Kama 2018, Kama et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2019,  Castelli et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kama et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2015) find that while  the abundance of volatiles among GI and GII Herbig  stars are equivalent, GI Herbig stars are depleted in re-  fractory elements by ∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5 dex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' These authors note that  all known disks with cavities among Herbig stars are  GI sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They note that pressure bumps in the disk  at the boundary of gaps (perhaps due to planet-disk  tidal interactions) trap and hold back grains (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1), leading to accretion onto the star from an inner  gas rich disk depleted in refractory elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Based on  their analysis they conclude that ∼1/3 of Herbig stars  could possess a planet with sufficient mass to open a  gap that results in a dust filtration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2 Falling Evaporative Bodies  As mentioned in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2, the narrow, intermittent  components of metallic absorption lines in the spectra  of Herbig stars have been interpreted as due to infalling,  evaporating material such as exo-comets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  In fact, the presence of these infalling comets is an-  other indirect signpost of planets in disks around Her-  big stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' These were first observed towards the young  debris disk β Pic by Ferlet et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (1987).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Beust et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  (1991) suggest that the presence of these infalling solid  bodies result from stirring by a planetary mass body.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Grady et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (1996) observed similar behaviour towards  a large sample of Herbig stars and suggest that this phe-  nomenon is evidence that planets have already formed  in the disk and thus perturb planetesimals onto eccen-  tric orbits that bring them close to the star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However,  the gas in the inner disk of Herbig stars should damp  the eccentricity of these orbits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Further study of the  association between the occurrence rate of red shifted  absorption features and clearing of the inner disk (or  perhaps the accretion rate) may clarify whether this  mechanism is plausible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  In the largest survey of this phenomenon to date,  Rebollido et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2020) studied a sample of 117 main  sequence stars with spectral types spanning G8 - B8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Their sample was selected on the basis of having either  1) previous evidence of β Pic like phenomena, 2) an  edge-on debris disk, 3) a debris disk with cold gas, 4)  an infrared excess, 5) membership in a young associa-  tion, 6) shell stars, or 6) a λ Bo¨o abundance pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Among this sample, 16 of the stars showed variable red  or blue shifted features that could be attributed to in-  falling evaporative bodies (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', exocomets) all of which  were earlier than A9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They note that this could be due  to the difficulty of detecting these signatures against  the structure in the cooler photospheres.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' An unbiased  survey of young A and B stars may shed additional  light on the presence of planets around these stars nec-  essary for stirring exocomets and thus the occurrence  of planets in disks around Herbig stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3 Rings and gaps in disks  The presence of a planet in a disk also has other ef-  fects on its structure, as we saw in section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' To  summarize, the radial drift that would naturally occur  in disks can only be halted by strong enough pressure  bumps, that in turn are caused by objects of certain  mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pressure bumps due to massive planets will lead  to disk structures like cavities or rings, while the ab-  sence of strong pressure bumps will not be able to halt  radial drift of the dust grains efficiently, making the  disk more compact over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In these disks, less mas-  sive planets such as super-earths could still form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' There-  fore, for a 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5 M⊙ star, disks with large cavities have  massive planets (> 200 M�, while ring-like disks host  somewhat lighter planets (M ∼ 70-200 M�), and lastly  compact disks have planets with a mass < 10 M� (van  der Marel and Mulders, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  From a comparison of exoplanet statistics with a  large ALMA disk survey, not only including Herbig  stars but also lower-mass T Tauri stars, van der Marel  and Mulders (2021) show that the occurrence rate of  exoplanets inferred from radial velocity and transit sur-  veys among stars in different mass bins is in agreement  with occurrence rate of disk structures (cavity, rings).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The authors also conclude that the mass of a planet  present in the disk is crucial in determining the disk  structure and size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4 Kinematic Planetary Signatures  When planets in a disk open a gap (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1), the  resulting pressure gradient will affect the orbital veloc-  ity of the gas (Perez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2015, P´erez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2018, Pinte  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2019, Disk Dynamics Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The gas exterior to the gap will experience a boost and  the gas interior to the orbit of the planet will be slowed  (see for example Armitage, 2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In the spiral struc-  tures emanating from the planet, the deviation from  a Keplerian orbit reaches a maximum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This results in  a ‘Doppler flip’ (for a review of this phenomenon see  Disk Dynamics Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2020, and refer-  ences therein).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' These authors propose a set of criteria  for confirming that such kinematic signatures of planets  Herbig Stars  49  (KSPs) are not artefacts due to processing and discuss  other effects that can mimic this phenomenon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  With the unparalleled sensitivity, spatial resolution,  and spectral resolution of ALMA, several authors have  presented evidence of KSPs in disks around Herbig stars:  AB Aur (Tang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2017), HD 163296 (Pinte et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2018b, Teague et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2018, 2021), HD 100546 (Walsh  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2017, Casassus and Perez, 2019, P´erez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2020), HD 97048 (Pinte et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2019), and MWC 480  (Teague et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' While these observations are too  expensive to have conducted an unbiased survey of nearby  Herbig stars, the results are suggestive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Application of  this technique to more sources will elucidate the fre-  quency of gas giant planet formation in disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5 Spiral arms in disks  High-resolution, high-contrast observations of Herbig  disks with 8m class telescopes have produced exquisite  images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Indeed, Dong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2018a) noted that of the  10 Herbig stars within 200 pc that had been imaged  and lack a stellar companion from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3′′-5′′ that could  drive spiral arms in the outer disk, five show spiral  structure (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 29).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Since then additional sources have  been imaged such as HD 139614 (Muro-Arena et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2020) which shows multiple rings and significant shad-  owing indicative of warped disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' There are at least two  mechanisms that can give rise to spiral structure: grav-  itational instabilities or planet-disk interactions with a  supra-Jovian mass planet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A gravitationally unstable  disk will form spiral structures (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', Hall et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  While disk masses of order MD ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5M⋆ are necessary  to drive two-armed spirals and only last for thousands  of years, multi-armed spirals can form with disk masses  as low as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1M⋆ and persist for Myrs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Are such masses  representative of disks around Herbig stars?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Typical dust masses in GI Herbig stars are around  1−3×10−4 M⊙(Garufi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2018), so assuming d/g =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='01, disk masses would be typically 1 − 3 × 10−2 M⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  However, measuring disk mass is fraught with uncer-  tainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Estimates of disk mass from CO isotopologues,  mm-continuum, and disk accretion rates span roughly  two orders of magnitude (Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' As disk mass es-  timates from stellar accretion rates are often consis-  tent with Mdisk ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1M⋆, multi-armed spirals observed  around Herbig stars could be the consequence of moder-  ately gravitationally unstable disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' On the other hand,  models of the upper limits on flux of HD suggest that  most Herbig stars’ disks may not be gravitationally un-  stable (Kama et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Whatever the case, two-  armed spirals require much higher disk masses and sur-  vive in that state for very short periods of time, so  it is unlikely that gravitational instability accounts for  these.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Alternatively, a massive planet can account for the  spiral structure observed in these disks (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', Fung et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2015, Dong and Fung, 2017, Dong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2018a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Thus it  appears that the population of supra-Jovian mass plan-  ets in the outer disk (≳ 30 au) of young intermediate  mass stars could be ∼20-50% which is consistent with  the occurrence rate inferred from Kama et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2015)  from the abundance patterns of Herbig stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However,  at this time there has only been one confirmed detec-  tion of a gas giant planet orbiting a Herbig star (AB Aur  b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Currie et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' see also Zhou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' While  the direct detection of young massive companions orbit-  ing intermediate mass stars remains quite low (Bowler,  2016, Nielsen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2019), indirect signposts of forming  massive companions are quite common.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The disparity  between the detection rate of supra-Jovian mass planets  beyond ∼30 au and the frequency of indirect signatures  of planet formation in this range is a puzzle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Summary: There are a number of indirect pieces of  evidence that point to the ubiquity of planet forma-  tion in the disks of Herbig stars including the λ Bo¨o  phenomenon, the presence of falling evaporative bod-  ies, rings and gaps in disks, KPSs, and spiral structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  While the exoplanet statistics and occurrence rate of  gaps/rings in disks are fairly consistent (van der Marel  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2021), there is tension between the detection  rate of supra-Jovian mass planets from 30-300au and  the occurrence rate of spiral structures pointing to the  presence of supraJovian gas giant planets in this region  (Dong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2018a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Validation of these indirect sig-  natures by connecting them to detections of planets is  crucial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3 Detecting forming planets in disks  The detectability of gas giant planets depends on their  formation pathway.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The two limits are the hot start  and cold start births (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', Marley et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2007, Fortney  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2008, Spiegel and Burrows, 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In the case  of the hot start, the accreting material goes into heat-  ing the planet making it more luminous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In the case of  the cold start, the accreting material radiates its en-  ergy away resulting in a colder, less luminous young  planet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' For the first 100 Myr of the planet’s life, this  makes a significant difference in the luminosity of the  planet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In the case of the young MS stars HR 8799 and  β Pic, it appears that the orbiting companions began  their life as hot start planets (Brandt et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2021a,b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  If this is the typical formation pathway for Jovian mass  planets, then it sharpens the discrepancy between the  50  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 29 10 single Herbig stars within 200pc that have been imaged with high contrast imagery (based on figures from Ginski  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2016, Kusakabe et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2012, Pohl et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2017, van der Marel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2021, Muro-Arena et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2018, Benisty et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2015,  Garufi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2013, Hashimoto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2011, Avenhaus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2017, Follette et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Of these 10 Herbig stars, five show  spiral structure indicative of the presence of a supra-Jovian mass planet (Dong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2018b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  evident signposts of forming massive companions and  the direct detection of such companions orbiting young  intermediate mass stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  One possibility is that the initial conditions of form-  ing planets span the whole cold start – hot start contin-  uum (Spiegel and Burrows, 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' If there is a signifi-  cant number of planets that begin their life as cold start  objects, then the escaping accretion energy from the cir-  cumplanetary disk should be readily detectable (Brit-  tain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Several complementary techniques  have been employed to detect the presence of form-  ing planets in disks such as sparse aperture masking  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', Hu´elamo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2011), angular differential imag-  ing (ADI;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', Marois et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2006), Hα imaging (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  Close et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2014), and deep searches with ALMA (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  Andrews et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' There have been several intrigu-  ing hints of planets imaged in disks around Herbig stars  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', HD 100546-Quanz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2013a, Currie et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2014,  Quanz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2015, Currie et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2015, Follette et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  2017, Rameau et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2017, Currie et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2017, MWC  758-Reggiani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2018, Wagner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2019, Boccaletti  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2021, HD 169142-Reggiani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2014, Ligi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  2018, Gratton et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2019, and AB Aur Currie et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  2022);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' however, AB Aur is the only Herbig star with a  confirmed planet detected in the disk thus far.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This low  detection rate is similar to that of T Tauri stars where  PDS 70 is the only one for which forming planets have  been imaged (Keppler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2018, M¨uller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2018,  Haffert et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2019, Isella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2019, Zurlo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2020,  Benisty et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  It could be that planets in disks accrete episodically,  and our sample is too small to have detected a forming  planet in its accretion outburst phase (Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Another possibility is that emission from circum-  planetary disks peaks in the MIR and current NIR sur-  veys for forming planets lack the requisite sensitivity  to detect a forming planet (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', Szul´agyi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  An alternative approach to direct imaging of a forming  planet is spectroscopic monitoring of warm gas emission  lines arising from the circumplanetary disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Rab and Kamp (2019) used the thermochemical code,  ProDiMo (Woitke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2009), to calculate the gas and  dust temperature of a circumplanetary disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They find  that the gas is much hotter than the dust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In their ref-  erence model, gas at a temperature of ≳1500 K extends  to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3 au before dropping to 500 K at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5 au and 150 K  at 1 au.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The temperature depends on the interstellar  background radiation, the accretion luminosity of the  planet, and shock heating as gas enters the circumplan-  etary disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' They showed that it is plausible to detect  rotational lines of CO from a circumplanetary disk with  ALMA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The spatial and spectral resolution of ALMA  will provide useful insight to the circumplanetary struc-  ture of material accreting onto forming planets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  While the circumplanetary disk is not resolvable  with 8m class telescopes, high-resolution spectroscopy  serves as a surrogate for spatial resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This tech-  nique was pioneered in the study of classical T Tauri  stars and has been applied extensively to the study of  warm CO and OH emission in disks around Herbig stars  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Such observations may also provide the means to de-  tect circumplanetary disks (Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Circumplanetary envelopes have complex structures  that likely include a rotationally supported circumplan-  HD 97048  MWC 480o  HD 169142  HD 163296  IRS 48  =134 au  :185.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='au  1"=137 au  =114 au  1"=101 au  SAO 206462  AB Aur  HD 142527  HD 100546  MWC  =160 au  1"=136 au  1\'=163 au  1"=157 au  "=110 auHerbig Stars  51  etary disk whose outer extent may range from one-third  to the full extent of the Hill sphere (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', Quillen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=',  2004, Ayliffe and Bate, 2009b,a, Martin and Lubow,  2011, Tanigawa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2012, Ayliffe and Bate, 2012,  Gressel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2013, Szul´agyi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2014, 2016, 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Models indicate that the temperature in the circum-  planetary disk is ≳ 1000 K in steady state (Szul´agyi,  2017) and perhaps much higher during an outburst  (Zhu, 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' At these sizes and temperatures, ro-vibrational  emission of CO in the NIR is also detectable (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', Na-  jita et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The ro-vibrational CO emission from the Herbig  star with a pre-transition disk, HD 100546, may arise  from such a scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The presence of an inner compan-  ion has been inferred from a component of the v = 1−0  ro-vibrational CO emission that varies relative to the  stable hot band (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', v′ ≥ 2) emission (Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The profile of the v = 1 − 0 ro-vibrational line  varied relative to the lines with v′ ≥ 2 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', the hot  band lines).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In 2003 the line profile of the v = 1 − 0  lines matched the profile of the hot band lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In 2006  the red side of the v = 1 − 0 line brightened.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In 2010,  the v = 1 − 0 line remained elevated relative to 2003,  but the Doppler shift of the emission was -1 km s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In  2013, the blue side of the v = 1 − 0 line was brighter  than in 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' By 2017, the line profile returned to the  profile of the gas in 2003 (Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The  Doppler shift and time between observations is consis-  tent with a source of warm gas orbiting at 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6 – 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3  au.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In the case of HD 100546, the CO flux is consis-  tent with emission from gas in a circumplanetary disk  with a radius of ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3 au (Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Py-  erin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2021) model the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='9mm ALMA images of  this HD 100546 and find that an 8MJup planet best re-  produces the ring structure that is observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The Hill  sphere of an object with this mass 12au from HD 100546  is ∼1au, so a circumplanetary disk that fills one-third  of the Hill sphere is comparable to the size of the emit-  ting region inferred from the CO emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Oberg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  (2022) applied thermochemical modeling of such a cir-  cumplanetary disk and found that the luminosity of the  emission of the CO rovibrational emission inferred from  their modeling is consistent with the observed luminos-  ity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The source of the CO emission is now behind the  near side of the disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' When it emerges in 2031, the  source of emission can be studied with 30 m class tele-  scopes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In the meantime, ongoing monitoring of CO  emission from similar transition disks around Herbig  stars may provide additional candidate sources (Ban-  zatti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Expansion of this sample will open  the door to more detailed studies of this important en-  vironment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Summary: There has only been one robust detection  of a planet in a disk around a Herbig star at the time  of this writing (Currie et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Improvements in  instrumentation and the commissioning of 30m class  telescopes will likely enable further detections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A com-  plimentary approach to detecting the presence of the  planet is to observe gas lines from the circumplanetary  disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Rab and Kamp (2019) show that rotational lines  of CO from circumstellar disks should be observable for  wide-orbit systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2019) provide evi-  dence of ro-vibrational CO emission arising from a cir-  cumplanetary disk that is consistent with expectations  from models (Oberg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  7 FUTURE PROSPECTS  Immense progress has been made since the last ded-  icated review of Herbig stars (Waters and Waelkens,  1998b), and there are several exciting lines of inquiry  available to astronomers that promise to advance our  understanding of these important objects even more  over the next 25 years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Here we summarize a few of  the key areas of investigation that we believe will be  particularly fruitful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Since George Herbig first proposed a class of in-  termediate mass pre-main sequence stars, identifying  objects of this class has been a challenge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Over the  years, catalogs of Herbig stars have included contro-  versial candidates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' As the number of objects in these  catalogs has been limited, the study of intermediate  mass pre-main sequence stars has necessarily been lim-  ited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Furthermore, once pre-main sequence intermedi-  ate mass stars shed their disk, they are difficult to iden-  tify due to a lack of activity signatures (the so-called  “Naked Herbigs” that are analogs to weak lined T Tauri  stars).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Large scale surveys such as from telescopes such  as Spitzer, WISE, and Gaia have improved this situa-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' For example, Mooley et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2013) used Spitzer and  Wise data to identify young A stars in Taurus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Using  the Gaia database, Vioque et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' (2020) used Machine  Learning to increase the number of Herbig-candidates  by an order of magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Upcoming large scale surveys  enabled by instrumentation such as WEAVE and facil-  ities such as Pan-STARRS and the Vera Rubin Obser-  vatory promise to enable further such advances in our  identification of Herbig stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The source of the X-ray emission observed from Her-  big stars is still not well understood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Roughly 70% of  Herbig stars are binaries (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1) and roughly 70% of  Herbig stars are detected in X-rays (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However,  there is little overlap among these samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A dedicated  study of multiplicity among Herbig stars for which X-  ray observations exist will clarify the extent to which  52  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  lower mass companions can account for the X-ray prop-  erties of Herbigs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Related to this is the structure of the stellar mag-  netic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' There is compelling evidence that Herbig  stars with masses ≲4 M⊙ accrete magnetospherically,  but the geometry of these fields has not been estab-  lished.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The more massive Herbig stars appear to be  accreting by some other process, with boundary layer  accretion being the leading contender.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Modeling this for  Herbig stars will clarify the situation and perhaps pro-  vide a more accurate means of converting accretion lu-  minosity to accretion rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' There is some evidence that  the accretion rate of 2-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5M⊙ Herbig stars declines as  t−2  age from ∼3-10Myr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, this may underestimate  the rate of decline as non-accreting A stars in this age  bin are not included in this sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Combining data  from the evolutionary precursors to Herbig stars (inter-  mediate mass T Tauri stars) and non-accreting A-stars  in this age bin will shed light on how the accretion rate  of intermediate mass stars evolves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  As the UV excess that veils the Balmer discontinu-  ity is difficult to measure for accretion rates less than  10−8M⊙ yr−1, we must rely on proxies such as Hi emis-  sion lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However, the underlying physics that drives  this correlation is not known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Optical and NIR inter-  ferometry at longer baselines is necessary to determine  the origin of these lines - particularly for very low ac-  creting sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' As it stands, the accretion rates in-  ferred for Herbig stars imply much higher disk masses  than typically observed by other indirect tracers such as  (sub)mm CO lines (and their isotopologues), (sub)mm  dust emission, and HD emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Excellent progress has been made on understanding  the distribution of dust in disks and the resultant SED.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  The evolutionary pathways that lead to GI and GII  disks and the metamorphosis of pre-transitional disks  to transition disks to debris disks remains an open ques-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' New instrumentation such as MATISSE on the  VLT will provide unparalleled interferometric imaging  in the thermal IR (L′−, M−, and N−) bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This will  clarify the radial structure of the inner disks around GI  and GII Herbig stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The James Webb Space Tele-  scope, with its dramatic increase in sensitivity, will en-  able the study of solid state features for a much larger  sample of Herbig stars allowing better characterization  of the role of environment on the dust properties of  these stars, and to detect weak emission from gas in  the inner disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Such studies will also enable studies of  the role stellar multiplicity plays in the development of  GI and GII disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ALMA has revolutionized our under-  standing of mm grains in disks, and now the Square  Kilometer Array (SKA) promises to do the same for  cm-sized grains (Ilee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Looking even fur-  ther ahead the Next Generation Very Long Array will  provide unprecedented resolution and sensitivity at fre-  quencies bridging SKA and ALMA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Our knowledge of the gas content of Herbig disks  has increased remarkably over the past 25yrs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Thermo-  chemical modeling of disks is able to reproduce many  of the trends observed among various gas emission lines  spanning the NIR to the mm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' JWST, with its enhanced  resolution and sensitivity, promises to open new win-  dows into the gas content of disks albeit many known  Herbig stars being too bright to be studied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Under-  standing how the gas content and excitation varies among  stars with different effective temperatures, degrees of  flaring, and dust properties will improve the charac-  terization of the initial chemical conditions of forming  planets;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' especially in the inner disk (<10 au) the syn-  ergy between continuum and emission line studies can  provide unique insights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' We note that ALMA observa-  tions have only scratched the surface of understanding  the chemistry in disks (MWC 480 and HD 163296 the  only two disks being studied in detail) and more efforts  are required to push beyond the commonly used tracer  CO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Perhaps the most direct tracer of disk mass is HD,  but the conversion of line flux from this molecule into  disk masses requires careful characterization of the disk  temperature which in turn depends sensitively on the  dust properties of the disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The mass of disks around  Herbig stars remains an ongoing puzzle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Finally, the detection of planets around Herbig stars  remains a challenge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The advent of 30m class telescopes  in the coming decade will enhance our sensitivity to the  presence of forming planets and move the inner working  angle closer to the star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The detection of a significant  sample of forming planets will provide the means to  probe the early evolution of forming planets and clar-  ify the range of initial conditions (bounded by the cold  start and hot start scenarios) are reflected in the pop-  ulation of planets and thus clarify the status of direct  imaging surveys of gas giant planets around young main  sequence stars in the solar neighborhood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  8 A NEW DEFINITION OF HERBIG STARS  While the empirical classification criteria that defined  the classes of Herbig and T Tauri stars have been, and  still are, very useful for many studies of star- and planet  formation, we already noted in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1 that a full view  on the evolution of intermediate mass stars should ide-  ally be based on the mass of the star (more difficult  to derive directly from observations) and not directly  on its temperature (evident from spectral type).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This  thought motivates the definition of a new, stellar mass-  based definition of the group of Herbig stars, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' leaving  Herbig Stars  53  out the spectral type limitation of the Herbig star or T  Tauri star definitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' As a lower mass boundary we  propose to use the criterion that the atmosphere has  to be radiative at the ZAMS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' We propose to define the  Herbig stars as the class of intermediate mass young  stars that are evolving towards the main sequence, with  mass ≳1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5 M⊙, that are surrounded by a remnant accre-  tion disk, as evidenced by the detection of circumstellar  gas at optical and/or longer wavelengths, and an IR ex-  cess caused by circumstellar dust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Herbig stars can be  subdivided into warmer Herbig Ae/Be stars and cooler  IMTT stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The upper mass boundary is more diffi-  cult establish.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The stars with masses ≳ 8-10M⊙ likely  reach the main sequence prior to the dissipation of the  surrounding envelope and are all but impossible to de-  tect on a pre-main sequence track.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' However there are  well established pre-main sequence B stars that exceed  this mass (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=', MWC 297).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' This definition carves out a  general area in the HR diagram whose boundaries are  set by the birth line, the ZAMS line, and evolutionary  tracks of stars with mass ≳1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5M⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Acknowledgements IK acknowledges funding from the Eu-  ropean Union H2020-MSCA-ITN-2019 under Grant Agree-  ment no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 860470 (CHAMELEON).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' GM acknowledges fund-  ing from the Spanish project ”On the Rocks II” (PGC2018-  101950-B-100).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' RDO acknowledges funding for the STARRY  project which received funding from the European Union’s  Horizon 2020 research and innovation programme under MSCA  ITN-EID grant agreement No 676036.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Conflict of interest  The authors declare that they have no conflict of inter-  est.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  References  Ababakr KM, Oudmaijer RD, Vink JS (2016) Linear  spectropolarimetry across the optical spectrum of  Herbig Ae/Be stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS461(3):3089–3110, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/mnras/stw1534, 1607.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='02440  Ababakr KM, Oudmaijer RD, Vink JS (2017) A sta-  tistical spectropolarimetric study of Herbig Ae/Be  stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  MNRAS472:854–868,  DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/mnras/  stx1891, 1707.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='08408  Acke B, Waelkens C (2004) Chemical analysis of  24 dusty (pre-)main-sequence stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A427:1009–  1017, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361:20041460, astro-ph/  0408221  Acke B, van den Ancker ME, Dullemond CP, van  Boekel R, Waters LBFM (2004) Correlation between  grain growth and disk geometry in Herbig Ae/Be  systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A422:621–626, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361:  20040197, astro-ph/0404553  Acke B, van den Ancker ME, Dullemond CP (2005)  [O I] 6300 ˚A emission in Herbig Ae/Be systems:  Signature of Keplerian rotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A436(1):209–  230, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361:20042484, astro-ph/  0502504  Acke B, Bouwman J, Juh´asz A, Henning T, van  den Ancker ME, Meeus G, Tielens AGGM, Wa-  ters LBFM (2010) Spitzer’s View on Aromatic and  Aliphatic Hydrocarbon Emission in Herbig Ae Stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  ApJ718(1):558–574, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/718/  1/558, 1006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1130  Adams SC, ´Ad´amkovics M, Carr JS, Najita JR, Brit-  tain SD (2019) Water and OH Emission from the  Inner Disk of a Herbig Ae/Be Star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ871(2):173,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4357/aaf9a4, 1812.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='07094  Ag´undez M, Roueff E, Le Petit F, Le Bourlot J (2018)  The chemistry of disks around T Tauri and Herbig  Ae/Be stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A616:A19, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  201732518, 1803.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='09450  Aikawa Y, Cataldi G, Yamato Y, Zhang K, Booth AS,  Furuya K, Andrews SM, Bae J, Bergin EA, Bergner  JB, Bosman AD, Cleeves LI, Czekala I, Guzm´an VV,  Huang J, Ilee JD, Law CJ, Le Gal R, Loomis RA,  M´enard F, Nomura H, ¨Oberg KI, Qi C, Schwarz  KR, Teague R, Tsukagoshi T, Walsh C, Wilner  DJ (2021) Molecules with ALMA at Planet-forming  Scales (MAPS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' XIII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' HCO+ and Disk Ionization  Structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJS257(1):13, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4365/  ac143c, 2109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06419  Alecian E, Wade GA, Catala C, Grunhut JH, Land-  street JD, Bagnulo S, B¨ohm T, Folsom CP, Mars-  den S, Waite I (2013) A high-resolution spectropo-  larimetric survey of Herbig Ae/Be stars - I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Obser-  vations and measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS429:1001–1026,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/mnras/sts383, 1211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2907  ALMA Partnership,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brogan CL,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' P´erez LM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hunter  TR,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Dent WRF,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hales AS,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hills RE,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Corder S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Fo-  malont EB,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Vlahakis C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Asaki Y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Barkats D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hi-  rota A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hodge JA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Impellizzeri CMV,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kneissl R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Li-  uzzo E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Lucas R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Marcelino N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Matsushita S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Nakan-  ishi K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Phillips N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Richards AMS,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Toledo I,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Aladro  R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Broguiere D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Cortes JR,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Cortes PC,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Espada D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Galarza F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Garcia-Appadoo D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Guzman-Ramirez L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Humphreys EM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Jung T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kameno S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Laing RA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Leon  S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Marconi G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mignano A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Nikolic B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Nyman LA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Radiszcz M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Remijan A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Rod´on JA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Sawada T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Taka-  hashi S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Tilanus RPJ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Vila Vilaro B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Watson LC,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Wiklind T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Akiyama E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Chapillon E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' de Gregorio-  Monsalvo I,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Di Francesco J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Gueth F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kawamura A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Lee CF,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Nguyen Luong Q,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mangum J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pietu V,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' San-  hueza P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Saigo K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Takakuwa S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ubach C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' van Kem-  54  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  pen T, Wootten A, Castro-Carrizo A, Francke H,  Gallardo J, Garcia J, Gonzalez S, Hill T, Kamin-  ski T, Kurono Y, Liu HY, Lopez C, Morales F,  Plarre K, Schieven G, Testi L, Videla L, Villard  E, Andreani P, Hibbard JE, Tatematsu K (2015)  The 2014 ALMA Long Baseline Campaign: First  Results from High Angular Resolution Observations  toward the HL Tau Region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ808(1):L3, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/2041-8205/808/1/L3, 1503.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='02649  Alonso-Albi T, Fuente A, Bachiller R, Neri R, Plane-  sas P, Testi L, Bern´e O, Joblin C (2009) Circumstel-  lar disks around Herbig Be stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A497:117–136,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/200810401, 0812.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1636  Andre P, Ward-Thompson D, Barsony M (1993) Sub-  millimeter Continuum Observations of rho Ophiuchi  A: The Candidate Protostar VLA 1623 and Prestel-  lar Clumps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ406:122, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/172425  Andrews SM (2020) Observations of Protoplanetary  Disk Structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ARA&A58:483–528, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1146/  annurev-astro-031220-010302, 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='05007  Andrews SM, Huang J, P´erez LM, Isella A, Dulle-  mond CP, Kurtovic NT, Guzm´an VV, Carpenter  JM, Wilner DJ, Zhang S, Zhu Z, Birnstiel T, Bai  XN, Benisty M, Hughes AM, ¨Oberg KI, Ricci L  (2018a) The Disk Substructures at High Angular  Resolution Project (DSHARP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Motivation, Sam-  ple, Calibration, and Overview.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ869:L41, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/2041-8213/aaf741, 1812.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='04040  Andrews SM, Huang J, P´erez LM, Isella A, Dulle-  mond CP, Kurtovic NT, Guzm´an VV, Carpenter  JM, Wilner DJ, Zhang S, Zhu Z, Birnstiel T, Bai  XN, Benisty M, Hughes AM, ¨Oberg KI, Ricci L  (2018b) The Disk Substructures at High Angular  Resolution Project (DSHARP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Motivation, Sam-  ple, Calibration, and Overview.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ869(2):L41, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/2041-8213/aaf741, 1812.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='04040  Andrews SM, Elder W, Zhang S, Huang J, Benisty  M,  Kurtovic  NT,  Wilner  DJ,  Zhu  Z,  Car-  penter  JM,  P´erez  LM,  Teague  R,  Isella  A,  Ricci  L  (2021)  Limits  on  Millimeter  Contin-  uum Emission from Circumplanetary Material in  the DSHARP Disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ916(1):51, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/  1538-4357/ac00b9, 2105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='08821  Ansdell M, Williams JP, van der Marel N, Carpenter  JM, Guidi G, Hogerheijde M, Mathews GS, Manara  CF, Miotello A, Natta A, Oliveira I, Tazzari M, Testi  L, van Dishoeck EF, van Terwisga SE (2016) ALMA  Survey of Lupus Protoplanetary Disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Dust and  Gas Masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ828(1):46, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/0004-637X/  828/1/46, 1604.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='05719  Ansdell M, Williams JP, Trapman L, van Terwisga SE,  Facchini S, Manara CF, van der Marel N, Miotello  A, Tazzari M, Hogerheijde M, Guidi G, Testi L, van  Dishoeck EF (2018) ALMA Survey of Lupus Proto-  planetary Disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Gas Disk Radii.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ859(1):21,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4357/aab890, 1803.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='05923  Antonellini  S  (2016)  Water  in  protoplanetary  disks Line  flux  modeling  and  disk  struc-  ture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  PhD  thesis,  Kapteyn  Astronomical  In-  stitute,  University  of  Groningen,  Landleven  12,  9700  AV  Groningen,  The  Netherlands  ¡EMAIL¿antonellini@astro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='rug.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='nl¡/EMAIL¿  Antonellini S, Kamp I, Riviere-Marichalar P, Meijerink  R, Woitke P, Thi WF, Spaans M, Aresu G, Lee  G (2015) Understanding the water emission in the  mid- and far-IR from protoplanetary disks around T  Tauri stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A582:A105, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  201525724, 1510.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='01482  Antonellini S, Banzatti A, Kamp I, Thi WF, Woitke  P (2020) Model exploration of near-IR ro-vibrational  CO emission as a tracer of inner cavities in protoplan-  etary disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A637:A29, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  201834077, 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='11788  Armitage PJ (2007) Lecture notes on the formation and  early evolution of planetary systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' arXiv e-prints  astro-ph/0701485, astro-ph/0701485  Armitage PJ (2019) Physical Processes in Protoplan-  etary Disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Saas-Fee Advanced Course 45:1, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1007/978-3-662-58687-7 1  Arun R, Mathew B, Manoj P, Ujjwal K, Kartha  SS, Viswanath G, Narang M, Paul KT (2019) On  the Mass Accretion Rate and Infrared Excess in  Herbig Ae/Be Stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' AJ157(4):159, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/  1538-3881/ab0ca1, 1903.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='01070  Arun R, Mathew B, Rengaswamy S, Manoj P, Narang  M, Kartha SS, Maheshwar G (2021) Discovery of  an M-type companion to the Herbig Ae Star V1787  Ori.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS501(1):1243–1252, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/mnras/  staa3652, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='10222  Asplund  M,  Grevesse  N,  Sauval  AJ,  Scott  P  (2009) The Chemical Composition of the Sun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  ARA&A47(1):481–522, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1146/annurev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='astro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='060407.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='145222, 0909.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0948  Augereau JC, Lagrange AM, Mouillet D, Papaloizou  JCB, Grorod PA (1999) On the HR 4796 A circum-  stellar disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A348:557–569, astro-ph/9906429  Avenhaus H, Quanz SP, Meyer MR, Brittain SD,  Carr JS, Najita JR (2014) HD100546 Multi-epoch  Scattered Light Observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ790(1):56, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/790/1/56, 1405.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6120  Avenhaus H, Quanz SP, Schmid HM, Dominik C,  Stolker T, Ginski C, de Boer J, Szul´agyi J, Garufi  A, Zurlo A, Hagelberg J, Benisty M, Henning T,  M´enard F, Meyer MR, Baruffolo A, Bazzon A,  Beuzit JL, Costille A, Dohlen K, Girard JH, Gisler  D, Kasper M, Mouillet D, Pragt J, Roelfsema R,  Herbig Stars  55  Salasnich B, Sauvage JF (2017) Exploring Dust  around HD 142527 down to 0.”025 (4 au) Us-  ing SPHERE/ZIMPOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' AJ154(1):33, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/  1538-3881/aa7560, 1705.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='09680  Ayliffe BA, Bate MR (2009a) Circumplanetary disc  properties obtained from radiation hydrodynam-  ical simulations of gas accretion by protoplan-  ets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS397:657–665, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='15002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='x, 0904.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4884  Ayliffe BA, Bate MR (2009b) Gas accretion on to plan-  etary cores: three-dimensional self-gravitating radi-  ation hydrodynamical calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS393:49–  64, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='14184.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='x, 0811.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  1259  Ayliffe BA, Bate MR (2012) The growth and hy-  drodynamic collapse of a protoplanet envelope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  MNRAS427:2597–2612,  DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='21979.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='x, 1208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5513  Bagnoli T, van Lieshout R, Waters LBFM, van der Plas  G, Acke B, van Winckel H, Raskin G, Meerburg PD  (2010) An Inner Gaseous Disk Around the Herbig  Be Star MWC 147.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ724(1):L5–L8, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/  2041-8205/724/1/L5, 1010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1414  Bai XN (2013) Wind-driven Accretion in Protoplane-  tary Disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Radial Dependence and Global Pic-  ture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ772(2):96, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/772/2/  96, 1305.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='7232  Baines  D,  Oudmaijer  RD,  Porter  JM,  Pozzo  M  (2006) On the binarity of Herbig Ae/Be stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  MNRAS367:737–753,  DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='10006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='x, astro-ph/0512534  Baldovin-Saavedra C, Audard M, Carmona A, G¨udel  M, Briggs K, Rebull LM, Skinner SL, Ercolano B  (2012) On the origin of [Ne II] emission in young  stars: mid-infrared and optical observations with the  Very Large Telescope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A543:A30, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/  0004-6361/201118329, 1205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2182  Banzatti A, Pontoppidan KM (2015) An Empirical  Sequence of Disk Gap Opening Revealed by Rovi-  brational CO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ809:167, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/  809/2/167, 1507.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06650  Banzatti A, Pontoppidan KM, Salyk C, Herczeg GJ,  van Dishoeck EF, Blake GA (2017a) The Depletion of  Water During Dispersal of Planet-forming Disk Re-  gions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ834(2):152, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4357/834/  2/152, 1611.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06230  Banzatti A, Pontoppidan KM, Salyk C, Herczeg GJ,  van Dishoeck EF, Blake GA (2017b) The Depletion  of Water During Dispersal of Planet-forming Disk  Regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ834:152, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4357/834/  2/152, 1611.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06230  Banzatti A, Garufi A, Kama M, Benisty M, Brittain  S, Pontoppidan KM, Rayner J (2018) Observing the  linked depletion of dust and CO gas at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1-10 au in  disks of intermediate-mass stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A609:L2, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201732034, 1711.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='09095  Banzatti A, Abernathy KM, Brittain S, Bosman AD,  Pontoppidan KM, Boogert A, Jensen S, Carr J, Na-  jita J, Grant S, Sigler RM, Sanchez MA, Kern J,  Rayner JT (2022) Scanning Disk Rings and Winds in  CO at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='01-10 au: A High-resolution M-band Spec-  troscopy Survey with IRTF-iSHELL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' AJ163(4):174,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-3881/ac52f0, 2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='03438  Beckwith SVW, Sargent AI, Chini RS, Guesten R  (1990) A survey for circumstellar disks around young  stellar objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' AJ99:924–945, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/115385  Behrend R, Maeder A (2001) Formation of mas-  sive stars by growing accretion rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A373:190–  198, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361:20010585, astro-ph/  0105054  Beltr´an MT, de Wit WJ (2016) Accretion disks in  luminous young stellar objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&ARv24:6, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1007/s00159-015-0089-z, 1509.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='08335  Benisty M, Perraut K, Mourard D, Stee P, Lima  GHRA, Le Bouquin JB, Borges Fernandes M, Ches-  neau O, Nardetto N, Tallon-Bosc I, McAlister H,  Ten Brummelaar T, Ridgway S, Sturmann J, Stur-  mann L, Turner N, Farrington C, Goldfinger PJ  (2013) Enhanced Hα activity at periastron in the  young and massive spectroscopic binary HD 200775.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&A555:A113, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201219893,  1306.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0390  Benisty M, Juhasz A, Boccaletti A, Avenhaus H, Milli  J, Thalmann C, Dominik C, Pinilla P, Buenzli E,  Pohl A, Beuzit JL, Birnstiel T, de Boer J, Bon-  nefoy M, Chauvin G, Christiaens V, Garufi A, Grady  C, Henning T, Huelamo N, Isella A, Langlois M,  M´enard F, Mouillet D, Olofsson J, Pantin E, Pinte  C, Pueyo L (2015) Asymmetric features in the proto-  planetary disk MWC 758.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A578:L6, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/  0004-6361/201526011, 1505.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='05325  Benisty M, Bae J, Facchini S, Keppler M, Teague R,  Isella A, Kurtovic NT, P´erez LM, Sierra A, Andrews  SM, Carpenter J, Czekala I, Dominik C, Henning  T, Menard F, Pinilla P, Zurlo A (2021) A Circum-  planetary Disk around PDS70c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ916(1):L2, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/2041-8213/ac0f83, 2108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='07123  Benisty M, Dominik C, Follette K, Garufi A, Gin-  ski C, Hashimoto J, Keppler M, Kley W, Mon-  nier J (2022) Optical and Near-infrared View of  Planet-forming Disks and Protoplanets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' arXiv e-  prints arXiv:2203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='09991, 2203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='09991  Bergin EA, Cleeves LI, Gorti U, Zhang K, Blake  GA, Green JD, Andrews SM, Evans NJ II, Hen-  ning T, ¨Oberg K, Pontoppidan K, Qi C, Salyk C,  van Dishoeck EF (2013) An old disk still capable  56  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  of forming a planetary system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Nature493:644–646,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1038/nature11805, 1303.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1107  Bergner JB, ¨Oberg KI, Guzm´an VV, Law CJ, Loomis  RA, Cataldi G, Bosman AD, Aikawa Y, Andrews  SM, Bergin EA, Booth AS, Cleeves LI, Czekala I,  Huang J, Ilee JD, Le Gal R, Long F, Nomura H,  M´enard F, Qi C, Schwarz KR, Teague R, Tsuk-  agoshi T, Walsh C, Wilner DJ, Yamato Y (2021)  Molecules with ALMA at Planet-forming Scales  (MAPS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' XI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' CN and HCN as Tracers of Photo-  chemistry in Disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJS257(1):11, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/  1538-4365/ac143a, 2109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06694  Berrilli F, Corciulo G, Ingrosso G, Lorenzetti D,  Nisini B, Strafella F (1992) Infrared Emission from  Dust Structures Surrounding Herbig Ae/Be Stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  ApJ398:254, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/171853  Bertout C (1989) T Tauri stars - Wild as dust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  ARA&A27:351–395,  DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1146/annurev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='aa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  090189.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='002031  Bertout C, Basri G, Bouvier J (1988) Accretion disks  around T Tauri stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ330:350–373, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/  166476  Beust H, Vidal-Madjar A, Ferlet R (1991) The beta  Pectoris protoplanetary system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' XII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Planetary per-  turbations in the disk and star-grazing bodies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&A247:505  Bibo EA, The PS (1990) A study of the Herbig Ae-  type star UX Orionis : its remarkable behaviour in  the colour-magnitude diagram, and the properties of  its dust shell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A236:155  Bik  A,  Thi  WF  (2004)  Evidence  for  an  inner  molecular disk around massive Young Stellar Ob-  jects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A427:L13–L16, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361:  200400088, astro-ph/0410098  Biller BA, Liu MC, Rice K, Wahhaj Z, Nielsen  E, Hayward T, Kuchner MJ, Close LM, Chun  M, Ftaclas C, Toomey DW (2015) The Gemini  NICI Planet-Finding Campaign: asymmetries in the  HD 141569 disc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS450(4):4446–4457, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/mnras/stv870, 1504.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='05224  Birnstiel T, Dullemond CP, Brauer F (2010) Gas- and  dust evolution in protoplanetary disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A513:A79,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/200913731, 1002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0335  Blondel PFC, Djie HRETA (2006) Modeling of PMS  Ae/Fe stars using UV spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A456(3):1045–  1068, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361:20040269  Boccaletti A, Di Folco E, Pantin E, Dutrey A, Guil-  loteau S, Tang YW, Pi´etu V, Habart E, Milli J,  Beck TL, Maire AL (2020) Possible evidence of on-  going planet formation in AB Aurigae.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A showcase  of the SPHERE/ALMA synergy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A637:L5, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/202038008, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='09064  Boccaletti A, Pantin E, M´enard F, Galicher R, Lan-  glois M, Benisty M, Gratton R, Chauvin G, Ginski C,  Lagrange AM, Zurlo A, Biller B, Bonavita M, Bon-  nefoy M, Brown-Sevilla S, Cantalloube F, Desidera S,  D’Orazi V, Feldt M, Hagelberg J, Lazzoni C, Mesa  D, Meyer M, Perrot C, Vigan A, Sauvage JF, Ramos  J, Rousset G, Magnard Y (2021) Investigating point  sources in MWC 758 with SPHERE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A652:L8,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/202141177, 2107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='07850  Boehler Y, Weaver E, Isella A, Ricci L, Grady C, Car-  penter J, Perez L (2017) A Close-up View of the  Young Circumbinary Disk HD 142527.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ840(1):60,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4357/aa696c, 1704.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='00787  Boersma C, Peeters E, Mart´ın-Hern´andez NL, van  der Wolk G, Verhoeff AP, Tielens AGGM, Wa-  ters LBFM, Pel JW (2009) A spatial study of  the mid-IR emission features in four Herbig Ae/Be  stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A502(1):175–187, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  200911820  Bohn AJ, Benisty M, Perraut K, van der Marel N,  W¨olfer L, van Dishoeck EF, Facchini S, Manara  CF, Teague R, Francis L, Berger JP, Garcia-Lopez  R, Ginski C, Henning T, Kenworthy M, Kraus S,  M´enard F, M´erand A, P´erez LM (2022) Probing in-  ner and outer disk misalignments in transition disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Constraints from VLTI/GRAVITY and ALMA ob-  servations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A658:A183, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  202142070, 2112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='00123  Bonnell IA, Bate MR, Clarke CJ, Pringle JE (2001)  Competitive accretion in embedded stellar clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  MNRAS323(4):785–794, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1046/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1365-8711.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='04270.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='x, astro-ph/0102074  Booth AS, Walsh C, Ilee JD, Notsu S, Qi C, Nomura  H, Akiyama E (2019) The First Detection of 13C17O  in a Protoplanetary Disk: A Robust Tracer of Disk  Gas Mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ882(2):L31, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/2041-8213/  ab3645, 1908.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='05045  Bosman AD, Banzatti A, Bruderer S, Tielens AGGM,  Blake GA, van Dishoeck EF (2019) Probing planet  formation and disk substructures in the inner disk  of Herbig Ae stars with CO rovibrational emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&A631:A133, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201935910,  1909.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='02031  Bosman AD, Alarc´on F, Bergin EA, Zhang K, van’t  Hoff MLR, ¨Oberg KI, Guzm´an VV, Walsh C, Aikawa  Y, Andrews SM, Bergner JB, Booth AS, Cataldi G,  Cleeves LI, Czekala I, Furuya K, Huang J, Ilee JD,  Law CJ, Le Gal R, Liu Y, Long F, Loomis RA,  M´enard F, Nomura H, Qi C, Schwarz KR, Teague  R, Tsukagoshi T, Yamato Y, Wilner DJ (2021)  Molecules with ALMA at Planet-forming Scales  (MAPS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Substellar O/H and C/H and Su-  perstellar C/O in Planet-feeding Gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJS257(1):7,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4365/ac1435, 2109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06221  Herbig Stars  57  Boss AP (1997) Giant planet formation by gravita-  tional instability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Science 276:1836–1839, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  1126/science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='276.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5320.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1836  Bouvier J, Corporon P (2001) Herbig Ae/Be Visual Bi-  naries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In: Zinnecker H, Mathieu R (eds) The Forma-  tion of Binary Stars, vol 200, p 155  Bouvier J, Alencar SHP, Harries TJ, Johns-Krull CM,  Romanova MM (2007) Magnetospheric Accretion in  Classical T Tauri Stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Protostars and Planets V pp  479–494, astro-ph/0603498  Bouwman J, Meeus G, de Koter A, Hony S, Dominik  C, Waters LBFM (2001) Processing of silicate dust  grains in Herbig Ae/Be systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A375:950–962,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361:20010878  Bowler BP (2016) Imaging Extrasolar Giant Planets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  PASP128(10):102001, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/1538-3873/128/  968/102001, 1605.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='02731  Brandt GM, Brandt TD, Dupuy TJ, Li Y, Michalik D  (2021a) Precise Dynamical Masses and Orbital Fits  for beta Pic β and β Pic c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' AJ161(4):179, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  3847/1538-3881/abdc2e, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06215  Brandt GM, Brandt TD, Dupuy TJ, Michalik D, Mar-  leau GD (2021b) The First Dynamical Mass Mea-  surement in the HR 8799 System.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ915(1):L16,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/2041-8213/ac0540, 2105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='12820  Braun TAM, Yen HW, Koch PM, Manara CF, Miotello  A, Testi L (2021) Dynamical Stellar Masses of Pre-  main-sequence Stars in Lupus and Taurus Obtained  with ALMA Surveys in Comparison with Stellar  Evolutionary Models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ908(1):46, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/  1538-4357/abd24f, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='07441  Bressan A, Marigo P, Girardi L, Salasnich B, Dal Cero  C, Rubele S, Nanni A (2012) PARSEC: stellar tracks  and isochrones with the PAdova and TRieste Stellar  Evolution Code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS427:127–145, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1111/  j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='21948.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='x, 1208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4498  Brittain SD, Rettig TW (2002) CO and H+  3 in the  protoplanetary disk around the star HD141569.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Nature418:57–59, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1038/nature800  Brittain SD, Simon T, Najita JR, Rettig TW (2007)  Warm  Gas  in  the  Inner  Disks  around  Young  Intermediate-Mass Stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ659:685–704, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  1086/511255, astro-ph/0612201  Brittain SD, Najita JR, Carr JS, Liskowsky J, Trout-  man MR, Doppmann GW (2013) High-resolution  Near-infrared  Spectroscopy  of  HD  100546.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Analysis of Variable Rovibrational CO Emission  Lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ767:159, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/767/2/  159, 1311.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5647  Brittain SD, Najita JR, Carr JS, ´Ad´amkovics M,  Reynolds N (2016) A Study of Ro-vibrational OH  Emission from Herbig Ae/Be Stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ830(2):112,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/0004-637X/830/2/112, 1608.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='00986  Brittain  SD,  Najita  JR,  Carr  JS  (2019)  High-  resolution Near-infrared Spectroscopy of HD 100546.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Orbiting  Companion  Disappears  on  Sched-  ule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ883(1):37, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4357/ab380b,  1908.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='00132  Brittain SD, Najita JR, Dong R, Zhu Z (2020) The  Planetary Luminosity Problem: “Missing Planets”  and the Observational Consequences of Episodic  Accretion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ895(1):48, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4357/  ab8388, 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='11980  Bruderer S (2013) Survival of molecular gas in cavi-  ties of transition disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' CO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A559:A46, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201321171, 1308.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2966  Bruderer S, van Dishoeck EF, Doty SD, Herczeg  GJ (2012) The warm gas atmosphere of the HD  100546 disk seen by Herschel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Evidence of a gas-  rich, carbon-poor atmosphere?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A541:A91, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201118218, 1201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4860  Bryden G, Chen X, Lin DNC, Nelson RP, Papaloizou  JCB (1999) Tidally Induced Gap Formation in Pro-  tostellar Disks: Gap Clearing and Suppression of  Protoplanetary Growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ514(1):344–367, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/306917  Calvet N, Muzerolle J, Brice˜no C, Hern´andez J, Hart-  mann L, Saucedo JL, Gordon KD (2004) The Mass  Accretion Rates of Intermediate-Mass T Tauri Stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  AJ128:1294–1318, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/422733  Calvet N, D’Alessio P, Watson DM, Franco-Hern´andez  R, Furlan E, Green J, Sutter PM, Forrest WJ, Hart-  mann L, Uchida KI, Keller LD, Sargent B, Najita J,  Herter TL, Barry DJ, Hall P (2005) Disks in Tran-  sition in the Taurus Population: Spitzer IRS Spectra  of GM Aurigae and DM Tauri.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ630:L185–L188,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/491652  Caratti o Garatti A, Tambovtseva LV, Garcia Lopez  R, Kraus S, Schertl D, Grinin VP, Weigelt G, Hof-  mann KH, Massi F, Lagarde S, Vannier M, Mal-  bet F (2015) AMBER/VLTI high spectral resolu-  tion observations of the Brγ emitting region in HD  98922.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A compact disc wind launched from the inner  disc region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A582:A44, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  201526002, 1508.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='00798  Carmona  A  (2021)  HD169142  with  CRIRES.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&Asubmitted  Carmona  A,  van  den  Ancker  ME,  Henning  T,  Pavlyuchenkov Y, Dullemond CP, Goto M, Thi WF,  Bouwman J, Waters LBFM (2008) A search for mid-  infrared molecular hydrogen emission from proto-  planetary disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A477(3):839–852, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/  0004-6361:20077846, 0710.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2813  Carmona A, Pinte C, Thi WF, Benisty M, M´enard F,  Grady C, Kamp I, Woitke P, Olofsson J, Roberge  A, Brittain S, Duchˆene G, Meeus G, Martin-Za¨ıdi C,  58  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Dent B, Le Bouquin JB, Berger JP (2014) Constrain-  ing the structure of the transition disk HD 135344B  (SAO 206462) by simultaneous modeling of multi-  wavelength gas and dust observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A567:A51,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201322534, 1403.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6193  Carmona A, Thi WF, Kamp I, Baruteau C, Matter A,  van den Ancker M, Pinte C, K´osp´al A, Audard M,  Liebhart A, Sicilia-Aguilar A, Pinilla P, Reg´aly Z,  G¨udel M, Henning T, Cieza LA, Baldovin-Saavedra  C, Meeus G, Eiroa C (2017) A gas density drop in the  inner 6 AU of the transition disk around the Herbig  Ae star HD 139614 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Further evidence for a giant  planet inside the disk?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A598:A118, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/  0004-6361/201628472, 1609.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06708  Carney MT, Fedele D, Hogerheijde MR, Favre C, Walsh  C, Bruderer S, Miotello A, Murillo NM, Klaassen  PD, Henning T, van Dishoeck EF (2018) Probing  midplane CO abundance and gas temperature with  DCO+ in the protoplanetary disk around HD 169142.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&A614:A106, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201732384,  1802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='09280  Carney MT, Hogerheijde MR, Guzm´an VV, Walsh C,  ¨Oberg KI, Fayolle EC, Cleeves LI, Carpenter JM,  Qi C (2019) Upper limits on CH3OH in the HD  163296 protoplanetary disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Evidence for a low gas-  phase CH3OH-to-H2CO ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A623:A124, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201834353, 1901.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='02689  Carr JS, Tokunaga AT, Najita J (2004) Hot H2O Emis-  sion and Evidence for Turbulence in the Disk of a  Young Star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ603:213–220, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/381356,  astro-ph/0312125  Casassus S, Perez S (2019) Kinematic detections of pro-  toplanets: a Doppler-flip in the disk of HD100546.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  arXiv e-prints arXiv:1906.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06302, 1906.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06302  Casassus S, van der Plas G, M SP, Dent WRF, Fo-  malont E, Hagelberg J, Hales A, Jord´an A, Mawet  D, M´enard F, Wootten A, Wilner D, Hughes AM,  Schreiber MR, Girard JH, Ercolano B, Canovas H,  Rom´an PE, Salinas V (2013) Flows of gas through a  protoplanetary gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Nature493(7431):191–194, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1038/nature11769, 1305.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6062  Casassus S, Wright CM, Marino S, Maddison ST, Woot-  ten A, Roman P, P´erez S, Pinilla P, Wyatt M,  Moral V, M´enard F, Christiaens V, Cieza L, van der  Plas G (2015) A Compact Concentration of Large  Grains in the HD 142527 Protoplanetary Dust Trap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  ApJ812(2):126, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/812/2/126,  1505.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='07743  Caselli P, Walmsley CM, Tafalla M, Dore L, Myers  PC (1999) CO Depletion in the Starless Cloud Core  L1544.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ523(2):L165–L169, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/312280  Casey MP, Zwintz K, Guenther DB, Weiss WW,  Amado PJ, D´ıaz-Fraile D, Rodriguez E, Kuschnig R,  Matthews JM, Moffat AFJ, Rowe JF, Rucinski SM,  Sasselov D (2013) MOST observations of the Herbig  Ae δ-Scuti star HD 34282.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS428(3):2596–2604,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/mnras/sts241, 1210.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4828  Castelli F, Hubrig S, J¨arvinen SP, Sch¨oller M (2020)  The chemical composition of the Herbig Ae SB2  system AK Sco (HD 152404).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS491(2):2010–  2024, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/mnras/stz3015, 1910.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='09372  Catala C (1994) The spectroscopic variability of the  Herbig Ae/Be stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In: The PS,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Perez MR,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' van den  Heuvel EPJ (eds) The Nature and Evolutionary Sta-  tus of Herbig Ae/Be Stars,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Astronomical Society of  the Pacific Conference Series,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' vol 62,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' p 91  Cataldi G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Yamato Y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Aikawa Y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bergner JB,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Fu-  ruya K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Guzm´an VV,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Huang J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Loomis RA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Qi C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Andrews SM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bergin EA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Booth AS,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bosman AD,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Cleeves LI,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Czekala I,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ilee JD,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Law CJ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Le Gal R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Liu Y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Long F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' M´enard F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Nomura H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ¨Oberg KI,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Schwarz KR,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Teague R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Tsukagoshi T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Walsh C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Wilner DJ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Zhang K (2021) Molecules with ALMA at  Planet-forming Scales (MAPS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Studying Deuter-  ation at High Angular Resolution toward Protoplane-  tary Disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJS257(1):10, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4365/  ac143d, 2109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06462  Cauley PW, Johns-Krull CM (2014) Diagnosing Mass  Flows around Herbig Ae/Be Stars Using the He I  λ10830 Line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ797:112, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/  797/2/112, 1410.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6964  Cazzoletti P, van Dishoeck EF, Visser R, Facchini  S, Bruderer S (2018) CN rings in full protoplan-  etary disks around young stars as probes of disk  structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A609:A93, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  201731457, 1709.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='01463  Chapillon E, Guilloteau S, Dutrey A, Pi´etu V, Gu´elin  M (2012) Chemistry in disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' CN and HCN in  protoplanetary disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A537:A60, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/  0004-6361/201116762, 1109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5595  Chiang EI, Goldreich P (1997) Spectral Energy Dis-  tributions of T Tauri Stars with Passive Circum-  stellar Disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ490:368–376, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/304869,  astro-ph/9706042  Close LM, Follette KB, Males JR, Puglisi A, Xom-  pero M, Apai D, Najita J, Weinberger AJ, Morzin-  ski K, Rodigas TJ, Hinz P, Bailey V, Briguglio R  (2014) Discovery of Hα Emission from the Close  Companion inside the Gap of Transitional Disk HD  142527.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ781:L30, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/2041-8205/781/  2/L30, 1401.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1273  Cohen M (1973) Infra-red observations of young stars  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' T Tauri stars and the Orion population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MN-  RAS161:97, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/mnras/161.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='97  Cohen  M  (1980)  Infrared  observations  of  young  stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  VIII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Spectra  in  the  ten-micronregion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Herbig Stars  59  MNRAS191:499–509, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/mnras/191.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='499  Corporon  P,  Lagrange  AM  (1999)  A  search  for  spectroscopic binaries among Herbig Ae/Be stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&AS136:429–444, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/aas:1999225  Costigan G, Vink JS, Scholz A, Ray T, Testi L (2014)  Temperaments of young stars: rapid mass accre-  tion rate changes in T Tauri and Herbig Ae stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  MNRAS440:3444–3461, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/mnras/stu529,  1403.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4088  Cuppen HM, van Dishoeck EF, Herbst E, Tielens  AGGM (2009) Microscopic simulation of methanol  and  formaldehyde  ice  formation  in  cold  dense  cores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A508(1):275–287, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  200913119, 0911.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0283  Currie T, Muto T, Kudo T, Honda M, Brandt TD,  Grady C, Fukagawa M, Burrows A, Janson M,  Kuzuhara M, McElwain MW, Follette K, Hashimoto  J, Henning T, Kandori R, Kusakabe N, Kwon J,  Mede K, Morino Ji, Nishikawa J, Pyo TS, Ser-  abyn G, Suenaga T, Takahashi Y, Wisniewski J,  Tamura M (2014) Recovery of the Candidate Pro-  toplanet HD 100546 b with Gemini/NICI and De-  tection of Additional (Planet-induced?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=') Disk Struc-  ture at Small Separations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ796(2):L30, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/2041-8205/796/2/L30, 1411.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0315  Currie T, Cloutier R, Brittain S, Grady C, Burrows  A, Muto T, Kenyon SJ, Kuchner MJ (2015) Re-  solving the HD 100546 Protoplanetary System with  the Gemini Planet Imager: Evidence for Multiple  Forming, Accreting Planets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ814(2):L27, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/2041-8205/814/2/L27, 1511.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='02526  Currie T, Brittain S, Grady CA, Kenyon SJ, Muto T  (2017) Clarifying the Status of HD 100546 as Ob-  served by the Gemini Planet Imager.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Research Notes  of the American Astronomical Society 1(1):40, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/2515-5172/aaa022, 1712.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='02819  Currie T, Lawson K, Schneider G, Lyra W, Wisniewski  J, Grady C, Guyon O, Tamura M, Kotani T, Kawa-  hara H, Brandt T, Uyama T, Muto T, Dong R,  Kudo T, Hashimoto J, Fukagawa M, Wagner K, Lozi  J, Chilcote J, Tobin T, Groff T, Ward-Duong K,  Januszewski W, Norris B, Tuthill P, van der Marel  N, Sitko M, Deo V, Vievard S, Jovanovic N, Mar-  tinache F, Skaf N (2022) Images of embedded Jo-  vian planet formation at a wide separation around  AB Aurigae.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Nature Astronomy 6:751–759, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1038/s41550-022-01634-x, 2204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='00633  Damiani F, Micela G, Sciortino S, Harnden J F R  (1994) Einstein X-Ray Observations of Herbig Ae/Be  Stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ436:807, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/174957  Danchi WC, Lopez B (2013) Effect of Metallicity on  the Evolution of the Habitable Zone from the Pre-  main Sequence to the Asymptotic Giant Branch and  the Search for Life.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ769(1):27, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/  0004-637X/769/1/27, 1304.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1464  Dartois E, Dutrey A, Guilloteau S (2003) Structure of  the DM Tau Outer Disk: Probing the vertical ki-  netic temperature gradient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A399:773–787, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361:20021638  de Gregorio-Monsalvo I, M´enard F, Dent W, Pinte C,  L´opez C, Klaassen P, Hales A, Cort´es P, Rawlings  MG, Tachihara K, Testi L, Takahashi S, Chapillon E,  Mathews G, Juhasz A, Akiyama E, Higuchi AE, Saito  M, Nyman L˚A, Phillips N, Rod´on J, Corder S, Van  Kempen T (2013) Unveiling the gas-and-dust disk  structure in HD 163296 using ALMA observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&A557:A133, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201321603,  1307.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1357  de Juan Ovelar M, Min M, Dominik C, Thalmann C,  Pinilla P, Benisty M, Birnstiel T (2013) Imaging di-  agnostics for transitional discs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A560:A111, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201322218, 1309.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1039  de Juan Ovelar M, Pinilla P, Min M, Dominik C,  Birnstiel T (2016) Constraining turbulence mixing  strength in transitional discs with planets using  SPHERE and ALMA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS459(1):L85–L89, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/mnrasl/slw051, 1603.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='09357  Dent WRF, Greaves JS, Coulson IM (2005) CO emis-  sion from discs around isolated HAeBe and Vega-  excess stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS359:663–676, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='08938.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='x,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' astro-ph/0502544  Dent WRF,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Thi WF,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kamp I,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Williams JP,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Menard F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Andrews S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ardila D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Aresu G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Augereau JC,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bar-  rado y Navascues D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Carmona A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ciardi  D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Danchi W,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Donaldson J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Duchene G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Eiroa C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Fedele D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Grady C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' de Gregorio-Molsalvo I,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Howard  C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hu´elamo N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Krivov A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Lebreton J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Liseau R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Martin-Zaidi C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mathews G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Meeus G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mendigut´ıa  I,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Montesinos B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Morales-Calderon M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mora A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' No-  mura H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pantin E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pascucci I,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Phillips N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pinte C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Podio L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ramsay SK,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Riaz B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Riviere-Marichalar P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Roberge A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Sandell G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Solano E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Tilling I,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Torrelles  JM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Vandenbusche B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Vicente S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' White GJ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Woitke  P (2013) GASPS—A Herschel Survey of Gas and  Dust in Protoplanetary Disks: Summary and Initial  Statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' PASP125:477–505, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/670826,  1306.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0275  Di Folco E, P´ericaud J, Dutrey A, Augereau JC,  Chapillon E, Guilloteau S, Pi´etu V, Boccaletti A  (2020) An ALMA/NOEMA study of gas dissipation  and dust evolution in the 5 Myr-old HD 141569A  hybrid disc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A635:A94, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  201732243  Disk Dynamics Collaboration, Armitage PJ, Bae J,  Benisty M, Bergin EA, Casassus S, Czekala I, Fac-  chini S, Fung J, Hall C, Ilee JD, Keppler M,  60  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Kuznetsova A, Le Gal R, Loomis RA, Lyra W,  Manger N, Perez S, Pinte C, Price DJ, Rosotti G,  Szulagyi J, Schwarz K, Simon JB, Teague R, Zhang K  (2020) Visualizing the Kinematics of Planet Forma-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' arXiv e-prints arXiv:2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='04345, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='04345  Doi K, Kataoka A (2021) Estimate on Dust Scale  Height from the ALMA Dust Continuum Image of  the HD 163296 Protoplanetary Disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ912(2):164,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4357/abe5a6, 2102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06209  Dominik C, Dullemond CP, Waters LBFM, Walch  S (2003) Understanding the spectra of isolated  Herbig  stars  in  the  frame  of  a  passive  disk  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A398:607–619, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361:  20021629, astro-ph/0212032  Donehew B, Brittain S (2011) Measuring the Stellar  Accretion Rates of Herbig Ae/Be Stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' AJ141:46,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-6256/141/2/46  Dong R, Fung J (2017) How Bright are Planet-induced  Spiral Arms in Scattered Light?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ835(1):38, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4357/835/1/38, 1612.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='00446  Dong R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Rafikov R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Zhu Z,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hartmann L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Whitney B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Brandt T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Muto T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hashimoto J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Grady C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Follette  K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kuzuhara M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Tanii R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Itoh Y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Thalmann C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wis-  niewski J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mayama S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Janson M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Abe L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brandner  W,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Carson J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Egner S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Feldt M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Goto M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Guyon O,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Hayano Y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hayashi M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hayashi S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Henning T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ho-  dapp KW,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Honda M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Inutsuka S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ishii M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Iye M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Kandori R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Knapp GR,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kudo T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kusakabe N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mat-  suo T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' McElwain MW,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Miyama S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Morino JI,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Moro-  Martin A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Nishimura T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pyo TS,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Suto H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Suzuki R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Takami M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Takato N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Terada H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Tomono D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Turner  EL,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Watanabe M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Yamada T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Takami H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Usuda  T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Tamura M (2012) The Missing Cavities in the  SEEDS Polarized Scattered Light Images of Transi-  tional Protoplanetary Disks: A Generic Disk Model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  ApJ750(2):161, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/750/2/161,  1203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1612  Dong R, Zhu Z, Rafikov RR, Stone JM (2015) Observa-  tional Signatures of Planets in Protoplanetary Disks:  Spiral Arms Observed in Scattered Light Imaging  Can be Induced by Planets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ809:L5, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  1088/2041-8205/809/1/L5, 1507.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='03596  Dong R, Fung J, Chiang E (2016) How Spirals and Gaps  Driven by Companions in Protoplanetary Disks Ap-  pear in Scattered Light at Arbitrary Viewing An-  gles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ826(1):75, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/0004-637X/826/1/  75, 1602.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='04814  Dong R, Liu Sy, Eisner J, Andrews S, Fung J, Zhu  Z, Chiang E, Hashimoto J, Liu HB, Casassus S,  Esposito T, Hasegawa Y, Muto T, Pavlyuchenkov  Y, Wilner D, Akiyama E, Tamura M, Wisniewski  J (2018a) The Eccentric Cavity, Triple Rings, Two-  armed Spirals, and Double Clumps of the MWC  758 Disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ860(2):124, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4357/  aac6cb, 1805.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='12141  Dong R, Najita JR, Brittain S (2018b) Spiral Arms  in  Disks:  Planets  or  Gravitational  Instability?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  ApJ862:103, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4357/aaccfc, 1806.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  05183  Doppmann GW, Najita JR, Carr JS, Graham JR  (2011) Warm H2O and OH Disk Emission in V1331  Cyg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ738(1):112, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/738/  1/112, 1106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5173  Drazkowska J, Bitsch B, Lambrechts M, Mulders GD,  Harsono D, Vazan A, Liu B, Ormel CW, Kretke K,  Morbidelli A (2022) Planet Formation Theory in the  Era of ALMA and Kepler: from Pebbles to Exoplan-  ets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' arXiv e-prints arXiv:2203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='09759, 2203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='09759  Duchˆene G (2015) Herbig AeBe stars: multiplicity and  consequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ap&SS355(2):291–301, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1007/  s10509-014-2173-7, 1410.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5883  Duchˆene G, Beust H, Adjali F, Konopacky QM, Ghez  AM (2006) Accurate stellar masses in the multiple  system T Tauri.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A457(1):L9–L12, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/  0004-6361:20065917, astro-ph/0608018  Dullemond  CP,  Dominik  C  (2004a)  Flaring  vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  self-shadowed disks: The SEDs of Herbig Ae/Be  stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A417:159–168, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361:  20031768, astro-ph/0401495  Dullemond CP, Dominik C (2004b) The effect of  dust settling on the appearance of protoplanetary  disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A421:1075–1086, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361:  20040284, astro-ph/0405226  Dullemond CP, Monnier JD (2010) The Inner Regions  of Protoplanetary Disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ARA&A48:205–239, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1146/annurev-astro-081309-130932, 1006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3485  Dullemond CP, Dominik C, Natta A (2001) Pas-  sive Irradiated Circumstellar Disks with an In-  ner Hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ560(2):957–969, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/323057,  astro-ph/0106470  Dullemond CP, van den Ancker ME, Acke B, van  Boekel R (2003) Explaining UX Orionis Star Vari-  ability with Self-shadowed Disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ594(1):L47–  L50, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/378400, astro-ph/0306113  Dullemond CP, Isella A, Andrews SM, Skobleva I,  Dzyurkevich N (2020) Midplane temperature and  outer edge of the protoplanetary disk around HD  163296.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&A633:A137,  DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  201936438, 1911.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='12434  Edwards S, Fischer W, Hillenbrand L, Kwan J (2006)  Probing T Tauri Accretion and Outflow with 1  Micron Spectroscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ646(1):319–341, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  1086/504832, astro-ph/0604006  Eiroa C, Oudmaijer RD, Davies JK, de Winter D,  Garz´on F, Palacios J, Alberdi A, Ferlet R, Grady  CA, Collier Cameron A, Deeg HJ, Harris AW, Horne  Herbig Stars  61  K, Mer´ın B, Miranda LF, Montesinos B, Mora A,  Penny A, Quirrenbach A, Rauer H, Schneider J,  Solano E, Tsapras Y, Wesselius PR (2002) On the  simultaneous optical and near-infrared variability of  pre-main sequence stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A384:1038–1049, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361:20020096  Ekstr¨om S, Georgy C, Eggenberger P, Meynet G,  Mowlavi N, Wyttenbach A, Granada A, Decressin  T, Hirschi R, Frischknecht U, Charbonnel C, Maeder  A (2012) Grids of stellar models with rotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Models from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='8 to 120 M⊙ at solar metallicity (Z  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A537:A146, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  201117751, 1110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5049  Ellerbroek LE, Kaper L, Bik A, de Koter A, Hor-  robin M, Puga E, Sana H, Waters LBFM (2011) The  Intermediate-mass Young Stellar Object 08576nr292:  Discovery of A Disk-Jet System.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ732(1):L9, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/2041-8205/732/1/L9, 1103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4611  Espaillat  C,  Muzerolle  J,  Najita  J,  Andrews  S,  Zhu Z, Calvet N, Kraus S, Hashimoto J, Kraus  A, D’Alessio P (2014) An Observational Perspec-  tive of Transitional Disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In: Beuther H, Klessen  RS, Dullemond CP, Henning T (eds) Protostars  and Planets VI, p 497, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2458/azu uapress  9780816531240-ch022, 1402.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='7103  Fabian D, J¨ager C, Henning T, Dorschner J, Mutschke  H (2000) Steps toward interstellar silicate mineral-  ogy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Thermal Evolution of Amorphous Magnesium  Silicates and Silica.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A364:282–292  Facchini S, Birnstiel T, Bruderer S, van Dishoeck  EF (2017) Different dust and gas radial extents  in protoplanetary disks: consistent models of grain  growth and CO emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A605:A16, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  1051/0004-6361/201630329, 1705.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06235  Fairlamb JR, Oudmaijer RD, Mendigut´ıa I, Ilee JD,  van den Ancker ME (2015) A spectroscopic survey  of Herbig Ae/Be stars with X-shooter - I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Stellar pa-  rameters and accretion rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS453:976–1001,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/mnras/stv1576, 1507.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='05967  Fairlamb JR, Oudmaijer RD, Mendigutia I, Ilee JD,  van den Ancker ME (2017) A spectroscopic survey  of Herbig Ae/Be stars with X-Shooter - II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Accre-  tion diagnostic lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS464:4721–4735, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/mnras/stw2643, 1610.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='09636  Fang M, Kim JS, van Boekel R, Sicilia-Aguilar A, Hen-  ning T, Flaherty K (2013) Young Stellar Objects in  Lynds 1641: Disks, Accretion, and Star Formation  History.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJS207:5, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0067-0049/207/1/  5, 1304.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='7777  Fedele D, van den Ancker ME, Acke B, van der Plas  G, van Boekel R, Wittkowski M, Henning T, Bouw-  man J, Meeus G, Rafanelli P (2008) The struc-  ture of the protoplanetary disk surrounding three  young intermediate mass stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Spatially resolved  dust and gas distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A491(3):809–820, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361:200810126, 0809.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3947  Fedele D, Pascucci I, Brittain S, Kamp I, Woitke P,  Williams JP, Dent WRF, Thi WF (2011) Water De-  pletion in the Disk Atmosphere of Herbig AeBe Stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  ApJ732(2):106, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/732/2/106,  1103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6039  Fedele D, Bruderer S, van Dishoeck EF, Herczeg GJ,  Evans NJ, Bouwman J, Henning T, Green J (2012)  Warm H2O and OH in the disk around the Her-  big star HD 163296.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A544:L9, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/  0004-6361/201219615, 1207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3969  Fedele D, Bruderer S, van Dishoeck EF, Carr J, Herczeg  GJ, Salyk C, Evans NJ, Bouwman J, Meeus G, Hen-  ning T, Green J, Najita JR, G¨udel M (2013) DIGIT  survey of far-infrared lines from protoplanetary disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' [O i], [C ii], OH, H2O, and CH+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A559:A77,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201321118, 1308.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1578  Fedele D, van Dishoeck EF, Kama M, Bruderer S,  Hogerheijde MR (2016) Probing the 2D temperature  structure of protoplanetary disks with Herschel ob-  servations of high-J CO lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A591:A95, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201526948, 1604.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='02055  Fedele D, Carney M, Hogerheijde MR, Walsh C,  Miotello A, Klaassen P, Bruderer S, Henning T,  van Dishoeck EF (2017) ALMA unveils rings and  gaps in the protoplanetary system ¡ASTROBJ¿HD  169142¡/ASTROBJ¿: signatures of two giant pro-  toplanets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A600:A72, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  201629860, 1702.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='02844  Ferlet R, Hobbs LM, Vidal-Madjar A (1987) The beta  Pictoris circumstellar disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Time variations of the  Ca II-K line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A185:267–270  Finkenzeller U (1985) Rotational velocities, spectral  types and forbidden lines of Herbig Ae/Be stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&A151:340–348  Finkenzeller U, Mundt R (1984) The Herbig Ae/Be  stars associated with nebulosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&AS55:109–141  Flaherty K, Hughes AM, Simon JB, Qi C, Bai  XN, Bulatek A, Andrews SM, Wilner DJ, K´osp´al  ´A (2020) Measuring Turbulent Motion in Planet-  forming Disks with ALMA: A Detection around DM  Tau and Nondetections around MWC 480 and V4046  Sgr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ895(2):109, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4357/ab8cc5,  2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='12176  Flaherty KM, Hughes AM, Rosenfeld KA, Andrews  SM, Chiang E, Simon JB, Kerzner S, Wilner DJ  (2015) Weak Turbulence in the HD 163296 Proto-  planetary Disk Revealed by ALMA CO Observa-  tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ813(2):99, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/813/  2/99, 1510.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='01375  Flaherty KM, Hughes AM, Rose SC, Simon JB, Qi  62  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  C, Andrews SM, K´osp´al ´A, Wilner DJ, Chiang E,  Armitage PJ, Bai Xn (2017) A Three-dimensional  View of Turbulence: Constraints on Turbulent Mo-  tions in the HD 163296 Protoplanetary Disk Us-  ing DCO+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ843(2):150, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4357/  aa79f9, 1706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='04504  Follette KB,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Rameau J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Dong R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pueyo L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Close LM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Duchˆene G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Fung J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Leonard C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Macintosh B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Males  JR,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Marois C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Millar-Blanchaer MA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Morzinski KM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Mullen W,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Perrin M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Spiro E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wang J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ammons SM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Bailey VP,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Barman T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bulger J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Chilcote J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Cot-  ten T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' De Rosa RJ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Doyon R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Fitzgerald MP,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Good-  sell SJ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Graham JR,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Greenbaum AZ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hibon P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hung  LW,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ingraham P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kalas P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Konopacky Q,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Larkin JE,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Maire J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Marchis F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Metchev S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Nielsen EL,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Oppen-  heimer R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Palmer D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Patience J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Poyneer L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Rajan A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Rantakyr¨o FT,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Savransky D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Schneider AC,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Sivara-  makrishnan A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Song I,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Soummer R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Thomas S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Vega  D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wallace JK,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ward-Duong K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wiktorowicz S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wolff  S (2017) Complex Spiral Structure in the HD 100546  Transitional Disk as Revealed by GPI and MagAO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  AJ153:264, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-3881/aa6d85, 1704.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  06260  Folsom CP, Bagnulo S, Wade GA, Alecian E, Land-  street JD, Marsden SC, Waite IA (2012) Chemical  abundances of magnetic and non-magnetic Herbig  Ae/Be stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS422:2072–2101, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1111/  j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='20718.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='x, 1202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1845  Fortney JJ, Marley MS, Saumon D, Lodders K (2008)  Synthetic Spectra and Colors of Young Giant Planet  Atmospheres: Effects of Initial Conditions and At-  mospheric Metallicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ683(2):1104–1116, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/589942, 0805.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1066  Frost  AJ,  Oudmaijer  RD,  de  Wit  WJ,  Lums-  den  SL  (2019)  A  multi-scale  exploration  of  a  massive young stellar object.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A transition disk  around G305.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='20+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='21?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A625:A44, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/  0004-6361/201834583, 1903.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='04393  Fung J, Artymowicz P, Wu Y (2015) The 3D Flow Field  Around an Embedded Planet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ811(2):101, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/811/2/101, 1505.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='03152  Gaia Collaboration, Brown AGA, Vallenari A, Prusti T,  de Bruijne JHJ, Mignard F, Drimmel R, Babusiaux  C, Bailer-Jones CAL, Bastian U, et al (2016) Gaia  Data Release 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Summary of the astrometric, pho-  tometric, and survey properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A595:A2, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201629512, 1609.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='04172  Gaia Collaboration, Brown AGA, Vallenari A, Prusti  T, de Bruijne JHJ, Babusiaux C, Bailer-Jones CAL,  Biermann M, Evans DW, Eyer L, et al (2018) Gaia  Data Release 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Summary of the contents and survey  properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A616:A1, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  201833051, 1804.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='09365  Garcia Lopez R, Natta A, Testi L, Habart E (2006)  Accretion rates in Herbig Ae stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A459:837–  842, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361:20065575, astro-ph/  0609032  Garcia Lopez R, Tambovtseva LV, Schertl D, Grinin  VP, Hofmann KH, Weigelt G, Caratti o Garatti  A (2015) Probing the accretion-ejection connec-  tion with VLTI/AMBER.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' High spectral resolution  observations of the Herbig Ae star HD 163296.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&A576:A84, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201424778,  1502.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='03027  Garcia Lopez R, Kurosawa R, Caratti o Garatti A,  Kreplin A, Weigelt G, Tambovtseva LV, Grinin VP,  Ray TP (2016) Investigating the origin and spectro-  scopic variability of the near-infrared H I lines in the  Herbig star VV Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS456(1):156–170, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/mnras/stv2664, 1511.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='03181  Garrison J L M (1978) Observational studies of  the Herbig Ae/Be stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Spectrophotometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  ApJ224:535–545, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/156401  Garufi A, Quanz SP, Avenhaus H, Buenzli E, Do-  minik C, Meru F, Meyer MR, Pinilla P, Schmid  HM, Wolf S (2013) Small vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' large dust grains in  transitional disks: do different cavity sizes indicate  a planet?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='. SAO 206462 (HD 135344B) in polar-  ized light with VLT/NACO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A560:A105, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201322429, 1311.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4195  Garufi A, Podio L, Kamp I, M´enard F, Brittain S,  Eiroa C, Montesinos B, Alonso-Mart´ınez M, Thi WF,  Woitke P (2014) The protoplanetary disk of FT  Tauri: multiwavelength data analysis and modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&A567:A141, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201321987,  1405.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='7692  Garufi A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Benisty M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Stolker T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Avenhaus H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' de Boer  J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pohl A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Quanz SP,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Dominik C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ginski C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Thal-  mann C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' van Boekel R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Boccaletti A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Henning T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Janson M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Salter G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Schmid HM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Sissa E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Langlois  M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Beuzit JL,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Chauvin G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mouillet D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Augereau  JC,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bazzon A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Biller B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bonnefoy M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Buenzli E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Cheetham A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Daemgen S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Desidera S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Engler N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Feldt M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Girard J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Gratton R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hagelberg J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Keller  C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Keppler M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kenworthy M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kral Q,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Lopez B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Maire AL,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Menard F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mesa D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Messina S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Meyer  MR,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Milli J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Min M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Muller A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Olofsson J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pawellek  N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pinte C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Szulagyi J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Vigan A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wahhaj Z,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wa-  ters R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Zurlo A (2017a) Three Years of SPHERE:  The Latest View of the Morphology and Evolution  of Protoplanetary Discs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The Messenger 169:32–37,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='18727/0722-6691/5036, 1710.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='02795  Garufi A, Meeus G, Benisty M, Quanz SP, Banzatti A,  Kama M, Canovas H, Eiroa C, Schmid HM, Stolker  T, Pohl A, Rigliaco E, M´enard F, Meyer MR, van  Boekel R, Dominik C (2017b) Evolution of proto-  Herbig Stars  63  planetary disks from their taxonomy in scattered  light: Group I vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Group II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A603:A21, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201630320, 1703.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='01512  Garufi A, Benisty M, Pinilla P, Tazzari M, Dominik C,  Ginski C, Henning T, Kral Q, Langlois M, M´enard  F, Stolker T, Szulagyi J, Villenave M, van der Plas  G (2018) Evolution of protoplanetary disks from  their taxonomy in scattered light: spirals, rings,  cavities, and shadows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A620:A94, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/  0004-6361/201833872, 1810.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='04564  Garufi A, Dominik C, Ginski C, Benisty M, van Hol-  stein RG, Henning T, Pawellek N, Pinte C, Aven-  haus H, Facchini S, Galicher R, Gratton R, M´enard  F, Muro-Arena G, Milli J, Stolker T, Vigan A, Vil-  lenave M, Moulin T, Origne A, Rigal F, Sauvage  JF, Weber L (2022) A SPHERE survey of self-  shadowed planet-forming disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A658:A137, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/202141692, 2111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='07856  Gillett FC, Stein WA (1971) Infrared Studies of Galac-  tic Nebulae.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' B Stars Associated with Nebulosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  ApJ164:77, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/150817  Ginski C, Stolker T, Pinilla P, Dominik C, Boccaletti  A, de Boer J, Benisty M, Biller B, Feldt M, Garufi  A, Keller CU, Kenworthy M, Maire AL, M´enard F,  Mesa D, Milli J, Min M, Pinte C, Quanz SP, van  Boekel R, Bonnefoy M, Chauvin G, Desidera S, Grat-  ton R, Girard JHV, Keppler M, Kopytova T, La-  grange AM, Langlois M, Rouan D, Vigan A (2016)  Direct detection of scattered light gaps in the tran-  sitional disk around HD 97048 with VLT/SPHERE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&A595:A112, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201629265,  1609.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='04027  Gorti U, Dullemond CP, Hollenbach D (2009) Time  Evolution  of  Viscous  Circumstellar  Disks  due  to Photoevaporation by Far-Ultraviolet, Extreme-  Ultraviolet, and X-ray Radiation from the Cen-  tral  Star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  ApJ705(2):1237–1251,  DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/  0004-637X/705/2/1237, 0909.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1836  Goto M, Usuda T, Dullemond CP, Henning T, Linz H,  Stecklum B, Suto H (2006) Inner Rim of a Molec-  ular Disk Spatially Resolved in Infrared CO Emis-  sion Lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ652:758–762, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/506582,  astro-ph/0606362  Grady CA, Perez MR, Talavera A, Bjorkman KS, de  Winter D, The PS, Molster FJ, van den Ancker ME,  Sitko ML, Morrison ND, Beaver ML, McCollum B,  Castelaz MW (1996) The β Pictoris phenomenon  among Herbig Ae/Be stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' UV and optical high dis-  persion spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Astronomy and Astrophysics Sup-  plement Series 120:157–177  Grady CA, Woodgate B, Bruhweiler FC, Boggess A,  Plait P, Lindler DJ, Clampin M, Kalas P (1999)  Hubble Space Telescope Space Telescope Imaging  Spectrograph Coronagraphic Imaging of the Herbig  AE Star AB Aurigae.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ523(2):L151–L154, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/312270  Grady CA, Hamaguchi K, Schneider G, Stecklum B,  Woodgate BE, McCleary JE, Williger GM, Sitko ML,  M´enard F, Henning T, Brittain S, Troutmann M,  Donehew B, Hines D, Wisniewski JP, Lynch DK,  Russell RW, Rudy RJ, Day AN, Shenoy A, Wilner  D, Silverstone M, Bouret JC, Meusinger H, Clampin  M, Kim S, Petre R, Sahu M, Endres M, Collins KA  (2010) Locating the Accretion Footprint on a Her-  big Ae Star: MWC 480.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ719(2):1565–1581, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/719/2/1565  Grady CA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Muto T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hashimoto J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Fukagawa M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Cur-  rie T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Biller B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Thalmann C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Sitko ML,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Russell R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Wisniewski J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Dong R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kwon J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Sai S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hornbeck  J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Schneider G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hines D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Moro Mart´ın A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Feldt  M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Henning T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pott JU,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bonnefoy M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bouwman  J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Lacour S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mueller A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Juh´asz A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Crida A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Chau-  vin G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Andrews S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wilner D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kraus A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Dahm S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Robitaille T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Jang-Condell H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Abe L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Akiyama E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Brandner W,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brandt T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Carson J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Egner S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Fol-  lette KB,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Goto M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Guyon O,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hayano Y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hayashi  M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hayashi S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hodapp K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ishii M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Iye M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Janson  M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kandori R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Knapp G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kudo T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kusakabe N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Kuzuhara M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mayama S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' McElwain M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Matsuo T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Miyama S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Morino JI,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Nishimura T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pyo TS,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Serabyn  G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Suto H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Suzuki R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Takami M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Takato N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Terada  H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Tomono D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Turner E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Watanabe M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Yamada T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Takami H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Usuda T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Tamura M (2013) Spiral Arms  in the Asymmetrically Illuminated Disk of MWC  758 and Constraints on Giant Planets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ762(1):48,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/762/1/48, 1212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1466  Grant SL, Espaillat CC, Brittain S, Scott-Joseph C,  Calvet N (2022) Tracing Accretion onto Herbig  Ae/Be Stars Using the Brγ Line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ926(2):229,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4357/ac450a, 2112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='10428  Gratton R, Ligi R, Sissa E, Desidera S, Mesa D, Bon-  nefoy M, Chauvin G, Cheetham A, Feldt M, La-  grange AM, Langlois M, Meyer M, Vigan A, Boc-  caletti A, Janson M, Lazzoni C, Zurlo A, De Boer  J, Henning T, D’Orazi V, Gluck L, Madec F, Jaquet  M, Baudoz P, Fantinel D, Pavlov A, Wildi F (2019)  Blobs, spiral arms, and a possible planet around  HD 169142.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A623:A140, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  201834760, 1901.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06555  Gravity Collaboration, Perraut K, Labadie L, Lazareff  B, Klarmann L, Segura-Cox D, Benisty M, Bou-  vier J, Brandner W, Caratti O Garatti A, Caselli  P, Dougados C, Garcia P, Garcia-Lopez R, Kendrew  S, Koutoulaki M, Kervella P, Lin CC, Pineda J,  Sanchez-Bermudez J, van Dishoeck E, Abuter R,  Amorim A, Berger JP, Bonnet H, Buron A, Can-  64  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  talloube F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Cl´enet Y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Coud´e Du Foresto V,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Dexter  J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' de Zeeuw PT,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Duvert G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Eckart A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Eisenhauer F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Eupen F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Gao F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Gendron E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Genzel R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Gillessen S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Gordo P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Grellmann R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Haubois X,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Haussmann F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Henning T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hippler S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Horrobin M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hubert Z,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Jocou  L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Lacour S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Le Bouquin JB,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' L´ena P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' M´erand A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ott  T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Paumard T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Perrin G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pfuhl O,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Rabien S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ray T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Rau C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Rousset G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Scheithauer S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Straub O,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Straub-  meier C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Sturm E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Vincent F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Waisberg I,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wank I,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Widmann F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wieprecht E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wiest M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wiezorrek E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Woillez J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Yazici S (2019) The GRAVITY Young  Stellar Object survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Probing the disks of Her-  big Ae/Be stars in terrestrial orbits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A632:A53,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201936403, 1911.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='00611  Gravity Collaboration,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Garcia Lopez R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Natta A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Caratti o Garatti A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ray TP,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Fedriani R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Koutoulaki  M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Klarmann L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Perraut K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Sanchez-Bermudez J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Benisty M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Dougados C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Labadie L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brandner W,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Garcia PJV,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Henning T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Caselli P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Duvert G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' de  Zeeuw T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Grellmann R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Abuter R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Amorim A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Baub¨ock M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Berger JP,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bonnet H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Buron A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Cl´enet  Y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Coud´e Du Foresto V,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' de Wit W,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Eckart A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Eisen-  hauer F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Filho M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Gao F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Garcia Dabo CE,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Gen-  dron E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Genzel R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Gillessen S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Habibi M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Haubois  X,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Haussmann F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hippler S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hubert Z,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Horrobin M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Jimenez Rosales A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Jocou L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kervella P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kolb J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' La-  cour S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Le Bouquin JB,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' L´ena P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ott T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Paumard  T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Perrin G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pfuhl O,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ramirez A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Rau C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Rousset  G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Scheithauer S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Shangguan J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Stadler J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Straub O,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Straubmeier C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Sturm E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' van Dishoeck E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Vincent F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  von Fellenberg S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Widmann F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wieprecht E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wiest  M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wiezorrek E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Woillez J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Yazici S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Zins G (2020)  A measure of the size of the magnetospheric ac-  cretion region in TW Hydrae.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Nature584(7822):547–  550, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1038/s41586-020-2613-1, 2104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06441  GRAVITY  Collaboration,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Sanchez-Bermudez  J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Caratti O Garatti A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Garcia Lopez R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Perraut K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Labadie L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Benisty M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brandner W,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Dougados C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Garcia PJV,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Henning T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Klarmann L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Amorim A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Baub¨ock M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Berger JP,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Le Bouquin JB,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Caselli  P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Cl´enet Y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Coud´e Du Foresto V,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' de Zeeuw PT,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Drescher A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Duvert G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Eckart A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Eisenhauer F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Filho M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Gao F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Gendron E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Genzel R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Gillessen  S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Grellmann R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Heissel G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Horrobin M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hubert Z,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Jim´enez-Rosales A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Jocou L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kervella P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Lacour S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Lapeyr`ere V,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' L´ena P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ott T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Paumard T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Perrin  G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pineda JE,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Rodr´ıguez-Coira G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Rousset G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Segura-Cox DM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Shangguan J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Shimizu T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Stadler  J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Straub O,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Straubmeier C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Sturm E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' van Dishoeck  E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Vincent F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' von Fellenberg SD,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Widmann F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Woillez J (2021) The GRAVITY young stellar  object  survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Mapping  the  variable  inner  disk of HD 163296 at sub-au scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A654:A97,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/202039600, 2107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='02391  Greenwood AJ, Kamp I, Waters LBFM, Woitke P, Thi  WF (2019) Effects of dust evolution on protoplan-  etary disks in the mid-infrared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A626:A6, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201834365  Gressel O, Nelson RP, Turner NJ, Ziegler U (2013)  Global Hydromagnetic Simulations of a Planet Em-  bedded in a Dead Zone: Gap Opening, Gas Accretion,  and Formation of a Protoplanetary Jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ779:59,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/779/1/59, 1309.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2871  Grinin VP (1992) Young stars with non-periodic algol-  type minima.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Astronomical and Astrophysical Trans-  actions 3(1):17–32, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1080/10556799208230535  Grinin VP, The PS, de Winter D, Giampapa M, Ros-  topchina AN, Tambovtseva LV, van den Ancker ME  (1994) The β Pictoris phenomenon among young  stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The case of the Herbig AE star UX Orio-  nis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A292:165–174  Guidi G, Tazzari M, Testi L, de Gregorio-Monsalvo  I, Chandler CJ, P´erez L, Isella A, Natta A, Or-  tolani S, Henning T, Corder S, Linz H, Andrews S,  Wilner D, Ricci L, Carpenter J, Sargent A, Mundy  L, Storm S, Calvet N, Dullemond C, Greaves J,  Lazio J, Deller A, Kwon W (2016) Dust properties  across the CO snowline in the HD 163296 disk from  ALMA and VLA observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A588:A112, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201527516, 1601.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='07542  Guilloteau S, Di Folco E, Dutrey A, Simon M, Grosso  N, Pi´etu V (2013) A sensitive survey for 13CO, CN,  H2CO, and SO in the disks of T Tauri and Her-  big Ae stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A549:A92, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  201220298, 1211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4776  Guilloteau S, Simon M, Pi´etu V, Di Folco E, Dutrey  A, Prato L, Chapillon E (2014) The masses of  young stars: CN as a probe of dynamical masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&A567:A117, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201423765,  1406.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3805  Guimar˜aes MM, Alencar SHP, Corradi WJB, Vieira  SLA (2006) Stellar parameters and evidence of cir-  cumstellar activity for a sample of Herbig Ae/Be  stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A457(2):581–589, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361:  20065005  Gundlach B, Schmidt KP, Kreuzig C, Bischoff D,  Rezaei F, Kothe S, Blum J, Grzesik B, Stoll E  (2018) The tensile strength of ice and dust ag-  gregates and its dependence on particle proper-  ties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS479(1):1273–1277, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/mnras/  sty1550  Guzm´an-D´ıaz J, Mendigut´ıa I, Montesinos B, Oud-  maijer RD, Vioque M, Rodrigo C, Solano E, Meeus  G, Marcos-Arenal P (2021) Homogeneous study of  Herbig Ae/Be stars from spectral energy distribu-  tions and Gaia EDR3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A650:A182, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/  Herbig Stars  65  0004-6361/202039519, 2104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='11759  Haffert SY, Bohn AJ, de Boer J, Snellen IAG, Brinch-  mann J, Girard JH, Keller CU, Bacon R (2019)  Two accreting protoplanets around the young star  PDS 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Nature Astronomy p 329, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1038/  s41550-019-0780-5, 1906.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='01486  Hales AS, De Gregorio-Monsalvo I, Montesinos B,  Casassus S, Dent WFR, Dougados C, Eiroa C,  Hughes AM, Garay G, Mardones D, M´enard F, Palau  A, P´erez S, Phillips N, Torrelles JM, Wilner D (2014)  A CO Survey in Planet-forming Disks: Character-  izing the Gas Content in the Epoch of Planet For-  mation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' AJ148(3):47, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-6256/148/  3/47, 1405.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6966  Hall C, Dong R, Rice K, Harries TJ, Najita J, Alexan-  der R, Brittain S (2019) The Temporal Requirements  of Directly Observing Self-gravitating Spiral Waves  in Protoplanetary Disks with ALMA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ871(2):228,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4357/aafac2, 1901.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='02407  Hamaguchi K, Yamauchi S, Koyama K (2005) X-Ray  Study of Herbig Ae/Be Stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ618(1):360–384,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/423192, astro-ph/0406489  Hartmann L, Kenyon SJ, Calvet N (1993) The Excess  Infrared Emission of Herbig Ae/Be Stars: Disks or  Envelopes?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ407:219, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/172507  Hartmann L, Calvet N, Gullbring E, D’Alessio P  (1998) Accretion and the Evolution of T Tauri Disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  ApJ495:385–400, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/305277  Hartmann L, Herczeg G, Calvet N (2016) Accretion  onto Pre-Main-Sequence Stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ARA&A54:135–180,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1146/annurev-astro-081915-023347  Hashimoto J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Tamura M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Muto T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kudo T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Fuka-  gawa M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Fukue T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Goto M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Grady CA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Henning  T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hodapp K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Honda M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Inutsuka S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kokubo E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Knapp G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' McElwain MW,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Momose M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ohashi N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Okamoto YK,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Takami M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Turner EL,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wisniewski J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Janson M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Abe L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brandner W,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Carson J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Egner S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Feldt M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Golota T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Guyon O,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hayano Y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hayashi M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Hayashi S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ishii M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kandori R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kusakabe N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Matsuo  T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mayama S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Miyama S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Morino JI,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Moro-Martin  A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Nishimura T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pyo TS,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Suto H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Suzuki R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Takato  N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Terada H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Thalmann C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Tomono D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Watanabe  M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Yamada T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Takami H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Usuda T (2011) Direct  Imaging of Fine Structures in Giant Planet-forming  Regions of the Protoplanetary Disk Around AB Au-  rigae.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ729(2):L17, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/2041-8205/729/  2/L17, 1102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4408  Hein Bertelsen RP, Kamp I, Goto M, van der Plas G,  Thi WF, Waters LBFM, van den Ancker ME, Woitke  P (2014) CO ro-vibrational lines in HD 100546.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A search for disc asymmetries and the role of flu-  orescence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A561:A102, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  201322574, 1311.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5353  Hein Bertelsen RP, Kamp I, van der Plas G, van  den Ancker ME, Waters LBFM, Thi WF, Woitke P  (2016) A proposed new diagnostic for Herbig disc ge-  ometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' FWHM versus J of CO ro-vibrational lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&A590:A98, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201527652,  1603.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='03546  Henning T, Meeus G (2011) Dust Processing and Min-  eralogy in Protoplanetary Accretion Disks, pp 114–  148  Henning T, Launhardt R, Steinacker J, Thamm E  (1994) Cold dust around southern Herbig Ae/Be  stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A291:546–556  Henning T, Semenov D, Guilloteau S, Dutrey A, Her-  sant F, Wakelam V, Chapillon E, Launhardt R, Pi´etu  V, Schreyer K (2010) Chemistry in Disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pho-  tochemistry and X-ray Driven Chemistry Probed by  the Ethynyl Radical (CCH) in DM Tau, LkCa 15,  and MWC 480.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ714(2):1511–1520, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/  0004-637X/714/2/1511, 1003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5793  Herbig GH (1960) The Spectra of Be- and Ae-Type  Stars Associated with Nebulosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJS4:337, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/190050  Herbig GH, Bell KR (1988) Third Catalog of Emission-  Line Stars of the Orion Population : 3 : 1988  Herbst W, Herbst DK, Grossman EJ, Weinstein D  (1994) Catalogue of UBVRI Photometry of T Tauri  Stars and Analysis of the Causes of Their Variability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  AJ108:1906, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/117204  Hillenbrand LA, Strom SE, Vrba FJ, Keene J (1992)  Herbig Ae/Be Stars: Intermediate-Mass Stars Sur-  rounded by Massive Circumstellar Accretion Disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  ApJ397:613, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/171819  Hillenbrand LA, Meyer MR, Strom SE, Skrutskie MF  (1995) Isolated Star-Forming Regions Containing  Herbig AE/BE Stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The Young Stellar Aggregate  Associated With BD +40 degrees 4124.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' AJ109:280,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/117272  Hiraoka K, Ohashi N, Kihara Y, Yamamoto K, Sato T,  Yamashita A (1994) Formation of formaldehyde and  methanol from the reactions of H atoms with solid  CO at 10-20 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Chemical Physics Letters 229(4):408–  414, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1016/0009-2614(94)01066-8  Hoffmeister VH, Chini R, Scheyda CM, Schulze D,  Watermann R, N¨urnberger D, Vogt N (2008) The  Stellar Population of M17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ686(1):310–324, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/591070  Honda M, Inoue AK, Fukagawa M, Oka A, Nakamoto  T, Ishii M, Terada H, Takato N, Kawakita H,  Okamoto YK, Shibai H, Tamura M, Kudo T,  Itoh  Y  (2009)  Detection  of  Water  Ice  Grains  on the Surface of the Circumstellar Disk Around  HD 142527.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ690(2):L110–L113, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/  0004-637X/690/2/L110  66  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Honda M, Maaskant K, Okamoto YK, Kataza H, Fuka-  gawa M, Waters LBFM, Dominik C, Tielens AGGM,  Mulders GD, Min M, Yamashita T, Fujiyoshi T,  Miyata T, Sako S, Sakon I, Fujiwara H, Onaka  T (2012) Mid-infrared Imaging of the Transitional  Disk of HD 169142: Measuring the Size of the Gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  ApJ752(2):143, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/752/2/143,  1204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5364  Honda M, Maaskant K, Okamoto YK, Kataza H, Ya-  mashita T, Miyata T, Sako S, Fujiyoshi T, Sakon  I, Fujiwara H, Kamizuka T, Mulders GD, Lopez-  Rodriguez E, Packham C, Onaka T (2015) High-  resolution 25 µm Imaging of the Disks around  Herbig Ae/Be Stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ804(2):143, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/  0004-637X/804/2/143, 1504.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='00096  Honda M, Kudo T, Takatsuki S, Inoue AK, Nakamoto  T, Fukagawa M, Tamura M, Terada H, Takato N  (2016) Water Ice at the Surface of the HD 100546  Disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ821(1):2, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/0004-637X/821/1/  2, 1603.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='09512  Hosokawa T, Omukai K (2009) Evolution of Mas-  sive  Protostars  with  High  Accretion  Rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  ApJ691(1):823–846,  DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/  691/1/823, 0806.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4122  Howard AW,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Marcy GW,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bryson ST,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Jenkins JM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Rowe JF,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Batalha NM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Borucki WJ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Koch DG,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Dunham EW,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Gautier I Thomas N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Van Cleve J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Cochran WD,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Latham DW,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Lissauer JJ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Torres G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Brown TM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Gilliland RL,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Buchhave LA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Caldwell  DA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Christensen-Dalsgaard J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ciardi D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Fressin F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Haas MR,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Howell SB,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kjeldsen H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Seager S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Rogers  L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Sasselov DD,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Steffen JH,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Basri GS,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Charbonneau  D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Christiansen J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Clarke B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Dupree A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Fabrycky  DC,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Fischer DA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ford EB,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Fortney JJ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Tarter J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Girouard FR,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Holman MJ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Johnson JA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Klaus TC,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Machalek P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Moorhead AV,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Morehead RC,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ragozzine  D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Tenenbaum P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Twicken JD,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Quinn SN,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Isaacson  H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Shporer A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Lucas PW,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Walkowicz LM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Welsh WF,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Boss A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Devore E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Gould A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Smith JC,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Morris RL,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Prsa A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Morton TD,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Still M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Thompson SE,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mul-  lally F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Endl M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MacQueen PJ (2012) Planet Occur-  rence within 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='25 AU of Solar-type Stars from Ke-  pler.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJS201(2):15, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0067-0049/201/2/  15, 1103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2541  Huang J,  ¨Oberg KI, Qi C, Aikawa Y, Andrews  SM, Furuya K, Guzm´an VV, Loomis RA, van  Dishoeck EF, Wilner DJ (2017) An ALMA Survey  of DCN/H13CN and DCO+/H13CO+ in Protoplane-  tary Disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ835(2):231, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4357/  835/2/231, 1701.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='01735  Hubrig S, Carroll TA, Scholler M, Ilyin I (2015) The  prevalence of weak magnetic fields in Herbig Ae stars:  the case of PDS 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS449:L118–L122, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  1093/mnrasl/slv034, 1502.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='05498  Hu´elamo  N,  Lacour  S,  Tuthill  P,  Ireland  M,  Kraus A, Chauvin G (2011) A companion candi-  date in the gap of the T Chamaeleontis transi-  tional disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A528:L7, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  201016395, 1102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4982  Hughes AM, Wilner DJ, Andrews SM, Qi C, Hogerhei-  jde MR (2011) Empirical Constraints on Turbulence  in Protoplanetary Accretion Disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ727(2):85,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/727/2/85, 1011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3826  Hughes  AM,  Duchˆene  G,  Matthews  BC  (2018)  Debris  Disks:  Structure,  Composition,  and  Variability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  ARA&A56:541–591,  DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1146/annurev-astro-081817-052035, 1802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='04313  Hung LW, Fitzgerald MP, Chen CH, Mittal T, Kalas  PG, Graham JR (2015) Discovery of Resolved De-  bris Disk around HD 131835.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ802(2):138, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/802/2/138, 1502.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='02035  Ilee JD, Wheelwright HE, Oudmaijer RD, de Wit WJ,  Maud LT, Hoare MG, Lumsden SL, Moore TJT,  Urquhart JS, Mottram JC (2013) CO bandhead  emission of massive young stellar objects: determin-  ing disc properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS429(4):2960–2973, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/mnras/sts537, 1212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0554  Ilee JD, Fairlamb J, Oudmaijer RD, Mendigut´ıa  I, van den Ancker ME, Kraus S, Wheelwright  HE (2014) Investigating the inner discs of Her-  big  Ae/Be  stars  with  CO  bandhead  and  Brγ  emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS445(4):3723–3736, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/  mnras/stu1942, 1409.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4897  Ilee JD, Hall C, Walsh C, Jim´enez-Serra I, Pinte C,  Terry J, Bourke TL, Hoare M (2020) Observing  protoplanetary discs with the Square Kilometre Ar-  ray - I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Characterizing pebble substructure caused  by forming planets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS498(4):5116–5127, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/mnras/staa2699, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='00562  Ilee JD, Walsh C, Booth AS, Aikawa Y, Andrews SM,  Bae J, Bergin EA, Bergner JB, Bosman AD, Cataldi  G, Cleeves LI, Czekala I, Guzm´an VV, Huang J,  Law CJ, Le Gal R, Loomis RA, M´enard F, No-  mura H, ¨Oberg KI, Qi C, Schwarz KR, Teague  R, Tsukagoshi T, Wilner DJ, Yamato Y, Zhang  K (2021) Molecules with ALMA at Planet-forming  Scales (MAPS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' IX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Distribution and Properties  of the Large Organic Molecules HC3N, CH3CN,  and c-C3H2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJS257(1):9, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4365/  ac1441, 2109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06319  Ingleby L, Calvet N, Herczeg G, Blaty A, Walter F,  Ardila D, Alexand er R, Edwards S, Espaillat C,  Gregory SG, Hillenbrand L, Brown A (2013) Accre-  tion Rates for T Tauri Stars Using Nearly Simultane-  ous Ultraviolet and Optical Spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ767(2):112,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/767/2/112, 1303.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0769  Herbig Stars  67  Isella A, Natta A (2005) The shape of the inner rim  in proto-planetary disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A438(3):899–907, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361:20052773, astro-ph/0503635  Isella A, Guidi G, Testi L, Liu S, Li H, Li S, Weaver  E, Boehler Y, Carperter JM, De Gregorio-Monsalvo  I, Manara CF, Natta A, P´erez LM, Ricci L, Sar-  gent A, Tazzari M, Turner N (2016) Ringed Struc-  tures of the HD 163296 Protoplanetary Disk Re-  vealed by ALMA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='117(25):251101,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='117.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='251101  Isella A, Benisty M, Teague R, Bae J, Keppler M, Fac-  chini S, P´erez L (2019) Detection of Continuum Sub-  millimeter Emission Associated with Candidate Pro-  toplanets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ879(2):L25, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/2041-8213/  ab2a12, 1906.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06308  Janson M, Squicciarini V, Delorme P, Gratton R, Bon-  nefoy M, Reffert S, Mamajek EE, Eriksson SC, Vi-  gan A, Langlois M, Engler N, Chauvin G, Desidera  S, Mayer L, Marleau GD, Bohn AJ, Samland M,  Meyer M, d’Orazi V, Henning T, Quanz S, Ken-  worthy M, Carson JC (2021) BEAST begins: sample  characteristics and survey performance of the B-star  Exoplanet Abundance Study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A646:A164, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/202039683, 2101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='02043  J¨arvinen SP, Carroll TA, Hubrig S, Ilyin I, Sch¨oller  M (2019) New evidence for weak magnetic fields in  Herbig Ae/Be stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS489(1):886–890, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/mnras/stz2190, 1908.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='02093  Jermyn AS, Kama M (2018) Stellar photospheric  abundances  as  a  probe  of  discs  and  plan-  ets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS476(4):4418–4434, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/mnras/  sty429, 1804.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06414  Jim´enez-Donaire MJ, Meeus G, Karska A, Montesinos  B, Bouwman J, Eiroa C, Henning T (2017) Herschel  observations of the circumstellar environments of the  Herbig Be stars R Mon and PDS 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A605:A62,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201629053, 1705.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='05860  Johnson JA, Howard AW, Bowler BP, Henry GW,  Marcy GW, Wright JT, Fischer DA, Isaacson H  (2010) Retired A Stars and Their Companions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Seven Jovian Exoplanets from Keck Observatory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  PASP122:701, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/653809, 1003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3445  Jonkheid  B,  Faas  FGA,  van  Zadelhoff  GJ,  van  Dishoeck EF (2004) The gas temperature in flaring  disks around pre-main sequence stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A428:511–  521, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361:20048013, astro-ph/  0408503  Juh´asz A, Bouwman J, Henning T, Acke B, van den  Ancker ME, Meeus G, Dominik C, Min M, Tie-  lens AGGM, Waters LBFM (2010) Dust Evolu-  tion in Protoplanetary Disks Around Herbig Ae/Be  Stars—the Spitzer View.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ721:431–455, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  1088/0004-637X/721/1/431, 1008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0083  Kama M, Min M, Dominik C (2009) The inner rim  structures of protoplanetary discs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A506(3):1199–  1213,  DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/200912068,  0908.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  1692  Kama M, Folsom CP, Pinilla P (2015) Fingerprints of  giant planets in the photospheres of Herbig stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&A582:L10, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201527094,  1509.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='02741  Kama M, Bruderer S, Carney M, Hogerheijde M, van  Dishoeck EF, Fedele D, Baryshev A, Boland W,  G¨usten R, Aikutalp A, Choi Y, Endo A, Frieswijk  W, Karska A, Klaassen P, Koumpia E, Kristensen L,  Leurini S, Nagy Z, Perez Beaupuits JP, Risacher C,  van der Marel N, van Kempen TA, van Weeren RJ,  Wyrowski F, Yıldız UA (2016a) Observations and  modelling of CO and [C I] in protoplanetary disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  First detections of [C I] and constraints on the carbon  abundance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A588:A108, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  201526791, 1601.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='01449  Kama M, Bruderer S, van Dishoeck EF, Hogerhei-  jde M, Folsom CP, Miotello A, Fedele D, Belloche  A, G¨usten R, Wyrowski F (2016b) Volatile-carbon  locking and release in protoplanetary disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A study  of TW Hya and HD 100546.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A592:A83, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201526991, 1605.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='05093  Kama  M,  Shorttle  O,  Jermyn  AS,  Folsom  CP,  Furuya  K,  Bergin  EA,  Walsh  C,  Keller  L  (2019) Abundant Refractory Sulfur in Protoplane-  tary Disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ885(2):114, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4357/  ab45f8, 1908.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='05169  Kama M, Trapman L, Fedele D, Bruderer S, Hoger-  heijde MR, Miotello A, van Dishoeck EF, Clarke  C, Bergin EA (2020) Mass constraints for 15 pro-  toplanetary discs from HD 1-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A634:A88, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201937124, 1912.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='11883  Kamp I, Dullemond CP (2004) The Gas Tempera-  ture in the Surface Layers of Protoplanetary Disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  ApJ615:991–999, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/424703, astro-ph/  0408501  Kamp I, Hempel M, Holweger H (2002) Do dusty  A stars exhibit accretion signatures in their photo-  spheres?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A388:978–984, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361:  20020493, astro-ph/0204449  Kamp I, Tilling I, Woitke P, Thi W, Hogerhei-  jde  M  (2010)  Radiation  thermo-chemical  mod-  els of protoplanetary disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Line diagnostics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&A510(26):A260000+,  DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  200913076, 0911.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1949  Kamp I, Woitke P, Pinte C, Tilling I, Thi WF,  Menard F, Duchene G, Augereau JC (2011) Con-  tinuum and line modelling of discs around young  stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Line diagnostics for GASPS from the  DENT grid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A532:A85, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  68  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  201016399, 1103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5763  Kemper F, Vriend WJ, Tielens AGGM (2004) The Ab-  sence of Crystalline Silicates in the Diffuse Inter-  stellar Medium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ609(2):826–837, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/  421339, astro-ph/0403609  Kenyon SJ, Najita JR, Bromley BC (2016) Rocky  Planet Formation: Quick and Neat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ831(1):8,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/0004-637X/831/1/8, 1608.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='05410  Keppler M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Benisty M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' M¨uller A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Henning T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' van  Boekel R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Cantalloube F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ginski C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' van Holstein RG,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Maire AL,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pohl A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Samland M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Avenhaus H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Baudino  JL,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Boccaletti A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' de Boer J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bonnefoy M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Chauvin  G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Desidera S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Langlois M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Lazzoni C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Marleau GD,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Mordasini C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pawellek N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Stolker T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Vigan A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Zurlo  A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Birnstiel T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brandner W,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Feldt M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Flock M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Gi-  rard J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Gratton R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hagelberg J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Isella A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Janson M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Juhasz A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kemmer J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kral Q,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Lagrange AM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Laun-  hardt R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Matter A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' M´enard F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Milli J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Molli`ere P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Olofsson J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' P´erez L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pinilla P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pinte C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Quanz SP,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Schmidt T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Udry S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wahhaj Z,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Williams JP,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Buenzli  E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Cudel M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Dominik C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Galicher R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kasper M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Lan-  nier J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mesa D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mouillet D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Peretti S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Perrot C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Salter  G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Sissa E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wildi F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Abe L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Antichi J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Augereau JC,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Baruffolo A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Baudoz P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bazzon A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Beuzit JL,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Blan-  chard P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brems SS,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Buey T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' De Caprio V,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Carbillet  M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Carle M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Cascone E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Cheetham A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Claudi R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Cos-  tille A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Delboulb´e A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Dohlen K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Fantinel D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Feautrier  P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Fusco T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Giro E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Gluck L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Gry C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hubin N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hugot  E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Jaquet M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Le Mignant D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Llored M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Madec F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Magnard Y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Martinez P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Maurel D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Meyer M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' M¨oller-  Nilsson O,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Moulin T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mugnier L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Orign´e A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pavlov  A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Perret D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Petit C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pragt J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Puget P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Rabou P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Ramos J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Rigal F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Rochat S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Roelfsema R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Rousset G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Roux A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Salasnich B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Sauvage JF,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Sevin A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Soenke C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Stadler E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Suarez M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Turatto M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Weber L (2018) Dis-  covery of a planetary-mass companion within the gap  of the transition disk around PDS 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A617:A44,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201832957, 1806.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='11568  Kessler-Silacci JE, Dullemond CP, Augereau JC, Mer´ın  B, Geers VC, van Dishoeck EF, Evans I N J, Blake  GA, Brown J (2007) Probing Protoplanetary Disks  with Silicate Emission: Where Is the Silicate Emis-  sion Zone?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ659(1):680–684, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/511853,  astro-ph/0612450  Khalafinejad S, Maaskant KM, Mari˜nas N, Tielens  AGGM (2016) Large dust gaps in the transitional  disks of HD 100453 and HD 34282.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Connecting the  gap size to the spectral energy distribution and  mid-infrared imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A587:A62, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/  0004-6361/201423984, 1509.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06531  Kim S, Nomura H, Tsukagoshi T, Kawabe R, Muto  T (2019) The Synthetic ALMA Multiband Analysis  of the Dust Properties of the TW Hya Protoplane-  tary Disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ872(2):179, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4357/  ab0304, 1902.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='00168  Kley W, Nelson RP (2012) Planet-Disk Interaction  and Orbital Evolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ARA&A50:211–249, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1146/annurev-astro-081811-125523, 1203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1184  Kluska J, Berger JP, Malbet F, Lazareff B, Benisty  M, Le Bouquin JB, Absil O, Baron F, Delboulb´e  A, Duvert G, Isella A, Jocou L, Juhasz A, Kraus  S, Lachaume R, M´enard F, Millan-Gabet R, Mon-  nier JD, Moulin T, Perraut K, Rochat S, Pinte C,  Soulez F, Tallon M, Thi WF, Thi´ebaut E, Traub  W, Zins G (2020) A family portrait of disk in-  ner rims around Herbig Ae/Be stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hunting for  warps, rings, self shadowing, and misalignments in  the inner astronomical units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A636:A116, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201833774, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='01594  K´osp´al ´A, Mo´or A, Juh´asz A, ´Abrah´am P, Apai D,  Csengeri T, Grady CA, Henning T, Hughes AM,  Kiss C (2013) ALMA Observations of the Molecu-  lar Gas in the Debris Disk of the 30 Myr Old Star  HD 21997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ776(2):77, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/  776/2/77, 1310.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5068  Koumpia E, Ababakr KM, de Wit WJ, Oudmai-  jer RD, Caratti o Garatti A, Boley P, Linz H,  Kraus S, Vink JS, Le Bouquin JB (2019) Re-  solving the MYSO binaries PDS 27 and PDS 37  with VLTI/PIONIER.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A623:L5, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/  0004-6361/201834624, 1903.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='02667  Kraus M (2019) A Census of B[e] Supergiants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Galaxies  7(4):83, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3390/galaxies7040083, 1909.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='12199  Kraus S, Hofmann KH, Benisty M, Berger JP, Ches-  neau O, Isella A, Malbet F, Meilland A, Nardetto  N, Natta A, Preibisch T, Schertl D, Smith M,  Stee P, Tatulli E, Testi L, Weigelt G (2008) The  origin of hydrogen line emission for five Herbig  Ae/Be stars spatially resolved by VLTI/AMBER  spectro-interferometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A489(3):1157–1173, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361:200809946, 0807.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1119  Kraus S, Kluska J, Kreplin A, Bate M, Harries TJ,  Hofmann KH, Hone E, Monnier JD, Weigelt G,  Anugu A, de Wit WJ, Wittkowski M (2017) A  High-mass Protobinary System with Spatially Re-  solved Circumstellar Accretion Disks and Circumbi-  nary Disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ835(1):L5, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/2041-8213/  835/1/L5, 1612.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='07804  Kreplin A, Tambovtseva L, Grinin V, Kraus S, Weigelt  G, Wang Y (2018) On the Brγ line emission of  the Herbig Ae/Be star MWC 120.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS476:4520–  4526, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/mnras/sty567  Krumholz MR, Bonnell IA (2009) Models for the for-  mation of massive stars, pp 288–320  Kurosawa R, Romanova MM, Harries TJ (2011) Mul-  tidimensional models of hydrogen and helium emis-  Herbig Stars  69  sion line profiles for classical T Tauri stars: method,  tests and examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS416(4):2623–2639, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='19216.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='x, 1102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0828  Kusakabe N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Grady CA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Sitko ML,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hashimoto J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Kudo T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Fukagawa M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Muto T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wisniewski JP,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Min  M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mayama S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Werren C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Day AN,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Beerman LC,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Lynch DK,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Russell RW,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brafford SM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kuzuhara M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Brandt TD,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Abe L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brandner W,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Carson J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Eg-  ner S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Feldt M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Goto M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Guyon O,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hayano Y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Hayashi M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hayashi SS,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Henning T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hodapp KW,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Ishii M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Iye M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Janson M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kandori R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Knapp GR,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Matsuo T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' McElwain MW,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Miyama S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Morino JI,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Moro-Martin A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Nishimura T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pyo TS,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Suto H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Suzuki R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Takami M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Takato N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Terada H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Thal-  mann C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Tomono D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Turner EL,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Watanabe M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ya-  mada T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Takami H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Usuda T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Tamura M (2012)  High-contrast Near-infrared Polarization Imaging of  MWC480.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ753(2):153, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/  753/2/153, 1205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3159  Lada CJ (1987) Star formation: from OB associations  to protostars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In: Peimbert M, Jugaku J (eds) Star  Forming Regions, IAU Symposium, vol 115, p 1  Lada CJ (2005) Star Formation in the Galaxy: An Ob-  servational Overview.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Progress of Theoretical Physics  Supplement 158:1–23, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1143/PTPS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='158.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1  Lada CJ, Wilking BA (1984) The nature of the em-  bedded population in the rho Ophiuchi dark cloud  : mid-infrared observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ287:610–621, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/162719  Lagage PO, Doucet C, Pantin E, Habart E, Duchˆene  G, M´enard F, Pinte C, Charnoz S, Pel JW (2006)  Anatomy of a Flaring Proto-Planetary Disk Around  a Young Intermediate-Mass Star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Science 314:621–  623, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1126/science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1131436  Landstreet JD (1992) Magnetic fields at the surfaces of  stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&ARv4(1):35–77, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1007/BF00873569  Law CJ, Crystian S, Teague R, ¨Oberg KI, Rich EA, An-  drews SM, Bae J, Flaherty K, Guzm´an VV, Huang  J, Ilee JD, Kastner JH, Loomis RA, Long F, P´erez  LM, P´erez S, Qi C, Rosotti GP, Ru´ız-Rodr´ıguez D,  Tsukagoshi T, Wilner DJ (2022) CO Line Emis-  sion Surfaces and Vertical Structure in Midincli-  nation Protoplanetary Disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ932(2):114, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4357/ac6c02, 2205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='01776  Lazareff B, Berger JP, Kluska J, Le Bouquin JB,  Benisty M, Malbet F, Koen C, Pinte C, Thi WF,  Absil O, Baron F, Delboulb´e A, Duvert G, Isella A,  Jocou L, Juhasz A, Kraus S, Lachaume R, M´enard  F, Millan-Gabet R, Monnier JD, Moulin T, Perraut  K, Rochat S, Soulez F, Tallon M, Thi´ebaut E, Traub  W, Zins G (2017) Structure of Herbig AeBe disks at  the milliarcsecond scale .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A statistical survey in the  H band using PIONIER-VLTI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A599:A85, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201629305, 1611.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='08428  Le Gal R, ¨Oberg KI, Loomis RA, Pegues J, Bergner JB  (2019) Sulfur Chemistry in Protoplanetary Disks: CS  and H2CS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ876(1):72, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4357/  ab1416, 1903.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='11105  Le Gal R, ¨Oberg KI, Teague R, Loomis RA, Law  CJ, Walsh C, Bergin EA, M´enard F, Wilner DJ,  Andrews SM, Aikawa Y, Booth AS, Cataldi G,  Bergner JB, Bosman AD, Cleeves LI, Czekala I, Fu-  ruya K, Guzm´an VV, Huang J, Ilee JD, Nomura  H, Qi C, Schwarz KR, Tsukagoshi T, Yamato Y,  Zhang K (2021) Molecules with ALMA at Planet-  forming Scales (MAPS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' XII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Inferring the C/O and  S/H Ratios in Protoplanetary Disks with Sulfur  Molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJS257(1):12, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4365/  ac2583, 2109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06286  Leemker  M,  van’t  Hoff  MLR,  Trapman  L,  van  Gelder ML, Hogerheijde MR, Ru´ız-Rodr´ıguez D,  van Dishoeck EF (2021) Chemically tracing the wa-  ter snowline in protoplanetary disks with HCO+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&A646:A3,  DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/202039387,  2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='12319  Leinert C, Richichi A, Haas M (1997) Binaries among  Herbig Ae/Be stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A318:472–484  Leinert C, Graser U, Waters LBFM, Perrin GS, Jaffe  W, Lopez B, Przygodda F, Chesneau O, Schuller PA,  Glazenborg-Kluttig AW, Laun W, Ligori S, Meisner  JA, Wagner K, Bakker EJ, Cotton B, de Jong J,  Mathar R, Neumann U, Storz C (2003) Ten-micron  instrument MIDI: getting ready for observations on  the VLTI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In: Traub WA (ed) Interferometry for Op-  tical Astronomy II, Society of Photo-Optical Instru-  mentation Engineers (SPIE) Conference Series, vol  4838, pp 893–904, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1117/12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='457027  Li ZY, Banerjee R, Pudritz RE, Jørgensen JK, Shang  H, Krasnopolsky R, Maury A (2014) The Earliest  Stages of Star and Planet Formation: Core Col-  lapse, and the Formation of Disks and Outflows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In:  Beuther H, Klessen RS, Dullemond CP, Henning T  (eds) Protostars and Planets VI, p 173, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2458/  azu\\ uapress\\ 9780816531240-ch008, 1401.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2219  Lieman-Sifry J, Hughes AM, Carpenter JM, Gorti  U, Hales A, Flaherty KM (2016) Debris Disks in  the Scorpius-Centaurus OB Association Resolved  by ALMA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ828(1):25, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/0004-637X/  828/1/25, 1606.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='07068  Ligi R, Vigan A, Gratton R, de Boer J, Benisty M,  Boccaletti A, Quanz SP, Meyer M, Ginski C, Sissa  E, Gry C, Henning T, Beuzit JL, Biller B, Bonnefoy  M, Chauvin G, Cheetham AC, Cudel M, Delorme  P, Desidera S, Feldt M, Galicher R, Girard J, Jan-  son M, Kasper M, Kopytova T, Lagrange AM, Lan-  glois M, Lecoroller H, Maire AL, M´enard F, Mesa  70  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  D, Peretti S, Perrot C, Pinilla P, Pohl A, Rouan D,  Stolker T, Samland M, Wahhaj Z, Wildi F, Zurlo  A, Buey T, Fantinel D, Fusco T, Jaquet M, Moulin  T, Ramos J, Suarez M, Weber L (2018) Investiga-  tion of the inner structures around HD 169142 with  VLT/SPHERE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS473(2):1774–1783, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  1093/mnras/stx2318, 1709.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='01734  Lin DNC, Papaloizou J (1979) On the structure of cir-  cumbinary accretion disks and the tidal evolution of  commensurable satellites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS188:191–201, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/mnras/188.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='191  Lin DNC, Papaloizou JCB (1993) On the Tidal Inter-  action Between Protostellar Disks and Companions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  In: Levy EH, Lunine JI (eds) Protostars and Planets  III, p 749  Lissauer JJ (1993) Planet formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ARA&A31:129–  174, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1146/annurev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='aa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='090193.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='001021  Liu SF, Jin S, Li S, Isella A, Li H (2018) New Con-  straints on Turbulence and Embedded Planet Mass in  the HD 163296 Disk from Planet-Disk Hydrodynamic  Simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ857(2):87, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4357/  aab718, 1803.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='05437  Long F, Pinilla P, Herczeg GJ, Harsono D, Dipierro G,  Pascucci I, Hendler N, Tazzari M, Ragusa E, Salyk  C, Edwards S, Lodato G, van de Plas G, Johnstone  D, Liu Y, Boehler Y, Cabrit S, Manara CF, Menard  F, Mulders GD, Nisini B, Fischer WJ, Rigliaco E,  Banzatti A, Avenhaus H, Gully-Santiago M (2018)  Gaps and Rings in an ALMA Survey of Disks in the  Taurus Star-forming Region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ869(1):17, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  3847/1538-4357/aae8e1, 1810.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06044  Loomis RA, ¨Oberg KI, Andrews SM, Bergin E, Bergner  J, Blake GA, Cleeves LI, Czekala I, Huang J, Le Gal  R, M´enard F, Pegues J, Qi C, Walsh C, Williams  JP, Wilner DJ (2020) An Unbiased ALMA Spectral  Survey of the LkCa 15 and MWC 480 Protoplane-  tary Disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ893(2):101, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4357/  ab7cc8, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='16187  Lopez B, Schneider J, Danchi WC (2005) Can Life  Develop in the Expanded Habitable Zones around  Red Giant Stars?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ627(2):974–985, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/  430416,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' astro-ph/0503520  Lopez B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Lagarde S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Petrov RG,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Jaffe W,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Antonelli  P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Allouche F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Berio P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Matter A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Meilland A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mil-  lour F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Robbe-Dubois S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Henning T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Weigelt G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Glindemann A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Agocs T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bailet C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Beckmann U,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Bettonvil F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' van Boekel R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bourget P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bresson Y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Bristow P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Cruzal`ebes P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Eldswijk E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Fante¨ı Cau-  jolle Y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Gonz´alez Herrera JC,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Graser U,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Guajardo  P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Heininger M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hofmann KH,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kroes G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Laun W,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Lehmitz M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Leinert C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Meisenheimer K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Morel S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Neumann U,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Paladini C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Percheron I,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Riquelme M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Schoeller M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Stee P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Venema L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Woillez J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Zins G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  ´Abrah´am P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Abadie S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Abuter R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Accardo M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Adler  T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Alonso J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Augereau JC,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' B¨ohm A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bazin G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bel-  tran J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bensberg A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Boland W,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brast R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Burtscher  L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Castillo R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Chelli A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Cid C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Clausse JM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Connot  C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Conzelmann RD,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Danchi WC,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Delbo M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Drevon J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Dominik C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' van Duin A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ebert M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Eisenhauer F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Fla-  ment S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Frahm R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' G´amez Rosas V,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Gabasch A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Gal-  lenne A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Garces E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Girard P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Glazenborg A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Gont´e  FYJ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Guitton F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' de Haan M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hanenburg H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Haubois  X,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hocd´e V,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hogerheijde M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ter Horst R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hron J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Hummel CA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hubin N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Huerta R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Idserda J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Isbell  JW,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ives D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Jakob G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Jask´o A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Jochum L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Klarmann  L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Klein R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kragt J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kuindersma S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kokoulina E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Labadie L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Lacour S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Leftley J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Le Poole R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Lizon JL,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Lopez M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Lykou F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' M´erand A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Marcotto A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mauclert  N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Maurer T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mehrgan LH,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Meisner J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Meixner K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Mellein M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Menut JL,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mohr L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mosoni L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Navarro  R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Nußbaum E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pallanca L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pantin E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pasquini L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Phan Duc T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pott JU,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pozna E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Richichi A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ridinger  A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Rigal F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Rivinius T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Roelfsema R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Rohloff RR,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Rousseau S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Salabert D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Schertl D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Schuhler N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Schuil  M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Shabun K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Soulain A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Stephan C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Toledo P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Tris-  tram K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Tromp N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Vakili F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Varga J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Vinther J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Waters LBFM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wittkowski M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wolf S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wrhel F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Yoffe G (2022) MATISSE,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' the VLTI mid-infrared  imaging spectro-interferometer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A659:A192, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/202141785, 2110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='15556  Lubow SH, D’Angelo G (2006) Gas Flow across Gaps  in Protoplanetary Disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ641(1):526–533, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/500356, astro-ph/0512292  Luhman  KL  (2012)  The  Formation  and  Early  Evolution  of  Low-Mass  Stars  and  Brown  Dwarfs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  ARA&A50:65–106,  DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1146/annurev-astro-081811-125528, 1208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5800  Luhn JK, Bastien FA, Wright JT, Johnson JA,  Howard AW, Isaacson H (2019) Retired A Stars  and Their Companions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' VIII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 15 New Planetary  Signals around Subgiants and Transit Parameters  for California Planet Search Planets with Sub-  giant Hosts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' AJ157(4):149, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-3881/  aaf5d0, 1811.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='03043  Lynden-Bell D, Pringle JE (1974) The evolution of vis-  cous discs and the origin of the nebular variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  MNRAS168:603–637, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/mnras/168.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='603  Maaskant KM, Honda M, Waters LBFM, Tielens  AGGM, Dominik C, Min M, Verhoeff A, Meeus  G, van den Ancker ME (2013) Identifying gaps  in flaring Herbig Ae/Be disks using spatially re-  solved mid-infrared imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Are all group I disks  transitional?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A555:A64, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  201321300, 1305.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3138  Maaskant KM, Min M, Waters LBFM, Tielens AGGM  (2014) Polycyclic aromatic hydrocarbon ionization  Herbig Stars  71  as a tracer of gas flows through protoplanetary  disk gaps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A563:A78, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  201323137, 1402.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0902  Maaskant KM, de Vries BL, Min M, Waters LBFM, Do-  minik C, Molster F, Tielens AGGM (2015) Location  and sizes of forsterite grains in protoplanetary disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Interpretation from the Herschel DIGIT programme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&A574:A140, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201423770,  1406.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3951  Mac´ıas  E,  Anglada  G,  Osorio  M,  Torrelles  JM,  Carrasco-Gonz´alez C, G´omez JF, Rodr´ıguez LF,  Sierra A (2017) Imaging a Central Ionized Compo-  nent, a Narrow Ring, and the CO Snowline in the  Multigapped Disk of HD 169142.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ838(2):97, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4357/aa6620, 1703.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='02957  Macintosh BA, Graham JR, Palmer DW, Doyon R,  Dunn J, Gavel DT, Larkin J, Oppenheimer B, Sad-  dlemyer L, Sivaramakrishnan A, Wallace JK, Bau-  man B, Erickson DA, Marois C, Poyneer LA, Soum-  mer R (2008) The Gemini Planet Imager: from sci-  ence to design to construction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In: Hubin N, Max  CE, Wizinowich PL (eds) Adaptive Optics Systems,  Society of Photo-Optical Instrumentation Engineers  (SPIE) Conference Series, vol 7015, p 701518, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1117/12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='788083  Malfait K, Bogaert E, Waelkens C (1998) An ultravio-  let, optical and infrared study of Herbig Ae/Be stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&A331:211–223  Malfait K, Waelkens C, Waters LBFM, Vandenbussche  B, Huygen E, de Graauw MS (1998) The spectrum  of the young star HD 100546 observed with the In-  frared Space Observatory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Astronomy & Astrophysics  332:L25–L28  Malfait K, Waelkens C, Bouwman J, de Koter A, Wa-  ters LBFM (1999) The ISO spectrum of the young  star HD 142527.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A345:181–186  Mannings V (1994) Submillimetre observations of Her-  big Ae/Be systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS271:587–600, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  1093/mnras/271.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='587  Mannings V, Sargent AI (1997) A High-Resolution  Study of Gas and Dust around Young Intermediate-  Mass Stars: Evidence for Circumstellar Disks in Her-  big Ae Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ490(2):792–802, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/  304897  Mannings V, Koerner DW, Sargent AI (1997) A rotat-  ing disk of gas and dust around a young counter-  part to β Pictoris.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Nature388(6642):555–557, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1038/41505  Marconi M, Ripepi V (2017) Pulsation in Herbig stars:  an idea of Francesco and its realization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Italiana88:597  Marigo P, Girardi L, Bressan A, Rosenfield P, Aringer  B, Chen Y, Dussin M, Nanni A, Pastorelli G, Ro-  drigues TS, Trabucchi M, Bladh S, Dalcanton J,  Groenewegen MAT, Montalb´an J, Wood PR (2017)  A New Generation of PARSEC-COLIBRI Stellar  Isochrones Including the TP-AGB Phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ835:77,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4357/835/1/77, 1701.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='08510  Marley MS, Fortney JJ, Hubickyj O, Bodenheimer P,  Lissauer JJ (2007) On the Luminosity of Young  Jupiters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ655(1):541–549, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/509759,  astro-ph/0609739  Marois C, Lafreni`ere D, Doyon R, Macintosh B, Nadeau  D (2006) Angular Differential Imaging: A Powerful  High-Contrast Imaging Technique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ641(1):556–  564, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/500401, astro-ph/0512335  Martin RG, Lubow SH (2011) The Gravo-magneto  Limit Cycle in Accretion Disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ740:L6, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/2041-8205/740/1/L6, 1108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4960  Mathews GS, Klaassen PD, Juh´asz A, Harsono D,  Chapillon E, van Dishoeck EF, Espada D, de  Gregorio-Monsalvo I, Hales A, Hogerheijde MR,  Mottram JC, Rawlings MG, Takahashi S, Testi L  (2013) ALMA imaging of the CO snowline of the  HD 163296 disk with DCO+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A557:A132, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201321600, 1307.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3420  McKee CF, Ostriker EC (2007) Theory of Star Forma-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ARA&A45(1):565–687, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1146/annurev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  astro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='051806.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='110602, 0707.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3514  Meeus G, Waters LBFM, Bouwman J, van den An-  cker ME, Waelkens C, Malfait K (2001) ISO spec-  troscopy of circumstellar dust in 14 Herbig Ae/Be  systems: Towards an understanding of dust pro-  cessing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A365:476–490, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361:  20000144, astro-ph/0012295  Meeus G, Bouwman J, Dominik C, Waters LBFM,  de Koter A (2002) The absence of the 10 mu  m silicate feature in the isolated Herbig Ae star  HD  100453.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&A392:1039–1046,  DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/  0004-6361:20020952  Meeus G, Montesinos B, Mendigut´ıa I, Kamp I, Thi  WF, Eiroa C, Grady CA, Mathews G, Sandell G,  Martin-Za¨ıdi C, Brittain S, Dent WRF, Howard  C, M´enard F, Pinte C, Roberge A, Vand enbuss-  che B, Williams JP (2012) Observations of Her-  big Ae/Be stars with Herschel/PACS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The atomic  and molecular contents of their protoplanetary discs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&A544:A78, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201219225,  1206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3413  Meeus G, Salyk C, Bruderer S, Fedele D, Maaskant K,  Evans NJ, van Dishoeck EF, Montesinos B, Herczeg  G, Bouwman J, Green JD, Dominik C, Henning T,  Vicente S (2013) DIGIT survey of far-infrared lines  from protoplanetary discs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' CO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A559:A84,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201321122, 1308.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4160  72  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Meijerink R, Aresu G, Kamp I, Spaans M, Thi WF,  Woitke P (2012) Far-ultraviolet and X-ray irradiated  protoplanetary disks: a grid of models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The disk  structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A547:A68, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  201219863, 1208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4959  Mendigut´ıa I (2020) On the Mass Accretion Rates of  Herbig Ae/Be Stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Magnetospheric Accretion or  Boundary Layer?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Galaxies 8(2):39, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3390/  galaxies8020039, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='01745  Mendigut´ıa I, Calvet N, Montesinos B, Mora A, Muze-  rolle J, Eiroa C, Oudmaijer RD, Mer´ın B (2011a)  Accretion rates and accretion tracers of Herbig  Ae/Be stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A535:A99, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  201117444, 1109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3288  Mendigut´ıa I, Eiroa C, Montesinos B, Mora A, Oud-  maijer RD, Mer´ın B, Meeus G (2011b) Optical  spectroscopic variability of Herbig Ae/Be stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&A529:A34, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201015821,  1102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5033  Mendigut´ıa I, Brittain S, Eiroa C, Meeus G, Mon-  tesinos B, Mora A, Muzerolle J, Oudmaijer RD,  Rigliaco E (2013) Accretion Variability of Herbig  Ae/Be Stars Observed by X-Shooter HD 31648 and  HD 163296.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ776(1):44, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/  776/1/44, 1308.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3248  Mendigut´ıa I, de Wit WJ, Oudmaijer RD, Fairlamb  JR, Carciofi AC, Ilee JD, Vieira RG (2015) High-  resolution Br γ spectro-interferometry of the tran-  sitional Herbig Ae/Be star HD 100546: a Keplerian  gaseous disc inside the inner rim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS453:2126–  2132, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/mnras/stv1777, 1509.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='05411  Mendigut´ıa I, Oudmaijer RD, Garufi A, Lumsden  SL, Hu´elamo N, Cheetham A, de Wit WJ, Nor-  ris B, Olguin FA, Tuthill P (2017) The protoplan-  etary system HD 100546 in Hα polarized light from  SPHERE/ZIMPOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A bar-like structure across the  disk gap?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A608:A104, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  201731131, 1711.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='00023  Menu J, van Boekel R, Henning T, Leinert C, Waelkens  C, Waters LBFM (2015) The structure of disks  around intermediate-mass young stars from mid-  infrared interferometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Evidence for a population  of group II disks with gaps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A581:A107, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201525654, 1506.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='03274  Miley JM, Pani´c O, Haworth TJ, Pascucci I, Wyatt M,  Clarke C, Richards AMS, Ratzka T (2019) Asym-  metric mid-plane gas in ALMA images of HD 100546.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  MNRAS485(1):739–752, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/mnras/stz426,  1902.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='07506  Min M, Dullemond CP, Dominik C, de Koter A, Hov-  enier JW (2009) Radiative transfer in very optically  thick circumstellar disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A497:155–166, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/200811470, 0902.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3092  Min M, Bouwman J, Dominik C, Waters LBFM, Pon-  toppidan KM, Hony S, Mulders GD, Henning T, van  Dishoeck EF, Woitke P, Evans NJ II, Digit Team  (2016a) The abundance and thermal history of wa-  ter ice in the disk surrounding HD 142527 from the  DIGIT Herschel Key Program.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A593:A11, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201425432, 1606.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='07266  Min M, Rab C, Woitke P, Dominik C, M´enard  F (2016b) Multiwavelength optical properties of  compact dust aggregates in protoplanetary disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&A585:A13, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201526048,  1510.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='05426  Miotello  A,  van  Dishoeck  EF,  Kama  M,  Brud-  erer S (2016) Determining protoplanetary disk gas  masses from CO isotopologues line observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&A594:A85, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201628159,  1605.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='07780  Miotello A, van Dishoeck EF, Williams JP, Ansdell M,  Guidi G, Hogerheijde M, Manara CF, Tazzari M,  Testi L, van der Marel N, van Terwisga S (2017) Lu-  pus disks with faint CO isotopologues: low gas/dust  or high carbon depletion?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A599:A113, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  1051/0004-6361/201629556, 1612.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='01538  Moe M, Kratter KM (2021) Impact of binary stars  on planet statistics - I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Planet occurrence rates and  trends with stellar mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS507(3):3593–3611,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/mnras/stab2328  Monnier  JD,  Millan-Gabet  R  (2002)  On  the  Interferometric  Sizes  of  Young  Stellar  Ob-  jects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  ApJ579(2):694–698,  DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/342917,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  astro-ph/0207292  Monnier JD,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Millan-Gabet R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Billmeier R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Akeson  RL,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wallace D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Berger JP,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Calvet N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' D’Alessio P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Danchi WC,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hartmann L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hillenbrand LA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kuch-  ner M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Rajagopal J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Traub WA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Tuthill PG,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Boden  A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Booth A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Colavita M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Gathright J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hrynevych  M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Le Mignant D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ligon R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Neyman C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Swain  M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Thompson R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Vasisht G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wizinowich P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Be-  ichman C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Beletic J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Creech-Eakman M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Koresko  C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Sargent A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Shao M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' van Belle G (2005) The  Near-Infrared Size-Luminosity Relations for Her-  big Ae/Be Disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ624(2):832–840, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/  429266, astro-ph/0502252  Mooley K, Hillenbrand L, Rebull L, Padgett D, Knapp  G (2013) B- and A-type Stars in the Taurus-Auriga  Star-forming Region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ771(2):110, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/  0004-637X/771/2/110, 1306.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0598  Mo´or A, Cur´e M, K´osp´al ´A, ´Abrah´am P, Csengeri  T, Eiroa C, Gunawan D, Henning T, Hughes AM,  Juh´asz A (2017) Molecular Gas in Debris Disks  around Young A-type Stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ849(2):123, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4357/aa8e4e, 1709.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='08414  Herbig Stars  73  Morgan WW, Keenan PC, Kellman E (1943) An atlas  of stellar spectra, with an outline of spectral classifi-  cation  Motte  F,  Bontemps  S,  Louvet  F  (2018)  High-  Mass  Star  and  Massive  Cluster  Formation  in  the Milky Way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ARA&A56:41–82, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1146/  annurev-astro-091916-055235, 1706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='00118  Moura T, Alencar SHP, Sousa AP, Alecian E, Lebreton  Y (2020) Spectroscopic analysis of accretion/ejection  signatures in the Herbig Ae/Be stars HD 261941 and  V590 Mon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS494(3):3512–3535, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/  mnras/staa695  Mulders GD, Dominik C (2012) Probing the turbu-  lent mixing strength in protoplanetary disks across  the stellar mass range: no significant variations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&A539:A9,  DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201118127,  1201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1453  Mulders GD, Waters LBFM, Dominik C, Sturm B,  Bouwman J, Min M, Verhoeff AP, Acke B, Augereau  JC, Evans NJ, Henning T, Meeus G, Olofsson J  (2011) Low abundance, strong features: window-  dressing crystalline forsterite in the disk wall of  HD 100546.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A531:A93, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  201116770, 1105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4817  Mulders GD, Paardekooper SJ, Pani´c O, Dominik  C, van Boekel R, Ratzka T (2013) Planet or  brown dwarf?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Inferring the companion mass in HD  100546 from the wall shape using mid-infrared inter-  ferometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A557:A68, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  201220930, 1306.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4264  Mulders GD, Pascucci I, Apai D (2015) A Stellar-  mass-dependent Drop in Planet Occurrence Rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  ApJ798(2):112, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/798/2/112,  1406.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='7356  Mulders GD, Drazkowska J, van der Marel N, Ciesla  FJ, Pascucci I (2021) Why Do M Dwarfs Have  More Transiting Planets?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ920(1):L1, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  3847/2041-8213/ac2947, 2110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='02971  Muley  D,  Fung  J,  van  der  Marel  N  (2019)  PDS 70: A Transition Disk Sculpted by a Sin-  gle Planet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ879(1):L2, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/2041-8213/  ab24d0, 1902.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='07191  M¨uller A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Keppler M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Henning T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Samland M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Chau-  vin G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Beust H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Maire AL,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Molaverdikhani K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' van  Boekel R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Benisty M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Boccaletti A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bonnefoy M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Cantalloube F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Charnay B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Baudino JL,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Gennaro  M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Long ZC,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Cheetham A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Desidera S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Feldt M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Fusco T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Girard J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Gratton R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hagelberg J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Jan-  son M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Lagrange AM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Langlois M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Lazzoni C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ligi  R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' M´enard F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mesa D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Meyer M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Molli`ere P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mor-  dasini C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Moulin T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pavlov A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pawellek N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Quanz  SP,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ramos J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Rouan D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Sissa E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Stadler E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Vigan A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Wahhaj Z,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Weber L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Zurlo A (2018) Orbital and at-  mospheric characterization of the planet within the  gap of the PDS 70 transition disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A617:L2, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201833584, 1806.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='11567  Muro-Arena GA, Dominik C, Waters LBFM, Min M,  Klarmann L, Ginski C, Isella A, Benisty M, Pohl  A, Garufi A, Hagelberg J, Langlois M, Menard F,  Pinte C, Sezestre E, van der Plas G, Villenave M,  Delboulb´e A, Magnard Y, M¨oller-Nilsson O, Pragt  J, Rabou P, Roelfsema R (2018) Dust modeling of  the combined ALMA and SPHERE datasets of HD  163296.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Is HD 163296 really a Meeus group II disk?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&A614:A24, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201732299,  1802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='03328  Muro-Arena GA, Benisty M, Ginski C, Dominik C,  Facchini S, Villenave M, van Boekel R, Chauvin G,  Garufi A, Henning T, Janson M, Keppler M, Matter  A, M´enard F, Stolker T, Zurlo A, Blanchard P, Mau-  rel D, Moeller-Nilsson O, Petit C, Roux A, Sevin A,  Wildi F (2020) Shadowing and multiple rings in the  protoplanetary disk of HD 139614.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A635:A121,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201936509, 1911.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='09612  Murphy SJ, Joyce M, Bedding TR, White TR, Kama  M (2021) A precise asteroseismic age and metal-  licity for HD 139614: a pre-main-sequence star  with a protoplanetary disc in Upper Centaurus-  Lupus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  MNRAS502(2):1633–1646,  DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/  mnras/stab144, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='11821  Muto T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Grady CA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hashimoto J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Fukagawa M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Horn-  beck JB,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Sitko M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Russell R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Werren C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Cur´e M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Currie T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ohashi N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Okamoto Y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Momose M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Honda  M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Inutsuka S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Takeuchi T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Dong R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Abe L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brandner  W,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brandt T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Carson J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Egner S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Feldt M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Fukue T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Goto M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Guyon O,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hayano Y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hayashi M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hayashi  S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Henning T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hodapp KW,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ishii M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Iye M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Janson  M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kandori R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Knapp GR,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kudo T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kusakabe N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Kuzuhara M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Matsuo T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mayama S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' McElwain MW,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Miyama S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Morino JI,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Moro-Martin A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Nishimura  T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pyo TS,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Serabyn E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Suto H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Suzuki R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Takami  M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Takato N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Terada H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Thalmann C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Tomono D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Turner EL,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Watanabe M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wisniewski JP,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Yamada  T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Takami H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Usuda T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Tamura M (2012) Discovery  of Small-scale Spiral Structures in the Disk of SAO  206462 (HD 135344B): Implications for the Physical  State of the Disk from Spiral Density Wave Theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  ApJ748(2):L22, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/2041-8205/748/2/L22,  1202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6139  Muzerolle J, D’Alessio P, Calvet N, Hartmann L  (2004) Magnetospheres and Disk Accretion in Herbig  Ae/Be Stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ617:406–417, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/425260,  astro-ph/0409008  Najita J, Carr JS, Glassgold AE, Shu FH, Toku-  naga AT (1996) Kinematic Diagnostics of Disks  around Young Stars: CO Overtone Emission from  74  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  WL 16 and 1548C27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ462:919, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/  177205, astro-ph/9512109  Najita J, Carr JS, Mathieu RD (2003) Gas in the Ter-  restrial Planet Region of Disks: CO Fundamental  Emission from T Tauri Stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ589:931–952, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/374809  Najita JR, Doppmann GW, Carr JS, Graham JR, Eis-  ner JA (2009) High-Resolution K-Band Spectroscopy  of MWC 480 and V1331 Cyg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ691(1):738–748,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/691/1/738, 0809.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4267  Natta A, Prusti T, Neri R, Wooden D, Grinin VP,  Mannings V (2001) A reconsideration of disk prop-  erties in Herbig Ae stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A371:186–197, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361:20010334  Natta A, Testi L, Randich S (2006) Accretion in the ρ-  Ophiuchi pre-main sequence stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A452(1):245–  252, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361:20054706,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' astro-ph/  0602618  Nielsen EL,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' De Rosa RJ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Macintosh B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wang JJ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ruf-  fio JB,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Chiang E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Marley MS,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Saumon D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Savran-  sky D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ammons SM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bailey VP,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Barman T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Blain C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Bulger J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Burrows A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Chilcote J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Cotten T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Czekala  I,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Doyon R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Duchˆene G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Esposito TM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Fabrycky D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Fitzgerald MP,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Follette KB,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Fortney JJ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Gerard BL,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Goodsell SJ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Graham JR,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Greenbaum AZ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hibon  P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hinkley S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hirsch LA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hom J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hung LW,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Daw-  son RI,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ingraham P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kalas P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Konopacky Q,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Larkin  JE,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Lee EJ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Lin JW,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Maire J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Marchis F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Marois  C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Metchev S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Millar-Blanchaer MA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Morzinski KM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Oppenheimer R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Palmer D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Patience J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Perrin M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Poyneer L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pueyo L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Rafikov RR,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Rajan A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Rameau  J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Rantakyr¨o FT,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ren B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Schneider AC,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Sivaramakr-  ishnan A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Song I,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Soummer R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Tallis M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Thomas S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Ward-Duong K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wolff S (2019) The Gemini Planet  Imager Exoplanet Survey: Giant Planet and Brown  Dwarf Demographics from 10 to 100 au.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' AJ158(1):13,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-3881/ab16e9, 1904.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='05358  Notsu S, Nomura H, Ishimoto D, Walsh C, Honda  M, Hirota T, Millar TJ (2017) Candidate Water  Vapor Lines to Locate the H2O Snowline through  High-dispersion Spectroscopic Observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The  Case of a Herbig Ae Star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ836(1):118, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4357/836/1/118, 1701.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='04381  Notsu S, Akiyama E, Booth A, Nomura H, Walsh  C, Hirota T, Honda M, Tsukagoshi T, Millar TJ  (2019) Dust Continuum Emission and the Upper  Limit Fluxes of Submillimeter Water Lines of the  Protoplanetary Disk around HD 163296 Observed  by ALMA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ875(2):96, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4357/  ab0ae9, 1902.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='09932  ¨Oberg KI, Qi C, Fogel JKJ, Bergin EA, Andrews  SM, Espaillat C, van Kempen TA, Wilner DJ, Pas-  cucci I (2010) The Disk Imaging Survey of Chem-  istry with SMA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Taurus Protoplanetary Disk  Data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ720:480–493, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/  720/1/480, 1007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1476  ¨Oberg KI, Murray-Clay R, Bergin EA (2011) The Ef-  fects of Snowlines on C/O in Planetary Atmospheres.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  ApJ743(1):L16, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/2041-8205/743/1/L16,  1110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5567  ¨Oberg KI, Guzm´an VV, Furuya K, Qi C, Aikawa  Y, Andrews SM, Loomis R, Wilner DJ (2015) The  comet-like composition of a protoplanetary disk as  revealed by complex cyanides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Nature520(7546):198–  201, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1038/nature14276, 1505.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06347  ¨Oberg KI, Guzm´an VV, Walsh C, Aikawa Y, Bergin  EA, Law CJ, Loomis RA, Alarc´on F, Andrews SM,  Bae J, Bergner JB, Boehler Y, Booth AS, Bosman  AD, Calahan JK, Cataldi G, Cleeves LI, Czekala  I, Furuya K, Huang J, Ilee JD, Kurtovic NT, Le  Gal R, Liu Y, Long F, M´enard F, Nomura H, P´erez  LM, Qi C, Schwarz KR, Sierra A, Teague R, Tsuk-  agoshi T, Yamato Y, van’t Hoff MLR, Waggoner  AR, Wilner DJ, Zhang K (2021) Molecules with  ALMA at Planet-forming Scales (MAPS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pro-  gram Overview and Highlights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJS257(1):1, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4365/ac1432, 2109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06268  Oberg N, Kamp I, Cazaux S, Woitke P, Thi WF  (2022) Circumplanetary disk ices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ice formation  vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' viscous evolution and grain drift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' arXiv e-prints  arXiv:2208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='11053, 2208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='11053  Ochsendorf BB, Ellerbroek LE, Chini R, Hartoog  OE, Hoffmeister V, Waters LBFM, Kaper L (2011)  First firm spectral classification of an early-B pre-  main-sequence star: B275 in ¡ASTROBJ¿M 17¡/AS-  TROBJ¿.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&A536:L1,  DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  201118089, 1110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5755  Owen JE (2014) Snow Lines as Probes of Turbulent Dif-  fusion in Protoplanetary Disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ790(1):L7, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/2041-8205/790/1/L7, 1406.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6707  Pagani L, Bourgoin A, Lique F (2012) A method to  measure CO and N2 depletion profiles inside prestel-  lar  cores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&A548:L4,  DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  201220137  Palla F, Stahler SW (1993) The Pre-Main-Sequence  Evolution of Intermediate-Mass Stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ418:414,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/173402  Pallavicini R, Golub L, Rosner R, Vaiana GS, Ayres  T, Linsky JL (1981) Relations among stellar X-  ray emission observed from Einstein, stellar rotation  and bolometric luminosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ248:279–290, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/159152  Pani´c O, Hogerheijde MR (2009) Characterising discs  around Herbig Ae/Be stars through modelling of  low-J 12CO lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A508:707–716, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/  0004-6361/200912584  Herbig Stars  75  Pani´c O, Holland WS, Wyatt MC, Kennedy GM,  Matthews BC, Lestrade JF, Sibthorpe B, Greaves  JS, Marshall JP, Phillips NM, Tottle J (2013) First  results of the SONS survey: submillimetre detec-  tions of debris discs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS435(2):1037–1046, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/mnras/stt1293  Pani´c O, Haworth TJ, Petr-Gotzens MG, Miley J,  van den Ancker M, Vioque M, Siess L, Parker R,  Clarke CJ, Kamp I, Kennedy G, Oudmaijer RD,  Pascucci I, Richards AMS, Ratzka T, Qi C (2021)  Planet formation in intermediate-separation binary  systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS501(3):4317–4328, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/  mnras/staa3834, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='07901  Pascual N, Montesinos B, Meeus G, Marshall JP,  Mendigut´ıa I, Sandell G (2016) The far-infrared  behaviour of Herbig Ae/Be discs: Herschel PACS  photometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A586:A6, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  201526605, 1511.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='08356  Pascucci I, Sterzik M, Alexander RD, Alencar SHP,  Gorti U, Hollenbach D, Owen J, Ercolano B, Edwards  S (2011) The Photoevaporative Wind from the Disk  of TW Hya.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ736(1):13, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/  736/1/13, 1105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0045  Patel P, Sigut TAA, Landstreet JD (2017) Photoion-  ization Models for the Inner Gaseous Disks of Her-  big Be Stars: Evidence against Magnetospheric Ac-  cretion?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ836(2):214, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4357/  aa5c3f, 1701.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06721  Paunzen E, Iliev IK, Kamp I, Barzova IS (2002) The  status of Galactic field λ Bootis stars in the post-  Hipparcos era.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS336(3):1030–1042, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  1046/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1365-8711.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='05865.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='x, astro-ph/0207488  Pegues J, ¨Oberg KI, Bergner JB, Loomis RA, Qi  C, Le Gal R, Cleeves LI, Guzm´an VV, Huang  J, Jørgensen JK, Andrews SM, Blake GA, Car-  penter JM, Schwarz KR, Williams JP, Wilner DJ  (2020) An ALMA Survey of H2CO in Protoplane-  tary Disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ890(2):142, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4357/  ab64d9, 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='12525  Perez MR, Grady CA (1997) Observational Overview  of Young Intermediate-Mass Objects: Herbig Ae/Be  Stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Space Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='82:407–450, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1023/A:  1005064108523  Perez S, Dunhill A, Casassus S, Roman P, Szul´agyi  J, Flores C, Marino S, Montesinos M (2015) Planet  Formation Signposts: Observability of Circumplane-  tary Disks via Gas Kinematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ811(1):L5, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/2041-8205/811/1/L5, 1505.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06808  P´erez S, Casassus S, Ben´ıtez-Llambay P (2018) Ob-  servability of planet-disc interactions in CO kinemat-  ics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS480(1):L12–L17, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/mnrasl/  sly109, 1806.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='05125  P´erez S, Casassus S, Hales A, Marino S, Cheetham  A, Zurlo A, Cieza L, Dong R, Alarc´on F, Ben´ıtez-  Llambay P, Fomalont E, Avenhaus H (2020) Long  Baseline Observations of the HD 100546 Protoplane-  tary Disk with ALMA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ889(1):L24, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/  2041-8213/ab6b2b, 1906.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06305  P´ericaud J, Di Folco E, Dutrey A, Guilloteau S, Pi´etu  V (2017) The hybrid disks: a search and study to  better understand evolution of disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A600:A62,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201629371, 1612.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06582  Perraut K, Dougados C, Lima GHRA, Benisty M,  Mourard D, Ligi R, Nardetto N, Tallon-Bosc I,  ten Brummelaar T, Farrington C (2016) A disk  wind in AB Aurigae traced with Hα interferometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&A596:A17, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201628931  Pi´etu V, Dutrey A, Kahane C (2003) A Keplerian disk  around the Herbig Ae star HD 34282.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A398:565–  569, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361:20021551, astro-ph/  0210097  Pi´etu V, Guilloteau S, Dutrey A (2005) Sub-arcsec  imaging of the AB Aur molecular disk and en-  velope at millimeter wavelengths: a non Keplerian  disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A443(3):945–954, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361:  20042050, astro-ph/0504023  Pi´etu V, Dutrey A, Guilloteau S (2007) Probing  the structure of protoplanetary disks: a compar-  ative study of DM Tau, LkCa 15, and MWC  480.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A467(1):163–178, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361:  20066537, astro-ph/0701425  Pineda JE, Quanz SP, Meru F, Mulders GD, Meyer  MR, Pani´c O, Avenhaus H (2014) Resolved Images  of the Protoplanetary Disk around HD 100546 with  ALMA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ788(2):L34, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/2041-8205/  788/2/L34, 1405.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5773  Pinilla P, Benisty M, Birnstiel T (2012) Ring shaped  dust accumulation in transition disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A545:A81,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201219315, 1207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6485  Pinilla P, Benisty M, Birnstiel T, Ricci L, Isella A,  Natta A, Dullemond CP, Quiroga-Nu˜nez LH, Hen-  ning T, Testi L (2014) Millimetre spectral indices  of transition disks and their relation to the cav-  ity radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A564:A51, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  201323322, 1402.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5778  Pinilla P, Flock M, Ovelar MdJ, Birnstiel T (2016)  Can dead zones create structures like a transi-  tion disk?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A596:A81, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  201628441, 1610.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='02044  Pinilla P, Tazzari M, Pascucci I, Youdin AN, Garufi  A, Manara CF, Testi L, van der Plas G, Barenfeld  SA, Canovas H, Cox EG, Hendler NP, P´erez LM,  van der Marel N (2018) Homogeneous Analysis of  the Dust Morphology of Transition Disks Observed  with ALMA: Investigating Dust Trapping and the  76  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Origin of the Cavities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ859(1):32, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/  1538-4357/aabf94, 1804.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='07301  Pinte C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Woitke P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' M´enard F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Duchˆene G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kamp I,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Meeus G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mathews G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Howard CD,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Grady CA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Thi  WF,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Tilling I,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Augereau JC,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Dent WRF,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Alacid JM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Andrews S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ardila DR,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Aresu G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Barrado D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brit-  tain S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ciardi DR,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Danchi W,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Eiroa C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Fedele D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' de  Gregorio-Monsalvo I,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Heras A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Huelamo N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Krivov  A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Lebreton J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Liseau R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Martin-Za¨ıdi C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mendigut´ıa  I,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Montesinos B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mora A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Morales-Calderon M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' No-  mura H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pantin E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pascucci I,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Phillips N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Podio L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Poelman DR,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ramsay S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Riaz B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Rice K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Riviere-  Marichalar P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Roberge A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Sandell G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Solano E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Van-  denbussche B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Walker H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Williams JP,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' White GJ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Wright G (2010) The Herschel view of GAS in Pro-  toplanetary Systems (GASPS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' First comparisons  with a large grid of models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A518:L126, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201014591, 1005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3826  Pinte C, Dent WRF, M´enard F, Hales A, Hill T,  Cortes P, de Gregorio-Monsalvo I (2016) Dust and  Gas in the Disk of HL Tauri: Surface Density, Dust  Settling, and Dust-to-gas Ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ816:25, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/0004-637X/816/1/25, 1508.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='00584  Pinte C, M´enard F, Duchˆene G, Hill T, Dent WRF,  Woitke P, Maret S, van der Plas G, Hales A, Kamp  I, Thi WF, de Gregorio-Monsalvo I, Rab C, Quanz  SP, Avenhaus H, Carmona A, Casassus S (2018a)  Direct mapping of the temperature and velocity  gradients in discs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Imaging the vertical CO snow  line around IM Lupi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A609:A47, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/  0004-6361/201731377, 1710.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06450  Pinte C, Price DJ, M´enard F, Duchˆene G, Dent WRF,  Hill T, de Gregorio-Monsalvo I, Hales A, Mentiplay D  (2018b) Kinematic Evidence for an Embedded Proto-  planet in a Circumstellar Disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ860(1):L13, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/2041-8213/aac6dc, 1805.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='10293  Pinte C, van der Plas G, M´enard F, Price DJ, Christi-  aens V, Hill T, Mentiplay D, Ginski C, Choquet E,  Boehler Y, Duchˆene G, Perez S, Casassus S (2019)  Kinematic detection of a planet carving a gap in a  protoplanetary disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Nature Astronomy 3:1109–1114,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1038/s41550-019-0852-6, 1907.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='02538  Pirzkal  N,  Spillar  EJ,  Dyck  HM  (1997)  A  Search  for  Close  Bright  Companions  to  AeBe  Stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  ApJ481(1):392–395,  DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/304055,  astro-ph/9702101  Poeckert R, Marlborough JM (1976) Intrinsic linear  polarization of Be stars as a function of V sini.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  ApJ206:182–195, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/154369  Poeckert R, Marlborough JM (1977) Linear polariza-  tion of Halpha in the Be star Gamma Cassiopeiae.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  ApJ218:220–226, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/155673  Pohl A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Benisty M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pinilla P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ginski C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' de Boer J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Avenhaus H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Henning T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Zurlo A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Boccaletti A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Augereau JC,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Birnstiel T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Dominik C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Facchini S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Fedele D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Janson M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Keppler M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kral Q,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Langlois  M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ligi R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Maire AL,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' M´enard F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Meyer M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pinte  C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Quanz SP,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Sauvage JF,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Sezestre ´E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Stolker T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Szul´agyi J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' van Boekel R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' van der Plas G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Villenave  M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Baruffolo A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Baudoz P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Le Mignant D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Maurel  D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ramos J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Weber L (2017) The Circumstellar Disk  HD 169142: Gas,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Dust,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' and Planets Acting in Con-  cert?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ850(1):52, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4357/aa94c2,  1710.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06485  Pollack JB, Hubickyj O, Bodenheimer P, Lissauer JJ,  Podolak M, Greenzweig Y (1996) Formation of the  Giant Planets by Concurrent Accretion of Solids  and Gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Icarus124(1):62–85, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1006/icar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  0190  Pontoppidan KM, Salyk C, Blake GA, Meijerink R,  Carr JS, Najita J (2010) A Spitzer Survey of Mid-  infrared Molecular Emission from Protoplanetary  Disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Detection Rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ720(1):887–903, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/720/1/887, 1006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4189  Powell D, Murray-Clay R, P´erez LM, Schlichting  HE, Rosenthal M (2019) New Constraints From  Dust Lines on the Surface Densities of Protoplane-  tary Disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ878(2):116, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4357/  ab20ce, 1905.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='03252  Pyerin MA, Delage TN, Kurtovic NT, G´arate M, Hen-  ning T, Pinilla P (2021) Constraining the properties  of the potential embedded planets in the disk around  HD 100546.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A656:A150, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  202141998  Qi C, D’Alessio P, ¨Oberg KI, Wilner DJ, Hughes AM,  Andrews SM, Ayala S (2011) Resolving the CO Snow  Line in the Disk around HD 163296.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ740(2):84,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/740/2/84, 1107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5061  Qi C, ¨Oberg KI, Andrews SM, Wilner DJ, Bergin  EA, Hughes AM, Hogherheijde M, D’Alessio P  (2015) Chemical Imaging of the CO Snow Line in  the HD 163296 Disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ813(2):128, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/  0004-637X/813/2/128, 1510.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='00968  Quanz SP, Amara A, Meyer MR, Kenworthy MA,  Kasper M, Girard JH (2013a) A Young Protoplanet  Candidate Embedded in the Circumstellar Disk of  HD 100546.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ766:L1, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/2041-8205/  766/1/L1, 1302.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='7122  Quanz SP, Avenhaus H, Buenzli E, Garufi A, Schmid  HM, Wolf S (2013b) Gaps in the HD 169142 Pro-  toplanetary Disk Revealed by Polarimetric Imaging:  Signs of Ongoing Planet Formation?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ766(1):L2,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/2041-8205/766/1/L2, 1302.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3029  Quanz SP, Amara A, Meyer MR, Girard JH, Kenwor-  thy MA, Kasper M (2015) Confirmation and Char-  Herbig Stars  77  acterization of the Protoplanet HD 100546 b—Direct  Evidence for Gas Giant Planet Formation at 50  AU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ807(1):64, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/807/1/  64, 1412.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5173  Quillen AC, Blackman EG, Frank A, Varni`ere P  (2004) On the Planet and the Disk of COKU  TAURI/4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  ApJ612(2):L137–L140,  DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/  424693, astro-ph/0406445  Rab C, Kamp I (2019) HD163296 paper DSHARP data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&Ain prep(1000):064301, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/1538-3873/  aaf4e5, 1812.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='02741  Rab C, Kamp I, Dominik C, Ginski C, Muro-Arena  GA, Thi WF, Waters LBFM, Woitke P (2020) In-  terpreting high spatial resolution line observations of  planet-forming disks with gaps and rings: the case of  HD 163296.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A642:A165, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  202038712, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='05941  Rameau J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Follette KB,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pueyo L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Marois C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Macintosh  B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Millar-Blanchaer M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wang JJ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Vega D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Doyon  R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Lafreni`ere D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Nielsen EL,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bailey V,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Chilcote  JK,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Close LM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Esposito TM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Males JR,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Metchev  S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Morzinski KM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ruffio JB,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wolff SG,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ammons  SM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Barman TS,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bulger J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Cotten T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' De Rosa RJ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Duchene G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Fitzgerald MP,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Goodsell S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Graham JR,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Greenbaum AZ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hibon P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hung LW,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ingraham P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Kalas P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Konopacky Q,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Larkin JE,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Maire J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Marchis  F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Oppenheimer R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Palmer D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Patience J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Perrin  MD,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Poyneer L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Rajan A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Rantakyr¨o FT,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Marley MS,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Savransky D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Schneider AC,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Sivaramakrishnan A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Song I,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Soummer R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Thomas S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wallace JK,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ward-  Duong K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wiktorowicz S (2017) An Optical/Near-  infrared Investigation of HD 100546 b with the Gem-  ini Planet Imager and MagAO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' AJ153:244, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-3881/aa6cae, 1704.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06317  Ram´ırez-Tannus MC, Kaper L, de Koter A, Tramper  F, Bik A, Ellerbroek LE, Ochsendorf BB, Ram´ırez-  Agudelo OH, Sana H (2017) Massive pre-main-  sequence stars in M17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A604:A78, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/  0004-6361/201629503, 1704.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='08216  Rebollido I, Eiroa C, Montesinos B, Maldonado J,  Villaver E, Absil O, Bayo A, Canovas H, Carmona  A, Chen C, Ertel S, Henning T, Iglesias DP, Laun-  hardt R, Liseau R, Meeus G, Mo´or A, Mora A, Olof-  sson J, Rauw G, Riviere-Marichalar P (2020) Exo-  comets: A spectroscopic survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A639:A11, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201936071, 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='11084  Reffert S, Bergmann C, Quirrenbach A, Trifonov T,  K¨unstler A (2015) Precise radial velocities of giant  stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Occurrence rate of giant extrasolar planets  as a function of mass and metallicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A574:A116,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201322360, 1412.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4634  Reg´aly Z, Juh´asz A, S´andor Z, Dullemond CP (2012)  Possible planet-forming regions on submillimetre  images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS419(2):1701–1712, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='19834.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='x, 1109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6177  Reggiani M, Quanz SP, Meyer MR, Pueyo L, Absil  O, Amara A, Anglada G, Avenhaus H, Girard JH,  Carrasco Gonzalez C, Graham J, Mawet D, Meru F,  Milli J, Osorio M, Wolff S, Torrelles JM (2014) Dis-  covery of a Companion Candidate in the HD 169142  Transition Disk and the Possibility of Multiple Planet  Formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ792(1):L23, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/2041-8205/  792/1/L23, 1408.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0813  Reggiani M, Christiaens V, Absil O, Mawet D, Huby  E, Choquet E, Gomez Gonzalez CA, Ruane G, Fe-  menia B, Serabyn E, Matthews K, Barraza M, Car-  lomagno B, Defr`ere D, Delacroix C, Habraken S, Jo-  livet A, Karlsson M, Orban de Xivry G, Piron P,  Surdej J, Vargas Catalan E, Wertz O (2018) Dis-  covery of a point-like source and a third spiral arm  in the transition disk around the Herbig Ae star  MWC 758.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A611:A74, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  201732016, 1710.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='11393  Rice WKM, Armitage PJ, Wood K, Lodato G (2006)  Dust filtration at gap edges: implications for the  spectral energy distributions of discs with embed-  ded planets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS373:1619–1626, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='11113.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='x, astro-ph/0609808  Rich EA, Wisniewski JP, Sitko ML, Grady CA, Tobin  JJ, Fukagawa M (2020) Disk Illumination and Jet  Variability of the Herbig Ae Star HD 163296 Using  Multi-epoch HST/STIS Optical, Near-IR, and Ra-  dio Imagery and Spectroscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ902(1):4, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4357/abb2a3, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='11606  Riols A, Lesur G (2018) Dust settling and rings in  the outer regions of protoplanetary discs subject to  ambipolar diffusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A617:A117, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/  0004-6361/201833212, 1805.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='00458  Rivinius T, Carciofi AC, Martayan C (2013) Clas-  sical Be stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Rapidly rotating B stars with vis-  cous Keplerian decretion disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&ARv21:69, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1007/s00159-013-0069-0, 1310.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3962  Romanova MM, Ustyugova GV, Koldoba AV, Lovelace  RVE (2012) MRI-driven accretion on to magnetized  stars: global 3D MHD simulations of magnetospheric  and boundary layer regimes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS421(1):63–77,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='20055.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='x, 1111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3068  Rosenfeld KA, Andrews SM, Hughes AM, Wilner DJ,  Qi C (2013) A Spatially Resolved Vertical Tempera-  ture Gradient in the HD 163296 Disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ774(1):16,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/774/1/16, 1306.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6475  Sacco GG, Flaccomio E, Pascucci I, Lahuis F, Ercolano  B, Kastner JH, Micela G, Stelzer B, Sterzik M (2012)  High-resolution Spectroscopy of Ne II Emission from  Young Stellar Objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ747(2):142, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/  0004-637X/747/2/142, 1201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0184  78  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Salyk C, Blake GA, Boogert ACA, Brown JM (2009)  High-resolution 5 µm Spectroscopy of Transitional  Disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ699:330–347, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/  699/1/330  Salyk C, Pontoppidan KM, Blake GA, Najita JR, Carr  JS (2011) A Spitzer Survey of Mid-infrared Molec-  ular Emission from Protoplanetary Disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Cor-  relations and Local Thermal Equilibrium Models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  ApJ731(2):130, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/731/2/130,  1104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0948  Schaefer GH, Dutrey A, Guilloteau S, Simon M, White  RJ (2009) A Millimeter-wave Interferometric Study  of Dust and CO Disks Around Late Spectral Type  Stars in Taurus-Auriga.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ701(1):698–709, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  1088/0004-637X/701/1/698  Sch¨oller M, Pogodin MA, Cahuasqu´ı JA, Drake NA,  Hubrig S, Petr-Gotzens MG, Savanov IS, Wolff B,  Gonz´alez JF, Mysore S, Ilyin I, J¨arvinen SP, Stelzer  B (2016) Spectroscopic signatures of magnetospheric  accretion in Herbig Ae/Be stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The case of  HD 101412.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A592:A50, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  201628361, 1606.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='03817  Segura-Cox DM, Schmiedeke A, Pineda JE, Stephens  IW, Fern´andez-L´opez M, Looney LW, Caselli P, Li  ZY, Mundy LG, Kwon W, Harris RJ (2020) Four  annular structures in a protostellar disk less than  500,000 years old.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Nature586(7828):228–231, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1038/s41586-020-2779-6, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='03657  Simon M, Dutrey A, Guilloteau S (2000) Dynamical  Masses of T Tauri Stars and Calibration of Pre-Main-  Sequence Evolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ545(2):1034–1043, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  1086/317838, astro-ph/0008370  Simon M, Guilloteau S, Di Folco E, Dutrey A, Grosso  N, Pi´etu V, Chapillon E, Prato L, Schaefer GH, Rice  E, Boehler Y (2017) Dynamical Masses of Low-mass  Stars in the Taurus and Ophiuchus Star-forming  Regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ844(2):158, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4357/  aa78f1, 1706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='03505  Spiegel DS, Burrows A (2012) Spectral and Photo-  metric Diagnostics of Giant Planet Formation Sce-  narios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ745:174, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/745/2/  174, 1108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5172  Stapper LM, Hogerheijde MR, van Dishoeck EF,  Mentel R (2022) The mass and size of Herbig disks  as seen by ALMA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A658:A112, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/  0004-6361/202142164, 2112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='03297  Steindl  T,  Zwintz  K,  Barnes  TG,  M¨ullner  M,  Vorobyov EI (2021) Pulsational instability of pre-  main-sequence models from accreting protostars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Constraining the input physics for accretion  with spectroscopic parameters and stellar pulsations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&A654:A36, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/202140818,  2107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='07568  Stelzer B, Micela G, Hamaguchi K, Schmitt JHMM  (2006) On the origin of the X-ray emission from Her-  big Ae/Be stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A457(1):223–235, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/  0004-6361:20065006, astro-ph/0605590  Stelzer  B,  Robrade  J,  Schmitt  JHMM,  Bou-  vier  J  (2009)  New  X-ray  detections  of  Herbig  stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&A493(3):1109–1119,  DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361:200810540, 0810.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1836  Stolker T, Dominik C, Avenhaus H, Min M, de Boer  J, Ginski C, Schmid HM, Juhasz A, Bazzon A, Wa-  ters LBFM, Garufi A, Augereau JC, Benisty M, Boc-  caletti A, Henning T, Langlois M, Maire AL, M´enard  F, Meyer MR, Pinte C, Quanz SP, Thalmann C,  Beuzit JL, Carbillet M, Costille A, Dohlen K, Feldt  M, Gisler D, Mouillet D, Pavlov A, Perret D, Petit C,  Pragt J, Rochat S, Roelfsema R, Salasnich B, Soenke  C, Wildi F (2016) Shadows cast on the transition disk  of HD 135344B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Multiwavelength VLT/SPHERE po-  larimetric differential imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A595:A113, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201528039, 1603.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='00481  St¨orzer H, Hollenbach D (2000) Optical Line Emission  from Photodissociation Regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ539(2):751–759,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/309251  Strom KM, Strom SE, Edwards S, Cabrit S, Skrut-  skie MF (1989) Circumstellar Material Associated  with Solar-Type Pre-Main-Sequence Stars: A Possi-  ble Constraint on the Timescale for Planet Building.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  AJ97:1451, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/115085  Strom SE (1972) Optical and Infrared Observations  of Young Stellar Objects - an Informal Review.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  PASP84(502):745, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/129375  Strom SE, Strom KM, Yost J, Carrasco L, Grasdalen G  (1972) The Nature of the Herbig Ae- and Be-TYPE  Stars Associated with Nebulosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ173:353, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/151425  Sturm B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bouwman J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Henning T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Evans NJ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Acke  B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mulders GD,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Waters LBFM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' van Dishoeck EF,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Meeus G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Green JD,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Augereau JC,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Olofsson J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Salyk  C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Najita J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Herczeg GJ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' van Kempen TA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kris-  tensen LE,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Dominik C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Carr JS,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Waelkens C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bergin  E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Blake GA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brown JM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Chen JH,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Cieza L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Dunham  MM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Glassgold A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' G¨udel M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Harvey PM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hogerhei-  jde MR,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Jaffe D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Jørgensen JK,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kim HJ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Knez C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Lacy JH,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Lee JE,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Maret S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Meijerink R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mer´ın B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Mundy L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pontoppidan KM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Visser R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Yıldız UA  (2010) First results of the Herschel key program  “Dust,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ice and Gas In Time” (DIGIT): Dust and  gas spectroscopy of HD 100546.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A518:L129, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201014674, 1005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3472  Sturm B, Bouwman J, Henning T, Evans NJ, Wa-  ters LBFM, van Dishoeck EF, Green JD, Olofsson  J, Meeus G, Maaskant K, Dominik C, Augereau JC,  Mulders GD, Acke B, Merin B, Herczeg GJ (2013)  Herbig Stars  79  The 69 µm forsterite band in spectra of protoplan-  etary disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Results from the Herschel DIGIT pro-  gramme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Astronomy & Astrophysics 553:5  Szul´agyi J (2017) Effects of the Planetary Tempera-  ture on the Circumplanetary Disk and on the Gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  ApJ842:103, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4357/aa7515, 1705.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  08444  Szul´agyi J, Morbidelli A, Crida A, Masset F (2014)  Accretion of Jupiter-mass Planets in the Limit  of Vanishing Viscosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ782:65, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/  0004-637X/782/2/65, 1312.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6302  Szul´agyi J, Masset F, Lega E, Crida A, Morbidelli A,  Guillot T (2016) Circumplanetary disc or circum-  planetary envelope?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS460:2853–2861, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/mnras/stw1160, 1605.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='04586  Szul´agyi J, Mayer L, Quinn T (2017) Circumplan-  etary discs around young giant planets: a com-  parison between core-accretion and disc instabil-  ity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS464(3):3158–3168, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/mnras/  stw2617, 1610.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='01791  Szul´agyi J, Dullemond CP, Pohl A, Quanz SP (2019)  Observability of forming planets and their cir-  cumplanetary discs II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' - SEDs and near-infrared  fluxes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  MNRAS487(1):1248–1258,  DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/  mnras/stz1326, 1905.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='03563  Tambovtseva LV, Grinin VP, Weigelt G (2016) Brack-  ett γ radiation from the inner gaseous accretion  disk, magnetosphere, and disk wind region of Herbig  AeBe stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A590:A97, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  201628256  Tamura M (2009) Subaru Strategic Exploration of Ex-  oplanets and Disks with HiCIAO/AO188 (SEEDS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  In: Usuda T, Tamura M, Ishii M (eds) Exoplanets  and Disks: Their Formation and Diversity, American  Institute of Physics Conference Series, vol 1158, pp  11–16, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3215811  Tang J, Bressan A, Rosenfield P, Slemer A, Marigo  P, Girardi L, Bianchi L (2014) New PARSEC evo-  lutionary tracks of massive stars at low metallic-  ity: testing canonical stellar evolution in nearby star-  forming dwarf galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS445:4287–4305, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/mnras/stu2029, 1410.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1745  Tang YW, Guilloteau S, Dutrey A, Muto T, Shen BT,  Gu PG, Inutsuka Si, Momose M, Pietu V, Fuka-  gawa M, Chapillon E, Ho PTP, di Folco E, Corder  S, Ohashi N, Hashimoto J (2017) Planet Formation  in AB Aurigae: Imaging of the Inner Gaseous Spi-  rals Observed inside the Dust Cavity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ840(1):32,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4357/aa6af7, 1704.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='02699  Tanigawa T, Ohtsuki K, Machida MN (2012) Dis-  tribution of Accreting Gas and Angular Momen-  tum onto Circumplanetary Disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ747:47, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/747/1/47, 1112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3706  Tazaki  R,  Tanaka  H,  Muto  T,  Kataoka  A,  Okuzumi  S  (2019)  Effect  of  dust  size  and  structure  on  scattered-light  images  of  proto-  planetary discs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS485(4):4951–4966, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/mnras/stz662, 1903.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='01890  Teague R, Bae J, Bergin EA, Birnstiel T, Foreman-  Mackey  D  (2018)  A  Kinematical  Detection  of  Two  Embedded  Jupiter-mass  Planets  in  HD  163296.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ860(1):L12, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/2041-8213/  aac6d7, 1805.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='10290  Teague R, Bae J, Aikawa Y, Andrews SM, Bergin EA,  Bergner JB, Boehler Y, Booth AS, Bosman AD,  Cataldi G, Czekala I, Guzm´an VV, Huang J, Ilee  JD, Law CJ, Le Gal R, Long F, Loomis RA, M´enard  F, ¨Oberg KI, P´erez LM, Schwarz KR, Sierra A,  Walsh C, Wilner DJ, Yamato Y, Zhang K (2021)  Molecules with ALMA at Planet-forming Scales  (MAPS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' XVIII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kinematic Substructures in the  Disks of HD 163296 and MWC 480.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJS257(1):18,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4365/ac1438, 2109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06218  Testi L, Palla F, Natta A (1999) The onset of cluster  formation around Herbig Ae/Be stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A342:515–  523, astro-ph/9811210  Testi L, Birnstiel T, Ricci L, Andrews S, Blum  J, Carpenter J, Dominik C, Isella A, Natta A,  Williams JP, Wilner DJ (2014) Dust Evolution  in Protoplanetary Disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In: Beuther H, Klessen  RS, Dullemond CP, Henning T (eds) Protostars  and Planets VI, p 339, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2458/azu uapress  9780816531240-ch015, 1402.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1354  Th´e PS, de Winter D, Perez MR (1994a) A new cata-  logue of members and candidate members of the Her-  big Ae/Be (HAEBE) stellar group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&AS104:315–  339  Th´e PS, Perez MR, J vEP (eds) (1994b) The nature  and evolutionary status of Herbig Ae/Be stars, As-  tronomical Society of the Pacific Conference Series,  vol 62  Thi WF (2014) TBD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A510(26):A260000+, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/200913076, 0911.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1949  Thi WF, van Dishoeck EF, Blake GA, van Zadel-  hoff GJ, Horn J, Becklin EE, Mannings V, Sar-  gent AI, van den Ancker ME, Natta A, Kessler J  (2001) H2 and CO Emission from Disks around T  Tauri and Herbig Ae Pre-Main-Sequence Stars and  from Debris Disks around Young Stars: Warm and  Cold Circumstellar Gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ561(2):1074–1094, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/323361, astro-ph/0107006  Thi WF, van Zadelhoff GJ, van Dishoeck EF (2004)  Organic molecules in protoplanetary disks around T  Tauri and Herbig Ae stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A425:955–972, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361:200400026, astro-ph/0406577  80  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Trapman L, Facchini S, Hogerheijde MR, van Dishoeck  EF,  Bruderer  S  (2019)  Gas  versus  dust  sizes  of protoplanetary discs: effects of dust evolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&A629:A79, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201834723,  1903.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06190  Tsukamoto Y, Okuzumi S, Kataoka A (2017) Appar-  ent Disk-mass Reduction and Planetisimal Forma-  tion in Gravitationally Unstable Disks in Class 0/I  Young Stellar Objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ838(2):151, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/  1538-4357/aa6081, 1608.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='03015  Tuthill PG, Monnier JD, Danchi WC (2001) A dusty  torus around the luminous young star LkHα101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Nature409(6823):1012–1014, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1038/35059014,  astro-ph/0102240  Tylenda R (1977) The continuous radiation emitted  by accretion discs in cataclysmic binaries: the dwarf  nova SS Cyg during outburst and the old novae V603  Aql and RR Pic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Acta Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='27:235–249  Valeg˚ard PG, Waters LBFM, Dominik C (2021) What  happened before?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='. Disks around the precursors of  young Herbig Ae/Be stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A652:A133, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/202039802, 2104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='14212  van Boekel R, Waters LBFM, Dominik C, Bouwman J,  de Koter A, Dullemond CP, Paresce F (2003) Grain  growth in the inner regions of Herbig Ae/Be star  disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A400:L21–L24, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361:  20030141  van Boekel R, Min M, Leinert C, Waters LBFM,  Richichi A, Chesneau O, Dominik C, Jaffe W, Dutrey  A, Graser U, Henning T, de Jong J, K¨ohler R, de  Koter A, Lopez B, Malbet F, Morel S, Paresce F,  Perrin G, Preibisch T, Przygodda F, Sch¨oller M,  Wittkowski M (2004) The building blocks of planets  within the ‘terrestrial’ region of protoplanetary disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Nature432(7016):479–482, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1038/nature03088  van Boekel R, Min M, Waters LBFM, de Koter A, Do-  minik C, van den Ancker ME, Bouwman J (2005) A  10 µm spectroscopic survey of Herbig Ae star disks:  Grain growth and crystallization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A437(1):189–  208, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361:20042339, astro-ph/  0503507  van Boekel R, ´Abrah´am P, Correia S, de Koter A, Do-  minik C, Dutrey A, Henning T, K´osp´al ´A, Lachaume  R, Leinert C, Linz H, Min M, Mosoni L, Preibisch  T, Quanz S, Ratzka T, Schegerer A, Waters R,  Wolf S, Zinnecker H (2006) Disks around young  stars with VLTI/MIDI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' In: Monnier JD, Sch¨oller  M, Danchi WC (eds) Society of Photo-Optical In-  strumentation Engineers (SPIE) Conference Series,  Society of Photo-Optical Instrumentation Engineers  (SPIE) Conference Series, vol 6268, p 62680D, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1117/12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='673777, astro-ph/0607387  van der Marel N, Mulders GD (2021) A Stellar Mass  Dependence of Structured Disks: A Possible Link  with Exoplanet Demographics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' AJ162(1):28, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-3881/ac0255, 2104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06838  van der Marel N, Verhaar BW, van Terwisga S, Mer´ın  B, Herczeg G, Ligterink NFW, van Dishoeck EF  (2016) The (w)hole survey: An unbiased sample  study of transition disk candidates based on Spitzer  catalogs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A592:A126, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  201628075, 1603.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='07255  van der Marel N, Williams JP, Bruderer S (2018)  Rings and Gaps in Protoplanetary Disks: Planets or  Snowlines?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ867(1):L14, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/2041-8213/  aae88e, 1810.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='05614  van der Marel N, Birnstiel T, Garufi A, Ragusa E,  Christiaens V, Price DJ, Sallum S, Muley D, Francis  L, Dong R (2021) On the Diversity of Asymmetries  in Gapped Protoplanetary Disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' AJ161(1):33, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-3881/abc3ba, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='10568  van der Plas G, van den Ancker ME, Fedele D, Acke B,  Dominik C, Waters LBFM, Bouwman J (2008) The  structure of protoplanetary disks surrounding three  young intermediate mass stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Resolving the disk  rotation in the [OI] 6300 ˚A line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A485(2):487–495,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361:20078867, 0802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0707  van der Plas G, van den Ancker ME, Acke B, Carmona  A, Dominik C, Fedele D, Waters LBFM (2009) Evi-  dence for CO depletion in the inner regions of gas-rich  protoplanetary disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A500(3):1137–1141, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/200811148, 0810.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3417  van der Plas G, Casassus S, M´enard F, Perez S, Thi  WF, Pinte C, Christiaens V (2014) Spatially Re-  solved HCN J = 4-3 and CS J = 7-6 Emission from  the Disk around HD 142527.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ792(2):L25, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/2041-8205/792/2/L25, 1407.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1735  van der Plas G, van den Ancker ME, Waters LBFM,  Dominik C (2015) The structure of disks around  Herbig Ae/Be stars as traced by CO ro-vibrational  emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A574:A75, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  201425052, 1412.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1311  van der Plas G, M´enard F, Canovas H, Avenhaus H,  Casassus S, Pinte C, Caceres C, Cieza L (2017a)  An 80 au cavity in the disk around HD 34282.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&A607:A55, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201731392,  1707.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='01688  van der Plas G, Wright CM, M´enard F, Casassus S,  Canovas H, Pinte C, Maddison ST, Maaskant K,  Avenhaus H, Cieza L, Perez S, Ubach C (2017b) Cav-  ity and other radial substructures in the disk around  HD 97048.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A597:A32, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  201629523, 1609.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='02488  van der Plas G, M´enard F, Gonzalez JF, Perez S,  Rodet L, Pinte C, Cieza L, Casassus S, Benisty  Herbig Stars  81  M (2019) ALMA study of the HD 100453 AB sys-  tem and the tidal interaction of the companion with  the disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A624:A33, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  201834134, 1902.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='00720  van der Wiel MHD, Naylor DA, Kamp I, M´enard  F, Thi WF, Woitke P, Olofsson G, Pontoppidan  KM, Di Francesco J, Glauser AM, Greaves JS, Ivi-  son RJ (2014) Signatures of warm carbon monox-  ide in protoplanetary discs observed with Her-  schel SPIRE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS444(4):3911–3925, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  1093/mnras/stu1462, 1408.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5432  van Dishoeck EF,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kristensen LE,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mottram JC,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Benz  AO,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bergin EA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Caselli P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Herpin F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hogerheijde  MR,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Johnstone D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Liseau R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Nisini B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Tafalla M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  van der Tak FFS,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wyrowski F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Baudry A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Benedet-  tini M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bjerkeli P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Blake GA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Braine J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bruderer  S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Cabrit S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Cernicharo J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Choi Y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Coutens A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' de  Graauw T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Dominik C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Fedele D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Fich M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Fuente A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Furuya K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Goicoechea JR,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Harsono D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Helmich FP,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Herczeg GJ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Jacq T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Karska A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kaufman M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Keto  E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Lamberts T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Larsson B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Leurini S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Lis DC,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mel-  nick G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Neufeld D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pagani L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Persson M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Shipman R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Taquet V,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' van Kempen TA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Walsh C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wampfler SF,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Yıldız U,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' WISH Team (2021) Water in star-forming  regions: physics and chemistry from clouds to disks  as probed by Herschel spectroscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A648:A24,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/202039084, 2102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='02225  van ’t Hoff MLR, Walsh C, Kama M, Facchini S, van  Dishoeck EF (2017) Robustness of N2H+ as tracer  of the CO snowline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A599:A101, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/  0004-6361/201629452, 1610.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06788  van Zadelhoff GJ, Aikawa Y, Hogerheijde MR, van  Dishoeck EF (2003) Axi-symmetric models of ul-  traviolet radiative transfer with applications to cir-  cumstellar disk chemistry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A397:789–802, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361:20021592, astro-ph/0211014  Varga J, ´Abrah´am P, Chen L, Ratzka T, Gab´anyi  K´E, K´osp´al ´A, Matter A, van Boekel R, Henning  T, Jaffe W, Juh´asz A, Lopez B, Menu J, Mo´or  A, Mosoni L, Sipos N (2018) VLTI/MIDI atlas of  disks around low- and intermediate-mass young stel-  lar objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A617:A83, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  201832599, 1805.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='02939  Varga J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hogerheijde M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' van Boekel R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Klarmann L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Petrov R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Waters LBFM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Lagarde S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pantin E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Be-  rio P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Weigelt G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Robbe-Dubois S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Lopez B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mil-  lour F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Augereau JC,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Meheut H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Meilland A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hen-  ning T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Jaffe W,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bettonvil F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bristow P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hofmann  KH,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Matter A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Zins G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wolf S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Allouche F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Donnan  F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Schertl D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Dominik C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Heininger M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Lehmitz M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Cruzal`ebes P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Glindemann A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Meisenheimer K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pal-  adini C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Sch¨oller M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Woillez J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Venema L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kokoulina  E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Yoffe G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ´Abrah´am P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Abadie S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Abuter R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ac-  cardo M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Adler T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ag´ocs T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Antonelli P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' B¨ohm A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Bailet C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bazin G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Beckmann U,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Beltran J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Boland  W,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bourget P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brast R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Bresson Y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Burtscher L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Castillo R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Chelli A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Cid C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Clausse JM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Connot C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Conzelmann RD,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Danchi WC,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' De Haan M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Delbo  M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ebert M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Elswijk E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Fantei Y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Frahm R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' G´amez  Rosas V,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Gabasch A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Gallenne A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Garces E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Girard  P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Gont´e FYJ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Gonz´alez Herrera JC,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Graser U,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Gua-  jardo P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Guitton F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Haubois X,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hron J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hubin N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Huerta R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Isbell JW,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ives D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Jakob G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Jask´o A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Jochum L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Klein R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kragt J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kroes G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Kuindersma  S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Labadie L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Laun W,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Le Poole R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Leinert C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Li-  zon JL,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Lopez M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' M´erand A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Marcotto A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mauclert  N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Maurer T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mehrgan LH,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Meisner J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Meixner K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Mellein M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mohr L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Morel S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mosoni L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Navarro R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Neumann U,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Nußbaum E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pallanca L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pasquini L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Percheron I,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pott JU,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Pozna E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ridinger A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Rigal F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Riquelme M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Rivinius T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Roelfsema R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Rohloff RR,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Rousseau S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Schuhler N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Schuil M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Soulain A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Stee  P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Stephan C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ter Horst R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Tromp N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Vakili F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' van  Duin A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Vinther J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wittkowski M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Wrhel F (2021)  The asymmetric inner disk of the Herbig Ae star  HD 163296 in the eyes of VLTI/MATISSE: evidence  for a vortex?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A647:A56, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  202039400, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='05697  Verhoeff AP, Waters LBFM, van den Ancker ME, Min  M, Stap FA, Pantin E, van Boekel R, Acke B, Tie-  lens AGGM, de Koter A (2012) A mid-IR study of  the circumstellar environment of Herbig Be stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&A538:A101, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201014916  Vieira SLA, Corradi WJB, Alencar SHP, Mendes LTS,  Torres CAO, Quast GR, Guimar˜aes MM, da Silva L  (2003) Investigation of 131 Herbig Ae/Be Candidate  Stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' AJ126(6):2971–2987, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/379553  Villebrun F, Alecian E, Hussain G, Bouvier J, Folsom  CP, Lebreton Y, Amard L, Charbonnel C, Gallet F,  Haemmerl´e L, B¨ohm T, Johns-Krull C, Kochukhov  O, Marsden SC, Morin J, Petit P (2019) Magnetic  fields of intermediate-mass T Tauri stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Mag-  netic detections and fundamental stellar parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&A622:A72, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201833545  Vink JS (2015) Linear line spectropolarimetry of Her-  big Ae/Be stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Ap&SS357(2):98, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1007/  s10509-015-2323-6, 1501.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='07436  Vink  JS,  Drew  JE,  Harries  TJ,  Oudmaijer  RD  (2002) Probing the circumstellar structure of Her-  big Ae/Be stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS337:356–368, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1046/  j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1365-8711.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='05920.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='x, astro-ph/0208137  Vink JS, Drew JE, Harries TJ, Oudmaijer RD, Un-  ruh Y (2005a) Probing the circumstellar structures  of T Tauri stars and their relationship to those of  Herbig stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS359:1049–1064, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1111/  j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='08969.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='x, astro-ph/0502535  82  Sean D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Brittain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Vink  JS,  Harries  TJ,  Drew  JE  (2005b)  Polari-  metric  line  profiles  for  scattering  off  rotating  disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A430:213–222, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361:  20041463, astro-ph/0409512  Vioque M, Oudmaijer RD, Baines D, Mendigut´ıa  I, P´erez-Mart´ınez R (2018) Gaia DR2 study of  Herbig Ae/Be stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A620:A128, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/  0004-6361/201832870, 1808.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='00476  Vioque M, Oudmaijer RD, Schreiner M, Mendigut´ıa  I, Baines D, Mowlavi N, P´erez-Mart´ınez R (2020)  Catalogue of new Herbig Ae/Be and classical Be  stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A machine learning approach to Gaia DR2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&A638:A21, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/202037731,  2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='01727  Wagner K, Apai D, Kasper M, Robberto M (2015)  Discovery of a Two-armed Spiral Structure in the  Gapped Disk around Herbig Ae Star HD 100453.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  ApJ813(1):L2,  DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/2041-8205/813/1/L2,  1510.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='02212  Wagner K, Follete KB, Close LM, Apai D, Gibbs A,  Keppler M, M¨uller A, Henning T, Kasper M, Wu  YL, Long J, Males J, Morzinski K, McClure M (2018)  Magellan Adaptive Optics Imaging of PDS 70: Mea-  suring the Mass Accretion Rate of a Young Giant  Planet within a Gapped Disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ863:L8, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/2041-8213/aad695, 1807.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='10766  Wagner K, Stone JM, Spalding E, Apai D, Dong  R, Ertel S, Leisenring J, Webster R (2019) Ther-  mal  Infrared  Imaging  of  MWC  758  with  the  Large Binocular Telescope: Planetary-driven Spi-  ral Arms?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ882(1):20, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4357/  ab32ea, 1907.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06655  Wahhaj Z, Koerner DW, Sargent AI (2007) High-  Resolution  Imaging  of  the  Dust  Disk  around  49 Ceti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ661(1):368–373, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/512716,  astro-ph/0701352  Walsh C, Nomura H, van Dishoeck E (2015) The molec-  ular composition of the planet-forming regions of  protoplanetary disks across the luminosity regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&A582:A88, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201526751,  1507.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='08544  Walsh C, Juh´asz A, Meeus G, Dent WRF, Maud LT,  Aikawa Y, Millar TJ, Nomura H (2016) ALMA Re-  veals the Anatomy of the mm-sized Dust and Molec-  ular Gas in the HD 97048 Disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ831(2):200, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/0004-637X/831/2/200, 1609.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='02011  Walsh C, Daley C, Facchini S, Juh´asz A (2017)  CO emission tracing a warp or radial flow within  ≲100 au in the HD 100546 protoplanetary disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&A607:A114, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201731334,  1710.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='00703  Walter FM (1986) X-Ray Sources in Regions of Star  Formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The Naked T Tauri Stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ306:573,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/164367  Watanabe N, Kouchi A (2002) Efficient Formation  of Formaldehyde and Methanol by the Addition of  Hydrogen Atoms to CO in H2O-CO Ice at 10 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  ApJ571(2):L173–L176, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/341412  Waters LBFM, Waelkens C (1998a) Herbig Ae/Be  Stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ARA&A36:233–266, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1146/annurev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  astro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='233  Waters LBFM, Waelkens C (1998b) Herbig Ae/Be  Stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ARA&A36:233–266, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1146/annurev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  astro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='233  Waters LBFM, Trams NR, Waelkens C (1992) A sce-  nario for the selective depletion of stellar atmo-  spheres.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A262:L37  Weidenschilling SJ (1977) Aerodynamics of solid bodies  in the solar nebula.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS180:57–70, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/  mnras/180.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='57  Weinberger AJ, Becklin EE, Schneider G, Smith BA,  Lowrance PJ, Silverstone MD, Zuckerman B, Terrile  RJ (1999) The Circumstellar Disk of HD 141569 Im-  aged with NICMOS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ525:L53–L56, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/  312334, astro-ph/9909097  Wheelwright HE, Oudmaijer RD, Goodwin SP (2010)  The mass ratio and formation mechanisms of Herbig  Ae/Be star binary systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS401:1199–1218,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='15708.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='x, 0910.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1774  Wheelwright HE, Vink JS, Oudmaijer RD, Drew JE  (2011) On the alignment between the circumstel-  lar disks and orbital planes of Herbig Ae/Be binary  systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  A&A532:A28,  DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/  201116996, 1106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3949  White JA, Boley AC (2018) Extended Millimeter  Emission in the HD 141569 Circumstellar Disk De-  tected with ALMA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ859(2):103, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/  1538-4357/aac088, 1804.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='09724  White RJ, Basri G (2003) Very Low Mass Stars and  Brown Dwarfs in Taurus-Auriga.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ582(2):1109–  1122, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/344673, astro-ph/0209164  Wichittanakom  C,  Oudmaijer  RD,  Fairlamb  JR,  Mendigut´ıa I, Vioque M, Ababakr KM (2020) The  accretion rates and mechanisms of Herbig Ae/Be  stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' MNRAS493(1):234–249, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1093/mnras/  staa169, 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='05971  Williams JP, Best WMJ (2014) A Parametric Modeling  Approach to Measuring the Gas Masses of Circum-  stellar Disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ788:59, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/  788/1/59, 1312.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0151  Williams JP, Cieza LA (2011) Protoplanetary Disks  and Their Evolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ARA&A49(1):67–117, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1146/annurev-astro-081710-102548, 1103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0556  Windmark F, Birnstiel T, G¨uttler C, Blum J, Dulle-  mond CP, Henning T (2012) Planetesimal forma-  tion by sweep-up: how the bouncing barrier can be  Herbig Stars  83  beneficial to growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A540:A73, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/  0004-6361/201118475, 1201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4282  Woitke P, Kamp I, Thi WF (2009) Radiation thermo-  chemical models of protoplanetary disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Hydro-  static disk structure and inner rim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A501:383–406,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/200911821, 0904.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='0334  Woitke P, Pinte C, Tilling I, M´enard F, Kamp I,  Thi WF, Duchˆene G, Augereau JC (2010) Contin-  uum and line modelling of discs around young stars  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' 300000 disc models for HERSCHEL/GASPS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  MNRAS405(1):L26–L30, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1745-3933.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='00852.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='x, 1003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2323  Woitke P, Kamp I, Antonellini S, Anthonioz F,  Baldovin-Saveedra C, Carmona A, Dionatos O, Do-  minik C, Greaves J, G¨udel M, Ilee JD, Liebhardt  A, Menard F, Min M, Pinte C, Rab C, Rigon L,  Thi WF, Thureau N, Waters LBFM (2019a) Con-  sistent Dust and Gas Models for Protoplanetary  Disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Models for Selected Objects from the  FP7 DIANA Project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' PASP131(1000):064301, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/1538-3873/aaf4e5, 1812.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='02741  Woitke P, Kamp I, Antonellini S, Anthonioz F,  Baldovin-Saveedra C, Carmona A, Dionatos O, Do-  minik C, Greaves J, G¨udel M, Ilee JD, Liebhardt  A, Menard F, Min M, Pinte C, Rab C, Rigon L,  Thi WF, Thureau N, Waters LBFM (2019b) Con-  sistent Dust and Gas Models for Protoplanetary  Disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Models for Selected Objects from the  FP7 DIANA Project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' PASP131(1000):064301, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/1538-3873/aaf4e5, 1812.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='02741  Wolfire MG, Cassinelli JP (1987) Conditions for the  Formation of Massive Stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ319:850, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  1086/165503  Yorke HW, Sonnhalter C (2002) On the Formation  of Massive Stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ569(2):846–862, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1086/  339264, astro-ph/0201041  Zhang K, Blake GA, Bergin EA (2015) Evidence of  Fast Pebble Growth Near Condensation Fronts in the  HL Tau Protoplanetary Disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ806(1):L7, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/2041-8205/806/1/L7, 1505.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='00882  Zhang K, Booth AS, Law CJ, Bosman AD, Schwarz  KR, Bergin EA, ¨Oberg KI, Andrews SM, Guzm´an  VV, Walsh C, Qi C, van’t Hoff MLR, Long F, Wilner  DJ, Huang J, Czekala I, Ilee JD, Cataldi G, Bergner  JB, Aikawa Y, Teague R, Bae J, Loomis RA, Calahan  JK, Alarc´on F, M´enard F, Le Gal R, Sierra A, Yam-  ato Y, Nomura H, Tsukagoshi T, P´erez LM, Trapman  L, Liu Y, Furuya K (2021) Molecules with ALMA  at Planet-forming Scales (MAPS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' CO Gas Dis-  tributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJS257(1):5, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/1538-4365/  ac1580, 2109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06233  Zhang  S,  Zhu  Z,  Huang  J,  Guzm´an  VV,  An-  drews SM, Birnstiel T, Dullemond CP, Carpenter  JM, Isella A, P´erez LM, Benisty M, Wilner DJ,  Baruteau C, Bai XN, Ricci L (2018) The Disk  Substructures at High Angular Resolution Project  (DSHARP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' The Planet-Disk Interactions Inter-  pretation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ869(2):L47, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/2041-8213/  aaf744, 1812.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='04045  Zhou Y, Sanghi A, Bowler BP, Wu YL, Close LM, Long  F, Ward-Duong K, Zhu Z, Kraus AL, Follette KB,  Bae J (2022) HST/WFC3 Hα Direct-imaging Detec-  tion of a Pointlike Source in the Disk Cavity of AB  Aur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ934(1):L13, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='3847/2041-8213/ac7fef,  2207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='06525  Zhu Z (2015) Accreting Circumplanetary Disks: Ob-  servational Signatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ799(1):16, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/  0004-637X/799/1/16, 1408.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='6554  Zhu Z, Stone JM (2014) Dust Trapping by Vortices  in Transitional Disks: Evidence for Non-ideal Mag-  netohydrodynamic Effects in Protoplanetary Disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  ApJ795(1):53,  DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/795/1/53,  1405.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='2790  Zhu Z, Nelson RP, Dong R, Espaillat C, Hartmann L  (2012) Dust Filtration by Planet-induced Gap Edges:  Implications for Transitional Disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' ApJ755(1):6,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1088/0004-637X/755/1/6, 1205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='5042  Zinnecker H, Preibisch T (1994) X-ray emission from  Herbig Ae/Be stars: a ROSAT survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A292:152–  164  Zuckerman B, Forveille T, Kastner JH (1995) Inhibi-  tion of giant-planet formation by rapid gas deple-  tion around young stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' Nature373:494–496, DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1038/373494a0  Zurlo A, Cugno G, Montesinos M, Perez S, Canovas  H, Casassus S, Christiaens V, Cieza L, Huelamo N  (2020) The widest Hα survey of accreting protoplan-  ets around nearby transition disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A633:A119,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/0004-6361/201936891, 1912.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='04911  Zwintz  K,  Kallinger  T,  Guenther  DB,  Gruber-  bauer M, Huber D, Rowe J, Kuschnig R, Weiss  WW, Matthews JM, Moffat AFJ, Rucinski SM,  Sasselov  D,  Walker  GAH,  Casey  MP  (2009)  MOST photometry of the enigmatic PMS pulsator  HD 142666.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content=' A&A494(3):1031–1040, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1051/  0004-6361:200811116, 0812.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1960  Zwintz K, Fossati L, Ryabchikova T, Guenther D,  Aerts C, Barnes TG, Themeßl N, Lorenz D, Cameron  C, Kuschnig R, Pollack-Drs S, Moravveji E, Baglin  A, Matthews JM, Moffat AFJ, Poretti E, Rainer  M, Rucinski SM, Sasselov D, Weiss WW (2014)  Echography of young stars reveals their evolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  Science  345(6196):550–553,  DOI  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='1126/science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='  1253645, 1407.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
+page_content='4928' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odAzT4oBgHgl3EQfOfsX/content/2301.01165v1.pdf'}
diff --git a/pNAzT4oBgHgl3EQfOfvU/content/2301.01168v1.pdf b/pNAzT4oBgHgl3EQfOfvU/content/2301.01168v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..635a970ad75fc243b1b34175d0fc4ae240395913
--- /dev/null
+++ b/pNAzT4oBgHgl3EQfOfvU/content/2301.01168v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:50c8d0e7b3786590c617830dcbe9eb5f768c285e354f108801e18f097f2a8bd8
+size 306652
diff --git a/pNAzT4oBgHgl3EQfOfvU/vector_store/index.faiss b/pNAzT4oBgHgl3EQfOfvU/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..9da9b3179a39380a877a9200612fd4cd920a01a9
--- /dev/null
+++ b/pNAzT4oBgHgl3EQfOfvU/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a707f73964ae799287765d8d744663cff1ca914aa6665c864c3dc7fca63c27cf
+size 3997741
diff --git a/pNAzT4oBgHgl3EQfOfvU/vector_store/index.pkl b/pNAzT4oBgHgl3EQfOfvU/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..ca74d1460bdf130f9b2d9cf6794d15cb4f40ad61
--- /dev/null
+++ b/pNAzT4oBgHgl3EQfOfvU/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e29440678ce8d5bddf4597758e897cc08eb5b4f91f9454992952bc190c34436d
+size 146685
diff --git a/pNE3T4oBgHgl3EQf7wtN/content/2301.04801v1.pdf b/pNE3T4oBgHgl3EQf7wtN/content/2301.04801v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..71f1c4d3ad171e4b0aee378bee593c52599c1f75
--- /dev/null
+++ b/pNE3T4oBgHgl3EQf7wtN/content/2301.04801v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:deca52d9a753252b98bb2e48204001fa08b31f929557f505d6ab1477909e929d
+size 898068
diff --git a/pNE3T4oBgHgl3EQf7wtN/vector_store/index.faiss b/pNE3T4oBgHgl3EQf7wtN/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..c3ed3c90028763c824100525710bea499e10ffaa
--- /dev/null
+++ b/pNE3T4oBgHgl3EQf7wtN/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:94faf38b6f2fc6a8d248867af5c43e57210942d29690a5e410e54fd5d1ecff39
+size 3801133
diff --git a/pdE0T4oBgHgl3EQfqgHp/content/2301.02555v1.pdf b/pdE0T4oBgHgl3EQfqgHp/content/2301.02555v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..926bfe104aa11a39fcc0089b37e3e63f84d94b3e
--- /dev/null
+++ b/pdE0T4oBgHgl3EQfqgHp/content/2301.02555v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:23df8ea49aaee321b492e67f54382db19af85aaccd0a0b19c0ca147fb79bbf7c
+size 6292192
diff --git a/pdE0T4oBgHgl3EQfqgHp/vector_store/index.faiss b/pdE0T4oBgHgl3EQfqgHp/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..d70cd23a26717d9b48bbba43b615cc781cb9c997
--- /dev/null
+++ b/pdE0T4oBgHgl3EQfqgHp/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2882527aaafaa50e02d2ad6042138b341fbd32caea81a5b31745d51822a4d326
+size 2424877
diff --git a/pdE0T4oBgHgl3EQfqgHp/vector_store/index.pkl b/pdE0T4oBgHgl3EQfqgHp/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..091b5c01022ad15ac099f37fe6a3e63daae30e63
--- /dev/null
+++ b/pdE0T4oBgHgl3EQfqgHp/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:77ade70bd8a7768b79f0205b9a346582e3ec0673d69ee916b418d31654d23614
+size 111545
diff --git a/qNE2T4oBgHgl3EQfKga-/content/tmp_files/2301.03704v1.pdf.txt b/qNE2T4oBgHgl3EQfKga-/content/tmp_files/2301.03704v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..23b9bd6e1554813c3df259ced7f4a15746e46ec5
--- /dev/null
+++ b/qNE2T4oBgHgl3EQfKga-/content/tmp_files/2301.03704v1.pdf.txt
@@ -0,0 +1,2546 @@
+Draft version January 11, 2023
+Typeset using LATEX twocolumn style in AASTeX631
+TESS-Gaia Light Curve: a PSF-based TESS FFI light curve product
+Te Han
+1, 2 and Timothy D. Brandt
+2
+1University of California, Irvine
+2University of California, Santa Barbara
+ABSTRACT
+The Transiting Exoplanet Survey Satellite (TESS) is continuing its second extended mission after
+55 sectors of observations.
+TESS publishes full-frame images (FFI) at a cadence of 1800, 600, or
+200 seconds, allowing light curves to be extracted for stars beyond a limited number of pre-selected
+stars. Simulations show that thousands of exoplanets, eclipsing binaries, variable stars, and other
+astrophysical transients can be found in these FFI light curves. To obtain high-precision light curves,
+we forward model the FFI with the effective point spread function to remove contamination from
+nearby stars. We adopt star positions and magnitudes from Gaia DR3 as priors. The resulting light
+curves, called TESS-Gaia Light Curves (TGLC), show a photometric precision closely tracking the
+pre-launch prediction of the noise level. TGLC’s photometric precision reaches ≲2% at 16th TESS
+magnitude even in crowded fields. We publish TGLC Aperture and PSF light curves for stars down
+to 16th TESS magnitude through the Mikulski Archive for Space Telescopes (MAST) for all available
+sectors and will continue to deliver future light curves via
+10.17909/610m-9474. The open-source
+package tglc is publicly available to enable any user to produce customized light curves.
+Keywords: Light curves (918) — Astronomy software (1855) — Astronomy databases (83) — Exoplanet
+astronomy (486) — Variable stars (1761) — Eclipsing binary stars (444)
+1. INTRODUCTION
+The Transiting Exoplanet Survey Satellite (TESS) of-
+fers nearly complete sky coverage, uniform cadence, and
+high-precision photometry. This enables a huge amount
+of time-domain science, from transiting planets (Huang
+et al. 2018; Vanderspek et al. 2019), to eclipsing bi-
+naries (Prˇsa et al. 2022; Powell et al. 2021; Borkovits
+et al. 2020), to stellar pulsations and variability (Antoci
+et al. 2019; C´orsico et al. 2019; Campante et al. 2016),
+to exotic binaries with accretion and complex variabil-
+ity (Rawat et al. 2022; Pichardo Marcano et al. 2021;
+Hernandez et al. 2022), to blazars (Weaver et al. 2020;
+Raiteri et al. 2021) and supernova transients (Vallely
+et al. 2019; Fausnaugh et al. 2021). The headline TESS
+science product is its two-minute photometry processed
+with the official Science Processing Operations Center
+(SPOC) pipeline (Jenkins et al. 2016), but this is only
+available for ∼105 stars in each 27-day observed sector.
+Most of the TESS data volume consists of full-frame
+images (FFIs) binned to an 1800-second, 600-second, or
+200-second cadence. Many of the aforementioned sci-
+ence cases require extraction of light curves from the
+FFIs for stars other than the pre-selected targets.
+TESS has the capability of reaching a photometric
+precision of ≈10−2 in a 30-minute exposure at 16th
+TESS magnitude (Ricker et al. 2015).
+This matches
+the per-epoch performance of the Zwicky Transient Fa-
+cility (ZTF, Bellm et al. 2019), but TESS offers ≈1000
+measurements over ≈27 days of nearly continuous view-
+ing. However, a user seeking a TESS light curve for a
+16th TESS magnitude star must currently download and
+process the raw full-frame images or relevant subimages
+with the help of TESScut (Brasseur et al. 2019) and, po-
+tentially, with a package like eleanor (Feinstein et al.
+2019). Powell et al. (2022) published all TESS FFI cor-
+rected aperture light curves for stars brighter than 16th
+TESS magnitude without flux contamination removal,
+which is essential to produce reliable light curves for
+dim stars.
+Several pipelines have published individual stars’ light
+curves on the Mikulski Archive for Space Telescopes
+(MAST). However, the Quick-Look Pipeline (Huang
+et al. 2020) and the SPOC full-frame images pipeline
+(Caldwell et al. 2020) only provide light curves for stars
+brighter than 13.5 TESS magnitude; the Cluster Dif-
+ference Imaging Photometric Survey (CDIPS) and the
+PSF-based Approach to TESS High quality data Of Stel-
+arXiv:2301.03704v1  [astro-ph.IM]  9 Jan 2023
+
+ID2
+lar clusters (PATHOS) only provide a subset of TESS
+data (Bouma et al. 2019; Nardiello et al. 2019); eleanor
+and the TESS Data for Asteroseismology collaboration
+can return a light curve of any star in a full-frame image
+at the price of a degree of user involvement. Many of
+these pipelines remove contamination from nearby stars
+and adjust for the background, but systematics do re-
+main. For all of these pipelines, the large size of TESS
+pixels (≈21′′) is an intrinsic limitation that is especially
+problematic for faint stars and crowded fields.
+In addition to the large size of TESS pixels and con-
+sequent blending from nearby stars, TESS also has fluc-
+tuating backgrounds from scattered sunlight, especially
+during certain phases of its orbit. Users interested in
+precise, high-cadence photometry for a fainter star must
+overcome all of these limitations by post-processing the
+full-frame images. The best extracted light curves for
+stars fainter than 13.5 TESS magnitude continue to re-
+quire significant user input (Feinstein et al. 2019).
+This paper presents a method to produce uniform,
+calibrated, light curves for all stars brighter than 16th
+TESS magnitude by leveraging astrometry and photom-
+etry from the Gaia mission. TESS and Gaia have full or
+nearly full-sky coverage, but their capabilities are com-
+plementary.
+Gaia has measured precise positions and
+brightnesses of about 1.5 billion stars with a Gaia Rp
+filter similar to that of TESS (Gaia Collaboration et al.
+2021). Gaia’s angular resolution of ≈0.′′2 is a factor of
+100 higher than TESS’s, while TESS brings a high, uni-
+form cadence with nearly continuous coverage over its
+observations of each 27-day sector.
+The precise mea-
+surements of Gaia can enable TESS to overcome its lim-
+itations of poor angular resolution and high, fluctuating
+backgrounds. We use Gaia astrometry and photometry
+to constrain the field stars in a TESS image, build a
+complete and local point spread function forward model
+of each TESS full-frame image, and extract percent-level
+precise light curves of approximately 3 million stars per
+sector down to 16th TESS magnitude. The final light
+curves of all sectors are being published in MAST’s High
+Level Science Product (HLSP) database continuously
+with the release of TESS FFI. We name them TESS-
+Gaia Light Curves (TGLC).
+The paper is structured as follows. Section 2 discusses
+the existing TESS FFI pipelines and their limitations.
+Section 3 explains our pipeline’s methodology. Section
+4 examines two types of TGLC light curves. We ana-
+lyze the photometric precision of TGLC in Section 5.
+Section 6 presents a case study of five known exoplanets
+using TGLC. Section 7 describes the publication of our
+data product and python package. Finally, we discuss
+the influence of TGLC on TESS time-domain science in
+Section 8.
+2. EXISTING TESS FFI LIGHT CURVE
+PRODUCTS
+In this section, we give an overview of the existing
+sources of FFI light curves, focusing on two that provide
+magnitude-limited samples:
+the Quick-Look Pipeline
+(Huang et al. 2020), and eleanor (Feinstein et al. 2019).
+The Quick-Look Pipeline (QLP) light curves are pro-
+duced with an aperture approach combined with differ-
+ence imaging. A template is first constructed by com-
+bining many comparison frames; each FFI is then differ-
+enced relative to this comparison frame. QLP performs
+aperture photometry on this difference image and then
+uses the TESS magnitude to scale the difference relative
+to the star’s average flux. However, the nature of aper-
+ture photometry involves a tradeoff: a larger aperture
+captures more of a star’s photons, but at the cost of in-
+creased backgrounds, contaminations, and, potentially,
+systematics. The performance of QLP also relies on the
+fidelity of its template and, as a result, on the temporal
+stability of systematics.
+Another popular TESS FFI light curve product,
+eleanor, has two versions of calibrated light curves:
+principal component analysis (PCA) and point spread
+function (PSF) light curves (Feinstein et al. 2019).
+The aperture photometry eleanor PCA utilizes the co-
+trending basis vectors published by the Science Pay-
+load Operations Center (SPOC, Jenkins et al. (2016))
+to remove systematics in each camera.
+eleanor
+PCA light curves are further calibrated to produce
+eleanor CORR. eleanor PSF uses an analytical two-
+dimensional Gaussian model to perform PSF photom-
+etry. Users can incorporate positions of several nearby
+stars in the PSF fit to remove contamination partially,
+but inputting each star’s position and magnitude in the
+fit manually becomes impractical for a full-sky light
+curve product. The eleanor documentation also sug-
+gests summing multiple two-dimensional Gaussians to
+accommodate irregular PSF shapes. However, the re-
+sults are still not ideal for some irregular PSF shapes
+and require a higher level of user involvement.
+Figure 1 compares the light curve products of three
+pipelines: eleanor CORR, eleanor PSF, and QLP, to
+the official SPOC 2-min light curves. We adopt five faint
+TESS planet hosts as our comparison stars: TOI-674
+(Murgas, F. et al. 2021), LHS 3844 (Vanderspek et al.
+2019), TOI-530 (Gan et al. 2021), TOI-2406 (Wells, R.
+D. et al. 2021), and TOI-519 (Parviainen, H. et al. 2021).
+We plot the light curves phase-folded around the cen-
+ter of their transits. The SPOC light curves are com-
+
+3
+Figure 1. Light curves of five TESS-discovered exoplanets from existing pipelines. Compared to the published work (similar
+to the SPOC 2-min light curves), the current FFI light curves perform poorer, especially for dimmer stars. The legend in each
+subplot indicates the sector(s) plotted. Light curves from extended missions are binned to a 30-minute cadence for compatible
+noise level with the primary mission.
+The periods and transit midpoints are adopted from each discovery literature.
+All
+lightcurves are detrended with wotan (Hippke et al. 2019) and the phases are normalized to 1.
+pared because all five publications above use the SPOC
+pipeline in their discoveries of the new exoplanets. All
+light curves from extended missions are binned to a 30-
+min cadence like the primary mission for a fair com-
+parison of noise levels. All light curves are detrended
+with wotan, an automated detrending algorithm (Hippke
+et al. 2019). It is especially powerful in preserving tran-
+sit signals while removing stellar trends. The detrending
+method is biweight, and the window length is set to 1
+for all detrended light curves in this paper.
+For the
+first two stars of ≈12 TESS magnitude, the FFI light
+curves mostly perform comparably to the 2-min light
+curves, but they become visibly worse for the dimmer
+stars. The light curves for these fainter stars have either
+a lower SNR, an inaccurate transit depth (compared to
+published work), inconsistency among sectors, or a com-
+bination of these issues.
+3. POINT SPREAD FUNCTION MODELING OF
+TESS FULL-FRAME IMAGES
+Point spread function (PSF) photometry is the most
+accurate way to obtain brightnesses, provided a suffi-
+ciently good PSF model is available. The PSF varies
+spatially across TESS fields, so PSF models must be fit
+locally to address the variation. PSFs can also be time-
+dependent, so they need to be fit for each frame. How-
+ever, building an accurate PSF model locally and frame-
+wise for TESS is daunting. Without prior knowledge of
+the positions and brightnesses of stars in the field, PSF
+fitting is hopelessly underconstrained: the number of
+
+SPOC 2-min
+eleanor CORR
+eleanor PSF
+QLP
+Normalized Flux
+mag=11.88
+TO1-674 b
+1.00
+6
+10
+10
+10
+10
+0.98
+36
+36
+36
+36
+-0.02
+0.00
+0.02
+-0.02
+0.00
+0.02
+-0.02
+0.00
+0.02
+-0.02
+0.00
+0.02
+Normalized Flux
+mag=11.92
+LHS 3844
+1.00
+27
+27
+27
+0.99
+28
+28
+28
+28
+-0.05
+0.00
+0.05
+-0.05
+0.00
+0.05
+-0.05
+0.00
+0.05
+-0.05
+0.00
+0.05
+Normalized Flux
+mag=13.53
+TOI-530
+1.00
+:
+6
+6
+44
+44 
+44
+q
+45
+45
+45
+6
+0.95
+-0.02
+0.00
+0.02
+-0.02
+0.00
+0.02
+-0.02
+0.00
+0.02
+-0.02
+0.00
+0.02
+Normalized Flux
+mag=14.31
+TO1-2406
+1.00
+42 
+42 
+42 
+43
+43
+43
+30
+0.95
+-0.03
+0
+0.03
+-0.03
+0
+0.03
+-0.03
+0
+0.03
+-0.03
+0
+0.03
+Normalized Flux
+Phase
+mag=14.43
+TOI-519
+1.00
+iin!m.
+0.90
+8
+q
+34 
+34
+-0.03
+0
+0.03
+-0.03
+0
+0.03
+-0.03
+0
+0.03
+Phase
+Phase
+Phase4
+free parameters of star positions and magnitudes can
+exceed the number of pixels because of the large TESS
+pixels. We have ∼ 1.5 billion stars in Gaia DR3, and
+each pixel is approximately 10−8 sr, which implies ∼1.2
+stars per pixel or ∼3.6 parameters to constrain with one
+pixel value on average.
+Any fit for the PSF and the
+stellar positions would also be fundamentally nonlinear.
+Even if one were to ignore enough low-brightness stars
+to reduce the number of free parameters, the computa-
+tional performance of such a nonlinear fit would still be
+impractical for a full-sky survey.
+Gaia’s astrometry and photometry offer a way to over-
+come this inability to measure the instrumental PSF. If
+we apply precise Gaia position and brightness measure-
+ments as fixed priors, we are left with only the PSF pa-
+rameters. We can construct this problem as a linear fit,
+solvable with standard linear algebra-based approaches
+as shown below. Furthermore, we can include all Gaia
+stars in the forward modeling to resolve the background
+contamination as deep as ∼20 TESS magnitude without
+unduly compromising computational performance.
+The fundamental assumption of our PSF modeling is
+that the PSF shape is spatially constant over each FFI
+cutout of the size of about 150 × 150 pixels for each
+epoch. In practice, the PSF variation is gradual among
+adjacent cutouts as shown in Section 3.4, and apply-
+ing the same PSF within one cutout is reasonable. We
+also allow the PSF to vary with time by fitting each
+frame independently. We first extract stellar positions
+and brightnesses from Gaia DR3. We then fit the PSF
+parameters of the simulated image to the FFI cutout.
+Using the best-fit PSF shape, we forward-model the FFI
+cutout with all stars except the target. Lastly, we gen-
+erate a decontaminated image by subtracting this mod-
+eled cutout from the measured FFI cutout. We can then
+perform aperture photometry or PSF photometry on the
+residual to produce photometry of a given star at a given
+epoch. By repeating this process for all stars and all
+frames, we can construct FFI light curves for all stars in
+TESS.
+3.1. Positions and Brightness from Gaia
+The Gaia mission has now measured positions and
+magnitudes of about 1.5 billion stars (Gaia Collabora-
+tion et al. 2021). The positions are typically accurate to
+≲0.1 mas or better, while magnitude uncertainties re-
+main ∼0.001 mag even down to a Gaia G magnitude of
+18. This extraordinary data set enables us to construct
+a full forward model of each TESS full-frame image.
+A forward model requires the positions and TESS
+magnitudes of all stars.
+We first propagate Gaia po-
+sitions from J2016.0 to the median TESS epoch of each
+sector using the measured Gaia proper motions.
+We
+then convert the Gaia DR3 right ascension and decli-
+nation to pixel positions based on the TESS FFI world
+coordinate system (WCS) headers. We do not account
+for either parallactic motion or perspective acceleration
+because both are typically orders of magnitude smaller
+than the proper motion correction and < 0.01 TESS
+pixels for all but a handful of stars within a few par-
+secs. The positions could have small, local offsets from
+the true coordinates due to the TESS spacecraft jitter
+motion. As we will show later, however, photometric
+products from our PSF approach are largely immune
+from systematic shifts over FFI cutouts. We rely only
+on the accurate relative positions in the TESS frame
+across ≈150 TESS pixels.
+In addition to astrometry, our approach also requires
+photometric anchors for all stars in the field. The TESS
+bands differ from the Gaia bands, requiring a color-
+dependent transformation. We adopt the conversion
+T = G − 0.00522555(GBP − GRP)3
++ 0.0891337(GBP − GRP)2
+− 0.633923(GBP − GRP) + 0.0324473
+(1)
+published in Stassun et al. (2019), where T is the ap-
+parent magnitude in the TESS bandpass, and G, GBP,
+and GRP are Gaia bandpasses. When GBP and GRP are
+missing, we adopt
+T = G − 0.430
+(2)
+from the same work. After this step, we have astrometry
+and photometry in the TESS system for all Gaia stars.
+3.2. Effective PSF Model
+With positions and magnitudes known for all stars in
+a TESS field, we can forward model a full-frame image.
+We approach the problem agnostic to the form of the
+PSF, using the effective PSF (ePSF) model successfully
+applied to Hubble data (Anderson & King 2000). The
+ePSF model notes that the actual PSF observed on the
+detector is the convolution of the PSF incident on the
+detector and the detector response function. This ePSF
+is continuous and is the only observable form of the PSF.
+The ePSF may be defined at anchor points spaced more
+finely than the pixels on the detector and then inter-
+polated at the position of a source. Interpolating the
+ePSF is equivalent to placing the PSF produced by the
+optics at the location of a star, multiplying by the pixel
+response function, and then integrating over the pixels
+(Anderson & King 2000).
+Figure 2 shows how the ePSF model works. The ePSF
+is shown at red anchor points and the simulated pixel
+
+5
+Figure 2. Interpolation example of an ePSF model. The
+white squares and dots represent the pixels and their centers;
+the red dots represent the twice oversampled ePSF model;
+the dot sizes represent the ePSF values. The star represented
+by the red ePSF values is located at (0, 0), the location of
+the largest red dot. Each pixel value (grayscale) is interpo-
+lated only by its nearest four values in the oversampled ePSF
+(red points) as shown in pixel (0, 1) by the white lines. This
+maintains the linearity (and therefore the computational ef-
+ficiency) of the model we use to forward model a subimage
+of a full-frame TESS image from an ePSF.
+values are interpolated among those red points. In the
+example figure, the ePSF is oversampled relative to the
+pixels on the detector by a factor of two. The size of
+the red points gives the intensity of the ePSF at that
+point, with the star centered at the point (0, 0). The
+data are interpolated from the ePSF at the pixel centers,
+indicated in white. The grayscale color over the pixels
+shows these interpolated values from the ePSF, which
+indicate the actual intensity observed for a point source
+centered at (0, 0), which in this case is displaced from
+the center of a pixel.
+The effective PSF (ePSF) method from Anderson &
+King (2000) interpolates the ePSF from a four-times-
+oversampled grid with cubic spline interpolation. Given
+the arbitrary nature of the oversampling factor, we ex-
+plore oversampling factors from 2, 4, and 6. We decide
+to use a factor of 2 because it produces the best qual-
+ity light curves (those derived in Section 4) and is much
+more computationally efficient.
+We also use bilinear instead of cubic interpolation.
+This choice enables us to write the optimization of the
+ePSF’s values at its anchor points as a linear least-
+squares problem.
+This fact is necessary to keep the
+model computationally tractable. Also, we assume that
+the PSF of a star is mostly contained within a square
+with a side length of 11 pixels. Fluxes in further pix-
+els are negligible according to TESS Instrument Hand-
+book v0.1 1. In a grid with side length Lgrid = 11, the
+oversampled grid side length is rLgrid + 1, where r is
+the oversampling factor. Depending on the position of
+a star to the center of its pixel, stars are interpolated
+by different sets of four interpolation points. We can
+now model all stars in a cutout by fitting a shared lo-
+cal ePSF while fixing stars’ positions and relative fluxes,
+but we must also consider the background to model the
+field completely. The derivation of our complete model
+is presented in Section 3.4 after the discussion of back-
+ground modeling.
+3.3. Background modeling
+The unevenness of the TESS FFI background is a re-
+sult of both stray light and CCD artifacts. Stray light
+from the Earth and the Moon usually produce a back-
+ground with a gradient and are strongest near the ends
+of each observation window. The gradient is mostly lin-
+ear in a small cutout and easy to fit. The CCD artifacts,
+including the straps shown in the first panel in Fig-
+ure 3, result from highly reflective metal straps beneath
+the CCD silicon.
+These straps, however, are strictly
+column-wise according to the TESS Instrument Hand-
+book v0.1. We model the straps as a column-dependent
+flatfield that applies only to a portion of the background.
+The visible effects of the straps are chromatic. They re-
+sult from photons that penetrate the CCD, are reflected,
+and then detected; wavelengths where the CCD is more
+transparent show stronger artifacts at the strap loca-
+tions according to TESS Instrument Handbook v0.1.
+While the straps reside at specific CCD columns,
+they can reflect photons into neighboring columns. We,
+therefore, model the effect of the straps as a column-
+dependent modification to the background.
+We con-
+struct a flat, column-dependent background by fitting
+the variation in the background intensity between neigh-
+boring columns, applying a low-pass filter, and averag-
+ing across sectors for a given CCD. We take the dimmest
+half of the pixels in each column and compute the me-
+dian of the ratio of the count rate between neighboring
+columns, using only pixels that are among the dimmest
+half in both columns. Multiplying these ratios across the
+detector produces an effective column-dependent back-
+1 https://archive.stsci.edu/files/live/sites/mast/files/home/
+missions-and-data/active-missions/tess/ documents/
+TESS Instrument Handbook v0.1.pdf
+
+2 
+0
+-1
+-2 
+-2
+-1
+0
+1
+26
+Figure 3. Example of background removal of TGLC. The left panel shows a FFI cutout with a background gradient and three
+vertical straps. We model the background as the middle panel. The residual image on the right shows a much cleaner field
+ready for an ePSF fit. Note that we preserve the resolution of the color map and only shift it down by 100 e−/s for the last
+panel.
+ground. We remove drifts in the count rate across the
+detector by dividing by a median-filtered processing of
+the background. Finally, we take the median for each
+CCD’s calibrated background over all primary mission
+sectors, since the straps are inherent to the CCD.
+The reflective straps on the back of the CCD have a
+strong chromatic effect. To account for this, we use our
+calibrated CCD-dependent background as a flatfield for
+only a fraction of the background. By allowing this frac-
+tion to be free, we fit the chromaticity of the strap reflec-
+tions frame-by-frame. We ultimately use six parameters
+to model the background: a flat background and a lin-
+ear gradient in each of two dimensions, plus these same
+parameters multiplying the CCD-dependent calibrated
+background. Figure 3 shows an example model of the
+background: both the linear gradient and straps have
+been removed from the FFI. In particular, strap removal
+is essential for avoiding systematic vertical lines in ePSF
+shapes.
+3.4. Fitting ePSF and background models
+Obtaining the ePSF requires a simultaneous fit to all
+of the parameters describing the ePSF itself together
+with the parameters that model the background. We
+construct a least squares fit P ≈ AF as
+�
+�����
+p1
+p2
+...
+pm
+�
+�����
+≈
+�
+�����
+a11
+a12
+· · · a1n
+a21
+a22
+· · · a2n
+...
+...
+...
+...
+am1 am2 · · · amn
+�
+�����
+�
+�����
+f1
+f2
+...
+fn
+�
+�����
+,
+(3)
+where p1 to pm are the observed count rate of each pixel
+from the FFI, a11 to amn are the matrix encoded with
+star information, and f1 to fn are best fits of both the
+ePSF and background parameters. m is the total num-
+Figure 4. Normalized median absolute deviation (MAD) of
+residual images with different weighting power l (Equation
+(4)). Larger values of p weight lower count-rate pixels more
+heavily in deriving the ePSF, with p = 1 weighting all pixels
+equally.
+These blue curves are generated from 196 differ-
+ent cutouts of Sector 7. The orange curve shows the MAD
+taken over all pixels from 196 residual images, which favors
+a weighting power l ≈ 1.4
+ber of pixels in the FFI cutout, and n is the total number
+of free parameters. Each star only adds weights to the
+rows of A (pixels) that are 5 pixels or closer to the star;
+the weights for each column are the bilinear translation
+weights from the oversampled ePSF grid to the corre-
+sponding pixel. Weights from all stars are summed to
+construct the full A. We solve for F in the least square
+fit.
+For example, if we fit for an 11 × 11 pixel ePSF
+(extending five pixels from the star) and oversample by
+a factor of two, this requires fitting n = 535 free param-
+
+TESS FFI cutout
+Simulated background
+≥140
+Background removed FFI
+≥40
+130
+30
+TESS Flux (e=/ s)
+120
+20
+110
+10
+1001.8
+MAD of each cutout
+Normalized MAD of residual image
+MAD of all cutouts
+1.6
+1.4
+1.2
+1.0
+0.4
+0.6
+0.8
+1.0
+1.2
+1.4
+1.6
+1.8
+2.0
+weighting power (l)7
+Figure 5. 7 × 14 effective PSF models for half of Sector 1, camera 4, CCD 3. Each ePSF model is fitted in a 150 × 150 pixels
+FFI cutout, and 14 × 14 models will exactly cover the 2048 × 2048 pixels image with two-pixel-wide overlaps. Each CCD is
+divided in this manner to produce light curves published on MAST. We can observe the gradual spatial variation of ePSF: An
+obvious trend is that the ePSFs are narrower in the upper right corner, which is the closest to the center of the lens. One
+plausible reason is the optics of the telescope produce more compact pixel response functions (PRF) near boresights according
+to TESS Instrument Handbook v0.1. The gradual variation supports our assumption of constant ePSF in each cutout at the
+beginning of Section 3.
+eters ((11 × 2 + 1)2 + 6). We need the number of pixels
+in a cutout to be much larger than the number of free
+parameters and for there to be many stars in the image
+for the fit to be over-constrained. Adopting 150 × 150
+pixel regions (m = 22500) provides more than enough
+pixels to constrain the ePSF, while such a region usually
+has at least thousands of stars detected in Gaia.
+Equation (3) cannot be solved exactly if there are
+more pixels than parameters. The best solution depends
+on the definition of “≈”. To allow a linear algebra solu-
+tion, we take it to mean the sum of the squares of the
+weighted differences between the observed and modeled
+pixel values.
+In classic χ2 statistics, these differences
+are normalized by the observational uncertainty. In our
+case, we explore different weightings to avoid heavily pri-
+oritizing the brightest pixels and to limit our vulnerabil-
+ity to detector nonlinearities. We parametrize a family
+of weights by an exponent l, weighting each residual by
+1/pl. This weighting modifies Equation (3) to read
+�
+�����
+p1/pl
+1
+p2/pl
+2
+...
+pm/pl
+m
+�
+�����
+≈
+�
+�����
+a11/pl
+1
+· · ·
+a1n/pl
+1
+a21/pl
+2
+· · ·
+a2n/pl
+2
+...
+...
+...
+am1/pl
+m · · · amn/pl
+m
+�
+�����
+�
+�����
+f1
+f2
+...
+fn
+�
+�����
+.
+(4)
+where we now take “≈” to simply mean the sum of the
+squares of the residuals over all pixels. A value of l = 0.5
+would approximate weighting by the uncertainty con-
+tributed by shot noise. At l = 1, each pixel is equally
+weighted, but this does not guarantee the smallest resid-
+ual for each pixel. One advantage of our ePSF model
+is its high precision for faint stars, so we prioritize min-
+imizing the residuals of dimmer pixels to enhance its
+performance on the faint end further. The median abso-
+lute deviation (MAD) of the residual is a natural choice
+of the goodness of fit to represent the majority (dim-
+mer) pixels. Figure 4 shows the normalized MAD of the
+residual versus different powers for 196 different cutouts
+sampled from Sector 7. We tested weights from l = 0.4
+(prioritizing brighter pixels) to l = 2 (prioritizing dim-
+mer pixels) and the smallest MAD happens near l = 1.4.
+We, therefore, adopt l = 1.4 in all fits.
+In addition,
+there are saturated pixels and dim vertical lines seem-
+ingly corresponding to bad CCD columns (different from
+the straps we discussed in Section 3.3) in some FFIs. We
+assign these pixels l = ∞ (i.e. zero weight) to exclude
+them from the fit. Figure 5 shows the resulting ePSF
+shapes from a part of Sector 1. The width of the ePSF
+gradually narrows down towards the upper-right of this
+CCD (the center of the camera lens) due to the TESS
+
+8
+optical design. The trend shown is indeed gradual, so
+it is appropriate to assume the PSF is constant in each
+cutout.
+Despite the 535 parameters that we must fit, the lin-
+earity of the problem results in a modest computational
+cost. Deriving the ePSF for a single FFI cutout requires
+setting up and solving a single matrix equation, and
+takes ≈ 0.4 seconds on a single core of a modern server
+processor 2. Processing thousands of these cutouts for
+each epoch, a precondition to producing light curves,
+takes 400 seconds for the primary mission on a single
+core. Extending this approach to all regions on a CCD
+(×142), and to all CCDs on the TESS camera (×16),
+brings the cost to about 350 CPU hours per primary
+mission sector. This remains computationally tractable
+on a modern server with tens of cores, requiring a wall-
+clock time of less than a day per primary mission sector
+(∼ 3 days for the first extended mission and ∼ 9 days
+for the second extended mission). In this way, the data
+may be reprocessed if needed.
+Deriving a local, free,
+non-parametric ePSF for every region of the TESS cam-
+era and every full-frame image is a linear problem, and
+thus a computationally tractable task.
+The ePSF approach to photometry has a further ad-
+vantage over fits using parametric formulae, e.g., a Gaus-
+sian or a Moffat model for the PSF. A Gaussian or Mof-
+fat model requires the modeled positions of all stars on
+the TESS image to be correct in absolute terms so that
+the star’s center corresponds to its peak intensity. An
+ePSF approach has the weaker requirement that only
+the relative positions of the stars are correct. If all stars
+are offset by a fraction of a pixel, then the modeled ePSF
+will have its peak flux correspondingly off-center. There
+will be no consequence to the quality of the forward
+model or the extracted photometry of any star.
+4. EXTRACTING LIGHT CURVES
+4.1. PSF photometry light curves
+Our final step after constructing the ePSF and estab-
+lishing the background is to extract a light curve for
+each star. In previous sections, we described our ePSF
+fit by fixing the brightness of each star to its value mea-
+sured by Gaia and converting it to the TESS photo-
+metric system. With the fitted ePSF, we first explore
+the possibility of allowing all stars in the field to float
+while extracting the light curve. As discussed in Sec-
+tion 3, we often have more stars than pixels in crowded
+fields, resulting in underconstrained fits. We try to re-
+solve this problem by assigning Gaussian priors to field
+2 AMD EPYC 7313 16-Core Processor
+Figure 6. Comparing the MADs of the PSF light curves
+if the field stars are assigned different priors.
+All curves
+are normalized to their MAD at prior = 10−5, effectively
+fixing the field stars to the Gaia-predicted flux. Top: The
+MAD curves of all Sector 17 stars (black) within 20 arcmin-
+utes of TIC 270022476 (an 11.5 TESS magnitude eclipsing
+binary (EB); orange).
+Gaia DR3 2015669353645091072 is
+highlighted in blue, a 15.2 TESS magnitude star 1 pixel away
+from the EB. The trend of all stars shows a strong preference
+towards fixing the field stars with only several exceptions.
+Bottom: The comparison among EB lightcurve with fixed
+field stars, dim star light curve fitted with fixed field stars,
+and dim star light curve fitted with the prior that returns
+the lowest MAD (prior = 0.01072; red diamond in the top
+panel). The dim star light curve with fixed field stars shows
+deep transits from the EB while allowing the field stars to
+float within the best prior removes most contamination.
+stars while fitting the target star. The priors are the
+fraction of each field star’s median flux derived from
+Gaia, so using a very small prior fundamentally sets the
+field stars as non-variables. Figure 6 shows the MADs
+of the PSF light curves when stars are fitted with differ-
+ent priors. The MADs of all stars from the vicinity of
+TIC 270022476 (an 11.5 TESS magnitude eclipsing bi-
+nary (EB)) in Sector 17 (black) show an increasing trend
+as the prior gets wider, which supports choosing fixed
+field stars in general.
+Several exceptions could reach
+
+3.0
+Eclipsing Binary
+MAD of normalized flux
+2.5
+Dim star close to EB
+Best Prior
+All Stars
+2.0
+1.5
+1.0
+0.5
+0.0
+10-5
+10-4
+10-3
+10-2
+10-1
+100
+Field Star Prior (fraction of median flux)
+1
+EB
+Fixed field
+0.8
+1
+Dim star
+flux
+Best prior
+0.8
+Normalized t
+1
+Dim star
+Fixed field
+0.8
+0.6
+0.4 -
+0.2
+1760
+1765
+1770
+1775
+1780
+1785
+TBJD9
+lower MADs at specific priors, and one of them is Gaia
+DR3 2015669353645091072 (blue). This dim star at 15.2
+TESS magnitude is only 1 pixel away from the EB and
+is vulnerable to its transit contaminations if the field
+stars (including the EB) are considered fixed (the last
+row of the lower panel). If we allow the field stars to
+float with the best prior (the prior that results in the
+lowest MAD), most of the contamination is removed.
+Therefore, this approach is useful for decontaminating
+stars near variable sources if one finds the best prior
+by sampling. However, running this fit requires ∼8000
+CPU hours for a single sector due to a large number of
+variables, not to mention that we have to sample the
+priors to find the one resulting in the largest decrease in
+MAD. It is thus impractical to fit all light curves with
+this method, especially when setting all stars fixed gives
+very high (if not the highest) precision at a very low
+computational cost. The function for sampling and ap-
+plying priors is kept in the tglc package for manually
+decontaminating certain stars.
+We now allow the photometry of a given target star
+to float while holding the photometry of its neighbors
+fixed and keeping the ePSF derived earlier for the full
+150 × 150 pixel region.
+This change is equivalent to
+modeling a FFI cutout for each cadence and then tak-
+ing the residual of this from the measured cutout. Since
+the field stars are fixed, the FFI cutout varies in time
+mainly due to background fluctuation.
+We can then
+perform PSF photometry using the known ePSF on the
+residual images. This gives a perturbation to the flux
+derived from Gaia using the conversion of 15000 e−/s
+for a 10th TESS magnitude star given in the TESS In-
+strument Handbook v0.1. Adding this perturbation to
+the Gaia-derived flux gives our PSF photometry flux of
+the target star. In this way, extracting a light curve for
+each star in the field incurs a negligible computational
+cost over that for constructing the ePSF.
+Figure 7 illustrates the process of extracting a light
+curve. The left-hand panel shows a small cutout of a
+TESS full-frame image, a subset of that used to build
+the ePSF model. The middle panel shows the results
+of a forward model of the image fixing all stars to their
+Gaia-inferred photometry; we have omitted the central
+target star from this model. The right-hand panel shows
+the residual from the model subimage after removing the
+neighboring stars (but not removing any modeled light
+from the target star). Performing PSF photometry on
+this image will produce one data point in the light curve
+of the target. The same can be done for all frames and
+all stars in this cutout to generate light curves from PSF
+photometry.
+4.2. Aperture photometry light curves
+We also generate TGLC Aperture light curves. Using
+the residual image described in Section 4.1, it is straight-
+forward to obtain a photometric data point by summing
+pixels within an arbitrary aperture shape.
+The opti-
+mal choice of aperture is a non-trivial problem for each
+star. We allow manual extraction of the time series from
+the reduced images in our package tglc. It is possible
+to choose the aperture and produce customized aper-
+ture light curves.
+We provide an empirical arbitrary
+choice of 3 × 3 aperture to produce the default aper-
+ture light curves published together with the PSF light
+curves. Since only a part of the light from a star falls
+onto this aperture, the background levels of the aper-
+ture light curves need to be corrected. We estimate the
+median total flux of each star based on Gaia and calcu-
+late the percentage of light that shall fall onto the 3 × 3
+pixels region based on the ePSF shape. We then shift
+the aperture light curve’s median to the Gaia-predicted
+median multiplied by this percentage.
+While the PSF light curves have consistently high
+quality, aperture photometry has an edge in most con-
+ditions. Figure 8 shows three variable stars of different
+types: SX Dor is a RR Lyrae star near the outskirts of
+the Large Magellanic Cloud and is considered challeng-
+ing to deblend by Moln´ar et al. (2022); TIC 177309964 is
+a rapid rotator with a period of 0.4533 days (Zhan et al.
+2019); AV Gru is a faint Cepheid star with a TESS mag-
+nitude of 16.94 (Plachy et al. 2021). The amplitudes of
+all three stars vary considerably in each cycle, but aper-
+ture light curves are more consistent across sectors than
+PSF light curves.
+The PSF light curves’ inconsistent
+amplitudes result from their vulnerability to imperfect
+decontamination. As the target star gets dimmer, the
+remaining contamination in the residual image becomes
+more noticeable. These constants are added to the pix-
+els’ function as ‘anchor points’ to drag the PSF fit closer
+to their value. This generally reduces the amplitude of
+the PSF light curve variations, like the Sector 11 PSF
+light curve of SX Dor. Removing this artifact requires
+better decontamination and is thus a non-trivial task.
+However, the remaining constants do not affect the aper-
+ture light curve because they only affect the background
+level which can be easily removed as discussed in the pre-
+vious paragraph. Therefore, aperture light curves have
+a more reliable amplitude estimation for crowded fields
+and dim stars.
+4.3. Weighted light curves
+The previous two sections described two different
+methods of deriving TESS FFI light curves. Each will
+have slightly different measurement errors. The pixels
+
+10
+Figure 7. Illustration of an ePSF-based fit to a cutout of a TESS full-frame image. The left image is a cutout of the FFI; the
+middle is our forward modeling of all stars except the target star (10.5 TESS magnitude); the right image is the residual image
+as the difference between the first two images. The residual image is decontaminated and is ready to generate light curves. The
+unevenness in the residual image is a combined result of the imperfections of our modeling, such as constant field stars, ePSF
+shape, and spatially variable background.
+Figure 8. TGLC light curves of 3 different type variable stars. TOP: SX Dor is an RR Lyrae star near the outskirts of the LMC
+and thus a difficult target to deblend. MID: TIC 177309964 is a rapid rotator. BOT: AV Gru is a faint Cepheid variable with
+a TESS magnitude of 16.94. TGLC Aperture light curves offer more reliable amplitude estimations for these highly variable
+stars in a crowded field than TGLC PSF light curves. Note: These light curves are detrended with wotan with a window length
+of 1 day (the default for all calibrated TGLC light curves). Users should consider the non-calibrated version if dealing with
+long-period variable stars because such signals could be removed by detrending.
+
+TESS FFI
+Simulated background stars
+Decontaminated target star
+5
+background stars
+target star
+s Flux (×1000 e-/ s)
+3
+Declination
+61°36'
+2
+1
+TESS
+34'
+0
+23h24m48s
+36s
+24s
+23h24m48s
+36s
+24s
+23h24m48s
+36s
+24s
+.1
+Right Ascension
+Right Ascension
+Right AscensionSector 2
+Sector 11
+Sector 38
+aperture
+1.5
+1.0
+RR
+SX Dor
+tiiititititrti
+0.5
+Lyrae
+1.5
+PSF 
+1.0
+Ttittititti
+0.5
+1360
+1370
+1605
+1610
+1615
+1620
+2340
+2350
+2360
+Sector 4
+Sector 12
+Sector 31
+aperture
+TIC
+000
+1.0
+0000
+177309964
+Rotator
+0.9
+PSF
+1.0
+0.9
+1410
+1420
+1430
+1630
+1640
+1650
+2150
+2160
+2170
+Sector 1
+Sector 28
+TBJD
+aperture
+2
+Cepheid
+AV Gru
+L
+2 
+PSF
+1330
+1340
+1350
+2065 2070 2075
+2080
+2085
+TBJD
+TBJD11
+used are the same, so the instrumental noise is shared,
+but the weighting of the individual pixels differs in the
+two approaches. As a result, we expect the measure-
+ment errors to be significantly, but not perfectly, corre-
+lated. A linear combination of the two light curves—
+aperture and PSF—should have lower noise than either
+light curve.
+To explore this possibility, we introduce
+TGLC Weighted light curves.
+TGLC Weighted light curve is the weighted average of
+TGLC PSF and TGLC Aperture light curve. In several
+test fields, we find that the weighted average of the two
+versions of the light curve can subtly increase photomet-
+ric precision over both versions. The optimal weights
+to produce the highest precision light curves are field-
+dependent, mostly correlated with the crowdedness of
+the field. We lack an analytical solution for each star’s
+best weight, so sampling is necessary for the best result.
+The TGLC Weighted light curves are not published with
+the PSF and aperture light curves, but they can be de-
+rived from these two versions with an arbitrary choice of
+weights. An example of the TGLC Weighted light curve
+precision improvement is shown in Section 5.
+5. LIGHT CURVE COMPARISON
+In this section, we compare the light curves from
+TGLC to those of the QLP (Huang et al. 2020) and
+eleanor (Feinstein et al. 2019). We begin with the light
+curves of five sample EBs that are all found in Sector
+17 near NGC 7654. Figure 9 shows our TGLC PSF to-
+gether with those of eleanor (Feinstein et al. 2019) and
+QLP (Huang et al. 2020), as well as Zwicky Transient
+Facility (ZTF) light curve (Bellm et al. 2019). ZTF has
+much better spatial resolution than TESS, greatly re-
+ducing the need to deblend in this moderately crowded
+field.
+For all five EBs, TGLC PSF shows the lowest noise
+and the best agreement with ZTF. At a TESS magni-
+tude of 11.5, an expected comfort zone for all pipelines,
+QLP performs well but eleanor struggles to deblend the
+photometry without modeling neighboring stars’ PSFs.
+The resulting inconsistency in eleanor is more promi-
+nent for dimmer stars: this is caused by a systematic
+lack in removing the contamination. An overestimate
+of the contamination could deepen the transit and vice
+versa. QLP, with its difference imaging approach an-
+chored to the TESS Input Catalog photometry, is rela-
+tively better for this issue, but it cuts off at 13.5 TESS
+magnitude. TGLC PSF also shows a smaller point-to-
+point scatter in its photometry, i.e., a higher photomet-
+ric precision.
+Finally, our ePSF background fit value
+enables us to implement quality flags that remove out-
+liers accurately and automatically (light curves of other
+pipelines may also be filtered by their quality flags). We
+label the frames that have background values 5 stan-
+dard deviations away from the median as bad frames
+in the quality flag. These sudden background increases
+are usually caused by scattered light from the Earth
+and the Moon at the ends of each ∼14 day observa-
+tion window. It is very hard to recover those irregularly
+contaminated frames, so we label them as low-quality
+frames with TGLC flag (see Appendix A.3).
+We next systematically analyze the photometric pre-
+cision of TGLC light curves by comparing all stars in
+two 35′ × 35′ regions in Sector 7 and 17. The Sector
+17 field is relatively sparse and has an average of 0.2
+Gaia stars (all magnitudes) per pixel; the Sector 7 field
+is crowded with 1.2 Gaia stars per pixel on average. We
+assess our photometric precision using a robust estimate
+of the point-to-point scatter in photometry.
+We first
+take the flux differences between adjacent fluxes (D).
+The root-mean-square of this difference is vulnerable to
+variable sources and outliers, so we adopt the median
+absolute deviation and multiply it by a factor of 1.48
+(the ratio of the median absolute deviation and the stan-
+dard deviation for Gaussian errors). We then divide the
+point-to-point scatter by
+√
+2 to estimate the photomet-
+ric precision of each point rather than on the difference
+between two points. The estimated photometric preci-
+sion for each light curve is then
+precision = 1.48
+√
+2 median(|D|).
+(5)
+All of our light curves and estimated precisions refer to
+a single 30-minute photometric point.
+The top row of Figure 10 shows the comparison among
+TGLC Weighted (orange diamonds), QLP (green trian-
+gles), and an aperture photometry prediction from Sul-
+livan et al. (2015) (black line). We empirically choose
+TGLC Weighted = 0.4 TGLC PSF + 0.6 TGLC Aper-
+ture for this analysis since these weights result in the
+highest precision in these fields.
+We derive the pre-
+launch prediction from Figure 14 of Sullivan et al.
+(2015), which summarizes the base noise level of TESS
+photometry. In both fields, the TGLC Weighted pre-
+cision almost reaches the base noise level and displays
+a narrow distribution, indicating good control over sys-
+tematics. QLP light curve precision closely tracks the
+pre-launch prediction until 13.5 TESS magnitude. We
+do not show eleanor on these plots. Its precision in
+a crowded field surpasses that in a sparse field. This
+indicates significant uncorrected dilution, where flux
+from neighboring stars and backgrounds contributes to
+a light curve (c.f.
+the flat eleanor light curves of TIC
+270023061 in Figure 9). This dilution can be mitigated
+with user involvement, but it prevents straightforward
+
+12
+Figure 9. Comparison of TGLC PSF light curves (first column) with eleanor (Feinstein et al. 2019) (second and third column)
+and QLP (Huang et al. 2020) databases (last column) for five sample eclipsing binaries. All light curves are detrended with
+wotan (Hippke et al. 2019). Stars range in brightness from 11.5 TESS magnitude (top) to 15th TESS magnitude (bottom). We
+omit TGLC Aperture light curves because they are indistinguishable from TGLC PSF light curves by eye. Phase-folded Zwicky
+Transient Facility light curves (Bellm et al. 2019) confirm the eclipse depths shown in the left column. Quality drops rapidly
+for other pipelines when the target gets dimmer while TGLC PSF has consistently high precision. Note that for both eleanor
+light curves for TIC 270023061, the transits are detected, but at a very shallow depth imperceptible in the figure.
+comparisons of precision across fields. The bottom row
+of Figure 10 compares the precision of TGLC PSF to
+the precision of TGLC Aperture normalized by the pre-
+cision of TGLC Weighted.
+The TGLC Aperture has
+higher precision than the TGLC PSF in general (exam-
+ples shown in Section 6), but TGLC PSF has an edge in
+sparse fields for stars dimmer than 15 TESS magnitude.
+The precision improvement of TGLC Weighted over the
+other two TGLC light curves is ∼20%. All three TGLC
+light curves reliably achieve a precision of ≲2% for 16th
+TESS magnitude stars in 30-minute data.
+6. EXOPLANET LIGHT CURVES CASE STUDY
+We perform another case study of TGLC, analyzing
+its light curves for five exoplanets from TESS’s primary
+mission. 90% of confirmed TESS exoplanet discoveries
+are from stars brighter than 12th TESS magnitude3, but
+there are vastly more potential exoplanet hosts dimmer
+than 12th TESS magnitude.Therefore, we choose five of
+the faintest TESS exoplanet hosts for our case study,
+ranging in TESS magnitude from 11.9 to 14.3.
+The
+analysis of these examples demonstrates the potential
+of TGLC to enable the discovery and characterization
+of new exoplanets.
+Figure 11 and Figure 12 show five exoplanets’ TGLC
+PSF and TGLC Aperture light curves respectively. All
+light curves are binned to a 30-min cadence (for the ex-
+tended mission) and are detrended with wotan (Hippke
+et al. 2019). Other pipelines’ light curves for the same
+exoplanets are shown in Figure 1.
+Both TGLC PSF
+3 https://tess.mit.edu/publications/
+
+TGLC PSE
+eleanor CORR
+eleanor PSF
+QLP
+mag=11.
+270022476
+Norm Flux
+1.0
+TIC
+5
+0.9
+mag=13.44
+270140796
+Norm Flux
+1.0
+:
+TIC
+11
+0.9
+.
+0.8
+0.0
+0.5
+1.0
+mag=13.90
+269820902
+Norm Flux
+Phase
+1.0
+TIC
+0.9
+mag=14.71
+270023061
+Norm Flux
+1.0
+TIC
+0.8
+0.6
+269820513
+Norm Flux
+mag=
+1.0
+TESS FFI
+TIC
+ZTF g-band
+0.8
+ZTF r-band
+3
+0.0
+0.5
+1.0 0.0
+0.5
+1.0 0.0
+0.5
+1.0
+Phase
+Phase
+Phase13
+Figure 10. The photometric precision (Equation 5) of TGLC compared to the pre-launch prediction (Sullivan et al. 2015)
+in both sparse (left column) and crowded field (right column). The highest point-to-point precision is achieved by a certain
+weighted average of TGLC PSF and TGLC Aperture; The shown TGLC Weighted is the photometric precision of 0.4PSF +
+0.6Aperture. Top: The TGLC Weighted light curve precision (orange diamond) closely tracks the pre-launch prediction (black
+line) even in the crowded field. The QLP (green triangles) precision is very close to the pre-launch prediction in the brighter end.
+Bottom: The precision ratio of TGLC PSF and Aperture versus TGLC Weighted. The TGLC PSF is possible to outperform
+TGLC Aperture in sparse field for dim stars (the smaller the ratio is, the better), but TGLC Aperture has higher precision in
+other cases.
+and TGLC Aperture show excellent results compared
+to other FFI pipelines (Figure 13). Up to 3 different
+sectors of observations of each star are distinguished in
+the phase-folded plots to show cross-sector consistency.
+Both methods show steady low noise levels and consis-
+tent transit shapes for all five exoplanets. It is challeng-
+ing to maintain consistent light curves between sectors
+or even between two observation windows in a single
+sector: for example, eleanor PSF in Figure 1 has in-
+consistent transit depth between sectors for TOI-674 b
+and within a sector for TOI-519 b. Spacecraft direction
+changes between sectors and rotates the field of view,
+which shifts and rotates all stars. The contaminations
+are thus different in each sector for the same star and
+require independent modeling. Only if the decontamina-
+tion method is robust against different contaminations
+can consistent results be produced in different sectors.
+TGLC fully models each frame independently from Gaia
+priors, so it can model the change of contamination be-
+tween sectors properly.
+We then use exoplanet (Foreman-Mackey et al. 2021)
+to model our light curves and the results are shown in
+Table 1. These light curve fits are kept to their simplest
+form with only the necessary free parameters (rows of
+Table 1). We compare our fitted values of the most im-
+portant orbit parameters, stellar and planet radii, and
+stellar masses to the published values. Four exoplanets’
+period fits are improved because of the extended time
+baseline with new sectors except LHS 3844 b, which has
+an ultra-short period of ≈ 0.46 days.
+The FFI light
+curves with a cadence of 10-min in Sector 27 and Sector
+28 are a bit sparse for the period to converge; in con-
+trast, SPOC 2-min light curves can be fitted well with
+the same priors. The relatively longer cadence is an in-
+trinsic disadvantage for FFI light curves, so we set the
+periods and reference transit time equal to published
+values from Vanderspek et al. (2019) for LHS 3844 b.
+Our fits mostly agree with the published values within
+2 standard deviations for the other fitted parameters.
+Since our fit is a lone light curve fit, we do not expect
+it to outperform the publication fits that use multiple
+instruments’ data in general. However, combined with
+radial velocity measurement and ground-based follow-
+up photometric measurement, a comprehensive TGLC
+
+Sparse Field
+Crowded Field
+Precision
+100
+10
+Estimated Photometric l
+10
+10-
+-3
+TGLC Weighted
+TGLC Weighted
+QLP
+QLP
+Sullivan (2015)
+Sullivan (2015)
+10
+.4
+1.5
+Ratio
+Precision
+1
+TGLC PSF Precision/TGLC Weighted Precision
+Median
+TGLC PSF Precision/TGLC Weighted Precision
+Median
+TGLC Aperture Precision/TGLC Weighted Precision
+ Median
+TGLC Aperture Precision/TGLC Weighted Precision
+Median
+0.5
+8
+10
+12
+14
+16
+18
+20
+8
+10
+12
+14
+16
+18
+20
+TESS magnitude
+TESS magnitude14
+Figure 11. TGLC PSF light curves of 5 exoplanets in multiple sectors. Light curves of the same exoplanets from existing
+pipelines are shown in Figure 1. These light curves show higher precision than FFI light curves from other pipelines. Phase
+fold periods are adopted from Table 1 TGLC PSF periods. Note that for TOI-519 b, the PSF light curve has unreliable transit
+depths across sectors due to the same reason discussed in Section 4.2
+exoplanet fit could improve the precision of all free pa-
+rameters.
+Our method has its limits.
+Comparing two TGLC
+light curves for TOI-519 b shows a percent-level discrep-
+ancy in transit depth for TGLC PSF. As we discussed
+in Section 5, TGLC PSF can achieve ≲2% photometric
+precision for a 16th TESS magnitude star; TOI-519 is
+14.4 TESS magnitude so we can expect a slightly bet-
+ter precision. The reason for this inconsistency is the
+same as the variable star case we discussed in Section
+4.2. It is also worth mentioning that the TGLC PSF
+photometry for Sector 44 and Sector 45 of TOI-530 b
+(Figure 11) has much fewer spikes than we see in the
+TGLC Aperture (Figure 12). TGLC PSF deblends bet-
+ter in the presence of nearby variable sources. Since PSF
+
+Sector 9
+Sector 10
+Sector 36
+TOI-674 b
+1.01
+1.00
+Normalized
+0.99
+10
+0.98
+36
+1550
+1560
+1580
+1590
+2290
+2300
+-0.02
+0.00
+0.02
+Sector 27
+Sector 28
+LHS 3844 b
+1.005
+lized
+1.000
+Normal
+0.995
+0.990
+28 
+2040
+2050
+2060
+2070
+2080
+-0.10 -0.05 0.00 0.05
+0.10
+Sector 6
+Sector 44
+Sector 45
+TOl-530 b
+1 Flux
+1.025
+1.000
+0.975
+44
+45
+0.950
+1470
+1480
+2500
+2510
+2520
+2530
+2540
+2550
+-0.02
+0.00
+0.02
+Sector 3
+Sector 42
+Sector 43
+TOI-2406 b
+xn
+Normalized
+.000
+0.975
+42
+43 
+0.950
+1390
+1400
+2450
+2460
+2470
+2480
+2490
+-0.04 -0.02 0.00 0.02
+0.04
+Sector 7
+Sector 8
+Sector 34
+TOl-519 b
+Normalized 
+0.9
+8
+34
+1500
+1510
+1520
+1530
+15402230
+2240
+2250
+-0.04
+0.00
+0.04
+Phase
+Time (TBJD)
+Time (TBJD)
+Time (TBJD)15
+Figure 12. TGLC Aperture light curves of 5 exoplanets (same as those in Figure 11) in multiple sectors.
+and aperture light curves both have their advantage in
+certain scenarios, we publish both in our data release.
+7. DATA AND AVAILABILITY
+All our TGLC data products are available at MAST as
+a High Level Science Product via 10.17909/610m-9474.
+The primary mission light curves are released with the
+paper via bulk download, and the first extended mission
+sectors of TGLC are continuously produced. The ingest-
+ing process for the MAST portal query takes longer than
+bulk download, but new sectors are updated weekly. As
+the second extended mission sectors are available, we
+will continue delivering new light curves. We cut each
+FFI (2048× 2048 pixels) into 14× 14 cutouts, each with
+150 × 150 pixels.
+This leaves two-pixel-wide overlaps
+between cutouts to keep most stars at least 2 pixels
+away from the edge.
+Each cutout is then passed to
+the ePSF model and background model to calculate the
+best fit ePSF. We then produce light curves of all stars
+
+Sector 9
+Sector 10
+Sector 36
+TOI-674 b
+1.01
+1.00
+Normalized
+0.99
+10
+0.98
+36
+1550
+1560
+1580
+1590
+2290
+2300
+-0.02
+0.00
+0.02
+Sector 27
+Sector 28
+LHS 3844 b
+1.005
+Normalized
+1.000
+0.995
+0.990
+28 
+2040
+2050
+2060
+2070
+2080
+-0.10 -0.05 0.00 0.05
+0.10
+Sector 6
+Sector 44
+Sector 45
+TOI-530 b
+ Flux
+1.025
+Normalized
+1.000
+0.975
+44
+45
+0.950
+1470
+1480
+2500
+2510
+2520
+2530
+2540
+2550
+-0.02
+0.00
+0.02
+Sector 3
+Sector 42
+Sector 43
+TOl-2406 b
+xni
+1.025
+Fl
+.000
+0.975
+42
+43 
+0.950
+1390
+1400
+2450
+2460
+2470
+2480
+2490
+-0.04 -0.02 0.00 0.02
+0.04
+Sector 7
+Sector 8
+Sector 34
+TOl-519 b
+Normalized Flux
+0.9
+8
+34
+1500
+1510
+1520
+1530
+15402230
+2240
+2250
+-0.04
+0.00
+0.04
+Phase
+Time (TBJD)
+Time (TBJD)
+Time (TBJD)16
+Figure 13. TGLC PSF light curves of five exoplanets in multiple sectors. Light curves of the same exoplanets of existing
+pipelines are shown in Figure 1. TGLCs have much higher precisions than FFI light curves from other pipelines. Phase fold
+periods are adopted from Table 1 TGLC PSF periods.
+brighter than 16th TESS magnitude, and each file in-
+cludes four light curves: a PSF light curve, an aperture
+light curve, and their calibrated versions. The calibrated
+light curves are detrended and normalized with wotan
+(Hippke et al. 2019). The format of the light curve FITS
+file is detailed in Appendix A. The package tglc4 is pip-
+installable5 and offers more customized options for light
+curve fitting. It is best used for a small cut (< 100×100
+pixels) of the sky and multi-sector comparison. The user
+can get light curves for any star from released sectors
+with comparable precision to the MAST-released light
+curves. One can also choose to save a decontaminated
+4 https://doi.org/10.5281/zenodo.7023845
+5 https://pypi.org/project/tglc/
+image like the last panel in Figure 7 for customized light
+curve extraction.
+8. DISCUSSION
+TESS-Gaia Light Curve achieves the photometric pre-
+cision close to the instrumental noise level by incorpo-
+rating the position and brightness measurements of Gaia
+DR3 in an effective PSF fit of TESS FFI. The photo-
+metric performance that we demonstrate in Section 5
+meets the noise levels assumed in predictions of TESS
+yields Sullivan et al. (2015). TESS full-frame images are
+expected to result in the discovery of thousands of tran-
+siting exoplanets, including ∼1000 around stars fainter
+than 12th TESS magnitude (Barclay et al. 2018). These
+predicted discoveries can be realized with the improve-
+ments in photometric precision such as those provided
+by TGLC.
+
+SPOC 2-min
+eleanor CORR
+QLP
+TGLC aperture
+TGLC PSF
+Normalized Flux
+TOI-674
+1.00
+·
+9
+9
+10
+10
+10
+10
+10
+0.98
+36
+36 
+36 
+36
+36
+-0.02
+0.00
+0.02
+-0.02
+0.00
+0.02
+-0.02
+0.00
+0.02
+-0.02
+0.00
+0.02
+-0.02
+0.00
+0.02
+mag:
+LHS
+Normalized
+1.00
+3844
+27
+27
+27
+27
+27
+0.99
+28
+28 
+28 
+28
+28
+-0.05
+0.05
+0.05
+0.05
+0.05
+-0.05
+0.00
+-0.05
+0.00
+0.00
+-0.05
+0.00
+0.00
+0.05
+0.05
+TOI-530
+Normalized
+1.00
+C
+:
+01
+6
+6
+6
+44
+·
+44
+44
+44 
+45 
+·
+45 
+6
+45 
+45
+0.95
+-0.02
+0.00
+0.02
+-0.02
+0.00
+0.02
+-0.02
+0.00
+0.02
+-0.02
+0.00
+0.02
+-0.02
+0.00
+0.02
+Normalized Flux
+:
+1.00
+8
+3
+3
+42
+42
+42
+43
+43 
+30
+43 
+43 
+q
+0.95
+0.03
+0
+0.03
+-0.03
+0
+0.03 -0.03
+0
+0.03 -0.03
+0
+0.03
+-0.03
+0
+0.03
+Xn
+Phase
+mag:
+TOI-519
+1.00
+Normalized I
+g=14.
+0.90
+/
+8
+8
+8
+34
+34 
+34 
+34
+-0.03
+0
+0.03
+-0.03
+0
+0.03
+-0.03
+0
+0.03
+-0.03
+0
+0.03
+Phase
+Phase
+Phase
+Phase17
+Table 1. Exoplanet modeling
+Identifier
+TOI 674 b
+LHS 3844 ba
+TOI 530 b
+TOI 2406 b
+TOI 519 b
+Ref.
+TESS
+magnitude
+11.8764
+11.9238
+13.5287
+14.3109
+14.4347
+Gaia DR3b
+Period
+(days)
+1.97716[5]
+0.46292[913]
+6.3875[83]
+3.0766[76]
+1.265232[0]
+TGLC PSF
+1.97716[2]
+6.3875[82]
+3.0766[15]
+1.265233[0]
+TGLC Aper.
+1.97714[3]
+6.3875[97]
+3.07668[96]
+1.265232[8]
+Literature
+Tc
+(TBJD)
+1546.501[4]
+1325.725[58]
+1470.20[20]
+1383.72[33]
+1493.142[45]
+TGLC PSF
+1546.502[0]
+1470.20[24]
+1383.3[23]
+1493.142[39]
+TGLC Aper.
+1546.501[7]
+1470.19[98]
+1383.723[35]
+1493.142[35]
+Literature
+b
+0.5 ± 0.2
+0.15 ± 0.10
+0.28 ± 0.18
+0.14 ± 0.08
+0.25 ± 0.15
+TGLC PSF
+0.4 ± 0.2
+0.15 ± 0.10
+0.25 ± 0.18
+0.17 ± 0.09
+0.22 ± 0.13
+TGLC Aper.
+0.624 ± 0.035
+0.186 ± 0.064
+0.33+0.08
+−0.11
+0.16+0.15
+−0.11
+0.19+0.06
+−0.09
+Literature
+Rplanet
+(R⊕)
+5.2 ± 0.3
+1.32 ± 0.04
+8.2 ± 0.6
+2.85 ± 0.16
+11.1 ± 0.6
+TGLC PSF
+5.5 ± 0.2
+1.41 ± 0.04
+9.0 ± 0.6
+2.30 ± 0.15
+12.7 ± 0.5
+TGLC Aper.
+5.25 ± 0.17
+1.303 ± 0.022
+9.3 ± 0.7
+2.94+0.17
+−0.16
+8.4 ± 2.4
+Literature
+Literature
+Ref.
+Murgas,
+F.
+et al. (2021)
+Vanderspek
+et al. (2019)
+Gan
+et
+al.
+(2021)
+Wells,
+R.
+D.
+et al. (2021)
+Parviainen, H.
+et al. (2021)
+aDue to its extremely short period, the 10-min cadence FFI data cannot fit LHS 3844’s period well. We fixed the period and
+reference transit time using the literature value for this fit.
+b Gaia DR3 magnitude converted to the TESS band using the relations from the TESS Instrument Handbook v0.1
+TESS full-frame images are yielding significant scien-
+tific results despite the limitations in data precision and
+availability. Cataclysmic variable light curves and su-
+pernova light curves may be derived with high preci-
+sion from full-frame images (Pichardo Marcano et al.
+2021; Vallely et al. 2019; Fausnaugh et al. 2021). Planet
+searches and eclipsing binary searches have been con-
+ducted on full-frame images, but on a limited scale
+(Bouma et al. 2019; Nardiello et al. 2019). Other studies
+have had results limited by precision: Sahoo et al. (2020)
+discovered 28 subdwarf B stars in the southern TESS
+full-frame images, mostly around 14-16 TESS magni-
+tude stars, but were able to identify asteroseismic pul-
+sations in only two of them. These 14-16 TESS magni-
+tude stars are precisely the ones where we achieve the
+largest improvements over existing pipelines. A follow-
+up study searching for eclipsing binaries and pulsating
+stars was further limited by crowded fields and blending
+(Baran et al. 2021). Our TESS-Gaia light curves over-
+come most limitations of blended stars down to 16th
+TESS magnitude.
+TGLC can open new horizons for
+TESS time-domain sciences and large-scale automated
+search for new periodic signals.
+TGLC still has several limitations that we will work to
+overcome in the future. The first is the possibility of fur-
+ther variations in the background level at a star’s loca-
+tion. TESS is subject to strong spatially variable back-
+grounds from scattered light. We will therefore measure
+whether a target star’s flux relative to the median of its
+neighbors matches this ratio as observed by Gaia. If the
+star is brighter or fainter than expected, it could point
+to an under-estimated or over-estimated background, re-
+spectively. We will determine whether such a correction
+is needed and if so, to apply it to our light curves.
+The second limitation of TGLC is in deblending. Vari-
+able targets are still partially contaminating all stars
+nearby because our published light curves assume back-
+ground stars to have constant flux.
+Fully deblending
+requires allowing all of a star’s immediate neighbors to
+have variable fluxes. We attempt this in Section 4.1 by
+assigning priors to field stars, which achieves better de-
+blending at a large computational cost. With the future
+release of Gaia, we may only allow the most variable field
+stars to float and keep the number of free parameters
+under a reasonable number to improve performance.
+With the release of Gaia DR3, including individual
+photometric time series in the vicinity of the Andromeda
+Galaxy, we plan to check our time series photometry
+against individual Gaia measurements. Gaia DR4 lacks
+an expected release date, but it will include thousands
+of photometric data points for nearly every star brighter
+than 20 TESS magnitude. These light curves will form
+
+18
+a coarsely sampled, but precise, check on the TESS pho-
+tometry. They will serve as a verification of the deblend-
+ing performed by the TESS-Gaia pipeline.
+We are grateful to Ben Montet and Chelsea Huang
+for their suggestions regarding the development of our
+method.
+We acknowledge James Davenport for his
+early inspiration. We are thankful to Hannah M. Lewis
+and Scott W. Fleming for their help with data publi-
+cation on MAST. We thank Corey Beard for helping
+with the exoplanet fitting.
+We appreciate Aomawa
+Shields and Paul Robertson for their comments on this
+paper. We thank Mirek Brandt for his help in inspect-
+ing documentation for tglc.
+We value the conversa-
+tion about FFI WCS with Clara E. Brasseur. We are
+grateful for the revision advice from the anonymous re-
+viewer.
+T.D.B. gratefully acknowledges support from
+the Heising-Simons Foundation under grant #2019-1493
+and from the Alfred P. Sloan Foundation.
+1
+2
+3
+4
+5
+6
+7
+8
+9
+10
+11
+12
+13
+14
+15
+Our pipeline uses numpy (van der Walt et al. 2011),
+scipy (Jones et al. 2001), astropy (Astropy Collabora-
+tion et al. 2013, 2018), and astroquery (Ginsburg et al.
+2019). This research made use of exoplanet(Foreman-
+Mackey et al. 2021; Foreman-Mackey et al. 2021) and its
+dependencies (Foreman-Mackey et al. 2017; Foreman-
+Mackey 2018; Agol et al. 2020; Kumar et al. 2019; As-
+tropy Collaboration et al. 2013, 2018; Kipping 2013a,b;
+Luger et al. 2019; Salvatier et al. 2016; Theano Devel-
+opment Team 2016).
+APPENDIX
+A. TGLC DATA PRODUCT DESCRIPTION
+The TESS Gaia Light Curves (TGLC) are published in MAST as a High Level Science Product (HLSP). The primary
+mission light curves are published with the paper and the following light curves are continuously produced. We follow
+the standard TESS light curve FITS file convention and make necessary adjustments. We describe the format of our
+data product in this appendix to help users utilize them efficiently. The most up-to-date information about the data
+product can be found in TGLC GitHub repository6.
+A.1. File format
+TGLC FITS files follow the naming convention of HLSP:
+hlsp tglc tess ffi gaiaid-{Gaia DR3 ID}-s{sector number}-cam{camera number}-ccd{CCD number} tess v1 llc.fits
+Each FITS file has two Header Data Units (HDUs). The primary HDU is only used when generating light curves with
+the option save aper=True when running tglc. All light curves on HLSP have empty primary HDU. The secondary
+HDU includes the light curves in a binary table.
+A.2. Light curve headers
+The primary header includes the Gaia measurements of the star and the TESS FFI information. The secondary
+header includes uncertainties of the light curves and other PSF fit parameters. Table 2 and 3 are the headers of
+TOI-519 b Sector 7 light curve.
+Table 2. Primary Headers
+Header Card
+Default/Example Value
+Data Type
+Description
+SIMPLE
+True
+bool
+conforms to FITS standard
+BITPIX
+8
+int
+8 / array data type
+Table 2 continued
+6 https://github.com/TeHanHunter/TESS Gaia Light Curve
+
+19
+Table 2 (continued)
+Header Card
+Default/Example Value
+Data Type
+Description
+NAXIS
+0
+int
+0 / number of array dimensions
+EXTEND
+True
+bool
+NEXTEND
+1
+int
+number of standard extensions
+EXTNAME
+‘PRIMARY’
+str
+name of extension
+EXTDATA
+‘aperture’
+str
+decontaminated FFI cut for aperture photometry
+EXTVER
+1
+int
+extension version
+TIMESYS
+‘TDB’
+str
+TESS Barycentric Dynamical Time
+BUNIT
+‘e-/s’
+str
+flux unit
+STAR X
+1.511527631847869
+float
+star x position in cuta
+STAR Y
+1.963850491691666
+float
+star y position in cuta
+COMMENT
+hdul[0].data[:,star y,star x]=lc
+ORIGIN
+‘UCSB/TGLC’
+str
+institution responsible for creating this file
+TELESCOP
+‘TESS’
+str
+telescope
+INSTRUME
+‘TESS Photometer’
+str
+detector type
+FILTER
+‘TESS’
+str
+the filter used for the observations
+OBJECT
+‘Gaia DR3 5707485527450614656’
+str
+string version of Gaia DR3 ID
+GAIADR3 =
+5707485527450614656
+int
+integer version of Gaia DR3 ID
+TICID
+‘218795833’
+str
+TESS Input Catalog ID
+SECTOR
+7
+int
+observation sector
+CAMERA
+2
+int
+camera No.
+CCD
+3
+int
+CCD No.
+CUT X
+0
+int
+FFI cut x index
+CUT Y
+0
+int
+FFI cut y index
+CUTSIZE
+90
+int
+FFI cut size
+RADESYS
+‘ICRS’
+str
+reference frame of celestial coordinates
+RA OBJ
+124.6067520456133
+float
+[deg] right ascension, J2000
+DEC OBJ =
+-19.66278772837456
+float
+[deg] declination, J2000
+TESSMAG =
+14.54195107475864
+float
+TESS magnitude, fitted by Gaia DR3 bandsb
+GAIA G
+15.67702007293701
+float
+Gaia DR3 g band magnitude
+GAIA BP =
+17.19266128540039
+float
+Gaia DR3 bp band magnitude
+GAIA RP =
+14.48194599151611
+float
+Gaia DR3 rp band magnitude
+RAWFLUX =
+147.7626953125
+float
+median flux of raw FFI
+CALIB
+‘TGLC’
+str
+pipeline used for image calibration
+aPixel position of the star in the 5*5 cutout if save aper=True
+b Caculated with Equation 1.
+
+20
+Table 3. Secondary Headersa
+Header Card
+Default/Example Value
+Data Type
+Description
+TIMEREF
+‘SOLARSYSTEM’
+str
+barycentric correction applied to times
+TASSIGN
+‘SPACECRAFT’
+str
+where time is assigned
+BJDREFI
+2457000
+int
+integer part of BJD reference date
+BJDREFR
+0.0
+float
+fraction of the day in BJD reference date
+TIMEUNIT
+‘d’
+str
+time unit for TIME
+TELAPS
+24.41693964503611
+float
+[d] TSTOP-TSTART
+TSTART
+1491.661149617617
+float
+[d] observation start time in TBJD
+TSTOP
+1516.078089262653
+float
+[d] observation end time in TBJD
+MJD BEG
+58491.16114961762
+float
+[d] start time in barycentric MJD
+MJD END
+58515.57808926265
+float
+[d] end time in barycentric MJD
+TIMEDEL
+0.02248336983889145
+float
+[d] time resolution of data
+XPTIME
+1800
+int
+[s] exposure time
+PSF ERR
+3.37816157065132
+float
+[e-/s] PSF flux error
+APER ERR
+1.880864044956725
+float
+[e-/s] aperture flux error
+CPSF ERR
+0.01337824161713607
+float
+[e-/s] calibrated PSF flux errorb
+CAPE ERR
+0.007316015100534172
+float
+[e-/s] calibrated aperture flux errorb
+NEAREDGE
+False
+bool
+distance to edges of FFI <= 2c
+LOC BG
+-292.0021735884076
+float
+[e-/s] locally modified background
+COMMENT
+str
+TRUE BG = hdul[1].data[’background’] + LOC BG
+WOTAN WL
+1
+int
+wotan detrending window length
+WOTAN MT
+‘biweight’
+str
+wotan detrending method
+aWe omit light curve extension headers and duplicate rows from the Primary header. Light curve extensions are
+discussed separately in A.3.
+b As discussed at the end of Section 6, the calibrated aperture flux has an almost halved uncertainty compared to the
+calibrated PSF flux for this light curve.
+c NEAREDGE indicates whether the star is 2 pixels or closer to the edge of the FFI. If True, the PSF light curves
+can not be fitted, and only the aperture light curves are available.
+A.3. Light curve extensions
+The light curve is stored in the second HDU as a binary table. All columns are listed in Table 4. The calibrated fluxes
+are ready for transit detections; the uncalibrated fluxes are best for variable star sciences. The PSF light curves usually
+provide better deblending, but the aperture light curves offer higher precision and a more consistent amplitude if the
+target is in a crowded field. The background fit shows the background variation and could indicate stray light from
+the Earth and the Moon. The cadence number is the cadence of the FFI. The TESS flag follows the FFI convention
+7. The TGLC flag has only the first bit monitoring the presence of stray light, which is achieved by marking cadences
+with backgrounds at least five standard deviations from the median background.
+7 https://outerspace.stsci.edu/display/TESS/2.0+-+Data+
+Product+Overview
+
+21
+Table 4. Light curve extensions
+Column
+Name
+Data Type
+Description
+1
+time
+numpy.ndarray
+Time (TBJD)
+2
+psf flux
+numpy.ndarray
+PSF flux (e−/ s)
+3
+aperture flux
+numpy.ndarray
+Aperture flux (e−/ s)
+4
+cal psf flux
+numpy.ndarray
+Calibrated PSF flux (normalized and detrended)
+5
+cal aper flux
+numpy.ndarray
+Calibrated aperture flux (normalized and detrended)
+6
+background
+numpy.ndarray
+Fitted background value (e−/ s)
+7
+cadence num
+numpy.ndarray
+FFI cadence number
+8
+TESS flags
+numpy.ndarray
+FFI quality flags (directly from FFI)
+9
+TGLC flags
+numpy.ndarray
+TGLC flags
+
+22
+REFERENCES
+Agol, E., Luger, R., & Foreman-Mackey, D. 2020, AJ, 159,
+123, doi: 10.3847/1538-3881/ab4fee
+Anderson, J., & King, I. R. 2000, PASP, 112, 1360,
+doi: 10.1086/316632
+Antoci, V., Cunha, M. S., Bowman, D. M., et al. 2019,
+MNRAS, 490, 4040, doi: 10.1093/mnras/stz2787
+Astropy Collaboration, Robitaille, T. P., Tollerud, E. J.,
+et al. 2013, A&A, 558, A33,
+doi: 10.1051/0004-6361/201322068
+Astropy Collaboration, Price-Whelan, A. M., Sip˝ocz, B. M.,
+et al. 2018, AJ, 156, 123, doi: 10.3847/1538-3881/aabc4f
+Baran, A. S., Sahoo, S. K., Sanjayan, S., & Ostrowski, J.
+2021, MNRAS, 503, 3828, doi: 10.1093/mnras/stab668
+Barclay, T., Pepper, J., & Quintana, E. V. 2018, ApJS,
+239, 2, doi: 10.3847/1538-4365/aae3e9
+Bellm, E. C., Kulkarni, S. R., Graham, M. J., et al. 2019,
+PASP, 131, 018002, doi: 10.1088/1538-3873/aaecbe
+Borkovits, T., Rappaport, S. A., Tan, T. G., et al. 2020,
+MNRAS, 496, 4624, doi: 10.1093/mnras/staa1817
+Bouma, L. G., Hartman, J. D., Bhatti, W., Winn, J. N., &
+Bakos, G. ´A. 2019, ApJS, 245, 13,
+doi: 10.3847/1538-4365/ab4a7e
+Brasseur, C. E., Phillip, C., Fleming, S. W., Mullally, S. E.,
+& White, R. L. 2019, Astrocut: Tools for creating cutouts
+of TESS images, Astrophysics Source Code Library,
+record ascl:1905.007. http://ascl.net/1905.007
+Caldwell, D. A., Tenenbaum, P., Twicken, J. D., et al.
+2020, Research Notes of the American Astronomical
+Society, 4, 201, doi: 10.3847/2515-5172/abc9b3
+Campante, T. L., Schofield, M., Kuszlewicz, J. S., et al.
+2016, ApJ, 830, 138, doi: 10.3847/0004-637X/830/2/138
+C´orsico, A. H., Althaus, L. G., Miller Bertolami, M. M., &
+Kepler, S. O. 2019, A&A Rv, 27, 7,
+doi: 10.1007/s00159-019-0118-4
+Fausnaugh, M. M., Vallely, P. J., Kochanek, C. S., et al.
+2021, ApJ, 908, 51, doi: 10.3847/1538-4357/abcd42
+Feinstein, A. D., Montet, B. T., Foreman-Mackey, D., et al.
+2019, PASP, 131, 094502, doi: 10.1088/1538-3873/ab291c
+Foreman-Mackey, D. 2018, Research Notes of the American
+Astronomical Society, 2, 31,
+doi: 10.3847/2515-5172/aaaf6c
+Foreman-Mackey, D., Agol, E., Ambikasaran, S., & Angus,
+R. 2017, AJ, 154, 220, doi: 10.3847/1538-3881/aa9332
+Foreman-Mackey, D., Luger, R., Agol, E., et al. 2021, arXiv
+e-prints, arXiv:2105.01994.
+https://arxiv.org/abs/2105.01994
+Foreman-Mackey, D., Savel, A., Luger, R., et al. 2021,
+exoplanet-dev/exoplanet v0.5.1,
+doi: 10.5281/zenodo.1998447
+Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al.
+2021, A&A, 649, A1, doi: 10.1051/0004-6361/202039657
+Gan, T., Lin, Z., Wang, S. X., et al. 2021, Monthly Notices
+of the Royal Astronomical Society, 511, 83,
+doi: 10.1093/mnras/stab3708
+Ginsburg, A., Sip˝ocz, B. M., Brasseur, C. E., et al. 2019,
+AJ, 157, 98, doi: 10.3847/1538-3881/aafc33
+Hernandez, M. S., Schreiber, M. R., Parsons, S. G., et al.
+2022, MNRAS, 512, 1843, doi: 10.1093/mnras/stac604
+Hippke, M., David, T. J., Mulders, G. D., & Heller, R.
+2019, AJ, 158, 143, doi: 10.3847/1538-3881/ab3984
+Huang, C. X., Burt, J., Vanderburg, A., et al. 2018, ApJL,
+868, L39, doi: 10.3847/2041-8213/aaef91
+Huang, C. X., Vanderburg, A., P´al, A., et al. 2020,
+Research Notes of the American Astronomical Society, 4,
+204, doi: 10.3847/2515-5172/abca2e
+Jenkins, J. M., Twicken, J. D., McCauliff, S., et al. 2016, in
+Society of Photo-Optical Instrumentation Engineers
+(SPIE) Conference Series, Vol. 9913, Software and
+Cyberinfrastructure for Astronomy IV, ed. G. Chiozzi &
+J. C. Guzman, 99133E, doi: 10.1117/12.2233418
+Jenkins, J. M., Twicken, J. D., McCauliff, S., et al. 2016, in
+Software and Cyberinfrastructure for Astronomy IV, ed.
+G. Chiozzi & J. C. Guzman, Vol. 9913, International
+Society for Optics and Photonics (SPIE), 1232 – 1251,
+doi: 10.1117/12.2233418
+Jones, E., Oliphant, T., & Peterson, P. 2001, SciPy: Open
+Source Scientific Tools for Python. http://www.scipy.org
+Kipping, D. M. 2013a, MNRAS, 435, 2152,
+doi: 10.1093/mnras/stt1435
+—. 2013b, MNRAS, 434, L51, doi: 10.1093/mnrasl/slt075
+Kumar, R., Carroll, C., Hartikainen, A., & Martin, O. A.
+2019, The Journal of Open Source Software,
+doi: 10.21105/joss.01143
+Luger, R., Agol, E., Foreman-Mackey, D., et al. 2019, AJ,
+157, 64, doi: 10.3847/1538-3881/aae8e5
+Moln´ar, L., B´odi, A., P´al, A., et al. 2022, ApJS, 258, 8,
+doi: 10.3847/1538-4365/ac2ee2
+Murgas, F., Astudillo-Defru, N., Bonfils, X., et al. 2021,
+A&A, 653, A60, doi: 10.1051/0004-6361/202140718
+Nardiello, D., Borsato, L., Piotto, G., et al. 2019, MNRAS,
+490, 3806, doi: 10.1093/mnras/stz2878
+Parviainen, H., Palle, E., Zapatero-Osorio, M. R., et al.
+2021, A&A, 645, A16, doi: 10.1051/0004-6361/202038934
+Pichardo Marcano, M., Rivera Sandoval, L. E., Maccarone,
+T. J., & Scaringi, S. 2021, MNRAS, 508, 3275,
+doi: 10.1093/mnras/stab2685
+
+23
+Plachy, E., P´al, A., B´odi, A., et al. 2021, The Astrophysical
+Journal Supplement Series, 253, 11,
+doi: 10.3847/1538-4365/abd4e3
+Powell, B. P., Kostov, V. B., Rappaport, S. A., et al. 2021,
+AJ, 161, 162, doi: 10.3847/1538-3881/abddb5
+Powell, B. P., Kruse, E., Montet, B. T., et al. 2022,
+Research Notes of the American Astronomical Society, 6,
+111, doi: 10.3847/2515-5172/ac74c4
+Prˇsa, A., Kochoska, A., Conroy, K. E., et al. 2022, ApJS,
+258, 16, doi: 10.3847/1538-4365/ac324a
+Raiteri, C. M., Villata, M., Larionov, V. M., et al. 2021,
+MNRAS, 504, 5629, doi: 10.1093/mnras/stab1268
+Rawat, N., Pandey, J. C., Joshi, A., & Yadava, U. 2022,
+MNRAS, 512, 6054, doi: 10.1093/mnras/stac844
+Ricker, G. R., Winn, J. N., Vanderspek, R., et al. 2015,
+Journal of Astronomical Telescopes, Instruments, and
+Systems, 1, 014003, doi: 10.1117/1.JATIS.1.1.014003
+Sahoo, S. K., Baran, A. S., Sanjayan, S., & Ostrowski, J.
+2020, MNRAS, 499, 5508, doi: 10.1093/mnras/staa2991
+Salvatier, J., Wiecki, T. V., & Fonnesbeck, C. 2016, PeerJ
+Computer Science, 2, e55
+Stassun, K. G., Oelkers, R. J., Paegert, M., et al. 2019, The
+Astronomical Journal, 158, 138,
+doi: 10.3847/1538-3881/ab3467
+Sullivan, P. W., Winn, J. N., Berta-Thompson, Z. K., et al.
+2015, ApJ, 809, 77, doi: 10.1088/0004-637X/809/1/77
+Theano Development Team. 2016, arXiv e-prints,
+abs/1605.02688. http://arxiv.org/abs/1605.02688
+Vallely, P. J., Fausnaugh, M., Jha, S. W., et al. 2019,
+MNRAS, 487, 2372, doi: 10.1093/mnras/stz1445
+van der Walt, S., Colbert, S. C., & Varoquaux, G. 2011,
+Computing in Science &amp Engineering, 13, 22,
+doi: 10.1109/mcse.2011.37
+Vanderspek, R., Huang, C. X., Vanderburg, A., et al. 2019,
+The Astrophysical Journal, 871, L24,
+doi: 10.3847/2041-8213/aafb7a
+Weaver, Z. R., Williamson, K. E., Jorstad, S. G., et al.
+2020, ApJ, 900, 137, doi: 10.3847/1538-4357/aba693
+Wells, R. D., Rackham, B. V., Schanche, N., et al. 2021,
+A&A, 653, A97, doi: 10.1051/0004-6361/202141277
+Zhan, Z., G¨unther, M. N., Rappaport, S., et al. 2019, The
+Astrophysical Journal, 876, 127,
+doi: 10.3847/1538-4357/ab158c
+
diff --git a/qNE2T4oBgHgl3EQfKga-/content/tmp_files/load_file.txt b/qNE2T4oBgHgl3EQfKga-/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0d2fd9a292cb440c2d3df9fc1300ff5fc082f72e
--- /dev/null
+++ b/qNE2T4oBgHgl3EQfKga-/content/tmp_files/load_file.txt
@@ -0,0 +1,1558 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf,len=1557
+page_content='Draft version January 11, 2023  Typeset using LATEX twocolumn style in AASTeX631  TESS-Gaia Light Curve: a PSF-based TESS FFI light curve product  Te Han  1, 2 and Timothy D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Brandt  2  1University of California, Irvine  2University of California, Santa Barbara  ABSTRACT  The Transiting Exoplanet Survey Satellite (TESS) is continuing its second extended mission after  55 sectors of observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  TESS publishes full-frame images (FFI) at a cadence of 1800, 600, or  200 seconds, allowing light curves to be extracted for stars beyond a limited number of pre-selected  stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Simulations show that thousands of exoplanets, eclipsing binaries, variable stars, and other  astrophysical transients can be found in these FFI light curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' To obtain high-precision light curves,  we forward model the FFI with the effective point spread function to remove contamination from  nearby stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We adopt star positions and magnitudes from Gaia DR3 as priors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The resulting light  curves, called TESS-Gaia Light Curves (TGLC), show a photometric precision closely tracking the  pre-launch prediction of the noise level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' TGLC’s photometric precision reaches ≲2% at 16th TESS  magnitude even in crowded fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We publish TGLC Aperture and PSF light curves for stars down  to 16th TESS magnitude through the Mikulski Archive for Space Telescopes (MAST) for all available  sectors and will continue to deliver future light curves via  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='17909/610m-9474.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The open-source  package tglc is publicly available to enable any user to produce customized light curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Keywords: Light curves (918) — Astronomy software (1855) — Astronomy databases (83) — Exoplanet  astronomy (486) — Variable stars (1761) — Eclipsing binary stars (444)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' INTRODUCTION  The Transiting Exoplanet Survey Satellite (TESS) of-  fers nearly complete sky coverage, uniform cadence, and  high-precision photometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' This enables a huge amount  of time-domain science, from transiting planets (Huang  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Vanderspek et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019), to eclipsing bi-  naries (Prˇsa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Powell et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Borkovits  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2020), to stellar pulsations and variability (Antoci  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' C´orsico et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Campante et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2016),  to exotic binaries with accretion and complex variabil-  ity (Rawat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Pichardo Marcano et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Hernandez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2022), to blazars (Weaver et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Raiteri et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2021) and supernova transients (Vallely  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Fausnaugh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The headline TESS  science product is its two-minute photometry processed  with the official Science Processing Operations Center  (SPOC) pipeline (Jenkins et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2016), but this is only  available for ∼105 stars in each 27-day observed sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Most of the TESS data volume consists of full-frame  images (FFIs) binned to an 1800-second, 600-second, or  200-second cadence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Many of the aforementioned sci-  ence cases require extraction of light curves from the  FFIs for stars other than the pre-selected targets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  TESS has the capability of reaching a photometric  precision of ≈10−2 in a 30-minute exposure at 16th  TESS magnitude (Ricker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  This matches  the per-epoch performance of the Zwicky Transient Fa-  cility (ZTF, Bellm et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019), but TESS offers ≈1000  measurements over ≈27 days of nearly continuous view-  ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' However, a user seeking a TESS light curve for a  16th TESS magnitude star must currently download and  process the raw full-frame images or relevant subimages  with the help of TESScut (Brasseur et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019) and, po-  tentially, with a package like eleanor (Feinstein et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Powell et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' (2022) published all TESS FFI cor-  rected aperture light curves for stars brighter than 16th  TESS magnitude without flux contamination removal,  which is essential to produce reliable light curves for  dim stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Several pipelines have published individual stars’ light  curves on the Mikulski Archive for Space Telescopes  (MAST).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' However, the Quick-Look Pipeline (Huang  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2020) and the SPOC full-frame images pipeline  (Caldwell et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2020) only provide light curves for stars  brighter than 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='5 TESS magnitude;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' the Cluster Dif-  ference Imaging Photometric Survey (CDIPS) and the  PSF-based Approach to TESS High quality data Of Stel-  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='03704v1  [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='IM]  9 Jan 2023  ID2  lar clusters (PATHOS) only provide a subset of TESS  data (Bouma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Nardiello et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' eleanor  and the TESS Data for Asteroseismology collaboration  can return a light curve of any star in a full-frame image  at the price of a degree of user involvement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Many of  these pipelines remove contamination from nearby stars  and adjust for the background, but systematics do re-  main.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' For all of these pipelines, the large size of TESS  pixels (≈21′′) is an intrinsic limitation that is especially  problematic for faint stars and crowded fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  In addition to the large size of TESS pixels and con-  sequent blending from nearby stars, TESS also has fluc-  tuating backgrounds from scattered sunlight, especially  during certain phases of its orbit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Users interested in  precise, high-cadence photometry for a fainter star must  overcome all of these limitations by post-processing the  full-frame images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The best extracted light curves for  stars fainter than 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='5 TESS magnitude continue to re-  quire significant user input (Feinstein et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  This paper presents a method to produce uniform,  calibrated, light curves for all stars brighter than 16th  TESS magnitude by leveraging astrometry and photom-  etry from the Gaia mission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' TESS and Gaia have full or  nearly full-sky coverage, but their capabilities are com-  plementary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Gaia has measured precise positions and  brightnesses of about 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='5 billion stars with a Gaia Rp  filter similar to that of TESS (Gaia Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Gaia’s angular resolution of ≈0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='′′2 is a factor of  100 higher than TESS’s, while TESS brings a high, uni-  form cadence with nearly continuous coverage over its  observations of each 27-day sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  The precise mea-  surements of Gaia can enable TESS to overcome its lim-  itations of poor angular resolution and high, fluctuating  backgrounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We use Gaia astrometry and photometry  to constrain the field stars in a TESS image, build a  complete and local point spread function forward model  of each TESS full-frame image, and extract percent-level  precise light curves of approximately 3 million stars per  sector down to 16th TESS magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The final light  curves of all sectors are being published in MAST’s High  Level Science Product (HLSP) database continuously  with the release of TESS FFI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We name them TESS-  Gaia Light Curves (TGLC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  The paper is structured as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Section 2 discusses  the existing TESS FFI pipelines and their limitations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Section 3 explains our pipeline’s methodology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Section  4 examines two types of TGLC light curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We ana-  lyze the photometric precision of TGLC in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Section 6 presents a case study of five known exoplanets  using TGLC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Section 7 describes the publication of our  data product and python package.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Finally, we discuss  the influence of TGLC on TESS time-domain science in  Section 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' EXISTING TESS FFI LIGHT CURVE  PRODUCTS  In this section, we give an overview of the existing  sources of FFI light curves, focusing on two that provide  magnitude-limited samples:  the Quick-Look Pipeline  (Huang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2020), and eleanor (Feinstein et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  The Quick-Look Pipeline (QLP) light curves are pro-  duced with an aperture approach combined with differ-  ence imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' A template is first constructed by com-  bining many comparison frames;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' each FFI is then differ-  enced relative to this comparison frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' QLP performs  aperture photometry on this difference image and then  uses the TESS magnitude to scale the difference relative  to the star’s average flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' However, the nature of aper-  ture photometry involves a tradeoff: a larger aperture  captures more of a star’s photons, but at the cost of in-  creased backgrounds, contaminations, and, potentially,  systematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The performance of QLP also relies on the  fidelity of its template and, as a result, on the temporal  stability of systematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Another popular TESS FFI light curve product,  eleanor, has two versions of calibrated light curves:  principal component analysis (PCA) and point spread  function (PSF) light curves (Feinstein et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  The aperture photometry eleanor PCA utilizes the co-  trending basis vectors published by the Science Pay-  load Operations Center (SPOC, Jenkins et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' (2016))  to remove systematics in each camera.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  eleanor  PCA light curves are further calibrated to produce  eleanor CORR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' eleanor PSF uses an analytical two-  dimensional Gaussian model to perform PSF photom-  etry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Users can incorporate positions of several nearby  stars in the PSF fit to remove contamination partially,  but inputting each star’s position and magnitude in the  fit manually becomes impractical for a full-sky light  curve product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The eleanor documentation also sug-  gests summing multiple two-dimensional Gaussians to  accommodate irregular PSF shapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' However, the re-  sults are still not ideal for some irregular PSF shapes  and require a higher level of user involvement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Figure 1 compares the light curve products of three  pipelines: eleanor CORR, eleanor PSF, and QLP, to  the official SPOC 2-min light curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We adopt five faint  TESS planet hosts as our comparison stars: TOI-674  (Murgas, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2021), LHS 3844 (Vanderspek et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  2019), TOI-530 (Gan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2021), TOI-2406 (Wells, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2021), and TOI-519 (Parviainen, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  We plot the light curves phase-folded around the cen-  ter of their transits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The SPOC light curves are com-  3  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Light curves of five TESS-discovered exoplanets from existing pipelines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Compared to the published work (similar  to the SPOC 2-min light curves), the current FFI light curves perform poorer, especially for dimmer stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The legend in each  subplot indicates the sector(s) plotted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Light curves from extended missions are binned to a 30-minute cadence for compatible  noise level with the primary mission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  The periods and transit midpoints are adopted from each discovery literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  All  lightcurves are detrended with wotan (Hippke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019) and the phases are normalized to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  pared because all five publications above use the SPOC  pipeline in their discoveries of the new exoplanets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' All  light curves from extended missions are binned to a 30-  min cadence like the primary mission for a fair com-  parison of noise levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' All light curves are detrended  with wotan, an automated detrending algorithm (Hippke  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' It is especially powerful in preserving tran-  sit signals while removing stellar trends.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The detrending  method is biweight, and the window length is set to 1  for all detrended light curves in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  For the  first two stars of ≈12 TESS magnitude, the FFI light  curves mostly perform comparably to the 2-min light  curves, but they become visibly worse for the dimmer  stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The light curves for these fainter stars have either  a lower SNR, an inaccurate transit depth (compared to  published work), inconsistency among sectors, or a com-  bination of these issues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' POINT SPREAD FUNCTION MODELING OF  TESS FULL-FRAME IMAGES  Point spread function (PSF) photometry is the most  accurate way to obtain brightnesses, provided a suffi-  ciently good PSF model is available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The PSF varies  spatially across TESS fields, so PSF models must be fit  locally to address the variation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' PSFs can also be time-  dependent, so they need to be fit for each frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' How-  ever, building an accurate PSF model locally and frame-  wise for TESS is daunting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Without prior knowledge of  the positions and brightnesses of stars in the field, PSF  fitting is hopelessly underconstrained: the number of  SPOC 2-min  eleanor CORR  eleanor PSF  QLP  Normalized Flux  mag=11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='88  TO1-674 b  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  6  10  10  10  10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='98  36  36  36  36  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  Normalized Flux  mag=11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='92  LHS 3844  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  27  27  27  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='99  28  28  28  28  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='05  Normalized Flux  mag=13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='53  TOI-530  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  :  6  6  44  44  44  q  45  45  45  6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='95  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  Normalized Flux  mag=14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='31  TO1-2406  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  42  42  42  43  43  43  30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='95  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='03  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='03  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='03  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='03  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='03  Normalized Flux  Phase  mag=14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='43  TOI-519  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  iin!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='90  8  q  34  34  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='03  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='03  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='03  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='03  Phase  Phase  Phase4  free parameters of star positions and magnitudes can  exceed the number of pixels because of the large TESS  pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We have ∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='5 billion stars in Gaia DR3, and  each pixel is approximately 10−8 sr, which implies ∼1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='2  stars per pixel or ∼3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='6 parameters to constrain with one  pixel value on average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Any fit for the PSF and the  stellar positions would also be fundamentally nonlinear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Even if one were to ignore enough low-brightness stars  to reduce the number of free parameters, the computa-  tional performance of such a nonlinear fit would still be  impractical for a full-sky survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Gaia’s astrometry and photometry offer a way to over-  come this inability to measure the instrumental PSF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' If  we apply precise Gaia position and brightness measure-  ments as fixed priors, we are left with only the PSF pa-  rameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We can construct this problem as a linear fit,  solvable with standard linear algebra-based approaches  as shown below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Furthermore, we can include all Gaia  stars in the forward modeling to resolve the background  contamination as deep as ∼20 TESS magnitude without  unduly compromising computational performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  The fundamental assumption of our PSF modeling is  that the PSF shape is spatially constant over each FFI  cutout of the size of about 150 × 150 pixels for each  epoch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' In practice, the PSF variation is gradual among  adjacent cutouts as shown in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='4, and apply-  ing the same PSF within one cutout is reasonable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We  also allow the PSF to vary with time by fitting each  frame independently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We first extract stellar positions  and brightnesses from Gaia DR3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We then fit the PSF  parameters of the simulated image to the FFI cutout.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Using the best-fit PSF shape, we forward-model the FFI  cutout with all stars except the target.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Lastly, we gen-  erate a decontaminated image by subtracting this mod-  eled cutout from the measured FFI cutout.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We can then  perform aperture photometry or PSF photometry on the  residual to produce photometry of a given star at a given  epoch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' By repeating this process for all stars and all  frames, we can construct FFI light curves for all stars in  TESS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Positions and Brightness from Gaia  The Gaia mission has now measured positions and  magnitudes of about 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='5 billion stars (Gaia Collabora-  tion et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The positions are typically accurate to  ≲0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1 mas or better, while magnitude uncertainties re-  main ∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='001 mag even down to a Gaia G magnitude of  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' This extraordinary data set enables us to construct  a full forward model of each TESS full-frame image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  A forward model requires the positions and TESS  magnitudes of all stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  We first propagate Gaia po-  sitions from J2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='0 to the median TESS epoch of each  sector using the measured Gaia proper motions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  We  then convert the Gaia DR3 right ascension and decli-  nation to pixel positions based on the TESS FFI world  coordinate system (WCS) headers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We do not account  for either parallactic motion or perspective acceleration  because both are typically orders of magnitude smaller  than the proper motion correction and < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='01 TESS  pixels for all but a handful of stars within a few par-  secs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The positions could have small, local offsets from  the true coordinates due to the TESS spacecraft jitter  motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' As we will show later, however, photometric  products from our PSF approach are largely immune  from systematic shifts over FFI cutouts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We rely only  on the accurate relative positions in the TESS frame  across ≈150 TESS pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  In addition to astrometry, our approach also requires  photometric anchors for all stars in the field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The TESS  bands differ from the Gaia bands, requiring a color-  dependent transformation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We adopt the conversion  T = G − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00522555(GBP − GRP)3  + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='0891337(GBP − GRP)2  − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='633923(GBP − GRP) + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='0324473  (1)  published in Stassun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' (2019), where T is the ap-  parent magnitude in the TESS bandpass, and G, GBP,  and GRP are Gaia bandpasses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' When GBP and GRP are  missing, we adopt  T = G − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='430  (2)  from the same work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' After this step, we have astrometry  and photometry in the TESS system for all Gaia stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Effective PSF Model  With positions and magnitudes known for all stars in  a TESS field, we can forward model a full-frame image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  We approach the problem agnostic to the form of the  PSF, using the effective PSF (ePSF) model successfully  applied to Hubble data (Anderson & King 2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The  ePSF model notes that the actual PSF observed on the  detector is the convolution of the PSF incident on the  detector and the detector response function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' This ePSF  is continuous and is the only observable form of the PSF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  The ePSF may be defined at anchor points spaced more  finely than the pixels on the detector and then inter-  polated at the position of a source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Interpolating the  ePSF is equivalent to placing the PSF produced by the  optics at the location of a star, multiplying by the pixel  response function, and then integrating over the pixels  (Anderson & King 2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Figure 2 shows how the ePSF model works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The ePSF  is shown at red anchor points and the simulated pixel  5  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Interpolation example of an ePSF model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The  white squares and dots represent the pixels and their centers;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  the red dots represent the twice oversampled ePSF model;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  the dot sizes represent the ePSF values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The star represented  by the red ePSF values is located at (0, 0), the location of  the largest red dot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Each pixel value (grayscale) is interpo-  lated only by its nearest four values in the oversampled ePSF  (red points) as shown in pixel (0, 1) by the white lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' This  maintains the linearity (and therefore the computational ef-  ficiency) of the model we use to forward model a subimage  of a full-frame TESS image from an ePSF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  values are interpolated among those red points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' In the  example figure, the ePSF is oversampled relative to the  pixels on the detector by a factor of two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The size of  the red points gives the intensity of the ePSF at that  point, with the star centered at the point (0, 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The  data are interpolated from the ePSF at the pixel centers,  indicated in white.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The grayscale color over the pixels  shows these interpolated values from the ePSF, which  indicate the actual intensity observed for a point source  centered at (0, 0), which in this case is displaced from  the center of a pixel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  The effective PSF (ePSF) method from Anderson &  King (2000) interpolates the ePSF from a four-times-  oversampled grid with cubic spline interpolation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Given  the arbitrary nature of the oversampling factor, we ex-  plore oversampling factors from 2, 4, and 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We decide  to use a factor of 2 because it produces the best qual-  ity light curves (those derived in Section 4) and is much  more computationally efficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  We also use bilinear instead of cubic interpolation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  This choice enables us to write the optimization of the  ePSF’s values at its anchor points as a linear least-  squares problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  This fact is necessary to keep the  model computationally tractable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Also, we assume that  the PSF of a star is mostly contained within a square  with a side length of 11 pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Fluxes in further pix-  els are negligible according to TESS Instrument Hand-  book v0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' In a grid with side length Lgrid = 11, the  oversampled grid side length is rLgrid + 1, where r is  the oversampling factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Depending on the position of  a star to the center of its pixel, stars are interpolated  by different sets of four interpolation points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We can  now model all stars in a cutout by fitting a shared lo-  cal ePSF while fixing stars’ positions and relative fluxes,  but we must also consider the background to model the  field completely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The derivation of our complete model  is presented in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='4 after the discussion of back-  ground modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Background modeling  The unevenness of the TESS FFI background is a re-  sult of both stray light and CCD artifacts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Stray light  from the Earth and the Moon usually produce a back-  ground with a gradient and are strongest near the ends  of each observation window.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The gradient is mostly lin-  ear in a small cutout and easy to fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The CCD artifacts,  including the straps shown in the first panel in Fig-  ure 3, result from highly reflective metal straps beneath  the CCD silicon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  These straps, however, are strictly  column-wise according to the TESS Instrument Hand-  book v0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We model the straps as a column-dependent  flatfield that applies only to a portion of the background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  The visible effects of the straps are chromatic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' They re-  sult from photons that penetrate the CCD, are reflected,  and then detected;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' wavelengths where the CCD is more  transparent show stronger artifacts at the strap loca-  tions according to TESS Instrument Handbook v0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  While the straps reside at specific CCD columns,  they can reflect photons into neighboring columns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We,  therefore, model the effect of the straps as a column-  dependent modification to the background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  We con-  struct a flat, column-dependent background by fitting  the variation in the background intensity between neigh-  boring columns, applying a low-pass filter, and averag-  ing across sectors for a given CCD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We take the dimmest  half of the pixels in each column and compute the me-  dian of the ratio of the count rate between neighboring  columns, using only pixels that are among the dimmest  half in both columns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Multiplying these ratios across the  detector produces an effective column-dependent back-  1 https://archive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='stsci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='edu/files/live/sites/mast/files/home/  missions-and-data/active-missions/tess/ documents/  TESS Instrument Handbook v0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='pdf  2  0  1  2  2  1  0  1  26  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Example of background removal of TGLC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The left panel shows a FFI cutout with a background gradient and three  vertical straps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We model the background as the middle panel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The residual image on the right shows a much cleaner field  ready for an ePSF fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Note that we preserve the resolution of the color map and only shift it down by 100 e−/s for the last  panel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  ground.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We remove drifts in the count rate across the  detector by dividing by a median-filtered processing of  the background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Finally, we take the median for each  CCD’s calibrated background over all primary mission  sectors, since the straps are inherent to the CCD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  The reflective straps on the back of the CCD have a  strong chromatic effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' To account for this, we use our  calibrated CCD-dependent background as a flatfield for  only a fraction of the background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' By allowing this frac-  tion to be free, we fit the chromaticity of the strap reflec-  tions frame-by-frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We ultimately use six parameters  to model the background: a flat background and a lin-  ear gradient in each of two dimensions, plus these same  parameters multiplying the CCD-dependent calibrated  background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Figure 3 shows an example model of the  background: both the linear gradient and straps have  been removed from the FFI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' In particular, strap removal  is essential for avoiding systematic vertical lines in ePSF  shapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Fitting ePSF and background models  Obtaining the ePSF requires a simultaneous fit to all  of the parameters describing the ePSF itself together  with the parameters that model the background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We  construct a least squares fit P ≈ AF as  �  �����  p1  p2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  pm  �  �����  ≈  �  �����  a11  a12  · · a1n  a21  a22  · · a2n  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  am1 am2 · · · amn  �  �����  �  �����  f1  f2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  fn  �  �����  ,  (3)  where p1 to pm are the observed count rate of each pixel  from the FFI, a11 to amn are the matrix encoded with  star information, and f1 to fn are best fits of both the  ePSF and background parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' m is the total num-  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Normalized median absolute deviation (MAD) of  residual images with different weighting power l (Equation  (4)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Larger values of p weight lower count-rate pixels more  heavily in deriving the ePSF, with p = 1 weighting all pixels  equally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  These blue curves are generated from 196 differ-  ent cutouts of Sector 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The orange curve shows the MAD  taken over all pixels from 196 residual images, which favors  a weighting power l ≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='4  ber of pixels in the FFI cutout, and n is the total number  of free parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Each star only adds weights to the  rows of A (pixels) that are 5 pixels or closer to the star;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  the weights for each column are the bilinear translation  weights from the oversampled ePSF grid to the corre-  sponding pixel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Weights from all stars are summed to  construct the full A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We solve for F in the least square  fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  For example, if we fit for an 11 × 11 pixel ePSF  (extending five pixels from the star) and oversample by  a factor of two, this requires fitting n = 535 free param-  TESS FFI cutout  Simulated background  ≥140  Background removed FFI  ≥40  130  30  TESS Flux (e=/ s)  120  20  110  10  1001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='8  MAD of each cutout  Normalized MAD of residual image  MAD of all cutouts  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='8  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='0  weighting power (l)7  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 7 × 14 effective PSF models for half of Sector 1, camera 4, CCD 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Each ePSF model is fitted in a 150 × 150 pixels  FFI cutout, and 14 × 14 models will exactly cover the 2048 × 2048 pixels image with two-pixel-wide overlaps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Each CCD is  divided in this manner to produce light curves published on MAST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We can observe the gradual spatial variation of ePSF: An  obvious trend is that the ePSFs are narrower in the upper right corner, which is the closest to the center of the lens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' One  plausible reason is the optics of the telescope produce more compact pixel response functions (PRF) near boresights according  to TESS Instrument Handbook v0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The gradual variation supports our assumption of constant ePSF in each cutout at the  beginning of Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  eters ((11 × 2 + 1)2 + 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We need the number of pixels  in a cutout to be much larger than the number of free  parameters and for there to be many stars in the image  for the fit to be over-constrained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Adopting 150 × 150  pixel regions (m = 22500) provides more than enough  pixels to constrain the ePSF, while such a region usually  has at least thousands of stars detected in Gaia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Equation (3) cannot be solved exactly if there are  more pixels than parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The best solution depends  on the definition of “≈”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' To allow a linear algebra solu-  tion, we take it to mean the sum of the squares of the  weighted differences between the observed and modeled  pixel values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  In classic χ2 statistics, these differences  are normalized by the observational uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' In our  case, we explore different weightings to avoid heavily pri-  oritizing the brightest pixels and to limit our vulnerabil-  ity to detector nonlinearities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We parametrize a family  of weights by an exponent l, weighting each residual by  1/pl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' This weighting modifies Equation (3) to read  �  �����  p1/pl  1  p2/pl  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  pm/pl  m  �  �����  ≈  �  �����  a11/pl  1  · ·  a1n/pl  1  a21/pl  2  · ·  a2n/pl  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  am1/pl  m · · · amn/pl  m  �  �����  �  �����  f1  f2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  fn  �  �����  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  (4)  where we now take “≈” to simply mean the sum of the  squares of the residuals over all pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' A value of l = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='5  would approximate weighting by the uncertainty con-  tributed by shot noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' At l = 1, each pixel is equally  weighted, but this does not guarantee the smallest resid-  ual for each pixel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' One advantage of our ePSF model  is its high precision for faint stars, so we prioritize min-  imizing the residuals of dimmer pixels to enhance its  performance on the faint end further.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The median abso-  lute deviation (MAD) of the residual is a natural choice  of the goodness of fit to represent the majority (dim-  mer) pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Figure 4 shows the normalized MAD of the  residual versus different powers for 196 different cutouts  sampled from Sector 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We tested weights from l = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='4  (prioritizing brighter pixels) to l = 2 (prioritizing dim-  mer pixels) and the smallest MAD happens near l = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  We, therefore, adopt l = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='4 in all fits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  In addition,  there are saturated pixels and dim vertical lines seem-  ingly corresponding to bad CCD columns (different from  the straps we discussed in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='3) in some FFIs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We  assign these pixels l = ∞ (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' zero weight) to exclude  them from the fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Figure 5 shows the resulting ePSF  shapes from a part of Sector 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The width of the ePSF  gradually narrows down towards the upper-right of this  CCD (the center of the camera lens) due to the TESS  8  optical design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The trend shown is indeed gradual, so  it is appropriate to assume the PSF is constant in each  cutout.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Despite the 535 parameters that we must fit, the lin-  earity of the problem results in a modest computational  cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Deriving the ePSF for a single FFI cutout requires  setting up and solving a single matrix equation, and  takes ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='4 seconds on a single core of a modern server  processor 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Processing thousands of these cutouts for  each epoch, a precondition to producing light curves,  takes 400 seconds for the primary mission on a single  core.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Extending this approach to all regions on a CCD  (×142), and to all CCDs on the TESS camera (×16),  brings the cost to about 350 CPU hours per primary  mission sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' This remains computationally tractable  on a modern server with tens of cores, requiring a wall-  clock time of less than a day per primary mission sector  (∼ 3 days for the first extended mission and ∼ 9 days  for the second extended mission).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' In this way, the data  may be reprocessed if needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Deriving a local, free,  non-parametric ePSF for every region of the TESS cam-  era and every full-frame image is a linear problem, and  thus a computationally tractable task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  The ePSF approach to photometry has a further ad-  vantage over fits using parametric formulae, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', a Gaus-  sian or a Moffat model for the PSF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' A Gaussian or Mof-  fat model requires the modeled positions of all stars on  the TESS image to be correct in absolute terms so that  the star’s center corresponds to its peak intensity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' An  ePSF approach has the weaker requirement that only  the relative positions of the stars are correct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' If all stars  are offset by a fraction of a pixel, then the modeled ePSF  will have its peak flux correspondingly off-center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' There  will be no consequence to the quality of the forward  model or the extracted photometry of any star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' EXTRACTING LIGHT CURVES  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' PSF photometry light curves  Our final step after constructing the ePSF and estab-  lishing the background is to extract a light curve for  each star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' In previous sections, we described our ePSF  fit by fixing the brightness of each star to its value mea-  sured by Gaia and converting it to the TESS photo-  metric system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' With the fitted ePSF, we first explore  the possibility of allowing all stars in the field to float  while extracting the light curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' As discussed in Sec-  tion 3, we often have more stars than pixels in crowded  fields, resulting in underconstrained fits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We try to re-  solve this problem by assigning Gaussian priors to field  2 AMD EPYC 7313 16-Core Processor  Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Comparing the MADs of the PSF light curves  if the field stars are assigned different priors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  All curves  are normalized to their MAD at prior = 10−5, effectively  fixing the field stars to the Gaia-predicted flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Top: The  MAD curves of all Sector 17 stars (black) within 20 arcmin-  utes of TIC 270022476 (an 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='5 TESS magnitude eclipsing  binary (EB);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' orange).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Gaia DR3 2015669353645091072 is  highlighted in blue, a 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='2 TESS magnitude star 1 pixel away  from the EB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The trend of all stars shows a strong preference  towards fixing the field stars with only several exceptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Bottom: The comparison among EB lightcurve with fixed  field stars, dim star light curve fitted with fixed field stars,  and dim star light curve fitted with the prior that returns  the lowest MAD (prior = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='01072;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' red diamond in the top  panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The dim star light curve with fixed field stars shows  deep transits from the EB while allowing the field stars to  float within the best prior removes most contamination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  stars while fitting the target star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The priors are the  fraction of each field star’s median flux derived from  Gaia, so using a very small prior fundamentally sets the  field stars as non-variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Figure 6 shows the MADs  of the PSF light curves when stars are fitted with differ-  ent priors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The MADs of all stars from the vicinity of  TIC 270022476 (an 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='5 TESS magnitude eclipsing bi-  nary (EB)) in Sector 17 (black) show an increasing trend  as the prior gets wider, which supports choosing fixed  field stars in general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Several exceptions could reach  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='0  Eclipsing Binary  MAD of normalized flux  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='5  Dim star close to EB  Best Prior  All Stars  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='0  10-5  10-4  10-3  10-2  10-1  100  Field Star Prior (fraction of median flux)  1  EB  Fixed field  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='8  1  Dim star  flux  Best prior  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='8  Normalized t  1  Dim star  Fixed field  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='4 -  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='2  1760  1765  1770  1775  1780  1785  TBJD9  lower MADs at specific priors, and one of them is Gaia  DR3 2015669353645091072 (blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' This dim star at 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='2  TESS magnitude is only 1 pixel away from the EB and  is vulnerable to its transit contaminations if the field  stars (including the EB) are considered fixed (the last  row of the lower panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' If we allow the field stars to  float with the best prior (the prior that results in the  lowest MAD), most of the contamination is removed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Therefore, this approach is useful for decontaminating  stars near variable sources if one finds the best prior  by sampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' However, running this fit requires ∼8000  CPU hours for a single sector due to a large number of  variables, not to mention that we have to sample the  priors to find the one resulting in the largest decrease in  MAD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' It is thus impractical to fit all light curves with  this method, especially when setting all stars fixed gives  very high (if not the highest) precision at a very low  computational cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The function for sampling and ap-  plying priors is kept in the tglc package for manually  decontaminating certain stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  We now allow the photometry of a given target star  to float while holding the photometry of its neighbors  fixed and keeping the ePSF derived earlier for the full  150 × 150 pixel region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  This change is equivalent to  modeling a FFI cutout for each cadence and then tak-  ing the residual of this from the measured cutout.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Since  the field stars are fixed, the FFI cutout varies in time  mainly due to background fluctuation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  We can then  perform PSF photometry using the known ePSF on the  residual images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' This gives a perturbation to the flux  derived from Gaia using the conversion of 15000 e−/s  for a 10th TESS magnitude star given in the TESS In-  strument Handbook v0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Adding this perturbation to  the Gaia-derived flux gives our PSF photometry flux of  the target star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' In this way, extracting a light curve for  each star in the field incurs a negligible computational  cost over that for constructing the ePSF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Figure 7 illustrates the process of extracting a light  curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The left-hand panel shows a small cutout of a  TESS full-frame image, a subset of that used to build  the ePSF model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The middle panel shows the results  of a forward model of the image fixing all stars to their  Gaia-inferred photometry;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' we have omitted the central  target star from this model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The right-hand panel shows  the residual from the model subimage after removing the  neighboring stars (but not removing any modeled light  from the target star).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Performing PSF photometry on  this image will produce one data point in the light curve  of the target.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The same can be done for all frames and  all stars in this cutout to generate light curves from PSF  photometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Aperture photometry light curves  We also generate TGLC Aperture light curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Using  the residual image described in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1, it is straight-  forward to obtain a photometric data point by summing  pixels within an arbitrary aperture shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  The opti-  mal choice of aperture is a non-trivial problem for each  star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We allow manual extraction of the time series from  the reduced images in our package tglc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' It is possible  to choose the aperture and produce customized aper-  ture light curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  We provide an empirical arbitrary  choice of 3 × 3 aperture to produce the default aper-  ture light curves published together with the PSF light  curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Since only a part of the light from a star falls  onto this aperture, the background levels of the aper-  ture light curves need to be corrected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We estimate the  median total flux of each star based on Gaia and calcu-  late the percentage of light that shall fall onto the 3 × 3  pixels region based on the ePSF shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We then shift  the aperture light curve’s median to the Gaia-predicted  median multiplied by this percentage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  While the PSF light curves have consistently high  quality, aperture photometry has an edge in most con-  ditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Figure 8 shows three variable stars of different  types: SX Dor is a RR Lyrae star near the outskirts of  the Large Magellanic Cloud and is considered challeng-  ing to deblend by Moln´ar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' (2022);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' TIC 177309964 is  a rapid rotator with a period of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='4533 days (Zhan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  2019);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' AV Gru is a faint Cepheid star with a TESS mag-  nitude of 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='94 (Plachy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The amplitudes of  all three stars vary considerably in each cycle, but aper-  ture light curves are more consistent across sectors than  PSF light curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  The PSF light curves’ inconsistent  amplitudes result from their vulnerability to imperfect  decontamination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' As the target star gets dimmer, the  remaining contamination in the residual image becomes  more noticeable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' These constants are added to the pix-  els’ function as ‘anchor points’ to drag the PSF fit closer  to their value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' This generally reduces the amplitude of  the PSF light curve variations, like the Sector 11 PSF  light curve of SX Dor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Removing this artifact requires  better decontamination and is thus a non-trivial task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  However, the remaining constants do not affect the aper-  ture light curve because they only affect the background  level which can be easily removed as discussed in the pre-  vious paragraph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Therefore, aperture light curves have  a more reliable amplitude estimation for crowded fields  and dim stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Weighted light curves  The previous two sections described two different  methods of deriving TESS FFI light curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Each will  have slightly different measurement errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The pixels  10  Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Illustration of an ePSF-based fit to a cutout of a TESS full-frame image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The left image is a cutout of the FFI;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' the  middle is our forward modeling of all stars except the target star (10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='5 TESS magnitude);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' the right image is the residual image  as the difference between the first two images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The residual image is decontaminated and is ready to generate light curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The  unevenness in the residual image is a combined result of the imperfections of our modeling, such as constant field stars, ePSF  shape, and spatially variable background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' TGLC light curves of 3 different type variable stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' TOP: SX Dor is an RR Lyrae star near the outskirts of the LMC  and thus a difficult target to deblend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' MID: TIC 177309964 is a rapid rotator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' BOT: AV Gru is a faint Cepheid variable with  a TESS magnitude of 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' TGLC Aperture light curves offer more reliable amplitude estimations for these highly variable  stars in a crowded field than TGLC PSF light curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Note: These light curves are detrended with wotan with a window length  of 1 day (the default for all calibrated TGLC light curves).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Users should consider the non-calibrated version if dealing with  long-period variable stars because such signals could be removed by detrending.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content="  TESS FFI  Simulated background stars  Decontaminated target star  5  background stars  target star  s Flux (×1000 e-/ s)  3  Declination  61°36'  2  1  TESS  34'  0  23h24m48s  36s  24s  23h24m48s  36s  24s  23h24m48s  36s  24s  ." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1  Right Ascension  Right Ascension  Right AscensionSector 2  Sector 11  Sector 38  aperture  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='0  RR  SX Dor  tiiititititrti  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='5  Lyrae  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='5  PSF  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='0  Ttittititti  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='5  1360  1370  1605  1610  1615  1620  2340  2350  2360  Sector 4  Sector 12  Sector 31  aperture  TIC  000  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='0  0000  177309964  Rotator  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='9  PSF  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='9  1410  1420  1430  1630  1640  1650  2150  2160  2170  Sector 1  Sector 28  TBJD  aperture  2  Cepheid  AV Gru  L  2  PSF  1330  1340  1350  2065 2070 2075  2080  2085  TBJD  TBJD11  used are the same, so the instrumental noise is shared,  but the weighting of the individual pixels differs in the  two approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' As a result, we expect the measure-  ment errors to be significantly, but not perfectly, corre-  lated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' A linear combination of the two light curves—  aperture and PSF—should have lower noise than either  light curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  To explore this possibility, we introduce  TGLC Weighted light curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  TGLC Weighted light curve is the weighted average of  TGLC PSF and TGLC Aperture light curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' In several  test fields, we find that the weighted average of the two  versions of the light curve can subtly increase photomet-  ric precision over both versions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The optimal weights  to produce the highest precision light curves are field-  dependent, mostly correlated with the crowdedness of  the field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We lack an analytical solution for each star’s  best weight, so sampling is necessary for the best result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  The TGLC Weighted light curves are not published with  the PSF and aperture light curves, but they can be de-  rived from these two versions with an arbitrary choice of  weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' An example of the TGLC Weighted light curve  precision improvement is shown in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' LIGHT CURVE COMPARISON  In this section, we compare the light curves from  TGLC to those of the QLP (Huang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2020) and  eleanor (Feinstein et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We begin with the light  curves of five sample EBs that are all found in Sector  17 near NGC 7654.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Figure 9 shows our TGLC PSF to-  gether with those of eleanor (Feinstein et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019) and  QLP (Huang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2020), as well as Zwicky Transient  Facility (ZTF) light curve (Bellm et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' ZTF has  much better spatial resolution than TESS, greatly re-  ducing the need to deblend in this moderately crowded  field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  For all five EBs, TGLC PSF shows the lowest noise  and the best agreement with ZTF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' At a TESS magni-  tude of 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='5, an expected comfort zone for all pipelines,  QLP performs well but eleanor struggles to deblend the  photometry without modeling neighboring stars’ PSFs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  The resulting inconsistency in eleanor is more promi-  nent for dimmer stars: this is caused by a systematic  lack in removing the contamination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' An overestimate  of the contamination could deepen the transit and vice  versa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' QLP, with its difference imaging approach an-  chored to the TESS Input Catalog photometry, is rela-  tively better for this issue, but it cuts off at 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='5 TESS  magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' TGLC PSF also shows a smaller point-to-  point scatter in its photometry, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', a higher photomet-  ric precision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Finally, our ePSF background fit value  enables us to implement quality flags that remove out-  liers accurately and automatically (light curves of other  pipelines may also be filtered by their quality flags).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We  label the frames that have background values 5 stan-  dard deviations away from the median as bad frames  in the quality flag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' These sudden background increases  are usually caused by scattered light from the Earth  and the Moon at the ends of each ∼14 day observa-  tion window.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' It is very hard to recover those irregularly  contaminated frames, so we label them as low-quality  frames with TGLC flag (see Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  We next systematically analyze the photometric pre-  cision of TGLC light curves by comparing all stars in  two 35′ × 35′ regions in Sector 7 and 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The Sector  17 field is relatively sparse and has an average of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='2  Gaia stars (all magnitudes) per pixel;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' the Sector 7 field  is crowded with 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='2 Gaia stars per pixel on average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We  assess our photometric precision using a robust estimate  of the point-to-point scatter in photometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  We first  take the flux differences between adjacent fluxes (D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  The root-mean-square of this difference is vulnerable to  variable sources and outliers, so we adopt the median  absolute deviation and multiply it by a factor of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='48  (the ratio of the median absolute deviation and the stan-  dard deviation for Gaussian errors).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We then divide the  point-to-point scatter by  √  2 to estimate the photomet-  ric precision of each point rather than on the difference  between two points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The estimated photometric preci-  sion for each light curve is then  precision = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='48  √  2 median(|D|).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  (5)  All of our light curves and estimated precisions refer to  a single 30-minute photometric point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  The top row of Figure 10 shows the comparison among  TGLC Weighted (orange diamonds), QLP (green trian-  gles), and an aperture photometry prediction from Sul-  livan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' (2015) (black line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We empirically choose  TGLC Weighted = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='4 TGLC PSF + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='6 TGLC Aper-  ture for this analysis since these weights result in the  highest precision in these fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  We derive the pre-  launch prediction from Figure 14 of Sullivan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  (2015), which summarizes the base noise level of TESS  photometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' In both fields, the TGLC Weighted pre-  cision almost reaches the base noise level and displays  a narrow distribution, indicating good control over sys-  tematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' QLP light curve precision closely tracks the  pre-launch prediction until 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='5 TESS magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We  do not show eleanor on these plots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Its precision in  a crowded field surpasses that in a sparse field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' This  indicates significant uncorrected dilution, where flux  from neighboring stars and backgrounds contributes to  a light curve (c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  the flat eleanor light curves of TIC  270023061 in Figure 9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' This dilution can be mitigated  with user involvement, but it prevents straightforward  12  Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Comparison of TGLC PSF light curves (first column) with eleanor (Feinstein et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019) (second and third column)  and QLP (Huang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2020) databases (last column) for five sample eclipsing binaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' All light curves are detrended with  wotan (Hippke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Stars range in brightness from 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='5 TESS magnitude (top) to 15th TESS magnitude (bottom).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We  omit TGLC Aperture light curves because they are indistinguishable from TGLC PSF light curves by eye.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Phase-folded Zwicky  Transient Facility light curves (Bellm et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019) confirm the eclipse depths shown in the left column.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Quality drops rapidly  for other pipelines when the target gets dimmer while TGLC PSF has consistently high precision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Note that for both eleanor  light curves for TIC 270023061, the transits are detected, but at a very shallow depth imperceptible in the figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  comparisons of precision across fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The bottom row  of Figure 10 compares the precision of TGLC PSF to  the precision of TGLC Aperture normalized by the pre-  cision of TGLC Weighted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  The TGLC Aperture has  higher precision than the TGLC PSF in general (exam-  ples shown in Section 6), but TGLC PSF has an edge in  sparse fields for stars dimmer than 15 TESS magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  The precision improvement of TGLC Weighted over the  other two TGLC light curves is ∼20%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' All three TGLC  light curves reliably achieve a precision of ≲2% for 16th  TESS magnitude stars in 30-minute data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' EXOPLANET LIGHT CURVES CASE STUDY  We perform another case study of TGLC, analyzing  its light curves for five exoplanets from TESS’s primary  mission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 90% of confirmed TESS exoplanet discoveries  are from stars brighter than 12th TESS magnitude3, but  there are vastly more potential exoplanet hosts dimmer  than 12th TESS magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='Therefore, we choose five of  the faintest TESS exoplanet hosts for our case study,  ranging in TESS magnitude from 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='9 to 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  The  analysis of these examples demonstrates the potential  of TGLC to enable the discovery and characterization  of new exoplanets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Figure 11 and Figure 12 show five exoplanets’ TGLC  PSF and TGLC Aperture light curves respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' All  light curves are binned to a 30-min cadence (for the ex-  tended mission) and are detrended with wotan (Hippke  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Other pipelines’ light curves for the same  exoplanets are shown in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Both TGLC PSF  3 https://tess.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='mit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='edu/publications/  TGLC PSE  eleanor CORR  eleanor PSF  QLP  mag=11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  270022476  Norm Flux  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='0  TIC  5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='9  mag=13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='44  270140796  Norm Flux  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='0  :  TIC  11  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='9  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='0  mag=13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='90  269820902  Norm Flux  Phase  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='0  TIC  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='9  mag=14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='71  270023061  Norm Flux  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='0  TIC  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='6  269820513  Norm Flux  mag=  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='0  TESS FFI  TIC  ZTF g-band  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='8  ZTF r-band  3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='0  Phase  Phase  Phase13  Figure 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The photometric precision (Equation 5) of TGLC compared to the pre-launch prediction (Sullivan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2015)  in both sparse (left column) and crowded field (right column).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The highest point-to-point precision is achieved by a certain  weighted average of TGLC PSF and TGLC Aperture;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The shown TGLC Weighted is the photometric precision of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='4PSF +  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='6Aperture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Top: The TGLC Weighted light curve precision (orange diamond) closely tracks the pre-launch prediction (black  line) even in the crowded field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The QLP (green triangles) precision is very close to the pre-launch prediction in the brighter end.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Bottom: The precision ratio of TGLC PSF and Aperture versus TGLC Weighted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The TGLC PSF is possible to outperform  TGLC Aperture in sparse field for dim stars (the smaller the ratio is, the better), but TGLC Aperture has higher precision in  other cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  and TGLC Aperture show excellent results compared  to other FFI pipelines (Figure 13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Up to 3 different  sectors of observations of each star are distinguished in  the phase-folded plots to show cross-sector consistency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Both methods show steady low noise levels and consis-  tent transit shapes for all five exoplanets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' It is challeng-  ing to maintain consistent light curves between sectors  or even between two observation windows in a single  sector: for example, eleanor PSF in Figure 1 has in-  consistent transit depth between sectors for TOI-674 b  and within a sector for TOI-519 b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Spacecraft direction  changes between sectors and rotates the field of view,  which shifts and rotates all stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The contaminations  are thus different in each sector for the same star and  require independent modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Only if the decontamina-  tion method is robust against different contaminations  can consistent results be produced in different sectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  TGLC fully models each frame independently from Gaia  priors, so it can model the change of contamination be-  tween sectors properly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  We then use exoplanet (Foreman-Mackey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2021)  to model our light curves and the results are shown in  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' These light curve fits are kept to their simplest  form with only the necessary free parameters (rows of  Table 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We compare our fitted values of the most im-  portant orbit parameters, stellar and planet radii, and  stellar masses to the published values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Four exoplanets’  period fits are improved because of the extended time  baseline with new sectors except LHS 3844 b, which has  an ultra-short period of ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='46 days.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  The FFI light  curves with a cadence of 10-min in Sector 27 and Sector  28 are a bit sparse for the period to converge;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' in con-  trast, SPOC 2-min light curves can be fitted well with  the same priors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The relatively longer cadence is an in-  trinsic disadvantage for FFI light curves, so we set the  periods and reference transit time equal to published  values from Vanderspek et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' (2019) for LHS 3844 b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Our fits mostly agree with the published values within  2 standard deviations for the other fitted parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Since our fit is a lone light curve fit, we do not expect  it to outperform the publication fits that use multiple  instruments’ data in general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' However, combined with  radial velocity measurement and ground-based follow-  up photometric measurement, a comprehensive TGLC  Sparse Field  Crowded Field  Precision  100  10  Estimated Photometric l  10  10-  3  TGLC Weighted  TGLC Weighted  QLP  QLP  Sullivan (2015)  Sullivan (2015)  10  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='5  Ratio  Precision  1  TGLC PSF Precision/TGLC Weighted Precision  Median  TGLC PSF Precision/TGLC Weighted Precision  Median  TGLC Aperture Precision/TGLC Weighted Precision  Median  TGLC Aperture Precision/TGLC Weighted Precision  Median  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='5  8  10  12  14  16  18  20  8  10  12  14  16  18  20  TESS magnitude  TESS magnitude14  Figure 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' TGLC PSF light curves of 5 exoplanets in multiple sectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Light curves of the same exoplanets from existing  pipelines are shown in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' These light curves show higher precision than FFI light curves from other pipelines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Phase  fold periods are adopted from Table 1 TGLC PSF periods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Note that for TOI-519 b, the PSF light curve has unreliable transit  depths across sectors due to the same reason discussed in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='2  exoplanet fit could improve the precision of all free pa-  rameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Our method has its limits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Comparing two TGLC  light curves for TOI-519 b shows a percent-level discrep-  ancy in transit depth for TGLC PSF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' As we discussed  in Section 5, TGLC PSF can achieve ≲2% photometric  precision for a 16th TESS magnitude star;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' TOI-519 is  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='4 TESS magnitude so we can expect a slightly bet-  ter precision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The reason for this inconsistency is the  same as the variable star case we discussed in Section  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' It is also worth mentioning that the TGLC PSF  photometry for Sector 44 and Sector 45 of TOI-530 b  (Figure 11) has much fewer spikes than we see in the  TGLC Aperture (Figure 12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' TGLC PSF deblends bet-  ter in the presence of nearby variable sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Since PSF  Sector 9  Sector 10  Sector 36  TOI-674 b  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='01  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  Normalized  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='99  10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='98  36  1550  1560  1580  1590  2290  2300  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  Sector 27  Sector 28  LHS 3844 b  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='005  lized  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='000  Normal  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='995  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='990  28  2040  2050  2060  2070  2080  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='10 -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='10  Sector 6  Sector 44  Sector 45  TOl-530 b  1 Flux  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='025  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='975  44  45  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='950  1470  1480  2500  2510  2520  2530  2540  2550  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  Sector 3  Sector 42  Sector 43  TOI-2406 b  xn  Normalized  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='975  42  43  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='950  1390  1400  2450  2460  2470  2480  2490  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='04 -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='04  Sector 7  Sector 8  Sector 34  TOl-519 b  Normalized  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='9  8  34  1500  1510  1520  1530  15402230  2240  2250  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='04  Phase  Time (TBJD)  Time (TBJD)  Time (TBJD)15  Figure 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' TGLC Aperture light curves of 5 exoplanets (same as those in Figure 11) in multiple sectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  and aperture light curves both have their advantage in  certain scenarios, we publish both in our data release.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' DATA AND AVAILABILITY  All our TGLC data products are available at MAST as  a High Level Science Product via 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='17909/610m-9474.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  The primary mission light curves are released with the  paper via bulk download, and the first extended mission  sectors of TGLC are continuously produced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The ingest-  ing process for the MAST portal query takes longer than  bulk download, but new sectors are updated weekly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' As  the second extended mission sectors are available, we  will continue delivering new light curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We cut each  FFI (2048× 2048 pixels) into 14× 14 cutouts, each with  150 × 150 pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  This leaves two-pixel-wide overlaps  between cutouts to keep most stars at least 2 pixels  away from the edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Each cutout is then passed to  the ePSF model and background model to calculate the  best fit ePSF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We then produce light curves of all stars  Sector 9  Sector 10  Sector 36  TOI-674 b  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='01  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  Normalized  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='99  10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='98  36  1550  1560  1580  1590  2290  2300  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  Sector 27  Sector 28  LHS 3844 b  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='005  Normalized  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='995  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='990  28  2040  2050  2060  2070  2080  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='10 -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='10  Sector 6  Sector 44  Sector 45  TOI-530 b  Flux  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='025  Normalized  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='975  44  45  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='950  1470  1480  2500  2510  2520  2530  2540  2550  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  Sector 3  Sector 42  Sector 43  TOl-2406 b  xni  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='025  Fl  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='975  42  43  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='950  1390  1400  2450  2460  2470  2480  2490  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='04 -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='04  Sector 7  Sector 8  Sector 34  TOl-519 b  Normalized Flux  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='9  8  34  1500  1510  1520  1530  15402230  2240  2250  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='04  Phase  Time (TBJD)  Time (TBJD)  Time (TBJD)16  Figure 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' TGLC PSF light curves of five exoplanets in multiple sectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Light curves of the same exoplanets of existing  pipelines are shown in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' TGLCs have much higher precisions than FFI light curves from other pipelines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Phase fold  periods are adopted from Table 1 TGLC PSF periods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  brighter than 16th TESS magnitude, and each file in-  cludes four light curves: a PSF light curve, an aperture  light curve, and their calibrated versions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The calibrated  light curves are detrended and normalized with wotan  (Hippke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The format of the light curve FITS  file is detailed in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The package tglc4 is pip-  installable5 and offers more customized options for light  curve fitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' It is best used for a small cut (< 100×100  pixels) of the sky and multi-sector comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The user  can get light curves for any star from released sectors  with comparable precision to the MAST-released light  curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' One can also choose to save a decontaminated  4 https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='5281/zenodo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='7023845  5 https://pypi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='org/project/tglc/  image like the last panel in Figure 7 for customized light  curve extraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' DISCUSSION  TESS-Gaia Light Curve achieves the photometric pre-  cision close to the instrumental noise level by incorpo-  rating the position and brightness measurements of Gaia  DR3 in an effective PSF fit of TESS FFI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The photo-  metric performance that we demonstrate in Section 5  meets the noise levels assumed in predictions of TESS  yields Sullivan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' TESS full-frame images are  expected to result in the discovery of thousands of tran-  siting exoplanets, including ∼1000 around stars fainter  than 12th TESS magnitude (Barclay et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' These  predicted discoveries can be realized with the improve-  ments in photometric precision such as those provided  by TGLC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  SPOC 2-min  eleanor CORR  QLP  TGLC aperture  TGLC PSF  Normalized Flux  TOI-674  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00 9  9  10  10  10  10  10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='98  36  36  36  36  36  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  mag:  LHS  Normalized  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  3844  27  27  27  27  27  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='99  28  28  28  28  28  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='05  TOI-530  Normalized  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  C  :  01  6  6  6  44 44  44  44  45 45  6  45  45  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='95  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02  Normalized Flux  :  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  8  3  3  42  42  42  43  43  30  43  43  q  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='95  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='03  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='03  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='03 -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='03  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='03 -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='03  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='03  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='03  Xn  Phase  mag:  TOI-519  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='00  Normalized I  g=14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='90  /  8  8  8  34  34  34  34  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='03  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='03  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='03  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='03  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='03  Phase  Phase  Phase  Phase17  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Exoplanet modeling  Identifier  TOI 674 b  LHS 3844 ba  TOI 530 b  TOI 2406 b  TOI 519 b  Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  TESS  magnitude  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='8764  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='9238  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='5287  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='3109  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='4347  Gaia DR3b  Period  (days)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='97716[5]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='46292[913]  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='3875[83]  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='0766[76]  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='265232[0]  TGLC PSF  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='97716[2]  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='3875[82]  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='0766[15]  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='265233[0]  TGLC Aper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='97714[3]  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='3875[97]  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='07668[96]  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='265232[8]  Literature  Tc  (TBJD)  1546.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='501[4]  1325.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='725[58]  1470.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='20[20]  1383.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='72[33]  1493.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='142[45]  TGLC PSF  1546.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='502[0]  1470.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='20[24]  1383.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='3[23]  1493.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='142[39]  TGLC Aper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  1546.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='501[7]  1470.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='19[98]  1383.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='723[35]  1493.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='142[35]  Literature  b  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='5 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='15 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='28 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='18  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='14 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='25 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='15  TGLC PSF  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='4 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='15 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='25 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='18  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='17 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='09  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='22 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='13  TGLC Aper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='624 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='035  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='186 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='064  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='33+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='08  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='11  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='16+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='15  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='11  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='19+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='06  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='09  Literature  Rplanet  (R⊕)  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='2 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='32 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='04  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='2 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='6  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='85 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='16  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='6  TGLC PSF  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='5 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='41 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='04  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='0 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='6  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='30 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='15  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='7 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='5  TGLC Aper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='25 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='17  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='303 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='022  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='3 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='7  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='94+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='17  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='16  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='4 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='4  Literature  Literature  Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Murgas,  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' (2021)  Vanderspek  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' (2019)  Gan  et  al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  (2021)  Wells,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' (2021)  Parviainen, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' (2021)  aDue to its extremely short period, the 10-min cadence FFI data cannot fit LHS 3844’s period well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We fixed the period and  reference transit time using the literature value for this fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  b Gaia DR3 magnitude converted to the TESS band using the relations from the TESS Instrument Handbook v0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1  TESS full-frame images are yielding significant scien-  tific results despite the limitations in data precision and  availability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Cataclysmic variable light curves and su-  pernova light curves may be derived with high preci-  sion from full-frame images (Pichardo Marcano et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Vallely et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Fausnaugh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Planet  searches and eclipsing binary searches have been con-  ducted on full-frame images, but on a limited scale  (Bouma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Nardiello et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Other studies  have had results limited by precision: Sahoo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' (2020)  discovered 28 subdwarf B stars in the southern TESS  full-frame images, mostly around 14-16 TESS magni-  tude stars, but were able to identify asteroseismic pul-  sations in only two of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' These 14-16 TESS magni-  tude stars are precisely the ones where we achieve the  largest improvements over existing pipelines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' A follow-  up study searching for eclipsing binaries and pulsating  stars was further limited by crowded fields and blending  (Baran et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Our TESS-Gaia light curves over-  come most limitations of blended stars down to 16th  TESS magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  TGLC can open new horizons for  TESS time-domain sciences and large-scale automated  search for new periodic signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  TGLC still has several limitations that we will work to  overcome in the future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The first is the possibility of fur-  ther variations in the background level at a star’s loca-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' TESS is subject to strong spatially variable back-  grounds from scattered light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We will therefore measure  whether a target star’s flux relative to the median of its  neighbors matches this ratio as observed by Gaia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' If the  star is brighter or fainter than expected, it could point  to an under-estimated or over-estimated background, re-  spectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We will determine whether such a correction  is needed and if so, to apply it to our light curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  The second limitation of TGLC is in deblending.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Vari-  able targets are still partially contaminating all stars  nearby because our published light curves assume back-  ground stars to have constant flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Fully deblending  requires allowing all of a star’s immediate neighbors to  have variable fluxes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We attempt this in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1 by  assigning priors to field stars, which achieves better de-  blending at a large computational cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' With the future  release of Gaia, we may only allow the most variable field  stars to float and keep the number of free parameters  under a reasonable number to improve performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  With the release of Gaia DR3, including individual  photometric time series in the vicinity of the Andromeda  Galaxy, we plan to check our time series photometry  against individual Gaia measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Gaia DR4 lacks  an expected release date, but it will include thousands  of photometric data points for nearly every star brighter  than 20 TESS magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' These light curves will form  18  a coarsely sampled, but precise, check on the TESS pho-  tometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' They will serve as a verification of the deblend-  ing performed by the TESS-Gaia pipeline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  We are grateful to Ben Montet and Chelsea Huang  for their suggestions regarding the development of our  method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  We acknowledge James Davenport for his  early inspiration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We are thankful to Hannah M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Lewis  and Scott W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Fleming for their help with data publi-  cation on MAST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We thank Corey Beard for helping  with the exoplanet fitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  We appreciate Aomawa  Shields and Paul Robertson for their comments on this  paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We thank Mirek Brandt for his help in inspect-  ing documentation for tglc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  We value the conversa-  tion about FFI WCS with Clara E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Brasseur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We are  grateful for the revision advice from the anonymous re-  viewer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' gratefully acknowledges support from  the Heising-Simons Foundation under grant #2019-1493  and from the Alfred P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Sloan Foundation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  Our pipeline uses numpy (van der Walt et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2011),  scipy (Jones et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2001), astropy (Astropy Collabora-  tion et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2013, 2018), and astroquery (Ginsburg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' This research made use of exoplanet(Foreman-  Mackey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Foreman-Mackey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2021) and its  dependencies (Foreman-Mackey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Foreman-  Mackey 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Agol et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Kumar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' As-  tropy Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2013, 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Kipping 2013a,b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Luger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Salvatier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Theano Devel-  opment Team 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  APPENDIX  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' TGLC DATA PRODUCT DESCRIPTION  The TESS Gaia Light Curves (TGLC) are published in MAST as a High Level Science Product (HLSP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The primary  mission light curves are published with the paper and the following light curves are continuously produced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We follow  the standard TESS light curve FITS file convention and make necessary adjustments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' We describe the format of our  data product in this appendix to help users utilize them efficiently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The most up-to-date information about the data  product can be found in TGLC GitHub repository6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' File format  TGLC FITS files follow the naming convention of HLSP:  hlsp tglc tess ffi gaiaid-{Gaia DR3 ID}-s{sector number}-cam{camera number}-ccd{CCD number} tess v1 llc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='fits  Each FITS file has two Header Data Units (HDUs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The primary HDU is only used when generating light curves with  the option save aper=True when running tglc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' All light curves on HLSP have empty primary HDU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The secondary  HDU includes the light curves in a binary table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Light curve headers  The primary header includes the Gaia measurements of the star and the TESS FFI information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The secondary  header includes uncertainties of the light curves and other PSF fit parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Table 2 and 3 are the headers of  TOI-519 b Sector 7 light curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Primary Headers  Header Card  Default/Example Value  Data Type  Description  SIMPLE  True  bool  conforms to FITS standard  BITPIX  8  int  8 / array data type  Table 2 continued  6 https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='com/TeHanHunter/TESS Gaia Light Curve  19  Table 2 (continued)  Header Card  Default/Example Value  Data Type  Description  NAXIS  0  int  0 / number of array dimensions  EXTEND  True  bool  NEXTEND  1  int  number of standard extensions  EXTNAME  ‘PRIMARY’  str  name of extension  EXTDATA  ‘aperture’  str  decontaminated FFI cut for aperture photometry  EXTVER  1  int  extension version  TIMESYS  ‘TDB’  str  TESS Barycentric Dynamical Time  BUNIT  ‘e-/s’  str  flux unit  STAR X  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='511527631847869  float  star x position in cuta  STAR Y  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='963850491691666  float  star y position in cuta  COMMENT  hdul[0].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='data[:,star y,star x]=lc  ORIGIN  ‘UCSB/TGLC’  str  institution responsible for creating this file  TELESCOP  ‘TESS’  str  telescope  INSTRUME  ‘TESS Photometer’  str  detector type  FILTER  ‘TESS’  str  the filter used for the observations  OBJECT  ‘Gaia DR3 5707485527450614656’  str  string version of Gaia DR3 ID  GAIADR3 =  5707485527450614656  int  integer version of Gaia DR3 ID  TICID  ‘218795833’  str  TESS Input Catalog ID  SECTOR  7  int  observation sector  CAMERA  2  int  camera No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  CCD  3  int  CCD No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  CUT X  0  int  FFI cut x index  CUT Y  0  int  FFI cut y index  CUTSIZE  90  int  FFI cut size  RADESYS  ‘ICRS’  str  reference frame of celestial coordinates  RA OBJ  124.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='6067520456133  float  [deg] right ascension, J2000  DEC OBJ =  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='66278772837456  float  [deg] declination, J2000  TESSMAG =  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='54195107475864  float  TESS magnitude, fitted by Gaia DR3 bandsb  GAIA G  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='67702007293701  float  Gaia DR3 g band magnitude  GAIA BP =  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='19266128540039  float  Gaia DR3 bp band magnitude  GAIA RP =  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='48194599151611  float  Gaia DR3 rp band magnitude  RAWFLUX =  147.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='7626953125  float  median flux of raw FFI  CALIB  ‘TGLC’  str  pipeline used for image calibration  aPixel position of the star in the 5*5 cutout if save aper=True  b Caculated with Equation 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  20  Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Secondary Headersa  Header Card  Default/Example Value  Data Type  Description  TIMEREF  ‘SOLARSYSTEM’  str  barycentric correction applied to times  TASSIGN  ‘SPACECRAFT’  str  where time is assigned  BJDREFI  2457000  int  integer part of BJD reference date  BJDREFR  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='0  float  fraction of the day in BJD reference date  TIMEUNIT  ‘d’  str  time unit for TIME  TELAPS  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='41693964503611  float  [d] TSTOP-TSTART  TSTART  1491.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='661149617617  float  [d] observation start time in TBJD  TSTOP  1516.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='078089262653  float  [d] observation end time in TBJD  MJD BEG  58491.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='16114961762  float  [d] start time in barycentric MJD  MJD END  58515.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='57808926265  float  [d] end time in barycentric MJD  TIMEDEL  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02248336983889145  float  [d] time resolution of data  XPTIME  1800  int  [s] exposure time  PSF ERR  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='37816157065132  float  [e-/s] PSF flux error  APER ERR  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='880864044956725  float  [e-/s] aperture flux error  CPSF ERR  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='01337824161713607  float  [e-/s] calibrated PSF flux errorb  CAPE ERR  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='007316015100534172  float  [e-/s] calibrated aperture flux errorb  NEAREDGE  False  bool  distance to edges of FFI <= 2c  LOC BG  292.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='0021735884076  float  [e-/s] locally modified background  COMMENT  str  TRUE BG = hdul[1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='data[’background’] + LOC BG  WOTAN WL  1  int  wotan detrending window length  WOTAN MT  ‘biweight’  str  wotan detrending method  aWe omit light curve extension headers and duplicate rows from the Primary header.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Light curve extensions are  discussed separately in A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  b As discussed at the end of Section 6, the calibrated aperture flux has an almost halved uncertainty compared to the  calibrated PSF flux for this light curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  c NEAREDGE indicates whether the star is 2 pixels or closer to the edge of the FFI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' If True, the PSF light curves  can not be fitted, and only the aperture light curves are available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Light curve extensions  The light curve is stored in the second HDU as a binary table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' All columns are listed in Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The calibrated fluxes  are ready for transit detections;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' the uncalibrated fluxes are best for variable star sciences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The PSF light curves usually  provide better deblending, but the aperture light curves offer higher precision and a more consistent amplitude if the  target is in a crowded field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The background fit shows the background variation and could indicate stray light from  the Earth and the Moon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The cadence number is the cadence of the FFI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The TESS flag follows the FFI convention  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' The TGLC flag has only the first bit monitoring the presence of stray light, which is achieved by marking cadences  with backgrounds at least five standard deviations from the median background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  7 https://outerspace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='stsci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='edu/display/TESS/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='0+-+Data+  Product+Overview  21  Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Light curve extensions  Column  Name  Data Type  Description  1  time  numpy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='ndarray  Time (TBJD)  2  psf flux  numpy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='ndarray  PSF flux (e−/ s)  3  aperture flux  numpy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='ndarray  Aperture flux (e−/ s)  4  cal psf flux  numpy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='ndarray  Calibrated PSF flux (normalized and detrended)  5  cal aper flux  numpy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='ndarray  Calibrated aperture flux (normalized and detrended)  6  background  numpy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='ndarray  Fitted background value (e−/ s)  7  cadence num  numpy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='ndarray  FFI cadence number  8  TESS flags  numpy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='ndarray  FFI quality flags (directly from FFI)  9  TGLC flags  numpy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='ndarray  TGLC flags  22  REFERENCES  Agol, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Luger, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', & Foreman-Mackey, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2020, AJ, 159,  123, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='3847/1538-3881/ab4fee  Anderson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', & King, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2000, PASP, 112, 1360,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1086/316632  Antoci, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Cunha, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Bowman, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019,  MNRAS, 490, 4040, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1093/mnras/stz2787  Astropy Collaboration, Robitaille, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Tollerud, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=',  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2013, A&A, 558, A33,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1051/0004-6361/201322068  Astropy Collaboration, Price-Whelan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Sip˝ocz, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=',  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2018, AJ, 156, 123, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='3847/1538-3881/aabc4f  Baran, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Sahoo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Sanjayan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', & Ostrowski, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  2021, MNRAS, 503, 3828, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1093/mnras/stab668  Barclay, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Pepper, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', & Quintana, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2018, ApJS,  239, 2, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='3847/1538-4365/aae3e9  Bellm, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Kulkarni, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Graham, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019,  PASP, 131, 018002, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1088/1538-3873/aaecbe  Borkovits, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Rappaport, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Tan, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2020,  MNRAS, 496, 4624, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1093/mnras/staa1817  Bouma, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Hartman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Bhatti, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Winn, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', &  Bakos, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' ´A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019, ApJS, 245, 13,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='3847/1538-4365/ab4a7e  Brasseur, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Phillip, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Fleming, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Mullally, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=',  & White, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019, Astrocut: Tools for creating cutouts  of TESS images, Astrophysics Source Code Library,  record ascl:1905.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' http://ascl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='net/1905.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='007  Caldwell, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Tenenbaum, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Twicken, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  2020, Research Notes of the American Astronomical  Society, 4, 201, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='3847/2515-5172/abc9b3  Campante, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Schofield, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Kuszlewicz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  2016, ApJ, 830, 138, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='3847/0004-637X/830/2/138  C´orsico, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Althaus, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Miller Bertolami, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', &  Kepler, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019, A&A Rv, 27, 7,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1007/s00159-019-0118-4  Fausnaugh, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Vallely, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Kochanek, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  2021, ApJ, 908, 51, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='3847/1538-4357/abcd42  Feinstein, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Montet, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Foreman-Mackey, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  2019, PASP, 131, 094502, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1088/1538-3873/ab291c  Foreman-Mackey, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2018, Research Notes of the American  Astronomical Society, 2, 31,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='3847/2515-5172/aaaf6c  Foreman-Mackey, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Agol, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Ambikasaran, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', & Angus,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2017, AJ, 154, 220, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='3847/1538-3881/aa9332  Foreman-Mackey, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Luger, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Agol, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2021, arXiv  e-prints, arXiv:2105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='01994.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='org/abs/2105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='01994  Foreman-Mackey, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Savel, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Luger, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2021,  exoplanet-dev/exoplanet v0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='5281/zenodo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1998447  Gaia Collaboration, Brown, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Vallenari, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  2021, A&A, 649, A1, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1051/0004-6361/202039657  Gan, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Lin, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Wang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2021, Monthly Notices  of the Royal Astronomical Society, 511, 83,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1093/mnras/stab3708  Ginsburg, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Sip˝ocz, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Brasseur, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019,  AJ, 157, 98, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='3847/1538-3881/aafc33  Hernandez, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Schreiber, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Parsons, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  2022, MNRAS, 512, 1843, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1093/mnras/stac604  Hippke, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', David, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Mulders, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', & Heller, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  2019, AJ, 158, 143, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='3847/1538-3881/ab3984  Huang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Burt, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Vanderburg, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2018, ApJL,  868, L39, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='3847/2041-8213/aaef91  Huang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Vanderburg, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', P´al, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2020,  Research Notes of the American Astronomical Society, 4,  204, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='3847/2515-5172/abca2e  Jenkins, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Twicken, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', McCauliff, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2016, in  Society of Photo-Optical Instrumentation Engineers  (SPIE) Conference Series, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 9913, Software and  Cyberinfrastructure for Astronomy IV, ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Chiozzi &  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Guzman, 99133E, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1117/12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='2233418  Jenkins, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Twicken, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', McCauliff, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2016, in  Software and Cyberinfrastructure for Astronomy IV, ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Chiozzi & J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' Guzman, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 9913, International  Society for Optics and Photonics (SPIE), 1232 – 1251,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1117/12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='2233418  Jones, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Oliphant, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', & Peterson, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2001, SciPy: Open  Source Scientific Tools for Python.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='scipy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='org  Kipping, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2013a, MNRAS, 435, 2152,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1093/mnras/stt1435  —.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2013b, MNRAS, 434, L51, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1093/mnrasl/slt075  Kumar, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Carroll, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Hartikainen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', & Martin, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  2019, The Journal of Open Source Software,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='21105/joss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='01143  Luger, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Agol, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Foreman-Mackey, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019, AJ,  157, 64, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='3847/1538-3881/aae8e5  Moln´ar, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', B´odi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', P´al, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2022, ApJS, 258, 8,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='3847/1538-4365/ac2ee2  Murgas, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Astudillo-Defru, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Bonfils, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2021,  A&A, 653, A60, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1051/0004-6361/202140718  Nardiello, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Borsato, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Piotto, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019, MNRAS,  490, 3806, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1093/mnras/stz2878  Parviainen, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Palle, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Zapatero-Osorio, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  2021, A&A, 645, A16, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1051/0004-6361/202038934  Pichardo Marcano, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Rivera Sandoval, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Maccarone,  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', & Scaringi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2021, MNRAS, 508, 3275,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1093/mnras/stab2685  23  Plachy, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', P´al, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', B´odi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2021, The Astrophysical  Journal Supplement Series, 253, 11,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='3847/1538-4365/abd4e3  Powell, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Kostov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Rappaport, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2021,  AJ, 161, 162, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='3847/1538-3881/abddb5  Powell, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Kruse, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Montet, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2022,  Research Notes of the American Astronomical Society, 6,  111, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='3847/2515-5172/ac74c4  Prˇsa, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Kochoska, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Conroy, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2022, ApJS,  258, 16, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='3847/1538-4365/ac324a  Raiteri, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Villata, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Larionov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2021,  MNRAS, 504, 5629, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1093/mnras/stab1268  Rawat, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Pandey, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Joshi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', & Yadava, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2022,  MNRAS, 512, 6054, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1093/mnras/stac844  Ricker, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Winn, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Vanderspek, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2015,  Journal of Astronomical Telescopes, Instruments, and  Systems, 1, 014003, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1117/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='JATIS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='014003  Sahoo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Baran, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Sanjayan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', & Ostrowski, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  2020, MNRAS, 499, 5508, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1093/mnras/staa2991  Salvatier, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Wiecki, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', & Fonnesbeck, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2016, PeerJ  Computer Science, 2, e55  Stassun, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Oelkers, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Paegert, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019, The  Astronomical Journal, 158, 138,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='3847/1538-3881/ab3467  Sullivan, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Winn, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Berta-Thompson, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  2015, ApJ, 809, 77, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1088/0004-637X/809/1/77  Theano Development Team.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2016, arXiv e-prints,  abs/1605.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02688.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='org/abs/1605.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='02688  Vallely, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Fausnaugh, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Jha, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019,  MNRAS, 487, 2372, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1093/mnras/stz1445  van der Walt, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Colbert, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', & Varoquaux, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2011,  Computing in Science &amp Engineering, 13, 22,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1109/mcse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='37  Vanderspek, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Huang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Vanderburg, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019,  The Astrophysical Journal, 871, L24,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='3847/2041-8213/aafb7a  Weaver, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Williamson, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Jorstad, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='  2020, ApJ, 900, 137, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='3847/1538-4357/aba693  Wells, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Rackham, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Schanche, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2021,  A&A, 653, A97, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='1051/0004-6361/202141277  Zhan, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', G¨unther, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', Rappaport, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content=' 2019, The  Astrophysical Journal, 876, 127,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
+page_content='3847/1538-4357/ab158c' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qNE2T4oBgHgl3EQfKga-/content/2301.03704v1.pdf'}
diff --git a/rNAyT4oBgHgl3EQfzvn1/content/tmp_files/2301.00708v1.pdf.txt b/rNAyT4oBgHgl3EQfzvn1/content/tmp_files/2301.00708v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6a09bf8a84e7681ab94c4fbbc8158efa3dba5f4f
--- /dev/null
+++ b/rNAyT4oBgHgl3EQfzvn1/content/tmp_files/2301.00708v1.pdf.txt
@@ -0,0 +1,1023 @@
+arXiv:2301.00708v1  [math.RA]  2 Jan 2023
+GENERALIZED PERIODICITY THEOREMS
+LEONID POSITSELSKI
+Abstract. Let R be a ring and S be a class of strongly finitely presented (FP∞)
+R-modules closed under extensions, direct summands, and syzygies. Let (A, B) be
+the (hereditary complete) cotorsion pair generated by S in Mod–R, and let (C, D)
+be the (also hereditary complete) cotorsion pair in which C = lim
+−→ A = lim
+−→ S. We
+show that any A-periodic module in C belongs to A, and any D-periodic module in
+B belongs to D. A further generalization of the latter result is obtained.
+Contents
+Introduction
+1
+1.
+Generalized Fp-injective/Injective and Cotorsion Periodicity
+4
+2.
+Generalized Flat/Projective and Fp-projective Periodicity
+8
+3.
+Direct Limit Closures of Classes of Finitely Presentables
+13
+References
+18
+Introduction
+0.0.
+Periodicity theorems in homological algebra apply to the following setup. Let
+R be an associative ring and
+(∗)
+0 −−→ M −−→ L −−→ M −−→ 0
+be a short exact sequence of (right) R-modules with the leftmost term isomorphic to
+the rightmost one. Then it is known that
+(1) if the R-module M is flat and the R-module L is projective, then the R-mod-
+ule M is projective (Benson and Goodearl 2000 [6], rediscovered by Neeman
+in 2008 [19]);
+(2) if the exact sequence (∗) is pure and the R-module L is pure-projective, then
+the R-module M is pure-projective (Simson 2002 [25]);
+(3) if the exact sequence (∗) is pure and the R-module L is pure-injective, then
+the R-module M is pure-injective (ˇSt’ov´ıˇcek 2014 [28]);
+(4) in particular, if the R-module M is fp-injective and the R-module L is injec-
+tive, then the R-module M is injective;
+(5) if the R-module L is cotorsion, then the R-module M is cotorsion (Bazzoni,
+Cort´es-Izurdiaga, and Estrada 2017 [3]);
+1
+
+(6) if the ring R is right coherent and the right R-module L is fp-projective, then
+the R-module M is fp-projective (ˇSaroch and ˇSt’ov´ıˇcek 2018 [24]);
+(7) over any ring R, if the R-module L is fp-projective, then the R-module M is
+weakly fp-projective (Bazzoni, Hrbek, and the present author 2022 [4]).
+Periodicity phenomena are linked to behavior of the modules of cocycles in acyclic
+complexes. This means that the assertions (1–7) can be restated as follows:
+(1c) in any acyclic complex of projective modules with flat modules of cocycles,
+the modules of cocycles are actually projective (so the complex is contactible);
+(2c) in any pure acyclic complex of pure-projective modules, the modules of cocy-
+cles are pure-projective (so the complex is contractible);
+(3c) in any pure acyclic complex of pure-injective modules, the modules of cocycles
+are pure-injective (so the complex is contractible);
+(4c) in any acyclic complex of injective modules with fp-injective modules of co-
+cycles, the modules of cocycles are actually injective (so the complex is con-
+tractible);
+(5c) in any acyclic complex of cotorsion modules, the modules of cocycles are
+cotorsion;
+(6c) in any acyclic complex of fp-projective right modules over a right coherent
+ring, the modules of cocycles are fp-projective;
+(7c) in any acyclic complex of fp-projective modules (over any ring), the modules
+of cocycles are weakly fp-projective.
+We refer to the introduction to the preprint [4] for a more detailed discussion of the
+periodicity theorems (1–7) and (1c–7c).
+0.1.
+The aim of this paper is to obtain a common generalization of (1) and (6),
+and also a common generalization of (4) and (5), in the context of a chosen class
+of modules or objects in a Grothendieck category. Let us start with presenting the
+most symmetric and nicely looking formulation of our results, and then proceed to a
+certain further generalization.
+Let R be a ring. An R-module is said to be strongly finitely presented if it has an
+(infinite) resolution by finitely generated projective R-modules. In the terminology
+of the book [16], such modules are called “FP∞-modules”.
+Let S be a class (up to an isomorphism, of course, a set) of strongly finitely pre-
+sented (right) R-modules. Assume that the free R-module R belongs to S, and that
+the class of modules S is closed under direct summands, extensions, and kernels of
+epimorphisms in Mod–R. In particular, for any module S ∈ S there exists a (finitely
+generated) projective R-module P together with an R-module epimorphism P −→ S
+whose kernels also belongs to S. The latter property is expressed by saying that “the
+class of modules S is closed under syzygies”.
+Denote by B = S⊥1 the class of all R-modules B such that Ext1
+R(S, B) = 0 for
+all S ∈ S. Furthermore, denote by A = ⊥1B the class of all R-modules A such that
+Ext1
+R(A, B) = 0 for all B ∈ B. The pair of classes of modules (A, B) is called the
+cotorsion pair generated by S in Mod–R.
+2
+
+Let C = lim
+−→ S denote the class of all R-modules that can be obtained as direct
+limits of diagrams of modules from S, indexed by directed posets. Since S is a class
+of finitely presented modules, one can see that lim
+−→ S coincides with the direct limit
+closure or S in Mod–R [18, 12, 17].
+Furthermore, since S is a class of strongly finitely presented modules (FP2 is suffi-
+cient), the class C is closed under extensions in Mod–R [2]. Taking into account the
+description of A as the class of all direct summands of transfinitely iterated extensions
+of modules from S [16, Corollary 6.14], one concludes that A ⊂ C. Hence C = lim
+−→ A
+is the class of all direct limits of modules from A.
+Denote by D = C⊥1 the class of all R-modules D such that Ext1
+R(C, D) = 0 for all
+C ∈ C. Then one has A ⊂ C and B ⊃ D.
+Part (a) of the following theorem is the main result of this paper, while part (b)
+follows rather easily from a result of Bazzoni, Cort´es-Izurdiaga, and Estrada [3, The-
+orem 4.7] together with a result of Angeleri H¨ugel and Trlifaj [2, Corollary 2.4].
+Theorem 0. Let R be a ring and S be a class of strongly finitely presented R-modules,
+containing the free R-module R and closed under direct summands, extensions, and
+kernels of epimorphisms. Put B = S⊥1, A = ⊥1B, C = lim
+−→ S, and D = C⊥1. Then
+the following assertions hold:
+(a) For any short exact sequence (∗) with L ∈ A and M ∈ C, one has M ∈ A. In
+other words, in any acyclic complex of modules from A with the modules of cocycles
+belonging to C, the modules of cocycles actually belong to A.
+(b) For any short exact sequence (∗) with L ∈ D and M ∈ B, one has M ∈ D. In
+other words, in any acyclic complex of modules from D with the modules of cocycles
+belonging to B, the modules of cocycles actually belong to D.
+Theorem 0(a) is a common generalization of items (1) or (1c) and (6) or (6c) on the
+list of Section 0.0. Taking S = {R} to be the class consisting of the free R-module
+R only, one obtains the flat/projective periodicity theorem of Benson–Goodearl [6,
+Theorem 2.5] and Neeman [19, Remark 2.15] as a particular case of Theorem 0(a).
+Assuming the ring R to be right coherent and taking S to be the class of all finitely pre-
+sented right R-modules, one obtains the fp-projective periodicity theorem of ˇSaroch
+and St’ov´ıˇcek [24, Example 4.3] as a particular case of Theorem 0(a).
+Theorem 0(b) is a common generalization of items (4) or (4c) (for coherent rings)
+and (5) or (5c) on the list of Section 0.0. Assuming the ring R to be right coherent
+and taking S to be the class of all finitely presented right R-modules, one obtains
+the fp-injective/injective periodicity theorem, essentially due to St’ov´ıˇcek [28, Corol-
+lary 5.5] (see also [3, Theorem 1.2(1) or 5.1(1)]), as a particular case of Theorem 0(b).
+Taking S = {R} to be the class consisting of the free R-module R only, one obtains
+the cotorsion periodicity theorem of Bazzoni, Cort´es-Izurdiaga, and Estrada [3, The-
+orem 1.2(2) or 5.1(2)] as a particular case of Theorem 0(b).
+0.2.
+Part (b) of Theorem 0 admits a far-reaching generalization (allowing, in partic-
+ular, to drop the coherence assumptions on the ring R in the preceding paragraph).
+We state this result as the following Theorem B.
+3
+
+Part B(i), which is the main claim, is rather easily deduced from a result of St’ov´ıˇcek
+and the present author [23, Theorem 6.1] (which, in turn, is a generalization of [3,
+Theorem 4.7]). Part B(ii), which is a supplementary comment on B(i) (explaining
+what B(i) means under some additional assumptions), turns out to be more involved.
+Theorem B. Let K be a Grothendieck category and S ⊂ K be a class of objects. Let
+T ⊂ K be any class of objects of finite projective dimension in K such that the union
+S∪T contains a set of generators for K. Denote by C ⊂ K the closure of S∪T under
+coproducts, direct limits, extensions, and kernels of epimorphisms in K. Then
+(i) Let B = S⊥1 be the class of all objects B ∈ K such that Ext1
+K(S, B) = 0 for all
+S ∈ S, and let D = C⊥1 be the class of all objects D ∈ K such that Ext1
+K(C, D) = 0
+for all C ∈ C. Then, for any acyclic complex of objects from D with the objects of
+cocycles belonging to B, the objects of cocycles actually belong to D.
+(ii) If the class S ∪ T consists of (some) finitely presentable objects and is closed
+under extensions and kernels of epimorphisms in K, then C = lim
+−→(S ∪ T) is the class
+of all direct limits of diagrams of objects from S ∪ T, indexed by directed posets.
+One can see that in the context of Theorem B(ii) the class S ∪ T has to consist
+of strongly finitely presentable (FP∞) objects. Taking T = ∅ makes Theorem 0(b)
+a particular case of Theorem B(i–ii) (for K = Mod–R).
+Taking S to be the class of all finitely presentable objects in a locally finitely
+presentable abelian category K and T = ∅, one obtains the assertion (4) or (4c) on
+the list of Section 0.0, essentially due to St’ov´ıˇcek [28, Corollary 5.5], as a particular
+case of Theorem B(i) (for K = Mod–R).
+0.3.
+The proofs of Theorems 0(b) and B(i) are presented in Section 1. Theorem 0(a)
+is proved in Section 2. The proof of Theorem B(ii) is given in Section 3.
+Acknowledgement. I want to thank Michal Hrbek, Silvana Bazzoni, and Jan Trlifaj
+for helpful discussions and comments. Long conversations with Jan St’ov´ıˇcek were
+particularly illuminating, and to him goes my special gratitude. The author is sup-
+ported by the GAˇCR project 20-13778S and research plan RVO: 67985840.
+1. Generalized Fp-injective/Injective and Cotorsion Periodicity
+In this section we prove Theorems 0(b) and B(i). This is not difficult, given the
+preceding results in [3, Theorem 4.7] and [23, Theorem 6.1]. The former theorem
+needs to be used together with [2, Corollary 2.4], and the latter one together with [23,
+Lemmas 4.2, 4.3, and 6.4].
+Let us formally introduce some notation and terminology which was already used
+throughout the introduction. Given an abelian (or exact [8]) category K and a class
+of objects A ⊂ K, one denotes by A⊥1 ⊂ K the class of all objects X ∈ K such that
+Ext1
+K(A, X) = 0 for all A ∈ A. Dually, for a class of objects B ⊂ K, the notation
+⊥1B ⊂ K stands for the class of all objects Y ∈ K such that Ext1
+K(Y, B) = 0 for all
+B ∈ B. Similarly, A⊥≥1 ⊂ K is the class of all objects X ∈ K such that Extn
+K(A, X) = 0
+4
+
+for all A ∈ A and n ≥ 1. Dually, ⊥≥1B ⊂ K is the class of all objects Y ∈ K such that
+Extn
+K(Y, B) = 0 for all B ∈ B and n ≥ 1.
+A class of objects A ⊂ K is said to be generating (or a class of generators) if every
+object of K is a quotient object of a coproduct of objects from A. A class of objects
+B ⊂ K is said to be cogenerating (or a class of cogenerators) if every object of K is a
+subobject of a product of objects from B.
+A pair of classes of objects (A, B) in K is said to be a cotorsion pair if A = ⊥1B and
+B = A⊥1. Notice that, for any cotorsion pair (A, B) in K, the class A ⊂ K is closed
+under coproducts (i. e., those coproducts that exist in K), and the class B ⊂ K is
+closed under products (in the same sense) [10, Corollary 8.3], [11, Corollary A.2].
+For any class of objects S ⊂ K, the pair of classes B = S⊥1 and A = ⊥1B is a
+cotorsion pair in K. The cotorsion pair (A, B) obtained in this way is said to be
+generated by the class S. Dually, for any class of objects T ⊂ K, the pair of classes
+A = ⊥1T and B = A⊥1 is also a cotorsion pair in K. The latter cotorsion pair (A, B)
+is said to be cogenerated by the class T.
+Let (A, B) be a cotorsion pair in K such that the class A is generating and the class
+B is cogenerating in K. So every object of K is a quotient object of an object from
+A and a subobject of an object from B. These conditions are satisfied automatically
+for any cotorsion pair in an abelian category K with enough projective and injective
+objects (because all projective objects belong to A and all injective objects belong
+to B). In particular, this applies to the module categories K = Mod–R.
+In the assumptions of the previous paragraph, the following conditions are equiv-
+alent [14, Theorem 1.2.10], [16, Lemma 5.24], [4, Section 1], [23, Lemma 4.1]:
+(1) the class A is closed under kernels of epimorphisms in K;
+(2) the class B is closed under cokernels of monomorphisms in K;
+(3) Ext2
+K(A, B) = 0 for all A ∈ A and B ∈ B;
+(4) Extn
+K(A, B) = 0 for all A ∈ A, B ∈ B, and n ≥ 1.
+A cotorsion pair (A, B) satisfying conditions (1–4) is said to be hereditary.
+Given a class of objects L ⊂ K, an object M ∈ K is said to be L-periodic if there
+exists a short exact sequence 0 −→ M −→ L −→ M −→ 0 (∗) in K with L ∈ L.
+We recall that the notation lim
+−→ L ⊂ K stands for the class of all direct limits in K of
+diagrams of objects from L (indexed by directed posets).
+A short exact sequence of right R-modules 0 −→ K −→ L −→ M −→ 0 is said to
+be pure if it remains exact after taking the tensor product with any left R-module.
+Equivalently, a short exact sequence 0 −→ K −→ L −→ M −→ 0 is pure if and only
+if it remains exact after the functor HomR(S, −) from any finitely presented right
+R-module S is applied [16, Definition 2.6 and Lemma 2.19]. If this is the case, the
+object K is said to be a pure subobject of L, while the object M is called a pure
+epimorphic image (or a pure quotient) of M. The pure exact structure on Mod–R is
+formed by the class of all pure exact sequences. The projective objects of the exact
+category Mod–R with the pure exact structure are called pure-projective R-modules,
+and the injective objects are called pure-injective.
+5
+
+An R-module S is said to be FPn (where n ≥ 0 is an integer) if it admits a
+fragment of projective resolution Pn −→ Pn−1 −→ · · · −→ P0 −→ S −→ 0 with
+finitely generated projective modules Pi.
+So a module is FP0 if and only if it is
+finitely generated, and it is FP1 if and only if it is finitely presented. A module S
+is said to be FP∞ if it admits a resolution by finitely generated projective modules;
+equivalently, this means that S is FPn for all n ≥ 0. Modules of type FP∞ are
+otherwise known as strongly finitely presented.
+A class of modules S is said to be closed under syzygies if for every module S ∈ S
+there exists a short exact sequence 0 −→ K −→ P −→ S −→ 0 with a projective
+module P and K ∈ S. For any other short exact sequence 0 −→ K′ −→ P ′ −→
+S −→ 0 with a projective module P ′, it then follows that K′ ⊕ P ≃ K ⊕ P ′, which
+often implies that K′ ∈ S as well.
+Dually, a class of modules T is closed under
+cosyzygies if for every module T ∈ T there exists a short exact sequence 0 −→ T −→
+J −→ L −→ 0 with an injective module J and L ∈ T. For any other short exact
+sequence 0 −→ T −→ J′ −→ L′ −→ 0 with an injective module J′, it then follows
+that L′ ⊕ J ≃ L ⊕ J′, which often implies that L′ ∈ T, too.
+Proof of Theorem 0(b) from Section 0.1. Let us first prove the first assertion, then
+deduce the second one. In order to apply [3, Theorem 4.7], we need to show that
+(C, D) is a hereditary cotorsion pair in Mod–R. First of all, (C, D) is indeed a cotorsion
+pair by [2, Corollary 2.4] (see also [16, Corollary 8.42]).
+To show that the cotorsion pair (C, D) is hereditary, one can argue as follows.
+The cotorsion pair (A, B) generated by S in Mod–R is hereditary, since the class S
+is closed under syzygies [16, Corollary 5.25(a)], [4, Lemma 1.3], [23, Lemma 4.1].
+Consequently, the class B is closed under the cokernels of monomorphisms, and in
+particular, under cosyzygies in Mod–R. By [2, Corollary 2.4] or [16, Corollary 8.42],
+the cotorsion pair (C, D) is cogenerated by the class of all pure-injective modules
+belonging to B. The class of all pure-injective modules is closed under cosyzygies
+by [16, Lemma 6.20], so the class of all pure-injective modules belonging to B is
+also closed under cosyzygies. Applying [16, Corollary 5.25(b)], we conclude that the
+cotorsion pair (C, D) is hereditary. Alternatively, one can use Proposition 3.5 below,
+which is a more general result.
+We also need to know that the class C is closed under pure epimorphic images. This
+is [18, Proposition 2.1], [12, Section 4.1], [2, Theorem 2.3], or [16, Theorem 8.40]. By
+the latter two references, we also have A ⊂ C, hence B ⊃ D.
+Therefore, the result of [3, Theorem 4.7] is applicable to the cotorsion pair (C, D),
+and it tells that the class ⊥1{M} ∩ C is closed under direct limits in Mod–R for any
+D-periodic module M. Now, if M ∈ B, then the class ⊥1{M} ∩ C contains A. Thus
+C = lim
+−→ A ⊂ ⊥1{M} and M ∈ D.
+To deduce the second assertion of Theorem 0(b) from the first one, suppose given
+an acyclic complex D• of modules from D with the modules of cocycles belonging
+to B. All one needs to do is to chop up the complex D• into short exact sequence
+pieces and take the infinite product of the pieces. The resulting short exact sequence
+has the form (∗) with L ∈ D and M ∈ B, and the first assertion of the theorem can be
+6
+
+applied to it, providing the desired conclusion. This argument uses the observations
+that countable products are exact in Mod–R, the classes D and B are closed under
+countable products, and the class D is closed under direct summands in Mod–R (cf. [9,
+proof of Proposition 7.6] or [13, Proposition 2]).
+□
+Let K be an abelian category.
+A class of objects C ⊂ K is said to be self-
+generating [4, Section 1], [23, Section 4] if for any epimorphism K −→ C in K
+with C ∈ C there exists a morphism C′ −→ K in K with C′ ∈ C such that the
+composition C′ −→ K −→ C is en epimorphism in K. A class of objects C is said
+to be self-resolving [23, Section 6] if it is self-generating and closed under extensions
+and kernels of epimorphisms.
+Proof of Theorem B(i) from from Section 0.2. As in the previous proof, let us first
+show that every D-periodic object from B belongs to D. The class of objects C contains
+a set of generators for K and is closed under coproducts; hence, in particular, it is self-
+generating. The class C is also closed under extensions and kernels of epimorphisms
+in K; so it is self-resolving. Finally, the class C is closed under direct limits in K,
+and the direct limits are exact in K. Thus the assumptions of [23, Theorem 6.1] are
+satisfied for the class C ⊂ K, which tells that, for any D-periodic object M ∈ K, the
+class ⊥1{M} ∩ C is closed under direct limits in K.
+By [4, Lemma 1.3] or [23, Lemma 4.1], we have Extn
+K(C, D) = 0 for all objects
+C ∈ C, D ∈ D, and integers n ≥ 1. By [23, Lemma 4.2], it follows that the class
+⊥1{M} ∩ C contains all objects of the class C which have finite projective dimension
+in K. Thus T ⊂ ⊥1{M} ∩ C. If M ∈ B, then we also have S ⊂ ⊥1{M} ∩ C.
+On the other hand, [23, Lemma 4.3] tells that the class ⊥1{M} ∩ C is closed under
+extensions and kernels of admissible epimorphisms in the exact category C (with the
+exact category structure inherited from the abelian exact structure of K). Since the
+class C is closed under extensions and kernels of epimorphisms in K, it follows that
+the class ⊥1{M} ∩ C is closed under extensions and kernels of epimorphisms in K.
+Finally, the class ⊥1{M} ∩ C is closed under coproducts in K, since it is closed under
+finite direct sums and direct limits.
+We have shown that the class ⊥1{M} ∩ C contains S ∪ T and is closed under
+extensions, kernels of epimorphisms, coproducts, and direct limits in K. Hence we
+can conclude that ⊥1{M} ∩ C = C, so C ⊂ ⊥1{M} and M ∈ D.
+Now we can prove the assertion of Theorem B(i). Let D• be an acyclic complex in
+K with the terms Di ∈ D and the objects of cocycles Bi ∈ B. So we have short exact
+sequences 0 −→ Bi −→ Di −→ Bi+1 −→ 0 in K. Taking the product of these short
+exact sequences over i ∈ Z, we obtain a sequence
+(1)
+0 −−→
+�
+i∈Z Bi −−→
+�
+i∈Z Di −−→
+�
+i∈Z Bi −−→ 0.
+In order to show that (1) is exact, we apply [23, Lemma 6.4]. By assumption, the
+class S∪T contains a set of generators of the Grothendieck category K. So there exists
+a family of objects (Gξ)ξ∈Ξ in S ∪ T together with an epimorphism G = �
+ξ∈Ξ Gξ −→
+�
+i∈Z Bi in K. It remains to show that Ext1
+K(G, Bi) = 0 for every i ∈ Z.
+7
+
+By [10, Corollary 8.3] or [11, Corollary A.2], it suffices to check that Ext1
+K(Gξ, Bi) =
+0 for every i ∈ Z and ξ ∈ Ξ. There are two cases. If Gξ ∈ S, then it remains to recall
+that Bi ∈ B = S⊥1. If Gξ ∈ T, then Gξ ∈ C and the projective dimension of Gξ in
+K is finite. From the short exact sequences 0 −→ Bj −→ Dj −→ Bj+1 −→ 0 we get
+Ext1
+K(Gξ, Bi) ≃ Ext2
+K(Gξ, Bi−1) ≃ Ext3
+K(Gξ, Bi−2) ≃ · · · = 0, since Extn
+K(Gξ, Dj) = 0
+for all j ∈ Z and n ≥ 1 as explained above (cf. [23, proof of Proposition 6.5]). So [23,
+Lemma 6.4] tells that the short sequence (1) is exact.
+Applying [10, Corollary 8.3] or [11, Corollary A.2] again, we see that both the
+classes B and D are closed under infinite products in K. Hence �
+i∈Z Bi ∈ B and
+�
+i∈Z Di ∈ D. So �
+i∈Z Bi is an D-periodic object in B, and it follows that �
+i∈Z Bi ∈
+D. Finally, the class D is closed under direct summands in K, hence Bi ∈ D for all
+i ∈ Z.
+□
+2. Generalized Flat/Projective and Fp-projective Periodicity
+The aim of this section is to prove Theorem 0(a). It is restated below as Theo-
+rem 2.10(a) and Corollary 2.11. The argument follows the ideas of the proof of [4,
+Theorems 0.7–0.8 or Corollaries 4.7–4.9]. The result is module-theoretic, but the
+proof has a category-theoretic flavor in that the approach of [4] needs to be applied
+within the class C viewed as an exact subcategory C ⊂ Mod–R.
+Let K be an exact category (in Quillen’s sense). We suggest the survey paper [8]
+as a general reference source on exact categories. The definition of a (hereditary)
+cotorsion pair (A, B) in K was already given in the beginning of Section 1.
+The
+intersection of the two classes A ∩ B ⊂ K is called the kernel of a cotorsion pair
+(A, B). Let us define the important concept of a complete cotorsion pair.
+A cotorsion pair (A, B) in K is said to be complete if for every object K ∈ K there
+exist (admissible) short exact sequences in K of the form
+0 −−→ B′ −−→ A −−→ K −−→ 0
+(2)
+0 −−→ K −−→ B −−→ A′ −−→ 0
+(3)
+with A, A′ ∈ A and B, B′ ∈ B.
+The sequence (2) is called a special precover
+sequence. The sequence (3) is called a special preenvelope sequence. Collectively, the
+sequences (2–3) are referred to as the approximation sequences.
+Let E ⊂ K be a full subcategory closed under extensions. Then we endow E with the
+exact category structure inherited from the exact category structure of K. The short
+exact sequences in the inherited exact structure on E are the short exact sequences
+in K with the terms belonging to E.
+Lemma 2.1. Let (C, D) be a complete cotorsion pair in an exact category K. Then
+the exact category C (with the exact structure inherited from K) has enough injective
+objects. The class of all injective objects in C is precisely the kernel C ∩ D of the
+cotorsion pair (C, D). Dually, the exact category D has enough projective objects, and
+the kernel C ∩ D is precisely the class of all projectives in D.
+8
+
+Proof. The proof is left to the reader.
+□
+Let K be an exact category and E ⊂ K be a full subcategory closed under exten-
+sions, endowed with the inherited exact category structure. Let (A, B) be a complete
+cotorsion pair in K. We will say that the cotorsion pair (A, B) restricts to (a complete
+cotorsion pair in) the exact subcategory E if the pair of classes (E ∩ A, E ∩ B) is a
+complete cotorsion pair in E.
+Lemma 2.2. Let (A, B) be a complete cotorsion pair in an exact category K, and
+let E ⊂ K be a full subcategory closed under extensions and kernels of admissible
+epimorphisms. Assume that A ⊂ E. Then
+(a) the cotorsion pair (A, B) restricts to E, so (A, E ∩ B) is a complete cotorsion
+pair in E;
+(b) if the cotorsion pair (A, B) is hereditary in K, then the restricted cotorsion pair
+(A, E ∩ B) is hereditary in E.
+Proof. This is fairly standard and easy to prove. The details can be found, e. g.,
+in [20, Lemmas 1.5(a) and 1.6].
+□
+Given an additive category K, we denote by C(K) the additive category of com-
+plexes in K (with the usual morphisms of complexes) and by H(K) the triangulated
+homotopy category of complexes in K. So the morphisms in H(K) are the cochain
+homotopy classes of morphisms in C(K). When K is an exact category, the category
+C(K) is endowed with the exact category structure in which a short sequence of com-
+plexes is exact if and only if it is exact at every degree. We denote by K• �−→ K•[n]
+the functor of grading shift on the complexes; so K•[n]i = Kn+i for all n, i ∈ Z.
+Lemma 2.3. Let K be an exact category, and let A• and B• be two complexes in K.
+Assume that Ext1
+K(An, Bn) = 0 for every n ∈ Z. Then there is a natural isomorphism
+of abelian groups
+Ext1
+C(K)(A•, B•) ≃ HomH(K)(A•, B•[1]).
+Proof. This is also standard and well-known. More generally, for any two complexes
+A• and B• in K, the subgroup of termwise split extensions 0 −→ B• −→ C• −→
+A• −→ 0 in Ext1
+K(A•, B•) is naturally isomorphic to the group of morphisms A• −→
+B• in the homotopy category H(K). We refer to [4, Lemma 1.6] for the details.
+□
+At this point, let us specialize our discussion to Grothendieck abelian categories K.
+Let F ∈ K be an object and α be an ordinal. A family of subobjects (Fβ ⊂ F)0≤β≤α
+is said to be an α-indexed filtration on F if the following conditions are satisfied:
+• F0 = 0 and Fα = F;
+• Fγ ⊂ Fβ for all 0 ≤ γ ≤ β ≤ α;
+• Fβ = �
+γ<β Fγ for all limit ordinals β ≤ α.
+An object F ∈ K endowed with an ordinal-indexed filtration (Fβ)0≤β≤α is said to
+be filtered by the quotient objects Sβ = Fβ+1/Fβ,
+0 ≤ β < α. In an alternative
+terminology, the object F is called a transfinitely iterated extension (in the sense of
+the direct limit) of the objects (Sβ)0≤β<α.
+9
+
+Given a class of objects S ⊂ K, the class of all objects in K filtered by (objects
+isomorphic to) objects from S is denoted by Fil(S) ⊂ K. A class of objects F ⊂ K is
+said to be deconstructible if there exists a set of objects S ⊂ K such that F = Fil(S).
+It is easy to see that any deconstructible class (in the sense of this definition) is closed
+under transfinitely iterated extensions.
+The following result is known as the Eklof lemma [16, Lemma 6.2].
+Lemma 2.4. For any class of objects B ⊂ K, the class ⊥1B is closed under trans-
+finitely iterated exensions. In other words, Fil(⊥1B) = ⊥1B.
+Proof. This assertion, properly understood, holds in any exact category K. See the
+references in [4, Lemma 1.1] (and the general formulation, e. g., in [23, Lemma 4.4.]).
+□
+We refer to the book [1, Definition 1.17 and Theorem 1.20] for the definition of
+a locally κ-presentable category (for a regular cardinal κ). We will have a detailed
+discussion of locally finitely presentable abelian categories (that is, the case of the
+countable cardinal κ = ℵ0) below in Section 3. Any Grothendieck abelian category
+is locally presentable, i. e., locally presentable for some regular cardinal κ.
+The next theorem is goes back to Eklof and Trlifaj [16, Theorem 6.11 and Corol-
+lary 6.14]. For any class of objects F ⊂ K, we denote by F⊕ ⊂ K the class of all direct
+summands of objects from F in K.
+Theorem 2.5. Let K be a Grothendieck category and (A, B) be the cotorsion pair
+generated by a set of objects S ⊂ K. Then
+(a) If the class A is generating in K, then the cotorsion pair (A, B) is complete.
+(b) If the class Fil(S) is generating in K, then A = Fil(S)⊕.
+Proof. This result, properly stated, holds in any locally presentable abelian cate-
+gory K. See [4, Theorem 1.2] for a discussion with references.
+□
+Proposition 2.6. Let κ be a regular cardinal and K be a locally κ-presentable
+Grothendieck category. Let S ⊂ K be a class of κ-presentable objects closed under
+transfinitely iterated extensions of families of objects of cardinality < κ (i. e.,
+indexed by ordinals α < κ). Let A• ∈ C(Fil(S)) be a complex in K whose terms are
+S-filtered objects. Then the complex A•, viewed as an object of the abelian category
+of complexes C(K), is filtered by bounded below complexes whose terms belong to S.
+Proof. This is [27, (proof of) Proposition 4.3]. The argument is based on the Hill
+lemma [27, Theorem 2.1].
+□
+In addition to the abelian exact structure on the module category K = Mod–R, we
+are interested in the pure exact structure. The definition of the pure exact structure
+on Mod–R was already given in Section 1. A complex in Mod–R is said to be pure
+acyclic (or pure exact) if it is acyclic in the pure exact structure, i. e., can be obtained
+by splicing pure short exact sequences. The following result due to Neeman [19] and
+ˇSt’ov´ıˇcek [28] is a stronger version of the pure pure-projective periodicity theorem
+(item (2) or (2c) on the list of Section 0.0).
+10
+
+Theorem 2.7. Let R be an associative ring. Let P • be a complex of pure-projective
+R-modules, and let X• be a pure acyclic complex of R-modules. Then any morphism
+of complexes of R-modules P • −→ X• is homotopic to zero.
+Proof. This was first stated in [28, Theorem 5.4] based on [19, Theorem 8.6]. We
+refer to the paper [3, Theorem 1.1] for a generalization, and to [4, Section 0.2 and
+proof of Theorem 4.3] for a discussion with some details.
+□
+Now let S be a class of finitely presented R-modules closed under finite direct sums
+and containing the free R-module R. Put C = lim
+−→ S ⊂ Mod–R.
+Lemma 2.8. The full subcategory C = lim
+−→ S is closed under pure extensions (as well
+as pure submodules and pure epimorphic images) in Mod–R. In the exact category
+structure on C inherited from the pure exact structure on Mod–R, a short sequence
+0 −→ K −→ L −→ M −→ 0 is exact if and only if the short sequence of abelian
+groups 0 −→ HomR(S, K) −→ HomR(S, L) −→ HomR(S, M) −→ 0 is exact for
+every module S ∈ S.
+Proof. The first assertion is the result of [18, Proposition 2.2]. The second assertion
+claims that a short sequence 0 −→ K −→ L −→ M −→ 0 with K, L, M ∈ C
+is pure exact in Mod–R if and only if the functor HomR(S, −) takes it to a short
+exact sequence for every S ∈ S. The point is that any morphism T −→ M from a
+finitely presented R-module T into the module M ∈ C = lim
+−→ S factorizes through
+some module S ∈ S. So if every morphism S −→ M lift to a morphism S −→ L,
+then also every morphism T −→ M lifts to a morphism T −→ L.
+□
+The next lemma tells that modules from the class B∩C are “absolutely pure within
+the exact category C”.
+Lemma 2.9. In the notation of Theorem 0, let 0 −→ B −→ L −→ C −→ 0 be a
+short exact sequence in Mod–R with the terms B, L, C ∈ C. Assume that the module
+B belongs to the class B ∩ C. Then the short exact sequence 0 −→ B −→ L −→
+C −→ 0 is pure in Mod–R.
+Proof. It is only important that C ∈ C and B ∈ B. By Lemma 2.8, it suffices to
+check that any morphism S −→ C with S ∈ S lifts to a morphism S −→ L. This
+holds because B ∈ B = S⊥1 ⊂ Mod–R.
+□
+Now we can formulate and prove the main results of the section.
+Theorem 2.10. Let R be a ring and S be a class of finitely presented R-modules,
+containing the free R-module R and closed under extensions and the kernels of epi-
+morphisms. Put B = S⊥1, A = ⊥1B, C = lim
+−→ S, and D = C⊥1 ⊂ Mod–R. Then
+(a) in any acyclic complex of modules from A with the modules of cocycles belonging
+to C, the modules of cocycles actually belong to A;
+(b) let A• be a complex in Mod–R whose terms belong to A, and let X• be an
+acyclic complex in Mod–R whose terms belong to B ∩ C and the modules of cocycles
+also belong to B ∩ C. Then any morphism of complexes of modules A• −→ X• is
+homotopic to zero.
+11
+
+Proof of Theorem 2.10(b). By the Eklof–Trlifaj theorem (Theorem 2.5(b)), we have
+A = Fil(S)⊕. Without loss of generality we can assume that the terms of the complex
+A• belong to Fil(S). Then, by Proposition 2.6 (applied in the case of the category
+K = Mod–R and the cardinal κ = ℵ0), the complex A• is filtered by (bounded below)
+complexes with the terms belonging to S.
+By Lemma 2.3, for any complex A• with the terms in A and any complex B• with
+the terms in B we have an isomorphism of abelian groups
+Ext1
+C(Mod–R)(A•, B•[−1]) ≃ HomH(Mod–R)(A•, B•).
+So, instead of showing that HomH(Mod–R)(A•, X•) = 0 as desired in the theorem,
+it suffices to prove that Ext1
+C(Mod–R)(A•, X•[−1]) = 0. In view of the Eklof lemma
+(Lemma 2.4) applied in the abelian category K = C(Mod–R), the question reduces
+to showing that Ext1
+C(Mod–R)(S•, X•[−1]) = 0 for any complex S• with the terms
+belonging to S and any complex X• as in the theorem. Using Lemma 2.3 again,
+we conclude that it suffices to show that any morphism of complexes S• −→ X• is
+homotopic to zero.
+Finally, we observe that all finitely presented R-modules are pure-projective (by
+the definitions), while any acyclic complex of modules with the modules of cocycles
+in B∩C is pure acyclic (by Lemma 2.9). Thus any morphism of complexes S• −→ X•
+is homotopic to zero by the Neeman–ˇSt’ov´ıˇcek theorem (Theorem 2.7).
+□
+Proof of Theorem 2.10(a). It is clear that in the assumptions of the theorem all the
+modules from S have to be strongly finitely presented (FP∞). Thus [2, Theorem 2.3
+and Corollary 2.4] or [16, Theorem 8.40, Corollary 8.42, and Theorem 6.19] are
+applicable, telling that (C, D) is a complete cotorsion pair in Mod–R. The cotorsion
+pair (A, B) is complete in Mod–R by the Eklof–Trlifaj theorem (Theorem 2.5(a)).
+Both the cotorsion pairs (A, B) and (C, D) are hereditary, as it was explained in
+the proof of Theorem 0(b) in Section 1. Applying Lemma 2.2 to the abelian category
+K = Mod–R and the full subcategory E = C, we conclude that (A, B ∩ C) is a
+hereditary complete cotorsion pair in the exact category C. Lemma 2.1 tells that
+there are enough injective objects in the exact category C, and the class of such
+injective objects coincides with the intersection C ∩ D.
+Let A• be an acyclic complex of modules from A. Then one can easily see that
+the modules of cocycles of A• belong to A if and only if the complex HomR(A•, B)
+is acyclic for any module B ∈ B. This holds because (A, B) is a cotorsion pair in
+Mod–R (so A = ⊥1B). We will use a version of this observation made within the
+exact category C.
+So let A• be an acyclic complex of modules from A with the modules of cocycles
+belonging to C. Then we observe that the modules of cocycles of A• belong to A if
+and only if the complex HomR(A•, B) is acyclic for any module B ∈ B ∩ C. This
+holds because (A, B ∩ C) is a cotorsion pair in C, so A = C ∩ ⊥1(B ∩ C).
+Now let D• be an injective resolution of the object B in the exact category C. So
+we have B ∈ B ∩ C by assumption, and 0 −→ B −→ D0 −→ D1 −→ D2 −→ · · ·
+is an acyclic complex in Mod–R with the modules Dn ∈ C ∩ D and the modules of
+12
+
+cocycles belonging to C. We observe that the modules of cocycles of the complex D•
+actually belong to B ∩ C, because D ⊂ B and the class B is closed under cokernels
+of monomorphisms. Essentially, this is a restatement of the claim that the cotorsion
+pair (A, B) is hereditary in Mod–R, or more specifically, that the cotorsion pair (A,
+B ∩ C) is hereditary in C.
+Denote by X• the acyclic complex (B → D•). Then the complex of abelian groups
+HomR(A•, X•) is acyclic by Theorem 2.10(b) (which we have proved above). This
+holds because A• is a complex with the terms in A, while X• is an acyclic complex
+with the terms in B ∩ C and the modules of cocycles in B ∩ C.
+On the other hand, the complex of abelian groups HomR(A•, D•) is acyclic as
+well. This holds quite generally for any acyclic complex A• and any bounded below
+complex of injective objects D• in any exact category C. Notice that in the situation
+at hand the complex of modules A• is acyclic in the exact category C, as its modules
+of cocycles belong to C by assumption.
+Since both the complexes HomR(A•, X•) and HomR(A•, D•) are acyclic, and the
+complex X• has the form X• = (B → D•), we can finally conclude that the complex
+of abelian groups HomR(A•, B) is acyclic.
+□
+Corollary 2.11. Let R be a ring and S be a class of finitely presented R-modules,
+containing the free R-module R and closed under extensions and the kernels of epi-
+morphisms. Put A = ⊥1(C⊥1) and C = lim
+−→ S. Then, for any short exact sequence (∗)
+as in Section 0.0 with modules L ∈ A and M ∈ C, one has M ∈ A. In other words,
+any A-periodic module belonging to C actually belongs to A.
+Proof. This is a corollary of Theorem 2.10(a), provable by splicing up a doubly un-
+bounded sequence of short exact sequences (∗) and applying Theorem 2.10(a) to the
+resulting doubly unbounded complex. (Cf. [13, Proposition 1].)
+□
+Proof of Theorem 0(a) from Section 0.1. The first assertion of Theorem 0(a) is pro-
+vided by Corollary 2.11, and the second one by Theorem 2.10(a).
+□
+3. Direct Limit Closures of Classes of Finitely Presentables
+The aim of this section is to prove Theorem B(ii). It is restated below as Proposi-
+tion 3.5.
+In this section we work with locally finitely presentable abelian categories.
+We
+suggest the book [1] as a general reference source on nonadditive locally (finitely)
+presentable and (finitely) accessible categories.
+The definition of a locally finitely presentable category can be found in [1, Def-
+inition 1.9 and Theorem 1.11] (it is helpful to keep in mind that in abelian cat-
+egories the notions of a generator and a strong generator coincide).
+All locally
+finitely presentable abelian categories have exact direct limit functors, so they are
+Grothendieck [1, Proposition 1.59].
+The abelian category of modules over an ar-
+bitrary ring K = Mod–R is an important example of a locally finitely presentable
+abelian category.
+13
+
+Finitely accessible categories [1, Definition 2.1 and Remark 2.2(1)] form a wider
+class than the locally finitely presentable ones.
+The theory of finitely accessible
+additive categories goes back to the paper [18, Section 2] (where they were not defined
+yet). Subsequently they were studied in the papers [12, 17] under the name of “locally
+finitely presented” additive categories.
+We suggest [22, Sections 8.1–8.2] as an additional reference source on locally finitely
+presentable abelian categories.
+Locally finitely generated categories also form a wider class than the locally finitely
+presentable ones.
+We refer to [1, Section 1.E] for a general discussion of locally
+generated (nonadditive) categories and to [21, Corollary 9.6] for a very general form
+of the assertion that any locally finitely generated abelian category is Grothendieck.
+A good reference source on locally finitely generated Grothendieck categories and
+finitely generated/finitely presentable objects in them is [26, §V.3].
+The following definitions are very general. Let K be a category with direct limits.
+An object S ∈ K is said to be finitely presentable if the functor HomK(P, −): K −→
+Sets preserves direct limits. An object S is said to be finitely generated if the same
+functor preserves the direct limits of diagrams of monomorphisms.
+An abelian category K with set-indexed coproducts is said to be locally finitely
+generated if it has a set of generators consisting of finitely generated objects. In
+particular, the category K is locally finitely presentable if it has a set of generators
+consisting of finitely presentable objects.
+Given a locally finitely presentable abelian category K, we denote by Kfp ⊂ K
+the full subcategory of finitely presentable objects in K. The full subcategory Kfp is
+closed under cokernels [1, Proposition 1.3] and extensions [22, Lemma 8.1] in K. Sim-
+ilarly, the full subcategory of finitely generated objects in a locally finitely generated
+abelian category K is closed under extensions and quotients [26, Lemma V.3.1 and
+Proposition V.3.2].
+Proposition 3.1. Let K be a locally finitely presentable abelian category and S ⊂ Kfp
+be a class of finitely presentable objects closed under finite direct sums. Then the class
+of objects lim
+−→ S ⊂ K is closed under coproducts and direct limits in K. An object L ∈ K
+belongs to lim
+−→ S if and only if, for any object T ∈ Kfp, any morphism T −→ L in K
+factorizes through an object from S.
+Proof. This is [18, Proposition 2.1], [12, Section 4.1], or [17, Proposition 5.11].
+□
+Corollary 3.2. Let K be a locally finitely presentable abelian category and S ⊂ Kfp
+be a class of finitely presentable objects closed under finite direct sums. Let (Hi)i∈I be
+a direct system of objects Hi ∈ lim
+−→ S, indexed by a directed poset I. Then the kernel
+of the natural epimorphism
+(4)
+�
+i∈I Hi −−→ lim
+−→i∈I Hi
+belongs to lim
+−→ S.
+Proof. One can argue from purity considerations, observing that the epimorphism (4)
+is pure (in the sense of the definition from [12, Section 3], [28, Section 4] reproduced
+14
+
+in [4, Sections 0.4 and 2]), and the class lim
+−→ S is closed under pure subobjects by the
+category-theoretic version of [18, Proposition 2.2]. Alternatively, one can notice that
+the kernel of (4) is a direct limit of coproducts of copies of the objects Hi, following [5,
+proof of Proposition 4.1]; then it remains to refer to Proposition 3.1.
+□
+The following definitions appeared in the papers [15, 7]. Let K be a Grothendieck
+category and n ≥ 1 be an integer. An object S ∈ K is said to be of type FPn if the
+functors Exti
+K(S, −): K −→ Ab preserve direct limits for all 0 ≤ i ≤ n − 1. So the
+objects of type FP1 are, by the definition, the finitely presentable ones, while the
+objects of type FPn for n ≥ 2 form more narrow classes.
+An object S ∈ K is said to be of type FP0 if it is finitely generated. An object S
+is said to be of type FP∞ if it is of type FPn for every n ≥ 0, that is, in other words,
+the functors Exti
+K(S, −): K −→ Ab preserve direct limits for all i ≥ 0.
+We use the term strongly finitely presentable object as a synonym for “type FP∞”.
+In the case of the module category K = Mod–R, these definitions are equivalent to
+the ones from Section 1 (see [7, Corollary 2.14]).
+Closure properties of the classes of objects of type FPn and FP∞ in locally finitely
+presentable abelian categories K are listed in [15, Corollary 3.3] and [7, Proposi-
+tion 2.8]. In particular, [7, Proposition 2.8(1)] tells that the class of all objects of
+type FPn is closed under extensions in K.
+Proposition 3.3. Let K be a locally finitely presentable abelian category and S be a
+class of (some) objects of type FP2 closed under extensions in K. Then the class of
+objects lim
+−→ S is also closed under extensions in K.
+Proof. We follow the proof of [22, Proposition 8.4]. Given an abelian category K and
+two classes of objects X, Y ⊂ K, denote by X∗Y the class of all objects Z ∈ K for which
+there exists a short exact sequence 0 −→ X −→ Z −→ Y −→ 0 in K with X ∈ X
+and Y ∈ Y. In the situation at hand, we need to prove that lim
+−→ S∗ lim
+−→ S ⊂ lim
+−→ S. For
+this purpose, we claim that the three inclusions
+(5)
+lim
+−→ T ∗ lim
+−→ T ⊂ lim
+−→(lim
+−→ T ∗ T) ⊂ lim
+−→ lim
+−→(T ∗ T) ⊂ lim
+−→(T ∗ T)
+hold for any class of FP2 objects T closed under finite direct sums in K.
+More generally, it is explained in [22, first part of the proof of Proposition 8.4] that
+the inclusion X ∗ lim
+−→ Y ⊂ lim
+−→(X ∗ Y) holds for any two classes of objects X and Y in
+a Grothendieck category K. This takes care of the leftmost inclusion in (5).
+Furthermore, any FP2 object is, by definition, finitely presentable; and the class
+of all finitely presentable objects is closed under extensions in K by [22, Lemma 8.1].
+So we certainly have T ∗ T ⊂ Kfp. It is clear that the class T ∗ T is closed under finite
+direct sums whenever the class T is. For any class of finitely presentable objects S
+closed under finite direct sums in K, we have lim
+−→ lim
+−→ S = lim
+−→ S by Proposition 3.1.
+This explains the rightmost inclusion in (5).
+Finally, the middle inclusion in (5) is provable similarly to the proof in [22]. Let
+K be a Grothendieck abelian category, X ⊂ K be a class of objects, and T ⊂ K be a
+class of objects such that the functor Ext1
+K(T, −): K −→ Ab preserves direct limits
+15
+
+for all objects T ∈ T. We claim that the inclusion (lim
+−→ X) ∗ T ⊂ lim
+−→(X ∗ T) holds.
+The argument from [22, second part of the proof of Proposition 8.4] applies.
+□
+Lemma 3.4. Let K be a Grothendieck category and S ⊂ K be a class of finitely
+generated objects containing a set of generators of K and closed under finite direct
+sums and kernels of epimorphisms. Then all the objects from S are strongly finitely
+presentable (type FP∞).
+Proof. First of all, the category K is locally finitely generated, since it has a set of
+finitely generated generators by assumption. In this context, it is explained in [26,
+Proposition V.3.4] that an object S ∈ K is finitely presentable if and only if the
+kernel of any epimorphism onto S from any finitely generated object T ∈ K is finitely
+generated. Following the argument in [26], based on [26, Lemma V.3.3], one can see
+that it suffices to let T range over the quotient objects of finite direct sums of objects
+from a chosen set G of finitely generated generators of K. Furthermore, the passage
+to the quotients holds automatically, and so it suffices to let T range over the finite
+direct sums of objects from G. In the situation at hand, choosing G ⊂ S, we conclude
+that all the objects in S are finitely presentable.
+The rest of the proof is similar to [22, proof of Lemma 8.3]. For any two objects
+X and Y in any abelian category K, the abelian group Extn
+K(X, Y ) can be computed
+as the filtered direct limit of cohomology groups Hn HomK(R•, Y ), taken over the
+(large) filtered category of exact complexes · · · −→ R2 −→ R1 −→ R0 −→ X −→ 0
+in K. Here the morphisms in the category of such arbitrary resolutions R• −→ X are
+the usual morphisms of complexes acting by the identity maps on the object X and
+viewed up to cochain homotopy.
+In the situation at hand, for any object S ∈ S, the full subcategory of resolutions
+T• −→ S consisting of objects Ti ∈ S is cofinal in the category of all resolutions
+R• −→ S with Ri ∈ K. So one can compute the group Extn
+K(S, Y ) as the filtered
+direct limit of Hn HomK(T•, Y ) taken over all the resolutions T• −→ S with Ti ∈ S.
+Now, since all the objects of S are finitely presentable, the functor HomK(T•, −) takes
+direct limits in K to direct limits of complexes of abelian groups. It remains to recall
+that the functors of cohomology of a complex of abelian groups preserve direct limits,
+and direct limits commute with direct limits.
+□
+Proposition 3.5. Let K be a Grothendieck category and S ⊂ K be a class of finitely
+generated objects containing a set of generators of K and closed under extensions
+and kernels of epimorphisms. Then the class of objects lim
+−→ S ⊂ K is closed under
+coproducts, direct limits, extensions, and kernels of epimorphisms.
+Proof. By Lemma 3.4, all objects in S are finitely presentable, and in fact even
+strongly finitely presentable. As the class S contains a set of generators for K, it
+follows that the category K is locally finitely presentable.
+So Proposition 3.1 is
+applicable, telling that the class lim
+−→ S is closed under coproducts and direct limits
+in K. Furthermore, Proposition 3.3 tells that the class lim
+−→ S is closed under extensions.
+It remains to prove its closedness under kernels of epimorphisms.
+16
+
+Let C −→ D be an epimorphism in K between two objects C, D ∈ lim
+−→ S. Then
+there exists a direct system (Si)i∈I, indexed by a directed poset I, such that Si ∈ S
+for all i ∈ I and D = lim
+−→i∈I Si. For every i ∈ I, consider the pullback diagram
+(6)
+Ci
+� �
+�
+Si
+�
+C
+� � D
+Here Ci is the pullback of the given epimorphism C −→ D and the natural morphism
+to the direct limit Si −→ D. As the index i ∈ I varies, the upper lines of (6) form a
+direct system of (epi)morphisms in K, whose direct limit is the epimorphism C −→ D
+in the lower line of the diagram.
+Choose a set of generators G ⊂ S of the category K, and put H = �
+G∈G G. For
+every index i ∈ I, denote by Ξi the underlying set of the image of the abelian group
+map HomK(H, Ci) −→ HomK(H, Si) induced by the morphism Ci −→ Si. Then, for
+every pair of indices i < j ∈ I, the transition morphism Si −→ Sj induces a map of
+sets Ξi −→ Ξj. So we obtain a direct system of sets (Ξi)i∈I.
+For any object K ∈ K and any set Ξ, let us denote by K(Ξ) the coproduct of Ξ
+copies of K in K. Notice that the assigment (K, Ξ) �−→ K(Ξ) is a covariant functor
+K×Sets −→ K (i. e., a covariant functor of both the arguments K ∈ K and Ξ ∈ Sets).
+For every index i ∈ I we have a natural morphism hi : H(Ξi) −→ Si in K. Since H
+is a generator of the category K, and the morphism Ci −→ Si is an epimorphism, the
+morphism hi is an epimorphism in K as well. As the index i varies, the morphisms hi
+form a direct system (hi)i∈I in the category of morphisms in K.
+Let us show that the kernel Li of the morphism hi belongs to lim
+−→ S. The object
+H(Ξi) is the coproduct of copies of all the objects G ∈ G, each of them taken with
+the multiplicity Ξi. Since the object Si is finitely generated, there exists a finite
+subcoproduct in this coproduct mapping epimorphically onto Si. So we have a direct
+sum decomposition H(Ξi) = H′
+i ⊕ H′′
+i , where H′
+i is a finite direct sum of objects from
+G and the restriction of hi onto H′
+i is an epimorphism h′
+i : H′
+i −→ Si. Denote by Ki
+the kernel of h′
+i. We have constructed a pushout diagram
+Ki �
+�
+�
+�
+H′
+i
+� �
+�
+�
+Si
+Li �
+�
+��
+Hi
+� �
+��
+Si
+H′′
+i
+H′′
+i
+Now H′
+i ∈ S, since the class S is closed under finite direct sums and G ⊂ S. Hence
+Ki ∈ S, as the class S is closed under kernels of epimorphisms. On the other hand,
+H′′
+i ∈ lim
+−→ S, since the class lim
+−→ S is closed under coproducts. As we already know
+17
+
+that the class lim
+−→ S is closed under extensions, we can conclude from the short exact
+sequence 0 −→ Ki −→ Li −→ H′′
+i −→ 0 that Li ∈ lim
+−→ S.
+Passing to the direct limit of hi over i ∈ I, we see that the kernel of the epimorphism
+lim
+−→i∈I H(Ξi) −−→ lim
+−→i∈I Si = D
+belongs to lim
+−→ lim
+−→ S = lim
+−→ S. We already know from Corollary 3.2 that the kernel of
+the epimorphism (4) (for Hi = H(Ξi)) belongs to lim
+−→ S. Since the class lim
+−→ S is closed
+under extensions, it follows that the kernel M of the composition of epimorphisms
+H =
+�
+i∈I H(Ξi) −−→ lim
+−→i∈I H(Ξi) −−→ D
+belongs to lim
+−→ S.
+The final observation is that the epimorphism H = �
+i∈I H(Ξi) −→ D factorizes
+through the epimorphism C −→ D, essentially due to the construction of the sets Ξi
+in the beginning of this proof. Now we consider the pullback diagram
+N�
+�
+N�
+�
+M �
+� X
+� �
+��
+C
+��
+M �
+� H
+� � D
+where X is the pullback of the pair of epimorphisms C −→ D and H −→ D, while N
+is the kernel of the morphism C −→ D. Since the epimorphism H −→ D factorizes
+through the epimorphism C −→ D, the short exact sequence 0 −→ N −→ X −→
+H −→ 0 splits. We have M ∈ lim
+−→ S and C ∈ lim
+−→ S, so it follows from the short exact
+sequence 0 −→ M −→ X −→ C −→ 0 that X ∈ lim
+−→ S. It remains to notice that
+the class lim
+−→ S is closed under direct summands (since it is closed under direct limits)
+in K. So N ∈ lim
+−→ S as N is a direct summand of X.
+□
+We conclude the section by presenting a formal proof of Theorem B(ii).
+Proof of Theorem B(ii) from from Section 0.2. Applying Proposition 3.5 to the class
+S ∪ T ⊂ K, we see that the class lim
+−→(S ∪ T) is closed under coproducts, direct limits,
+extensions, and kernels of epimorphisms in K. So lim
+−→(S ∪ T) is precisely the class C
+as defined in the formulation of Theorem B.
+□
+References
+[1] J. Ad´amek, J. Rosick´y. Locally presentable and accessible categories. London Math. Society
+Lecture Note Series 189, Cambridge University Press, 1994.
+[2] L. Angeleri H¨ugel, J. Trlifaj. Direct limits of modules of finite projective dimension. Rings, mod-
+ules, algebras, and abelian groups, Proceedings of the Algebra Conference in Venezia, Lecture
+Notes in Pure and Appl. Math. 236, Marcel Dekker, New York–Basel, 2004, p. 27–44.
+18
+
+[3] S. Bazzoni, M. Cort´es-Izurdiaga, S. Estrada. Periodic modules and acyclic complexes. Algebras
+and Represent. Theory 23, #5, p. 1861–1883, 2020. arXiv:1704.06672 [math.RA]
+[4] S.
+Bazzoni,
+M.
+Hrbek,
+L.
+Positselski.
+Fp-projective
+periodicity.
+Electronic
+preprint
+arXiv:2212.02300 [math.CT].
+[5] S. Bazzoni, L. Positselski, J. ˇSt’ov´ıˇcek. Projective covers of flat contramodules. Internat. Math.
+Research Notices 2022, #12, p. 19527–19564, 2022. arXiv:1911.11720 [math.RA]
+[6] D. J. Benson, K. R. Goodearl. Periodic flat modules, and flat modules for finite groups. Pacific
+Journ. of Math. 196, #1, p. 45–67, 2000.
+[7] D. Bravo, J. Gillespie, M. A. P´erez. Locally type FPn and n-coherent categories. Electronic
+preprint arXiv:1908.10987 [math.CT]
+[8] T. B¨uhler. Exact categories. Expositiones Math. 28, #1, p. 1–69, 2010. arXiv:0811.1480
+[math.HO]
+[9] L. W. Christensen, H. Holm. The direct limit closure of perfect complexes. Journ. of Pure and
+Appl. Algebra 219, #3, p. 449–463, 2015. arXiv:1301.0731 [math.RA]
+[10] R. Colpi, K. R. Fuller. Tilting objects in abelian categories and quasitilted rings. Trans. of the
+Amer. Math. Soc. 359, #2, p. 741–765, 2007.
+[11] P. ˇCoupek, J. ˇSt’ov´ıˇcek. Cotilting sheaves on Noetherian schemes. Math. Zeitschrift 296, #1–2,
+p. 275–312, 2020. arXiv:1707.01677 [math.AG]
+[12] W. Crawley-Boevey. Locally finitely presented additive categories. Communicat. in Algebra 22,
+#5, p. 1641–1674, 1994.
+[13] S. Estrada, X. Fu, A. Iacob. Totally acyclic complexes. Journ. of Algebra 470, p. 300–319,
+2017. arXiv:1603.03850 [math.AC]
+[14] J. R. Garc´ıa Rozas. Covers and envelopes in the category of complexes of modules. Chapman
+& Hall/CRC Research Notes in Math., 407, Boca Raton, FL, 1999.
+[15] J. Gillespie. Models for homotopy categories of injectives and Gorenstein injectives. Commu-
+nicat. in Algebra 45, #6, p. 2520–2545, 2017. arXiv:1502.05530 [math.CT]
+[16] R. G¨obel, J. Trlifaj. Approximations and endomorphism algebras of modules. Second Revised
+and Extended Edition. De Gruyter Expositions in Mathematics 41, De Gruyter, Berlin–Boston,
+2012.
+[17] H. Krause. Functors on locally finitely presented additive categories. Colloquium Math. 75, #1,
+p. 105–132, 1998.
+[18] H. Lenzing. Homological transfer from finitely presented to infinite modules. Abelian group
+theory (Honolulu, Hawaii), Lecture Notes in Math. 1006, Springer, Berlin, 1983, p. 734–761.
+[19] A. Neeman. The homotopy category of flat modules, and Grothendieck duality. Inventiones
+Math. 174, #2, p. 225–308, 2008.
+[20] L. Positselski. Local, colocal, and antilocal properties of modules and complexes over commu-
+tative rings. Electronic preprint arXiv:2212.10163 [math.AC].
+[21] L. Positselski, J. ˇSt’ov´ıˇcek. The tilting-cotilting correspondence. Internat. Math. Research No-
+tices 2021, #1, p. 189–274, 2021. arXiv:1710.02230 [math.CT]
+[22] L. Positselski, J. ˇSt’ov´ıˇcek. Coderived and contraderived categories of locally presentable abelian
+DG-categories. Electronic preprint arXiv:2210.08237 [math.CT].
+[23] L. Positselski, J. ˇSt’ov´ıˇcek. Flat quasi-coherent sheaves as direct limits, and quasi-coherent
+cotorsion periodicity. Electronic preprint arXiv:2212.09639 [math.AG].
+[24] J. ˇSaroch, J. ˇSt’ov´ıˇcek. Singular compactness and definability for Σ-cotorsion and Gorenstein
+modules. Selecta Math. (New Ser.) 26, #2, Paper No. 23, 40 pp., 2020. arXiv:1804.09080
+[math.RT]
+[25] D. Simson. Pure-periodic modules and a structure of pure-projective resolutions. Pacific Journ.
+of Math. 207, #1, p. 235–256, 2002.
+[26] B. Stenstr¨om. Rings of quotients. An Introduction to Methods of Ring Theory. Die Grundlehren
+der Mathematischen Wissenschaften, Band 217. Springer-Verlag, New York, 1975.
+19
+
+[27] J. ˇSt’ov´ıˇcek. Deconstructibility and the Hill Lemma in Grothendieck categories. Forum Math.
+25, #1, p. 193–219, 2013. arXiv:1005.3251 [math.CT]
+[28] J. ˇSt’ov´ıˇcek. On purity and applications to coderived and singularity categories. Electronic
+preprint arXiv:1412.1615 [math.CT].
+Institute of Mathematics, Czech Academy of Sciences, ˇZitn´a 25, 115 67 Praha 1,
+Czech Republic
+Email address: positselski@math.cas.cz
+20
+
diff --git a/rNAyT4oBgHgl3EQfzvn1/content/tmp_files/load_file.txt b/rNAyT4oBgHgl3EQfzvn1/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2b3735af6e7dfca606468162899746b0c6868eb8
--- /dev/null
+++ b/rNAyT4oBgHgl3EQfzvn1/content/tmp_files/load_file.txt
@@ -0,0 +1,903 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf,len=902
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='00708v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='RA]  2 Jan 2023  GENERALIZED PERIODICITY THEOREMS  LEONID POSITSELSKI  Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Let R be a ring and S be a class of strongly finitely presented (FP∞)  R-modules closed under extensions, direct summands, and syzygies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Let (A, B) be  the (hereditary complete) cotorsion pair generated by S in Mod–R, and let (C, D)  be the (also hereditary complete) cotorsion pair in which C = lim  −→ A = lim  −→ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' We  show that any A-periodic module in C belongs to A, and any D-periodic module in  B belongs to D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' A further generalization of the latter result is obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Contents  Introduction  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Generalized Fp-injective/Injective and Cotorsion Periodicity  4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Generalized Flat/Projective and Fp-projective Periodicity  8  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Direct Limit Closures of Classes of Finitely Presentables  13  References  18  Introduction  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Periodicity theorems in homological algebra apply to the following setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Let  R be an associative ring and  (∗)  0 −−→ M −−→ L −−→ M −−→ 0  be a short exact sequence of (right) R-modules with the leftmost term isomorphic to  the rightmost one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Then it is known that  (1) if the R-module M is flat and the R-module L is projective, then the R-mod-  ule M is projective (Benson and Goodearl 2000 [6], rediscovered by Neeman  in 2008 [19]);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  (2) if the exact sequence (∗) is pure and the R-module L is pure-projective, then  the R-module M is pure-projective (Simson 2002 [25]);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  (3) if the exact sequence (∗) is pure and the R-module L is pure-injective, then  the R-module M is pure-injective (ˇSt’ov´ıˇcek 2014 [28]);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  (4) in particular, if the R-module M is fp-injective and the R-module L is injec-  tive, then the R-module M is injective;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  (5) if the R-module L is cotorsion, then the R-module M is cotorsion (Bazzoni,  Cort´es-Izurdiaga, and Estrada 2017 [3]);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  1  (6) if the ring R is right coherent and the right R-module L is fp-projective, then  the R-module M is fp-projective (ˇSaroch and ˇSt’ov´ıˇcek 2018 [24]);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  (7) over any ring R, if the R-module L is fp-projective, then the R-module M is  weakly fp-projective (Bazzoni, Hrbek, and the present author 2022 [4]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Periodicity phenomena are linked to behavior of the modules of cocycles in acyclic  complexes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' This means that the assertions (1–7) can be restated as follows:  (1c) in any acyclic complex of projective modules with flat modules of cocycles,  the modules of cocycles are actually projective (so the complex is contactible);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  (2c) in any pure acyclic complex of pure-projective modules, the modules of cocy-  cles are pure-projective (so the complex is contractible);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  (3c) in any pure acyclic complex of pure-injective modules, the modules of cocycles  are pure-injective (so the complex is contractible);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  (4c) in any acyclic complex of injective modules with fp-injective modules of co-  cycles, the modules of cocycles are actually injective (so the complex is con-  tractible);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  (5c) in any acyclic complex of cotorsion modules, the modules of cocycles are  cotorsion;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  (6c) in any acyclic complex of fp-projective right modules over a right coherent  ring, the modules of cocycles are fp-projective;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  (7c) in any acyclic complex of fp-projective modules (over any ring), the modules  of cocycles are weakly fp-projective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  We refer to the introduction to the preprint [4] for a more detailed discussion of the  periodicity theorems (1–7) and (1c–7c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  The aim of this paper is to obtain a common generalization of (1) and (6),  and also a common generalization of (4) and (5), in the context of a chosen class  of modules or objects in a Grothendieck category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Let us start with presenting the  most symmetric and nicely looking formulation of our results, and then proceed to a  certain further generalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Let R be a ring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' An R-module is said to be strongly finitely presented if it has an  (infinite) resolution by finitely generated projective R-modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' In the terminology  of the book [16], such modules are called “FP∞-modules”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Let S be a class (up to an isomorphism, of course, a set) of strongly finitely pre-  sented (right) R-modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Assume that the free R-module R belongs to S, and that  the class of modules S is closed under direct summands, extensions, and kernels of  epimorphisms in Mod–R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' In particular, for any module S ∈ S there exists a (finitely  generated) projective R-module P together with an R-module epimorphism P −→ S  whose kernels also belongs to S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' The latter property is expressed by saying that “the  class of modules S is closed under syzygies”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Denote by B = S⊥1 the class of all R-modules B such that Ext1  R(S, B) = 0 for  all S ∈ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Furthermore, denote by A = ⊥1B the class of all R-modules A such that  Ext1  R(A, B) = 0 for all B ∈ B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' The pair of classes of modules (A, B) is called the  cotorsion pair generated by S in Mod–R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  2  Let C = lim  −→ S denote the class of all R-modules that can be obtained as direct  limits of diagrams of modules from S, indexed by directed posets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Since S is a class  of finitely presented modules, one can see that lim  −→ S coincides with the direct limit  closure or S in Mod–R [18, 12, 17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Furthermore, since S is a class of strongly finitely presented modules (FP2 is suffi-  cient), the class C is closed under extensions in Mod–R [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Taking into account the  description of A as the class of all direct summands of transfinitely iterated extensions  of modules from S [16, Corollary 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='14], one concludes that A ⊂ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Hence C = lim  −→ A  is the class of all direct limits of modules from A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Denote by D = C⊥1 the class of all R-modules D such that Ext1  R(C, D) = 0 for all  C ∈ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Then one has A ⊂ C and B ⊃ D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Part (a) of the following theorem is the main result of this paper, while part (b)  follows rather easily from a result of Bazzoni, Cort´es-Izurdiaga, and Estrada [3, The-  orem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='7] together with a result of Angeleri H¨ugel and Trlifaj [2, Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Theorem 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Let R be a ring and S be a class of strongly finitely presented R-modules,  containing the free R-module R and closed under direct summands, extensions, and  kernels of epimorphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Put B = S⊥1, A = ⊥1B, C = lim  −→ S, and D = C⊥1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Then  the following assertions hold:  (a) For any short exact sequence (∗) with L ∈ A and M ∈ C, one has M ∈ A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' In  other words, in any acyclic complex of modules from A with the modules of cocycles  belonging to C, the modules of cocycles actually belong to A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  (b) For any short exact sequence (∗) with L ∈ D and M ∈ B, one has M ∈ D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' In  other words, in any acyclic complex of modules from D with the modules of cocycles  belonging to B, the modules of cocycles actually belong to D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Theorem 0(a) is a common generalization of items (1) or (1c) and (6) or (6c) on the  list of Section 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Taking S = {R} to be the class consisting of the free R-module  R only, one obtains the flat/projective periodicity theorem of Benson–Goodearl [6,  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='5] and Neeman [19, Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='15] as a particular case of Theorem 0(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Assuming the ring R to be right coherent and taking S to be the class of all finitely pre-  sented right R-modules, one obtains the fp-projective periodicity theorem of ˇSaroch  and St’ov´ıˇcek [24, Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='3] as a particular case of Theorem 0(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Theorem 0(b) is a common generalization of items (4) or (4c) (for coherent rings)  and (5) or (5c) on the list of Section 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Assuming the ring R to be right coherent  and taking S to be the class of all finitely presented right R-modules, one obtains  the fp-injective/injective periodicity theorem, essentially due to St’ov´ıˇcek [28, Corol-  lary 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='5] (see also [3, Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='2(1) or 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='1(1)]), as a particular case of Theorem 0(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Taking S = {R} to be the class consisting of the free R-module R only, one obtains  the cotorsion periodicity theorem of Bazzoni, Cort´es-Izurdiaga, and Estrada [3, The-  orem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='2(2) or 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='1(2)] as a particular case of Theorem 0(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Part (b) of Theorem 0 admits a far-reaching generalization (allowing, in partic-  ular, to drop the coherence assumptions on the ring R in the preceding paragraph).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  We state this result as the following Theorem B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  3  Part B(i), which is the main claim, is rather easily deduced from a result of St’ov´ıˇcek  and the present author [23, Theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='1] (which, in turn, is a generalization of [3,  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='7]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Part B(ii), which is a supplementary comment on B(i) (explaining  what B(i) means under some additional assumptions), turns out to be more involved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Theorem B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Let K be a Grothendieck category and S ⊂ K be a class of objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Let  T ⊂ K be any class of objects of finite projective dimension in K such that the union  S∪T contains a set of generators for K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Denote by C ⊂ K the closure of S∪T under  coproducts, direct limits, extensions, and kernels of epimorphisms in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Then  (i) Let B = S⊥1 be the class of all objects B ∈ K such that Ext1  K(S, B) = 0 for all  S ∈ S, and let D = C⊥1 be the class of all objects D ∈ K such that Ext1  K(C, D) = 0  for all C ∈ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Then, for any acyclic complex of objects from D with the objects of  cocycles belonging to B, the objects of cocycles actually belong to D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  (ii) If the class S ∪ T consists of (some) finitely presentable objects and is closed  under extensions and kernels of epimorphisms in K, then C = lim  −→(S ∪ T) is the class  of all direct limits of diagrams of objects from S ∪ T, indexed by directed posets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  One can see that in the context of Theorem B(ii) the class S ∪ T has to consist  of strongly finitely presentable (FP∞) objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Taking T = ∅ makes Theorem 0(b)  a particular case of Theorem B(i–ii) (for K = Mod–R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Taking S to be the class of all finitely presentable objects in a locally finitely  presentable abelian category K and T = ∅, one obtains the assertion (4) or (4c) on  the list of Section 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='0, essentially due to St’ov´ıˇcek [28, Corollary 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='5], as a particular  case of Theorem B(i) (for K = Mod–R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  The proofs of Theorems 0(b) and B(i) are presented in Section 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Theorem 0(a)  is proved in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' The proof of Theorem B(ii) is given in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Acknowledgement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' I want to thank Michal Hrbek, Silvana Bazzoni, and Jan Trlifaj  for helpful discussions and comments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Long conversations with Jan St’ov´ıˇcek were  particularly illuminating, and to him goes my special gratitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' The author is sup-  ported by the GAˇCR project 20-13778S and research plan RVO: 67985840.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Generalized Fp-injective/Injective and Cotorsion Periodicity  In this section we prove Theorems 0(b) and B(i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' This is not difficult, given the  preceding results in [3, Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='7] and [23, Theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' The former theorem  needs to be used together with [2, Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='4], and the latter one together with [23,  Lemmas 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='2, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='3, and 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Let us formally introduce some notation and terminology which was already used  throughout the introduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Given an abelian (or exact [8]) category K and a class  of objects A ⊂ K, one denotes by A⊥1 ⊂ K the class of all objects X ∈ K such that  Ext1  K(A, X) = 0 for all A ∈ A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Dually, for a class of objects B ⊂ K, the notation  ⊥1B ⊂ K stands for the class of all objects Y ∈ K such that Ext1  K(Y, B) = 0 for all  B ∈ B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Similarly, A⊥≥1 ⊂ K is the class of all objects X ∈ K such that Extn  K(A, X) = 0  4  for all A ∈ A and n ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Dually, ⊥≥1B ⊂ K is the class of all objects Y ∈ K such that  Extn  K(Y, B) = 0 for all B ∈ B and n ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  A class of objects A ⊂ K is said to be generating (or a class of generators) if every  object of K is a quotient object of a coproduct of objects from A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' A class of objects  B ⊂ K is said to be cogenerating (or a class of cogenerators) if every object of K is a  subobject of a product of objects from B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  A pair of classes of objects (A, B) in K is said to be a cotorsion pair if A = ⊥1B and  B = A⊥1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Notice that, for any cotorsion pair (A, B) in K, the class A ⊂ K is closed  under coproducts (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=', those coproducts that exist in K), and the class B ⊂ K is  closed under products (in the same sense) [10, Corollary 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='3], [11, Corollary A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  For any class of objects S ⊂ K, the pair of classes B = S⊥1 and A = ⊥1B is a  cotorsion pair in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' The cotorsion pair (A, B) obtained in this way is said to be  generated by the class S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Dually, for any class of objects T ⊂ K, the pair of classes  A = ⊥1T and B = A⊥1 is also a cotorsion pair in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' The latter cotorsion pair (A, B)  is said to be cogenerated by the class T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Let (A, B) be a cotorsion pair in K such that the class A is generating and the class  B is cogenerating in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' So every object of K is a quotient object of an object from  A and a subobject of an object from B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' These conditions are satisfied automatically  for any cotorsion pair in an abelian category K with enough projective and injective  objects (because all projective objects belong to A and all injective objects belong  to B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' In particular, this applies to the module categories K = Mod–R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  In the assumptions of the previous paragraph, the following conditions are equiv-  alent [14, Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='10], [16, Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='24], [4, Section 1], [23, Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='1]:  (1) the class A is closed under kernels of epimorphisms in K;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  (2) the class B is closed under cokernels of monomorphisms in K;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  (3) Ext2  K(A, B) = 0 for all A ∈ A and B ∈ B;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  (4) Extn  K(A, B) = 0 for all A ∈ A, B ∈ B, and n ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  A cotorsion pair (A, B) satisfying conditions (1–4) is said to be hereditary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Given a class of objects L ⊂ K, an object M ∈ K is said to be L-periodic if there  exists a short exact sequence 0 −→ M −→ L −→ M −→ 0 (∗) in K with L ∈ L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  We recall that the notation lim  −→ L ⊂ K stands for the class of all direct limits in K of  diagrams of objects from L (indexed by directed posets).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  A short exact sequence of right R-modules 0 −→ K −→ L −→ M −→ 0 is said to  be pure if it remains exact after taking the tensor product with any left R-module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Equivalently, a short exact sequence 0 −→ K −→ L −→ M −→ 0 is pure if and only  if it remains exact after the functor HomR(S, −) from any finitely presented right  R-module S is applied [16, Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='6 and Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' If this is the case, the  object K is said to be a pure subobject of L, while the object M is called a pure  epimorphic image (or a pure quotient) of M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' The pure exact structure on Mod–R is  formed by the class of all pure exact sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' The projective objects of the exact  category Mod–R with the pure exact structure are called pure-projective R-modules,  and the injective objects are called pure-injective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  5  An R-module S is said to be FPn (where n ≥ 0 is an integer) if it admits a  fragment of projective resolution Pn −→ Pn−1 −→ · · · −→ P0 −→ S −→ 0 with  finitely generated projective modules Pi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  So a module is FP0 if and only if it is  finitely generated, and it is FP1 if and only if it is finitely presented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' A module S  is said to be FP∞ if it admits a resolution by finitely generated projective modules;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  equivalently, this means that S is FPn for all n ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Modules of type FP∞ are  otherwise known as strongly finitely presented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  A class of modules S is said to be closed under syzygies if for every module S ∈ S  there exists a short exact sequence 0 −→ K −→ P −→ S −→ 0 with a projective  module P and K ∈ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' For any other short exact sequence 0 −→ K′ −→ P ′ −→  S −→ 0 with a projective module P ′, it then follows that K′ ⊕ P ≃ K ⊕ P ′, which  often implies that K′ ∈ S as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Dually, a class of modules T is closed under  cosyzygies if for every module T ∈ T there exists a short exact sequence 0 −→ T −→  J −→ L −→ 0 with an injective module J and L ∈ T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' For any other short exact  sequence 0 −→ T −→ J′ −→ L′ −→ 0 with an injective module J′, it then follows  that L′ ⊕ J ≃ L ⊕ J′, which often implies that L′ ∈ T, too.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Proof of Theorem 0(b) from Section 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Let us first prove the first assertion, then  deduce the second one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' In order to apply [3, Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='7], we need to show that  (C, D) is a hereditary cotorsion pair in Mod–R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' First of all, (C, D) is indeed a cotorsion  pair by [2, Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='4] (see also [16, Corollary 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='42]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  To show that the cotorsion pair (C, D) is hereditary, one can argue as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  The cotorsion pair (A, B) generated by S in Mod–R is hereditary, since the class S  is closed under syzygies [16, Corollary 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='25(a)], [4, Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='3], [23, Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Consequently, the class B is closed under the cokernels of monomorphisms, and in  particular, under cosyzygies in Mod–R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' By [2, Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='4] or [16, Corollary 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='42],  the cotorsion pair (C, D) is cogenerated by the class of all pure-injective modules  belonging to B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' The class of all pure-injective modules is closed under cosyzygies  by [16, Lemma 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='20], so the class of all pure-injective modules belonging to B is  also closed under cosyzygies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Applying [16, Corollary 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='25(b)], we conclude that the  cotorsion pair (C, D) is hereditary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Alternatively, one can use Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='5 below,  which is a more general result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  We also need to know that the class C is closed under pure epimorphic images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' This  is [18, Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='1], [12, Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='1], [2, Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='3], or [16, Theorem 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' By  the latter two references, we also have A ⊂ C, hence B ⊃ D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Therefore, the result of [3, Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='7] is applicable to the cotorsion pair (C, D),  and it tells that the class ⊥1{M} ∩ C is closed under direct limits in Mod–R for any  D-periodic module M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Now, if M ∈ B, then the class ⊥1{M} ∩ C contains A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Thus  C = lim  −→ A ⊂ ⊥1{M} and M ∈ D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  To deduce the second assertion of Theorem 0(b) from the first one, suppose given  an acyclic complex D• of modules from D with the modules of cocycles belonging  to B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' All one needs to do is to chop up the complex D• into short exact sequence  pieces and take the infinite product of the pieces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' The resulting short exact sequence  has the form (∗) with L ∈ D and M ∈ B, and the first assertion of the theorem can be  6  applied to it, providing the desired conclusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' This argument uses the observations  that countable products are exact in Mod–R, the classes D and B are closed under  countable products, and the class D is closed under direct summands in Mod–R (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' [9,  proof of Proposition 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='6] or [13, Proposition 2]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  □  Let K be an abelian category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  A class of objects C ⊂ K is said to be self-  generating [4, Section 1], [23, Section 4] if for any epimorphism K −→ C in K  with C ∈ C there exists a morphism C′ −→ K in K with C′ ∈ C such that the  composition C′ −→ K −→ C is en epimorphism in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' A class of objects C is said  to be self-resolving [23, Section 6] if it is self-generating and closed under extensions  and kernels of epimorphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Proof of Theorem B(i) from from Section 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' As in the previous proof, let us first  show that every D-periodic object from B belongs to D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' The class of objects C contains  a set of generators for K and is closed under coproducts;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' hence, in particular, it is self-  generating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' The class C is also closed under extensions and kernels of epimorphisms  in K;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' so it is self-resolving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Finally, the class C is closed under direct limits in K,  and the direct limits are exact in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Thus the assumptions of [23, Theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='1] are  satisfied for the class C ⊂ K, which tells that, for any D-periodic object M ∈ K, the  class ⊥1{M} ∩ C is closed under direct limits in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  By [4, Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='3] or [23, Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='1], we have Extn  K(C, D) = 0 for all objects  C ∈ C, D ∈ D, and integers n ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' By [23, Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='2], it follows that the class  ⊥1{M} ∩ C contains all objects of the class C which have finite projective dimension  in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Thus T ⊂ ⊥1{M} ∩ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' If M ∈ B, then we also have S ⊂ ⊥1{M} ∩ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  On the other hand, [23, Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='3] tells that the class ⊥1{M} ∩ C is closed under  extensions and kernels of admissible epimorphisms in the exact category C (with the  exact category structure inherited from the abelian exact structure of K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Since the  class C is closed under extensions and kernels of epimorphisms in K, it follows that  the class ⊥1{M} ∩ C is closed under extensions and kernels of epimorphisms in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Finally, the class ⊥1{M} ∩ C is closed under coproducts in K, since it is closed under  finite direct sums and direct limits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  We have shown that the class ⊥1{M} ∩ C contains S ∪ T and is closed under  extensions, kernels of epimorphisms, coproducts, and direct limits in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Hence we  can conclude that ⊥1{M} ∩ C = C, so C ⊂ ⊥1{M} and M ∈ D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Now we can prove the assertion of Theorem B(i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Let D• be an acyclic complex in  K with the terms Di ∈ D and the objects of cocycles Bi ∈ B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' So we have short exact  sequences 0 −→ Bi −→ Di −→ Bi+1 −→ 0 in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Taking the product of these short  exact sequences over i ∈ Z, we obtain a sequence  (1)  0 −−→  �  i∈Z Bi −−→  �  i∈Z Di −−→  �  i∈Z Bi −−→ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  In order to show that (1) is exact, we apply [23, Lemma 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' By assumption, the  class S∪T contains a set of generators of the Grothendieck category K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' So there exists  a family of objects (Gξ)ξ∈Ξ in S ∪ T together with an epimorphism G = �  ξ∈Ξ Gξ −→  �  i∈Z Bi in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' It remains to show that Ext1  K(G, Bi) = 0 for every i ∈ Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  7  By [10, Corollary 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='3] or [11, Corollary A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='2], it suffices to check that Ext1  K(Gξ, Bi) =  0 for every i ∈ Z and ξ ∈ Ξ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' There are two cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' If Gξ ∈ S, then it remains to recall  that Bi ∈ B = S⊥1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' If Gξ ∈ T, then Gξ ∈ C and the projective dimension of Gξ in  K is finite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' From the short exact sequences 0 −→ Bj −→ Dj −→ Bj+1 −→ 0 we get  Ext1  K(Gξ, Bi) ≃ Ext2  K(Gξ, Bi−1) ≃ Ext3  K(Gξ, Bi−2) ≃ · · · = 0, since Extn  K(Gξ, Dj) = 0  for all j ∈ Z and n ≥ 1 as explained above (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' [23, proof of Proposition 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='5]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' So [23,  Lemma 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='4] tells that the short sequence (1) is exact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Applying [10, Corollary 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='3] or [11, Corollary A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='2] again, we see that both the  classes B and D are closed under infinite products in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Hence �  i∈Z Bi ∈ B and  �  i∈Z Di ∈ D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' So �  i∈Z Bi is an D-periodic object in B, and it follows that �  i∈Z Bi ∈  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Finally, the class D is closed under direct summands in K, hence Bi ∈ D for all  i ∈ Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  □  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Generalized Flat/Projective and Fp-projective Periodicity  The aim of this section is to prove Theorem 0(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' It is restated below as Theo-  rem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='10(a) and Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' The argument follows the ideas of the proof of [4,  Theorems 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='7–0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='8 or Corollaries 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='7–4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' The result is module-theoretic, but the  proof has a category-theoretic flavor in that the approach of [4] needs to be applied  within the class C viewed as an exact subcategory C ⊂ Mod–R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Let K be an exact category (in Quillen’s sense).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' We suggest the survey paper [8]  as a general reference source on exact categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' The definition of a (hereditary)  cotorsion pair (A, B) in K was already given in the beginning of Section 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  The  intersection of the two classes A ∩ B ⊂ K is called the kernel of a cotorsion pair  (A, B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Let us define the important concept of a complete cotorsion pair.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  A cotorsion pair (A, B) in K is said to be complete if for every object K ∈ K there  exist (admissible) short exact sequences in K of the form  0 −−→ B′ −−→ A −−→ K −−→ 0  (2)  0 −−→ K −−→ B −−→ A′ −−→ 0  (3)  with A, A′ ∈ A and B, B′ ∈ B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  The sequence (2) is called a special precover  sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' The sequence (3) is called a special preenvelope sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Collectively, the  sequences (2–3) are referred to as the approximation sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Let E ⊂ K be a full subcategory closed under extensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Then we endow E with the  exact category structure inherited from the exact category structure of K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' The short  exact sequences in the inherited exact structure on E are the short exact sequences  in K with the terms belonging to E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Let (C, D) be a complete cotorsion pair in an exact category K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Then  the exact category C (with the exact structure inherited from K) has enough injective  objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' The class of all injective objects in C is precisely the kernel C ∩ D of the  cotorsion pair (C, D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Dually, the exact category D has enough projective objects, and  the kernel C ∩ D is precisely the class of all projectives in D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  8  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' The proof is left to the reader.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  □  Let K be an exact category and E ⊂ K be a full subcategory closed under exten-  sions, endowed with the inherited exact category structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Let (A, B) be a complete  cotorsion pair in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' We will say that the cotorsion pair (A, B) restricts to (a complete  cotorsion pair in) the exact subcategory E if the pair of classes (E ∩ A, E ∩ B) is a  complete cotorsion pair in E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Let (A, B) be a complete cotorsion pair in an exact category K, and  let E ⊂ K be a full subcategory closed under extensions and kernels of admissible  epimorphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Assume that A ⊂ E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Then  (a) the cotorsion pair (A, B) restricts to E, so (A, E ∩ B) is a complete cotorsion  pair in E;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  (b) if the cotorsion pair (A, B) is hereditary in K, then the restricted cotorsion pair  (A, E ∩ B) is hereditary in E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' This is fairly standard and easy to prove.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' The details can be found, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=',  in [20, Lemmas 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='5(a) and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  □  Given an additive category K, we denote by C(K) the additive category of com-  plexes in K (with the usual morphisms of complexes) and by H(K) the triangulated  homotopy category of complexes in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' So the morphisms in H(K) are the cochain  homotopy classes of morphisms in C(K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' When K is an exact category, the category  C(K) is endowed with the exact category structure in which a short sequence of com-  plexes is exact if and only if it is exact at every degree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' We denote by K• �−→ K•[n]  the functor of grading shift on the complexes;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' so K•[n]i = Kn+i for all n, i ∈ Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Let K be an exact category, and let A• and B• be two complexes in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Assume that Ext1  K(An, Bn) = 0 for every n ∈ Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Then there is a natural isomorphism  of abelian groups  Ext1  C(K)(A•, B•) ≃ HomH(K)(A•, B•[1]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' This is also standard and well-known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' More generally, for any two complexes  A• and B• in K, the subgroup of termwise split extensions 0 −→ B• −→ C• −→  A• −→ 0 in Ext1  K(A•, B•) is naturally isomorphic to the group of morphisms A• −→  B• in the homotopy category H(K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' We refer to [4, Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='6] for the details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  □  At this point, let us specialize our discussion to Grothendieck abelian categories K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Let F ∈ K be an object and α be an ordinal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' A family of subobjects (Fβ ⊂ F)0≤β≤α  is said to be an α-indexed filtration on F if the following conditions are satisfied:  F0 = 0 and Fα = F;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Fγ ⊂ Fβ for all 0 ≤ γ ≤ β ≤ α;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Fβ = �  γ<β Fγ for all limit ordinals β ≤ α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  An object F ∈ K endowed with an ordinal-indexed filtration (Fβ)0≤β≤α is said to  be filtered by the quotient objects Sβ = Fβ+1/Fβ,  0 ≤ β < α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' In an alternative  terminology, the object F is called a transfinitely iterated extension (in the sense of  the direct limit) of the objects (Sβ)0≤β<α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  9  Given a class of objects S ⊂ K, the class of all objects in K filtered by (objects  isomorphic to) objects from S is denoted by Fil(S) ⊂ K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' A class of objects F ⊂ K is  said to be deconstructible if there exists a set of objects S ⊂ K such that F = Fil(S).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  It is easy to see that any deconstructible class (in the sense of this definition) is closed  under transfinitely iterated extensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  The following result is known as the Eklof lemma [16, Lemma 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' For any class of objects B ⊂ K, the class ⊥1B is closed under trans-  finitely iterated exensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' In other words, Fil(⊥1B) = ⊥1B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' This assertion, properly understood, holds in any exact category K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' See the  references in [4, Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='1] (and the general formulation, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=', in [23, Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' ]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  □  We refer to the book [1, Definition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='17 and Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='20] for the definition of  a locally κ-presentable category (for a regular cardinal κ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' We will have a detailed  discussion of locally finitely presentable abelian categories (that is, the case of the  countable cardinal κ = ℵ0) below in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Any Grothendieck abelian category  is locally presentable, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=', locally presentable for some regular cardinal κ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  The next theorem is goes back to Eklof and Trlifaj [16, Theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='11 and Corol-  lary 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' For any class of objects F ⊂ K, we denote by F⊕ ⊂ K the class of all direct  summands of objects from F in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Let K be a Grothendieck category and (A, B) be the cotorsion pair  generated by a set of objects S ⊂ K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Then  (a) If the class A is generating in K, then the cotorsion pair (A, B) is complete.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  (b) If the class Fil(S) is generating in K, then A = Fil(S)⊕.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' This result, properly stated, holds in any locally presentable abelian cate-  gory K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' See [4, Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='2] for a discussion with references.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  □  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Let κ be a regular cardinal and K be a locally κ-presentable  Grothendieck category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Let S ⊂ K be a class of κ-presentable objects closed under  transfinitely iterated extensions of families of objects of cardinality < κ (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=',  indexed by ordinals α < κ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Let A• ∈ C(Fil(S)) be a complex in K whose terms are  S-filtered objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Then the complex A•, viewed as an object of the abelian category  of complexes C(K), is filtered by bounded below complexes whose terms belong to S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' This is [27, (proof of) Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' The argument is based on the Hill  lemma [27, Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  □  In addition to the abelian exact structure on the module category K = Mod–R, we  are interested in the pure exact structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' The definition of the pure exact structure  on Mod–R was already given in Section 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' A complex in Mod–R is said to be pure  acyclic (or pure exact) if it is acyclic in the pure exact structure, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=', can be obtained  by splicing pure short exact sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' The following result due to Neeman [19] and  ˇSt’ov´ıˇcek [28] is a stronger version of the pure pure-projective periodicity theorem  (item (2) or (2c) on the list of Section 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  10  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Let R be an associative ring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Let P • be a complex of pure-projective  R-modules, and let X• be a pure acyclic complex of R-modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Then any morphism  of complexes of R-modules P • −→ X• is homotopic to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' This was first stated in [28, Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='4] based on [19, Theorem 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' We  refer to the paper [3, Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='1] for a generalization, and to [4, Section 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='2 and  proof of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='3] for a discussion with some details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  □  Now let S be a class of finitely presented R-modules closed under finite direct sums  and containing the free R-module R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Put C = lim  −→ S ⊂ Mod–R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' The full subcategory C = lim  −→ S is closed under pure extensions (as well  as pure submodules and pure epimorphic images) in Mod–R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' In the exact category  structure on C inherited from the pure exact structure on Mod–R, a short sequence  0 −→ K −→ L −→ M −→ 0 is exact if and only if the short sequence of abelian  groups 0 −→ HomR(S, K) −→ HomR(S, L) −→ HomR(S, M) −→ 0 is exact for  every module S ∈ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' The first assertion is the result of [18, Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' The second assertion  claims that a short sequence 0 −→ K −→ L −→ M −→ 0 with K, L, M ∈ C  is pure exact in Mod–R if and only if the functor HomR(S, −) takes it to a short  exact sequence for every S ∈ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' The point is that any morphism T −→ M from a  finitely presented R-module T into the module M ∈ C = lim  −→ S factorizes through  some module S ∈ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' So if every morphism S −→ M lift to a morphism S −→ L,  then also every morphism T −→ M lifts to a morphism T −→ L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  □  The next lemma tells that modules from the class B∩C are “absolutely pure within  the exact category C”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' In the notation of Theorem 0, let 0 −→ B −→ L −→ C −→ 0 be a  short exact sequence in Mod–R with the terms B, L, C ∈ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Assume that the module  B belongs to the class B ∩ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Then the short exact sequence 0 −→ B −→ L −→  C −→ 0 is pure in Mod–R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' It is only important that C ∈ C and B ∈ B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' By Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='8, it suffices to  check that any morphism S −→ C with S ∈ S lifts to a morphism S −→ L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' This  holds because B ∈ B = S⊥1 ⊂ Mod–R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  □  Now we can formulate and prove the main results of the section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Let R be a ring and S be a class of finitely presented R-modules,  containing the free R-module R and closed under extensions and the kernels of epi-  morphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Put B = S⊥1, A = ⊥1B, C = lim  −→ S, and D = C⊥1 ⊂ Mod–R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Then  (a) in any acyclic complex of modules from A with the modules of cocycles belonging  to C, the modules of cocycles actually belong to A;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  (b) let A• be a complex in Mod–R whose terms belong to A, and let X• be an  acyclic complex in Mod–R whose terms belong to B ∩ C and the modules of cocycles  also belong to B ∩ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Then any morphism of complexes of modules A• −→ X• is  homotopic to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  11  Proof of Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='10(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' By the Eklof–Trlifaj theorem (Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='5(b)), we have  A = Fil(S)⊕.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Without loss of generality we can assume that the terms of the complex  A• belong to Fil(S).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Then, by Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='6 (applied in the case of the category  K = Mod–R and the cardinal κ = ℵ0), the complex A• is filtered by (bounded below)  complexes with the terms belonging to S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  By Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='3, for any complex A• with the terms in A and any complex B• with  the terms in B we have an isomorphism of abelian groups  Ext1  C(Mod–R)(A•, B•[−1]) ≃ HomH(Mod–R)(A•, B•).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  So, instead of showing that HomH(Mod–R)(A•, X•) = 0 as desired in the theorem,  it suffices to prove that Ext1  C(Mod–R)(A•, X•[−1]) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' In view of the Eklof lemma  (Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='4) applied in the abelian category K = C(Mod–R), the question reduces  to showing that Ext1  C(Mod–R)(S•, X•[−1]) = 0 for any complex S• with the terms  belonging to S and any complex X• as in the theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Using Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='3 again,  we conclude that it suffices to show that any morphism of complexes S• −→ X• is  homotopic to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Finally, we observe that all finitely presented R-modules are pure-projective (by  the definitions), while any acyclic complex of modules with the modules of cocycles  in B∩C is pure acyclic (by Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Thus any morphism of complexes S• −→ X•  is homotopic to zero by the Neeman–ˇSt’ov´ıˇcek theorem (Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  □  Proof of Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='10(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' It is clear that in the assumptions of the theorem all the  modules from S have to be strongly finitely presented (FP∞).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Thus [2, Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='3  and Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='4] or [16, Theorem 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='40, Corollary 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='42, and Theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='19] are  applicable, telling that (C, D) is a complete cotorsion pair in Mod–R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' The cotorsion  pair (A, B) is complete in Mod–R by the Eklof–Trlifaj theorem (Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='5(a)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Both the cotorsion pairs (A, B) and (C, D) are hereditary, as it was explained in  the proof of Theorem 0(b) in Section 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Applying Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='2 to the abelian category  K = Mod–R and the full subcategory E = C, we conclude that (A, B ∩ C) is a  hereditary complete cotorsion pair in the exact category C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='1 tells that  there are enough injective objects in the exact category C, and the class of such  injective objects coincides with the intersection C ∩ D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Let A• be an acyclic complex of modules from A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Then one can easily see that  the modules of cocycles of A• belong to A if and only if the complex HomR(A•, B)  is acyclic for any module B ∈ B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' This holds because (A, B) is a cotorsion pair in  Mod–R (so A = ⊥1B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' We will use a version of this observation made within the  exact category C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  So let A• be an acyclic complex of modules from A with the modules of cocycles  belonging to C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Then we observe that the modules of cocycles of A• belong to A if  and only if the complex HomR(A•, B) is acyclic for any module B ∈ B ∩ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' This  holds because (A, B ∩ C) is a cotorsion pair in C, so A = C ∩ ⊥1(B ∩ C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Now let D• be an injective resolution of the object B in the exact category C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' So  we have B ∈ B ∩ C by assumption, and 0 −→ B −→ D0 −→ D1 −→ D2 −→ · · ·  is an acyclic complex in Mod–R with the modules Dn ∈ C ∩ D and the modules of  12  cocycles belonging to C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' We observe that the modules of cocycles of the complex D•  actually belong to B ∩ C, because D ⊂ B and the class B is closed under cokernels  of monomorphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Essentially, this is a restatement of the claim that the cotorsion  pair (A, B) is hereditary in Mod–R, or more specifically, that the cotorsion pair (A,  B ∩ C) is hereditary in C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Denote by X• the acyclic complex (B → D•).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Then the complex of abelian groups  HomR(A•, X•) is acyclic by Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='10(b) (which we have proved above).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' This  holds because A• is a complex with the terms in A, while X• is an acyclic complex  with the terms in B ∩ C and the modules of cocycles in B ∩ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  On the other hand, the complex of abelian groups HomR(A•, D•) is acyclic as  well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' This holds quite generally for any acyclic complex A• and any bounded below  complex of injective objects D• in any exact category C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Notice that in the situation  at hand the complex of modules A• is acyclic in the exact category C, as its modules  of cocycles belong to C by assumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Since both the complexes HomR(A•, X•) and HomR(A•, D•) are acyclic, and the  complex X• has the form X• = (B → D•), we can finally conclude that the complex  of abelian groups HomR(A•, B) is acyclic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  □  Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Let R be a ring and S be a class of finitely presented R-modules,  containing the free R-module R and closed under extensions and the kernels of epi-  morphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Put A = ⊥1(C⊥1) and C = lim  −→ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Then, for any short exact sequence (∗)  as in Section 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='0 with modules L ∈ A and M ∈ C, one has M ∈ A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' In other words,  any A-periodic module belonging to C actually belongs to A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' This is a corollary of Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='10(a), provable by splicing up a doubly un-  bounded sequence of short exact sequences (∗) and applying Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='10(a) to the  resulting doubly unbounded complex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' (Cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' [13, Proposition 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=')  □  Proof of Theorem 0(a) from Section 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' The first assertion of Theorem 0(a) is pro-  vided by Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='11, and the second one by Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='10(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  □  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Direct Limit Closures of Classes of Finitely Presentables  The aim of this section is to prove Theorem B(ii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' It is restated below as Proposi-  tion 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  In this section we work with locally finitely presentable abelian categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  We  suggest the book [1] as a general reference source on nonadditive locally (finitely)  presentable and (finitely) accessible categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  The definition of a locally finitely presentable category can be found in [1, Def-  inition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='9 and Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='11] (it is helpful to keep in mind that in abelian cat-  egories the notions of a generator and a strong generator coincide).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  All locally  finitely presentable abelian categories have exact direct limit functors, so they are  Grothendieck [1, Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  The abelian category of modules over an ar-  bitrary ring K = Mod–R is an important example of a locally finitely presentable  abelian category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  13  Finitely accessible categories [1, Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='1 and Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='2(1)] form a wider  class than the locally finitely presentable ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  The theory of finitely accessible  additive categories goes back to the paper [18, Section 2] (where they were not defined  yet).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Subsequently they were studied in the papers [12, 17] under the name of “locally  finitely presented” additive categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  We suggest [22, Sections 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='1–8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='2] as an additional reference source on locally finitely  presentable abelian categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Locally finitely generated categories also form a wider class than the locally finitely  presentable ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  We refer to [1, Section 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='E] for a general discussion of locally  generated (nonadditive) categories and to [21, Corollary 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='6] for a very general form  of the assertion that any locally finitely generated abelian category is Grothendieck.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  A good reference source on locally finitely generated Grothendieck categories and  finitely generated/finitely presentable objects in them is [26, §V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  The following definitions are very general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Let K be a category with direct limits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  An object S ∈ K is said to be finitely presentable if the functor HomK(P, −): K −→  Sets preserves direct limits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' An object S is said to be finitely generated if the same  functor preserves the direct limits of diagrams of monomorphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  An abelian category K with set-indexed coproducts is said to be locally finitely  generated if it has a set of generators consisting of finitely generated objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' In  particular, the category K is locally finitely presentable if it has a set of generators  consisting of finitely presentable objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Given a locally finitely presentable abelian category K, we denote by Kfp ⊂ K  the full subcategory of finitely presentable objects in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' The full subcategory Kfp is  closed under cokernels [1, Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='3] and extensions [22, Lemma 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='1] in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Sim-  ilarly, the full subcategory of finitely generated objects in a locally finitely generated  abelian category K is closed under extensions and quotients [26, Lemma V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='1 and  Proposition V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Let K be a locally finitely presentable abelian category and S ⊂ Kfp  be a class of finitely presentable objects closed under finite direct sums.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Then the class  of objects lim  −→ S ⊂ K is closed under coproducts and direct limits in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' An object L ∈ K  belongs to lim  −→ S if and only if, for any object T ∈ Kfp, any morphism T −→ L in K  factorizes through an object from S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' This is [18, Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='1], [12, Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='1], or [17, Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  □  Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Let K be a locally finitely presentable abelian category and S ⊂ Kfp  be a class of finitely presentable objects closed under finite direct sums.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Let (Hi)i∈I be  a direct system of objects Hi ∈ lim  −→ S, indexed by a directed poset I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Then the kernel  of the natural epimorphism  (4)  �  i∈I Hi −−→ lim  −→i∈I Hi  belongs to lim  −→ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' One can argue from purity considerations, observing that the epimorphism (4)  is pure (in the sense of the definition from [12, Section 3], [28, Section 4] reproduced  14  in [4, Sections 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='4 and 2]), and the class lim  −→ S is closed under pure subobjects by the  category-theoretic version of [18, Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Alternatively, one can notice that  the kernel of (4) is a direct limit of coproducts of copies of the objects Hi, following [5,  proof of Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='1];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' then it remains to refer to Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  □  The following definitions appeared in the papers [15, 7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Let K be a Grothendieck  category and n ≥ 1 be an integer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' An object S ∈ K is said to be of type FPn if the  functors Exti  K(S, −): K −→ Ab preserve direct limits for all 0 ≤ i ≤ n − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' So the  objects of type FP1 are, by the definition, the finitely presentable ones, while the  objects of type FPn for n ≥ 2 form more narrow classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  An object S ∈ K is said to be of type FP0 if it is finitely generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' An object S  is said to be of type FP∞ if it is of type FPn for every n ≥ 0, that is, in other words,  the functors Exti  K(S, −): K −→ Ab preserve direct limits for all i ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  We use the term strongly finitely presentable object as a synonym for “type FP∞”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  In the case of the module category K = Mod–R, these definitions are equivalent to  the ones from Section 1 (see [7, Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='14]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Closure properties of the classes of objects of type FPn and FP∞ in locally finitely  presentable abelian categories K are listed in [15, Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='3] and [7, Proposi-  tion 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' In particular, [7, Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='8(1)] tells that the class of all objects of  type FPn is closed under extensions in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Let K be a locally finitely presentable abelian category and S be a  class of (some) objects of type FP2 closed under extensions in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Then the class of  objects lim  −→ S is also closed under extensions in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' We follow the proof of [22, Proposition 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Given an abelian category K and  two classes of objects X, Y ⊂ K, denote by X∗Y the class of all objects Z ∈ K for which  there exists a short exact sequence 0 −→ X −→ Z −→ Y −→ 0 in K with X ∈ X  and Y ∈ Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' In the situation at hand, we need to prove that lim  −→ S∗ lim  −→ S ⊂ lim  −→ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' For  this purpose, we claim that the three inclusions  (5)  lim  −→ T ∗ lim  −→ T ⊂ lim  −→(lim  −→ T ∗ T) ⊂ lim  −→ lim  −→(T ∗ T) ⊂ lim  −→(T ∗ T)  hold for any class of FP2 objects T closed under finite direct sums in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  More generally, it is explained in [22, first part of the proof of Proposition 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='4] that  the inclusion X ∗ lim  −→ Y ⊂ lim  −→(X ∗ Y) holds for any two classes of objects X and Y in  a Grothendieck category K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' This takes care of the leftmost inclusion in (5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Furthermore, any FP2 object is, by definition, finitely presentable;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' and the class  of all finitely presentable objects is closed under extensions in K by [22, Lemma 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  So we certainly have T ∗ T ⊂ Kfp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' It is clear that the class T ∗ T is closed under finite  direct sums whenever the class T is.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' For any class of finitely presentable objects S  closed under finite direct sums in K, we have lim  −→ lim  −→ S = lim  −→ S by Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  This explains the rightmost inclusion in (5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Finally, the middle inclusion in (5) is provable similarly to the proof in [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Let  K be a Grothendieck abelian category, X ⊂ K be a class of objects, and T ⊂ K be a  class of objects such that the functor Ext1  K(T, −): K −→ Ab preserves direct limits  15  for all objects T ∈ T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' We claim that the inclusion (lim  −→ X) ∗ T ⊂ lim  −→(X ∗ T) holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  The argument from [22, second part of the proof of Proposition 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='4] applies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  □  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Let K be a Grothendieck category and S ⊂ K be a class of finitely  generated objects containing a set of generators of K and closed under finite direct  sums and kernels of epimorphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Then all the objects from S are strongly finitely  presentable (type FP∞).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' First of all, the category K is locally finitely generated, since it has a set of  finitely generated generators by assumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' In this context, it is explained in [26,  Proposition V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='4] that an object S ∈ K is finitely presentable if and only if the  kernel of any epimorphism onto S from any finitely generated object T ∈ K is finitely  generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Following the argument in [26], based on [26, Lemma V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='3], one can see  that it suffices to let T range over the quotient objects of finite direct sums of objects  from a chosen set G of finitely generated generators of K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Furthermore, the passage  to the quotients holds automatically, and so it suffices to let T range over the finite  direct sums of objects from G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' In the situation at hand, choosing G ⊂ S, we conclude  that all the objects in S are finitely presentable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  The rest of the proof is similar to [22, proof of Lemma 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' For any two objects  X and Y in any abelian category K, the abelian group Extn  K(X, Y ) can be computed  as the filtered direct limit of cohomology groups Hn HomK(R•, Y ), taken over the  (large) filtered category of exact complexes · · · −→ R2 −→ R1 −→ R0 −→ X −→ 0  in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Here the morphisms in the category of such arbitrary resolutions R• −→ X are  the usual morphisms of complexes acting by the identity maps on the object X and  viewed up to cochain homotopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  In the situation at hand, for any object S ∈ S, the full subcategory of resolutions  T• −→ S consisting of objects Ti ∈ S is cofinal in the category of all resolutions  R• −→ S with Ri ∈ K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' So one can compute the group Extn  K(S, Y ) as the filtered  direct limit of Hn HomK(T•, Y ) taken over all the resolutions T• −→ S with Ti ∈ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Now, since all the objects of S are finitely presentable, the functor HomK(T•, −) takes  direct limits in K to direct limits of complexes of abelian groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' It remains to recall  that the functors of cohomology of a complex of abelian groups preserve direct limits,  and direct limits commute with direct limits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  □  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Let K be a Grothendieck category and S ⊂ K be a class of finitely  generated objects containing a set of generators of K and closed under extensions  and kernels of epimorphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Then the class of objects lim  −→ S ⊂ K is closed under  coproducts, direct limits, extensions, and kernels of epimorphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' By Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='4, all objects in S are finitely presentable, and in fact even  strongly finitely presentable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' As the class S contains a set of generators for K, it  follows that the category K is locally finitely presentable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  So Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='1 is  applicable, telling that the class lim  −→ S is closed under coproducts and direct limits  in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Furthermore, Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='3 tells that the class lim  −→ S is closed under extensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  It remains to prove its closedness under kernels of epimorphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  16  Let C −→ D be an epimorphism in K between two objects C, D ∈ lim  −→ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Then  there exists a direct system (Si)i∈I, indexed by a directed poset I, such that Si ∈ S  for all i ∈ I and D = lim  −→i∈I Si.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' For every i ∈ I, consider the pullback diagram  (6)  Ci  � �  �  Si  �  C  � � D  Here Ci is the pullback of the given epimorphism C −→ D and the natural morphism  to the direct limit Si −→ D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' As the index i ∈ I varies, the upper lines of (6) form a  direct system of (epi)morphisms in K, whose direct limit is the epimorphism C −→ D  in the lower line of the diagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Choose a set of generators G ⊂ S of the category K, and put H = �  G∈G G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' For  every index i ∈ I, denote by Ξi the underlying set of the image of the abelian group  map HomK(H, Ci) −→ HomK(H, Si) induced by the morphism Ci −→ Si.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Then, for  every pair of indices i < j ∈ I, the transition morphism Si −→ Sj induces a map of  sets Ξi −→ Ξj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' So we obtain a direct system of sets (Ξi)i∈I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  For any object K ∈ K and any set Ξ, let us denote by K(Ξ) the coproduct of Ξ  copies of K in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Notice that the assigment (K, Ξ) �−→ K(Ξ) is a covariant functor  K×Sets −→ K (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=', a covariant functor of both the arguments K ∈ K and Ξ ∈ Sets).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  For every index i ∈ I we have a natural morphism hi : H(Ξi) −→ Si in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Since H  is a generator of the category K, and the morphism Ci −→ Si is an epimorphism, the  morphism hi is an epimorphism in K as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' As the index i varies, the morphisms hi  form a direct system (hi)i∈I in the category of morphisms in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Let us show that the kernel Li of the morphism hi belongs to lim  −→ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' The object  H(Ξi) is the coproduct of copies of all the objects G ∈ G, each of them taken with  the multiplicity Ξi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Since the object Si is finitely generated, there exists a finite  subcoproduct in this coproduct mapping epimorphically onto Si.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' So we have a direct  sum decomposition H(Ξi) = H′  i ⊕ H′′  i , where H′  i is a finite direct sum of objects from  G and the restriction of hi onto H′  i is an epimorphism h′  i : H′  i −→ Si.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Denote by Ki  the kernel of h′  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' We have constructed a pushout diagram  Ki �  �  �  �  H′  i  � �  �  �  Si  Li �  �  ��  Hi  � �  ��  Si  H′′  i  H′′  i  Now H′  i ∈ S, since the class S is closed under finite direct sums and G ⊂ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Hence  Ki ∈ S, as the class S is closed under kernels of epimorphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' On the other hand,  H′′  i ∈ lim  −→ S, since the class lim  −→ S is closed under coproducts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' As we already know  17  that the class lim  −→ S is closed under extensions, we can conclude from the short exact  sequence 0 −→ Ki −→ Li −→ H′′  i −→ 0 that Li ∈ lim  −→ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Passing to the direct limit of hi over i ∈ I, we see that the kernel of the epimorphism  lim  −→i∈I H(Ξi) −−→ lim  −→i∈I Si = D  belongs to lim  −→ lim  −→ S = lim  −→ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' We already know from Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='2 that the kernel of  the epimorphism (4) (for Hi = H(Ξi)) belongs to lim  −→ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Since the class lim  −→ S is closed  under extensions, it follows that the kernel M of the composition of epimorphisms  H =  �  i∈I H(Ξi) −−→ lim  −→i∈I H(Ξi) −−→ D  belongs to lim  −→ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  The final observation is that the epimorphism H = �  i∈I H(Ξi) −→ D factorizes  through the epimorphism C −→ D, essentially due to the construction of the sets Ξi  in the beginning of this proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Now we consider the pullback diagram  N�  �  N�  �  M �  � X  � �  ��  C  ��  M �  � H  � � D  where X is the pullback of the pair of epimorphisms C −→ D and H −→ D, while N  is the kernel of the morphism C −→ D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Since the epimorphism H −→ D factorizes  through the epimorphism C −→ D, the short exact sequence 0 −→ N −→ X −→  H −→ 0 splits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' We have M ∈ lim  −→ S and C ∈ lim  −→ S, so it follows from the short exact  sequence 0 −→ M −→ X −→ C −→ 0 that X ∈ lim  −→ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' It remains to notice that  the class lim  −→ S is closed under direct summands (since it is closed under direct limits)  in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' So N ∈ lim  −→ S as N is a direct summand of X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  □  We conclude the section by presenting a formal proof of Theorem B(ii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Proof of Theorem B(ii) from from Section 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Applying Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='5 to the class  S ∪ T ⊂ K, we see that the class lim  −→(S ∪ T) is closed under coproducts, direct limits,  extensions, and kernels of epimorphisms in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' So lim  −→(S ∪ T) is precisely the class C  as defined in the formulation of Theorem B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  □  References  [1] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Ad´amek, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Rosick´y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Locally presentable and accessible categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' London Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Society  Lecture Note Series 189, Cambridge University Press, 1994.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  [2] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Angeleri H¨ugel, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Trlifaj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Direct limits of modules of finite projective dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Rings, mod-  ules, algebras, and abelian groups, Proceedings of the Algebra Conference in Venezia, Lecture  Notes in Pure and Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' 236, Marcel Dekker, New York–Basel, 2004, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' 27–44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  18  [3] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Bazzoni, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Cort´es-Izurdiaga, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Estrada.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Periodic modules and acyclic complexes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Algebras  and Represent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Theory 23, #5, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' 1861–1883, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' arXiv:1704.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='06672 [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='RA]  [4] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Bazzoni,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Hrbek,  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Positselski.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Fp-projective  periodicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Electronic  preprint  arXiv:2212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='02300 [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='CT].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  [5] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Bazzoni, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Positselski, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' ˇSt’ov´ıˇcek.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Projective covers of flat contramodules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Internat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Research Notices 2022, #12, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' 19527–19564, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' arXiv:1911.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='11720 [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='RA]  [6] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Benson, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Goodearl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Periodic flat modules, and flat modules for finite groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Pacific  Journ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' of Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' 196, #1, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' 45–67, 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  [7] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Bravo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Gillespie, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' P´erez.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Locally type FPn and n-coherent categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Electronic  preprint arXiv:1908.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='10987 [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='CT]  [8] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' B¨uhler.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Exact categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Expositiones Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' 28, #1, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' 1–69, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' arXiv:0811.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='1480  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='HO]  [9] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Christensen, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Holm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' The direct limit closure of perfect complexes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Journ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' of Pure and  Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Algebra 219, #3, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' 449–463, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' arXiv:1301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='0731 [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='RA]  [10] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Colpi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Fuller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Tilting objects in abelian categories and quasitilted rings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' of the  Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' 359, #2, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' 741–765, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  [11] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' ˇCoupek, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' ˇSt’ov´ıˇcek.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Cotilting sheaves on Noetherian schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Zeitschrift 296, #1–2,  p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' 275–312, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' arXiv:1707.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='01677 [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='AG]  [12] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Crawley-Boevey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Locally finitely presented additive categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Communicat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' in Algebra 22,  #5, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' 1641–1674, 1994.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  [13] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Estrada, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Fu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Iacob.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Totally acyclic complexes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Journ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' of Algebra 470, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' 300–319,  2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' arXiv:1603.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='03850 [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='AC]  [14] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Garc´ıa Rozas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Covers and envelopes in the category of complexes of modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Chapman  & Hall/CRC Research Notes in Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=', 407, Boca Raton, FL, 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  [15] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Gillespie.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Models for homotopy categories of injectives and Gorenstein injectives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Commu-  nicat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' in Algebra 45, #6, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' 2520–2545, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' arXiv:1502.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='05530 [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='CT]  [16] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' G¨obel, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Trlifaj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Approximations and endomorphism algebras of modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Second Revised  and Extended Edition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' De Gruyter Expositions in Mathematics 41, De Gruyter, Berlin–Boston,  2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  [17] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Krause.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Functors on locally finitely presented additive categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Colloquium Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' 75, #1,  p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' 105–132, 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  [18] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Lenzing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Homological transfer from finitely presented to infinite modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Abelian group  theory (Honolulu, Hawaii), Lecture Notes in Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' 1006, Springer, Berlin, 1983, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' 734–761.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  [19] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Neeman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' The homotopy category of flat modules, and Grothendieck duality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Inventiones  Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' 174, #2, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' 225–308, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  [20] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Positselski.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Local, colocal, and antilocal properties of modules and complexes over commu-  tative rings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Electronic preprint arXiv:2212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='10163 [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='AC].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  [21] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Positselski, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' ˇSt’ov´ıˇcek.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' The tilting-cotilting correspondence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Internat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Research No-  tices 2021, #1, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' 189–274, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' arXiv:1710.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='02230 [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='CT]  [22] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Positselski, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' ˇSt’ov´ıˇcek.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Coderived and contraderived categories of locally presentable abelian  DG-categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Electronic preprint arXiv:2210.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='08237 [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='CT].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  [23] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Positselski, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' ˇSt’ov´ıˇcek.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Flat quasi-coherent sheaves as direct limits, and quasi-coherent  cotorsion periodicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Electronic preprint arXiv:2212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='09639 [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='AG].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  [24] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' ˇSaroch, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' ˇSt’ov´ıˇcek.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Singular compactness and definability for Σ-cotorsion and Gorenstein  modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Selecta Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' (New Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=') 26, #2, Paper No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' 23, 40 pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=', 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' arXiv:1804.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='09080  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='RT]  [25] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Simson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Pure-periodic modules and a structure of pure-projective resolutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Pacific Journ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  of Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' 207, #1, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' 235–256, 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  [26] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Stenstr¨om.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Rings of quotients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' An Introduction to Methods of Ring Theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Die Grundlehren  der Mathematischen Wissenschaften, Band 217.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Springer-Verlag, New York, 1975.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  19  [27] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' ˇSt’ov´ıˇcek.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Deconstructibility and the Hill Lemma in Grothendieck categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Forum Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  25, #1, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' 193–219, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' arXiv:1005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='3251 [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='CT]  [28] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' ˇSt’ov´ıˇcek.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' On purity and applications to coderived and singularity categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content=' Electronic  preprint arXiv:1412.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='1615 [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='CT].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='  Institute of Mathematics, Czech Academy of Sciences, ˇZitn´a 25, 115 67 Praha 1,  Czech Republic  Email address: positselski@math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='cas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
+page_content='cz  20' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNAyT4oBgHgl3EQfzvn1/content/2301.00708v1.pdf'}
diff --git a/s9E2T4oBgHgl3EQf1wgV/vector_store/index.faiss b/s9E2T4oBgHgl3EQf1wgV/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..7db30639d0effaed27feb0bdc0e33f05a27d7fbc
--- /dev/null
+++ b/s9E2T4oBgHgl3EQf1wgV/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:211a69311d1f670fb57c38ed087bcc1d5d2fc2d5f74bdd5de691ea4d6f87ad3e
+size 4522029
diff --git a/sNE0T4oBgHgl3EQfawDH/content/tmp_files/2301.02340v1.pdf.txt b/sNE0T4oBgHgl3EQfawDH/content/tmp_files/2301.02340v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..23434131013ae53d86b83a382d460d7ce45a62ec
--- /dev/null
+++ b/sNE0T4oBgHgl3EQfawDH/content/tmp_files/2301.02340v1.pdf.txt
@@ -0,0 +1,514 @@
+arXiv:2301.02340v1  [physics.acc-ph]  6 Jan 2023
+Wakefield damping in a distributed coupling LINAC
+Evan Ericson,1, 2 Alexej Grudiev,1, ∗ Drew Bertwistle,2, 3 and Mark J. Boland2, 3
+1CERN, European Organization for Nuclear Research, Geneva 1221, Switzerland
+2Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, Canada.
+3Canadian Light Source, Saskatoon, Canada
+(Dated: January 9, 2023)
+The number of cells in a π-mode standing wave (SW) accelerating structure for the Compact
+linear Collider (CLIC) project is limited by mode overlap with nearby modes.
+The distributed
+coupling scheme avoids mode overlap by treating each cell as independent. Designs of cells suitable
+for distributed coupling with strong wakefield damping have not previously been studied. In this
+paper we develop a SW cell to be used in a distributed coupling structure that can satisfy the
+CLIC transverse wakepotential limit. From the middle cell of the CLIC-G* travelling wave (TW)
+structure, a SW cell is designed. The cell is adapted to be suitable for distributed coupling. Its
+wakepotentials in an ideal case of open boundaries are reduced to satisfy the wakepotential threshold.
+An electric boundary is added to the model to simulate total reflection at the distribution network.
+A horizontal coupler cell that connects to the distribution network such that the reflected wakefields
+remain similar to the open boundary case is simulated. A triplet module which takes advantage of
+cell-to-cell coupling to reduce reflected wakepotential is presented.
+I.
+INTRODUCTION
+The main linear accelerator (LINAC) of the CLIC
+project uses accelerating structures to generate high-
+energy particles for particle physics experiments [1]. The
+current LINAC design consists of TW X-band radio fre-
+quency (RF) accelerating structures.
+These structures
+consist of 26 regular accelerating cells and two coupler
+cells.
+The cell irises radii are tapered from 3.15 mm
+to 2.35 mm to maintain a constant loaded gradient of
+100 MV/m. All cells feature waveguides with silicon car-
+bide loads to dissipate power from higher order modes
+(HOM) [2]. Figure 1 shows an example of a TW cell.
+Recent work has shown converting the 2π/3-mode TW
+structure to a π-mode SW structure of equal length gives
+an increase in rf-to-beam efficiency of ∼ 3 % [3]. A SW
+FIG. 1. Accelerating cell from the CLIC-G* TW structure
+for CLIC with quarter symmetry.
+∗ alexej.grudiev@cern.ch
+structure operating in the π-mode is limited to the num-
+ber of cells, N, given by Equation 1.
+�
+Qππ2k
+4
+> N.
+(1)
+For a SW cell based on CLIC-G* cell shape, the max-
+imum number of cells before mode overlap is 9. With
+this many cells, the π-mode is separated from the next
+adjacent mode by
+∆f π
+N,N−1 = fr
+kπ2
+4N 2 = 2 MHz.
+(2)
+Operating a side-coupled structure in the π/2-mode si-
+multaneously increases the number of cells in a structure
+before mode overlap while keeping the shunt impedance
+high.
+A side-coupled geometry is not easily amenable
+to cells with four HOM waveguides.
+Distributed cou-
+pling topologies also allow for a SW structure to in-
+crease the number of cells by treating each cell as in-
+dependent. In this configuration, each accelerating cell
+is connected directly to the power source by a waveg-
+uide which runs parallel to the structure [4, 5]. Because
+the structure does not rely on coupling between cells,
+the cells’ iris aperture can be made small to increase
+the shunt impedance. Distributed coupling schemes can
+also increase high-gradient performance by limiting the
+amount of power flow through the cell irises which are
+prone to RF breakdown events [6, 7]. As the iris aper-
+ture decreases, the effects of wakefields increase [8]. Ex-
+isting designs reduce wakefields by use of detuning such
+that problematic dipole modes add coherently later, ide-
+ally after the end of the bunch train [9]. Detuning can
+provide dipole modes with Qext = 1000 while CLIC re-
+quires modes with Qext ∼ 10 [10, 11]. In this work, we
+present the development of an RF accelerating cell suit-
+able for a distributed coupling structure that satisfies the
+
+2
+CLIC transverse wakefield damping requirement. Section
+II outlines the procedure followed to get a SW cell de-
+sign. The cell is adapted to include a power input and
+then further to reduce the wakepotential of the cell. In
+Section III the reflected wakepotential from a distribu-
+tion network is analyzed and Section IV describes cell
+designs capable of reducing the reflected wakepotentials
+to an acceptable level. The final findings are summarized
+in V.
+II.
+OPEN BOUNDARY WAKES
+The middle cell of the TW structure was chosen as a
+starting point for the design.
+The cell length was ad-
+justed so the π-mode was synchronous with a relativistic
+beam. Parameters sweeps of the iris thickness and el-
+lipticity were performed in CST’s eigenmode solver [12]
+to select an iris shape that minimized the surface elec-
+tric field. Sweeps of the outer wall parameters A0 and
+A2, described in [2], confirmed the values of the TW cell
+also minimized the surface magnetic field in this case.
+The outer wall was adjusted to obtain the operating fre-
+quency. The RF parameters of the resulting cell are listed
+in Table I. An accelerating structure based on this SW
+cell design having the same length as the TW structure
+would have an RF-to-beam efficiency of 31 %.
+TABLE I. RF parameters of SW cell.
+Quantity
+Unit
+Value
+cell outer radius, b
+mm
+8.5638
+iris thickness, d
+mm
+2.6
+iris ellipticity, e
+mm
+2.4
+f0
+GHz
+11.9945
+Q0
+-
+6,927
+R/Q0
+Ω/m
+10,962
+R
+MΩ
+75.93
+Es/Ea
+-
+1.80
+Hs/Ea
+mA/V
+4.67
+Sc/E2
+a
+mA/V
+0.35
+A cell with four HOM waveguides is fed by cell-to-cell
+coupling. To make the cell suitable for a distributed cou-
+pling structure, a coupler cell was generated based on the
+TW coupling cell. The TW coupler cells have only two
+HOM waveguides and therefore the expected wakepoten-
+tial of a structure of repeating coupler cells was higher
+than the four HOM waveguide cell.
+The SW coupler
+cell included only one coupler waveguide and three HOM
+waveguides. The cell was matched to the source by ad-
+justing the cell’s outer radius and the aperture between
+the coupler waveguide and the cell. The x-polarization
+of the wakepotential was found to be lower in amplitude
+than the y-polarization. The evaluated transverse wake-
+potential of the coupler cell wacs above the threshold
+of 6 V(pC · m · mm)−1 [13]. A hybrid cell design with a
+HOM waveguide transition between the coupler waveg-
+FIG. 2.
+Long slot cell geometry with half symmetry. The
+cell is matched by adjusting the cell outer radius and the
+length of the HOM waveguide between the cell and the coupler
+waveguide.
+uide and the cell shown in Figure 2 had a transverse
+wakepotential between the coupler cell and four HOM
+waveguide cell at the second bunch position.
+To decrease the wakepotential below the threshold, two
+approaches were taken. First, the aperture of the HOM
+waveguides were increased. Changing the geometry in
+this way caused the Qext of the dominant dipole mode
+to decrease at the expense of a lower Q0 and a larger
+expected temperature rise on the surface of the cell. The
+cells needed to be tuned for each simulated value. The
+second approach was to increase the HOM waveguide
+widths. The wakepotentials from these sweeps are shown
+in Figure 3. The wakepotential at the second bunch lo-
+cation was more sensitive to changes in w. A value of w
+= 10.7 mm was selected. Both polarization of the trans-
+verse wakepotentials and their impedances are shown in
+Figure 4.
+III.
+REFLECTED WAKES
+To model the effect of a distribution network, par-
+allel waveguide or otherwise, on the wakepotential of
+the structure, an electric boundary condition was placed
+on the coupler waveguide surfaces.
+This represents a
+worst-case-scenario in which all the wakefields extracted
+through the coupler waveguide are reflected back into the
+cell where they may act on following bunches. Figure 5
+shows the geometry simulated to include the effect of
+perfect reflection at the coupler waveguide.
+An example of a reflected wakepotential is shown in
+Figure 6. After the drive bunch passes through the struc-
+ture, the remaining wakefields are extracted through the
+HOM waveguides.
+The fields propagating out of the
+cell through the coupler waveguide encounter the electric
+
+3
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+s (m)
+10−1
+100
+101
+102
+|Wy| (V(pC·m·mm)−1)
+iw (mm)
+8.09
+8.19
+8.29
+8.39
+8.49
+8.59
+8.69
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+s (m)
+10−1
+100
+101
+102
+|Wy| (V(pC·m·mm)−1)
+w (mm)
+10.1
+10.2
+10.3
+10.4
+10.5
+10.6
+10.7
+FIG. 3. Transverse wakepotential envelopes of long slot cell
+with various HOM aperture widths, iw (top) and various
+HOM waveguide widths, w (bottom).
+boundary and are reflected back into the cell. At this
+time, the wakepotential diverges from the open bound-
+ary case, increasing above the wakepotential threshold.
+The position where the reflected wakepotential diverges
+from the open boundary case is determined by the dis-
+tance between the electric boundary and the beam axis.
+We call this distance the offset. The spectrogram of Fig-
+ure 7 shows the mode evolution of the reflected wake-
+potential.
+The 17 and 22 GHz modes of Figure 4 are
+quickly damped. The reflected wakepotential first con-
+sists of modes near 17 GHz. While these modes are being
+damped, modes near 22 GHz arrive. The length of the
+reflected wake is due to the difference in arrival time of
+the two sets of modes and because of the slow damping
+of these modes. Increasing the offset decreased the max-
+imum amplitude of the reflected wakepotential. A larger
+offset accentuated the difference in arrival time causing
+the cell to damp one set of modes at a time. The reflected
+wakepotential duration increased as a result. The modes
+also spread in time due to dispersion in the waveguides.
+The electric boundary, position of the distribution net-
+work relative to the beam, can be adjusted such that
+the reflected wake arrives after the a particular bunch
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+s (m)
+10−1
+100
+101
+102
+|Wx,y| (V(pC·m·mm)−1)
+Wy
+Wx
+0
+20
+40
+f (GHz)
+0
+2000
+4000
+6000
+8000
+Re{Zx,y} (Ω(m·mm)−1)
+Zy
+Zx
+FIG. 4.
+Transverse wakepotentials (top) and impedances
+(bottom) of long slot cell w = 10.7 mm (bottom).
+but because the reflected wakepotential is damped slowly
+and lasts longer than the bunch spacing, the reflected
+wakepotential would be above the threshold at the next
+bunch.
+Increasing the HOM waveguide aperture and
+width, which previously had an effect on the wakepo-
+tential, proved ineffective at reducing the reflected wake-
+potential.
+The strategy of evaluating different iris ge-
+ometries in an attempt to change the mode beating to
+form a minimum at the bunch located in the reflected
+wakepotential wasof unsuccessful.
+IV.
+DESIGNS TO REDUCE REFLECTED
+WAKEFIELDS
+Two configurations were found to reduce the reflected
+wakepotentials to an acceptable level. First, the horizon-
+tal coupler cell design shown in Figure 8 feeds power to
+the cell from a coupler waveguide through an aperture in
+one of the HOM waveguides. The aperture’s dimensions
+and location allow power to enter the cell to establish the
+accelerating field while being sufficiently small that the
+wakefields couple weakly to the coupler waveguide. The
+wakefields are damped in the HOM waveguides instead of
+
+4
+FIG. 5. Model simulated to obtain wakepotential of reflected
+wakefields of the long slot cell using half symmetry. The HOM
+waveguide ports (red) are connected to an open boundary.
+The coupler waveguides are slightly shorter than the HOM
+waveguides and experience an electric boundary. The model
+was parameterized to maintain these boundary conditions as
+the coupler waveguide length was increased.
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+s (m)
+10−1
+100
+101
+102
+|Wy| (V(pC·m·mm)−1)
+150 mm
+Open BC
+FIG. 6. Reflected transverse wakepotential envelopes of long
+slot cell with w = 10.7 mm and offset = 150 mm.
+being reflected at the coupler waveguide. The reflected
+wakepotentials of Figure 9 do not depend strongly on
+the offset meaning the horizontal coupler is transparent
+to the wakefields and a distribution network can be de-
+signed separately.
+A second scheme where modules were formed of cou-
+pler cells and four HOM waveguide cells like the triplet
+shown in Figure 10 also reduced the reflected wakepoten-
+tials below the CLIC threshold. The reflected wakepo-
+tential amplitudes were lowered by reducing the number
+of coupler waveguides from which reflections occur and
+by increasing the number of HOM waveguides that damp
+the wakefields. The module takes advantage of an iris
+size of 2.75 mm, which is large enough to allow for cou-
+pling between cells. Operating a group of modules as a
+10−1
+100
+101
+102
+|Wy| (V(pC·m·mm)−1)
+0
+10000
+Re{Zy} (Ω(m·mm)−1)
+0
+20
+40
+f (GHz)
+0
+0.9
+1.8
+s (m)
+FIG. 7. Evolution of the mode content of the reflected wake-
+potential with offset = 100 mm.
+FIG. 8. Horizontal coupler cell geometry.
+structure reduces the total number of coupler waveguides
+required compared to distributed coupling structure de-
+signs where each cell has a feed to a power source. Figure
+11 shows the reflected wakepotential amplitude decreases
+as the number of four HOM waveguide cells increases.
+The wakepotential of the triplet is below the threshold at
+all bunch positions out to 1 m. The outer radii of the cells
+in the doublet and triplets need to be tuned to achieve a
+flat longitudinal field. A triplet module where the coupler
+cell is a horizontal coupler cell, previously shown to con-
+siderably reduce the reflected wakepotential, combines a
+reduction of feed waveguides and effective mitigation of
+reflected wakefields.
+
+5
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+s (m)
+10−1
+100
+101
+102
+|Wy| (V(pC·m·mm)−1)
+60 mm
+70 mm
+80 mm
+90 mm
+Open BC
+FIG. 9. Reflected transverse wakepotential of horizontal cou-
+pler cell for various offsets.
+FIG. 10. Triplet module based on the long slot cell with half
+symmetry.
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+s (m)
+10−1
+100
+101
+102
+|Wy| (V(pC·m·mm)−1)
+singlet
+doublet
+triplet
+FIG. 11.
+Reflected transverse wakepotentials of structures
+composed of singlets (long slot cell), doublet (one long slot
+and one four HOM waveguide cells) and triplet (one long slot
+and two four HOM waveguide cells).
+V.
+CONCLUSION
+A SW cell applicable to distributed coupling struc-
+tures was developed.
+The HOM waveguide width, w,
+was effective at lowering the wakepotential at the sec-
+ond bunch position. The wakepotentials were found to
+be generally less sensitive to changes in the HOM waveg-
+uide aperture, iw. From the SW cell, two configurations
+were developed capable of supporting 100 MV/m loaded
+gradient and gave transverse wakepotentials below the
+threshold. The wakefields horizontal coupler cell couple
+weakly to the high power waveguide and are kept close to
+open boundary levels. The triplet module increases the
+number of HOM waveguides and decreases the number
+of coupler waveguides from which reflections originate to
+keep the reflected wakepotential low.
+[1] M. Aicheler, P. Burrows, M. Draper, and T. Garvey, A
+Multi-TeV Linear Collider Based on CLIC Technology,
+Tech. Rep. (2012).
+[2] H. Zha and A. Grudiev, Design and optimization of Com-
+pact Linear Collider main linac accelerating structure,
+Physical Review Accelerators and Beams 19, 1 (2016).
+[3] V.
+Khan,
+A
+Standing
+Wave
+Structure
+Possibility
+For CLIC Main LINACs, in International Workshop
+on Breakdown Science and High Gradient Technology
+HG2013, Trieste, Italy (2013).
+[4] S. Tantawi, M. Nasr, Z. Li, C. Limborg, and P. Borchard,
+Design and demonstration of a distributed-coupling lin-
+ear accelerator structure, Physical Review Accelerators
+and Beams 23, 92001 (2020).
+[5] Y. Jiang, J. Shi, H. Zha, J. Liu, X. Lin, and H. Chen,
+Analysis and design of parallel-coupled high-gradient
+structure for ultrashort input power pulses, Physical Re-
+view Accelerators and Beams 24, 112002 (2021).
+[6] V. A. Dolgashev and S. G. Tantawi, Study of Basic
+RF Breakdown Phenomena in Hight Gradient Vacuum
+Structures, in Proceedings of Linear Accelerator Confer-
+ence LINAC2010, Tsukuba, Japan (2010) pp. 1043–1047.
+[7] E. I. Simakov, V. A. Dolgashev, and S. G. Tantawi, Ad-
+vances in high gradient normal conducting accelerator
+structures, Nuclear Instruments and Methods in Physics
+Research, Section A: Accelerators, Spectrometers, Detec-
+tors and Associated Equipment 907, 221 (2018).
+[8] K. L. F. Bane, Short range dipole wakefields in acceler-
+ating structures for the NLC, 94309, 1 (2003).
+[9] R. A. Rimmer, Extraction and Absorption of Higher
+Order Modes in Room Temperature Accelerators, in
+Worskhop on Microwave-Absorbing Materials for Ac-
+celerators, Newport News, VA, February 22-24, 1993
+(1993).
+[10] K. L. Bane, T. L. Barklow, M. Breidenbach, C. P.
+Burkhart, E. A. Fauve, A. R. Gold, V. Heloin, Z. Li,
+
+6
+E. A. Nanni, M. Nasr, M. Oriunno, J. M. Paterson, M. E.
+Peskin, T. O. Raubenheimer, and S. G. Tantawi, An Ad-
+vanced NCRF Linac Concept for a High Energy e+e−
+Linear Collider, Tech. Rep. (2018) arXiv:1807.10195.
+[11] A. Grudiev and W. Wuensch, Design of the CLIC Main
+Linac Accelerating Structure for CLIC Conceptual De-
+sign Report, in Proceedings of Linear Accelerator Con-
+ference LINAC2010 (2010).
+[12] Computer Simulation Technology, CST Studio Suite.
+[13] D. Schulte, Multi-Bunch Calculations in the CLIC Main
+Linac, in Proceedings, 23rd Conference, PAC’09, Van-
+couver, Canada, May 4-8, 2009 (2010).
+
diff --git a/sNE0T4oBgHgl3EQfawDH/content/tmp_files/load_file.txt b/sNE0T4oBgHgl3EQfawDH/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fd036cc76e34de5208129f9f2e88b74e57cd67a8
--- /dev/null
+++ b/sNE0T4oBgHgl3EQfawDH/content/tmp_files/load_file.txt
@@ -0,0 +1,296 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf,len=295
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='02340v1  [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='acc-ph]  6 Jan 2023  Wakefield damping in a distributed coupling LINAC  Evan Ericson,1, 2 Alexej Grudiev,1, ∗ Drew Bertwistle,2, 3 and Mark J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Boland2, 3  1CERN, European Organization for Nuclear Research, Geneva 1221, Switzerland  2Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, Canada.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  3Canadian Light Source, Saskatoon, Canada  (Dated: January 9, 2023)  The number of cells in a π-mode standing wave (SW) accelerating structure for the Compact  linear Collider (CLIC) project is limited by mode overlap with nearby modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  The distributed  coupling scheme avoids mode overlap by treating each cell as independent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Designs of cells suitable  for distributed coupling with strong wakefield damping have not previously been studied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' In this  paper we develop a SW cell to be used in a distributed coupling structure that can satisfy the  CLIC transverse wakepotential limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' From the middle cell of the CLIC-G* travelling wave (TW)  structure, a SW cell is designed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' The cell is adapted to be suitable for distributed coupling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Its  wakepotentials in an ideal case of open boundaries are reduced to satisfy the wakepotential threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  An electric boundary is added to the model to simulate total reflection at the distribution network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  A horizontal coupler cell that connects to the distribution network such that the reflected wakefields  remain similar to the open boundary case is simulated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' A triplet module which takes advantage of  cell-to-cell coupling to reduce reflected wakepotential is presented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  INTRODUCTION  The main linear accelerator (LINAC) of the CLIC  project uses accelerating structures to generate high-  energy particles for particle physics experiments [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' The  current LINAC design consists of TW X-band radio fre-  quency (RF) accelerating structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  These structures  consist of 26 regular accelerating cells and two coupler  cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  The cell irises radii are tapered from 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='15 mm  to 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='35 mm to maintain a constant loaded gradient of  100 MV/m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' All cells feature waveguides with silicon car-  bide loads to dissipate power from higher order modes  (HOM) [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Figure 1 shows an example of a TW cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  Recent work has shown converting the 2π/3-mode TW  structure to a π-mode SW structure of equal length gives  an increase in rf-to-beam efficiency of ∼ 3 % [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' A SW  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Accelerating cell from the CLIC-G* TW structure  for CLIC with quarter symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  ∗ alexej.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='grudiev@cern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='ch  structure operating in the π-mode is limited to the num-  ber of cells, N, given by Equation 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  �  Qππ2k  4  > N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  (1)  For a SW cell based on CLIC-G* cell shape, the max-  imum number of cells before mode overlap is 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' With  this many cells, the π-mode is separated from the next  adjacent mode by  ∆f π  N,N−1 = fr  kπ2  4N 2 = 2 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  (2)  Operating a side-coupled structure in the π/2-mode si-  multaneously increases the number of cells in a structure  before mode overlap while keeping the shunt impedance  high.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  A side-coupled geometry is not easily amenable  to cells with four HOM waveguides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  Distributed cou-  pling topologies also allow for a SW structure to in-  crease the number of cells by treating each cell as in-  dependent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' In this configuration, each accelerating cell  is connected directly to the power source by a waveg-  uide which runs parallel to the structure [4, 5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Because  the structure does not rely on coupling between cells,  the cells’ iris aperture can be made small to increase  the shunt impedance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Distributed coupling schemes can  also increase high-gradient performance by limiting the  amount of power flow through the cell irises which are  prone to RF breakdown events [6, 7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' As the iris aper-  ture decreases, the effects of wakefields increase [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Ex-  isting designs reduce wakefields by use of detuning such  that problematic dipole modes add coherently later, ide-  ally after the end of the bunch train [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Detuning can  provide dipole modes with Qext = 1000 while CLIC re-  quires modes with Qext ∼ 10 [10, 11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' In this work, we  present the development of an RF accelerating cell suit-  able for a distributed coupling structure that satisfies the  2  CLIC transverse wakefield damping requirement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Section  II outlines the procedure followed to get a SW cell de-  sign.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' The cell is adapted to include a power input and  then further to reduce the wakepotential of the cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' In  Section III the reflected wakepotential from a distribu-  tion network is analyzed and Section IV describes cell  designs capable of reducing the reflected wakepotentials  to an acceptable level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' The final findings are summarized  in V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  OPEN BOUNDARY WAKES  The middle cell of the TW structure was chosen as a  starting point for the design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  The cell length was ad-  justed so the π-mode was synchronous with a relativistic  beam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Parameters sweeps of the iris thickness and el-  lipticity were performed in CST’s eigenmode solver [12]  to select an iris shape that minimized the surface elec-  tric field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Sweeps of the outer wall parameters A0 and  A2, described in [2], confirmed the values of the TW cell  also minimized the surface magnetic field in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  The outer wall was adjusted to obtain the operating fre-  quency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' The RF parameters of the resulting cell are listed  in Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' An accelerating structure based on this SW  cell design having the same length as the TW structure  would have an RF-to-beam efficiency of 31 %.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  TABLE I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' RF parameters of SW cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  Quantity  Unit  Value  cell outer radius, b  mm  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='5638  iris thickness, d  mm  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='6  iris ellipticity, e  mm  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='4  f0  GHz  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='9945  Q0 6,927  R/Q0  Ω/m  10,962  R  MΩ  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='93  Es/Ea 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='80  Hs/Ea  mA/V  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='67  Sc/E2  a  mA/V  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='35  A cell with four HOM waveguides is fed by cell-to-cell  coupling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' To make the cell suitable for a distributed cou-  pling structure, a coupler cell was generated based on the  TW coupling cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' The TW coupler cells have only two  HOM waveguides and therefore the expected wakepoten-  tial of a structure of repeating coupler cells was higher  than the four HOM waveguide cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  The SW coupler  cell included only one coupler waveguide and three HOM  waveguides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' The cell was matched to the source by ad-  justing the cell’s outer radius and the aperture between  the coupler waveguide and the cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' The x-polarization  of the wakepotential was found to be lower in amplitude  than the y-polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' The evaluated transverse wake-  potential of the coupler cell wacs above the threshold  of 6 V(pC · m · mm)−1 [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' A hybrid cell design with a  HOM waveguide transition between the coupler waveg-  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  Long slot cell geometry with half symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' The  cell is matched by adjusting the cell outer radius and the  length of the HOM waveguide between the cell and the coupler  waveguide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  uide and the cell shown in Figure 2 had a transverse  wakepotential between the coupler cell and four HOM  waveguide cell at the second bunch position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  To decrease the wakepotential below the threshold, two  approaches were taken.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' First, the aperture of the HOM  waveguides were increased.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Changing the geometry in  this way caused the Qext of the dominant dipole mode  to decrease at the expense of a lower Q0 and a larger  expected temperature rise on the surface of the cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' The  cells needed to be tuned for each simulated value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' The  second approach was to increase the HOM waveguide  widths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' The wakepotentials from these sweeps are shown  in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' The wakepotential at the second bunch lo-  cation was more sensitive to changes in w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' A value of w  = 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='7 mm was selected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Both polarization of the trans-  verse wakepotentials and their impedances are shown in  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  REFLECTED WAKES  To model the effect of a distribution network, par-  allel waveguide or otherwise, on the wakepotential of  the structure, an electric boundary condition was placed  on the coupler waveguide surfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  This represents a  worst-case-scenario in which all the wakefields extracted  through the coupler waveguide are reflected back into the  cell where they may act on following bunches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Figure 5  shows the geometry simulated to include the effect of  perfect reflection at the coupler waveguide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  An example of a reflected wakepotential is shown in  Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' After the drive bunch passes through the struc-  ture, the remaining wakefields are extracted through the  HOM waveguides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  The fields propagating out of the  cell through the coupler waveguide encounter the electric  3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='5  s (m)  10−1  100  101  102  |Wy| (V(pC·m·mm)−1)  iw (mm)  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='09  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='19  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='29  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='39  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='49  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='59  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='69  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='5  s (m)  10−1  100  101  102  |Wy| (V(pC·m·mm)−1)  w (mm)  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='1  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='2  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='3  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='4  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='6  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='7  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Transverse wakepotential envelopes of long slot cell  with various HOM aperture widths, iw (top) and various  HOM waveguide widths, w (bottom).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  boundary and are reflected back into the cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' At this  time, the wakepotential diverges from the open bound-  ary case, increasing above the wakepotential threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  The position where the reflected wakepotential diverges  from the open boundary case is determined by the dis-  tance between the electric boundary and the beam axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  We call this distance the offset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' The spectrogram of Fig-  ure 7 shows the mode evolution of the reflected wake-  potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  The 17 and 22 GHz modes of Figure 4 are  quickly damped.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' The reflected wakepotential first con-  sists of modes near 17 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' While these modes are being  damped, modes near 22 GHz arrive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' The length of the  reflected wake is due to the difference in arrival time of  the two sets of modes and because of the slow damping  of these modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Increasing the offset decreased the max-  imum amplitude of the reflected wakepotential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' A larger  offset accentuated the difference in arrival time causing  the cell to damp one set of modes at a time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' The reflected  wakepotential duration increased as a result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' The modes  also spread in time due to dispersion in the waveguides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  The electric boundary, position of the distribution net-  work relative to the beam, can be adjusted such that  the reflected wake arrives after the a particular bunch  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='5  s (m)  10−1  100  101  102  |Wx,y| (V(pC·m·mm)−1)  Wy  Wx  0  20  40  f (GHz)  0  2000  4000  6000  8000  Re{Zx,y} (Ω(m·mm)−1)  Zy  Zx  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  Transverse wakepotentials (top) and impedances  (bottom) of long slot cell w = 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='7 mm (bottom).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  but because the reflected wakepotential is damped slowly  and lasts longer than the bunch spacing, the reflected  wakepotential would be above the threshold at the next  bunch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  Increasing the HOM waveguide aperture and  width, which previously had an effect on the wakepo-  tential, proved ineffective at reducing the reflected wake-  potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  The strategy of evaluating different iris ge-  ometries in an attempt to change the mode beating to  form a minimum at the bunch located in the reflected  wakepotential wasof unsuccessful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  DESIGNS TO REDUCE REFLECTED  WAKEFIELDS  Two configurations were found to reduce the reflected  wakepotentials to an acceptable level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' First, the horizon-  tal coupler cell design shown in Figure 8 feeds power to  the cell from a coupler waveguide through an aperture in  one of the HOM waveguides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' The aperture’s dimensions  and location allow power to enter the cell to establish the  accelerating field while being sufficiently small that the  wakefields couple weakly to the coupler waveguide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' The  wakefields are damped in the HOM waveguides instead of  4  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Model simulated to obtain wakepotential of reflected  wakefields of the long slot cell using half symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' The HOM  waveguide ports (red) are connected to an open boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  The coupler waveguides are slightly shorter than the HOM  waveguides and experience an electric boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' The model  was parameterized to maintain these boundary conditions as  the coupler waveguide length was increased.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='5  s (m)  10−1  100  101  102  |Wy| (V(pC·m·mm)−1)  150 mm  Open BC  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Reflected transverse wakepotential envelopes of long  slot cell with w = 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='7 mm and offset = 150 mm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  being reflected at the coupler waveguide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' The reflected  wakepotentials of Figure 9 do not depend strongly on  the offset meaning the horizontal coupler is transparent  to the wakefields and a distribution network can be de-  signed separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  A second scheme where modules were formed of cou-  pler cells and four HOM waveguide cells like the triplet  shown in Figure 10 also reduced the reflected wakepoten-  tials below the CLIC threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' The reflected wakepo-  tential amplitudes were lowered by reducing the number  of coupler waveguides from which reflections occur and  by increasing the number of HOM waveguides that damp  the wakefields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' The module takes advantage of an iris  size of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='75 mm, which is large enough to allow for cou-  pling between cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Operating a group of modules as a  10−1  100  101  102  |Wy| (V(pC·m·mm)−1)  0  10000  Re{Zy} (Ω(m·mm)−1)  0  20  40  f (GHz)  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='8  s (m)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Evolution of the mode content of the reflected wake-  potential with offset = 100 mm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Horizontal coupler cell geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  structure reduces the total number of coupler waveguides  required compared to distributed coupling structure de-  signs where each cell has a feed to a power source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Figure  11 shows the reflected wakepotential amplitude decreases  as the number of four HOM waveguide cells increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  The wakepotential of the triplet is below the threshold at  all bunch positions out to 1 m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' The outer radii of the cells  in the doublet and triplets need to be tuned to achieve a  flat longitudinal field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' A triplet module where the coupler  cell is a horizontal coupler cell, previously shown to con-  siderably reduce the reflected wakepotential, combines a  reduction of feed waveguides and effective mitigation of  reflected wakefields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='5  s (m)  10−1  100  101  102  |Wy| (V(pC·m·mm)−1)  60 mm  70 mm  80 mm  90 mm  Open BC  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Reflected transverse wakepotential of horizontal cou-  pler cell for various offsets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Triplet module based on the long slot cell with half  symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='0  s (m)  10−1  100  101  102  |Wy| (V(pC·m·mm)−1)  singlet  doublet  triplet  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  Reflected transverse wakepotentials of structures  composed of singlets (long slot cell), doublet (one long slot  and one four HOM waveguide cells) and triplet (one long slot  and two four HOM waveguide cells).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  CONCLUSION  A SW cell applicable to distributed coupling struc-  tures was developed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  The HOM waveguide width, w,  was effective at lowering the wakepotential at the sec-  ond bunch position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' The wakepotentials were found to  be generally less sensitive to changes in the HOM waveg-  uide aperture, iw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' From the SW cell, two configurations  were developed capable of supporting 100 MV/m loaded  gradient and gave transverse wakepotentials below the  threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' The wakefields horizontal coupler cell couple  weakly to the high power waveguide and are kept close to  open boundary levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' The triplet module increases the  number of HOM waveguides and decreases the number  of coupler waveguides from which reflections originate to  keep the reflected wakepotential low.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  [1] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Aicheler, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Burrows, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Draper, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Garvey, A  Multi-TeV Linear Collider Based on CLIC Technology,  Tech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  [2] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Zha and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Grudiev, Design and optimization of Com-  pact Linear Collider main linac accelerating structure,  Physical Review Accelerators and Beams 19, 1 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  [3] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  Khan,  A  Standing  Wave  Structure  Possibility  For CLIC Main LINACs, in International Workshop  on Breakdown Science and High Gradient Technology  HG2013, Trieste, Italy (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  [4] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Tantawi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Nasr, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Li, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Limborg, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Borchard,  Design and demonstration of a distributed-coupling lin-  ear accelerator structure, Physical Review Accelerators  and Beams 23, 92001 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  [5] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Jiang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Shi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Zha, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Liu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Lin, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Chen,  Analysis and design of parallel-coupled high-gradient  structure for ultrashort input power pulses, Physical Re-  view Accelerators and Beams 24, 112002 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  [6] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Dolgashev and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Tantawi, Study of Basic  RF Breakdown Phenomena in Hight Gradient Vacuum  Structures, in Proceedings of Linear Accelerator Confer-  ence LINAC2010, Tsukuba, Japan (2010) pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' 1043–1047.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  [7] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Simakov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Dolgashev, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Tantawi, Ad-  vances in high gradient normal conducting accelerator  structures, Nuclear Instruments and Methods in Physics  Research, Section A: Accelerators, Spectrometers, Detec-  tors and Associated Equipment 907, 221 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  [8] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Bane, Short range dipole wakefields in acceler-  ating structures for the NLC, 94309, 1 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  [9] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Rimmer, Extraction and Absorption of Higher  Order Modes in Room Temperature Accelerators, in  Worskhop on Microwave-Absorbing Materials for Ac-  celerators, Newport News, VA, February 22-24, 1993  (1993).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  [10] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Bane, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Barklow, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Breidenbach, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  Burkhart, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Fauve, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Gold, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Heloin, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Li,  6  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Nanni, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Nasr, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Oriunno, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Paterson, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  Peskin, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Raubenheimer, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Tantawi, An Ad-  vanced NCRF Linac Concept for a High Energy e+e−  Linear Collider, Tech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' (2018) arXiv:1807.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='10195.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  [11] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Grudiev and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Wuensch, Design of the CLIC Main  Linac Accelerating Structure for CLIC Conceptual De-  sign Report, in Proceedings of Linear Accelerator Con-  ference LINAC2010 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  [12] Computer Simulation Technology, CST Studio Suite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content='  [13] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
+page_content=' Schulte, Multi-Bunch Calculations in the CLIC Main  Linac, in Proceedings, 23rd Conference, PAC’09, Van-  couver, Canada, May 4-8, 2009 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sNE0T4oBgHgl3EQfawDH/content/2301.02340v1.pdf'}
diff --git a/tNFAT4oBgHgl3EQfgx22/content/tmp_files/2301.08590v1.pdf.txt b/tNFAT4oBgHgl3EQfgx22/content/tmp_files/2301.08590v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..98fb58ba2d199319a3399d4c797ee2b8059420a8
--- /dev/null
+++ b/tNFAT4oBgHgl3EQfgx22/content/tmp_files/2301.08590v1.pdf.txt
@@ -0,0 +1,914 @@
+1
+Pattern Recognition Letters
+journal homepage: www.elsevier.com
+Improving Sketch Colorization using Adversarial Segmentation Consistency
+Samet Hicsonmeza,∗∗, Nermin Sametb, Emre Akbasc, Pinar Duygulua
+aHacettepe University, Ankara, Turkey
+bLIGM, Ecole des Ponts, Univ Gustave Eiffel, CNRS, Marne-la-Vallée, France
+cMiddle East Technical University, Ankara, Turkey
+Article history:
+sketch colorization,
+sketch to image
+translation, Generative Adversarial Net-
+works (GAN), image segmentation, im-
+age to image translation
+ABSTRACT
+We propose a new method for producing color images from sketches. Current solutions
+in sketch colorization either necessitate additional user instruction or are restricted to
+the "paired" translation strategy. We leverage semantic image segmentation from a gen-
+eral-purpose panoptic segmentation network to generate an additional adversarial loss
+function. The proposed loss function is compatible with any GAN model. Our method is
+not restricted to datasets with segmentation labels and can be applied to unpaired trans-
+lation tasks as well. Using qualitative, and quantitative analysis, and based on a user
+study, we demonstrate the efficacy of our method on four distinct image datasets. On the
+FID metric, our model improves the baseline by up to 35 points. Our code, pretrained
+models, scripts to produce newly introduced datasets and corresponding sketch images
+are available at https://github.com/giddyyupp/AdvSegLoss.
+© 2023 Elsevier Ltd. All rights reserved.
+1. Introduction
+The task of image generation from an input sketch or edge
+map is known as "sketch to image translation", or "sketch col-
+orization". Sketches capture essential content of the images and
+they can be easily acquired. Yet, vast amount of domain dif-
+ference between single channel edge maps and color images
+makes sketch colorization a challenging process. Lack of de-
+tails in sketches especially for background is another problem.
+Sketch colorization has been investigated in numerous do-
+mains: faces [1, 2, 3, 4], objects [5, 6, 7, 8], animes [9, 10, 11,
+12, 13, 14, 15], art [16], icons [17] and scenes [18, 19, 20]. The
+majority of the approaches require user direction in the form of
+supplementary input, such as a reference color, patch, or image.
+These approaches usually generate surreal colorizations other-
+wise. Except for a few studies (e.g., Liu et al. [8]), most of the
+approaches follow the “paired” strategy, which is restricted to
+use datasets with a ground-truth image for each sketch.
+∗∗Corresponding author
+e-mail: samethicsonmez@hacettepe.edu.tr (Samet
+Hicsonmez), nermin.samet@enpc.fr (Nermin Samet),
+emre@ceng.metu.edu.tr (Emre Akbas),
+pinar@cs.hacettepe.edu.tr (Pinar Duygulu)
+In this study, we aim to leverage general purpose semantic
+image segmentation to alleviate the aforementioned shortcom-
+ings. We argue that an accurately colored sketch would pro-
+duce a “real” segmentation result, i.e., a result that looks like
+the segmentation of a real image. Thus, for sketch based image
+colorization problem, we exploit semantic segmentation meth-
+ods that have reached to a degree of maturity even for datasets
+on which they were not trained (Section 4). We introduce a
+segmentation-based adversarial loss to be used in a GAN (Gen-
+erative Adversarial Network) setup. With our approach, neither
+extra user instruction nor "paired" input is required.
+We introduce three models for varying levels of segmenta-
+tion feedback in the sketch to image translation pipeline. Our
+models could be integrated into both paired and unpaired GAN
+models. We illustrate the effectiveness of applying segmenta-
+tion cues via comprehensive experimental analyses. This pa-
+per extends our previous work [21] in the following ways: (i)
+We apply our method to a new task: label-to-photo transla-
+tion. Our experiments on two challenging datasets show that
+our segmentation-based adversarial loss is useful in this task,
+too. Again, ground-truth segmentation labels are not a require-
+ment for our approach.
+(ii) We perform experiments to set
+the optimal values for weights of two additional discriminators.
+(iii) We incorporate an outdoor dataset, Cityscapes [22], to both
+arXiv:2301.08590v1  [cs.CV]  20 Jan 2023
+
+NON
+SOLUS
+ELSEVIER2
+Fake Segmentation
+Real Segmentation
+Real Image
+Input Sketch
+Inference
+GAN Model
+Generated 
+Image
+Segmentation 
+Network
+Real?
+0/1
+Real?
+0/1
+Real?
+0/1
+Fig. 1: The proposed model for sketch colorization with Adversarial Segmentation Loss (ASL). It is composed of two parts; a general purpose image translation
+GAN model, and an image segmentation model. During training, input sketches are first colorized using the baseline GAN model. Then, generated and ground truth
+color images are fed to the pre-trained panoptic segmentation model to extract fake and real segmentation maps. Finally, two additional discriminators are used to
+classify the segmentation maps as fake or real, respectively. The box with dashed yellow borders shows the inference stage. Red border marks the GAN model used
+for sketch to image translation. Here, Pix2Pix is used as an example image translation model, which could be replaced by any paired or unpaired model.
+sketch colorization and label to photo translation tasks. (iv) We
+add a new metric, mean Intersection over Union (mIoU), in ad-
+dition to FID score to measure the performance of all the mod-
+els more reliably.
+2. Related Work
+Even though the sketch and the edge map of an image are
+different concepts, in practice, XDoG [23] or HED [24] based
+edge maps are considered as sketches (e.g., [18, 11]). More-
+over, some sketch based models [5] use edge maps for data aug-
+mentation. Hence, we refer to all these models as "sketch-to-
+image translation" or "sketch colorization" models. Although
+general purpose image-to-image translation methods [25, 26,
+27, 28, 29] could be used for sketch-to-image translation tasks,
+the results are not satisfactory.
+One widely used solution to improve the colorization per-
+formance is to employ additional color [18, 11, 12, 10, 14, 15],
+patch [6], image [2, 13, 16, 9, 17, 30] or language guidance [20,
+31, 32]. For instance, in color guidance, users specify their de-
+sired colors for the regions in the sketch image, and the model
+utilizes this information to generate the same or similar colors
+for these regions. Some automatic methods also utilize user
+guidance to improve their performance as a hybrid approach.
+Most of the sketch-to-image translation methods are based on
+“paired” training approach [18, 11, 5, 19], but, recently un-
+paired methods have also been presented [8, 16].
+Scribbler [18] presents one of the very first paired and user
+guided scene sketch colorization models. In addition to pixel,
+perceptual and GAN losses, Scribbler uses total variation loss
+to encourage smoothness. XDoG is used to generate sketch
+images of 200k bedroom photos. DCSGAN [15] uses HSV
+color space in addition to the RGB, for line art colorization
+task. Zou et al. [20] use text inputs to progressively colorize an
+input sketch, in such a way that a novel text guided sketch seg-
+menter locates the objects in the scene. EdgeGAN [19] maps
+edge images to a latent space during training using an edge en-
+coder. During inference, the edge encoder is used to encode
+the input sketch to the latent space to subsequently generate a
+color image. Experiments are provided for 14 foreground and
+3 background objects from COCO [33] dataset.
+EdgeGAN [19] and Scribbler [18] use a supervised approach
+where input sketches and corresponding output images exist.
+However, it is hard to collect sketch image pairs. Liu et al. [8]
+propose a two stage method to convert object sketches to color
+images in an unsupervised (unpaired) way. They first convert
+sketches to gray scale images, and then to color images. Self
+supervision is used to complete the deliberately deleted sketch
+parts and clear the added noisy edges from sketch images.
+In Sketch-to-Art [16], an art image is generated using an in-
+put sketch, with the additional help of the target style art image.
+Content of the input sketch and style of the art image are en-
+coded, and then fused to generate a stylized art image. In [17]
+authors proposed a method to colorize icons which utilizes col-
+ored icon images as input in addition to the black-white icons.
+The user input is valuable not only in helping the coloriza-
+tion network to put the right colors to indicated regions, but also
+in removing the color bleeding problems. In [34], users draw
+scribbles to the regions on the generated image suffered from
+color bleeding artifacts for guiding the model to fix them.
+Unlike these methods, our method does not require any user
+input to generate satisfactory colorization. Instead, we utilize
+adversarial segmentation guidance to improve performance.
+3. Adversarial Segmentation Consistency
+Figure 1 shows the overall structure of our proposed model
+for sketch colorization, which we refer to as Adversarial Seg-
+mentation Loss (ASL) based model.
+In this work, we used
+Pix2Pix and CycleGAN methods as our baselines for paired and
+unpaired training, respectively. This preference is made based
+on the effectiveness of these methods across a variety of tasks
+and datasets. In the figure, Pix2Pix is used to show ASL based
+
+paper
+mirror-stuff
+wall
+light
+tv96%
+teddy bear 66%
+table
+cabinet
+bed99%wall
+66%
+bed 51%3
+model for paired approach. Our model could be integrated into
+any other paired or unpaired GAN model.
+Our model consists of a baseline GAN, a panoptic segmen-
+tation network (Seg) and two discriminators (DM and DB). Panop-
+tic segmentation network is trained offline on the COCO Stuff [35]
+dataset and its weights are frozen during the training of our
+model. Fake and real images are fed to the Seg network to get
+real and fake segmentation maps. Then, these two segmenta-
+tion maps are given to the discriminators to classify them as
+fake or real. We designed three variants of our model to embed
+different levels of segmentation feedback to the sketch to image
+translation pipeline.
+The first variant utilizes the full (multiclass) segmentation
+map of an image where all foreground and background classes
+(a total of 135 classes) are considered. In this model, ground-
+truth color image Ireal and the generated color image Ifake are
+fed to Seg which outputs full segmentation maps for both im-
+ages. Then, these two outputs are given to a discriminator net-
+work DM to discriminate between real and fake segmentation
+maps. We call this model as Multi-class in the rest of the paper.
+As a higher level of abstraction, grouping objects as back-
+ground and foreground alone may yield sufficient information.
+The second variant of our model uses only two classes (back-
+ground and foreground) in the segmentation map by grouping
+all foreground classes into one and all background classes into
+another class. In this model, which we refer to as Binary, bi-
+nary segmentation outputs for real and fake images are fed to a
+discriminator network DB to discriminate between real and fake
+ones. Finally, our third variant is the union of the above two. It
+contains both discriminators, and is named as Combined.
+Overall loss function for our model is the sum of losses of
+the baseline GAN model (LG) and the two additional discrimi-
+nators’ (LB and LM). That is, the objective function is:
+L = wgLG + wbLB + wmLM
+Let S egB and S egM correspond to the panoptic segmenta-
+tion networks in Binary and Multi-class cases. The additional
+losses that we introduce, LB and LM, are defined as:
+LB(G, DB, S egB) =
+�
+i
+log(DB(S egB(yi)))+
+�
+i
+log(1 − DB(S egB(G(xi)))
+LM(G, DM, S egM) =
+�
+i
+log(DM(S egM(yi)))+
+�
+i
+log(1 − DM(S egM(G(xi)))
+Let xi be an input sketch image, and yi be the corresponding
+ground truth color image. When the baseline GAN model is
+Pix2Pix [27], GAN loss LG is formulated as:
+LG(G, D) =
+�
+i
+log(D(xi))+
+�
+i
+log(1−D(G(xi))+
+�
+i
+∥yi−G(xi)∥
+Fig. 2: Sample segmentations using general purpose panoptic segmentation
+network on different datasets. The model generalizes well to several domains.
+Table 1: Statistics of the datasets used in our experiments.
+Dataset
+Train Images
+Test Images
+ADE20k Bedroom
+1355
+135
+Cityscapes
+2975
+500
+Illustration
+659
+131
+COCO Elephant
+1800
+343
+COCO Sheep
+1300
+229
+When baseline is CycleGAN [25], LG for direction X → Y is:
+LG(GX,GY, DX) =
+�
+j
+log(DX(y j)) +
+�
+i
+log(1 − DX(GX(xi))
++
+�
+i
+∥xi − GY(GX(xi))∥
+where GX maps input sketches to color images, and GY maps
+the color images back to sketch domain. DX is the discriminator
+for domain X, i.e. sketches. Final LG for CycleGAN is the sum
+of above formulation for two directions.
+We analysed the effect of each component in the objective
+function and, set wg, wb and wm to 1 based on the experimental
+analysis (see Section 5.1). Note that, for the Binary model wm,
+and for the Multi-class model wb is set to 0 respectively.
+4. Datasets
+We evaluated our models on five challenging datasets (see
+Table 1). The first dataset consists of bedroom images from the
+ADE20k indoor dataset [36], with 1355 train and 135 test im-
+ages. The second dataset is Cityscapes [22] dataset which con-
+tains 2975 training and 500 test images. The third dataset [28]
+contains illustrations from children’s books by Alex Scheffler,
+with 659 train and 131 test images. The fourth and fifth ones
+were curated by us from the COCO dataset. We collected im-
+ages containing elephant or sheep. Note that these images may
+also contain other foreground/background objects such as per-
+son, animals, mountains, grass and sky. Elephant dataset con-
+tains 1800 train and 343 test images, and the sheep dataset has
+1300 train and 229 test images. Example images from these
+datasets and their segmentation outputs are shown in Figure 2.
+
+window
+curtain
+pottedplant98%
+wall
+person98%
+bed89%
+diningtable82%
+chair78%
+chair55%
+bird60%
+floor-woodtree
+elephant100%
+elephant100%
+grasstree
+sheep9csheep10(sheep99%
+grassceiling
+window
+wall
+window-blind
+pottedplant89%
+tted plant 66%
+light
+chair100%
+chair100%
+bed 100%
+cabinet
+vase98%
+rug
+floor-woodceiling
+mirror-stuff
+tv 92%
+wall
+light
+chair57%
+dining table 68%
+table
+chair 100%
+couch80%
+floor-wood
+bed 90%
+rug4
+Input
+GT
+CycleGAN
+C-ASL
+(Multi-class)
+C-ASL
+(Binary)
+C-ASL
+(Combined)
+Input
+GT
+Pix2Pix
+P-ASL
+(Multi-class)
+P-ASL
+(Binary)
+P-ASL
+(Combined)
+Fig. 3: Sample results from baselines and our model with different settings. Input images on each row are from bedroom, illustration, elephants and sheep datasets,
+respectively. First two rows display results of unpaired training (baseline is CycleGAN), and last two rows show results for paired training (baseline is Pix2Pix). On
+bedroom and elephant datasets Binary, on illustration and sheep datasets Combined setting gave best results for both training schemes.
+Table 2: Comparison with CycleGAN [25] on unpaired sketch-to-image
+translation task in terms of FID scores, lower is better.
+Dataset
+CycleGAN
+C-ASL
+(Multi-class)
+C-ASL
+(Binary)
+C-ASL
+(Combined)
+Bedroom
+113.1
+111.7
+87.1
+93.2
+Cityscapes
+62.9
+64.1
+64.9
+59.1
+Illustration
+213.6
+206.9
+204.8
+189.4
+Elephant
+126.4
+103.9
+91.9
+116.9
+Sheep
+209.3
+207.2
+236.1
+196.8
+Edge images are extracted using the HED [24] method. In
+the first two columns of Figure 3, we present sample natural and
+edge images for all the datasets. It can be seen that the images
+contain a variety of foreground and background objects, also it
+is hard to figure out the source dataset for some images.
+5. Experiments
+We used PyTorch [37] to implement our models. We use
+sketch images as source domain, and color images as target do-
+main. All training images (i.e. color and sketch images) are
+resized to 256 × 256 pixels. We train all models for 200 epochs
+using the Adam optimizer [38] with a learning rate of 0.0002.
+We conducted all our experiments on a NVIDIA Tesla V100
+GPU.
+We compared our models with Pix2Pix [27] and AutoPainter
+(AP) [11] for paired and CycleGAN [25] for unpaired setting
+on sketch-to-image translation task. We used the official im-
+plementations that are publicly available. Baseline models are
+trained for 200 epochs. Our proposed ASL model that uses
+Pix2Pix as the baseline GAN model is referred to as P-ASL,
+and similarly C-ASL refers to the model that uses CycleGAN.
+5.1. Quantitative Analysis
+To quantitatively evaluate the quality of generated images,
+we used the widely adopted Frechet Inception Distance (FID) [39]
+metric. FID score measures the distance between the distribu-
+tions of the generated and real images. Lower FID score indi-
+cates the higher similarity between two image sets.
+On Bedroom and Cityscapes datasets where ground truth
+segmentation maps are available, we also calculate the mean
+Intersection over Union (mIoU) scores on colorized images. We
+forward each colorized image to an off-the-shelf segmentation
+model trained on these two datasets separately. mIoU score
+measures the quality of the segmentation. We argue that better
+colorized images should yield higher mIoU scores.
+
+5
+Table 3: Comparison with AutoPainter [11] and Pix2Pix [27] on paired sketch-
+to-image translation task in terms of FID scores, lower is better.
+Dataset
+Auto
+Painter
+Pix2Pix
+P-ASL
+(Multi-class)
+P-ASL
+(Binary)
+P-ASL
+(Combined)
+Bedroom
+206.8
+100.5
+100.0
+95.1
+110.1
+Cityscapes
+151.3
+74.1
+69.9
+71.6
+71.2
+Illustration
+272.0
+180.0
+176.9
+178.0
+175.7
+Elephant
+155.1
+83.5
+85.8
+78.8
+82.8
+Sheep
+233.1
+157.0
+159.9
+162.0
+150.5
+Table 4: Comparison with CycleGAN on unpaired sketch-to-image transla-
+tion task in terms of mIoU scores, higher is better.
+Dataset
+CycleGAN
+C-ASL
+(Multi-class)
+C-ASL
+(Binary)
+C-ASL
+(Combined)
+Oracle
+Bedroom
+5.20
+6.71
+6.58
+6.44
+20.62
+Cityscapes
+15.67
+14.63
+13.56
+15.68
+44.85
+We present FID scores for unpaired translation in Table 2
+and paired translation in Table 3. FID scores are inline with the
+visual inspections (see Figure 3), for all the datasets, at least
+one variant of our model performed better than the baseline.
+First of all, when we compare FID scores of two training
+schemes and baseline models, paired training (Pix2Pix) per-
+formed better than unpaired training, as expected. However, our
+“adversarial segmentation loss” affected the results of paired
+and unpaired cases differently. For instance, on elephant dataset
+our models improved baseline up to 35 points for unpaired case,
+but only 5 points for paired case.
+Another crucial observation is that segmentation guidance
+closed the gap between unpaired and paired training results.
+Best FID scores for unpaired models on bedroom, illustration
+and elephant datasets become very close to or even better than
+paired training. For instance on the elephant dataset, the ini-
+tial 40+ point FID gap (126 vs 83) dropped to 13 (92 vs 79)
+on Binary setting. Here the only exception is the sheep dataset.
+Since the sheep dataset contains various complex objects, un-
+paired and paired models failed to generate plausible images.
+We show mIoU scores for unpaired translation in Table 4
+and paired translation in Table 5. We also present oracle perfor-
+mances of the segmentation method on both datasets. On mIoU
+metric, again for all the datasets, at least one of the variants of
+our model performed better than the baseline.
+When we look at the best performing settings on different
+datasets, structure of the dataset has an effect on the results. For
+instance, even though one is an indoor and the other one is an
+outdoor dataset, bedroom and elephant images are composed
+of similar structure. FG/BG ratios and placements of them in
+these datasets are similar across all images, i.e. walls, ceiling
+Table 5: Comparison with Pix2Pix on paired sketch-to-image translation task
+in terms of mIoU scores, higher is better.
+Dataset
+Auto
+Painter
+Pix2Pix
+P-ASL
+(Multi-class)
+P-ASL
+(Binary)
+P-ASL
+(Combined)
+Oracle
+Bedroom
+2.08
+6.49
+6.95
+7.39
+6.60
+20.62
+Cityscapes
+6.02
+18.71
+18.63
+18.70
+18.74
+44.85
+Table 6: User Study results.
+Dataset
+CycleGAN
+C-ASL
+Bedroom
+20.0
+80.0
+Illustration
+27.0
+73.0
+Elephant
+39.1
+60.9
+Sheep
+19.1
+80.9
+Cityscapes (L2P)
+25.7
+74.3
+Table 7: Effect of changing the wb and wm values, wb is used as 1.0 for all ex-
+periments. Using 1.0 for both weights yields the best FID score on the ADE20k
+bedroom images for the task of sketch-to-image translation.
+wb and wm
+0.1
+0.5
+1.0
+5.0
+10.0
+FID
+114.8
+114.5
+93.2
+147.8
+104.6
+and floors in bedroom images are always positioned in the same
+places on different images. Also elephant images contain very
+few FG objects, i.e. only elephants most of the time, and large
+BG areas such as grass, trees and sky. On these two datasets,
+Binary setting which considers FG/BG classes only gave the
+best FID score. On the other hand, illustration and sheep images
+got a variety of FG objects and scenes. On such datasets, using
+only a FG/BG discriminator even degrades the performance.
+Our model has two important parameters, wb and wm, to
+control the effect of segmentation discriminators. To find the
+best possible values, we conducted experiments by training our
+models on the ADE20k bedroom images on the unpaired sketch
+to image translation task (see Table 7). Using a small value
+like 0.1 gives a similar score to baseline CycleGAN. On the
+other hand using a big value like 5.0 increased the FID score
+dramatically. Setting wb and wm to 1.0 resulted in the best FID
+score, thus the weights are set to 1.0 in all experiments.
+5.2. Qualitative Analysis and User Study
+We present visual results of sketch colorization for our model
+and the baseline models in the Figure 3. On bedroom and illus-
+tration datasets, we show results of unpaired training, and on
+elephant and sheep datasets we show paired training results.
+On the bedroom dataset, the Binary setting generates bet-
+ter images compared to baselines and other settings. Colors
+are uniform across the object parts in this setting. There are
+defective colors in the CycleGAN results such as the bottom
+of the bed and floor. On the illustration dataset, the baseline
+model performed poorly. Objects are hard to recognize and
+most importantly colors are not proper at all. On the other hand,
+Multi-class and Combined settings generate significantly better
+images i.e. generated objects and background got consistent
+colors. Finally, on elephant and sheep datasets although gener-
+ated images are not very visually appealing for all the methods,
+segmentation guided images are quite appealing compared to
+baseline models’. On the elephant dataset Binary, on the sheep
+dataset Combined setting performed the best.
+We conducted a user study to measure realism of generated
+images. We show two random images (at random positions,
+
+6
+Input
+GT
+CycleGAN
+Binary
+Fig. 4: Sample results on Cityscapes dataset for CycleGAN and our best model.
+In the first image, CycleGAN generates buildings instead of trees, also there are
+defects on the road. Other two images are blurry and lack details. On the other
+hand, in all cases our Binary setting generates more visually appealing images.
+Table 8: Comparison with CycleGAN [25] on unpaired label-to-photo trans-
+lation task in terms of FID scores, lower is better.
+Dataset
+CycleGAN
+C-ASL
+(Multi-class)
+C-ASL
+(Binary)
+C-ASL
+(Combined)
+Bedroom
+84.2
+86.9
+85.6
+78.9
+Cityscapes
+83.0
+70.9
+64.8
+66.0
+left or right) which were generated with CycleGAN and our
+best setting (lowest FID score) for all four datasets, and asked
+participants to select the more realistic one.
+We collected a total of 115 survey inputs from 39 different
+users. We ask users to evaluate 4 S2P models and 1 L2P model.
+In Table 6, we present results of the user study in terms of pref-
+erence percentages of each model. User study results are inline
+with the FID score results, on all datasets, images generated
+by our model were preferred by the users most of the time. On
+sheep and elephant datasets, users struggled to select an answer.
+Color distributions and shapes of FG objects are two dominant
+factors which lead user preferences.
+5.3. Label to Photo Translation
+We also experimented with label-to-photo (L2P) translation
+task to show the effectiveness of our model in a different task
+where adversarial segmentation loss could be helpful. In L2P
+task, we use ADE20k bedroom and Cityscapes datasets. Sim-
+ilar to S2P task, all images are resized to 256x256 pixels. We
+Table 9: Comparison with Pix2Pix [27] on paired label-to-photo translation
+task in terms of FID scores, lower is better.
+Dataset
+Pix2Pix
+P-ASL
+(Multi-class)
+P-ASL
+(Binary)
+P-ASL
+(Combined)
+Bedroom
+128.1
+118.2
+122.3
+110.1
+Cityscapes
+79.5
+78.4
+72.9
+77.6
+Table 10: Comparison with CycleGAN on unpaired label-to-photo transla-
+tion task in terms of mIoU scores, higher is better.
+Dataset
+CycleGAN
+C-ASL
+(Multi-class)
+C-ASL
+(Binary)
+C-ASL
+(Combined)
+Oracle
+Bedroom
+5.70
+5.88
+6.10
+6.69
+20.62
+Cityscapes
+20.13
+21.45
+20.70
+19.61
+44.85
+Table 11: Comparison with Pix2Pix on paired label-to-photo translation task
+in terms of mIoU scores, higher is better.
+Dataset
+Pix2Pix
+P-ASL
+(Multi-class)
+P-ASL
+(Binary)
+P-ASL
+(Combined)
+Oracle
+Bedroom
+1.56
+1.59
+1.54
+1.62
+20.62
+Cityscapes
+8.62
+8.66
+8.69
+8.56
+44.85
+train L2P models for 200 epochs using the Adam optimizer [38]
+with a learning rate of 0.0002. We show FID scores for unpaired
+L2P in Table 8 and paired translation in Table 9. For unpaired
+translation our best performing method improves the baseline
+for more than 5 points on Bedroom and almost 20 points on
+Cityscapes datasets. Similarly on the paired translation, the im-
+provements regard to the baseline reaches 18 points.
+In Table 10 and Table 11, we present mIoU scores for un-
+paired and paired L2P translation, respectively. For both cases,
+our best performing variant outperforms the baseline method.
+We present visual results in Figure 4 for only the base-
+line model and our best performing setting Binary for unpaired
+translation. Our model generates more photo-realistic images,
+also generated images comply with the input label maps better.
+Input
+GT
+CycleGAN
++ASL
+Fig. 5: Sample results on elephant and sheep datasets for CycleGAN and our
+best model. Realism of both models are not satisfactory, however, especially
+colors of BG areas are better in our results.
+5.4. Limitations
+Figure 5 presents examples on elephant and sheep datasets
+where both baseline and our best performing model suffer from
+low visual realism. The main reason for that is these datasets
+contains complex foreground and background objects. How-
+ever, our method performs significantly better than the baseline.
+Especially on the first row, colorized image using our method
+resembles more to the ground truth image.
+6. Conclusion
+In this study, we present a new method for the sketch col-
+orization problem. Our method utilizes a general purpose im-
+
+7
+age segmentation network and adds an adversarial segmenta-
+tion loss (ASL) to the regular GAN loss. ASL could be inte-
+grated to any GAN model, and works even if the dataset does
+not have segmentation labels. We used CycleGAN and Pix2Pix
+as baseline GAN models. We conducted extensive evaluations
+on various datasets including bedroom, sheep, elephant and il-
+lustration images and evaluate the performance both quantita-
+tively (using FID and mIoU scores) and qualitatively (through
+a user study). We showed that our model outperforms baselines
+on all datasets on both FID score and user study analysis.
+Regarding the limitations of our method, although we im-
+prove the baseline both qualitatively and quantitatively, espe-
+cially elephant and sheep results lack realism. Even the paired
+training results are not visually appealing on these two datasets,
+most probably due to the fact that the baseline models are not
+very successful at generating complex scenes.
+Acknowledgment
+The numerical calculations reported in this paper were fully
+performed at TUBITAK ULAKBIM, High Performance and
+Grid Computing Center (TRUBA resources). Dr. Akbas is sup-
+ported by the “Young Scientist Awards Program (BAGEP)” of
+Science Academy, Turkey.
+References
+[1] S.-Y. Chen, W. Su, L. Gao, S. Xia, H. Fu, Deepfacedrawing: deep genera-
+tion of face images from sketches, ACM Transactions on Graphics (TOG)
+39 (4) (2020) 72–1.
+[2] J. Lee, E. Kim, Y. Lee, D. Kim, J. Chang, J. Choo, Reference-based sketch
+image colorization using augmented-self reference and dense semantic
+correspondence, in: IEEE Conference on Computer Vision and Pattern
+Recognition, 2020.
+[3] Y. Li, X. Chen, F. Wu, Z.-J. Zha, Linestofacephoto: Face photo generation
+from lines with conditional self-attention generative adversarial networks,
+in: ACM International Conference on Multimedia, 2019.
+[4] J. Huang, L. Jing, Z. Tan, S. Kwong, Multi-density sketch-to-image trans-
+lation network, IEEE Transactions on Multimedia 24 (2022) 4002–4015.
+[5] W. Chen, J. Hays, Sketchygan: Towards diverse and realistic sketch to
+image synthesis, in: IEEE Conference on Computer Vision and Pattern
+Recognition, 2018.
+[6] W. Xian, P. Sangkloy, V. Agrawal, A. Raj, J. Lu, C. Fang, F. Yu, J. Hays,
+Texturegan: Controlling deep image synthesis with texture patches, in:
+IEEE Conference on Computer Vision and Pattern Recognition, 2018.
+[7] Y. Lu, S. Wu, Y.-W. Tai, C.-K. Tang, Image generation from sketch con-
+straint using contextual gan, in: IEEE European Conference on Computer
+Vision, 2018.
+[8] R. Liu, Q. Yu21, S. X. Yu, Unsupervised sketch to photo synthesis, in:
+IEEE European Conference on Computer Vision, 2020.
+[9] C. Furusawa, K. sHiroshiba, K. Ogaki, Y. Odagiri, Comicolorization:
+semi-automatic manga colorization, in:
+SIGGRAPH Asia Technical
+Briefs, 2017.
+[10] Y. Ci, X. Ma, Z. Wang, H. Li, Z. Luo, User-guided deep anime line art
+colorization with conditional adversarial networks, in: ACM International
+Conference on Multimedia, 2018.
+[11] Y. Liu, Z. Qin, T. Wan, Z. Luo, Auto-painter: Cartoon image generation
+from sketch by using conditional wasserstein generative adversarial net-
+works, Neurocomputing 311 (2018) 78 – 87.
+[12] L. Zhang, C. Li, T.-T. Wong, Y. Ji, C. Liu, Two-stage sketch colorization,
+ACM Transactions on Graphics (TOG) 37 (6) (2018) 1–14.
+[13] L. Zhang, Y. Ji, X. Lin, C. Liu, Style transfer for anime sketches with
+enhanced residual u-net and auxiliary classifier gan, in: Asian Conference
+on Pattern Recognition, 2017.
+[14] M. Yuan, E. Simo-Serra, Line art colorization with concatenated spatial
+attention, in: CVPR Workshops, 2021.
+[15] Z. Dou, N. Wang, B. Li, Z. Wang, H. Li, B. Liu, Dual color space guided
+sketch colorization, IEEE Transactions on Image Processing 30 (2021)
+7292–7304.
+[16] B. Liu, K. Song, Y. Zhu, A. Elgammal, Sketch-to-art: Synthesizing styl-
+ized art images from sketches, in: Proceedings of the Asian Conference
+on Computer Vision, 2020.
+[17] Y.-k. Li, Y.-H. Lien, Y.-S. Wang, Style-structure disentangled features and
+normalizing flows for diverse icon colorization, in: IEEE Conference on
+Computer Vision and Pattern Recognition, 2022, pp. 11244–11253.
+[18] P. Sangkloy, J. Lu, C. Fang, F. Yu, J. Hays, Scribbler: Controlling deep
+image synthesis with sketch and color, in: IEEE Conference on Computer
+Vision and Pattern Recognition, 2017.
+[19] C. Gao, Q. Liu, Q. Xu, L. Wang, J. Liu, C. Zou, Sketchycoco: Image gen-
+eration from freehand scene sketches, in: IEEE Conference on Computer
+Vision and Pattern Recognition, 2020.
+[20] C. Zou, H. Mo, C. Gao, R. Du, H. Fu, Language-based colorization of
+scene sketches, ACM Transactions on Graphics (TOG) 38 (6) (2019) 1–
+16.
+[21] S. Hicsonmez, N. Samet, E. Akbas, P. Duygulu, Adversarial segmentation
+loss for sketch colorization, in: IEEE International Conference on Image
+Processing, 2021.
+[22] M. Cordts, M. Omran, S. Ramos, T. Rehfeld, M. Enzweiler, R. Benen-
+son, U. Franke, S. Roth, B. Schiele, The cityscapes dataset for semantic
+urban scene understanding, in: IEEE Conference on Computer Vision and
+Pattern Recognition, 2016.
+[23] H. Winnemöller, J. E. Kyprianidis, S. C. Olsen, Xdog: an extended
+difference-of-gaussians compendium including advanced image styliza-
+tion, Computers & Graphics 36 (6) (2012) 740–753.
+[24] S. Xie, Z. Tu, Holistically-nested edge detection, in: IEEE International
+Conference on Computer Vision, 2015.
+[25] J.-Y. Zhu, T. Park, P. Isola, A. A. Efros, Unpaired image-to-image trans-
+lation using cycle-consistent adversarial networks, 2017.
+[26] Z. Yi, H. Zhang, P. Tan, M. Gong, Dualgan: Unsupervised dual learning
+for image-to-image translation, 2017.
+[27] P. Isola, J.-Y. Zhu, T. Zhou, A. A. Efros, Image-to-image translation with
+conditional adversarial networks, 2017.
+[28] S. Hicsonmez, N. Samet, E. Akbas, P. Duygulu, Ganilla: Generative ad-
+versarial networks for image to illustration translation, Image and Vision
+Computing (2020) 103886.
+[29] X. Huang, M.-Y. Liu, S. Belongie, J. Kautz, Multimodal unsupervised
+image-to-image translation, in: IEEE European Conference on Computer
+Vision, 2018.
+[30] J. Lee, E. Kim, Y. Lee, D. Kim, J. Chang, J. Choo, Reference-based sketch
+image colorization using augmented-self reference and dense semantic
+correspondence, in: IEEE Conference on Computer Vision and Pattern
+Recognition, 2020.
+[31] C. Zou, Q. Yu, R. Du, H. Mo, Y.-Z. Song, T. Xiang, C. Gao, B. Chen,
+H. Zhang, Sketchyscene: Richly-annotated scene sketches, in: IEEE Eu-
+ropean Conference on Computer Vision, 2018.
+[32] H. Kim, H. Y. Jhoo, E. Park, S. Yoo, Tag2pix: Line art colorization using
+text tag with secat and changing loss, in: IEEE International Conference
+on Computer Vision, 2019.
+[33] T.-Y. Lin, M. Maire, S. Belongie, J. Hays, P. Perona, D. Ramanan, P. Dol-
+lár, C. L. Zitnick, Microsoft COCO: Common objects in context, in: IEEE
+European Conference on Computer Vision, 2014.
+[34] E. Kim, S. Lee, J. Park, S. Choi, C. Seo, J. Choo, Deep edge-aware inter-
+active colorization against color-bleeding effects, in: IEEE International
+Conference on Computer Vision, 2021.
+[35] H. Caesar, J. Uijlings, V. Ferrari, Coco-stuff: Thing and stuff classes in
+context, in: IEEE Conference on Computer Vision and Pattern Recogni-
+tion, 2018.
+[36] B. Zhou, H. Zhao, X. Puig, T. Xiao, S. Fidler, A. Barriuso, A. Torralba,
+Semantic understanding of scenes through the ade20k dataset, Interna-
+tional Journal of Computer Vision 127 (3) (2019) 302–321.
+[37] A. Paszke, S. Gross, S. Chintala, G. Chanan, E. Yang, Z. DeVito, Z. Lin,
+A. Desmaison, L. Antiga, A. Lerer, Automatic differentiation in pytorch
+(2017).
+[38] D. P. Kingma, J. Ba, Adam: A method for stochastic optimization (2014).
+arXiv:1412.6980.
+[39] M. Heusel, H. Ramsauer, T. Unterthiner, B. Nessler, S. Hochreiter, Gans
+trained by a two time-scale update rule converge to a local nash equilib-
+rium, in: Advances in Neural Information Processing Systems, 2017.
+
diff --git a/tNFAT4oBgHgl3EQfgx22/content/tmp_files/load_file.txt b/tNFAT4oBgHgl3EQfgx22/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2ca18437e88e852e7ad6edd01836d166b24c8bae
--- /dev/null
+++ b/tNFAT4oBgHgl3EQfgx22/content/tmp_files/load_file.txt
@@ -0,0 +1,733 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf,len=732
+page_content='1  Pattern Recognition Letters  journal homepage: www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='com  Improving Sketch Colorization using Adversarial Segmentation Consistency  Samet Hicsonmeza,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='∗∗,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Nermin Sametb,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Emre Akbasc,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Pinar Duygulua  aHacettepe University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Ankara,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Turkey  bLIGM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Ecole des Ponts,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Univ Gustave Eiffel,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' CNRS,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Marne-la-Vallée,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' France  cMiddle East Technical University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Ankara,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Turkey  Article history:  sketch colorization,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  sketch to image  translation,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Generative Adversarial Net-  works (GAN),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' image segmentation,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' im-  age to image translation  ABSTRACT  We propose a new method for producing color images from sketches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Current solutions  in sketch colorization either necessitate additional user instruction or are restricted to  the "paired" translation strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' We leverage semantic image segmentation from a gen-  eral-purpose panoptic segmentation network to generate an additional adversarial loss  function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' The proposed loss function is compatible with any GAN model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Our method is  not restricted to datasets with segmentation labels and can be applied to unpaired trans-  lation tasks as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Using qualitative, and quantitative analysis, and based on a user  study, we demonstrate the efficacy of our method on four distinct image datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' On the  FID metric, our model improves the baseline by up to 35 points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Our code, pretrained  models, scripts to produce newly introduced datasets and corresponding sketch images  are available at https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='com/giddyyupp/AdvSegLoss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  © 2023 Elsevier Ltd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' All rights reserved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Introduction  The task of image generation from an input sketch or edge  map is known as "sketch to image translation", or "sketch col-  orization".' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Sketches capture essential content of the images and  they can be easily acquired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Yet, vast amount of domain dif-  ference between single channel edge maps and color images  makes sketch colorization a challenging process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Lack of de-  tails in sketches especially for background is another problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  Sketch colorization has been investigated in numerous do-  mains: faces [1, 2, 3, 4], objects [5, 6, 7, 8], animes [9, 10, 11,  12, 13, 14, 15], art [16], icons [17] and scenes [18, 19, 20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' The  majority of the approaches require user direction in the form of  supplementary input, such as a reference color, patch, or image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  These approaches usually generate surreal colorizations other-  wise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Except for a few studies (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=', Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' [8]), most of the  approaches follow the “paired” strategy, which is restricted to  use datasets with a ground-truth image for each sketch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  ∗∗Corresponding author  e-mail: samethicsonmez@hacettepe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='tr (Samet  Hicsonmez), nermin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='samet@enpc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='fr (Nermin Samet),  emre@ceng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='metu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='tr (Emre Akbas),  pinar@cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='hacettepe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='tr (Pinar Duygulu)  In this study, we aim to leverage general purpose semantic  image segmentation to alleviate the aforementioned shortcom-  ings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' We argue that an accurately colored sketch would pro-  duce a “real” segmentation result, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=', a result that looks like  the segmentation of a real image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Thus, for sketch based image  colorization problem, we exploit semantic segmentation meth-  ods that have reached to a degree of maturity even for datasets  on which they were not trained (Section 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' We introduce a  segmentation-based adversarial loss to be used in a GAN (Gen-  erative Adversarial Network) setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' With our approach, neither  extra user instruction nor "paired" input is required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  We introduce three models for varying levels of segmenta-  tion feedback in the sketch to image translation pipeline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Our  models could be integrated into both paired and unpaired GAN  models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' We illustrate the effectiveness of applying segmenta-  tion cues via comprehensive experimental analyses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' This pa-  per extends our previous work [21] in the following ways: (i)  We apply our method to a new task: label-to-photo transla-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Our experiments on two challenging datasets show that  our segmentation-based adversarial loss is useful in this task,  too.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Again, ground-truth segmentation labels are not a require-  ment for our approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  (ii) We perform experiments to set  the optimal values for weights of two additional discriminators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  (iii) We incorporate an outdoor dataset, Cityscapes [22], to both  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='08590v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='CV]  20 Jan 2023  NON  SOLUS  ELSEVIER2  Fake Segmentation  Real Segmentation  Real Image  Input Sketch  Inference  GAN Model  Generated  Image  Segmentation  Network  Real?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  0/1  Real?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  0/1  Real?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  0/1  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' 1: The proposed model for sketch colorization with Adversarial Segmentation Loss (ASL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' It is composed of two parts;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' a general purpose image translation  GAN model, and an image segmentation model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' During training, input sketches are first colorized using the baseline GAN model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Then, generated and ground truth  color images are fed to the pre-trained panoptic segmentation model to extract fake and real segmentation maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Finally, two additional discriminators are used to  classify the segmentation maps as fake or real, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' The box with dashed yellow borders shows the inference stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Red border marks the GAN model used  for sketch to image translation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Here, Pix2Pix is used as an example image translation model, which could be replaced by any paired or unpaired model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  sketch colorization and label to photo translation tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' (iv) We  add a new metric, mean Intersection over Union (mIoU), in ad-  dition to FID score to measure the performance of all the mod-  els more reliably.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Related Work  Even though the sketch and the edge map of an image are  different concepts, in practice, XDoG [23] or HED [24] based  edge maps are considered as sketches (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=', [18, 11]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' More-  over, some sketch based models [5] use edge maps for data aug-  mentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Hence, we refer to all these models as "sketch-to-  image translation" or "sketch colorization" models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Although  general purpose image-to-image translation methods [25, 26,  27, 28, 29] could be used for sketch-to-image translation tasks,  the results are not satisfactory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  One widely used solution to improve the colorization per-  formance is to employ additional color [18, 11, 12, 10, 14, 15],  patch [6], image [2, 13, 16, 9, 17, 30] or language guidance [20,  31, 32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' For instance, in color guidance, users specify their de-  sired colors for the regions in the sketch image, and the model  utilizes this information to generate the same or similar colors  for these regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Some automatic methods also utilize user  guidance to improve their performance as a hybrid approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  Most of the sketch-to-image translation methods are based on  “paired” training approach [18, 11, 5, 19], but, recently un-  paired methods have also been presented [8, 16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  Scribbler [18] presents one of the very first paired and user  guided scene sketch colorization models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' In addition to pixel,  perceptual and GAN losses, Scribbler uses total variation loss  to encourage smoothness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' XDoG is used to generate sketch  images of 200k bedroom photos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' DCSGAN [15] uses HSV  color space in addition to the RGB, for line art colorization  task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Zou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' [20] use text inputs to progressively colorize an  input sketch, in such a way that a novel text guided sketch seg-  menter locates the objects in the scene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' EdgeGAN [19] maps  edge images to a latent space during training using an edge en-  coder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' During inference, the edge encoder is used to encode  the input sketch to the latent space to subsequently generate a  color image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Experiments are provided for 14 foreground and  3 background objects from COCO [33] dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  EdgeGAN [19] and Scribbler [18] use a supervised approach  where input sketches and corresponding output images exist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  However, it is hard to collect sketch image pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' [8]  propose a two stage method to convert object sketches to color  images in an unsupervised (unpaired) way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' They first convert  sketches to gray scale images, and then to color images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Self  supervision is used to complete the deliberately deleted sketch  parts and clear the added noisy edges from sketch images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  In Sketch-to-Art [16], an art image is generated using an in-  put sketch, with the additional help of the target style art image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  Content of the input sketch and style of the art image are en-  coded, and then fused to generate a stylized art image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' In [17]  authors proposed a method to colorize icons which utilizes col-  ored icon images as input in addition to the black-white icons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  The user input is valuable not only in helping the coloriza-  tion network to put the right colors to indicated regions, but also  in removing the color bleeding problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' In [34], users draw  scribbles to the regions on the generated image suffered from  color bleeding artifacts for guiding the model to fix them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  Unlike these methods, our method does not require any user  input to generate satisfactory colorization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Instead, we utilize  adversarial segmentation guidance to improve performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Adversarial Segmentation Consistency  Figure 1 shows the overall structure of our proposed model  for sketch colorization, which we refer to as Adversarial Seg-  mentation Loss (ASL) based model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  In this work, we used  Pix2Pix and CycleGAN methods as our baselines for paired and  unpaired training, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' This preference is made based  on the effectiveness of these methods across a variety of tasks  and datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' In the figure, Pix2Pix is used to show ASL based  paper  mirror-stuff  wall  light  tv96%  teddy bear 66%  table  cabinet  bed99%wall  66%  bed 51%3  model for paired approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Our model could be integrated into  any other paired or unpaired GAN model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  Our model consists of a baseline GAN, a panoptic segmen-  tation network (Seg) and two discriminators (DM and DB).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Panop-  tic segmentation network is trained offline on the COCO Stuff [35]  dataset and its weights are frozen during the training of our  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Fake and real images are fed to the Seg network to get  real and fake segmentation maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Then, these two segmenta-  tion maps are given to the discriminators to classify them as  fake or real.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' We designed three variants of our model to embed  different levels of segmentation feedback to the sketch to image  translation pipeline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  The first variant utilizes the full (multiclass) segmentation  map of an image where all foreground and background classes  (a total of 135 classes) are considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' In this model, ground-  truth color image Ireal and the generated color image Ifake are  fed to Seg which outputs full segmentation maps for both im-  ages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Then, these two outputs are given to a discriminator net-  work DM to discriminate between real and fake segmentation  maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' We call this model as Multi-class in the rest of the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  As a higher level of abstraction, grouping objects as back-  ground and foreground alone may yield sufficient information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  The second variant of our model uses only two classes (back-  ground and foreground) in the segmentation map by grouping  all foreground classes into one and all background classes into  another class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' In this model, which we refer to as Binary, bi-  nary segmentation outputs for real and fake images are fed to a  discriminator network DB to discriminate between real and fake  ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Finally, our third variant is the union of the above two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' It  contains both discriminators, and is named as Combined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  Overall loss function for our model is the sum of losses of  the baseline GAN model (LG) and the two additional discrimi-  nators’ (LB and LM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' That is, the objective function is:  L = wgLG + wbLB + wmLM  Let S egB and S egM correspond to the panoptic segmenta-  tion networks in Binary and Multi-class cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' The additional  losses that we introduce, LB and LM, are defined as:  LB(G, DB, S egB) =  �  i  log(DB(S egB(yi)))+  �  i  log(1 − DB(S egB(G(xi)))  LM(G, DM, S egM) =  �  i  log(DM(S egM(yi)))+  �  i  log(1 − DM(S egM(G(xi)))  Let xi be an input sketch image, and yi be the corresponding  ground truth color image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' When the baseline GAN model is  Pix2Pix [27], GAN loss LG is formulated as:  LG(G, D) =  �  i  log(D(xi))+  �  i  log(1−D(G(xi))+  �  i  ∥yi−G(xi)∥  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' 2: Sample segmentations using general purpose panoptic segmentation  network on different datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' The model generalizes well to several domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  Table 1: Statistics of the datasets used in our experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  Dataset  Train Images  Test Images  ADE20k Bedroom  1355  135  Cityscapes  2975  500  Illustration  659  131  COCO Elephant  1800  343  COCO Sheep  1300  229  When baseline is CycleGAN [25], LG for direction X → Y is:  LG(GX,GY, DX) =  �  j  log(DX(y j)) +  �  i  log(1 − DX(GX(xi))  +  �  i  ∥xi − GY(GX(xi))∥  where GX maps input sketches to color images, and GY maps  the color images back to sketch domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' DX is the discriminator  for domain X, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' sketches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Final LG for CycleGAN is the sum  of above formulation for two directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  We analysed the effect of each component in the objective  function and, set wg, wb and wm to 1 based on the experimental  analysis (see Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Note that, for the Binary model wm,  and for the Multi-class model wb is set to 0 respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Datasets  We evaluated our models on five challenging datasets (see  Table 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' The first dataset consists of bedroom images from the  ADE20k indoor dataset [36], with 1355 train and 135 test im-  ages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' The second dataset is Cityscapes [22] dataset which con-  tains 2975 training and 500 test images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' The third dataset [28]  contains illustrations from children’s books by Alex Scheffler,  with 659 train and 131 test images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' The fourth and fifth ones  were curated by us from the COCO dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' We collected im-  ages containing elephant or sheep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Note that these images may  also contain other foreground/background objects such as per-  son, animals, mountains, grass and sky.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Elephant dataset con-  tains 1800 train and 343 test images, and the sheep dataset has  1300 train and 229 test images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Example images from these  datasets and their segmentation outputs are shown in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='window  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='curtain  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='pottedplant98%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='wall  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='person98%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='bed89%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='diningtable82%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='chair78%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='chair55%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='bird60%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='floor-woodtree  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='elephant100%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='elephant100%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='grasstree  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='sheep9csheep10(sheep99%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='grassceiling  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='window  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='wall  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='window-blind  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='pottedplant89%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='tted plant 66%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='light  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='chair100%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='chair100%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='bed 100%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='cabinet  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='vase98%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='rug  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='floor-woodceiling  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='mirror-stuff  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='tv 92%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='wall  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='light  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='chair57%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='dining table 68%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='table  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='chair 100%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='couch80%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='floor-wood  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='bed 90%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='rug4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='Input  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='GT  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='CycleGAN  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='C-ASL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='(Multi-class)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='C-ASL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='(Binary)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='C-ASL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='(Combined)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='Input  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='GT  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='Pix2Pix  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='P-ASL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='(Multi-class)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='P-ASL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='(Binary)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='P-ASL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='(Combined)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' 3: Sample results from baselines and our model with different settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Input images on each row are from bedroom, illustration, elephants and sheep datasets,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' First two rows display results of unpaired training (baseline is CycleGAN), and last two rows show results for paired training (baseline is Pix2Pix).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' On  bedroom and elephant datasets Binary, on illustration and sheep datasets Combined setting gave best results for both training schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  Table 2: Comparison with CycleGAN [25] on unpaired sketch-to-image  translation task in terms of FID scores, lower is better.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  Dataset  CycleGAN  C-ASL  (Multi-class)  C-ASL  (Binary)  C-ASL  (Combined)  Bedroom  113.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='1  111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='7  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='1  93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='2  Cityscapes  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='9  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='1  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='9  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='1  Illustration  213.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='6  206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='9  204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='8  189.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='4  Elephant  126.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='4  103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='9  91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='9  116.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='9  Sheep  209.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='3  207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='2  236.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='1  196.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='8  Edge images are extracted using the HED [24] method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' In  the first two columns of Figure 3, we present sample natural and  edge images for all the datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' It can be seen that the images  contain a variety of foreground and background objects, also it  is hard to figure out the source dataset for some images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Experiments  We used PyTorch [37] to implement our models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' We use  sketch images as source domain, and color images as target do-  main.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' All training images (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' color and sketch images) are  resized to 256 × 256 pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' We train all models for 200 epochs  using the Adam optimizer [38] with a learning rate of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='0002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  We conducted all our experiments on a NVIDIA Tesla V100  GPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  We compared our models with Pix2Pix [27] and AutoPainter  (AP) [11] for paired and CycleGAN [25] for unpaired setting  on sketch-to-image translation task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' We used the official im-  plementations that are publicly available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Baseline models are  trained for 200 epochs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Our proposed ASL model that uses  Pix2Pix as the baseline GAN model is referred to as P-ASL,  and similarly C-ASL refers to the model that uses CycleGAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Quantitative Analysis  To quantitatively evaluate the quality of generated images,  we used the widely adopted Frechet Inception Distance (FID) [39]  metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' FID score measures the distance between the distribu-  tions of the generated and real images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Lower FID score indi-  cates the higher similarity between two image sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  On Bedroom and Cityscapes datasets where ground truth  segmentation maps are available, we also calculate the mean  Intersection over Union (mIoU) scores on colorized images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' We  forward each colorized image to an off-the-shelf segmentation  model trained on these two datasets separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' mIoU score  measures the quality of the segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' We argue that better  colorized images should yield higher mIoU scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  5  Table 3: Comparison with AutoPainter [11] and Pix2Pix [27] on paired sketch-  to-image translation task in terms of FID scores, lower is better.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  Dataset  Auto  Painter  Pix2Pix  P-ASL  (Multi-class)  P-ASL  (Binary)  P-ASL  (Combined)  Bedroom  206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='8  100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='5  100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='0  95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='1  110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='1  Cityscapes  151.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='3  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='1  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='9  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='6  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='2  Illustration  272.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='0  180.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='0  176.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='9  178.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='0  175.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='7  Elephant  155.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='1  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='5  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='8  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='8  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='8  Sheep  233.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='1  157.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='0  159.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='9  162.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='0  150.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='5  Table 4: Comparison with CycleGAN on unpaired sketch-to-image transla-  tion task in terms of mIoU scores, higher is better.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  Dataset  CycleGAN  C-ASL  (Multi-class)  C-ASL  (Binary)  C-ASL  (Combined)  Oracle  Bedroom  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='20  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='71  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='58  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='44  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='62  Cityscapes  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='67  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='63  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='56  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='68  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='85  We present FID scores for unpaired translation in Table 2  and paired translation in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' FID scores are inline with the  visual inspections (see Figure 3), for all the datasets, at least  one variant of our model performed better than the baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  First of all, when we compare FID scores of two training  schemes and baseline models, paired training (Pix2Pix) per-  formed better than unpaired training, as expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' However, our  “adversarial segmentation loss” affected the results of paired  and unpaired cases differently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' For instance, on elephant dataset  our models improved baseline up to 35 points for unpaired case,  but only 5 points for paired case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  Another crucial observation is that segmentation guidance  closed the gap between unpaired and paired training results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  Best FID scores for unpaired models on bedroom, illustration  and elephant datasets become very close to or even better than  paired training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' For instance on the elephant dataset, the ini-  tial 40+ point FID gap (126 vs 83) dropped to 13 (92 vs 79)  on Binary setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Here the only exception is the sheep dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  Since the sheep dataset contains various complex objects, un-  paired and paired models failed to generate plausible images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  We show mIoU scores for unpaired translation in Table 4  and paired translation in Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' We also present oracle perfor-  mances of the segmentation method on both datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' On mIoU  metric, again for all the datasets, at least one of the variants of  our model performed better than the baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  When we look at the best performing settings on different  datasets, structure of the dataset has an effect on the results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' For  instance, even though one is an indoor and the other one is an  outdoor dataset, bedroom and elephant images are composed  of similar structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' FG/BG ratios and placements of them in  these datasets are similar across all images, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' walls, ceiling  Table 5: Comparison with Pix2Pix on paired sketch-to-image translation task  in terms of mIoU scores, higher is better.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  Dataset  Auto  Painter  Pix2Pix  P-ASL  (Multi-class)  P-ASL  (Binary)  P-ASL  (Combined)  Oracle  Bedroom  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='08  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='49  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='95  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='39  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='60  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='62  Cityscapes  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='02  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='71  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='63  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='70  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='74  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='85  Table 6: User Study results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  Dataset  CycleGAN  C-ASL  Bedroom  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='0  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='0  Illustration  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='0  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='0  Elephant  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='1  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='9  Sheep  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='1  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='9  Cityscapes (L2P)  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='7  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='3  Table 7: Effect of changing the wb and wm values, wb is used as 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='0 for all ex-  periments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Using 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='0 for both weights yields the best FID score on the ADE20k  bedroom images for the task of sketch-to-image translation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  wb and wm  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='0  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='0  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='0  FID  114.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='8  114.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='5  93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='2  147.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='8  104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='6  and floors in bedroom images are always positioned in the same  places on different images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Also elephant images contain very  few FG objects, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' only elephants most of the time, and large  BG areas such as grass, trees and sky.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' On these two datasets,  Binary setting which considers FG/BG classes only gave the  best FID score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' On the other hand, illustration and sheep images  got a variety of FG objects and scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' On such datasets, using  only a FG/BG discriminator even degrades the performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  Our model has two important parameters, wb and wm, to  control the effect of segmentation discriminators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' To find the  best possible values, we conducted experiments by training our  models on the ADE20k bedroom images on the unpaired sketch  to image translation task (see Table 7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Using a small value  like 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='1 gives a similar score to baseline CycleGAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' On the  other hand using a big value like 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='0 increased the FID score  dramatically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Setting wb and wm to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='0 resulted in the best FID  score, thus the weights are set to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='0 in all experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Qualitative Analysis and User Study  We present visual results of sketch colorization for our model  and the baseline models in the Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' On bedroom and illus-  tration datasets, we show results of unpaired training, and on  elephant and sheep datasets we show paired training results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  On the bedroom dataset, the Binary setting generates bet-  ter images compared to baselines and other settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Colors  are uniform across the object parts in this setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' There are  defective colors in the CycleGAN results such as the bottom  of the bed and floor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' On the illustration dataset, the baseline  model performed poorly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Objects are hard to recognize and  most importantly colors are not proper at all.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' On the other hand,  Multi-class and Combined settings generate significantly better  images i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' generated objects and background got consistent  colors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Finally, on elephant and sheep datasets although gener-  ated images are not very visually appealing for all the methods,  segmentation guided images are quite appealing compared to  baseline models’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' On the elephant dataset Binary, on the sheep  dataset Combined setting performed the best.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  We conducted a user study to measure realism of generated  images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' We show two random images (at random positions,  6  Input  GT  CycleGAN  Binary  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' 4: Sample results on Cityscapes dataset for CycleGAN and our best model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  In the first image, CycleGAN generates buildings instead of trees, also there are  defects on the road.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Other two images are blurry and lack details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' On the other  hand, in all cases our Binary setting generates more visually appealing images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  Table 8: Comparison with CycleGAN [25] on unpaired label-to-photo trans-  lation task in terms of FID scores, lower is better.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  Dataset  CycleGAN  C-ASL  (Multi-class)  C-ASL  (Binary)  C-ASL  (Combined)  Bedroom  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='2  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='9  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='6  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='9  Cityscapes  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='0  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='9  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='8  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='0  left or right) which were generated with CycleGAN and our  best setting (lowest FID score) for all four datasets, and asked  participants to select the more realistic one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  We collected a total of 115 survey inputs from 39 different  users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' We ask users to evaluate 4 S2P models and 1 L2P model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  In Table 6, we present results of the user study in terms of pref-  erence percentages of each model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' User study results are inline  with the FID score results, on all datasets, images generated  by our model were preferred by the users most of the time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' On  sheep and elephant datasets, users struggled to select an answer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  Color distributions and shapes of FG objects are two dominant  factors which lead user preferences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Label to Photo Translation  We also experimented with label-to-photo (L2P) translation  task to show the effectiveness of our model in a different task  where adversarial segmentation loss could be helpful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' In L2P  task, we use ADE20k bedroom and Cityscapes datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Sim-  ilar to S2P task, all images are resized to 256x256 pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' We  Table 9: Comparison with Pix2Pix [27] on paired label-to-photo translation  task in terms of FID scores, lower is better.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  Dataset  Pix2Pix  P-ASL  (Multi-class)  P-ASL  (Binary)  P-ASL  (Combined)  Bedroom  128.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='1  118.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='2  122.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='3  110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='1  Cityscapes  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='5  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='4  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='9  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='6  Table 10: Comparison with CycleGAN on unpaired label-to-photo transla-  tion task in terms of mIoU scores, higher is better.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  Dataset  CycleGAN  C-ASL  (Multi-class)  C-ASL  (Binary)  C-ASL  (Combined)  Oracle  Bedroom  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='70  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='88  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='10  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='69  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='62  Cityscapes  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='13  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='45  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='70  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='61  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='85  Table 11: Comparison with Pix2Pix on paired label-to-photo translation task  in terms of mIoU scores, higher is better.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  Dataset  Pix2Pix  P-ASL  (Multi-class)  P-ASL  (Binary)  P-ASL  (Combined)  Oracle  Bedroom  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='56  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='59  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='54  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='62  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='62  Cityscapes  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='62  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='66  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='69  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='56  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='85  train L2P models for 200 epochs using the Adam optimizer [38]  with a learning rate of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='0002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' We show FID scores for unpaired  L2P in Table 8 and paired translation in Table 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' For unpaired  translation our best performing method improves the baseline  for more than 5 points on Bedroom and almost 20 points on  Cityscapes datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Similarly on the paired translation, the im-  provements regard to the baseline reaches 18 points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  In Table 10 and Table 11, we present mIoU scores for un-  paired and paired L2P translation, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' For both cases,  our best performing variant outperforms the baseline method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  We present visual results in Figure 4 for only the base-  line model and our best performing setting Binary for unpaired  translation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Our model generates more photo-realistic images,  also generated images comply with the input label maps better.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  Input  GT  CycleGAN  +ASL  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' 5: Sample results on elephant and sheep datasets for CycleGAN and our  best model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Realism of both models are not satisfactory, however, especially  colors of BG areas are better in our results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Limitations  Figure 5 presents examples on elephant and sheep datasets  where both baseline and our best performing model suffer from  low visual realism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' The main reason for that is these datasets  contains complex foreground and background objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' How-  ever, our method performs significantly better than the baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  Especially on the first row, colorized image using our method  resembles more to the ground truth image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Conclusion  In this study, we present a new method for the sketch col-  orization problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Our method utilizes a general purpose im-  7  age segmentation network and adds an adversarial segmenta-  tion loss (ASL) to the regular GAN loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' ASL could be inte-  grated to any GAN model, and works even if the dataset does  not have segmentation labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' We used CycleGAN and Pix2Pix  as baseline GAN models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' We conducted extensive evaluations  on various datasets including bedroom, sheep, elephant and il-  lustration images and evaluate the performance both quantita-  tively (using FID and mIoU scores) and qualitatively (through  a user study).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' We showed that our model outperforms baselines  on all datasets on both FID score and user study analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  Regarding the limitations of our method, although we im-  prove the baseline both qualitatively and quantitatively, espe-  cially elephant and sheep results lack realism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Even the paired  training results are not visually appealing on these two datasets,  most probably due to the fact that the baseline models are not  very successful at generating complex scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  Acknowledgment  The numerical calculations reported in this paper were fully  performed at TUBITAK ULAKBIM, High Performance and  Grid Computing Center (TRUBA resources).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Dr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Akbas is sup-  ported by the “Young Scientist Awards Program (BAGEP)” of  Science Academy, Turkey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  References  [1] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Chen, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Su, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Gao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Xia, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Fu, Deepfacedrawing: deep genera-  tion of face images from sketches, ACM Transactions on Graphics (TOG)  39 (4) (2020) 72–1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [2] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Lee, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Kim, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Lee, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Kim, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Chang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Choo, Reference-based sketch  image colorization using augmented-self reference and dense semantic  correspondence, in: IEEE Conference on Computer Vision and Pattern  Recognition, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [3] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Chen, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Wu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Zha, Linestofacephoto: Face photo generation  from lines with conditional self-attention generative adversarial networks,  in: ACM International Conference on Multimedia, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [4] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Huang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Jing, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Tan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Kwong, Multi-density sketch-to-image trans-  lation network, IEEE Transactions on Multimedia 24 (2022) 4002–4015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [5] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Hays, Sketchygan: Towards diverse and realistic sketch to  image synthesis, in: IEEE Conference on Computer Vision and Pattern  Recognition, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [6] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Xian, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Sangkloy, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Agrawal, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Raj, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Lu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Fang, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Yu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Hays,  Texturegan: Controlling deep image synthesis with texture patches, in:  IEEE Conference on Computer Vision and Pattern Recognition, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [7] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Lu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Wu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Tai, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='-K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Tang, Image generation from sketch con-  straint using contextual gan, in: IEEE European Conference on Computer  Vision, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [8] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Liu, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Yu21, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Yu, Unsupervised sketch to photo synthesis, in:  IEEE European Conference on Computer Vision, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [9] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Furusawa, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' sHiroshiba, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Ogaki, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Odagiri, Comicolorization:  semi-automatic manga colorization, in:  SIGGRAPH Asia Technical  Briefs, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [10] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Ci, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Ma, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Li, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Luo, User-guided deep anime line art  colorization with conditional adversarial networks, in: ACM International  Conference on Multimedia, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [11] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Liu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Qin, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Wan, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Luo, Auto-painter: Cartoon image generation  from sketch by using conditional wasserstein generative adversarial net-  works, Neurocomputing 311 (2018) 78 – 87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [12] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Zhang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Li, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='-T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Wong, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Ji, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Liu, Two-stage sketch colorization,  ACM Transactions on Graphics (TOG) 37 (6) (2018) 1–14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [13] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Ji, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Lin, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Liu, Style transfer for anime sketches with  enhanced residual u-net and auxiliary classifier gan, in: Asian Conference  on Pattern Recognition, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [14] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Yuan, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Simo-Serra, Line art colorization with concatenated spatial  attention, in: CVPR Workshops, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [15] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Dou, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Wang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Li, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Li, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Liu, Dual color space guided  sketch colorization, IEEE Transactions on Image Processing 30 (2021)  7292–7304.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [16] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Liu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Song, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Zhu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Elgammal, Sketch-to-art: Synthesizing styl-  ized art images from sketches, in: Proceedings of the Asian Conference  on Computer Vision, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [17] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='-k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Lien, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Wang, Style-structure disentangled features and  normalizing flows for diverse icon colorization, in: IEEE Conference on  Computer Vision and Pattern Recognition, 2022, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' 11244–11253.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [18] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Sangkloy, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Lu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Fang, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Yu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Hays, Scribbler: Controlling deep  image synthesis with sketch and color, in: IEEE Conference on Computer  Vision and Pattern Recognition, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [19] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Gao, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Liu, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Xu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Liu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Zou, Sketchycoco: Image gen-  eration from freehand scene sketches, in: IEEE Conference on Computer  Vision and Pattern Recognition, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [20] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Zou, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Mo, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Gao, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Du, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Fu, Language-based colorization of  scene sketches, ACM Transactions on Graphics (TOG) 38 (6) (2019) 1–  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [21] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Hicsonmez, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Samet, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Akbas, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Duygulu, Adversarial segmentation  loss for sketch colorization, in: IEEE International Conference on Image  Processing, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [22] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Cordts, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Omran, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Ramos, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Rehfeld, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Enzweiler, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Benen-  son, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Franke, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Roth, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Schiele, The cityscapes dataset for semantic  urban scene understanding, in: IEEE Conference on Computer Vision and  Pattern Recognition, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [23] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Winnemöller, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Kyprianidis, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Olsen, Xdog: an extended  difference-of-gaussians compendium including advanced image styliza-  tion, Computers & Graphics 36 (6) (2012) 740–753.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [24] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Xie, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Tu, Holistically-nested edge detection, in: IEEE International  Conference on Computer Vision, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [25] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Zhu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Park, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Isola, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Efros, Unpaired image-to-image trans-  lation using cycle-consistent adversarial networks, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [26] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Yi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Zhang, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Tan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Gong, Dualgan: Unsupervised dual learning  for image-to-image translation, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [27] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Isola, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Zhu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Zhou, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Efros, Image-to-image translation with  conditional adversarial networks, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [28] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Hicsonmez, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Samet, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Akbas, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Duygulu, Ganilla: Generative ad-  versarial networks for image to illustration translation, Image and Vision  Computing (2020) 103886.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [29] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Huang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Liu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Belongie, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Kautz, Multimodal unsupervised  image-to-image translation, in: IEEE European Conference on Computer  Vision, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [30] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Lee, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Kim, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Lee, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Kim, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Chang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Choo, Reference-based sketch  image colorization using augmented-self reference and dense semantic  correspondence, in: IEEE Conference on Computer Vision and Pattern  Recognition, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [31] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Zou, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Yu, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Du, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Mo, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='-Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Song, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Xiang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Gao, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Chen,  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Zhang, Sketchyscene: Richly-annotated scene sketches, in: IEEE Eu-  ropean Conference on Computer Vision, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [32] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Kim, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Jhoo, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Park, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Yoo, Tag2pix: Line art colorization using  text tag with secat and changing loss, in: IEEE International Conference  on Computer Vision, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [33] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Lin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Maire, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Belongie, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Hays, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Perona, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Ramanan, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Dol-  lár, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Zitnick, Microsoft COCO: Common objects in context, in: IEEE  European Conference on Computer Vision, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [34] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Kim, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Park, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Choi, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Seo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Choo, Deep edge-aware inter-  active colorization against color-bleeding effects, in: IEEE International  Conference on Computer Vision, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [35] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Caesar, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Uijlings, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Ferrari, Coco-stuff: Thing and stuff classes in  context, in: IEEE Conference on Computer Vision and Pattern Recogni-  tion, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [36] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Zhou, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Zhao, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Puig, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Xiao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Fidler, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Barriuso, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Torralba,  Semantic understanding of scenes through the ade20k dataset, Interna-  tional Journal of Computer Vision 127 (3) (2019) 302–321.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [37] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Paszke, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Gross, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Chintala, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Chanan, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Yang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' DeVito, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Lin,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Desmaison, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Antiga, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Lerer, Automatic differentiation in pytorch  (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [38] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Kingma, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Ba, Adam: A method for stochastic optimization (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  arXiv:1412.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='6980.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content='  [39] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Heusel, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Ramsauer, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Unterthiner, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Nessler, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
+page_content=' Hochreiter, Gans  trained by a two time-scale update rule converge to a local nash equilib-  rium, in: Advances in Neural Information Processing Systems, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNFAT4oBgHgl3EQfgx22/content/2301.08590v1.pdf'}
diff --git a/ttE1T4oBgHgl3EQf3wUi/content/2301.03492v1.pdf b/ttE1T4oBgHgl3EQf3wUi/content/2301.03492v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..433f97cf9c99487ea83607af43bee4c685e480d1
--- /dev/null
+++ b/ttE1T4oBgHgl3EQf3wUi/content/2301.03492v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4cbaa5793787a8f4ba235dc51ef5856018d2b9e93b8f2048d1d67a1bb0cf604d
+size 170632
diff --git a/ttE1T4oBgHgl3EQf3wUi/vector_store/index.faiss b/ttE1T4oBgHgl3EQf3wUi/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..7dcd5d3aee2d694d88d6b8b43cb994bb36067d43
--- /dev/null
+++ b/ttE1T4oBgHgl3EQf3wUi/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4dc85196b09dec3ce6ceb73db3679ab57265cc1c40337899b4a7558ae9aa54f1
+size 4784173
diff --git a/ttE1T4oBgHgl3EQf3wUi/vector_store/index.pkl b/ttE1T4oBgHgl3EQf3wUi/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..53efcbc3a45be8cbee1d8d4986f3d5a8ae8a8d45
--- /dev/null
+++ b/ttE1T4oBgHgl3EQf3wUi/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:48bf1e67c2d8a365c0489bcfe0be3e036e6b27633bb37a2a7c621727c8a3ab13
+size 147673
diff --git a/udAyT4oBgHgl3EQfm_hJ/content/tmp_files/2301.00480v1.pdf.txt b/udAyT4oBgHgl3EQfm_hJ/content/tmp_files/2301.00480v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..be1b4ec54426ad22e569d47818fe16ff04ad52a7
--- /dev/null
+++ b/udAyT4oBgHgl3EQfm_hJ/content/tmp_files/2301.00480v1.pdf.txt
@@ -0,0 +1,1347 @@
+Can unconventional pairing arise from a bare isotropic electron-phonon coupling?
+Philip M. Dee,1, 2 Benjamin Cohen-Stead,3, 4 Steven Johnston,3, 4 and P. J. Hirschfeld1
+1Department of Physics, University of Florida, Gainesville, Florida, 32611, USA
+2Department of Materials Science and Engineering, University of Florida, Gainesville, Florida, 32611, USA
+3Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996, USA
+4Institute of Advanced Materials and Manufacturing, The University of Tennessee, Knoxville, Tennessee 37996, USA
+(Dated: January 3, 2023)
+In a recent work by Schrodi et al.
+[Phys.
+Rev.
+B. 104, L140506 (2021)], the authors find
+an unconventional superconducting state with a sign-changing order parameter using the Migdal-
+Eliashberg theory, including the first vertex correction. This unconventional solution arises despite
+using an isotropic bare electron-phonon coupling in the Hamiltonian. We examine this claim using
+hybrid quantum Monte Carlo for a single-band Holstein model with a cuprate-like noninteracting
+band structure and identical parameters to Schrodi et al.. Our Monte Carlo results for these pa-
+rameters suggest that unconventional pairing correlations do not become dominant at any carrier
+concentration we have checked. Instead, strong charge-density-wave correlations persist at the low-
+est accessible temperatures for dilute and nearly half-filled bands. Lastly, we present arguments for
+how vertex-corrected Migdal-Eliashberg calculation schemes can lead to uncontrolled results in the
+presence of Fermi surface nesting.
+I.
+INTRODUCTION
+The possible role of electron-phonon (e-ph) interac-
+tions in high-temperature (high-Tc) superconductors is
+a long-standing problem. Coupling at small momentum
+transfer, q, can lead to attractive interactions in uncon-
+ventional pairing channels [1–10]. There are also theoret-
+ical studies suggesting that the e-ph coupling can be en-
+hanced at small q transfers by the Coulomb interaction
+through screening [11, 12] and anisotropy in the trans-
+port properties [8, 12]. In these scenarios, the momen-
+tum structure of the e-ph coupling constant g(k, q) gives
+rise to attractive contributions λl in multiple angular mo-
+mentum channels. For any realistic g(k, q), the coupling
+in the s-wave channel is dominant, and the interaction
+will lead to an s-wave order parameter in the absence
+of any repulsive interactions. However, strong repulsive
+interactions like a large Hubbard U or µ∗ can suppress
+s-wave pairing in favor of an unconventional pairing sym-
+metry [13, 14]. Once this occurs, the next leading order
+contribution from the e-ph interaction can provide an
+additional boost to the pairing glue, provided it is an
+attractive interaction in the appropriate pairing channel
+(e.g., λx2−y2 for cuprates or λ±s for the Fe-based super-
+conductors).
+Recently, Schrodi et al. [15], proposed that a Holstein
+interaction – i.e. a momentum independent e-ph interac-
+tion – can mediate an attractive interaction in uncon-
+ventional channels without the additional influence of
+electron correlations. Ref. 15 examined several models,
+including a single-band Holstein model for the high-Tc
+cuprates, as well as multiband models for the Fe-based,
+and heavy-fermion superconductors with nested Fermi
+surfaces. In each case, they considered a Holstein e-ph
+coupling within a vertex-corrected Eliashberg-theory cal-
+culation (see Fig. 1), where the rainbow and first vertex
+correction diagrams for the electron self-energy are com-
+puted self-consistently. In doing so, they found that the
+inclusion of the vertex corrections leads to instabilities in
+unconventional pairing channels. Moreover, the symme-
+try of the derived order parameter in each case was con-
+sistent with those derived from weak coupling repulsive
+spin-fluctuation-based models and Fermi surface nesting
+arguments [13, 16].
+The results of Schrodi et al. [15] are at odds with
+many nonperturbative studies of the single-band Holstein
+model, which find that the temperature-doping phase di-
+agram is dominated by charge-density-wave or s-wave
+pairing correlations [17–33]. Here, we explicitly explore
+their claim using a state-of-the-art hybrid Monte Carlo
+(HMC) method [34]. Specifically, we obtain numerically
+exact solutions to the same cuprate model examined in
+Ref. 15, covering temperatures across the reported Tc in
+some cases. The model is dominated by charge-density-
+wave (CDW) correlations down to the lowest tempera-
+tures we examine, which overlap the range studied by
+Ref. 15. We further find that the dominant pairing cor-
+relations are weak and have an s-wave symmetry at all
+temperatures when simulations are performed at a fixed
+filling. Alternatively, when simulations are performed for
+a fixed chemical potential, we find the bands shift above
+the Fermi level as the temperature decreases, indicating
+that the self-energy effects from the e-ph coupling are
+substantial. At no point do we observe an instability to-
+wards a superconducting phase with an unconventional
+order parameter. With this result in mind, we then ex-
+amine the momentum structure of the first vertex correc-
+tion and argue that truncating the expansion at the first
+vertex correction is an uncontrolled approximation when
+the Fermi surface is well nested.
+II.
+MODEL AND METHODS
+We study a single-band Holstein model, defined on a
+two-dimensional square lattice. The Hamiltonian is given
+arXiv:2301.00480v1  [cond-mat.supr-con]  1 Jan 2023
+
+2
+Γ(k, q) =
+=
++
++ . . .
+= igk,q(1 + Γ(2)(k, q) + . . .)
+FIG. 1.
+The electron phonon vertex of a simple electron-
+phonon system Γ(k, q) ≡ Γ(k, iωn; q, iνm) is a sum of Feyn-
+man diagrams where the first term is simply the bare vertex
+igk,q. The “first vertex correction” is given by Γ(2)(q). Higher
+order diagrams are not considered in this work.
+by
+ˆH = −
+�
+i,j
+ti,jˆc†
+i,σˆcj,σ − µ
+�
+i,σ
+ˆni,σ +
+�
+i
+� ˆP 2
+i
+2M + MΩ2
+2
+ˆX2
+i
+�
++ α
+�
+i,σ
+ˆni,σ ˆXi,
+(1)
+where ˆc†
+i,σ creates a spin-σ (=↑, ↓) electron on site i,
+ˆni,σ = ˆc†
+i,σˆci,σ is the Fermion number operator for site
+i, ti,j is the hopping integral between sites i and j, µ is
+the chemical potential, ˆXi and ˆPi are the position and
+momentum operators for the atom at site i, M is the ion
+mass, Ω is oscillator frequency, and α is the e-ph coupling
+strength. The single-band tight-binding dispersion ϵk for
+this model is given by ξk = ϵk − µ, where
+ϵk = −2t[cos(kx) + cos(ky)] − 4t′[cos(kx) cos(ky)]
+(2)
+and we have set the lattice spacing a = 1.
+Throughout, we set M = ℏ = 1 such that the energy
+of the phonon modes ℏΩ → Ω, and restrict the hopping
+to nearest- (t) and next-nearest-neighbors (t′), only. We
+then adopted t = 1, t′/t = −0.2, Ω/t = 0.4, and α =
+1.059, following Ref. 15.1 These values result in a large
+dimensionless e-ph coupling of λ = α2/(WΩ2) ≈ 0.88,
+where W ≈ 8t is the noninteracting bandwidth.
+The
+chemical potential µ controls the filling in our simula-
+tions. Later, we will show results for fixed µ/t = −0.56
+and as well as for a fixed average filling n ≡ ⟨ˆn⟩ =
+1
+N
+�
+i,σ⟨ˆni,σ⟩ = 0.8 and 0.2. In the latter cases, µ is de-
+termined dynamically within the HMC simulation using
+a recently developed µ-tuning algorithm [35].
+We solve the model using a recently developed
+method [34], which leverages HMC [36, 37] and Fourier
+acceleration to reduce decorrelation time of the phonon
+fields [38], a physics-inspired preconditioner, and near-
+linear scaling measurement techniques.
+This approach
+1 Ref.
+15
+defines
+the
+bare
+band
+structure
+as
+ξk
+=
+−t [cos(kxa) + cos(kya)] − t′ cos(kxa) cos(kya) − µ.
+We have,
+therefore, selected our t and t′ values to match their bare band
+dispersion.
+allows us to simulate large system sizes and consider op-
+tical phonons with energies much smaller than the elec-
+tron hopping and equal to those used in Ref. 15. Unless
+stated otherwise, all results are obtained on N = 12 × 12
+clusters.
+The strength of the charge correlations is determined
+by measuring the charge structure factor
+S(q, τ) = 1
+N
+�
+i,j
+e−iq·(ri−rj)⟨ ˆ
+Tτ[ˆni(τ)ˆnj(0)]⟩,
+(3)
+where
+ˆ
+Tτ is the time-ordering operator, and charge sus-
+ceptibility
+χCDW(q) =
+� β
+0
+S(q, τ) dτ.
+(4)
+The strength of the pairing correlations is determined by
+the pair-field susceptibility
+χSC
+α
+= 1
+N
+� β
+0
+dτ ⟨ ˆ
+Tτ[ ˆ∆α(τ) ˆ∆†
+α(0)]⟩,
+(5)
+for some pairing symmetry α = s, d, p, etc., the operator
+ˆ∆†
+α is defined [39] as
+ˆ∆†
+α = 1
+2
+�
+i,γ
+f α
+γ ˆc†
+i,↑ˆc†
+i+γ,↓.
+(6)
+Here, the sum over γ is restricted up to nearest neighbors
+only. For s-wave pairing, f s
+γ = δγ,0, where δi,j is the usual
+Kronecker-delta. For d-wave pairing, f d
+γ = δγ,±ˆx −δγ,±ˆy.
+III.
+RESULTS
+A.
+Hybrid Monte Carlo
+Ref. [15] is unclear in how it treats the filling of the
+system, specifically whether µ or n is held fixed during
+the self-consistency loop of their calculations. We will
+consider both cases in what follows.
+We begin with a fixed chemical potential, which we
+set to µ/t = −0.56 as indicated by Ref. [15].
+Fig. 2a
+plots the evolution of the charge χCDW(q) and pairing
+correlations as a function of temperature. We find that
+χCDW(q) is most prominent at q = (π, π) for nearly all
+temperatures but displays non-monotonic behavior tak-
+ing on a maximum at T/t ≈ 0.4 before it turns over and
+rapidly decays to zero. At these lowest temperatures, the
+d-wave pair-field susceptibility is indeed larger than the
+s-wave, but neither are significantly larger than their val-
+ues at high-temperature, indicating no strong tendency
+to pairing. The non-monotonicity in χCDW(q) occurs be-
+cause the filling of the system is not fixed and n → 0 as
+the temperature is lowered (Fig. 2b). This behavior is
+likely due to significant growth in the self-energy, which
+shifts the bands above the Fermi level. Regardless of the
+
+3
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+χCDW(q)
+(a)
+χCDW(π, π)
+χCDW(qmax)
+χs
+χd
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+T/t
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+n
+(b)
+0.00
+0.05
+0.10
+0.15
+0.20
+χs, χd
+FIG. 2.
+The temperature evolution of the (a) charge and
+superconducting pair-field susceptibilities and (b) electronic
+filling n ≡ ⟨ˆn⟩ in the Holstein model for a fixed chemical po-
+tential µ/t = 0.56. The largest filling at T/t = 2 is n = 0.809
+(outside the plot window). As the temperature is lowered, the
+band shifts to energies above the Fermi level, and the band
+is depleted n → 0. Results were obtained on N = 12 × 12
+clusters.
+origin, we find no evidence for a d-wave instability when
+we simulate the system with a fixed chemical potential.
+Next, we fix the average filling to n = 0.8, correspond-
+ing to the approximate band filling for µ/t = −0.56 ob-
+tained at T/t = 2.
+Figure 3 plots the corresponding
+temperature dependence of the charge and pair-field sus-
+ceptibilities in this case.
+Here the q = (π, π) charge
+susceptibility dominates at all temperatures and is up to
+five orders magnitude larger than both the s- and d-wave
+pair-field susceptibilities for T/t < 0.2. We can conclude
+that the low-temperature ground state of the system is
+dominated by charge correlations and is not supercon-
+ducting.
+Turning to the superconducting correlations,
+we find that χs > χd at all temperatures, with the latter
+dropping significantly once the CDW correlations begin
+to dominate. We find no evidence for enhanced d-wave
+pairing or a superconducting instability for this filling. It
+should also be noted that the vertex-corrected ME calcu-
+lations of Ref. [15] placed the superconducting transition
+at Tc/t = 0.036 (52 K), which falls within our simulation
+temperatures.
+Our results demonstrate that charge correlations are
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+T/t
+0
+500
+1000
+1500
+2000
+2500
+χCDW(q)
+χCDW(qmax)
+χCDW(π, π)
+χs
+χd
+0.00
+0.02
+0.04
+0.06
+0.08
+0.10
+χs, χd
+FIG. 3.
+The temperature evolution of the charge and su-
+perconducting pair-field susceptibilities in the Holstein model
+at a fixed filling n = 0.8.
+The remaining parameters are
+t′/t = −0.2, Ω/t = 0.4, and λ = 0.8762. Results are obtained
+on N = 12 × 12 clusters.
+dominant in the Holstein model near half-filling, in agree-
+ment with many prior numerical studies [17, 18, 21, 24,
+26–29, 31–33].
+Many of those same studies also find
+strong superconducting correlations for carrier concen-
+trations away from half-filling. Motivated by this, we also
+performed calculations for a dilute filling n = 0.2. Fig. 4
+plots the resulting temperature evolution of the charge
+and pairing susceptibilities in this case. The noninteract-
+ing Fermi surface in the case is free-electron-like (circu-
+lar) and is far from any nesting conditions. Nevertheless,
+we find that q = (π, π) charge correlations dominate the
+system at low temperatures, while the superconducting
+correlations remain weak over the temperatures we can
+access. In this case, the large value of χCDW(π, π) reflects
+a strong tendency towards bipolaron formation [29, 32],
+which is not unexpected given the large value of λ. Our
+results show that the Holstein model for the parameters
+considered in Ref. [15] is dominated by bipolaron forma-
+tion at all carrier concentrations, which tend to order
+and localize for this value of λ. We find no indications
+that they condense into a superconducting state of any
+symmetry.
+Our results contradict those of Ref. [15], which ob-
+tained a d-wave superconducting solution.
+There are
+several contributions to this discrepancy, but one partic-
+ularly important factor is that their calculations do not
+include the renormalization of the phonon propagator.
+This approximation is, understandably, motivated by a
+need to reduce the computational complexity stemming
+from the inclusion of the vertex correction. However, this
+approximation is severe, as it prevents CDW correlations
+driven by conventional phonon softening from growing
+large enough to compete with superconductivity. Schrodi
+et al. [40] and others [29, 41, 42] have included these ef-
+fects in previous calculations without the first vertex cor-
+rection. All have found that including the phonon self-
+
+4
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+T/t
+0
+5
+10
+15
+20
+25
+χCDW(q)
+χCDW(qmax)
+χCDW(π, π)
+χs
+χd
+0.000
+0.025
+0.050
+0.075
+0.100
+0.125
+χs, χd
+FIG. 4.
+The temperature evolution of the charge and su-
+perconducting pair-field susceptibilities in the Holstein model
+at a fixed filling n = 0.2.
+The remaining parameters are
+t′/t = −0.2, Ω/t = 0.4, and λ = 0.8762 Results are obtained
+on N = 12 × 12 clusters.
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+T/t
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+χCDW(q)
+χCDW(qmax)
+χCDW(π, π)
+χs
+χd
+0.0
+0.3
+0.6
+0.9
+1.2
+1.5
+χs, χd
+FIG. 5. For reference, we include the temperature evolution
+of the charge and superconducting pair-field susceptibilities
+in the noninteracting case at a fixed filling n = 0.2.
+The
+remaining parameters are t′/t = −0.2, Ω/t = 0.4, and λ = 0
+Results are obtained on N = 12 × 12 clusters.
+energy in a self-consistent manner reintroduces the ten-
+dency toward a charge instability, especially for a nested
+Fermi surface. Our numerically exact solutions include
+these phonon self-energy effects, which may account for
+our results’ discrepancies. However, it is noteworthy that
+Ref. [15] also obtained unconventional order parameters
+using a momentum-independent e-ph interaction in two
+other systems with well-nested Fermi surfaces. This ob-
+servation motivates us to examine the structure of the
+first vertex correction as a function of nesting in order
+to assess whether truncating at this order is a controlled
+approximation.
+B.
+Analysis of the first vertex correction
+The Feynman diagram for the first-order correction to
+the bare e-ph interaction vertex gk,q is shown in the right-
+most diagram of Fig. 1. It is given by
+Γ(2)(k, q) = kBT
+Nℏ3
+�
+q′,σ′
+|gk,q′|2D0(q′)G0(k − q − q′)
+× G0(k − q′).
+(7)
+Here, we use the shorthand notation k ≡ (k, iωn) and q ≡
+(q, iνm) with fermionic and bosonic Matsubara frequen-
+cies given by ωn = (2n+1)πkBT/ℏ and νm = 2πmkBT/ℏ
+(with n, m ∈ Z), respectively. Eqn. (7) follows directly2
+from its Feynman diagram and contains the e-ph cou-
+pling matrix elements gk,q′, the noninteracting phonon
+propagator
+D0(q′) ≡ D0(q′, iνm′) = −
+2Ωq′
+ν2
+m′ + Ω2
+q′ ,
+(8)
+and two noninteracting electron propagators where, for
+example,
+G0(k − q′) ≡ G0(k − q′, iωn − iνm′)
+=
+1
+i(ωn − νm′) − ℏ−1ξk−q′ ,
+(9)
+and ξk ≡ ϵk − µ. We have suppressed spin and band in-
+dices since we are working with a single-band model with
+parity in the up and down spin directions (e.g., G↑ = G↓).
+Since we are only interested in comparing the relative
+strength of the bare vertex to the vertex correction, we
+will work exclusively in units such that kB = ℏ = M = 1.
+For a Holstein model,
+the phonon dispersion is
+Einstein-like, and the bare e-ph coupling is isotropic;
+hence, Ωq′ → Ω and gk,q → g = α/
+√
+2Ω. With these
+simplifications, the vertex correction reduces to
+Γ(2)(k, q) = g2T
+N
+�
+q′,σ′
+D0(iνm′)G0(k − q − q′)G0(k − q′).
+(10)
+We evaluate the sums directly on finite momentum and
+frequency grids, thereby approximating the vertex in the
+thermodynamic limit. For our calculations, we take N =
+24 × 24 and 128 frequencies for a model temperature of
+T/t = 0.1. The number of Matsubara frequencies was
+chosen such that the high energy cutoff ℏωc ≈ 5W, where
+W is the noninteracting bandwidth.
+2 Our specific choice of momenta arguments is readily seen by ex-
+amining the vertex in the context of the first self-energy crossing
+diagram, the latter of which is the second-order correction Σ(2).
+The incoming and outgoing fermionic lines are labeled by k, the
+first phonon line is labeled by q, and the second is labeled by q′.
+
+5
+0
+π
+4
+π
+2
+3π
+4
+π
+ky
+� 1
+a
+�
+(a)
+µ = −0.56t
+0
+π
+4
+π
+2
+3π
+4
+π
+ky
+� 1
+a
+�
+(b)
+0.3
+0.3
+0.4
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+1.1
+1.2
+1.2
+0
+π
+4
+π
+2
+3π
+4
+π
+kx
+� 1
+a
+�
+0
+π
+4
+π
+2
+3π
+4
+π
+ky
+� 1
+a
+�
+(c)
+-0.1
+-0.1
+0.1
+0.1
+0.1
+−6
+−4
+−2
+0
+2
+4
+6
+ε(k) − µ
+� 1
+t
+�
+−1.0
+−0.6
+−0.2
+0.2
+0.6
+1.0
+ReΓ(2)(q)
+−1.0
+−0.6
+−0.2
+0.2
+0.6
+1.0
+ImΓ(2)(q)
+FIG. 6. Contour plots of the (a) Electronic dispersion (ε(k)−
+µ)/t and the (b) real and (c) imaginary parts of the first vertex
+correction Γ(2)(q) for µ/t = 0.56 and T/t = 0.1. In (a), the
+solid line indicates the fermi surface contour corresponding to
+ε(k)−µ = 0. In plots (b) and (c), the reported Γ(2)(q) follows
+from taking the vertex Γ(2)(k, iωn; q, iνm) has been evaluated
+at iω0 and iν0 and then reduced to q-dependence by carrying
+out a fermi surface average over k ∈ FS.
+Figure 6 plots vertex correction as a function of mo-
+mentum transfer.
+Here, we have simplified the multi-
+dimensional vertex function by focusing on the lowest
+Matsubara frequency (i.e., iωn=0 = πT and iνm=0 = 0),
+and performing a Fermi surface average over the fermion
+wave vectors k. Denoting the simplified vertex correction
+as Γ(2)(q), the averaging procedure is given by
+Γ(2)(q) ≡ ⟨Γ(2)(k, πT, q, 0)⟩k∈FS
+=
+�
+k∈BZ
+Γ(2)(k, πT, q, 0)˜δfd(ξk)
+�
+k∈BZ
+˜δfd(ξk)
+.
+(11)
+The wave vectors k are restricted to the Fermi surface by
+use of a “smeared” delta function ˜δfd(ξk) given by
+˜δfd(x) = − d
+dx
+�
+1
+ex/σ + 1
+�
+=
+1
+4σ cosh2 � x
+2σ
+�,
+(12)
+where the broadening parameter σ = kBT.
+Figure 6(a) shows a contour plot of the underlying
+band structure ξk in the upper quadrant of the first Bril-
+louin zone for µ/t = −0.56. The thick black line follows
+the Fermi surface contour ξk = 0 and thin dashed (solid)
+contour lines are used to plot ξk < 0 (ξk > 0). The val-
+ues of t, t′ and µ chosen here (to match Ref. [15]) are
+somewhat typical for modeling a 2D “cuprate”-like Fermi
+surface. The non-interacting Fermi surface is well nested
+for transfer vectors near q = (π, π), which coincides with
+the peak in χCDW(q) seen in our HMC results.
+The
+corresponding q-dependence of the real and imaginary
+parts of Γ(2)(q) are displayed in Figs. 6(b) and 6(c), re-
+spectively. (Here, we restrict the plot axes qx, qy ∈ [0, π]
+because the remaining quadrants are symmetrically iden-
+tical.) A Gaussian interpolation was used to smooth the
+24 × 24 q-grid, and contours were added to help identify
+the features and overall magnitude of the Fermi surface
+averaged vertex correction.
+It is clear from Fig. 6(b) that the real part of the Fermi-
+surface averaged vertex correction is of order O(1) near
+q = (π, π). For this case, the imaginary part of Γ(2)(q)
+[Fig. 6(c)] is relatively small and at most ∼ 0.1 − 0.2.
+This result implies that an expansion for the vertex
+Γ(q) ≈ ig[1 + Γ(2)(q) + . . . ] involves corrections that are
+on the order of the bare vertex, and thus higher order
+terms would likely be needed to obtain a converged re-
+sult. Consequently, a self-consistent treatment the first
+vertex correction in this context is likely uncontrolled,
+and one should assess the strength of the second-order
+diagrams before proceeding.
+We now investigate the changes in Γ(2)(q) as µ is tuned
+away from µ/t = −0.56 to determine the role of the
+Fermi surface nesting in the setting the magnitude of the
+correction. Figure 7 plots ξk along with ReΓ(2)(q) and
+ImΓ(2)(q) row-wise, but now each of the five columns
+corresponds to a different choice of µ/t ∈ [−1.5, 0.5] in
+steps of 0.5.
+The results for µ/t = −0.5 (middle col-
+umn) are similar to those shown in Fig. 6; the FS is
+strongly nested for q ≈ (π, π) and ReΓ(2)(π, π) ∼ O(1).
+The nesting condition survives when µ/t is adjusted by
+±0.5 but shifts to different momentum transfers in both
+
+6
+0
+π
+4
+π
+2
+3π
+4
+π
+ky
+� 1
+a
+�
+(a)
+µ = −1.5t
+(b)
+µ = −1.0t
+(c)
+µ = −0.5t
+(d)
+µ = 0.0t
+(e)
+µ = 0.5t
+0
+π
+4
+π
+2
+3π
+4
+π
+ky
+� 1
+a
+�
+(f)
+-0.1
+0.1
+0.2
+0.3
+0.3
+0.4
+0.4
+0.5
+0.5
+(g)
+0.4
+0.4
+0.4
+0.5
+0.5
+0.6
+0.6
+0.7
+0.7
+0.8
+0.8
+(h)
+0.3
+0.3
+0.4
+0.4
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+(i)
+0.2
+0.3
+0.4
+0.5
+0.6
+(j)
+0.2
+0.3
+0.3
+0
+π
+4
+π
+2
+3π
+4
+π
+kx
+� 1
+a
+�
+0
+π
+4
+π
+2
+3π
+4
+π
+ky
+� 1
+a
+�
+(k)
+-0.3
+-0.2
+-0.1
+-0.1
+0
+π
+4
+π
+2
+3π
+4
+π
+kx
+� 1
+a
+�
+(l)
+-0.5
+-0.4
+-0.3
+-0.2
+-0.1
+-0.1
+0
+π
+4
+π
+2
+3π
+4
+π
+kx
+� 1
+a
+�
+(m)
+0.1
+0.1
+0.1
+0.1
+0.2
+0
+π
+4
+π
+2
+3π
+4
+π
+kx
+� 1
+a
+�
+(n)
+0.1
+0.1
+0.2
+0.3
+0
+π
+4
+π
+2
+3π
+4
+π
+kx
+� 1
+a
+�
+(o)
+0.1
+0.1
+0.2
+0.3
+−6
+−4
+−2
+0
+2
+4
+6
+ε(k) − µ
+� 1
+t
+�
+−1.0
+−0.6
+−0.2
+0.2
+0.6
+1.0
+ReΓ(2)(q)
+−1.0
+−0.6
+−0.2
+0.2
+0.6
+1.0
+ImΓ(2)(q)
+FIG. 7. A survey of effects of the Fermi surface features on the first Fermi-surface averaged vertex correction (see Eq. 11).
+Results in each column correspond to µ/t = −1.5, -1, -0.5, 0, and 0.5 reading left to right. The top row shows contour plots
+of the bare band dispersion ξk. The thick black line denotes the Fermi surface contour. The thin dashed (solid) lines show
+contours for ξk < 0 (ξk > 0). The second and third rows show the real and imaginary parts of the Fermi surface averaged
+vertex Γ(2)(q) for momentum transfer in the positive quadrant of the first Brillouin zone (FBZ). The values of Γ(2)(q) at other
+points in the FBZ can be inferred from C4 symmetry.
+cases. This fact is evidenced by the strong incommensu-
+rate peaks in ReΓ(2)(q) for these values of the chemical
+potential. The peak heights also decrease in these cases
+but remain large enough to invalidate a low-order per-
+turbation expansion in the vertex function.
+The nesting conditions are strongly suppressed for
+µ/t = −1.5 and 0.5, as shown in the first and fifth
+columns, respectively. In these cases, the band structure
+begins to resemble a free electron (hole) dispersion with
+a circular Fermi surface. (For µ/t = −1.5, the electron-
+like Fermi surface is more diamond-like.) As one might
+expect, the real and imaginary parts of Γ(2)(q) are corre-
+spondingly smaller than 1. For example, ReΓ(2)(q) has
+a weak peak near q ≈ ( 1
+4, 4
+5)π for the free-electron-like
+case (µ/t = −1.5), while it has a very weak peak near
+q ≈ (0.9, 0.9)π for the free-hole-like case (µ/t = 0.5). We
+expect that a self-consistent treatment of the first order
+vertex corrections may be more controlled in these cases.
+C.
+Discussion
+In the previous section, we showed that the first vertex
+correction acquires a momentum anisotropy that follows
+directly from the geometry of the electronic dispersion
+near the Fermi level. This result occurs, even with a bare
+Holstein coupling and a dispersionless Einstein phonon
+mode, both of which are isotropic in momentum space.
+Improving upon this simplified picture by reintroducing
+dispersive phonons or using the dressed propagators in
+the vertex diagram could significantly alter our conclu-
+sion. Using dressed propagators G(k) and D(q) instead
+of G0(k) and D0(q) in Eqn. (10) and generating second-
+order corrections to the electron and phonon self-energies
+[i.e., Σ(2)(k) and Π(2)(q)] constitute a fully self-consistent
+evaluation within the vertex-corrected Migdal-Eliashberg
+theory.
+Such a procedure introduces additional e-ph-
+induced renormalization effects on both the phonons and
+electrons beyond the usual self-consistent Eliashberg for-
+malism. Even without the vertex correction, treating the
+electron and phonon self-energies on equal footing allows
+for phonon softening, manifesting as a Kohn anomaly in
+the phonon dispersion at the nesting vector [42]. If such
+
+7
+softening were also present in the vertex-corrected the-
+ory, the peaks in Γ(2)(q) could be quite strongly affected.
+Our results would reflect the first iteration of such a self-
+consistent procedure.
+Using HMC simulations as a stand-in for summing all
+the Feynman diagrams, we observed that reintroducing
+the neglected diagrams greatly favors CDW correlations
+at the expense of superconductivity for the parameters
+studied. This result is relatively unsurprising given the
+sizable dimensionless coupling λ ≈ 0.88, which, along-
+side the frequency of Ω/t = 0.4, fits into a regime asso-
+ciated with large lattice fluctuations [30]. In the large
+coupling limit λ ≥ 0.5, these correlations reflect bipo-
+laron formation [29] not captured within the framework
+of Migdal’s theory. How many additional vertex correc-
+tions are needed to describe bipolarons and the CDW
+transition remains unclear. It is also unclear if a finite
+number of corrections would be sufficient.
+The study of corrections to the electron-phonon ver-
+tex has a long history [29, 30, 43–59].
+Many of these
+works studied the ramifications of vertex corrections on
+superconductivity and consider, for instance, how vertex
+corrections affect: the critical temperature and or pair-
+ing [46–53, 55, 60], the isotope coefficient[49], predictions
+for non/antiadiabatic materials like fullerenes [49, 54],
+and unconventional superconductivity, often by including
+them alongside electronic correlations and spin fluctua-
+tions [46, 48, 61–68]. This body of literature is extensive,
+so we have not attempted to review these works compre-
+hensively. Instead, we highlight a potential blind spot
+concerning lurking charge instabilities in vertex-corrected
+Eliashberg approaches. Some findings of the current work
+have been discussed in the works above to varying degrees
+of rigor. In particular, when considering problems in 2D,
+it has been pointed out that Fermi surface nesting con-
+ditions can invalidate Migdal’s approximation, primarily
+due to geometric singularities appearing in the skeleton
+diagrams [69]. Schrodi et al. mention the issue of nest-
+ing and several other potential caveats in their Ref. [60],
+which debuts the same state-of-the-art full-bandwidth
+implementation of a vertex-corrected Eliashberg formal-
+ism used in Ref. [15]. However, as was shown here and
+by Esterlis et al.
+[29], comparing Eliashberg-type cal-
+culations with nonperturbative methods (e.g., quantum
+Monte Carlo) can be a vital means of addressing the va-
+lidity of approximate methods.
+IV.
+SUMMARY & CONCLUSION
+Analytic attempts at describing the nature of vertex
+corrections often entail simplifications to the electronic
+dispersion, typically reducing εk to the single parabolic
+band of free electrons.
+With modern computing re-
+sources, self-consistent solutions of the Migdal-Eliashberg
+equations, including the first vertex correction, are now
+technically feasible for lattice models with some tight-
+binding dispersion (e.g., Ref [15]).
+However, we have
+shown that while it may be easier to carry out these
+calculations, the results could be misleading in some in-
+stances. In particular, we performed HMC simulations
+using the same parameters associated with an uncon-
+ventional superconducting state in Ref. [15] and instead
+found a leading charge-density wave instability. We did
+not attempt to explore the entire parameter space to rule
+out a possible unconventional ground state somewhere in
+the phase diagram. However, to our knowledge, the ex-
+tensive literature on nonperturbative studies of the Hol-
+stein model does not contain any robust evidence for a
+leading unconventional order parameter thus far.
+To better understand the origin of the d-wave order
+parameter in the first-vertex-corrected Eliashberg theory,
+we evaluated a finite size approximation of the vertex
+correction. Due to the relative simplicity of the Holstein
+model, much of the momentum-space structure of Γ(2)(q)
+follows directly from the Fermi surface. For a cuprate-like
+Fermi surface, we observe peaks in Γ(2)(q) of O(1) near
+a nesting vector q = (π, π), indicating that higher-order
+diagrams may be crucial for these parameters, matching
+the conclusions from our HMC results.
+It remains an open question as to when and how vertex
+corrections should be included within Migdal-Eliashberg
+formalism for specific applications. What is clear is that
+there are scenarios where the perturbative expansion is
+somewhat ill-defined and blind to competing phenom-
+ena such as bipolaron formation. The standard Eliash-
+berg formalism below Tc comes equipped with the usual
+anomalous propagators, which admit a superconducting
+order parameter but not a competing CDW. A possible
+way forward would be to study the effect of vertex correc-
+tions in the normal state and tracking both pairing and
+the CDW correlations in the self-consistent Migdal ap-
+proximation [41, 42]. However, to truly understand the
+physics contained in the corrections, it may be necessary
+to study the diagrams beyond the first correction. Find-
+ing the middle ground where the first correction Γ(2)(q)
+[and possibly Γ(4)(q)] could be used to safely fine-tune
+predictions is a direction of future study.
+Acknowledgments — The authors thank Yan Wang for
+fruitful discussions about this topic. P. M. D. and P. J. H.
+acknowledge support from the U.S. Department of En-
+ergy, Office of Science, Office of Basic Energy Sciences,
+under Award Number DE-SC-0020385. B.C. S. and S. J.
+acknowledge support from the U.S. Department of En-
+ergy, Office of Science, Office of Basic Energy Sciences,
+under Award Number DE-SC0022311.
+[1] N. F. Mott, Polaron models of high-temperature super-
+conductors, Journal of Physics:
+Condensed Matter 5,
+3487 (1993).
+
+8
+[2] M. L. Kulić and R. Zeyher, Influence of strong electron
+correlations on the electron-phonon coupling in high-Tc
+oxides, Phys. Rev. B 49, 4395 (1994).
+[3] G. Santi, T. Jarlborg, M. Peter, and M. Weger, s- and d-
+wave symmetries of the solutions of the Eliashberg equa-
+tions, Physica C: Superconductivity 259, 253 (1996).
+[4] G.
+Varelogiannis,
+A.
+Perali,
+E.
+Cappelluti,
+and
+L. Pietronero, Density-of-states-driven anisotropies in-
+duced by momentum decoupling in Bi2Sr2CaCu2O8,
+Phys. Rev. B 54, R6877 (1996).
+[5] T. P. Devereaux, T. Cuk, Z.-X. Shen, and N. Na-
+gaosa, Anisotropic Electron-Phonon Interaction in the
+Cuprates, Phys. Rev. Lett. 93, 117004 (2004).
+[6] M. L. Kulić and O. V. Dolgov, Forward scattering peak in
+the electron–phonon interaction and impurity scattering
+of cuprate superconductors, physica status solidi (b) 242,
+151 (2005).
+[7] S. Johnston, I. M. Vishik, W. S. Lee, F. Schmitt,
+S. Uchida, K. Fujita, S. Ishida, N. Nagaosa, Z. X. Shen,
+and T. P. Devereaux, Evidence for the Importance of Ex-
+tended Coulomb Interactions and Forward Scattering in
+Cuprate Superconductors, Phys. Rev. Lett. 108, 166404
+(2012).
+[8] J. J. Lee, F. T. Schmitt, R. G. Moore, S. Johnston, Y. T.
+Cui, W. Li, M. Yi, Z. K. Liu, M. Hashimoto, Y. Zhang,
+D. H. Lu, T. P. Devereaux, D. H. Lee, and Z. X. Shen, In-
+terfacial mode coupling as the origin of the enhancement
+of Tc in FeSe films on SrTiO3, Nature 515, 245 (2014).
+[9] X. Wan and S. Y. Savrasov, Turning a band insulator
+into an exotic superconductor, Nature Communications
+5, 4144 (2014).
+[10] L. Rademaker, Y. Wang, T. Berlijn, and S. Johnston,
+Enhanced superconductivity due to forward scattering
+in FeSe thin films on SrTiO3 substrates, New Journal of
+Physics 18, 022001 (2016).
+[11] Z. B. Huang, W. Hanke, E. Arrigoni, and D. J. Scalapino,
+Electron-phonon vertex in the two-dimensional one-band
+Hubbard model, Phys. Rev. B 68, 220507 (2003).
+[12] S. Johnston, F. Vernay, B. Moritz, Z.-X. Shen, N. Na-
+gaosa, J. Zaanen, and T. P. Devereaux, Systematic study
+of electron-phonon coupling to oxygen modes across the
+cuprates, Phys. Rev. B 82, 064513 (2010).
+[13] D. J. Scalapino, A common thread: The pairing inter-
+action for unconventional superconductors, Rev. Mod.
+Phys. 84, 1383 (2012).
+[14] P. J. Hirschfeld, Using gap symmetry and structure to re-
+veal the pairing mechanism in Fe-based superconductors,
+Comptes Rendus Physique 17, 197 (2016).
+[15] F. Schrodi, P. M. Oppeneer, and A. Aperis, Uncon-
+ventional superconductivity mediated solely by isotropic
+electron-phonon interaction, Phys. Rev. B 104, L140506
+(2021).
+[16] I. I. Mazin and J. Schmalian, Pairing symmetry and pair-
+ing state in ferropnictides: Theoretical overview, Physica
+C: Superconductivity 469, 614 (2009).
+[17] J. K. Freericks, M. Jarrell, and D. J. Scalapino, Hol-
+stein model in infinite dimensions, Phys. Rev. B 48, 6302
+(1993).
+[18] R. T. Scalettar, N. E. Bickers, and D. J. Scalapino, Com-
+petition of pairing and Peierls–charge-density-wave cor-
+relations in a two-dimensional electron-phonon model,
+Phys. Rev. B 40, 197 (1989).
+[19] D. Meyer, A. C. Hewson, and R. Bulla, Gap formation
+and soft phonon mode in the Holstein model, Phys. Rev.
+Lett. 89, 196401 (2002).
+[20] M. Capone and S. Ciuchi, Polaron Crossover and Bipo-
+laronic Metal-Insulator Transition in the Half-Filled Hol-
+stein Model, Phys. Rev. Lett. 91, 186405 (2003).
+[21] M. Capone, P. Carta, and S. Ciuchi, Dynamical mean
+field theory of polarons and bipolarons in the half-filled
+Holstein model, Phys. Rev. B 74, 045106 (2006).
+[22] M. Tezuka, R. Arita, and H. Aoki, Phase diagram for
+the one-dimensional Hubbard-Holstein model: A density-
+matrix renormalization group study, Phys. Rev. B 76,
+155114 (2007).
+[23] Y. Murakami, P. Werner, N. Tsuji, and H. Aoki, Super-
+solid Phase Accompanied by a Quantum Critical Point in
+the Intermediate Coupling Regime of the Holstein Model,
+Phys. Rev. Lett. 113, 266404 (2014).
+[24] S. Karakuzu, L. F. Tocchio, S. Sorella, and F. Becca,
+Superconductivity, charge-density waves, antiferromag-
+netism, and phase separation in the Hubbard-Holstein
+model, Phys. Rev. B 96, 205145 (2017).
+[25] T. Ohgoe and M. Imada, Competition among Super-
+conducting, Antiferromagnetic, and Charge Orders with
+Intervention by Phase Separation in the 2D Holstein-
+Hubbard Model, Phys. Rev. Lett. 119, 197001 (2017).
+[26] C. Chen, X. Y. Xu, J. Liu, G. Batrouni, R. Scalettar,
+and Z. Y. Meng, Symmetry-enforced self-learning Monte
+Carlo method applied to the Holstein model, Phys. Rev.
+B 98, 041102 (2018).
+[27] M. Hohenadler and G. G. Batrouni, Dominant charge
+density wave correlations in the Holstein model on the
+half-filled square lattice, Phys. Rev. B 100, 165114
+(2019).
+[28] S. Li, P. M. Dee, E. Khatami, and S. Johnston, Accel-
+erating lattice quantum Monte Carlo simulations using
+artificial neural networks: Application to the Holstein
+model, Phys. Rev. B 100, 020302 (2019).
+[29] I. Esterlis, B. Nosarzewski, E. W. Huang, B. Moritz, T. P.
+Devereaux, D. J. Scalapino, and S. A. Kivelson, Break-
+down of the Migdal-Eliashberg theory: A determinant
+quantum Monte Carlo study, Phys. Rev. B 97, 140501
+(2018).
+[30] P. M. Dee, J. Coulter, K. G. Kleiner, and S. Johnston,
+Relative importance of nonlinear electron-phonon cou-
+pling and vertex corrections in the Holstein model, Com-
+munications Physics 3, 145 (2020).
+[31] O. Bradley, G. G. Batrouni, and R. T. Scalettar, Super-
+conductivity and charge density wave order in the two-
+dimensional Holstein model, Phys. Rev. B 103, 235104
+(2021).
+[32] B. Nosarzewski, E. W. Huang, P. M. Dee, I. Esterlis,
+B. Moritz, S. A. Kivelson, S. Johnston, and T. P. De-
+vereaux, Superconductivity, charge density waves, and
+bipolarons in the Holstein model, Phys. Rev. B 103,
+235156 (2021).
+[33] G. Paleari, F. Hébert, B. Cohen-Stead, K. Barros,
+R. Scalettar, and G. G. Batrouni, Quantum Monte Carlo
+study of an anharmonic Holstein model, Phys. Rev. B
+103, 195117 (2021).
+[34] B. Cohen-Stead, O. Bradley, C. Miles, G. Batrouni,
+R. Scalettar, and K. Barros, Fast and scalable quan-
+tum Monte Carlo simulations of electron-phonon models,
+Phys. Rev. E 105, 065302 (2022).
+[35] C. Miles, B. Cohen-Stead, O. Bradley, S. Johnston,
+R. Scalettar, and K. Barros, Dynamical tuning of the
+chemical potential to achieve a target particle number in
+
+9
+grand canonical Monte Carlo simulations, Phys. Rev. E
+105, 045311 (2022).
+[36] S. Duane, A. Kennedy, B. J. Pendleton, and D. Roweth,
+Hybrid Monte Carlo, Physics Letters B 195, 216 (1987).
+[37] S. Beyl, F. Goth, and F. F. Assaad, Revisiting the hybrid
+quantum Monte Carlo method for Hubbard and electron-
+phonon models, Phys. Rev. B 97, 085144 (2018).
+[38] G. G. Batrouni and R. T. Scalettar, Langevin simulations
+of a long-range electron-phonon model, Phys. Rev. B 99,
+035114 (2019).
+[39] E. A. Nowadnick, S. Johnston, B. Moritz, and T. P. Dev-
+ereaux, Renormalization of spectra by phase competition
+in the half-filled Hubbard-Holstein model, Phys. Rev. B
+91, 165127 (2015).
+[40] F. Schrodi, A. Aperis, and P. M. Oppeneer, Influence
+of phonon renormalization in eliashberg theory for su-
+perconductivity in two- and three-dimensional systems,
+Phys. Rev. B 103, 064511 (2021).
+[41] F. Marsiglio, Pairing and charge-density-wave correla-
+tions in the Holstein model at half-filling, Phys. Rev. B
+42, 2416 (1990).
+[42] P. M. Dee, K. Nakatsukasa, Y. Wang, and S. John-
+ston, Temperature-filling phase diagram of the two-
+dimensional Holstein model in the thermodynamic limit
+by self-consistent Migdal approximation, Phys. Rev. B
+99, 024514 (2019).
+[43] A. B. Migdal, Interaction between electrons and lattice
+vibrations in a normal metal, Sov. Phys. JETP 7, 996
+(1958), [Zh. Eksp. Teor. Fiz. 34, 1438 (1958)].
+[44] G. M. Eliashberg, Interactions between electrons and lat-
+tice vibrations in a superconductor, Sov. Phys. JETP 11,
+696 (1960), [Zh. Eksp. Teor. Fiz. 38, 966 (1960)].
+[45] G. M. Eliashberg, Temperature Green’s Function For
+Electrons In a Supercondutor, Sov. Phys. JETP 12, 1000
+(1961).
+[46] V. N. Kostur and B. C. V. Mitrović, Calculations of the
+superconducting critical temperature with vertex correc-
+tions, Phys. Rev. B 50, 12774 (1994).
+[47] P. Benedetti, C. Grimaldi, L. Pietronero, and G. Varel-
+ogiannis, Superconductivity beyond Migdal’s theorem
+and high-Tc phenomenology, Europhysics Letters 28, 351
+(1994).
+[48] H. R. Krishnamurthy, D. M. Newns, P. C. Pattnaik, C. C.
+Tsuei, and C. C. Chi, Vertex correction to pairing at a
+Van Hove singularity, Phys. Rev. B 49, 3520 (1994).
+[49] E. Nicol and J. Freericks, Vertex corrections to the theory
+of superconductivity, Physica C: Superconductivity 235-
+240, 2379 (1994).
+[50] C. Grimaldi, L. Pietronero, and S. Strässler, Nonadi-
+abatic Superconductivity: Electron-Phonon Interaction
+Beyond Migdal’s Theorem, Phys. Rev. Lett. 75, 1158
+(1995).
+[51] L. Pietronero, S. Strässler, and C. Grimaldi, Nonadi-
+abatic superconductivity. I. Vertex corrections for the
+electron-phonon interactions, Phys. Rev. B 52, 10516
+(1995).
+[52] C. Grimaldi, L. Pietronero, and S. Strässler, Nonadia-
+batic superconductivity. II. Generalized Eliashberg equa-
+tions beyond Migdal’s theorem, Phys. Rev. B 52, 10530
+(1995).
+[53] J. K. Freericks, E. J. Nicol, A. Y. Liu, and A. A. Quong,
+Vertex-corrected tunneling inversion in electron-phonon
+mediated superconductors: Pb, Phys. Rev. B 55, 11651
+(1997).
+[54] O. Gunnarsson, Superconductivity in fullerides, Rev.
+Mod. Phys. 69, 575 (1997).
+[55] A. Perali, C. Grimaldi, and L. Pietronero, Nonadiabatic
+pairing effects for tight-binding electrons interacting with
+phonons, Phys. Rev. B 58, 5736 (1998).
+[56] O. V. Danylenko and O. V. Dolgov, Nonadiabatic contri-
+bution to the quasiparticle self-energy in systems with
+strong electron-phonon interaction, Phys. Rev. B 63,
+094506 (2001).
+[57] J. P. Hague, Electron and phonon dispersions of the two-
+dimensional Holstein model: effects of vertex and non-
+local corrections, Journal of Physics: Condensed Matter
+15, 2535 (2003).
+[58] J. P. Hague, d-wave superconductivity from electron-
+phonon interactions, Phys. Rev. B 73, 060503 (2006).
+[59] A. V. Chubukov, A. Abanov, I. Esterlis, and S. A. Kivel-
+son, Eliashberg theory of phonon-mediated superconduc-
+tivity — When it is valid and how it breaks down, Annals
+of Physics 417, 168190 (2020), Eliashberg theory at 60:
+Strong-coupling superconductivity and beyond.
+[60] F. Schrodi,
+P. M. Oppeneer, and A. Aperis, Full-
+bandwidth Eliashberg theory of superconductivity be-
+yond Migdal’s approximation, Phys. Rev. B 102, 024503
+(2020).
+[61] M. Grabowski and L. J. Sham, Superconductivity from
+nonphonon interactions, Phys. Rev. B 29, 6132 (1984).
+[62] M. Mierzejewski, J. Zieliński, and P. Entel, Eliashberg
+equations of electrons on a square lattice: Interplay of
+strong electron-phonon interactions and electron correla-
+tions, Phys. Rev. B 57, 590 (1998).
+[63] J. Zieliński, M. Mierzejewski, and P. Entel, Supercon-
+ductivity in the two-dimensional Hubbard model close
+to the metal-insulator transition: A strong-coupling de-
+scription, Phys. Rev. B 57, 10311 (1998).
+[64] J. R. Schrieffer, Ward’s identity and the suppression of
+spin fluctuation superconductivity, Journal of Low Tem-
+perature Physics 99, 397 (1995).
+[65] E. Cappelluti and L. Pietronero, Van Hove singulari-
+ties and nonadiabatic effects in superconductivity, Eu-
+rophysics Letters 36, 619 (1996).
+[66] V. A. Moskalenko, P. Entel, and D. F. Digor, Strong in-
+teraction of correlated electrons with phonons: A dia-
+grammatic approach, Phys. Rev. B 59, 619 (1999).
+[67] C. C. Tsuei and J. R. Kirtley, Pairing symmetry in
+cuprate superconductors, Rev. Mod. Phys. 72, 969
+(2000).
+[68] M. L. Kulić, Interplay of electron–phonon interaction and
+strong correlations: the possible way to high-temperature
+superconductivity, Physics Reports 338, 1 (2000).
+[69] V. N. Kostur and B. c. v. Mitrović, Electron-phonon in-
+teraction in two dimensions: Variation of ImΣ(ϵp,ω) with
+increasing ωD/EF, Phys. Rev. B 48, 16388 (1993).
+
diff --git a/udAyT4oBgHgl3EQfm_hJ/content/tmp_files/load_file.txt b/udAyT4oBgHgl3EQfm_hJ/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3680847070dbc32f8dc2717cbd9ffbfc79a21e48
--- /dev/null
+++ b/udAyT4oBgHgl3EQfm_hJ/content/tmp_files/load_file.txt
@@ -0,0 +1,1056 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf,len=1055
+page_content='Can unconventional pairing arise from a bare isotropic electron-phonon coupling?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  Philip M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Dee,1, 2 Benjamin Cohen-Stead,3, 4 Steven Johnston,3, 4 and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Hirschfeld1  1Department of Physics, University of Florida, Gainesville, Florida, 32611, USA  2Department of Materials Science and Engineering, University of Florida, Gainesville, Florida, 32611, USA  3Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996, USA  4Institute of Advanced Materials and Manufacturing, The University of Tennessee, Knoxville, Tennessee 37996, USA  (Dated: January 3, 2023)  In a recent work by Schrodi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' 104, L140506 (2021)], the authors find  an unconventional superconducting state with a sign-changing order parameter using the Migdal-  Eliashberg theory, including the first vertex correction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' This unconventional solution arises despite  using an isotropic bare electron-phonon coupling in the Hamiltonian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' We examine this claim using  hybrid quantum Monte Carlo for a single-band Holstein model with a cuprate-like noninteracting  band structure and identical parameters to Schrodi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='. Our Monte Carlo results for these pa-  rameters suggest that unconventional pairing correlations do not become dominant at any carrier  concentration we have checked.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Instead, strong charge-density-wave correlations persist at the low-  est accessible temperatures for dilute and nearly half-filled bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Lastly, we present arguments for  how vertex-corrected Migdal-Eliashberg calculation schemes can lead to uncontrolled results in the  presence of Fermi surface nesting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  INTRODUCTION  The possible role of electron-phonon (e-ph) interac-  tions in high-temperature (high-Tc) superconductors is  a long-standing problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Coupling at small momentum  transfer, q, can lead to attractive interactions in uncon-  ventional pairing channels [1–10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' There are also theoret-  ical studies suggesting that the e-ph coupling can be en-  hanced at small q transfers by the Coulomb interaction  through screening [11, 12] and anisotropy in the trans-  port properties [8, 12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' In these scenarios, the momen-  tum structure of the e-ph coupling constant g(k, q) gives  rise to attractive contributions λl in multiple angular mo-  mentum channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' For any realistic g(k, q), the coupling  in the s-wave channel is dominant, and the interaction  will lead to an s-wave order parameter in the absence  of any repulsive interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' However, strong repulsive  interactions like a large Hubbard U or µ∗ can suppress  s-wave pairing in favor of an unconventional pairing sym-  metry [13, 14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Once this occurs, the next leading order  contribution from the e-ph interaction can provide an  additional boost to the pairing glue, provided it is an  attractive interaction in the appropriate pairing channel  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=', λx2−y2 for cuprates or λ±s for the Fe-based super-  conductors).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  Recently, Schrodi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' [15], proposed that a Holstein  interaction – i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' a momentum independent e-ph interac-  tion – can mediate an attractive interaction in uncon-  ventional channels without the additional influence of  electron correlations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' 15 examined several models,  including a single-band Holstein model for the high-Tc  cuprates, as well as multiband models for the Fe-based,  and heavy-fermion superconductors with nested Fermi  surfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' In each case, they considered a Holstein e-ph  coupling within a vertex-corrected Eliashberg-theory cal-  culation (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' 1), where the rainbow and first vertex  correction diagrams for the electron self-energy are com-  puted self-consistently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' In doing so, they found that the  inclusion of the vertex corrections leads to instabilities in  unconventional pairing channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Moreover, the symme-  try of the derived order parameter in each case was con-  sistent with those derived from weak coupling repulsive  spin-fluctuation-based models and Fermi surface nesting  arguments [13, 16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  The results of Schrodi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' [15] are at odds with  many nonperturbative studies of the single-band Holstein  model, which find that the temperature-doping phase di-  agram is dominated by charge-density-wave or s-wave  pairing correlations [17–33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Here, we explicitly explore  their claim using a state-of-the-art hybrid Monte Carlo  (HMC) method [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Specifically, we obtain numerically  exact solutions to the same cuprate model examined in  Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' 15, covering temperatures across the reported Tc in  some cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' The model is dominated by charge-density-  wave (CDW) correlations down to the lowest tempera-  tures we examine, which overlap the range studied by  Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' We further find that the dominant pairing cor-  relations are weak and have an s-wave symmetry at all  temperatures when simulations are performed at a fixed  filling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Alternatively, when simulations are performed for  a fixed chemical potential, we find the bands shift above  the Fermi level as the temperature decreases, indicating  that the self-energy effects from the e-ph coupling are  substantial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' At no point do we observe an instability to-  wards a superconducting phase with an unconventional  order parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' With this result in mind, we then ex-  amine the momentum structure of the first vertex correc-  tion and argue that truncating the expansion at the first  vertex correction is an uncontrolled approximation when  the Fermi surface is well nested.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  MODEL AND METHODS  We study a single-band Holstein model, defined on a  two-dimensional square lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' The Hamiltonian is given  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='00480v1  [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='supr-con]  1 Jan 2023  2  Γ(k, q) =  =  +  + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  = igk,q(1 + Γ(2)(k, q) + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=')  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  The electron phonon vertex of a simple electron-  phonon system Γ(k, q) ≡ Γ(k, iωn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' q, iνm) is a sum of Feyn-  man diagrams where the first term is simply the bare vertex  igk,q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' The “first vertex correction” is given by Γ(2)(q).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Higher  order diagrams are not considered in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  by  ˆH = −  �  i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='j  ti,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='jˆc†  i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='σˆcj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='σ − µ  �  i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='σ  ˆni,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='σ +  �  i  � ˆP 2  i  2M + MΩ2  2  ˆX2  i  �  + α  �  i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='σ  ˆni,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='σ ˆXi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  (1)  where ˆc†  i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='σ creates a spin-σ (=↑,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' ↓) electron on site i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  ˆni,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='σ = ˆc†  i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='σˆci,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='σ is the Fermion number operator for site  i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' ti,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='j is the hopping integral between sites i and j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' µ is  the chemical potential,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' ˆXi and ˆPi are the position and  momentum operators for the atom at site i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' M is the ion  mass,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Ω is oscillator frequency,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' and α is the e-ph coupling  strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' The single-band tight-binding dispersion ϵk for  this model is given by ξk = ϵk − µ, where  ϵk = −2t[cos(kx) + cos(ky)] − 4t′[cos(kx) cos(ky)]  (2)  and we have set the lattice spacing a = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  Throughout, we set M = ℏ = 1 such that the energy  of the phonon modes ℏΩ → Ω, and restrict the hopping  to nearest- (t) and next-nearest-neighbors (t′), only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' We  then adopted t = 1, t′/t = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='2, Ω/t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='4, and α =  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='059, following Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='1 These values result in a large  dimensionless e-ph coupling of λ = α2/(WΩ2) ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='88,  where W ≈ 8t is the noninteracting bandwidth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  The  chemical potential µ controls the filling in our simula-  tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Later, we will show results for fixed µ/t = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='56  and as well as for a fixed average filling n ≡ ⟨ˆn⟩ =  1  N  �  i,σ⟨ˆni,σ⟩ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='8 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' In the latter cases, µ is de-  termined dynamically within the HMC simulation using  a recently developed µ-tuning algorithm [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  We solve the model using a recently developed  method [34], which leverages HMC [36, 37] and Fourier  acceleration to reduce decorrelation time of the phonon  fields [38], a physics-inspired preconditioner, and near-  linear scaling measurement techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  This approach  1 Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  15  defines  the  bare  band  structure  as  ξk  =  −t [cos(kxa) + cos(kya)] − t′ cos(kxa) cos(kya) − µ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  We have,  therefore, selected our t and t′ values to match their bare band  dispersion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  allows us to simulate large system sizes and consider op-  tical phonons with energies much smaller than the elec-  tron hopping and equal to those used in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Unless  stated otherwise, all results are obtained on N = 12 × 12  clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  The strength of the charge correlations is determined  by measuring the charge structure factor  S(q, τ) = 1  N  �  i,j  e−iq·(ri−rj)⟨ ˆ  Tτ[ˆni(τ)ˆnj(0)]⟩,  (3)  where  ˆ  Tτ is the time-ordering operator, and charge sus-  ceptibility  χCDW(q) =  � β  0  S(q, τ) dτ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  (4)  The strength of the pairing correlations is determined by  the pair-field susceptibility  χSC  α  = 1  N  � β  0  dτ ⟨ ˆ  Tτ[ ˆ∆α(τ) ˆ∆†  α(0)]⟩,  (5)  for some pairing symmetry α = s, d, p, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=', the operator  ˆ∆†  α is defined [39] as  ˆ∆†  α = 1  2  �  i,γ  f α  γ ˆc†  i,↑ˆc†  i+γ,↓.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  (6)  Here, the sum over γ is restricted up to nearest neighbors  only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' For s-wave pairing, f s  γ = δγ,0, where δi,j is the usual  Kronecker-delta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' For d-wave pairing, f d  γ = δγ,±ˆx −δγ,±ˆy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  RESULTS  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  Hybrid Monte Carlo  Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' [15] is unclear in how it treats the filling of the  system, specifically whether µ or n is held fixed during  the self-consistency loop of their calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' We will  consider both cases in what follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  We begin with a fixed chemical potential, which we  set to µ/t = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='56 as indicated by Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' 2a  plots the evolution of the charge χCDW(q) and pairing  correlations as a function of temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' We find that  χCDW(q) is most prominent at q = (π, π) for nearly all  temperatures but displays non-monotonic behavior tak-  ing on a maximum at T/t ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='4 before it turns over and  rapidly decays to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' At these lowest temperatures, the  d-wave pair-field susceptibility is indeed larger than the  s-wave, but neither are significantly larger than their val-  ues at high-temperature, indicating no strong tendency  to pairing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' The non-monotonicity in χCDW(q) occurs be-  cause the filling of the system is not fixed and n → 0 as  the temperature is lowered (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' 2b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' This behavior is  likely due to significant growth in the self-energy, which  shifts the bands above the Fermi level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Regardless of the  3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='5  χCDW(q)  (a)  χCDW(π, π)  χCDW(qmax)  χs  χd  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='0  T/t  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='7  n  (b)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='20  χs, χd  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  The temperature evolution of the (a) charge and  superconducting pair-field susceptibilities and (b) electronic  filling n ≡ ⟨ˆn⟩ in the Holstein model for a fixed chemical po-  tential µ/t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' The largest filling at T/t = 2 is n = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='809  (outside the plot window).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' As the temperature is lowered, the  band shifts to energies above the Fermi level, and the band  is depleted n → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Results were obtained on N = 12 × 12  clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  origin, we find no evidence for a d-wave instability when  we simulate the system with a fixed chemical potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  Next, we fix the average filling to n = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='8, correspond-  ing to the approximate band filling for µ/t = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='56 ob-  tained at T/t = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  Figure 3 plots the corresponding  temperature dependence of the charge and pair-field sus-  ceptibilities in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  Here the q = (π, π) charge  susceptibility dominates at all temperatures and is up to  five orders magnitude larger than both the s- and d-wave  pair-field susceptibilities for T/t < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' We can conclude  that the low-temperature ground state of the system is  dominated by charge correlations and is not supercon-  ducting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  Turning to the superconducting correlations,  we find that χs > χd at all temperatures, with the latter  dropping significantly once the CDW correlations begin  to dominate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' We find no evidence for enhanced d-wave  pairing or a superconducting instability for this filling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' It  should also be noted that the vertex-corrected ME calcu-  lations of Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' [15] placed the superconducting transition  at Tc/t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='036 (52 K), which falls within our simulation  temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  Our results demonstrate that charge correlations are  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='0  T/t  0  500  1000  1500  2000  2500  χCDW(q)  χCDW(qmax)  χCDW(π, π)  χs  χd  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='10  χs, χd  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  The temperature evolution of the charge and su-  perconducting pair-field susceptibilities in the Holstein model  at a fixed filling n = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  The remaining parameters are  t′/t = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='2, Ω/t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='4, and λ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='8762.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Results are obtained  on N = 12 × 12 clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  dominant in the Holstein model near half-filling, in agree-  ment with many prior numerical studies [17, 18, 21, 24,  26–29, 31–33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  Many of those same studies also find  strong superconducting correlations for carrier concen-  trations away from half-filling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Motivated by this, we also  performed calculations for a dilute filling n = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' 4  plots the resulting temperature evolution of the charge  and pairing susceptibilities in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' The noninteract-  ing Fermi surface in the case is free-electron-like (circu-  lar) and is far from any nesting conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Nevertheless,  we find that q = (π, π) charge correlations dominate the  system at low temperatures, while the superconducting  correlations remain weak over the temperatures we can  access.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' In this case, the large value of χCDW(π, π) reflects  a strong tendency towards bipolaron formation [29, 32],  which is not unexpected given the large value of λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Our  results show that the Holstein model for the parameters  considered in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' [15] is dominated by bipolaron forma-  tion at all carrier concentrations, which tend to order  and localize for this value of λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' We find no indications  that they condense into a superconducting state of any  symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  Our results contradict those of Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' [15], which ob-  tained a d-wave superconducting solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  There are  several contributions to this discrepancy, but one partic-  ularly important factor is that their calculations do not  include the renormalization of the phonon propagator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  This approximation is, understandably, motivated by a  need to reduce the computational complexity stemming  from the inclusion of the vertex correction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' However, this  approximation is severe, as it prevents CDW correlations  driven by conventional phonon softening from growing  large enough to compete with superconductivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Schrodi  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' [40] and others [29, 41, 42] have included these ef-  fects in previous calculations without the first vertex cor-  rection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' All have found that including the phonon self-  4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='0  T/t  0  5  10  15  20  25  χCDW(q)  χCDW(qmax)  χCDW(π, π)  χs  χd  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='025  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='050  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='075  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='100  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='125  χs, χd  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  The temperature evolution of the charge and su-  perconducting pair-field susceptibilities in the Holstein model  at a fixed filling n = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  The remaining parameters are  t′/t = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='2, Ω/t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='4, and λ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='8762 Results are obtained  on N = 12 × 12 clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='0  T/t  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='5  χCDW(q)  χCDW(qmax)  χCDW(π, π)  χs  χd  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='5  χs, χd  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' For reference, we include the temperature evolution  of the charge and superconducting pair-field susceptibilities  in the noninteracting case at a fixed filling n = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  The  remaining parameters are t′/t = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='2, Ω/t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='4, and λ = 0  Results are obtained on N = 12 × 12 clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  energy in a self-consistent manner reintroduces the ten-  dency toward a charge instability, especially for a nested  Fermi surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Our numerically exact solutions include  these phonon self-energy effects, which may account for  our results’ discrepancies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' However, it is noteworthy that  Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' [15] also obtained unconventional order parameters  using a momentum-independent e-ph interaction in two  other systems with well-nested Fermi surfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' This ob-  servation motivates us to examine the structure of the  first vertex correction as a function of nesting in order  to assess whether truncating at this order is a controlled  approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  Analysis of the first vertex correction  The Feynman diagram for the first-order correction to  the bare e-ph interaction vertex gk,q is shown in the right-  most diagram of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' It is given by  Γ(2)(k, q) = kBT  Nℏ3  �  q′,σ′  |gk,q′|2D0(q′)G0(k − q − q′)  × G0(k − q′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  (7)  Here, we use the shorthand notation k ≡ (k, iωn) and q ≡  (q, iνm) with fermionic and bosonic Matsubara frequen-  cies given by ωn = (2n+1)πkBT/ℏ and νm = 2πmkBT/ℏ  (with n, m ∈ Z), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' (7) follows directly2  from its Feynman diagram and contains the e-ph cou-  pling matrix elements gk,q′, the noninteracting phonon  propagator  D0(q′) ≡ D0(q′, iνm′) = −  2Ωq′  ν2  m′ + Ω2  q′ ,  (8)  and two noninteracting electron propagators where, for  example,  G0(k − q′) ≡ G0(k − q′, iωn − iνm′)  =  1  i(ωn − νm′) − ℏ−1ξk−q′ ,  (9)  and ξk ≡ ϵk − µ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' We have suppressed spin and band in-  dices since we are working with a single-band model with  parity in the up and down spin directions (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=', G↑ = G↓).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  Since we are only interested in comparing the relative  strength of the bare vertex to the vertex correction, we  will work exclusively in units such that kB = ℏ = M = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  For a Holstein model,  the phonon dispersion is  Einstein-like, and the bare e-ph coupling is isotropic;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  hence, Ωq′ → Ω and gk,q → g = α/  √  2Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' With these  simplifications, the vertex correction reduces to  Γ(2)(k, q) = g2T  N  �  q′,σ′  D0(iνm′)G0(k − q − q′)G0(k − q′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  (10)  We evaluate the sums directly on finite momentum and  frequency grids, thereby approximating the vertex in the  thermodynamic limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' For our calculations, we take N =  24 × 24 and 128 frequencies for a model temperature of  T/t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' The number of Matsubara frequencies was  chosen such that the high energy cutoff ℏωc ≈ 5W, where  W is the noninteracting bandwidth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  2 Our specific choice of momenta arguments is readily seen by ex-  amining the vertex in the context of the first self-energy crossing  diagram, the latter of which is the second-order correction Σ(2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  The incoming and outgoing fermionic lines are labeled by k, the  first phonon line is labeled by q, and the second is labeled by q′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  5  0  π  4  π  2  3π  4  π  ky  � 1  a  �  (a)  µ = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='56t  0  π  4  π  2  3π  4  π  ky  � 1  a  �  (b)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='2  0  π  4  π  2  3π  4  π  kx  � 1  a  �  0  π  4  π  2  3π  4  π  ky  � 1  a  �  (c)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='1  −6  −4  −2  0  2  4  6  ε(k) − µ  � 1  t  �  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='0  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='6  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='0  ReΓ(2)(q)  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='0  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='6  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='0  ImΓ(2)(q)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Contour plots of the (a) Electronic dispersion (ε(k)−  µ)/t and the (b) real and (c) imaginary parts of the first vertex  correction Γ(2)(q) for µ/t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='56 and T/t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' In (a), the  solid line indicates the fermi surface contour corresponding to  ε(k)−µ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' In plots (b) and (c), the reported Γ(2)(q) follows  from taking the vertex Γ(2)(k, iωn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' q, iνm) has been evaluated  at iω0 and iν0 and then reduced to q-dependence by carrying  out a fermi surface average over k ∈ FS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  Figure 6 plots vertex correction as a function of mo-  mentum transfer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  Here, we have simplified the multi-  dimensional vertex function by focusing on the lowest  Matsubara frequency (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=', iωn=0 = πT and iνm=0 = 0),  and performing a Fermi surface average over the fermion  wave vectors k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Denoting the simplified vertex correction  as Γ(2)(q), the averaging procedure is given by  Γ(2)(q) ≡ ⟨Γ(2)(k, πT, q, 0)⟩k∈FS  =  �  k∈BZ  Γ(2)(k, πT, q, 0)˜δfd(ξk)  �  k∈BZ  ˜δfd(ξk)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  (11)  The wave vectors k are restricted to the Fermi surface by  use of a “smeared” delta function ˜δfd(ξk) given by  ˜δfd(x) = − d  dx  �  1  ex/σ + 1  �  =  1  4σ cosh2 � x  2σ  �,  (12)  where the broadening parameter σ = kBT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  Figure 6(a) shows a contour plot of the underlying  band structure ξk in the upper quadrant of the first Bril-  louin zone for µ/t = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' The thick black line follows  the Fermi surface contour ξk = 0 and thin dashed (solid)  contour lines are used to plot ξk < 0 (ξk > 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' The val-  ues of t, t′ and µ chosen here (to match Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' [15]) are  somewhat typical for modeling a 2D “cuprate”-like Fermi  surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' The non-interacting Fermi surface is well nested  for transfer vectors near q = (π, π), which coincides with  the peak in χCDW(q) seen in our HMC results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  The  corresponding q-dependence of the real and imaginary  parts of Γ(2)(q) are displayed in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' 6(b) and 6(c), re-  spectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' (Here, we restrict the plot axes qx, qy ∈ [0, π]  because the remaining quadrants are symmetrically iden-  tical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=') A Gaussian interpolation was used to smooth the  24 × 24 q-grid, and contours were added to help identify  the features and overall magnitude of the Fermi surface  averaged vertex correction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  It is clear from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' 6(b) that the real part of the Fermi-  surface averaged vertex correction is of order O(1) near  q = (π, π).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' For this case, the imaginary part of Γ(2)(q)  [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' 6(c)] is relatively small and at most ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='1 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  This result implies that an expansion for the vertex  Γ(q) ≈ ig[1 + Γ(2)(q) + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' ] involves corrections that are  on the order of the bare vertex, and thus higher order  terms would likely be needed to obtain a converged re-  sult.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Consequently, a self-consistent treatment the first  vertex correction in this context is likely uncontrolled,  and one should assess the strength of the second-order  diagrams before proceeding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  We now investigate the changes in Γ(2)(q) as µ is tuned  away from µ/t = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='56 to determine the role of the  Fermi surface nesting in the setting the magnitude of the  correction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Figure 7 plots ξk along with ReΓ(2)(q) and  ImΓ(2)(q) row-wise, but now each of the five columns  corresponds to a different choice of µ/t ∈ [−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='5] in  steps of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  The results for µ/t = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='5 (middle col-  umn) are similar to those shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' 6;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' the FS is  strongly nested for q ≈ (π, π) and ReΓ(2)(π, π) ∼ O(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  The nesting condition survives when µ/t is adjusted by  ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='5 but shifts to different momentum transfers in both  6  0  π  4  π  2  3π  4  π  ky  � 1  a  �  (a)  µ = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='5t  (b)  µ = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='0t  (c)  µ = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='5t  (d)  µ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='0t  (e)  µ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='5t  0  π  4  π  2  3π  4  π  ky  � 1  a  �  (f)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='5  (g)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='8  (h)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='0  (i)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='6  (j)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='3  0  π  4  π  2  3π  4  π  kx  � 1  a  �  0  π  4  π  2  3π  4  π  ky  � 1  a  �  (k)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='1  0  π  4  π  2  3π  4  π  kx  � 1  a  �  (l)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='1  0  π  4  π  2  3π  4  π  kx  � 1  a  �  (m)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='2  0  π  4  π  2  3π  4  π  kx  � 1  a  �  (n)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='3  0  π  4  π  2  3π  4  π  kx  � 1  a  �  (o)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='3  −6  −4  −2  0  2  4  6  ε(k) − µ  � 1  t  �  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='0  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='6  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='0  ReΓ(2)(q)  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='0  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='6  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='0  ImΓ(2)(q)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' A survey of effects of the Fermi surface features on the first Fermi-surface averaged vertex correction (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' 11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  Results in each column correspond to µ/t = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='5, -1, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='5, 0, and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='5 reading left to right.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' The top row shows contour plots  of the bare band dispersion ξk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' The thick black line denotes the Fermi surface contour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' The thin dashed (solid) lines show  contours for ξk < 0 (ξk > 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' The second and third rows show the real and imaginary parts of the Fermi surface averaged  vertex Γ(2)(q) for momentum transfer in the positive quadrant of the first Brillouin zone (FBZ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' The values of Γ(2)(q) at other  points in the FBZ can be inferred from C4 symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' This fact is evidenced by the strong incommensu-  rate peaks in ReΓ(2)(q) for these values of the chemical  potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' The peak heights also decrease in these cases  but remain large enough to invalidate a low-order per-  turbation expansion in the vertex function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  The nesting conditions are strongly suppressed for  µ/t = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='5 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='5, as shown in the first and fifth  columns, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' In these cases, the band structure  begins to resemble a free electron (hole) dispersion with  a circular Fermi surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' (For µ/t = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='5, the electron-  like Fermi surface is more diamond-like.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=') As one might  expect, the real and imaginary parts of Γ(2)(q) are corre-  spondingly smaller than 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' For example, ReΓ(2)(q) has  a weak peak near q ≈ ( 1  4, 4  5)π for the free-electron-like  case (µ/t = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='5), while it has a very weak peak near  q ≈ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='9, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='9)π for the free-hole-like case (µ/t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' We  expect that a self-consistent treatment of the first order  vertex corrections may be more controlled in these cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  Discussion  In the previous section, we showed that the first vertex  correction acquires a momentum anisotropy that follows  directly from the geometry of the electronic dispersion  near the Fermi level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' This result occurs, even with a bare  Holstein coupling and a dispersionless Einstein phonon  mode, both of which are isotropic in momentum space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  Improving upon this simplified picture by reintroducing  dispersive phonons or using the dressed propagators in  the vertex diagram could significantly alter our conclu-  sion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Using dressed propagators G(k) and D(q) instead  of G0(k) and D0(q) in Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' (10) and generating second-  order corrections to the electron and phonon self-energies  [i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=', Σ(2)(k) and Π(2)(q)] constitute a fully self-consistent  evaluation within the vertex-corrected Migdal-Eliashberg  theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  Such a procedure introduces additional e-ph-  induced renormalization effects on both the phonons and  electrons beyond the usual self-consistent Eliashberg for-  malism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Even without the vertex correction, treating the  electron and phonon self-energies on equal footing allows  for phonon softening, manifesting as a Kohn anomaly in  the phonon dispersion at the nesting vector [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' If such  7  softening were also present in the vertex-corrected the-  ory, the peaks in Γ(2)(q) could be quite strongly affected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  Our results would reflect the first iteration of such a self-  consistent procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  Using HMC simulations as a stand-in for summing all  the Feynman diagrams, we observed that reintroducing  the neglected diagrams greatly favors CDW correlations  at the expense of superconductivity for the parameters  studied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' This result is relatively unsurprising given the  sizable dimensionless coupling λ ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='88, which, along-  side the frequency of Ω/t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='4, fits into a regime asso-  ciated with large lattice fluctuations [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' In the large  coupling limit λ ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='5, these correlations reflect bipo-  laron formation [29] not captured within the framework  of Migdal’s theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' How many additional vertex correc-  tions are needed to describe bipolarons and the CDW  transition remains unclear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' It is also unclear if a finite  number of corrections would be sufficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  The study of corrections to the electron-phonon ver-  tex has a long history [29, 30, 43–59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  Many of these  works studied the ramifications of vertex corrections on  superconductivity and consider, for instance, how vertex  corrections affect: the critical temperature and or pair-  ing [46–53, 55, 60], the isotope coefficient[49], predictions  for non/antiadiabatic materials like fullerenes [49, 54],  and unconventional superconductivity, often by including  them alongside electronic correlations and spin fluctua-  tions [46, 48, 61–68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' This body of literature is extensive,  so we have not attempted to review these works compre-  hensively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Instead, we highlight a potential blind spot  concerning lurking charge instabilities in vertex-corrected  Eliashberg approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Some findings of the current work  have been discussed in the works above to varying degrees  of rigor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' In particular, when considering problems in 2D,  it has been pointed out that Fermi surface nesting con-  ditions can invalidate Migdal’s approximation, primarily  due to geometric singularities appearing in the skeleton  diagrams [69].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Schrodi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' mention the issue of nest-  ing and several other potential caveats in their Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' [60],  which debuts the same state-of-the-art full-bandwidth  implementation of a vertex-corrected Eliashberg formal-  ism used in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' However, as was shown here and  by Esterlis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [29], comparing Eliashberg-type cal-  culations with nonperturbative methods (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=', quantum  Monte Carlo) can be a vital means of addressing the va-  lidity of approximate methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  SUMMARY & CONCLUSION  Analytic attempts at describing the nature of vertex  corrections often entail simplifications to the electronic  dispersion, typically reducing εk to the single parabolic  band of free electrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  With modern computing re-  sources, self-consistent solutions of the Migdal-Eliashberg  equations, including the first vertex correction, are now  technically feasible for lattice models with some tight-  binding dispersion (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=', Ref [15]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  However, we have  shown that while it may be easier to carry out these  calculations, the results could be misleading in some in-  stances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' In particular, we performed HMC simulations  using the same parameters associated with an uncon-  ventional superconducting state in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' [15] and instead  found a leading charge-density wave instability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' We did  not attempt to explore the entire parameter space to rule  out a possible unconventional ground state somewhere in  the phase diagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' However, to our knowledge, the ex-  tensive literature on nonperturbative studies of the Hol-  stein model does not contain any robust evidence for a  leading unconventional order parameter thus far.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  To better understand the origin of the d-wave order  parameter in the first-vertex-corrected Eliashberg theory,  we evaluated a finite size approximation of the vertex  correction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Due to the relative simplicity of the Holstein  model, much of the momentum-space structure of Γ(2)(q)  follows directly from the Fermi surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' For a cuprate-like  Fermi surface, we observe peaks in Γ(2)(q) of O(1) near  a nesting vector q = (π, π), indicating that higher-order  diagrams may be crucial for these parameters, matching  the conclusions from our HMC results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  It remains an open question as to when and how vertex  corrections should be included within Migdal-Eliashberg  formalism for specific applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' What is clear is that  there are scenarios where the perturbative expansion is  somewhat ill-defined and blind to competing phenom-  ena such as bipolaron formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' The standard Eliash-  berg formalism below Tc comes equipped with the usual  anomalous propagators, which admit a superconducting  order parameter but not a competing CDW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' A possible  way forward would be to study the effect of vertex correc-  tions in the normal state and tracking both pairing and  the CDW correlations in the self-consistent Migdal ap-  proximation [41, 42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' However, to truly understand the  physics contained in the corrections, it may be necessary  to study the diagrams beyond the first correction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Find-  ing the middle ground where the first correction Γ(2)(q)  [and possibly Γ(4)(q)] could be used to safely fine-tune  predictions is a direction of future study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  Acknowledgments — The authors thank Yan Wang for  fruitful discussions about this topic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  acknowledge support from the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Department of En-  ergy, Office of Science, Office of Basic Energy Sciences,  under Award Number DE-SC-0020385.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  acknowledge support from the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Department of En-  ergy, Office of Science, Office of Basic Energy Sciences,  under Award Number DE-SC0022311.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [1] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Mott, Polaron models of high-temperature super-  conductors, Journal of Physics:  Condensed Matter 5,  3487 (1993).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  8  [2] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Kulić and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Zeyher, Influence of strong electron  correlations on the electron-phonon coupling in high-Tc  oxides, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B 49, 4395 (1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [3] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Santi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Jarlborg, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Peter, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Weger, s- and d-  wave symmetries of the solutions of the Eliashberg equa-  tions, Physica C: Superconductivity 259, 253 (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [4] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  Varelogiannis,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  Perali,  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  Cappelluti,  and  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Pietronero, Density-of-states-driven anisotropies in-  duced by momentum decoupling in Bi2Sr2CaCu2O8,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B 54, R6877 (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [5] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Devereaux, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Cuk, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Shen, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Na-  gaosa, Anisotropic Electron-Phonon Interaction in the  Cuprates, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' 93, 117004 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [6] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Kulić and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Dolgov, Forward scattering peak in  the electron–phonon interaction and impurity scattering  of cuprate superconductors, physica status solidi (b) 242,  151 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [7] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Johnston, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Vishik, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Lee, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Schmitt,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Uchida, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Fujita, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Ishida, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Nagaosa, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Shen,  and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Devereaux, Evidence for the Importance of Ex-  tended Coulomb Interactions and Forward Scattering in  Cuprate Superconductors, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' 108, 166404  (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [8] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Lee, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Schmitt, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Moore, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Johnston, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  Cui, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Li, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Yi, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Liu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Hashimoto, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Zhang,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Lu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Devereaux, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Lee, and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Shen, In-  terfacial mode coupling as the origin of the enhancement  of Tc in FeSe films on SrTiO3, Nature 515, 245 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [9] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Wan and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Savrasov, Turning a band insulator  into an exotic superconductor, Nature Communications  5, 4144 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [10] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rademaker, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Wang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Berlijn, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Johnston,  Enhanced superconductivity due to forward scattering  in FeSe thin films on SrTiO3 substrates, New Journal of  Physics 18, 022001 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [11] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Huang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Hanke, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Arrigoni, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Scalapino,  Electron-phonon vertex in the two-dimensional one-band  Hubbard model, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B 68, 220507 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [12] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Johnston, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Vernay, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Moritz, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Shen, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Na-  gaosa, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Zaanen, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Devereaux, Systematic study  of electron-phonon coupling to oxygen modes across the  cuprates, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B 82, 064513 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [13] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Scalapino, A common thread: The pairing inter-  action for unconventional superconductors, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' 84, 1383 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [14] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Hirschfeld, Using gap symmetry and structure to re-  veal the pairing mechanism in Fe-based superconductors,  Comptes Rendus Physique 17, 197 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [15] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Schrodi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Oppeneer, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Aperis, Uncon-  ventional superconductivity mediated solely by isotropic  electron-phonon interaction, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B 104, L140506  (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [16] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Mazin and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Schmalian, Pairing symmetry and pair-  ing state in ferropnictides: Theoretical overview, Physica  C: Superconductivity 469, 614 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [17] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Freericks, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Jarrell, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Scalapino, Hol-  stein model in infinite dimensions, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B 48, 6302  (1993).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [18] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Scalettar, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Bickers, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Scalapino, Com-  petition of pairing and Peierls–charge-density-wave cor-  relations in a two-dimensional electron-phonon model,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B 40, 197 (1989).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [19] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Meyer, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Hewson, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Bulla, Gap formation  and soft phonon mode in the Holstein model, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' 89, 196401 (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [20] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Capone and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Ciuchi, Polaron Crossover and Bipo-  laronic Metal-Insulator Transition in the Half-Filled Hol-  stein Model, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' 91, 186405 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [21] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Capone, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Carta, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Ciuchi, Dynamical mean  field theory of polarons and bipolarons in the half-filled  Holstein model, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B 74, 045106 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [22] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Tezuka, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Arita, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Aoki, Phase diagram for  the one-dimensional Hubbard-Holstein model: A density-  matrix renormalization group study, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B 76,  155114 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [23] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Murakami, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Werner, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Tsuji, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Aoki, Super-  solid Phase Accompanied by a Quantum Critical Point in  the Intermediate Coupling Regime of the Holstein Model,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' 113, 266404 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [24] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Karakuzu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Tocchio, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Sorella, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Becca,  Superconductivity, charge-density waves, antiferromag-  netism, and phase separation in the Hubbard-Holstein  model, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B 96, 205145 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [25] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Ohgoe and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Imada, Competition among Super-  conducting, Antiferromagnetic, and Charge Orders with  Intervention by Phase Separation in the 2D Holstein-  Hubbard Model, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' 119, 197001 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [26] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Chen, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Xu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Liu, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Batrouni, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Scalettar,  and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Meng, Symmetry-enforced self-learning Monte  Carlo method applied to the Holstein model, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  B 98, 041102 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [27] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Hohenadler and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Batrouni, Dominant charge  density wave correlations in the Holstein model on the  half-filled square lattice, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B 100, 165114  (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [28] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Li, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Dee, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Khatami, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Johnston, Accel-  erating lattice quantum Monte Carlo simulations using  artificial neural networks: Application to the Holstein  model, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B 100, 020302 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [29] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Esterlis, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Nosarzewski, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Huang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Moritz, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  Devereaux, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Scalapino, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Kivelson, Break-  down of the Migdal-Eliashberg theory: A determinant  quantum Monte Carlo study, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B 97, 140501  (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [30] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Dee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Coulter, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Kleiner, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Johnston,  Relative importance of nonlinear electron-phonon cou-  pling and vertex corrections in the Holstein model, Com-  munications Physics 3, 145 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [31] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Bradley, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Batrouni, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Scalettar, Super-  conductivity and charge density wave order in the two-  dimensional Holstein model, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B 103, 235104  (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [32] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Nosarzewski, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Huang, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Dee, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Esterlis,  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Moritz, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Kivelson, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Johnston, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' De-  vereaux, Superconductivity, charge density waves, and  bipolarons in the Holstein model, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B 103,  235156 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [33] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Paleari, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Hébert, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Cohen-Stead, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Barros,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Scalettar, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Batrouni, Quantum Monte Carlo  study of an anharmonic Holstein model, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B  103, 195117 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [34] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Cohen-Stead, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Bradley, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Miles, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Batrouni,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Scalettar, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Barros, Fast and scalable quan-  tum Monte Carlo simulations of electron-phonon models,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' E 105, 065302 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [35] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Miles, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Cohen-Stead, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Bradley, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Johnston,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Scalettar, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Barros, Dynamical tuning of the  chemical potential to achieve a target particle number in  9  grand canonical Monte Carlo simulations, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' E  105, 045311 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [36] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Duane, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Kennedy, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Pendleton, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Roweth,  Hybrid Monte Carlo, Physics Letters B 195, 216 (1987).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [37] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Beyl, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Goth, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Assaad, Revisiting the hybrid  quantum Monte Carlo method for Hubbard and electron-  phonon models, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B 97, 085144 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [38] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Batrouni and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Scalettar, Langevin simulations  of a long-range electron-phonon model, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B 99,  035114 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [39] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Nowadnick, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Johnston, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Moritz, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Dev-  ereaux, Renormalization of spectra by phase competition  in the half-filled Hubbard-Holstein model, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B  91, 165127 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [40] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Schrodi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Aperis, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Oppeneer, Influence  of phonon renormalization in eliashberg theory for su-  perconductivity in two- and three-dimensional systems,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B 103, 064511 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [41] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Marsiglio, Pairing and charge-density-wave correla-  tions in the Holstein model at half-filling, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B  42, 2416 (1990).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [42] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Dee, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Nakatsukasa, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Wang, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' John-  ston, Temperature-filling phase diagram of the two-  dimensional Holstein model in the thermodynamic limit  by self-consistent Migdal approximation, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B  99, 024514 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [43] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Migdal, Interaction between electrons and lattice  vibrations in a normal metal, Sov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' JETP 7, 996  (1958), [Zh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Eksp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Teor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Fiz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' 34, 1438 (1958)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [44] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Eliashberg, Interactions between electrons and lat-  tice vibrations in a superconductor, Sov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' JETP 11,  696 (1960), [Zh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Eksp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Teor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Fiz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' 38, 966 (1960)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [45] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Eliashberg, Temperature Green’s Function For  Electrons In a Supercondutor, Sov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' JETP 12, 1000  (1961).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [46] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Kostur and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Mitrović, Calculations of the  superconducting critical temperature with vertex correc-  tions, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B 50, 12774 (1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [47] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Benedetti, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Grimaldi, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Pietronero, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Varel-  ogiannis, Superconductivity beyond Migdal’s theorem  and high-Tc phenomenology, Europhysics Letters 28, 351  (1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [48] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Krishnamurthy, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Newns, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Pattnaik, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  Tsuei, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Chi, Vertex correction to pairing at a  Van Hove singularity, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B 49, 3520 (1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [49] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Nicol and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Freericks, Vertex corrections to the theory  of superconductivity, Physica C: Superconductivity 235-  240, 2379 (1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [50] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Grimaldi, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Pietronero, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Strässler, Nonadi-  abatic Superconductivity: Electron-Phonon Interaction  Beyond Migdal’s Theorem, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' 75, 1158  (1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [51] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Pietronero, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Strässler, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Grimaldi, Nonadi-  abatic superconductivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Vertex corrections for the  electron-phonon interactions, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B 52, 10516  (1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [52] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Grimaldi, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Pietronero, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Strässler, Nonadia-  batic superconductivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Generalized Eliashberg equa-  tions beyond Migdal’s theorem, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B 52, 10530  (1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [53] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Freericks, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Nicol, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Liu, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Quong,  Vertex-corrected tunneling inversion in electron-phonon  mediated superconductors: Pb, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B 55, 11651  (1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [54] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Gunnarsson, Superconductivity in fullerides, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' 69, 575 (1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [55] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Perali, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Grimaldi, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Pietronero, Nonadiabatic  pairing effects for tight-binding electrons interacting with  phonons, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B 58, 5736 (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [56] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Danylenko and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Dolgov, Nonadiabatic contri-  bution to the quasiparticle self-energy in systems with  strong electron-phonon interaction, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B 63,  094506 (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [57] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Hague, Electron and phonon dispersions of the two-  dimensional Holstein model: effects of vertex and non-  local corrections, Journal of Physics: Condensed Matter  15, 2535 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [58] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Hague, d-wave superconductivity from electron-  phonon interactions, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B 73, 060503 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [59] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Chubukov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Abanov, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Esterlis, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Kivel-  son, Eliashberg theory of phonon-mediated superconduc-  tivity — When it is valid and how it breaks down, Annals  of Physics 417, 168190 (2020), Eliashberg theory at 60:  Strong-coupling superconductivity and beyond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [60] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Schrodi,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Oppeneer, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Aperis, Full-  bandwidth Eliashberg theory of superconductivity be-  yond Migdal’s approximation, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B 102, 024503  (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [61] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Grabowski and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Sham, Superconductivity from  nonphonon interactions, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B 29, 6132 (1984).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [62] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Mierzejewski, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Zieliński, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Entel, Eliashberg  equations of electrons on a square lattice: Interplay of  strong electron-phonon interactions and electron correla-  tions, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B 57, 590 (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [63] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Zieliński, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Mierzejewski, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Entel, Supercon-  ductivity in the two-dimensional Hubbard model close  to the metal-insulator transition: A strong-coupling de-  scription, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B 57, 10311 (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [64] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Schrieffer, Ward’s identity and the suppression of  spin fluctuation superconductivity, Journal of Low Tem-  perature Physics 99, 397 (1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [65] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Cappelluti and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Pietronero, Van Hove singulari-  ties and nonadiabatic effects in superconductivity, Eu-  rophysics Letters 36, 619 (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [66] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Moskalenko, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Entel, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Digor, Strong in-  teraction of correlated electrons with phonons: A dia-  grammatic approach, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B 59, 619 (1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [67] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Tsuei and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Kirtley, Pairing symmetry in  cuprate superconductors, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' 72, 969  (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [68] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Kulić, Interplay of electron–phonon interaction and  strong correlations: the possible way to high-temperature  superconductivity, Physics Reports 338, 1 (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content='  [69] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Kostur and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Mitrović, Electron-phonon in-  teraction in two dimensions: Variation of ImΣ(ϵp,ω) with  increasing ωD/EF, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
+page_content=' B 48, 16388 (1993).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udAyT4oBgHgl3EQfm_hJ/content/2301.00480v1.pdf'}
diff --git a/utE_T4oBgHgl3EQf-Rwc/content/tmp_files/2301.08385v1.pdf.txt b/utE_T4oBgHgl3EQf-Rwc/content/tmp_files/2301.08385v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..efb504ea8d541dedbef396584a2c42319b0b9058
--- /dev/null
+++ b/utE_T4oBgHgl3EQf-Rwc/content/tmp_files/2301.08385v1.pdf.txt
@@ -0,0 +1,807 @@
+Computational budget optimization for Bayesian parameter estimation in
+heavy ion collisions
+Brandon Weiss,1 Jean-Fran¸cois Paquet,2, 3, 1 and Steffen A. Bass1
+1Department of Physics, Duke University, Durham NC 27708.
+2Department of Physics and Astronomy, Vanderbilt University, Nashville TN 37235.
+3Department of Mathematics, Vanderbilt University, Nashville TN 37235.
+(Dated: August 2021)
+Bayesian parameter estimation provides a systematic approach to compare heavy ion collision
+models with measurements, leading to constraints on the properties of nuclear matter with proper
+accounting of experimental and theoretical uncertainties.
+Aside from statistical and systematic
+model uncertainties, interpolation uncertainties can also play a role in Bayesian inference, if the
+model’s predictions can only be calculated at a limited set of model parameters. This uncertainty
+originates from using an emulator to interpolate the model’s prediction across a continuous space
+of parameters.
+In this work, we study the trade-offs between the emulator (interpolation) and
+statistical uncertainties.
+We perform the analysis using spatial eccentricities from the TRENTo
+model of initial conditions for nuclear collisions. Given a fixed computational budget, we study
+the optimal compromise between the number of parameter samples and the number of collisions
+simulated per parameter sample. For the observables and parameters used in the present study, we
+find that the best constraints are achieved when the number of parameter samples is slightly smaller
+than the number of collisions simulated per parameter sample.
+I.
+INTRODUCTION
+One of the main goals of the heavy ion program pursued at the Relativistic Heavy Ion Collider (RHIC) and
+the Large Hadron Collider (LHC) is a quantitative understanding of the properties of nuclear matter under
+extreme conditions as described by Quantum Chromodynamics (QCD). At sufficiently high temperatures
+and densities accessible during these nuclear collisions, a transient state of matter, the quark-gluon plasma
+(QGP), is formed, but decays again as the collision systems cools down and disintegrates. Collisions of heavy
+ions leading to QGP formation are multistage processes: the initial impact of the nuclei, the formation and
+expansion of the QGP, reconfinement into hadrons, and subsequent hadronic interactions [1–4]. A wide range
+of properties of nuclear matter enter numerical simulations of heavy ion collisions. Some of these properties
+are constrained by external means, for example lattice Quantum Chromodynamics calculations of the equa-
+tion of state of nuclear matter [5]. Other properties, such as transport coefficients or parameters entering the
+description of the early stage of the collision, are often parametrized and constrained by comparison with
+data.
+Measurements from the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) can
+constrain these physical parameters. Because of the heterogeneity and large number of measurements and
+model parameters, it is beneficial to perform model-to-data comparisons using statistical techniques such as
+Bayesian parameter estimation: this allows for a systematic propagation of uncertainties from experimental
+measurements to physical parameters. A number of such studies have been performed over the past decade [6–
+20].
+A key ingredient of Bayesian parameter estimation as used in heavy ion collisions is emulation: given the
+model’s prediction at a discrete sample of parameters, an emulator will interpolate the model’s prediction over
+a continuous range of parameters. Furthermore, emulators such as Gaussian processes provide an estimate of
+their own interpolation uncertainty; in effect, this allows emulation to be used in model-to-data comparisons
+even if the emulator’s interpolation uncertainty is not negligible compared to the other uncertainties in the
+problem — a situation that is often unavoidable in simulations with large number of parameters. In Bayesian
+parameter estimation, this emulator uncertainty is included into the physical parameter’s final uncertainty
+determination, alongside experimental, statistical and other theoretical uncertainties.
+The most straightforward approach to reducing emulator uncertainty is to increase the number of parame-
+ter samples at which the model observables are evaluated; these parameter samples are generally referred to
+as the emulator’s “design points”. Evidently, this increase in the number of design points must be balanced
+with other demands on the available computational budget. In particular, simulations of heavy ion collisions
+are stochastic: there are event-by-event fluctuations in the outcome of the collisions. Comparisons with
+arXiv:2301.08385v1  [nucl-th]  20 Jan 2023
+
+2
+measurements require simulating and averaging over a large number of collisions. At a fixed computational
+budget, one must determine the proper trade-off between reducing emulator interpolation uncertainties or
+statistical ones. In this work, we use the TRENTo model of initial conditions for heavy ion collisions [21] to
+study this trade-off between statistical and emulator uncertainties.
+II.
+METHODOLOGY
+We use the model TRENTo as proxy for observables in heavy ion collisions; this is based on the known
+correlation [22] between (i) initial spatial anisotropies of models like TRENTo, and (ii) measurable momentum
+anisotropies of final state hadrons. To interpolate the output of the TRENTo model, we use Gaussian process
+emulators, which have been the standard emulation technique used for model-to-data comparisons in heavy
+ion physics [6–8, 10]. To quantify the optimal trade-off between statistical and emulator uncertainty, we use
+“closure tests”, which apply Bayesian parameter inference to model calculations. We summarize the overall
+approach and methods below.
+A.
+TRENTo
+TRENTo is a parametric initial condition ansatz for simulating relativistic heavy ion collisions [21]. It
+takes as input the type of colliding nuclei and the inelastic nucleon-nucleon cross-section corresponding to
+the center-of-mass energy of the collision.
+We vary three parameters of the TRENTo model: the effective nucleon size w, the fluctuation parameter
+k and the reduced thickness p. The fluctuation parameter k allows for variation in the amount of energy
+carried by each nucleon, while the reduced thickness p parametrize how the energy or entropy density is
+constructed from the profile of nucleons sampled from each nuclei.
+The output of TRENTo is a density profile in the plane transverse to the collision axis. We interpret
+TRENTo’s output as an energy density profile ϵ(r, φ) with arbitrary normalization. From this density profile
+ϵ(r, φ), we compute single-event spatial anisotropies εn [22]:
+εneinΦn =
+� ∞
+0
+drr
+� 2π
+0
+dφ rnϵ(r, φ)einφ
+� ∞
+0
+drr
+� 2π
+0
+dφ rnϵ(r, φ)
+(1)
+Although these anisotropies can be related to the momentum anisotropy of hadrons measured at the end
+of the collision [23–27], in this work, we focus on the initial spatial eccentricies themselves.
+We compute the average of an ensemble of TRENTo events with an arithmetic average:
+⟨εn⟩ =
+1
+Mev
+Mev
+�
+j=1
+εn{event j} .
+(2)
+We used up to four harmonics in this work, n = 2 to 5.
+We studied minimum bias Pb-Pb collisions with Woods-Saxon nucleon distributions. We used an inelastic
+nucleon-nucleon cross-section of 64 mb, corresponding approximately to √sNN = 2.76 TeV collisions.
+B.
+Bayesian parameter estimation
+We note yth,j(p) the model’s prediction for the “j”-th observables of interest, evaluated when the model’s
+parameters are set to p. At p, we compute yth,j(p) = ⟨εnj⟩(p), where the index j runs over all the observables
+of interest, which in our case are the different “n” in Eq. 2.
+In general, given this information, we want to find the probability that parameters p are consistent with
+the data {yexp,j} and with the experimental and theoretical uncertainties {σexp,j} and {σth,j(p)}. The first
+step is to define a metric to quantify the level of model-to-data agreement: the likelihood function. We make
+
+3
+the typical choice of a Gaussian likelihood function:
+L({yexp,j}|p) = exp
+�
+�−1
+2
+�
+j
+[yth,j(p) − yexp,j]2
+σth,j(p)2 + σ2
+exp,j
+�
+�
+��
+(2π)n �
+j
+�
+σth,j(p)2 + σ2
+exp,j
+�
+.
+(3)
+We assumed a diagonal covariance matrix. In this work, instead of comparing the model with data, we will
+use closure tests: we will replace yexp,j by model calculations, as discussed later. These model calculations
+do stand for experimental data, and consequently we keep the label “exp” to denote these quantities.
+Given our model of the collision, the probability that the parameter set p is consistent with the data and
+the uncertainties is given by the posterior distribution of model parameters, P(p|({yexp}):
+P(p|({yexp}) =
+L({yexp}|p)Prior(p)
+�
+dpL({yexp}|p)Prior(p)
+(4)
+where Prior(p) is the prior distribution. In this work we take the prior to be constant over a finite parameter
+range, for all the parameters.
+The posterior distribution P(p|({yexp}) is a probability distribution whose dimensionality is equal to the
+number of model parameters. Different projections of the posterior distribution summarize the constraints
+on the model parameters. As long as the number of parameters is small and the model is relatively fast
+computationally, it is straightforward to sample and marginalize the posterior P(p|({yexp}).
+When the
+number of parameters increases or if the model is expensive, it can become overly burdensome to evaluate
+a model’s prediction at a large number of values of the parameter p to compute P(p|({yexp}). A solution
+is to prepare a fast proxy, such as a Gaussian process [28], to emulate the model’s prediction. We review
+Gaussian process emulators briefly in the next subsection. As far as the Bayesian inference is concerned, the
+consequence of using Gaussian process emulators is substituting the model’s prediction by the emulator’s
+prediction,
+yth,j(p) → yemul,j(p) ,
+(5)
+as well as adding the emulator interpolation uncertainty into the sum of uncertainties,
+σth,j(p)2 → σth,j(p)2 + σemul,j(p)2 .
+(6)
+C.
+Emulation with Gaussian processes
+The idea behind emulation is to first sample the parameter space of the model, {pk}; the parameter
+samples are the design points. The model’s predictions are then calculated for all design points: {yth,j(pk)}.
+The emulator then interpolates the model’s predictions over a continuous range of model parameters p.
+To sample the parameter space, we use a low discrepancy sequence generator [29, 30]. Figure 1 shows an
+example for 16 design points within a two-dimensional parameter space.
+For each observable (⟨ϵn⟩), a Gaussian process is trained on the set of values of ⟨ϵn⟩(p) calculated at the
+design points {pk}. Gaussian process emulators are probabilistic interpolators, which assume that each point
+in parameter space is a probability distribution. At the design points, the width of the probability distribution
+should include the statistical uncertainty of the observables. Between the design points, the width of the
+probability distribution should increase to account for the interpolation uncertainty. To handle stochastic
+simulations, Gaussian process emulators must be set up such that variations between parameter samples
+are divided into (i) statistical uncertainty, and (ii) the actual variation from the parameter dependence
+of the model. A mathematical description of the approach can be found in Ref. [15, Section V-B-2]. In
+short, a white noise kernel accounts for the uncorrelated (“short range”) fluctuations originating from the
+statistical uncertainty, and a squared-exponential kernel accounts for the longer-range parameter dependence.
+The parameters of these kernels, for example the relative size of the kernels, is determined by numerical
+optimization.
+This approach is used in most applications of Bayesian parameter inference in heavy ion
+physics. The result of this implementation is that the emulator uncertainty accounts for both the statistical
+and interpolation uncertainties.
+Figure 2 shows the mean-value predictions of the emulator for ⟨ϵ2⟩ and ⟨ϵ3⟩ compared to the actual value
+of these observables. The points all lie close to the line yemul,j(p) = yth,j(p), which shows that the emulator
+
+4
+FIG. 1. 16 design points in a two-dimensional parameter space (reduced thickness on the x-axis and nucleon width
+on the y-axis), as sampled with a low discrepancy sequence generator [29, 30].
+FIG. 2. (Left) Value for ⟨ε2⟩ as predicted by a Gaussian process emulator trained with 16 design points (y-axis),
+compared to the actual value of the model at the design points (x-axis); (Right) Same as left, for ⟨ε3⟩ with 256 design
+points. The red line corresponding to perfect emulation, yemul,j(p) = yth,j(p), is shown for reference. Statistical
+uncertainties on each sample are not shown for clarity.
+does indeed interpolate well. On the other hand, ⟨ϵ3⟩ tends to have a larger statistical uncertainty than
+⟨ϵ2⟩, and as the right-hand side of Figure 2 shows, increasing the number of design points will not lead to
+perfect deterministic-like prediction from the emulator because the values of ⟨ϵ3⟩ have significant statistical
+uncertainties. This is the trade-off that we focus on in this work.
+D.
+Closure tests
+Closure tests are a straightforward application of Bayesian parameter inference, with experimental data
+replaced by calculations from the model itself. It is a self-consistency check made non-trivial by (i) the
+presence of uncertainties, as well as (ii) loss of information from the model to the observables. A longer
+discussion of closure tests, in the context of heavy ion collisions, can be found in Section VI of Ref. [15]. We
+describe it briefly here, with focus on metrics to quantify the success of closure tests.
+
+1.2
+1.1
+Nucleon width
+1.0
+0.9
+0.8
+0.7
+0.1
+0.2
+0.3
+0.4
+0.50.34
+0.32
+(e2) emulator
+0.30
+0.28
+0.26
+0.24
+0.24
+0.26
+0.28
+0.30
+0.32
+0.34
+(e2> truth0.24
+0.22
+>emulator
+0.20
+0.18
+(E3)
+0.16
+0.14
+0.12
+0.12
+0.14
+0.16
+0.18
+0.20
+0.22
+0.24
+(3)truth5
+FIG. 3.
+Schematic comparison of 1-parameter posterior distributions (red solid, green dashed and blue dotted
+Gaussians) with a single fixed “truth” value of the parameter (vertical teal line). The green dashed line shows how
+the posterior increases as accuracy increases when compared to the blue dotted line, and the red solid line shows how
+the posterior increases as precision increases when compared to the blue dotted line.
+In closure tests, we first select a set of parameters that are considered the reference parameter for the
+closure test; we refer to these parameters as the “reference” or “truth” parameters, ptruth. We then compute
+event-averaged eccentricities ⟨ϵtruth
+n
+⟩ = ⟨εn⟩(ptruth), which have a statistical uncertainty ∆⟨ϵtruth
+n
+⟩. While
+these uncertainties are purely statistical, they are meant to mimic statistical and systematic uncertainties
+found in measurements. This uncertainty can be dialed by changing the number of TRENTo events M truth
+ev
+used to compute ⟨ϵtruth
+n
+⟩.
+Separately, we train Gaussian process emulators for ⟨εn⟩(p) over a chosen range of model parameters, as
+described in the previous section. The two sources of uncertainties in the emulator are the number of design
+points (parameter samples) Nd, which controls the interpolation uncertainty, and the number of TRENTo
+events per design point, Mev, which control the statistical uncertainty of ⟨εn⟩(p) at each design point.
+Using the Gaussian process emulators as proxy for TRENTo, we then perform Bayesian parameter esti-
+mation to attempt to recover the parameters ptruth from the values of the observables ⟨ϵtruth
+n
+⟩ ± ∆⟨ϵtruth
+n
+⟩.
+The result of the Bayesian inference is the posterior P(p|{⟨ϵtruth
+n
+⟩}) (Eq. 4). This posterior distribution
+depends on three sources of uncertainties: the uncertainty on the reference observables (∆⟨ϵtruth
+n
+⟩), which
+mimics experimental uncertainty, and the statistical and interpolation uncertainty in the emulator. If all
+uncertainties were small, one would expect the posterior to be a narrow peak at the parameter truth ptruth.
+In practice, some of these uncertainties are significant, and the posterior distribution thus has some finite
+width in parameter space. If closure is successful, the posterior should enclose the parameter set ptruth.
+To quantify the degree of agreement of the posterior — P(p|{⟨ϵtruth
+n
+⟩}) — with the known true value
+ptruth of the parameters used in the closure test, we use two different metrics. The first one is the value of
+the posterior at the parameter truth, P(ptruth|{⟨ϵtruth
+n
+⟩}). The posterior at the parameter truth balances
+accuracy and precision. As illustrated in Fig. 3, an increase in accuracy (shift towards true value of the
+parameter) will increase the posterior value. An increase in precision (narrower posterior) will also increase
+the posterior at the parameter truth, but only to a certain extent: the posterior at the truth will actually
+start to decrease if the results get too confident about the incorrect value. The posterior at the truth has
+the benefit of being simple to interpret and inexpensive to compute.
+For completeness, we studied a second metric, the Akaike Information Criterion (AIC) [31], given by:
+AIC ≡ −2 ln(Lmax) + 2k
+(7)
+where Lmax is the maximum likelihood in the parameter space and k is the number of parameters. The Akaike
+Information Criterion is a metric used for model selection, to help determine how successful a model is at
+describing measurements given its number of parameters [32, 33]. In the case of closure tests, while we know
+that the emulator and the reference (truth) calculations originate from the same model, the uncertainties
+in the problem can evidently obscure this fact. We will see in this work the AIC’s success at quantifying
+closure. Note that the AIC is more expensive to compute, as it requires identifying the maximum of the
+likelihood.
+
+0.20
+0.15
+posterior
+0.10
+0.05
+0.00
+5
+10
+15
+20
+parameter6
+FIG. 4. Closure tests with NdMev = 216 total events, M truth
+ev
+= 216 events to compute the reference observables, two
+parameters (nucleon width and reduced thickness on the left, and nucleon width and reduced fluctuation parameter
+on the right), and two observables (⟨ε2⟩ and ⟨ε3⟩ in Pb-Pb collisions at √sNN = 2.76 TeV). Top two panels show
+the mode and width of the one-parameter marginalized likelihood, while the bottom panel shows the value of the
+posterior at the true value of the parameter as well as the Akaike Information Criterion (AIC), all as a function of
+the ratio of the number of design points Nd to the number of TRENTo simulations per design points Mev.
+III.
+RESULTS
+As discussed in Section II, the result of Bayesian parameter inference generally depends on the experimental
+uncertainty as well as on the statistical and interpolation uncertainty of the emulator. Additional theoretical
+uncertainties can also play a role [15].
+Because we use closure tests in this manuscript, the experimental uncertainty is replaced by the statistical
+uncertainty of the reference (“truth”) calculations, which is controlled by changing the number M truth
+ev
+of TRENTo events that are averaged over to compute the reference observables. As for the emulator, its
+uncertainty is determined by the number of samples of the model parameters Nd and the number of collisions
+simulated per parameter sample Mev.
+Tests are performed at a fixed computation budget: the product Ntot = NdMev is kept fixed. The set
+of (Nd, Mev) pairs is chosen to vary by a factor of 2 (e.g. {8, 128} → {16, 64} → {32, 32}). We use nine
+different sets of (Nd, Mev), resulting in nine different groups of emulators, each group having one Gaussian
+process emulator per observable.
+As a base case, we first used Ntot = NdMev = 216 total events for a Pb-Pb collision. We used M truth
+ev
+= 216
+collisions to compute the reference “truth” observables. We begin with only two TRENTo parameters at the
+time — nucleon width and reduced thickness in one case, and nucleon width and fluctuation in the other. To
+test the robustness of the methodology, we later vary the data uncertainty, and the number of parameters
+and of observables.
+After performing Bayesian parameter inference in the framework described above, we obtain a 2-parameter
+posterior distribution. By marginalizing over each parameter, we obtain 1-parameter marginalized posterior
+distributions, whose mode and width (variance) we calculate and plot as a function of the ratio of the number
+of design points Nd to the number of TRENTo simulations per design points Mev; this is shown in the left
+top two panels of Figure 4. The true (reference) value of the parameters used in the tests is shown as a
+red horizontal line. We first see that, for any number of design points, the constraints from the posterior
+are consistent with the true value of the parameters. This is not a trivial observation: it indicates that
+the emulator is quantifying properly the interpolation and statistical uncertainties, however large or small
+these uncertainties are. In this sense, we see that Bayesian parameter inference provides valid constraints
+for any set of design points Nd and number of TRENTo events Mev. On the other hand, one can optimize
+the results of the Bayesian inference by a careful compromise between emulator and statistical uncertainty.
+With large numbers of design points (large Nd/Mev), the emulator uncertainty is expected to be small, but
+large statistical uncertainties on the ⟨ϵn⟩ of each design point prevent accurate constraints on the parameter.
+Using a large number of TRENTo events with a small number of design points (small Nd/Mev) leads to
+
+thickness
+0.4
+Reduced
+0.2
+0.0
+0.8
+Nucleon width
+0.6
+Akaike Information
+the truth [arb.u.]
+Posterior at
+Posterior
+AIC
+-5
+1000
+Criterion
+:10
+500
+15
+0
+10-2
+100
+102
+Na/Mev4
+Fluctuation
+2
+0.8
+0.6
+Akaike Information
+Posterior at
+Posterior
+AIC
+Criterion
+20
+10
+15
+0
+10-2
+100
+102
+Na/Mev7
+FIG. 5. Same as left side of Fig. 4, with (left) M truth
+ev
+= 214 events and (right) M truth
+ev
+= 218 events.
+similar sub-optimal results. To quantify this tension, we use the two metrics discussed in Section II D: the
+value of the posterior at the true value of the closure test parameters, and the Akaike Information Criterion
+(AIC). Both are plotted on the bottom left panel of Figure 4, still as a function of the ratio Nd/Mev. The
+maximum value of the posterior at the truth, and the minimum value of the AIC, are observed around
+Nd/Mev = 0.25, which corresponds to Nd = 27 design points. Overall, the different panels all indicate
+that certain apportionment of the number of design points does result in significantly better constraints
+on the model parameter for the same computational expense. The optimal number is found to be between
+Nd/Mev = 0.1 and 1. This suggests that the optimal value of Nd is of the order of √Ntot or slightly smaller.
+Repeating this exercise by swapping one of the TRENTo parameters (reduced thickness) by another
+(fluctuation parameter) yields the right panels of Figure 4.
+Because the fluctuation parameter is more
+challenging to constrain from ⟨ε2⟩ and ⟨ε3⟩, the dependence on the number of design point Nd of the top
+panel is modest. Yet this does not prevent the other parameter to be better constrained (middle right panel),
+and the optimal number of design points remain in the vicinity of Nd/Mev = 0.25.
+To ensure the robustness of our conclusions, we repeat this same analysis varying the uncertainty on the
+reference calculations (which are proxy for data uncertainty) as well as varying the number of parameters
+and observables.
+A.
+Dependence on the uncertainty of the reference calculation (“data”)
+To compute the reference (“truth”) observables, M truth
+ev
+TRENTo events are averaged. Changing M truth
+ev
+controls the uncertainty on the reference observables, ∆⟨ϵtruth
+n
+⟩. In this section, we vary M truth
+ev
+to verify the
+effect on the optimal number of design points.
+In the previous example, because Ntot = NdMev and M truth
+ev
+were both equal to 216, the interpolation and
+statistical uncertainty in the emulator (controlled by Ntot) were always large compared to the uncertainty of
+the reference calculations that are stand-in for measurements (controlled by M truth
+ev
+): at best, the statistical
+uncertainties for the calculations used in the emulator could be equal to the statistical uncertainty from the
+reference calculations (uncertainty ∝ 1/
+√
+216) when Nd = 1, which would evidently be a case with extreme
+interpolation uncertainty.
+We first repeat the previous example with M truth
+ev
+= 214 events while keeping Ntot = NdMev = 216. This
+means that, when Nd = 22 = 4, the statistical uncertainty of the reference calculation is similar to that in
+the calculations used for the emulator; when Nd = 24 = 16, the statistical uncertainty in the emulator is
+approximately a factor 2 larger than in that of the reference calculations, etc. The results of the closure tests
+are shown on the left panel of Fig. 5. Overall, the results are similar: the constraints on the model parameters
+are consistent with the true value of the parameters at any ratio Nd/Mev, but the range Nd/Mev ≈ 0.1–1 is
+found to be optimal.
+We repeat this test in the opposite direction, using M truth
+ev
+= 218 events to reduce the uncertainty on the
+reference calculations while keeping the emulator budget the same (Ntot = NdMev = 216). This is equivalent
+
+thickness
+0.4
+Reduced
+0.2
+0.0
+0.8
+0.6
+Akaike Information
+Posterior at
+Posterior
+AIC
+400
+Criterion
+10
+200
+0
+10-2
+100
+102
+Na/Mevthickness
+0.4
+Reduced
+0.2
+0.0
+0.8
+Nucleon width
+0.6
+Akaike Information
+the truth [arb.u.]
+1000
+Posterior at
+Posterior
+AIC
+-5
+Criterion
+500
+-10
+-15
+0
+10-2
+100
+102
+Na/Mev8
+FIG. 6. Same as left side of Fig. 4, with (left) three observables (⟨εn⟩, n = 2, 3, 4), and (right) four observables (⟨εn⟩,
+n = 2, 3, 4, 5).
+FIG. 7. Same as Fig. 4, with three TRENTo parameters instead of two, and between two (left), three (center) or four
+(right) observables, with the observables being ⟨εn⟩, n = 2, 3, n = 2, 3, 4 and n = 2, 3, 4, 5 respectively.
+to a scenario where the emulator uncertainties are always being much larger than the data uncertainties.
+This yields the right panel of Fig. 5. Again, the optimal range of design points remains Nd/Mev ≈ 0.1–1.
+B.
+Dependence on the observables and the parameters
+Emulator performance depends on multiple factors, in particular the number of parameters, and the
+complexity of the parameter dependence of the observables. The results of Bayesian parameter inference
+evidently also depend on the factors just listed that impact emulator performance, and further depends on
+the information carried by the different observables. We repeat the closure test shown on Fig. 4 by adding
+new observables: we first add ⟨ε4⟩, and then ⟨ε5⟩. The results are shown respectively on the left and right
+panels of Fig. 6. Again, the results remain similar, with the optimal number of design points in the same
+
+thickness
+0.4
+Reduced
+0.2
+0.0
+0.8
+Nucleon width
+0.6
+Akaike Information
+the truth [arb.u.]
+Posterior at
+-10
+Posterior
+AIC
+Criterion
+1000
+-20
+30
+10-2
+100
+102
+Na/Mevthickness
+0.4
+Reduced
+0.2
+0.0
+Nucleon width
+0.8
+0.6
+4
+Fluctuation
+2
+Akaike Information
+the truth [arb.u.
+100
+Posterior
+AIC
+5
+Criterion
+一
+Posterior
+50
+0
+100
+10-2
+102
+Na/Mevthickness
+0.4
+Reduced
+0.2
+0.0
+Nucleon width
+0.8
+0.6
+4
+Fluctuation
+2
+Akaike Information
+the truth [arb.u.
+at
+Posterior
+AIC
+Criterion
+Posterior
+-10
+200
+0
+100
+10-2
+102
+Na/Mevthickness
+0.4
+Reduced
+0.2
+0.0
+Nucleon width
+0.8
+0.6
+4
+Fluctuation
+2
+Akaike Information
+the truth [arb.u.
+at
+Posterior
+AIC
+-10
+500
+Criterion
+Posterior
+250
+0
+100
+10-2
+102
+Na/Mevthickness
+0.4
+Reduced
+0.2
+0.0
+0.8
+Nucleon width
+0.6
+Akaike Information
+the truth [arb.u.]
+Posterior at
+Posterior
+AIC
+-10
+Criterion
+1000
+-20
+O
+10-2
+100
+102
+Na/Mev9
+range as found in previous tests.
+We repeat this test, this time with three TRENTo parameters instead of two, starting with two observables
+(⟨εn⟩, n = 2, 3), then three (n = 2, 3, 4) and four (n = 2, 3, 4, 5) observables.
+The results are shown
+respectively on the left, center and right panels of Fig. 7.
+The results are consistent with all previous
+ones: closure is successful since the constraints on all parameters are consistent with the truth value of the
+parameter for any number of design points. Moreover, constraints on the parameters are still best when the
+ratio of the number of design points Nd to the number of TRENTo simulations per design points Mev is in
+the range Nd/Mev ≈ 0.1–1.
+IV.
+DISCUSSION
+There is a consistent trend among the results shown in Figs. 4–7: closure was best when the number
+of design points was slightly smaller than the square root of the total number of events (√Ntot), which is
+equivalent to Nd/Mev ≈ 0.1–1. This trend holds true for all the variations tested in this study.
+A rule of thumb that is used at times to determine the number of parameter samples (design points) for a
+Gaussian process emulator is 10 times the number of parameters (10Nparams) [34]. This guidance is evidently
+not meant to be precise, if only because it does not take into account the unavoidable trade-offs between
+statistical and emulator uncertainty. In the two-parameter case, Nd = 10Nparams ≈ 24, which is considerably
+smaller than the optimal Nd ≈ 26–28 found in the previous section. We also note that the optimal number
+of design points did not change significantly when three model parameters were used instead of two (Fig. 7),
+which suggests a modest dependence of this optimum on the number of parameters.
+While statistical uncertainties generally converge at the rate 1/√Mev, interpolation uncertainties depend
+on the details of the model’s parameter dependence, and the range of parameters (the prior) over which an
+emulator is being trained. Rather than attempting to provide general guidance, we focus on application to
+heavy ion physics, where our results guidance will apply most directly.
+V.
+IMPLICATIONS FOR BAYESIAN INFERENCE IN HEAVY ION COLLISIONS
+As seen in the results from Section III, emulator uncertainty is propagated properly in the Bayesian
+parameter estimation: even if one uses an emulator with large interpolation or statistical uncertainties, the
+parameter constraints remain consistent with the true value of the parameter used in the closure test. In
+this sense, we expect the Gaussian process emulators used in Bayesian inference procedure of heavy ion data
+to be robust. On the other hand, we saw that optimizing the interpolation and statistical uncertainty of the
+emulator can lead to considerably improved constraints on the model parameters at the same computational
+cost. In our study, we found an optimal ratio of design points to TRENTo events per design point, Nd/Mev,
+around 0.1–1.
+The optimum Nd/Mev ≈ 1 is expected if the interpolation uncertainty in the emulator scales approximately
+as 1/√Nd: that is, if both interpolation and statistical uncertainties scale the same, one should aim for a
+roughly even number for Nd and Mev. Tests published in Ref. [17] found some evidence of 1/√Nd convergence
+of observables in realistic models of heavy ion collisions.
+To apply our work’s conclusions to heavy ion collisions, one must remember that there are different sources
+of stochasticity in the collisions, only one of which was considered in this work: fluctuations in the initial
+impact geometry of the nuclei. Fluctuations in the number of particles produced will also introduce statistical
+uncertainty, which was not studied in this work. It is common, though not universal, that the two statistical
+uncertainties are reduced by oversampling the particles produced for each initial geometry of the collision.
+The factor Mev in the ratio Nd/Mev ≈ 0.1–1 corresponds to the number of initial geometries samples, and
+not the total number of oversamples.
+Finally, we note that the choice of Mev might be guided by the need for accuracy for certain statistics-
+hungry observables, rather than the benefits of the emulator as a whole [19, 20]. It will be useful to repeat
+the current study with a broader range of observables.
+
+10
+VI.
+CONCLUSION
+We studied the interplay between interpolation and statistical uncertainties for Bayesian parameter in-
+ference using Gaussian process emulators. We used the TRENTo model of initial conditions in heavy ion
+collisions, with observables given by the event-averaged spatial anisotropies ⟨εn⟩ (Eq. 2), which are analogous
+to momentum anisotropy observables encountered in heavy ion collisions. Using Nd samples of the TRENTo
+parameter space and Mev TRENTo events at each parameter point, we performed closure tests to determine
+the impact of the emulator uncertainty on constraining model parameters. We found that, for a budget of
+Ntot total TRENTo events, the optimal number of design points was around Nd ≈ (0.25–1.0)√Ntot, which
+corresponds to Nd/Mev ≈ 0.1–1.
+We found this optimum by looking at multiple different metrics: the
+maximum value and width of the marginalized posterior, the value of the posterior at the true value of the
+parameter, and the Akaike Information Criterion (AIC). We found the posterior at the truth to be very
+effective at quantifying closure.
+In view of our results, we believe it would be beneficial for Bayesian inference applications in heavy ion
+physics to experiment with different ratios Nd/Mev.
+Simulating large number of collision events, which
+reduce all sources of stochastic uncertainties, can give access to statistics-hungry observables [19, 20]; yet
+using a large number Mev of events at each parameter sample will not provide significant benefits for the
+large number of observables whose emulation is limited by interpolation uncertainty. An improved balance
+between interpolation and statistical uncertainties can help reduce the emulator’s uncertainty below current
+experimental uncertainties, allowing us to make full use of heavy ion measurements from the RHIC and the
+LHC.
+VII.
+ACKNOWLEDGEMENTS
+The authors thank Simon Mak for insightful discussions, and Ron Solz and Matthew Luzum for valuable
+feedback. B.W. thanks Duke University and Wayne State University for financial support. S.A.B. and J.-
+F.P. have been supported by the U.S. Department of Energy Grant no. DE-FG02-05ER41367 This research
+used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User
+Facility supported by the Office of Science of the U.S. Department of Energy under Contract No.
+DE-
+AC02-05CH11231 using NERSC award NP-ERCAP0022230. Calculations were also performed on the Duke
+Compute Cluster.
+[1] S. A. Bass, “Microscopic reaction dynamics at SPS and RHIC,” Nucl. Phys. A, vol. 698, pp. 164–170, 2002.
+[2] C. Gale, S. Jeon, and B. Schenke, “Hydrodynamic Modeling of Heavy-Ion Collisions,” Int. J. Mod. Phys. A,
+vol. 28, p. 1340011, 2013.
+[3] U. Heinz and R. Snellings, “Collective flow and viscosity in relativistic heavy-ion collisions,” Ann. Rev. Nucl.
+Part. Sci., vol. 63, pp. 123–151, 2013.
+[4] R. Derradi de Souza, T. Koide, and T. Kodama, “Hydrodynamic Approaches in Relativistic Heavy Ion Reac-
+tions,” Prog. Part. Nucl. Phys., vol. 86, pp. 35–85, 2016.
+[5] O. Philipsen, “The QCD equation of state from the lattice,” Prog. Part. Nucl. Phys., vol. 70, pp. 55–107, 2013.
+[6] H. Petersen, C. Coleman-Smith, S. A. Bass, and R. Wolpert, “Constraining the initial state granularity with
+bulk observables in Au+Au collisions at √sNN = 200 GeV,” J. Phys. G, vol. 38, p. 045102, 2011.
+[7] J. Novak, K. Novak, S. Pratt, J. Vredevoogd, C. Coleman-Smith, and R. Wolpert, “Determining Fundamental
+Properties of Matter Created in Ultrarelativistic Heavy-Ion Collisions,” Phys. Rev. C, vol. 89, no. 3, p. 034917,
+2014.
+[8] E. Sangaline and S. Pratt, “Toward a deeper understanding of how experiments constrain the underlying physics
+of heavy-ion collisions,” Phys. Rev. C, vol. 93, no. 2, p. 024908, 2016.
+[9] S. Pratt, E. Sangaline, P. Sorensen, and H. Wang, “Constraining the Eq. of State of Super-Hadronic Matter from
+Heavy-Ion Collisions,” Phys. Rev. Lett., vol. 114, p. 202301, 2015.
+[10] J. E. Bernhard, P. W. Marcy, C. E. Coleman-Smith, S. Huzurbazar, R. L. Wolpert, and S. A. Bass, “Quantifying
+properties of hot and dense QCD matter through systematic model-to-data comparison,” Phys. Rev. C, vol. 91,
+no. 5, p. 054910, 2015.
+
+11
+[11] J. E. Bernhard, J. S. Moreland, S. A. Bass, J. Liu, and U. Heinz, “Applying Bayesian parameter estimation
+to relativistic heavy-ion collisions: simultaneous characterization of the initial state and quark-gluon plasma
+medium,” Phys. Rev. C, vol. 94, no. 2, p. 024907, 2016.
+[12] J. S. Moreland, J. E. Bernhard, and S. A. Bass, “Bayesian calibration of a hybrid nuclear collision model using
+p-Pb and Pb-Pb data at energies available at the CERN Large Hadron Collider,” Phys. Rev. C, vol. 101, no. 2,
+p. 024911, 2020.
+[13] J. E. Bernhard, Bayesian parameter estimation for relativistic heavy-ion collisions. PhD thesis, Duke U., 4 2018.
+[14] J. E. Bernhard, J. S. Moreland, and S. A. Bass, “Bayesian estimation of the specific shear and bulk viscosity of
+quark–gluon plasma,” Nature Phys., vol. 15, no. 11, pp. 1113–1117, 2019.
+[15] D. Everett et al., “Multisystem Bayesian constraints on the transport coefficients of QCD matter,” Phys. Rev.
+C, vol. 103, no. 5, p. 054904, 2021.
+[16] G. Nijs, W. van der Schee, U. G¨ursoy, and R. Snellings, “Transverse Momentum Differential Global Analysis of
+Heavy-Ion Collisions,” Phys. Rev. Lett., vol. 126, no. 20, p. 202301, 2021.
+[17] G. Nijs, W. van der Schee, U. G¨ursoy, and R. Snellings, “Bayesian analysis of heavy ion collisions with the heavy
+ion computational framework Trajectum,” Phys. Rev. C, vol. 103, no. 5, p. 054909, 2021.
+[18] D. Everett et al., “Phenomenological constraints on the transport properties of QCD matter with data-driven
+model averaging,” Phys. Rev. Lett., vol. 126, no. 24, p. 242301, 2021.
+[19] J. E. Parkkila, A. Onnerstad, and D. J. Kim, “Bayesian estimation of the specific shear and bulk viscosity of the
+quark-gluon plasma with additional flow harmonic observables,” Phys. Rev. C, vol. 104, no. 5, p. 054904, 2021.
+[20] J. E. Parkkila, A. Onnerstad, S. F. Taghavi, C. Mordasini, A. Bilandzic, M. Virta, and D. J. Kim, “New
+constraints for QCD matter from improved Bayesian parameter estimation in heavy-ion collisions at LHC,”
+Phys. Lett. B, vol. 835, p. 137485, 2022.
+[21] J. S. Moreland, J. E. Bernhard, and S. A. Bass, “Alternative ansatz to wounded nucleon and binary collision
+scaling in high-energy nuclear collisions,” Phys. Rev. C, vol. 92, no. 1, p. 011901, 2015.
+[22] M. Luzum and H. Petersen, “Initial State Fluctuations and Final State Correlations in Relativistic Heavy-Ion
+Collisions,” J. Phys. G, vol. 41, p. 063102, 2014.
+[23] J.-Y. Ollitrault, “Anisotropy as a signature of transverse collective flow,” Phys. Rev. D, vol. 46, pp. 229–245,
+1992.
+[24] M. Miller and R. Snellings, “Eccentricity fluctuations and its possible effect on elliptic flow measurements,” 12
+2003.
+[25] B. Alver et al., “System size, energy, pseudorapidity, and centrality dependence of elliptic flow,” Phys. Rev. Lett.,
+vol. 98, p. 242302, 2007.
+[26] B. Alver and G. Roland, “Collision geometry fluctuations and triangular flow in heavy-ion collisions,” Phys. Rev.
+C, vol. 81, p. 054905, 2010. [Erratum: Phys.Rev.C 82, 039903 (2010)].
+[27] F. G. Gardim, F. Grassi, M. Luzum, and J.-Y. Ollitrault, “Mapping the hydrodynamic response to the initial
+geometry in heavy-ion collisions,” Phys. Rev. C, vol. 85, p. 024908, 2012.
+[28] C. K. Williams and C. E. Rasmussen, Gaussian processes for machine learning, vol. 2. MIT press Cambridge,
+MA, 2006.
+[29] M. Roberts.
+https://github.com/j-f-paquet/bayesian_parameter_estimation_tutorial/blob/master/
+parameter_space_sampling/param_sampling.ipynb.
+[30] H. Niederreiter, Random number generation and quasi-Monte Carlo methods. SIAM, 1992.
+[31] H. Akaike, “A new look at the statistical model identification,” IEEE transactions on automatic control, vol. 19,
+no. 6, pp. 716–723, 1974.
+[32] A. R. Liddle, “Information criteria for astrophysical model selection,” Mon. Not. Roy. Astron. Soc., vol. 377,
+pp. L74–L78, 2007.
+[33] A. R. Liddle, “How many cosmological parameters,” Monthly Notices of the Royal Astronomical Society, vol. 351,
+no. 3, pp. L49–L53, 2004.
+[34] J. L. Loeppky, J. Sacks, and W. J. Welch, “Choosing the sample size of a computer experiment: A practical
+guide,” Technometrics, vol. 51, no. 4, pp. 366–376, 2009.
+
diff --git a/utE_T4oBgHgl3EQf-Rwc/content/tmp_files/load_file.txt b/utE_T4oBgHgl3EQf-Rwc/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6a1eec151955036f2ef03f087b1bb69f8666cf60
--- /dev/null
+++ b/utE_T4oBgHgl3EQf-Rwc/content/tmp_files/load_file.txt
@@ -0,0 +1,701 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf,len=700
+page_content='Computational budget optimization for Bayesian parameter estimation in  heavy ion collisions  Brandon Weiss,1 Jean-Fran¸cois Paquet,2, 3, 1 and Steffen A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Bass1  1Department of Physics, Duke University, Durham NC 27708.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  2Department of Physics and Astronomy, Vanderbilt University, Nashville TN 37235.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  3Department of Mathematics, Vanderbilt University, Nashville TN 37235.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  (Dated: August 2021)  Bayesian parameter estimation provides a systematic approach to compare heavy ion collision  models with measurements, leading to constraints on the properties of nuclear matter with proper  accounting of experimental and theoretical uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  Aside from statistical and systematic  model uncertainties, interpolation uncertainties can also play a role in Bayesian inference, if the  model’s predictions can only be calculated at a limited set of model parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' This uncertainty  originates from using an emulator to interpolate the model’s prediction across a continuous space  of parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  In this work, we study the trade-offs between the emulator (interpolation) and  statistical uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  We perform the analysis using spatial eccentricities from the TRENTo  model of initial conditions for nuclear collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Given a fixed computational budget, we study  the optimal compromise between the number of parameter samples and the number of collisions  simulated per parameter sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' For the observables and parameters used in the present study, we  find that the best constraints are achieved when the number of parameter samples is slightly smaller  than the number of collisions simulated per parameter sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  INTRODUCTION  One of the main goals of the heavy ion program pursued at the Relativistic Heavy Ion Collider (RHIC) and  the Large Hadron Collider (LHC) is a quantitative understanding of the properties of nuclear matter under  extreme conditions as described by Quantum Chromodynamics (QCD).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' At sufficiently high temperatures  and densities accessible during these nuclear collisions, a transient state of matter, the quark-gluon plasma  (QGP), is formed, but decays again as the collision systems cools down and disintegrates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Collisions of heavy  ions leading to QGP formation are multistage processes: the initial impact of the nuclei, the formation and  expansion of the QGP, reconfinement into hadrons, and subsequent hadronic interactions [1–4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' A wide range  of properties of nuclear matter enter numerical simulations of heavy ion collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Some of these properties  are constrained by external means, for example lattice Quantum Chromodynamics calculations of the equa-  tion of state of nuclear matter [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Other properties, such as transport coefficients or parameters entering the  description of the early stage of the collision, are often parametrized and constrained by comparison with  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  Measurements from the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) can  constrain these physical parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Because of the heterogeneity and large number of measurements and  model parameters, it is beneficial to perform model-to-data comparisons using statistical techniques such as  Bayesian parameter estimation: this allows for a systematic propagation of uncertainties from experimental  measurements to physical parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' A number of such studies have been performed over the past decade [6–  20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  A key ingredient of Bayesian parameter estimation as used in heavy ion collisions is emulation: given the  model’s prediction at a discrete sample of parameters, an emulator will interpolate the model’s prediction over  a continuous range of parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Furthermore, emulators such as Gaussian processes provide an estimate of  their own interpolation uncertainty;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' in effect, this allows emulation to be used in model-to-data comparisons  even if the emulator’s interpolation uncertainty is not negligible compared to the other uncertainties in the  problem — a situation that is often unavoidable in simulations with large number of parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' In Bayesian  parameter estimation, this emulator uncertainty is included into the physical parameter’s final uncertainty  determination, alongside experimental, statistical and other theoretical uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  The most straightforward approach to reducing emulator uncertainty is to increase the number of parame-  ter samples at which the model observables are evaluated;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' these parameter samples are generally referred to  as the emulator’s “design points”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Evidently, this increase in the number of design points must be balanced  with other demands on the available computational budget.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' In particular, simulations of heavy ion collisions  are stochastic: there are event-by-event fluctuations in the outcome of the collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Comparisons with  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='08385v1  [nucl-th]  20 Jan 2023  2  measurements require simulating and averaging over a large number of collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' At a fixed computational  budget, one must determine the proper trade-off between reducing emulator interpolation uncertainties or  statistical ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' In this work, we use the TRENTo model of initial conditions for heavy ion collisions [21] to  study this trade-off between statistical and emulator uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  METHODOLOGY  We use the model TRENTo as proxy for observables in heavy ion collisions;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' this is based on the known  correlation [22] between (i) initial spatial anisotropies of models like TRENTo, and (ii) measurable momentum  anisotropies of final state hadrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' To interpolate the output of the TRENTo model, we use Gaussian process  emulators, which have been the standard emulation technique used for model-to-data comparisons in heavy  ion physics [6–8, 10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' To quantify the optimal trade-off between statistical and emulator uncertainty, we use  “closure tests”, which apply Bayesian parameter inference to model calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' We summarize the overall  approach and methods below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  TRENTo  TRENTo is a parametric initial condition ansatz for simulating relativistic heavy ion collisions [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' It  takes as input the type of colliding nuclei and the inelastic nucleon-nucleon cross-section corresponding to  the center-of-mass energy of the collision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  We vary three parameters of the TRENTo model: the effective nucleon size w, the fluctuation parameter  k and the reduced thickness p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' The fluctuation parameter k allows for variation in the amount of energy  carried by each nucleon, while the reduced thickness p parametrize how the energy or entropy density is  constructed from the profile of nucleons sampled from each nuclei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  The output of TRENTo is a density profile in the plane transverse to the collision axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' We interpret  TRENTo’s output as an energy density profile ϵ(r, φ) with arbitrary normalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' From this density profile  ϵ(r, φ), we compute single-event spatial anisotropies εn [22]:  εneinΦn =  � ∞  0  drr  � 2π  0  dφ rnϵ(r, φ)einφ  � ∞  0  drr  � 2π  0  dφ rnϵ(r, φ)  (1)  Although these anisotropies can be related to the momentum anisotropy of hadrons measured at the end  of the collision [23–27], in this work, we focus on the initial spatial eccentricies themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  We compute the average of an ensemble of TRENTo events with an arithmetic average:  ⟨εn⟩ =  1  Mev  Mev  �  j=1  εn{event j} .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  (2)  We used up to four harmonics in this work, n = 2 to 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  We studied minimum bias Pb-Pb collisions with Woods-Saxon nucleon distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' We used an inelastic  nucleon-nucleon cross-section of 64 mb, corresponding approximately to √sNN = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='76 TeV collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  Bayesian parameter estimation  We note yth,j(p) the model’s prediction for the “j”-th observables of interest, evaluated when the model’s  parameters are set to p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' At p, we compute yth,j(p) = ⟨εnj⟩(p), where the index j runs over all the observables  of interest, which in our case are the different “n” in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  In general, given this information, we want to find the probability that parameters p are consistent with  the data {yexp,j} and with the experimental and theoretical uncertainties {σexp,j} and {σth,j(p)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' The first  step is to define a metric to quantify the level of model-to-data agreement: the likelihood function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' We make  3  the typical choice of a Gaussian likelihood function:  L({yexp,j}|p) = exp  �  �−1  2  �  j  [yth,j(p) − yexp,j]2  σth,j(p)2 + σ2  exp,j  �  �  ��  (2π)n �  j  �  σth,j(p)2 + σ2  exp,j  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  (3)  We assumed a diagonal covariance matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' In this work, instead of comparing the model with data, we will  use closure tests: we will replace yexp,j by model calculations, as discussed later.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' These model calculations  do stand for experimental data, and consequently we keep the label “exp” to denote these quantities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  Given our model of the collision, the probability that the parameter set p is consistent with the data and  the uncertainties is given by the posterior distribution of model parameters, P(p|({yexp}):  P(p|({yexp}) =  L({yexp}|p)Prior(p)  �  dpL({yexp}|p)Prior(p)  (4)  where Prior(p) is the prior distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' In this work we take the prior to be constant over a finite parameter  range, for all the parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  The posterior distribution P(p|({yexp}) is a probability distribution whose dimensionality is equal to the  number of model parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Different projections of the posterior distribution summarize the constraints  on the model parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' As long as the number of parameters is small and the model is relatively fast  computationally, it is straightforward to sample and marginalize the posterior P(p|({yexp}).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  When the  number of parameters increases or if the model is expensive, it can become overly burdensome to evaluate  a model’s prediction at a large number of values of the parameter p to compute P(p|({yexp}).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' A solution  is to prepare a fast proxy, such as a Gaussian process [28], to emulate the model’s prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' We review  Gaussian process emulators briefly in the next subsection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' As far as the Bayesian inference is concerned, the  consequence of using Gaussian process emulators is substituting the model’s prediction by the emulator’s  prediction,  yth,j(p) → yemul,j(p) ,  (5)  as well as adding the emulator interpolation uncertainty into the sum of uncertainties,  σth,j(p)2 → σth,j(p)2 + σemul,j(p)2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  (6)  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  Emulation with Gaussian processes  The idea behind emulation is to first sample the parameter space of the model, {pk};' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' the parameter  samples are the design points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' The model’s predictions are then calculated for all design points: {yth,j(pk)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  The emulator then interpolates the model’s predictions over a continuous range of model parameters p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  To sample the parameter space, we use a low discrepancy sequence generator [29, 30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Figure 1 shows an  example for 16 design points within a two-dimensional parameter space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  For each observable (⟨ϵn⟩), a Gaussian process is trained on the set of values of ⟨ϵn⟩(p) calculated at the  design points {pk}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Gaussian process emulators are probabilistic interpolators, which assume that each point  in parameter space is a probability distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' At the design points, the width of the probability distribution  should include the statistical uncertainty of the observables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Between the design points, the width of the  probability distribution should increase to account for the interpolation uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' To handle stochastic  simulations, Gaussian process emulators must be set up such that variations between parameter samples  are divided into (i) statistical uncertainty, and (ii) the actual variation from the parameter dependence  of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' A mathematical description of the approach can be found in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' [15, Section V-B-2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' In  short, a white noise kernel accounts for the uncorrelated (“short range”) fluctuations originating from the  statistical uncertainty, and a squared-exponential kernel accounts for the longer-range parameter dependence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  The parameters of these kernels, for example the relative size of the kernels, is determined by numerical  optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  This approach is used in most applications of Bayesian parameter inference in heavy ion  physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' The result of this implementation is that the emulator uncertainty accounts for both the statistical  and interpolation uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  Figure 2 shows the mean-value predictions of the emulator for ⟨ϵ2⟩ and ⟨ϵ3⟩ compared to the actual value  of these observables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' The points all lie close to the line yemul,j(p) = yth,j(p), which shows that the emulator  4  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 16 design points in a two-dimensional parameter space (reduced thickness on the x-axis and nucleon width  on the y-axis), as sampled with a low discrepancy sequence generator [29, 30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' (Left) Value for ⟨ε2⟩ as predicted by a Gaussian process emulator trained with 16 design points (y-axis),  compared to the actual value of the model at the design points (x-axis);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' (Right) Same as left, for ⟨ε3⟩ with 256 design  points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' The red line corresponding to perfect emulation, yemul,j(p) = yth,j(p), is shown for reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Statistical  uncertainties on each sample are not shown for clarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  does indeed interpolate well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' On the other hand, ⟨ϵ3⟩ tends to have a larger statistical uncertainty than  ⟨ϵ2⟩, and as the right-hand side of Figure 2 shows, increasing the number of design points will not lead to  perfect deterministic-like prediction from the emulator because the values of ⟨ϵ3⟩ have significant statistical  uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' This is the trade-off that we focus on in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  Closure tests  Closure tests are a straightforward application of Bayesian parameter inference, with experimental data  replaced by calculations from the model itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' It is a self-consistency check made non-trivial by (i) the  presence of uncertainties, as well as (ii) loss of information from the model to the observables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' A longer  discussion of closure tests, in the context of heavy ion collisions, can be found in Section VI of Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' We  describe it briefly here, with focus on metrics to quantify the success of closure tests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='1  Nucleon width  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='34  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='32  (e2) emulator  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='28  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='26  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='24  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='24  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='26  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='28  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='32  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='34  (e2> truth0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='24  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='22  >emulator  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='18  (E3)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='16  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='14  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='12  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='12  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='14  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='16  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='18  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='22  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='24  (3)truth5  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  Schematic comparison of 1-parameter posterior distributions (red solid, green dashed and blue dotted  Gaussians) with a single fixed “truth” value of the parameter (vertical teal line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' The green dashed line shows how  the posterior increases as accuracy increases when compared to the blue dotted line, and the red solid line shows how  the posterior increases as precision increases when compared to the blue dotted line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  In closure tests, we first select a set of parameters that are considered the reference parameter for the  closure test;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' we refer to these parameters as the “reference” or “truth” parameters, ptruth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' We then compute  event-averaged eccentricities ⟨ϵtruth  n  ⟩ = ⟨εn⟩(ptruth), which have a statistical uncertainty ∆⟨ϵtruth  n  ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' While  these uncertainties are purely statistical, they are meant to mimic statistical and systematic uncertainties  found in measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' This uncertainty can be dialed by changing the number of TRENTo events M truth  ev  used to compute ⟨ϵtruth  n  ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  Separately, we train Gaussian process emulators for ⟨εn⟩(p) over a chosen range of model parameters, as  described in the previous section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' The two sources of uncertainties in the emulator are the number of design  points (parameter samples) Nd, which controls the interpolation uncertainty, and the number of TRENTo  events per design point, Mev, which control the statistical uncertainty of ⟨εn⟩(p) at each design point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  Using the Gaussian process emulators as proxy for TRENTo, we then perform Bayesian parameter esti-  mation to attempt to recover the parameters ptruth from the values of the observables ⟨ϵtruth  n  ⟩ ± ∆⟨ϵtruth  n  ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  The result of the Bayesian inference is the posterior P(p|{⟨ϵtruth  n  ⟩}) (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' This posterior distribution  depends on three sources of uncertainties: the uncertainty on the reference observables (∆⟨ϵtruth  n  ⟩), which  mimics experimental uncertainty, and the statistical and interpolation uncertainty in the emulator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' If all  uncertainties were small, one would expect the posterior to be a narrow peak at the parameter truth ptruth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  In practice, some of these uncertainties are significant, and the posterior distribution thus has some finite  width in parameter space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' If closure is successful, the posterior should enclose the parameter set ptruth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  To quantify the degree of agreement of the posterior — P(p|{⟨ϵtruth  n  ⟩}) — with the known true value  ptruth of the parameters used in the closure test, we use two different metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' The first one is the value of  the posterior at the parameter truth, P(ptruth|{⟨ϵtruth  n  ⟩}).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' The posterior at the parameter truth balances  accuracy and precision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' As illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 3, an increase in accuracy (shift towards true value of the  parameter) will increase the posterior value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' An increase in precision (narrower posterior) will also increase  the posterior at the parameter truth, but only to a certain extent: the posterior at the truth will actually  start to decrease if the results get too confident about the incorrect value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' The posterior at the truth has  the benefit of being simple to interpret and inexpensive to compute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  For completeness, we studied a second metric, the Akaike Information Criterion (AIC) [31], given by:  AIC ≡ −2 ln(Lmax) + 2k  (7)  where Lmax is the maximum likelihood in the parameter space and k is the number of parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' The Akaike  Information Criterion is a metric used for model selection, to help determine how successful a model is at  describing measurements given its number of parameters [32, 33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' In the case of closure tests, while we know  that the emulator and the reference (truth) calculations originate from the same model, the uncertainties  in the problem can evidently obscure this fact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' We will see in this work the AIC’s success at quantifying  closure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Note that the AIC is more expensive to compute, as it requires identifying the maximum of the  likelihood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='15  posterior  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='00  5  10  15  20  parameter6  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Closure tests with NdMev = 216 total events, M truth  ev  = 216 events to compute the reference observables, two  parameters (nucleon width and reduced thickness on the left, and nucleon width and reduced fluctuation parameter  on the right), and two observables (⟨ε2⟩ and ⟨ε3⟩ in Pb-Pb collisions at √sNN = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='76 TeV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Top two panels show  the mode and width of the one-parameter marginalized likelihood, while the bottom panel shows the value of the  posterior at the true value of the parameter as well as the Akaike Information Criterion (AIC), all as a function of  the ratio of the number of design points Nd to the number of TRENTo simulations per design points Mev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  RESULTS  As discussed in Section II, the result of Bayesian parameter inference generally depends on the experimental  uncertainty as well as on the statistical and interpolation uncertainty of the emulator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Additional theoretical  uncertainties can also play a role [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  Because we use closure tests in this manuscript, the experimental uncertainty is replaced by the statistical  uncertainty of the reference (“truth”) calculations, which is controlled by changing the number M truth  ev  of TRENTo events that are averaged over to compute the reference observables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' As for the emulator, its  uncertainty is determined by the number of samples of the model parameters Nd and the number of collisions  simulated per parameter sample Mev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  Tests are performed at a fixed computation budget: the product Ntot = NdMev is kept fixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' The set  of (Nd, Mev) pairs is chosen to vary by a factor of 2 (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' {8, 128} → {16, 64} → {32, 32}).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' We use nine  different sets of (Nd, Mev), resulting in nine different groups of emulators, each group having one Gaussian  process emulator per observable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  As a base case, we first used Ntot = NdMev = 216 total events for a Pb-Pb collision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' We used M truth  ev  = 216  collisions to compute the reference “truth” observables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' We begin with only two TRENTo parameters at the  time — nucleon width and reduced thickness in one case, and nucleon width and fluctuation in the other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' To  test the robustness of the methodology, we later vary the data uncertainty, and the number of parameters  and of observables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  After performing Bayesian parameter inference in the framework described above, we obtain a 2-parameter  posterior distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' By marginalizing over each parameter, we obtain 1-parameter marginalized posterior  distributions, whose mode and width (variance) we calculate and plot as a function of the ratio of the number  of design points Nd to the number of TRENTo simulations per design points Mev;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' this is shown in the left  top two panels of Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' The true (reference) value of the parameters used in the tests is shown as a  red horizontal line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' We first see that, for any number of design points, the constraints from the posterior  are consistent with the true value of the parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' This is not a trivial observation: it indicates that  the emulator is quantifying properly the interpolation and statistical uncertainties, however large or small  these uncertainties are.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' In this sense, we see that Bayesian parameter inference provides valid constraints  for any set of design points Nd and number of TRENTo events Mev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' On the other hand, one can optimize  the results of the Bayesian inference by a careful compromise between emulator and statistical uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  With large numbers of design points (large Nd/Mev), the emulator uncertainty is expected to be small, but  large statistical uncertainties on the ⟨ϵn⟩ of each design point prevent accurate constraints on the parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  Using a large number of TRENTo events with a small number of design points (small Nd/Mev) leads to  thickness  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='4  Reduced  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='8  Nucleon width  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='6  Akaike Information  the truth [arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=']  Posterior at  Posterior  AIC  5  1000  Criterion  :10  500  15  0  10-2  100  102  Na/Mev4  Fluctuation  2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='6  Akaike Information  Posterior at  Posterior  AIC  Criterion  20  10  15  0  10-2  100  102  Na/Mev7  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Same as left side of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 4, with (left) M truth  ev  = 214 events and (right) M truth  ev  = 218 events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  similar sub-optimal results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' To quantify this tension, we use the two metrics discussed in Section II D: the  value of the posterior at the true value of the closure test parameters, and the Akaike Information Criterion  (AIC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Both are plotted on the bottom left panel of Figure 4, still as a function of the ratio Nd/Mev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' The  maximum value of the posterior at the truth, and the minimum value of the AIC, are observed around  Nd/Mev = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='25, which corresponds to Nd = 27 design points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Overall, the different panels all indicate  that certain apportionment of the number of design points does result in significantly better constraints  on the model parameter for the same computational expense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' The optimal number is found to be between  Nd/Mev = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='1 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' This suggests that the optimal value of Nd is of the order of √Ntot or slightly smaller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  Repeating this exercise by swapping one of the TRENTo parameters (reduced thickness) by another  (fluctuation parameter) yields the right panels of Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  Because the fluctuation parameter is more  challenging to constrain from ⟨ε2⟩ and ⟨ε3⟩, the dependence on the number of design point Nd of the top  panel is modest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Yet this does not prevent the other parameter to be better constrained (middle right panel),  and the optimal number of design points remain in the vicinity of Nd/Mev = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  To ensure the robustness of our conclusions, we repeat this same analysis varying the uncertainty on the  reference calculations (which are proxy for data uncertainty) as well as varying the number of parameters  and observables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  Dependence on the uncertainty of the reference calculation (“data”)  To compute the reference (“truth”) observables, M truth  ev  TRENTo events are averaged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Changing M truth  ev  controls the uncertainty on the reference observables, ∆⟨ϵtruth  n  ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' In this section, we vary M truth  ev  to verify the  effect on the optimal number of design points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  In the previous example,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' because Ntot = NdMev and M truth  ev  were both equal to 216,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' the interpolation and  statistical uncertainty in the emulator (controlled by Ntot) were always large compared to the uncertainty of  the reference calculations that are stand-in for measurements (controlled by M truth  ev  ): at best,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' the statistical  uncertainties for the calculations used in the emulator could be equal to the statistical uncertainty from the  reference calculations (uncertainty ∝ 1/  √  216) when Nd = 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' which would evidently be a case with extreme  interpolation uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  We first repeat the previous example with M truth  ev  = 214 events while keeping Ntot = NdMev = 216.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' This  means that, when Nd = 22 = 4, the statistical uncertainty of the reference calculation is similar to that in  the calculations used for the emulator;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' when Nd = 24 = 16, the statistical uncertainty in the emulator is  approximately a factor 2 larger than in that of the reference calculations, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' The results of the closure tests  are shown on the left panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Overall, the results are similar: the constraints on the model parameters  are consistent with the true value of the parameters at any ratio Nd/Mev, but the range Nd/Mev ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='1–1 is  found to be optimal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  We repeat this test in the opposite direction, using M truth  ev  = 218 events to reduce the uncertainty on the  reference calculations while keeping the emulator budget the same (Ntot = NdMev = 216).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' This is equivalent  thickness  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='4  Reduced  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='6  Akaike Information  Posterior at  Posterior  AIC  400  Criterion  10  200  0  10-2  100  102  Na/Mevthickness  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='4  Reduced  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='8  Nucleon width  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='6  Akaike Information  the truth [arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=']  1000  Posterior at  Posterior  AIC  5  Criterion  500  10  15  0  10-2  100  102  Na/Mev8  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Same as left side of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 4, with (left) three observables (⟨εn⟩, n = 2, 3, 4), and (right) four observables (⟨εn⟩,  n = 2, 3, 4, 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Same as Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 4, with three TRENTo parameters instead of two, and between two (left), three (center) or four  (right) observables, with the observables being ⟨εn⟩, n = 2, 3, n = 2, 3, 4 and n = 2, 3, 4, 5 respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  to a scenario where the emulator uncertainties are always being much larger than the data uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  This yields the right panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Again, the optimal range of design points remains Nd/Mev ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='1–1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  Dependence on the observables and the parameters  Emulator performance depends on multiple factors, in particular the number of parameters, and the  complexity of the parameter dependence of the observables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' The results of Bayesian parameter inference  evidently also depend on the factors just listed that impact emulator performance, and further depends on  the information carried by the different observables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' We repeat the closure test shown on Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 4 by adding  new observables: we first add ⟨ε4⟩, and then ⟨ε5⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' The results are shown respectively on the left and right  panels of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Again, the results remain similar, with the optimal number of design points in the same  thickness  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='4  Reduced  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='8  Nucleon width  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='6  Akaike Information  the truth [arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=']  Posterior at  10  Posterior  AIC  Criterion  1000  20  30  10-2  100  102  Na/Mevthickness  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='4  Reduced  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='0  Nucleon width  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='6  4  Fluctuation  2  Akaike Information  the truth [arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  100  Posterior  AIC  5  Criterion  一  Posterior  50  0  100  10-2  102  Na/Mevthickness  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='4  Reduced  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='0  Nucleon width  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='6  4  Fluctuation  2  Akaike Information  the truth [arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  at  Posterior  AIC  Criterion  Posterior  10  200  0  100  10-2  102  Na/Mevthickness  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='4  Reduced  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='0  Nucleon width  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='6  4  Fluctuation  2  Akaike Information  the truth [arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  at  Posterior  AIC  10  500  Criterion  Posterior  250  0  100  10-2  102  Na/Mevthickness  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='4  Reduced  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='8  Nucleon width  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='6  Akaike Information  the truth [arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=']  Posterior at  Posterior  AIC  10  Criterion  1000  20  O  10-2  100  102  Na/Mev9  range as found in previous tests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  We repeat this test, this time with three TRENTo parameters instead of two, starting with two observables  (⟨εn⟩, n = 2, 3), then three (n = 2, 3, 4) and four (n = 2, 3, 4, 5) observables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  The results are shown  respectively on the left, center and right panels of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  The results are consistent with all previous  ones: closure is successful since the constraints on all parameters are consistent with the truth value of the  parameter for any number of design points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Moreover, constraints on the parameters are still best when the  ratio of the number of design points Nd to the number of TRENTo simulations per design points Mev is in  the range Nd/Mev ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='1–1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  DISCUSSION  There is a consistent trend among the results shown in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 4–7: closure was best when the number  of design points was slightly smaller than the square root of the total number of events (√Ntot), which is  equivalent to Nd/Mev ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='1–1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' This trend holds true for all the variations tested in this study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  A rule of thumb that is used at times to determine the number of parameter samples (design points) for a  Gaussian process emulator is 10 times the number of parameters (10Nparams) [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' This guidance is evidently  not meant to be precise, if only because it does not take into account the unavoidable trade-offs between  statistical and emulator uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' In the two-parameter case, Nd = 10Nparams ≈ 24, which is considerably  smaller than the optimal Nd ≈ 26–28 found in the previous section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' We also note that the optimal number  of design points did not change significantly when three model parameters were used instead of two (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 7),  which suggests a modest dependence of this optimum on the number of parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  While statistical uncertainties generally converge at the rate 1/√Mev, interpolation uncertainties depend  on the details of the model’s parameter dependence, and the range of parameters (the prior) over which an  emulator is being trained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Rather than attempting to provide general guidance, we focus on application to  heavy ion physics, where our results guidance will apply most directly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  IMPLICATIONS FOR BAYESIAN INFERENCE IN HEAVY ION COLLISIONS  As seen in the results from Section III, emulator uncertainty is propagated properly in the Bayesian  parameter estimation: even if one uses an emulator with large interpolation or statistical uncertainties, the  parameter constraints remain consistent with the true value of the parameter used in the closure test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' In  this sense, we expect the Gaussian process emulators used in Bayesian inference procedure of heavy ion data  to be robust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' On the other hand, we saw that optimizing the interpolation and statistical uncertainty of the  emulator can lead to considerably improved constraints on the model parameters at the same computational  cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' In our study, we found an optimal ratio of design points to TRENTo events per design point, Nd/Mev,  around 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='1–1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  The optimum Nd/Mev ≈ 1 is expected if the interpolation uncertainty in the emulator scales approximately  as 1/√Nd: that is, if both interpolation and statistical uncertainties scale the same, one should aim for a  roughly even number for Nd and Mev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Tests published in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' [17] found some evidence of 1/√Nd convergence  of observables in realistic models of heavy ion collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  To apply our work’s conclusions to heavy ion collisions, one must remember that there are different sources  of stochasticity in the collisions, only one of which was considered in this work: fluctuations in the initial  impact geometry of the nuclei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Fluctuations in the number of particles produced will also introduce statistical  uncertainty, which was not studied in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' It is common, though not universal, that the two statistical  uncertainties are reduced by oversampling the particles produced for each initial geometry of the collision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  The factor Mev in the ratio Nd/Mev ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='1–1 corresponds to the number of initial geometries samples, and  not the total number of oversamples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  Finally, we note that the choice of Mev might be guided by the need for accuracy for certain statistics-  hungry observables, rather than the benefits of the emulator as a whole [19, 20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' It will be useful to repeat  the current study with a broader range of observables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  10  VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  CONCLUSION  We studied the interplay between interpolation and statistical uncertainties for Bayesian parameter in-  ference using Gaussian process emulators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' We used the TRENTo model of initial conditions in heavy ion  collisions, with observables given by the event-averaged spatial anisotropies ⟨εn⟩ (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 2), which are analogous  to momentum anisotropy observables encountered in heavy ion collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Using Nd samples of the TRENTo  parameter space and Mev TRENTo events at each parameter point, we performed closure tests to determine  the impact of the emulator uncertainty on constraining model parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' We found that, for a budget of  Ntot total TRENTo events, the optimal number of design points was around Nd ≈ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='25–1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='0)√Ntot, which  corresponds to Nd/Mev ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='1–1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  We found this optimum by looking at multiple different metrics: the  maximum value and width of the marginalized posterior, the value of the posterior at the true value of the  parameter, and the Akaike Information Criterion (AIC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' We found the posterior at the truth to be very  effective at quantifying closure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  In view of our results, we believe it would be beneficial for Bayesian inference applications in heavy ion  physics to experiment with different ratios Nd/Mev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  Simulating large number of collision events, which  reduce all sources of stochastic uncertainties, can give access to statistics-hungry observables [19, 20];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' yet  using a large number Mev of events at each parameter sample will not provide significant benefits for the  large number of observables whose emulation is limited by interpolation uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' An improved balance  between interpolation and statistical uncertainties can help reduce the emulator’s uncertainty below current  experimental uncertainties, allowing us to make full use of heavy ion measurements from the RHIC and the  LHC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  ACKNOWLEDGEMENTS  The authors thank Simon Mak for insightful discussions, and Ron Solz and Matthew Luzum for valuable  feedback.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' thanks Duke University and Wayne State University for financial support.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='-  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' have been supported by the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Department of Energy Grant no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' DE-FG02-05ER41367 This research  used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User  Facility supported by the Office of Science of the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Department of Energy under Contract No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  DE-  AC02-05CH11231 using NERSC award NP-ERCAP0022230.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Calculations were also performed on the Duke  Compute Cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  [1] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Bass, “Microscopic reaction dynamics at SPS and RHIC,” Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' A, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 698, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 164–170, 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  [2] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Gale, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Jeon, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Schenke, “Hydrodynamic Modeling of Heavy-Ion Collisions,” Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' A,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 28, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 1340011, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  [3] U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Heinz and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Snellings, “Collective flow and viscosity in relativistic heavy-ion collisions,” Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  Part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 63, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 123–151, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  [4] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Derradi de Souza, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Koide, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Kodama, “Hydrodynamic Approaches in Relativistic Heavy Ion Reac-  tions,” Prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 86, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 35–85, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  [5] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Philipsen, “The QCD equation of state from the lattice,” Prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 70, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 55–107, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  [6] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Petersen, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Coleman-Smith, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Bass, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Wolpert, “Constraining the initial state granularity with  bulk observables in Au+Au collisions at √sNN = 200 GeV,” J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' G, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 38, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 045102, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  [7] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Novak, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Novak, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Pratt, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Vredevoogd, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Coleman-Smith, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Wolpert, “Determining Fundamental  Properties of Matter Created in Ultrarelativistic Heavy-Ion Collisions,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' C, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 89, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 3, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 034917,  2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  [8] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Sangaline and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Pratt, “Toward a deeper understanding of how experiments constrain the underlying physics  of heavy-ion collisions,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' C, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 93, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 2, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 024908, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  [9] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Pratt, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Sangaline, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Sorensen, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Wang, “Constraining the Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' of State of Super-Hadronic Matter from  Heavy-Ion Collisions,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 114, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 202301, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  [10] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Bernhard, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Marcy, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Coleman-Smith, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Huzurbazar, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Wolpert, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Bass, “Quantifying  properties of hot and dense QCD matter through systematic model-to-data comparison,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' C, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 91,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 5, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 054910, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  11  [11] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Bernhard, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Moreland, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Bass, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Liu, and U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Heinz, “Applying Bayesian parameter estimation  to relativistic heavy-ion collisions: simultaneous characterization of the initial state and quark-gluon plasma  medium,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' C, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 94, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 2, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 024907, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  [12] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Moreland, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Bernhard, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Bass, “Bayesian calibration of a hybrid nuclear collision model using  p-Pb and Pb-Pb data at energies available at the CERN Large Hadron Collider,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' C, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 101, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 2,  p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 024911, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  [13] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Bernhard, Bayesian parameter estimation for relativistic heavy-ion collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' PhD thesis, Duke U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=', 4 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  [14] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Bernhard, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Moreland, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Bass, “Bayesian estimation of the specific shear and bulk viscosity of  quark–gluon plasma,” Nature Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 15, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 11, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 1113–1117, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  [15] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Everett et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=', “Multisystem Bayesian constraints on the transport coefficients of QCD matter,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  C, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 103, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 5, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 054904, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  [16] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Nijs, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' van der Schee, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' G¨ursoy, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Snellings, “Transverse Momentum Differential Global Analysis of  Heavy-Ion Collisions,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 126, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 20, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 202301, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  [17] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Nijs, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' van der Schee, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' G¨ursoy, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Snellings, “Bayesian analysis of heavy ion collisions with the heavy  ion computational framework Trajectum,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' C, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 103, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 5, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 054909, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  [18] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Everett et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=', “Phenomenological constraints on the transport properties of QCD matter with data-driven  model averaging,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 126, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 24, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 242301, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  [19] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Parkkila, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Onnerstad, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Kim, “Bayesian estimation of the specific shear and bulk viscosity of the  quark-gluon plasma with additional flow harmonic observables,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' C, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 104, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 5, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 054904, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  [20] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Parkkila, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Onnerstad, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Taghavi, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Mordasini, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Bilandzic, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Virta, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Kim, “New  constraints for QCD matter from improved Bayesian parameter estimation in heavy-ion collisions at LHC,”  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' B, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 835, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 137485, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  [21] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Moreland, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Bernhard, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Bass, “Alternative ansatz to wounded nucleon and binary collision  scaling in high-energy nuclear collisions,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' C, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 92, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 1, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 011901, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  [22] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Luzum and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Petersen, “Initial State Fluctuations and Final State Correlations in Relativistic Heavy-Ion  Collisions,” J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' G, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 41, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 063102, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  [23] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Ollitrault, “Anisotropy as a signature of transverse collective flow,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' D, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 46, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 229–245,  1992.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  [24] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Miller and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Snellings, “Eccentricity fluctuations and its possible effect on elliptic flow measurements,” 12  2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  [25] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Alver et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=', “System size, energy, pseudorapidity, and centrality dependence of elliptic flow,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=',  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 98, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 242302, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  [26] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Alver and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Roland, “Collision geometry fluctuations and triangular flow in heavy-ion collisions,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  C, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 81, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 054905, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' [Erratum: Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='C 82, 039903 (2010)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  [27] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Gardim, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Grassi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Luzum, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Ollitrault, “Mapping the hydrodynamic response to the initial  geometry in heavy-ion collisions,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' C, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 85, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 024908, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  [28] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Williams and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Rasmussen, Gaussian processes for machine learning, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' MIT press Cambridge,  MA, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  [29] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Roberts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='com/j-f-paquet/bayesian_parameter_estimation_tutorial/blob/master/  parameter_space_sampling/param_sampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='ipynb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  [30] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Niederreiter, Random number generation and quasi-Monte Carlo methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' SIAM, 1992.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  [31] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Akaike, “A new look at the statistical model identification,” IEEE transactions on automatic control, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 19,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 716–723, 1974.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  [32] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Liddle, “Information criteria for astrophysical model selection,” Mon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Roy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 377,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' L74–L78, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  [33] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Liddle, “How many cosmological parameters,” Monthly Notices of the Royal Astronomical Society, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 351,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' L49–L53, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content='  [34] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Loeppky, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Sacks, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' Welch, “Choosing the sample size of a computer experiment: A practical  guide,” Technometrics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 51, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
+page_content=' 366–376, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/utE_T4oBgHgl3EQf-Rwc/content/2301.08385v1.pdf'}
diff --git a/v9AzT4oBgHgl3EQfsf3v/vector_store/index.faiss b/v9AzT4oBgHgl3EQfsf3v/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..24b0785aad3eec35f285143fe685ea4f85dca30f
--- /dev/null
+++ b/v9AzT4oBgHgl3EQfsf3v/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6f56b7adebe4ef1d3db8ede72d0a13fc52a8cef6deba4ded803428736420bba0
+size 5046317
diff --git a/vdFJT4oBgHgl3EQffCyN/content/tmp_files/load_file.txt b/vdFJT4oBgHgl3EQffCyN/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e9470be80897a8fab8a2a3065c1633a5383f2e69
--- /dev/null
+++ b/vdFJT4oBgHgl3EQffCyN/content/tmp_files/load_file.txt
@@ -0,0 +1,7016 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf,len=7015
+page_content='박 사 학 위 논 문  Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Dissertation  KSTAR 플라즈마 평형을 위한  베이즈 추론 신경망  Bayesian neural network for plasma equilibria  in the Korea Superconducting Tokamak Advanced Research  2022  정 세 민  (丁 世 敏 Joung, Semin)  한 국 과 학 기 술 원  Korea Advanced Institute of Science and Technology  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='11555v1  [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='plasm-ph]  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='27 Jan 2023  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='박 사 학 위 논 문  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='KSTAR 플라즈마 평형을 위한  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='베이즈 추론 신경망  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2022  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='정 세 민  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='한 국 과 학 기 술 원  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='원자력 및 양자공학과  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='KSTAR 플라즈마 평형을 위한  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='베이즈 추론 신경망  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='정 세 민  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='위 논문은 한국과학기술원 박사학위논문으로  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='학위논문 심사위원회의 심사를 통과하였음  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2022년 5월 31일  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='심사위원장  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='김 영 철  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='(인)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='심 사 위 원  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='김 현 석  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='(인)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='심 사 위 원  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='성 충 기  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='(인)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='심 사 위 원  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='윤 시 우  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='(인)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='심 사 위 원  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='최 원 호  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='(인)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='Bayesian neural network for plasma equilibria  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='in the Korea Superconducting Tokamak Advanced  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='Research  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='Semin Joung  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='Advisor: Young-chul Ghim  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='A dissertation submitted to the faculty of  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='Korea Advanced Institute of Science and Technology in  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='partial fulfillment of the requirements for the degree of  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='Doctor of Philosophy in Nuclear and Quantum Engineering  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='Daejeon,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Korea  May 31,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 2022  Approved by  Young-chul Ghim  Professor of Nuclear and Quantum Engineering  The study was conducted in accordance with Code of Research Ethics1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  1 Declaration of Ethical Conduct in Research: I, as a graduate student of Korea Advanced Institute of Science and  Technology, hereby declare that I have not committed any act that may damage the credibility of my research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  This  includes, but is not limited to, falsification, thesis written by someone else, distortion of research findings, and plagiarism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  I confirm that my thesis contains honest conclusions based on my own careful research under the guidance of my advisor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  DNQE  정세민.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' KSTAR 플라즈마 평형을 위한 베이즈 추론 신경망.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 원자  력 및 양자공학과 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 2022년.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 192+vi 쪽.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 지도교수: 김영철.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (영문  논문)  Semin Joung.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Bayesian neural network for plasma equilibria  in the Korea Superconducting Tokamak Advanced Research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Department of Nuclear and Quantum Engineering .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  192+vi pages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Advisor: Young-chul Ghim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (Text in English)  초 록  핵융합 플라즈마는 물리적으로 복잡한 시스템 중 하나이기에 핵융합로 제어를 위  하여 여러 물리 현상에 대한 추가적인 이론 정비가 지속적으로 요구된다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 따라서  여러 물리 현상에 대한 심층적인 이해가 없어도 장치 제어에 도움을 일조하는 딥  러닝 (심층 학습 기법) 이용은 과거 수십 년간 핵융합 플라즈마 분야에 큰 화두가  되어 왔었다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 그러나 다양한 딥러닝 기법들이 핵융합 플라즈마의 여러 분야에 연  구되어 왔지만 본질적인 물리 현상에 대한 심층적 이해의 부재로 과학적인 사용에  있어서 딥러닝 기법의 신뢰성 정량화가 지속적으로 요구되어 왔었다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 이러한 요  구들로 핵융합 플라즈마 분야에서 신뢰성 검증 가능하며 물리 이론까지 만족시킬  수 있는 딥러닝 개발이 새롭게 대두되었다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 우리는 본 논문에서 지배 방정식을  만족하며 관측된 물리 현상을 핵융합로 장치 제어 관련 정보로 변환시킬 수 있는  신경망 개발에 주안점을 둔다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 본 학위 논문에서는 토로이달 및 폴로이달 자기장  으로 핵융합 플라즈마를 가두는 핵융합로 실험 장치 중 하나인 토카막을 활용한다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  토카막은 플라즈마를 자기적으로 가두기에 플라즈마 압력과 자기장 및 플라즈마  전류로 인한 로렌츠 힘의 균형 유지가 필수이다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 플라즈마 평형은 바로 이 균형이  유지된 상태를 이야기하는 것으로 토카막 외부 자기장 코일 전류에 의해 제어되는  플라즈마의 형상과 위치를 제공한다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 다만 약 1 억 도의 초고온 환경인 플라즈마로  인하여 플라즈마 형상을 직접 진단할 수 없기에 간접 및 국소 측정 기기로 진단  된 플라즈마 물리 정보 활용으로 힘의 균형 및 맥스웰 방정식을 따르는 플라즈마  형상을 간접적으로 재구성한다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 이 재구성에 사용되는 식이 바로 힘의 균형과 맥  스웰 방정식으로부터 유도된 Grad-Shafranov (GS) 식이다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 이 식은 2 차원 2 계  비선형 미분 방정식으로 수치 해석이 반드시 요구되며 수치적인 수렴을 위해 진단  데이터의 취사 선택과 같은 인간의 선택이 종종 요구된다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 또한 수치 해석의 반복  계산으로 인한 근본적인 계산 시간 한계로 실시간 토카막 운전에 활용되기 위해  서는 정확도의 희생 등을 필요로 한다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 과거에 실시간 계산 한계 극복으로 인해  개발된 지도 학습 기반 신경망이 과거 제시 되었지만 결과적으로 인간의 선택을  바탕으로 한 결과로 훈련된 신경망이란 사실에는 변함이 없었다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 그러므로 이 논  문은 신경망을 기반으로 하되 기존 수치 해석과 독립적이며 물리 이론을 스스로  만족함과 동시에 신뢰성의 정량화가 가능한 플라즈마 형상 재구성 방법을 제안  한다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 즉 신경망을 통해 GS 식의 해를 직접 구하며 베이즈 추론 신경망을 통해  재구성된 플라즈마 평형의 신뢰성을 평가한다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 또한 자유 경계 문제 중 하나인  GS 식 해의 탐색을 위해 경계 추적이 가능한 보조 모듈을 고안하였다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 나아가  베이지안 추론과 가우시안 프로세스 및 기계 학습을 기반으로 하는 진단된 자기장  신호의 표류 현상, 신호 간의 비 일관성, 진단 신호 손실을 해결하는 방법을 소개하  여 어떠한 운전 환경에서도 우리의 신경망이 사용될 수 있음을 입증한다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 그리고  신경망 훈련이 GS 식에 기반할 수 있는지를 검증하기 위해 기존 수치 해석의 데이  터 및 GS 식을 신경망의 비용 함수로써 사용한 결과를 소개한다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 추가로 우리는  이 학위 논문에 활용된 원리 및 방법이 여러 딥러닝이 활용될 법한 전통적인 과학  분야에 충분히 응용될 수 있음을 밝힌다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 그리하여 단순한 딥러닝 사용을 벗어나  여러 공학 및 물리 분야에 물리적 신뢰성을 획득한 신경망 사용 방안을 제안할 수  있을 것이라고 우리는 희망한다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  핵 심 낱 말 케이스타, 플라즈마 평형 재구성, EFIT, 자기 진단법, 톰슨 산란 진단,  전하 교환 분광계, 가우시안 프로세스, 베이지안 추론, 베이즈 추론 신경망, 비지도  학습  Abstract  Fusion-graded plasmas are one of the physically complex systems, resulting in  continuous establishment of plasma theories for unclarified physical phenomena  in order to thoroughly control nuclear fusion reactors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Deep learning has drawn  vast attention to this field of controlled fusion plasma to link physical phenom-  ena with control-relevant parameters without a deepened understanding about  plasma theories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Albeit, quantifying the uncertainty of deep learning models has  been constantly requested due to their fundamental shortage of physical under-  standing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, a concept of a reliable deep learning model to be able to present  their probability distributions is raised as well as a method to inculcate physical  theories in the model is also concerned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' These are the main concept focused in  this thesis with a tokamak experiment, one of the nuclear fusion experiments by  confining the plasmas via toroidal and poloidal magnetic fields in a torus shape  device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Since the tokamak confines a plasma magnetically, balancing the Lorentz  force due to the magnetic field with the plasma pressure is crucial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This bal-  anced state with equilibrium assumption is called plasma equilibrium, giving us  the shape and location of the plasma determined and controlled by the exter-  nal coil currents of the tokamak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' However, this plasma shape cannot be directly  measured due to the harsh environment caused by the plasma itself of 100 million  degrees Celsius, thus the shape is indirectly reconstructed from the force balance  and Maxwell’s equations consistent with externally and locally measured plasma  information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The Grad-Shafranov (GS) equation derived from those equations is  used to reconstruct the plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This equation is a two-dimensional second-order  differential equation, inherently requiring numerical analysis so that human de-  cisions such as selecting some of the measured signals arbitrarily for numerical  convergence are followed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Furthermore, it is likely to sacrifice accuracy of solu-  tions of the equation for real-time tokamak controls due to multiple iterations  in numerical analysis which requires intensive computations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Although there  were neural network based real-time approaches via supervised learning with  databases from numerical algorithms, they were inevitably under the influence  of human decisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Hence, this thesis suggests a reconstruction method based  on deep neural networks which are able to not only estimate their uncertainties  but also learn the governing equation themselves without depending on previous  numerical algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Namely, our neural networks solve the GS equation via  a unsupervised learning algorithm and show probability distributions of their  solutions based on Bayesian neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Since solving the GS equation is  a free-boundary problem, our networks are supported by an auxiliary module  that detects the plasma boundary from the network outputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Furthermore, we  introduce preprocessing methods for the network inputs to address the magnetic  signal drift, the flux loop inconsistency and the magnetic signal impairment based  on Bayesian inference, Gaussian processes and neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' These methods  are developed to guarantee the use of the networks in any circumstance of the  tokamak experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In addition, we also prove that the Grad-Shafranov equa-  tion can be used as a cost function of the networks with a given equilibrium  database.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The principles and methods applied here are not only acceptable for  fusion research but also applicable to various engineering and scientific fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Thus, we expect that our proposal which fulfills physical reliability for the use  of deep learning deserves further studies for various complex physics systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Keywords KSTAR, Grad-Shafranov equation, EFIT, Magnetic diagnostics, Thom-  son scattering system, Charge exchange spectroscopy, Gaussian processes, Bayesian  inference, Bayesian neural networks, Unsupervised learning  Contents  Contents  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  i  List of Tables  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  v  List of Figures  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  vi  Chapter 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Preface: what would we do with a Black  Box for fusion research?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  1  Chapter 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Nuclear Fusion  7  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  Tokamak .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  11  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  Equilibrium .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  13  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  Biot-Savart Law .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  15  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3  Plasma diagnostics .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  18  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  Magnetic diagnostics .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  19  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  Pressure measurements .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  20  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4  Deep learning for tokamak equilibrium .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  22  Chapter 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Deep learning and Bayesian Inference  23  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  Feedforward Neural Network .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  24  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  Bayesian Inference  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  27  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  Sine function Regression: Part 1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  29  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3  Sine function Regression: Part 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  31  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  Advanced topic: GAN .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  33  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3  Outlook  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  40  i  CONTENTS  Chapter 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Bayesian neural network in fusion re-  search  42  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  Article I: Signal drift correction .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  43  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  Introduction  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  45  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  Real-time drift correction based on  Bayesian inference .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  47  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3  Two-step drift correction method .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  47  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4  Results with KSTAR experimental  data .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  53  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  Discussions .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  61  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6  Conclusions .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  64  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  Article II: Imputation .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  65  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  Introduction  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  66  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  Imputation Scheme: Based on Bayes’  model .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  67  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3  Based on Gaussian Process  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  70  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4  Based on Bayes’ model coupled with  Gaussian Process  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  73  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  Discussion and Conclusion .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  76  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3  Article III: Preprocessing flux loop .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  78  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  Introduction  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  79  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  Magnetic data collection .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  80  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3  Domain knowledge regarding the poloidal  magnetic field  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  80  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4  Modelling the network architecture  82  ii  CONTENTS  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  Recovering flux loop consistency via  the deep neural network .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  84  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6  Quantitative assessment of the net-  work .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  85  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='7  Equilibrium reconstruction using the  network magnetic flux  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  86  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='8  Discussion  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  87  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4  Article IV: Preliminary result under super-  vised learning .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  89  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  Introduction  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  90  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  Collection and real-time preprocess-  ing of data  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  94  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3  Neural network model and training  97  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4  Performance of the developed neural  networks: Benchmark tests  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  101  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  Discussions and Conclusions .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  116  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  Article V: Plasma reconstruction via unsu-  pervised learning .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  119  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  Introduction  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  120  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  Modelling Grad-Shafranov Deep Neu-  ral Networks .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  122  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3  Statistical analysis of GS-DeepNet train-  ing .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  129  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4  Physical knowledge learned by GS-  DeepNet  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  132  iii  CONTENTS  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  Final performance of GS-DeepNet with  the kinetic constraints  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  135  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6  Materials and Methods .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  137  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='7  Discussion  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  142  Chapter 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Conclusions  144  Chapter A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Bayesian Deep Learning: Model uncer-  tainty  147  Chapter B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Neural Network Differentiation  152  Bibliography  159  Acknowledgments in Korean  188  Curriculum Vitae  190  iv  List of Tables  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  Designed ranges of major paramters of KSTAR [1] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  12  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  Summary of the data samples to train and validate the networks .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  95  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  The imputation results shown in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='32 with KSTAR shot  #20341 at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1 sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 114  v  List of Figures  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  Sine function regressions .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  Fusion reaction rates .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  8  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  Lawson criterion  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  10  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3  Tokamak configuration .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  11  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4  Circular wire  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  16  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  Magnetic diagnostics .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  19  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6  KSTAR TS and CES systems .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  20  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  Simple neural network  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  25  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  Learning curve  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  26  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3  Bayesian neural network regressions .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  30  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4  Bayesian neural network differentiation .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  32  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  GAN architecture .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  33  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6  GAN results .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  40  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  Configuration of magnetic diagnostics on a poloidal cross-section  of KSTAR at a certain toroidal position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Blue dots show the posi-  tions of both MPn and MPt, and red open circles for the positions  of the FLs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The black thick line shows the first wall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Note that we  only show five FL sensor numbers out of 45 of them for simplicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  44  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  An example of temporal evolutions of (a) currents in the PF coils,  (b) normal and (c) tangential components of magnetic fields mea-  sured by an MPn and an MPt, respectively, and (d) magnetic flux  measured by an FL during the initial magnetization stage, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=',  t < 0, for a typical KSTAR discharge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Information from the time  interval d1 (d2) is used to estimate am  i (bm  i ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  46  vi  LIST OF FIGURES  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3  Examples of the proposed two-step drift correction method for  the MDs of (a) MPn #6, (b) MPt #27 and (c) FL #45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Left  and middle panels show the posteriors of the slope and the offset  for each MD where the red dots depict the maximum a posterior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Right panel shows both the original magnetic signals with the  signal drifts (red) and the drift corrected signals (blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  48  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4  Histograms of the validation errors for randomly selected 297 KSTAR  discharges before (left panel) and after (right panel) the two-step  drift correction for (a) m =MPn measuring Bn, (b) m =MPt mea-  suring Bt, and (c) m =FL measuring magnetic fluxes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' MD # in  horizontal axes denote the MD sensor numbers, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', subscript i in  ϵm  i,s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Colors represent the relative occurrence normalized to a unity  for every sensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Non-existing magnetic signals are displayed as  white streaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  49  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  Averaged validation errors ⟨ϵm  i ⟩ for 297 KSTAR discharges for (a)  the normal (MPn) and (b) the tangential (MPt) components of  magnetic signals, and for (c) the flux loop (FL) measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Blue circles indicate the validation errors after the two-step drift  correction method, and red crosses mean the validation errors be-  fore applying our correction method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  50  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6  Qualitative comparisons between a typical chi-square linear fitting  method (blue line) and our proposed two-step method (red line)  with the raw (before correction) signal (green line) in (a) KSTAR  shot #17016 and (b) #9387 for the tangential component of mag-  netic signal MPt #14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (c) and (d) show temporal evolutions of  currents through KSTAR PF coils, and vertical dotted lines indi-  cate the time where we expect all the magnetic signals return to  zeros if there were no signal drifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Note that the blue line in (b)  is almost overlapped with the red line, but it is slightly more off  from the zero compared to the red line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  53  vii  LIST OF FIGURES  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='7  Histograms of the degree of corrections (DoC’s), where signal drift  corrections are performed based on a typical chi-square linear fit-  ting method (left panel) and our proposed two-step drift correction  method (right panel) for (a) MPn measuring Bn, (b) MPt measur-  ing Bt, and (c) FL measuring magnetic fluxes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' MD # in horizontal  axes denote the MD sensor numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Colors represent the relative  occurrence normalized to a unity for every sensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Same sets of  magnetic signals used to generate Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4 are used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Non-existing  magnetic signals are displayed as white streaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  54  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='8  Averaged validation errors as in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5 before (red crosses) and  after the correction (blue circle) for (a) the normal component  (MPn) and (b) the tangential component (MPt) of magnetic sig-  nals and for (c) flux loop measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Left panels show the re-  sults for the 286 short pulse discharges (< 40 sec), while the right  panels show the results for the 11 long pulse discharges (> 40 sec).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Note the different scales for y-axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  56  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9  Temporal evolutions of the magnetic signals measured by MPn  #07 (blue) and MPn #36 (red) for (a) KSTAR shot #16051 (ab-  normal MPn #36) and (b) #16447 (normal MPn #36).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' These two  magnetic sensors are located at the up-down symmetric positions  as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1, and the discrepancy between MPn #07 and  #36 in (a) are too large compared to (b) to be explained by the  slight up-down asymmetry of the KSTAR plasmas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Vertical dot-  ted lines indicate where all the currents through the PF coils are  returned to zeros.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  57  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='10 Temporal evolutions of the magnetic signals measured by (a) FL  #25 (KSTAR shot #14262), (b) FL #27 (KSTAR shot #17320)  and (c) FL #35 (KSTAR shot #16369).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' These signals are basi-  cally noises (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3(c) as an example of working FL signal).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Vertical dotted lines indicate where all the currents through the  PF coils are returned to zeros.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  58  viii  LIST OF FIGURES  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='11 Temporal evolutions of the magnetic signals measured by (a) FL  #01 (KSTAR shot #17321), (b) FL #23 (KSTAR shot #13366)  and (c) FL #34 (KSTAR shot #17039).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Blue (green) line is the  signal after (before) the correction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Vertical dotted lines indicate  where all the currents through the PF coils are returned to zeros.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  60  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='12 Schematics of (a) the Amperian loop (blue line connecting blue  dots) for ∇ × ⃗B = µ0 ⃗J and (b) the pancake-shaped Gaussian  surface with three surfaces s1, s2 and s3 for ∇ · ⃗B = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Blue dots  with the numbers in (a) indicate the magnetic probes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' [2] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  67  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='13 Log-posterior, ln[p(B∗  ⊕|B⊕, Ω⊕)], of the missing magnetic signals  inferred by the Bayes’ model with the Maxwell’s equations, when  two tangential components (Bt from MPs #15 and #16) of the  magnetic signals are missing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thick black line marks where the  posterior is maximum indicating that infinite number of solutions  are possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Data are inferred for KSTAR shot #9010 at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1 sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  68  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='14 Successful GP predictions (red crosses) compared with the actual  data (blue circles) for (a) Bt and (b) Bn at 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='70 sec of KSTAR  shot #9010 where we remove nine non-consecutive signals (indi-  cated by red arrows) simultaneously to examine the proposed GP  imputation scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' On the other hand, if the magnetic signals  are spatially varying fast such as (c) Bt of MPs #15 and #16 and  (d) Bn of MPs #17 and #18 at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='10 sec of the same shot, the GP  imputation scheme fails to infer the correct values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  71  ix  LIST OF FIGURES  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='15 (a) Bt from MPs #15 and #16 and (b) Bn from MPs #17 and #18  from KSTAR shot #9010 at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1 sec as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='14(c) and  (d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Green triangles obtained by the Bayes’ mode with the GP  match the measured values (blue circles) well, while the GP-only  method (red crosses) fails to do so as has been discussed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Comparisons of temporal evolutions for (c) Bt from MP  #15 and (d) Bn from MP #17 from KSTAR shot #9427 where  blue line is the measured values, red line for the GP-only and green  line for the Baye’s model with the GP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Green lines agree well with  blue lines well throughout the whole discharge including ramp-up  and ramp-down phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  73  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='16 Schematic diagram of FL recovery via a deep neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (A)  The positions of magnetic measurements on the KSTAR poloidal  cross-section where both Bn and Bt exist (blue dots), only Bn  exists (pink dot), only Bt exists (green dots), and FLs exist (red  crosses).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (B) Schematics of the deep neural network whose output  stands for the flux function converted into BR and BZ through  analytic differentiation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  (C) Temporal evolution of the plasma  current for KSTAR 24445 shot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (D–G) The network results (blue  area) at the red dotted lines in (C) are presented compared with  the measured signals (red dots).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' First row is for BR, second row  is for BZ, and the last row is for FL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  81  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='17 Statistical analysis of the trained network with test dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (A)  Statistics of the coefficient of determination between the measured  and the network BR (left) and BZ (right) from the ramp-up phase,  and (B) from the flat-top phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (C) Distributions of the plasma  current measured from the Rogowski coil (purple line) and the  network (purple area) of the ramp-up phase (top) and the flat-top  phase (bottom).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (D) Using 24445 shot, Statistics on the difference  between the measured ψ and the network ψa  rel of the ramp-up  phase (blue) and the flat-top phase (red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  82  x  LIST OF FIGURES  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='18 Comparison of equilibrium reconstructions based on the network  (black), the expert (green) and the novice (orange).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  (A) Left:  comparison of the equilibrium results at 498.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5 msec of 24445 shot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Right: a novice producing equilibrium overlaid with the plasma  boundaries from the network and the expert (dotted lines).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (B)  Spatial profiles of the plasma current density at Z=0 location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  (C) Chi-square results of the ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (D-F) Same results with (A-C)  at 2704.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3 msec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  84  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='19 A poloidal cross-section of KSTAR with the first wall (blue dotted  line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Green dotted line indicates a Rogowski coil measuring the  plasma current (Ip).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Green open circles and crosses depict loca-  tions of the magnetic pick-up coils measuring 32 normal (Bn) and  36 tangential (Bt) magnetic fields, respectively, whereas green tri-  angles represent 22 flux loops measuring poloidal magnetic fluxes  (ΨFL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Black asterisks (22 × 13 spatial positions) show locations  where we obtain the values of ψ from the off-line EFIT results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  91  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='20 Before (blue) and after (red) the magnetic signal adjustments for  (a) normal and (b) tangential components of magnetic fields mea-  sured by the magnetic pick-up coils, and (c) poloidal magnetic  flux measured by one of the flux loops.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The signals return closer  to zeros after the adjustment when all the external magnetic coils  (except the toroidal field coils) are turned off at around 30 sec in  this KSTAR discharge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  93  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='21 An example of the two networks’ results trained with the cost func-  tion (a) ϵ and (b) ϵnew for KSTAR shot# 17939 at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='950 sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Both  networks (red dashed line) reproduce the ψTarget (black line) well  (left panels), but only the network trained with ϵnew reproduces  ∆∗ψTarget (right panels).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  97  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='22 The descending feature of training (blue line) and validation (red  dashed line) errors as a function of iterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Shaded areas rep-  resent standard deviation of the errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  99  xi  LIST OF FIGURES  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='23 Performance tests of the NN2017,2018 network on the unseen KSTAR  discharges from (a)(b) 2017 campaign and (c)(d) 2018 campaign.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The values of R2 and histograms of (a)(c) ψNN vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' ψTarget and  (b)(d) ∆∗ψNN vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' ∆∗ψTarget with colors representing number of  counts manifest goodness of the NN2017,2018 network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Red dashed  line is the y = x line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 101  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='24 The actual reconstruction results for the KSTAR shot#18057,  comparing the network results and off-line EFIT reconstructions  for ramp-up ((b) and (c)), flat-top ((d) and (e)), ramp-down ((f)  and (g)) phases following (a) the plasma current evolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Black  lines indicate the flux surfaces from the off-line EFIT, overlaid  with the red dotted lines which stand for the NN reconstructions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  As a figure of merit, magnitudes of PSNR metric are written on  each figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 102  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='25 Same as Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='23 for the the NN2017 network, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', trained with  the data sets from 2017 campaign.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 103  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='26 Same as Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='23 for the the NN2018 network, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', trained with  the data sets from 2018 campaign.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 104  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='27 Histograms of MSSIM (left panel) and PSNR (right panel) for (a)  NN2017, (b) NN2018 and (c) NN2017,2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Red (green) line indicates  the test results on the data sets from 2017 (2018) campaign.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In  each sub-figure, top (bottom) panel show the results for ψ (∆∗ψ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The off-line EFIT results are used as reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 106  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='28 An example of reconstructed ψ (R, Z) (left panel) and ∆∗ψ (R, Z)  (right panel) for KSTAR shot #17975 at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='7 sec comparing (a) rt-  EFIT (green) and off-line EFIT (black) and (b) nn-EFIT (NN2017,2018)  (red) and off-line EFIT (black).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 108  xii  LIST OF FIGURES  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='29 Histograms of MSSIM (left panel) and PSNR (right panel) of ψ  (top) and ∆∗ψ (bottom) calculated by the nn-EFIT (black) and  the rt-EFIT (green), where the nn-EFIT is the NN2017,2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' For  both the nn-EFIT and the rt-EFIT, the off-line EFIT is treated  as reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 109  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='30 Same as Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='29 with the NN2017 as the nn-EFIT where the  test data sets are obtained from (a) 2017 campaign and (b) 2018  campaign.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 110  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='31 Same as Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='29 with the NN2018 as the nn-EFIT where the  test data sets are obtained from (a) 2017 campaign and (b) 2018  campaign.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 111  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='32 Measured (blue open circles) and inferred with the imputation  method [3] (red crosses with their uncertainties) values for (a)  Bn and (b) Bt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Probe # on the horizontal axis is used as an  identification index of magnetic pick-up coils.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Inferred probes are  Probe #3, 4, 6, 14, 18, 24, 30, 35, 37 for Bn and Probe #4, 6, 8,  11, 17, 29, 30, 32, 35 for Bt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 112  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='33 Top panel: nn-EFIT (NN2017,2018 network) reconstructed equilibria  without any missing values (black line), and with two missing val-  ues replaced with the inferred values using the imputation method  (green line) or with the zeros using the zero-padding method (pink  dashed line), where the missing values are (a) Bn Probe #14 and  30 (left panel) and (b) Bt Probe #4 and 8 (right panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bottom  panels: histograms of MSSIM and PSNR using the imputation  method (green) and the zero-padding method (pink) for all the  equilibria obtained from KSTAR shot #20341, where the refer-  ence values are those obtained using nn-EFIT without any missing  values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Note that there are many more counts less than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9 for  MSSIM with the zero-padding method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 113  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='34 Same color code as in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Missing values are (a) eight Bt  (except only Probe #6) and (b) all nine Bt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 115  xiii  LIST OF FIGURES  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='35 Same color code as in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Missing values are (a) eight Bn  (except only Probe #37), (b) all nine Bn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 116  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='36 Same color code as in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Combinations of missing Bn  and Bt are examined: (a) four missing Bn and four mssing Bt case  and (b) nine missing Bn and nine missing Bt case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 117  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='37 Self-teaching unsupervised learning scheme in GS-DeepNet .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 123  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='38 Statistical evaluation of GS-DeepNet training  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 128  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='39 Equilibrium knowledge learned by GS-DeepNet  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 131  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='40 Performance of GS-DeepNet with local pressure constraints .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 132  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1 Simple neural network 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 153  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2 Simple neural network 3 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 156  xiv  Chapter 1  Preface: what would we do with  a Black Box for fusion research?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  “No one has ever proved that EL DORADO or  SKYPIEA doesn’t exist!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' !”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', “Well, Let them laugh!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  That’s what makes it A GREAT ADVENTURE!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' !”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  — Oda Eiichiro,  ONE PIECE  When I started studying nuclear fusion and deep learning for the first time, I  was totally absorbed in two tasks: (1) surveying the whole history of Neural  Network used in the field of nuclear fusion;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (2) neural network regressions for  sine functions with various signal-to-noise ratios (SNRs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' When it comes to the  usage of neural networks, in brief, there were two major pedigrees such that one  wished to control tokamaks accurately via neural networks, and the others tried  to make neural networks predict tokamak disruptions (violent events undoubtedly  forcibly terminating tokamak operations).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Starting with an idea of real-time prediction of plasma positions [4], mapping  measurement signals of the plasma to the positions of that was extensively studied  by Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' [5–11] in the 1990s as well as a review article introducing the studies to  readers with no previous knowledge of the network [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Yet there had been  no significant change in this research field [13] until advanced neural network  techniques (deep learning) contributed to the field again [14–16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Regarding  the disruption prediction, in 1994, there was a master’s thesis [17] trying to  predict disruptions in a tokamak plasma (probably for the first time) by using  a neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Afterward, this disruption prediction field has grown rapidly  1  CHAPTER 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Preface: what would we do with a Black Box for fusion research?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  over decades, being able to predict multi-tokamak disruptions based on a single  neural network [18,19] by taking advantage of previous researches that focused  on disruptions occurring in a single fusion device [20, 21] as a cornerstone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Of  course, there is other genealogy of the neural network in fusion community which  dealt with tokamak transport [22–28], but I would like to spare the details of it  since I believe that two main start points of the history of the neural network in  fusion research are definitely tokamak control and disruption prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  In short, the neural networks have been simply used to connect control-  relevant parameters of the plasma generated from plasma equilibrium (a force-  balanced state of the plasma) with given diagnostic signals as a viewpoint of  tokamak control as well as they have been used to let a tokamak discharge be on  a disruption alert by looking at tokamak measurements in real time in case that  a disruption is about to occur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' However, in either case, all the neural network  did was merely to link given inputs to certain plasma physically meaningful  parameters without understanding any physics behind.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' If the neural network  doesn’t know physics, how can it be used in the physics field?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, the idea  that I have always had in my mind after finding these results is that the neural  network just acts as a “good but not great” supporting actor in nuclear fusion  since the network seems to be such a magical tool that maps any inputs to any  outputs, which does not require enough physics interpretation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, I thought  “Isn’t that a limitation of the neural network for nuclear fusion research (but also  other scientific fields) because its working principle might be hard to be trusted  (or scrutable)?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The ability of the neural network is actually impressive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The neural network  has the ability to extract relations between two (or more) phenomena in terms  of basic arithmetic operations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' As well as two dimensional data regression in  multidimensional space [29–31], deep learning is powerful to handle image pro-  cessing [32,33], which is far beyond human abilities, and able to perform natural  language understanding [34], video processing [35] and language generation [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  These applications show that deep learning is (nearly) close to human level in  various fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  2  CHAPTER 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Preface: what would we do with a Black Box for fusion research?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1: The network regression results compared to the sine functions  with various noise levels, σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The blue, the orange dots, the red lines and the  black lines are the training, the validation sets, the network results and the  noise-free sine functions, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  This remarkable strength of deep learning can be found even with a simple  regression analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' I would like to discuss sine function regressions here which  I started figuring out when I studied neural networks for the first time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Figure  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1 shows the results of neural networks trained with data points generated from  sine functions, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=',  t(x) = sin 6πx + ϵ  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1)  where t is the observed data and ϵ stands for the level of Gaussian noise, ϵ =  N(µ, σ2), whose mean value µ is zero, and standard deviation σ is set arbitrar-  3  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='05  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  =3CHAPTER 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Preface: what would we do with a Black Box for fusion research?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  ily.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' To train the networks, I divide the dataset into training (blue dots) and  validation data (orange dots) which are used to train and validate the networks  during the training procedure, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The black line is the noise-free sine  function, and the red line is the network results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The data points are prepared  within the interval of 0 – 1 along the x-axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' From top to bottom of Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1,  with one significant figure, the standard deviation σ are 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='05, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5 and 3 where  the SNRs are approximately 200, 2 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='05 (20, 3 and -10 in decibel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The de-  tailed explanation about the network training will be discussed in the following  chapters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  As shown in the figure, the first two plots have the relatively less noisy  observed data which is straightforward to be identified as sinusoidal functions  even with our bare eyes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, it is quite acceptable that the networks seem to  be the sine functions since they are matched well with our intuition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' However,  let us take a look at the last figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Could anyone find any features of the sine  function from the blue (and orange) dots with the naked eye only?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' I swear that  no one can do that.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' It means that even if the networks tell us the blue dots are  possibly produced from a sinusoidal function, because our intuition (we indeed  have our intuition in this case although the intuition is not proper anymore)  refuses to accept the argument provided by the network since it is difficult to  determine that the network fits to our intuition or not, therefore we cannot  believe and trust what the network insists on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The result above is quite surprising since the network actually “did not  know” what the observed data is made from, but “infer” the sine function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This  process is seemingly “magical” like a black box to those who were not involved  in the process of generation of the training data, which could be the fact that  makes us doubt the network’s capabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In other words, I would like to argue  that the sine function can be regarded as physical parameters of interest, and  similarly the intuition can turn out to be physical theories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Namely, although  the neural network is able to generate physically reliable outputs, we would not  depend on the results since we can think the network never fully follows laws of  physics of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4  CHAPTER 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Preface: what would we do with a Black Box for fusion research?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Then how can the neural network be counted on for scientific uses (or nuclear  fusion research)?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' To answer this question, I shall start from defining uncertainty  in deep learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' First of all, there are situations such that observed (or collected)  data is too noisy or too sparse to sufficiently cover possible phenomena, which  leads to the first type of uncertainty, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', aleatoric uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This is yielded by  the poor quality of observed (or collected) data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The other type of uncertainty  is caused by a network model itself such that the model is not as complex as  collected data, or free-parameters of the model is poorly determined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1 These yield  epistemic uncertainty (also referred to as model uncertainty).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Both uncertainties  result in predictive uncertainty which quantifies how the network is sure about  its prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Perhaps, if we have a lot of data which can sufficiently cover all possible  physical phenomena, then we can possibly give credence to whatever a neural  network outputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This is unfortunately almost impossible, and does not always  guarantee that the neural network follows physics theories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Then, what if we  train a neural network with physics theories?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Does this way quantify (or reduce)  the network’s epistemic uncertainty (knowledge uncertainty) related to the “the-  ories”?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' As a result, does this mean the network truly follows the theories and  shows how it is confident with respect to given inputs (and given theories)?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In  particular, unlike the past “magic” approaches, can’t that lead us to trust the  neural network a little more (or further)?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Answers to these questions are the  main gist of this thesis, which will be provided in the following chapters from the  perspective of tokamak control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  With the Korea Superconducting Tokamak Advanced Research (KSTAR),  Article IV has been developed to show that a neural network can learn a plasma  ‘theory’ with the support of a database prepared from a numerical algorithm by  1The etymology of the word aleatoric is the Latin “aleator”, or “dice player”, meaning that  aleatoric uncertainty is the “dice player’s uncertainty”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The etymology of the word epistemic is  the Greek “episteme” known as “knowledge”, meaning that epistemic uncertainty is “knowledge  uncertainty”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Epistemic uncertainty can be often reducible through having more knowledge,  while aleatoric uncertainty sometimes cannot be reduced due to the measurement noise or the  inherent stochasticity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  5  CHAPTER 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Preface: what would we do with a Black Box for fusion research?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  reconstructing plasma equilibria based on the Grad-Shafranov (GS) equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  This is a preliminary application for the network to provide the possibility of a  complete unsupervised learning for the reconstruction such that the neural net-  work can understand the GS equation itself, and the database from the numerical  algorithm is no longer required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This is described in Article V, providing how  a principle of the unsupervised learning works, and why this kind of network  is required for tokamak control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Article I, Article II and Article III have been  developed to preprocess KSTAR measurements used to inputs of our networks  since baseline increases of measured signals in time (signal drift), missing signals  due to mechanical issues and inconsistency between signals should be handled  to use our networks in any experimental circumstances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' From Bayesian neural  networks, our applications are able to quantify the epistemic uncertainty related  to the plasma theory by obtaining inference results of the GS equation as well  as plasma information such as positions and locations of the plasmas (which are  hard to be measured directly) in the KSTAR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' One can find the detailed funda-  mentals and analyses in the next chapters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  I have recognized that the neural network is treated as a black box, in-  scrutable as well as unbelievable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' How can this prejudice be resolved?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Let me  leave this here: solving differential equations numerically also faced a tough  proof back then around 1950.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' I would say, we are simply taking a look at a novel  method whose detail is not fully figured out yet, and I hope this thesis corrobo-  rates it is fine to use a neural network in nuclear fusion research, including the  controls of the tokamak plasmas in real time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  6  Chapter 2  Nuclear Fusion  나가와 도깨비, 인간, 레콘이 살고 있는 집에서  누군가가 바닥에 바늘을 떨어뜨렸다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 잘 보이지 않는  바늘을 찾아내는 방법은?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  답 : 도깨비가 바늘이 뜨거워질 정도의 도깨비불을  퍼뜨리고 나가가 뜨겁게 달아오른 바늘을 눈으로  확인하여 집어 올린다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 그리고 인간은 온 힘을 다해  레콘을 말려야 한다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 설득력이 충분하다면 레콘이  집을 들어 흔드는 것은 막을 수 있을 것이다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  — 이영도,  피를 마시는 새  What is nuclear fusion?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  It is the morning and the evening star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  I slightly  transform a Sinclair Lewis (Harry Sinclair Lewis, February 7, 1885 – January  10, 1951) quote to start explaining what nuclear fusion is in the less heavy mood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The energy from the nucleus can be obtained by combining light nuclei into  heavier ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This is called nuclear fusion energy [37], which is a foundation of  energy generated from the Sun and stars in outer space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Before deepening our  sight about nuclear fusion, let me consider three very different time scales which  are involved in climate change or energy sources if one considers either of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The first view is a few months – a few years scale that is a short time scale to  be required to take temporary solutions such as making an agreement like the  Kyoto Protocol, issuing carbon credits, limiting the speed limit of automobiles,  offering tax credits for renewable energy plants, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' As a relatively longer time  scale, 10 – 50 years, we can use this to take such solutions like developing new  clean (or carbon-free) energy sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The last perspective about the time scales  7  CHAPTER 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1: Fusion reaction rates of deuterium and tritium (D-T) and  deuterium and deuterium (D-D) with some well-known cross sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The D-T  fusion reaction rate is remarkably higher than the other reaction rates at the  temperature of the order of 10–100 keV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  is the longest time scale, 100 – 5000 years, which is the faraway future, so we  barely know what will happen in the future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The problem is we are already  facing global warming and sea level rise as well as rising fuel prices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' A more  vicious truth is that we do not have much time to prepare them and, especially,  the intermediate time scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (I largely take this information from Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' [38]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  In these circumstances, nuclear fusion is a solution as a clean energy source  which has ideally no blemish to be worried about generating any carbon-like  byproducts and a vast resource of fusion fuels available from the sea.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Although  fusion power will take time (and money also) to be realized, however, we are  living in the land and era of taking photos of Pluto, trying to reuse space rockets  8  T /million K  15  150  1500  0009  10-14  D-T  D-D  D _3 He  p-11 B  10~15  T-T  T _3 He  3He 3 He  10-16  10-17  (n0)  10-18  10~19  10~20  10  100  1000  T /keVCHAPTER 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion  and build AI technology in our daily life, thus, they can be affordable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Over  decades, we have been trying to build nuclear fusion power plants which are able  to contain and sustain fusion reactions occurring only in really extreme conditions  on Earth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The sequence of the fusion reaction of interest is following: two small  nuclei are given enough kinetic energy to pass over a potential (Coulomb) barrier  due to their charges, then they fuse together and are transformed into another  nuclei, and then they produce large energy which is often called fusion energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  We often tap deuterium and tritium as the two nuclei since their reaction rate is  extraordinarily superior to the other famous reaction rates shown in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1,  which is  2  1D + 3  1T −→ 4  2He (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5 MeV) + 1  0n (14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1 MeV)  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1)  where the goal to crash through the Coulomb barrier is to heat them up to the  temperature of the order of 10 keV (≈ 108 K), which makes the deuterium and  the tritium to become plasma, the fourth state of matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In this state, the  dynamics of the plasma is governed by a collective behaviour and sensitive to  externally applied electromagnetic fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Sensitivity to external fields can be  interpreted as a way to control the plasma through the fields, allowing us to have  a fusion reactor confining the plasma magnetically for a sufficiently long time  to acquire enough fusion reactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The alpha particles (4  2He) confined in the  magnetic cage can heat the plasma through collisions, while the neutrons (1  0n)  ignoring magnetic fields can be used for a blanket [39] to capture the neutrons  and convert their energy into heat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  From now on, let me consider an actual time scale that we need to have  in order to see enough fusion reactions in the fusion reactors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' There is a rela-  tion portraying how much time do the reactions require when a certain amount  of plasma and a certain plasma temperature are given.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This is known as the  Lawson Criterion which describes the relation between plasma density n, ion  temperature T and confinement time τE as shown below  nTτE ≥ 3 × 1021 keV s/m3  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2)  where the confinement time τE is the ratio of the plasma thermal energy density  9  CHAPTER 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2: Lawson criterion for D-T fusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The ordinate stands for nτE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  This figure is taken from [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  W to the power Pheat that is needed to keep the plasma at a certain temperature  as shown below  τE = W/Pheat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3)  A modified Lawson Criterion is shown in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2 where BREAKEVEN  stands for balances between the fusion energy and the energy needed to sustain  the plasma, and IGNITION is a condition to ignite a self-sustaining plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The figure says that we need at least nτE of the order of 1020s/m3 to achieve the  breakeven condition with τE of the order of 1 sec if we expect that a reasonable  plasma density is ∼ 1020#/m3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Dramatically speaking, we must hold the plasma  for 1 sec inside of the fusion reactors, and I develop a neural network to control  the plasma for the time scale of 1 sec really precisely by reconstructing a better  plasma equilibrium in real time, which will be introduced out of this thesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Thus, we can probably say that nuclear fusion is figuratively the morning and  the evening star of which awakens us to reach a future of using the clean and  carbon-free energy invented by humankind’s knowledge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  10  1E+16  Density x time  1E+15  IGNITION  1E+14  BREAKEVEN  1E+13  0  20  40  60  80  100  lon temperature (keV)CHAPTER 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3: (a) A typical tokamak configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Image courtesy of  EUROfusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (b) Elevation view of ths KSTAR tokamak [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  Tokamak  Previously, I mentioned that the plasma responds to the external electromag-  netic fields sensitively, and this leads us to build the fusion reactor generating  the magnetic fields to confine and control the plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' One of the reactors working  such a way is tokamak whose name comes from the Russian words toroidalnaya  kamera magnitnaya katushka.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' These words mean toroidal chamber magnetic  coils.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Although there are various concepts of magnetic confinement devices such  as stellarator and reversed field pinch device, I would like to consider the tokamak  solely in this thesis since this thesis is mainly based on tokamak experimental  results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' As shown in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3 (a), the tokamak generates two major direc-  tions of the magnetic fields;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' toroidal magnetic field and poloidal magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The toroidal field coils represented as the gray structures generate the toroidal  magnetic field in the direction of the red arrow in the figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Similarly, The  poloidal field coils (green) and the central solenoids (blue) produce the poloidal  magnetic field in the direction of the purple arrows, while purposes of those coils  are slightly different: the poloidal field coils are generally used to control the  plasma position;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' the object of the central solenoids is to induce a current to the  plasma in order to generate a plasma current in toroidal direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Therefore,  the plasma current is the main source of the poloidal magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  I would like to note that the tokamak experiments done by the Korea  11  Outerpoloidal  A  field coil  Cryostat  B  Central solenoid  PF5U  PF6U  Toroidal field coil  X  PF7U  PF2U  Vacuum  PFIU  Vessel  PFIL  PF2L  PF3L  PF4L  proida  PF7L  Central  PF6L  Gravity  Solenoid  toddns  PF5L  Poloidal  field  netic  ConcreteFloorCHAPTER 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion  Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1: Designed ranges of major paramters of KSTAR [1]  Symbol  Parameter  Baseline  Upgrade  BT  Toroidal field [T]  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  Ip  Plasma current [MA]  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='0  R0  Major radius [m]  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='8  a  Minor raidus [m]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  κ  Elongation  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='0  δ  Triangularity  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='8 Pulse length [s]  20  300 Neutral beam [MW]  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='0  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='0 Ion cyclotron [MW]  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='0  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='0 Lower hybrid [MW]  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='0 Electron cyclotron [MW]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='0  Superconducting Tokamak Advanced Research (KSTAR) which is one of the  first research tokamaks with fully superconducting magnets in the world located  at South Korea have been dedicated to developments of this thesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The elevation  view of KSTAR is shown in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3 (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' I outline briefly below KSTAR and  its specifications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  KSTAR is one of the first fusion experimental reactors using superconducting  magnets in the world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The typical and designed ranges of the major specifications  of KSTAR are shown in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' It is worth mentioning that KSTAR recently  sustained the ion (deuterium) temperature up to ∼100 million degree Kelvin at  the center of the plasma for ∼20 sec for the first time [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' KSTAR has a major  radius of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='8 m and a minor radius of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5 m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The central solenoids of KSTAR are  designed to induce the plasma current of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='0 MA, and the toroidal field coils are  capable of generating the toroidal magnetic field of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5 T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The application in this  thesis provides a self-sustained deep learning approach for the plasma equilibrium  from KSTAR plasma diagnostic data which has been supported from developed  preprocessors based on Bayesian inference and deep learning respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' I will  12  CHAPTER 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion  introduce what I mean by the plasma equilibrium in the next section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  Equilibrium  In the field of nuclear fusion, Equilibrium, Tokamak Equilibrium, Plasma Equilib-  rium and Magnetic Equilibrium all mean the same phenomenon that the Lorentz  force exerted on the plasma balances the plasma pressure (or pressure gradient)  in a macroscopic equilibrium state inside the tokamak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The basic condition  for the plasma equilibrium suggest that the force on the plasma be zero at all  plasma regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This equilibrium comes from the single fluid magnetohydrody-  namic (MHD) equations [42] which explain fluid-like, macroscopic behaviors of  ionized ions and electrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Before explaining equations of the plasma equilibrium, I would like to state  two fundamental aspects of the equilibrium: (1) the internal balance between the  two forces as introduced above;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (2) there is the shape and position of the plasma  determined and controlled by the external coil currents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  From now on, Let us take a look at the MHD equation to arrive at the force  balance equation and beyond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The MHD momentum is given by,  ρ  �∂⃗v  ∂t +  �  ⃗v · ∇  �  ⃗v  �  = ⃗J × ⃗B − ∇p  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4)  where ρ is the mass density, ⃗v is the bulk plasma velocity field, ⃗J is the (plasma  and external) current density, ⃗B is the magnetic field, and p is the plasma pres-  sure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' If the static equilibrium conditions (⃗v = 0 and ∂/∂t = 0) are assumed, the  equation turns out to be the force balance equation which is  ⃗J × ⃗B = ∇p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5)  From this equation, it is obvious that there is no pressure gradient along the  magnetic field lines, which is  ⃗B · ∇p = 0  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6)  13  CHAPTER 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion  where it also means that the plasma forms magnetic surfaces of constant pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Likewise, the force balance equation tells us a relation:  ⃗J · ∇p = 0  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='7)  which also imply that the current lines lie in the magnetic surfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Furthermore,  it is convenient to define the poloidal magnetic function ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This is a constant  quantity on each magnetic surface acting as the poloidal flux lying within that  surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, there is another relation with the magnetic field:  ⃗B · ∇ψ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='8)  Through the force balance equation, based on a cylindrical coordinate and  an axisymmetric systems with Maxwell’s equations (∇· ⃗B = 0 and ∇× ⃗B = µ0 ⃗J),  we can now derive a differential equation for the poloidal flux function ψ which  is called the Grad-Shafranov (GS) equation [43,44] as shown below  ∆∗ψ = R ∂  ∂R  1  R  ∂ψ  ∂R + ∂2ψ  ∂Z2  = −µ0RJt  = −R2µ0  ∂p  �  ψ  �  ∂ψ  − F  �  ψ  �∂F  �  ψ  �  ∂ψ  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9)  where F  �  ψ  �  is the poloidal current function as a function of ψ, which is related  with the toroidal magnetic field BT as F  �  ψ  �  = R BT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The first two lines of the  equation include effects of Maxwell’s equations, and the second to third lines are  influenced by the force-balance equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  To obtain the solution of the equation, ψ(R, Z), it is required to observe Jt  over the whole plasma volume.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Unfortunately, magnetic measurements externally  installed from the plasma are generally available, together with local temperature  and density data of the plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Furthermore, the plasma exists in a certain region  inside the tokamak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' A boundary dividing the plasma with a vacuum region is  called plasma boundary, last closed flux surface and separatrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This boundary  is determined after the solution ψ is found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, this leads us to solve a free  boundary and inverse problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  14  CHAPTER 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion  Usually, a Green function’s formulation is carried out to solve the GS equa-  tion as follows:  ψ(R, Z) =  � �  G(R, Z;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' R′, Z′)Jφ(R′, Z′)dR′dZ′  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='10)  where G is the free-space Green’s function, and (R′, Z′) is the position of a current  source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' But, one can raise a question like “Does the GS equation just give us a  relation between given current densities and structures of the poloidal magnetic  field (or flux surfaces) after all?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', “If that is true, can we use the Biot-Savart law  instead of such complex differential equations?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Well, as a conclusion, it turns  out that the formulation of the Green function and using the Biot-Savart law are  the same eventually, meaning that using the law is viable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Therefore, I would like  to introduce how to use the Biot-Savart law in our case and what is insufficient  if we use the law only in the following subsection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  Biot-Savart Law  In the tokamak, there are four major sources of the poloidal magnetic field,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', the poloidal field coils, the central solenoids, in-vessel coils [45] and the  plasma (current).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Eddy currents (vessel currents) which are currents induced on  tokamak vessel structures are ignored for simplicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' As one can find in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' [46]  and Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' [45], all the external current coils have rectangular cross-sections, and  they carry constant currents at a certain time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This means that if we assume  the plasma current as a collection of wires whose cross-sections look rectangular  shapes, we can use the Biot-Savart law for the vector potential and the magnetic  field due to an arbitrary three-dimensional volume current with a rectangular  cross-section (R2−R1)×(Z2−Z1) shown in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4 in cylindrical coordinates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  It is worth to mention that derivations introduced in this subsection are mainly  based on Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Let me consider the Biot-Savart law for the vector potential and the magnetic  field by a volume current:  ⃗A (⃗r) = 1  4π  �  l  �  s  jd⃗l |⃗r − ⃗r′|−1 ds,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='11)  15  CHAPTER 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4: A segment of the circular wire showing rectangular cross-section  and carrying toroidal current in cylinder coordinates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  ⃗B (⃗r) = µ0  4π  �  l  �  s  j  �  d⃗l × (⃗r − ⃗r′)  �  d⃗l |⃗r − ⃗r′|−3 ds,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='12)  where ⃗r and ⃗r′ are positions of the field and source respectively, j is a constant  current, ds is a differential element of cross-sectional area perpendicular to d⃗l  which is a segmented line element along the current.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Then, as shown in Figure  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4, set the field and source positions as ⃗r = (r, φ, z) and ⃗r′ = (r′, φ′, z′), respec-  tively, where a current-carrying arc segment has properties such as R1 ≤ r′ ≤ R2,  Z1 ≤ z′ ≤ Z2 and (φ2 − φ1) as the azimuthal length of the arc segment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  I can rewrite the above equations as the following simple expressions  ⃗A (⃗r) = J  4π  � R2  R1  dr′  � Z2  Z1  dz′ ⃗ˆA (⃗r) ,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='13)  ⃗B (⃗r) = µ0J  4π  � R2  R1  dr′  � Z2  Z1  dz′ ⃗ˆH (⃗r) ,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='14)  where J is the azimuthal constant current density, and Az = 0 due to the con-  16  CHAPTER 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion  ductor structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Now, I can define the relevant forms as follows:  ˆAj (⃗r) = 1  2  � φ2  φ1  dΦ  �  γD(Φ) + 2γr cos Φ sinh−1 β1(Φ)  +  �  r′2 − r2 cos 2Φ sinh−1 β2(Φ)  �  − r2 sin 2Φ tan−1 β3(Φ)  �  �  �  �  − sin Φ,  cos Φ,  j = r, φ,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='15)  where the first and the second terms inside the bracket correspond to r and φ  directions, respectively, and  ˆHl (⃗r) =  � φ2  φ1  dΦ  �  �  �  �  �  �  �  �  �  cos Φ  �  D(Φ) + r cos Φ sinh−1 β1(Φ)  �  ,  sin Φ  �  D(Φ) + r cos Φ sinh−1 β1(Φ)  �  ,  γ sinh−1 β1(Φ) − r cos Φ sinh−1 β2(Φ) − r sin Φ tan−1 β3(Φ),  l = r, φ, z,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='16)  where the components inside the brackets correspond to r, φ and z directions  from the top.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' I also define the following expressions as:  γ = z′ − z,  Φ = φ′ − φ,  D2(Φ) = γ2 + B2(Φ),  B2(Φ) = r′2 + r2 − 2rr′ cos Φ,  G2(Φ) = γ2 + r2 sin2 (Φ),  β1(Φ) = (r′ − r cos Φ)/G(Φ),  β2(Φ) = γ/B(Φ),  β3(Φ) = γ(r′ − r cos φ)/[r sin φD(Φ)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='17)  Therefore, for all the conductors in the tokamak, the only task left is calculating  the equations above for each conductor with a condition of (φ2 −φ1) = 2π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Now,  17  CHAPTER 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion  we finally have the poloidal flux function ψ related to the Biot-Savart law given  by ψ(R, Z) = 2πRAφ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  At this moment, it seems that we have a complete formula for a solution  of the tokamak equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' However, we should remember that our problem is  a free-boundary and inverse problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' For simplicity, let us consider the inverse  problem only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, if we assume an arbitrary distribution of the plasma current  density, then we can obtain a distribution of ψ from the equations above and  update the plasma current density again using the obtained ψ based on ∇ ×  ⃗B = µ0 ⃗J or the first and second lines of the GS equation to be consistent with  the external magnetic measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' If we keep carrying out those sequences  repeatedly, we may end up with a converged distribution of ψ, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', flux surfaces;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  seemingly we finish solving the tokamak equilibrium!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' However, what we must  never forget during the sequences is whether or not the result satisfies the force  balance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In other words, if our result does not meet the second and third lines  of the GS equation, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', Jφ = Jφ(R, ψ), then our result is totally meaningless.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  We fully contemplate this in order to design a neural network that solves the  GS equation without any support of solutions of the GS equation, which will be  presented soon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3  Plasma diagnostics  In this section, I briefly introduce plasma diagnostics used in this thesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The GS  equation shows that the spatial variation of ψ is related to the current density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Namely, if the current density is exactly known, then the solution ψ would be  obtained through the GS equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Unfortunately, knowing internal information  of the plasma is barely straightforward due to the temperature of the plasma  (∼ 108 K), therefore the current density should be inferred as well by taking ad-  vantage of externally and locally measured data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' From the inferred current, the  GS equation is iteratively solved until an estimated equilibrium fits the measured  data reasonably.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Here, the external and the local measurements are magnetic  measurements and plasma pressure measurements, respectively, which are essen-  18  CHAPTER 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5: A schematic of the magnetic diagnostics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Image courtesy of  Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  tial to observe the plasma equilibrium and energy transport in nuclear fusion  experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  Magnetic diagnostics  Here, I would like to deal with magnetic diagnostics relevant to the poloidal  magnetic field since solving the GS equation is highlighted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  KSTAR has in-  stalled the magnetic measurements [49] on the KSTAR vessel wall far away from  the plasma as induction coil-type measurements with analogue integrators [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Among them, I take advantage of 84 magnetic pick-up coils (magnetic probes)  which measure the poloidal magnetic fields of the normal and the tangential  directions to the vessel wall and 45 flux loops (FLs) measuring the poloidal mag-  netic fluxes, respectively [2, 49].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' I also use Rogowski coils measuring the total  plasma current, the poloidal field coil currents and the in-vessel coil currents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Basic forms of the diagnostics are shown in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The brief history of the KSTAR magnetic diagnostic system is as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  A schematic design of the diagnostics and how to install it to the KSTAR were  suggested [49], and performances of the designed magnetic pick-up coils were  tested in a vacuum chamber [50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The designs were improved and analyzed in a  radio-frequency environment [51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' After that, it was reported that some of the  fabricated magnetic measurements were installed at the KSTAR vessel [52] as  well as the design of the integrators for the systems was reported [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In 2008,  19  Diamagnetic  loop  Magnetic  Flux loop  Saddle  field  loop  probe  Rogowski  coilCHAPTER 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6: (a) Port allocation of KSTAR TS system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Image courtesy of  Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' [65].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (b) KSTAR CES layout composed of a window, mirror, collection  lens, a spectrometer and a CCD camera.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Image courtesy of Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' [66].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  only some of the poloidal field coils were driven to analyze operation performances  of the measurements [2] for the first plasma on KSTAR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Diamagnetic loops were  also designed and installed [54], and their performances were reported in 2011  [55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' An outline of the first plasma of the KSTAR was published in 2010 [56]  with measured magnetic data from various measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  In 2017, a study  about how to improve a plasma operation based on the magnetic diagnostics was  introduced [57].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  When it comes to the integrator, several hardware designs were introduced  [53, 58–62] to correct a phenomenon called signal drift, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', a baseline of a  measured signal drifting in time, and software correction approaches were sug-  gested [58,59,63,64].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  Pressure measurements  To solve the GS equation, the plasma pressure on the ψ coordinate is necessary  over the whole tokamak region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Currently, all we can do is measuring local  thermal pressures of the plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' These pressures are estimated from the ideal gas  law, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', the pressure p = nT where n and T are the density and the temperature,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The reason why I stress the term “thermal” is there is the fast  ion pressure, pfast, which is contributed by the fast ion (more energetic than a  thermal ion) populations coming from the Neutral Beam Injection (NBI) system  20  KSTAR hall  Diagnostic room  Beamdumpsystem  B  D  ControlPC  Optic system &  Cassette  CCD  PhotonMax  512B  M  Wal  Spectrometer  A  Laserinputsystem  McPherson  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='33 m  Tangential Beam  Nd:YAG  (1064nm)CHAPTER 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion  [67] in the KSTAR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Profile measurement systems for this pressure still need to  be developed further [68–70].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  To estimate the plasma pressure, we need to measure n and T of the elec-  tron and the ion, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The Thomson Scattering (TS) system is used  detect the electron density ne and the electron temperature Te simultaneously,  which is one of the major methods to obtain those information by measuring the  scattered and Doppler-shifted photons from an interaction between high-power  laser photons and the plasma electrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The KSTAR TS system provides 31  local measurements with a spatial resolution of 6 mm to 13 mm, together with  a temporal resolution of 50 Hz, as shown in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6 (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Regarding the ion density, quasi-neutrality works here, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', ni ≈ ne.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' For  the ion temperature, the Charge Exchange Spectroscopy (CES) system, which  obtain local carbon density and flow velocity measurements along the NBI beam  path by capturing the Doppler line width and deviation of a spectrum emitted  from an interaction between the neutral beam ions and the carbon ions in the  tokamak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The KSTAR CES system has 32 local measurements with a spatial  resolution < 5 mm, together with a temporal resolution < 100 Hz, as shown in  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6 (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Therefore, based on the equation below, we can relate the density and tem-  perature measurements with the plasma pressure, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=',  ptot = neTe + niTi + pfast + prest  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='18)  where prest is the pressure of impurities in the tokamak whose profile is not  sufficiently available yet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, we can use this for p(ψ) term in the GS equation,  which will be dealt with in Article V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  One can have curiosity about the F(ψ) term in the GS equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In fact,  the Motional Stark Effect (MSE) system [71] which measures local magnetic field  pitch angles along the NBI path from the polarization of the motional Stark effect  emission signals by the NBI beam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In this thesis, I would like to prove the fact  whether deep learning can solve the GS equation by only using the equation itself  or not, and a way of using the MSE measurements is considerably similar with  21  CHAPTER 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion  that of the plasma pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, I would like to leave this as a future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  It is worth to mention that the KSTAR MSE system has 25 local measurements  with a spatial resolution of 1 cm to 3 cm, together with a temporal resolution of  100 Hz [72].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4  Deep learning for tokamak equilibrium  This thesis addresses reconstructing “tokamak equilibria” in real time in the  field of magnetically controlled nuclear fusion, from the perspective of solving  the GS equation by an application of deep learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' As explained before, the GS  equation gives us two facts: (1) balancing the plasma pressure and the Lorentz  force and (2) information of plasma positions in the tokamak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Although there  were previous approaches [73–77] to find a solution of the GS equation, sacrificing  accuracy or depending on human subjectivity (manually determined complexity  of the solutions) is still left to be resolved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, we present a deep learning  method which solves the GS equation by itself with no guess of the GS equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  How can we believe that the networks truly understand the GS equation?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Are they soluble if the network’s outputs are trained with well-calculated toka-  mak equilibria given by the previous methods?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Unfortunately, I do not think  so.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The networks may not be able to capture the force balance behind the  dataset [78], and there is still the human decision regarding numerical conver-  gence such that some of the measured signal are arbitrarily selected for the re-  construction, although the network can produce the equilibria outstandingly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' To  answer those questions, I make the networks find the equilibria after they fully  understand the GS equation without any human selection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Eventually, they can  generate the equilibria consistent with given measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' How this is possi-  ble will be served in Article V in chapter 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Article IV provides a prototype of  Article V by trying to learn the GS equation by means of the KSTAR EFIT  database [79].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Article I, Article II and Article III provides how to preprocess  inputs of the networks, which guarantees that the networks can be used in any  circumstance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  22  Chapter 3  Deep learning and Bayesian  Inference  “황새의 울음을 듣겠느냐?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  정우는 놀란 얼굴로 새장을 바라보다가 말했다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  “동백꽃의 향기요?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  회의장의 사람들은 자신들의 이해력에 도대체 무슨  문제가 있나 고민했다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  — 이영도,  피를 마시는 새  The human brain is a extremely complex, non-linear and parallel information-  processing system, which is constituted with neurons, the brain’s structural el-  ements, performing logical, cognitive and unconscious reasoning relatively effi-  ciently compared to contemporary digital computers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This ability is purportedly  built up over time with certain rules called experience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This keeps continuing the  development of our brain constantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Artificial neural networks (simply referred  to as neural networks) are designed to mimic our brain’s functioning by using  a massive interconnection of simple digital units called neurons, perceptrons or  nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This intuitive structure, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', plasticity is an inception of deep learning,  an enormous pile of the interconnection to perform human-like or superhuman  capabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  In 1943–1958, the formation of neural networks begins with McCulloch and  Pitts (1943) [80] suggesting the idea of neural networks as computing machines,  Hebb (1949) [81] underlying self-organizing learning, and Rosenblatt (1958) [82]  introducing the perceptron as the first model for supervised learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Although  23  CHAPTER 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Deep learning and Bayesian Inference  there were critics pointed out by Minsky and Selfridge (1961, 1969, 1988) [83–85]  that the perceptron is not essentially capable of being globally generalized based  on locally learned examples, it would not be an overstatement that we are living  in an era of neural networks and deep learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Then, how can we implement physically reliable deep learning?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The methods  that I propose in this thesis are to develop a Bayesian neural network which is  capable of perceiving physics theories and quantifying its confidence level with  given input information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Although the ways are not restricted to the field of  nuclear fusion, I would like to propose a neural network available for tokamak  control based on learning with plasma magnetohydrodynamic (MHD) theory [42]  and Maxwell’s equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, I would like to prove that there is definitely a  physically reliable neural network based on the arguments in this thesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  From the next section, I will describe a structure of a feedforward neural  network and a basic notion of supervised learning on the basis of the simple sine  regression introduced in Chapter 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Then I will introduce uncertainty in neural  networks in light of Bayesian neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' How networks are taught with  physics theories will be also given later.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Finally, I will convey a short discussion  about the usage of Generative Adversarial Networks (GANs) in light of tokamak  control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  Feedforward Neural Network  Feedforward neural networks basically have an input layer, hidden layers and an  output layer, and Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1 shows an example of them with a simple architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Given arbitrary inputs R and Z, the input information flows through the hidden  layer toward the output node after going through an activation function in each  layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This process is non-linear, which lends the network to resemble any forms  of data distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Each layer has its own bias as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  24  CHAPTER 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Deep learning and Bayesian Inference  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1: A simple neural network having two input nodes (except the input  bias), a single hidden layer and an output node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The formula for the network in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1 can be expressed as follows:  ˆy = v0 + v1f  �  w10 + w11R + w21Z  �  + v2f  �  w20 + w12R + w22Z  �  + v3f  �  w30 + w13R + w23Z  �  + v4f  �  w40 + w14R + w24Z  �  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1)  where w and v are the weights between the input and the hidden layers, and  between the hidden and the output layers, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' f is an activation func-  tion originated from the biological activation function where sigmoid, tanh, and  ReLU functions are popular to be used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Among the training methods for the network, here I would like to introduce  supervised learning whose cost function is a function of observed quantities t and  the network outputs ˆy as shown below:  ϵ = (ti − ˆyi)2  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2)  where i is the feature of a database for training the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' With the sine  function regression mentioned in Chapter 1, we can define ti ∼ 0 at xi = 0 as an  instance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This makes the network be almost zero when the input is zero if the  25  W11  V1  W-  R  W12  W13  V2  W14  y  Z  W10  b1  W30  VA  WA  W40  Vo  b2CHAPTER 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Deep learning and Bayesian Inference  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2: Training (blue) and validation (orange) costs versus epochs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  network has a single input node by taking advantage of the well-known gradient  descent method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  In general, there are features involved in training set and validation set  separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  With the sine example again, I create (observe) a total of 1024  features (data points) in interval (0, 1) along x-axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 90 percent of these features  are used to build the training set, while the remaining features form the validation  set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The training set indeed takes part in the training process, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', updating  weights of the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Conversely, the validation set does not contribute to the  update process, while it is used to stop the training early to avoid over-fitting  issue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The over-fitting is a problem that the network try to follow all the sporadic  data points exactly, deteriorating the network’s prediction ability, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', network  generality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2 shows the training (blue) and validation (orange) costs calculated  based on Equation 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2 over epochs (a single loop of the update procedure).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The  epoch is identical to an iteration if we use whole features to update the weights  26  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6  E  MSI  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3  0  Q0QT  2000  QOCE  EpochCHAPTER 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Deep learning and Bayesian Inference  at once in the single iteration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This figure is from σ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5 case in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The training cost keeps decreasing in the figure, while the validation cost shows  a stagnation (or increase) after decreasing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This shows the network is over-fitted  to the data points at epoch = 3000 since the network follows the training data  points well compared to the validation data points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In other words, the network  generality is degenerated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Therefore, the network at epoch ∼ 2000 is possibly  optimal where the validation cost is about to increase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' It is worth mentioning  that I construct the neural network having four hidden layers and 300 nodes  each.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The activation used is swish function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The generalized equational forms for the neural network are as follows:  �y = f(xW 1 + b)W 2,  EW 1,W 2,b(X, Y ) =  1  2N  N  �  i=1  ||yi − �yi||2,  L(W 1, W 2, b) ≡ EW 1,W 2,b(X, Y ) + λ1||W 1||2 + λ2||W 2||2 + λ3||b||2  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3)  where we slightly change a notation such that y is the observed data, the boldface  of the uppercase letters are the matrices, the boldfaces of the lowercase letters  are the vectors, and the lowercase letters are the scalars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  X and Y are the  observed input and output data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Based on these notations, I will relate the  neural network to Bayesian inference to quantify the predictive uncertainty, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=',  Bayesian neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Furthermore, the training method is related to the  principle of Occam’s razor (if no evidence, avoid over-fitting), which will be also  discussed in the following sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  Bayesian Inference  Before discussing Bayesian neural network, I would like to explain Bayesian infer-  ence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The power of Bayes’ theorem is the fact that the probability of hypothesis  being true given data is linked to the probability of the data being able to be  observed if the hypothesis was true:  prob(hypothesis|data, I) ∝ prob(data|hypothesis, I) × prob(hypothesis|I).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4)  27  CHAPTER 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Deep learning and Bayesian Inference  where prob(hypothesis|I) is the prior probability (representing our state of igno-  rance before the data have been measured regarding the truth of the hypothesis),  prob(data|hypothesis, I) is the likelihood probability (modifying the prior by the  measurements), and prob(hypothesis|data, I) is the posterior probability (illus-  trating our state of knowledge in the data point of view regarding the truth of the  hypothesis).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' prob(data|I) that is not shown in the equation is called evidence  which plays an important role in some situations like modelselection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The  quantities on the right hand side can be denoted as prob(data, hypothesis|I) =  prob(data|hypothesis, I)×prob(hypothesis|I), which means that if we first spec-  ify how much we believe that the hypothesis is true, and then state how much we  believe that the data is true given that the hypothesis is true, then we must im-  plicitly have specified how much we believe that both the data and the hypothesis  are true [86].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  In light of the neural network, the quantities of interest to be found through  Bayesian inference are the weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Given training inputs X and their corre-  sponding outputs Y , the posterior probability of the network weights is:  p  �  ω|X, Y  �  = p  �  Y |X, ω  �  p(ω)  p  �  Y |X  �  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5)  where ω is the weight matrix of the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The posterior represents the most  probable weights given the training data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Like the evidence that I describe above, we can perform an integration of  the posterior over the space of the weights which is called marginalization as  shown below:  p  �  Y |X  �  =  �  p  �  Y |X, ω  �  p  �  ω)dω,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6)  which is in other words we marginalize over all unknown parameters, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', an  weighted average of ω with respect to its prior distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  In light of real world observations, inferring p  �  ω|X, Y  �  analytically is often  unavailable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Therefore, an arbitrary variational distribution whose parameter  is θ, qθ(ω), is defined to be used for the inference straightforwardly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' qθ(ω) is  suggested to be closer to the original posterior distribution, driving us to use  28  CHAPTER 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Deep learning and Bayesian Inference  the Kullback-Leibler (KL) divergence over θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This tells us how similar both two  distributions are:  KL  �  qθ(ω)  ����p  �  ω|X, Y  ��  =  �  qθ(ω) log  qθ(ω)  p  �  ω|X, Y  �dω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='7)  Minimizing the KL divergence is identical to maximization of the evidence  lower bound (ELBO) with respect to qθ(ω) also known as variational lower bound,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=',  LV I(θ) ≡  �  qθ(ω) log p  �  Y |X, ω  �  dω − KL  �  qθ(ω)  ����p(ω)  �  ≤ log p  �  Y |X  �  =  �  qθ(ω) log p  �  Y |X, ω  �  dω  −  �  qθ(ω) log qθ(ω)dω +  �  qθ(ω) log p  �  ω  �  dω  −  �  qθ(ω) log p  �  Y |X  �  dω +  �  qθ(ω) log p  �  Y |X  �  dω  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='8)  where we can find the evidence of the posterior on the far right in the first line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  This plays a role of “Occam’s razor” which penalize qθ(ω) since the first term  in the middle of the first line increases the degree of freedom of qθ(ω), while the  second term in the same line let qθ(ω) be as close as the prior p(ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This will  show up in Appendix A to explain that this also governs the degree of freedom  of the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The procedure above is known as variational inference (VI) which results in  capturing model uncertainty, and allows us to replace the marginalization with  the optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The Bayes’ theorem and the marginalization have enormously  attracted attention in nuclear fusion in light of Bayesian forward models [87–89]  and physical parameter regressions [90–94].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  Sine function Regression: Part 1  With Appendix A explaining what Bayesian deep learning is, we have explored  dropout in terms of Bayesian neural networks and predictive uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' To im-  plement the uncertainty mentioned in Chapter 1 from dropout, we simply need  29  CHAPTER 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Deep learning and Bayesian Inference  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3: A Bayesian neural network posterior with various SNR of the  observed sine functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The networks have the dropout probability p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  This figure is identical to Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1 except the predictive uncertainty expressed  in the red area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  to go through the stochastic process of dropout.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In other words, we can obtain a  Bayesian neural network posterior if dropout is applied during the training, nat-  urally giving us the network’s uncertainty over the network’s parameter space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  I apply this process for the sine function regressions, which I have covered pre-  viously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' As a coincidence, I already used dropout for the problem, and let me  confirm the predictive uncertainty of the network with the scattered data points  of the sine functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3 shows the Bayesian neural network posteriors with their uncer-  30  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='05  α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  α=3CHAPTER 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Deep learning and Bayesian Inference  tainty expressed in the red areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Same with Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1, the black line is the  noise-free sine functions, the blue and orange dots are the training and validation  sets, and the red areas represent 1 σ standard deviation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Since I synthesized a  total of 1024 data points, I used the dropout probability of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2 following Figure  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='14 in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' [95].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Without being caught in over-fitting (following all the data  points exactly), the network results are close to the correct answers (black line)  with reasonable uncertainty even though the observed data are quite sporadic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Furthermore, the thickness of the red area is gradually noticeably increased when  SNR of the sine data is increased.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This means that the magic approach men-  tioned in Chapter 1 is no longer magic, rather is expressed in the quantified  uncertainty through Bayesian inference, convincing us it is reliable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Now, I would like to mention that we partially prove the neural networks  are out of the black box except that we yet prove the networks can understand  physics explained in Chapter 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' To make this a total belief, we extend our result  to show neural networks learning physical theories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3  Sine function Regression: Part 2  With Appendix B describing neural network differentiation, I, here, wish to train  a neural network by Equation B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3 whose solution is t(x) = sin (14πx) + const  where we simply set const to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Following the procedure explained before, I  train the neural network which has four hidden layers with 100 neurons and a bias  each by using Equation B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3 as a cost function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The training data is generated  from the first order derivative of the solution, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', 14π cos (14πx) between zero  and one on the x-axis without adding noises.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4 (b) shows the first order  derivative as the black line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Similarly, Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4 (a) shows the solution as well  as I prepare the second order derivative as well in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4 (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In the figure,  the blue lines are the network results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  As one can see, the network is capable of generating its first order derivative  with respect to the input x corresponding to our differential equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Further-  more, its own output and the second order derivative (with respect to x) are  truly matched with the solution and the second order derivative of Equation B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3  31  CHAPTER 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Deep learning and Bayesian Inference  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4: (a) The black line is sin (14πx) which is the solution of Equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  (b) The first order derivative of the solution with respect to x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (c) The second  order derivative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The red areas are the network results with their uncertainty,  while the blue lines are the means of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (d) The distribution of the random  offset from 300 different networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  as long as we shift the blue line in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4 (a) to the origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This shift results  from the fact that I do not explicitly control an offset (bias) of the network out-  put from the cost function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Instead, I provide Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4 (d), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', a distribution  of the random offset from 300 different networks which seemingly follows a nor-  mal distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Lastly, Bayesian neural network posterior is also applied here  where the red (and orange) areas indicate the network uncertainties analyzed by  dropout.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, this fulfills the concept of the total belief such that we believe  not only the network is able to quantify its confidence but also it can grasp a  differential equation or a certain physical theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  So far, how to teach a network physics has been introduced with the simple  32  offsetCHAPTER 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Deep learning and Bayesian Inference  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5: A fundamental GAN architectures  first order differential equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' It is worth to mention that this training method  is somewhat close to supervised learning since the network can be taught with the  data generated from the cosine function although it never notices how the sine  function looks like.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Then what if we would like to teach high order differential  equations or what if we cannot prepare not only solutions of differential equations  but also their corresponding derivatives at all?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Could it be called supervised  learning as well?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In fact, these are raised when I deal with applying a network to  the purpose of tokamak control based on a plasma governing equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' I teach  a second order (elliptical) partial differential equation without having a dataset  for its derivatives through a neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Therefore, one can find answers to  the questions in the following chapters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  Advanced topic: GAN  This section is prepared to find other research fields where the method we have  looked at can be helpful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Generative Adversarial Networks (GANs) [96,97] have  emerged as a type of unsupervised learning to generate network representations  from distributions of data without experiencing them explicitly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5 shows  a basic structure of GAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  In this figure, there are the generator G and the discriminator D which act  as the forger and the expert.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The forger falsifies a network output to be realistic  33  real  fake  D  (z)  x  ZCHAPTER 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Deep learning and Bayesian Inference  data from a random noise, while the expert identifies real data from the forgeries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The equation below is a realization of the forger-expert relation as a cost function  of GAN:  min  G max  D V (D, G) =Ex∼pdata(x)[log D(x)]  + Ez∼pz(z)[log(1 − D(G(z)))]  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9)  where the first line on the right hand side is a cost for the discriminator, the  second line is for the generator, x is the real data, and z is the random noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  This is powerful for data generation even not being contained in a prepared  dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, there was studies to use GANs to replace typical numerical simu-  lations in the field of physics such as accelerator [98–100] and materials [101,102].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  I would like to briefly introduce the use of GAN in the field of tokamak control  by using plasma equilibria database.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Plasma equilibrium is a reconstructed mag-  netic topology of the plasma which will be discussed in the next chapter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Below  are the relevant python codes using TensorFlow [103].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  1 import  h5py  2 import  matplotlib.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='pyplot as plt  3 import  numpy as np  4  5 import  tensorflow as tf  6 from  tensorflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='keras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='layers  import  Activation ,  BatchNormalization , Dense , Dropout , Flatten , Reshape  7 from  tensorflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='keras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='layers  import  LeakyReLU , ZeroPadding2D  8 from  tensorflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='keras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='layers  import Conv2D , Conv2DTranspose  9 from  tensorflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='keras  import  Input  10 from  tensorflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='keras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='layers  import  InputLayer  11 from  tensorflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='keras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='models  import  Sequential  12 from  tensorflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='keras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='optimizers  import  Adam  13  14 from  sklearn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='model_selection  import  train_test_split  15 from  collections  import  defaultdict  16 import  argparse  Listing 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1: The use of GAN with plasma equilibria: Load essential libraries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  34  CHAPTER 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Deep learning and Bayesian Inference  1 X = f3[’psi’][:].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' transpose (2, 0, 1)  2  3 ix = list(range(X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='shape [0]))  4 np.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='random.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='shuffle(ix)  5 # ix = ix[: results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='nb_points]  6  7 X = X[ix]  8 X_train , X_test = train_test_split (X, train_size =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9)  9 X_train = np.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='expand_dims(X_train , axis =-1)  10 X_test = np.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='expand_dims(X_test , axis =-1)  11 X_train = X_train.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='astype(np.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='float32)  12 X_test = X_test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='astype(np.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='float32)  13  14 nb_train , nb_test = X_train.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='shape [0], X_test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='shape [0]  Listing 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2: The use of GAN with plasma equilibria: Load equilibria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  1 img_rows = 64  2 img_cols = 64  3 channels = 1  4  5 # input  image  dimension  6 img_shape = (img_rows , img_cols , channels)  7  8 # latent  space  dimension  9 z_dim = 100  10  11 def  build_generator (z_dim):  12  13  model = Sequential ()  14  # From  Dense 8x8x256  15  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='add(Dense (256 * 8 * 8, input_dim=z_dim))  16  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='add(Reshape ((8, 8, 256)))  17  # 8x8x256 => 16 x16x128  18  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='add( Conv2DTranspose (128,  kernel_size =3, strides =2,  padding=’same ’))  19  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='add( BatchNormalization ())  20  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='add(LeakyReLU(alpha =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='01))  35  CHAPTER 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Deep learning and Bayesian Inference  21  # 16 x16x128 => 32 x32x64  22  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='add( Conv2DTranspose (64, kernel_size =3, strides =2,  padding=’same ’))  23  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='add( BatchNormalization ())  24  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='add(LeakyReLU(alpha =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='01))  25  # 32 x32x64 => 32 x32x32  26  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='add( Conv2DTranspose (32, kernel_size =3, strides =1,  padding=’same ’))  27  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='add( BatchNormalization ())  28  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='add(LeakyReLU(alpha =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='01))  29  # 32 x32x32 => 64 x64x1  30  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='add( Conv2DTranspose (1, kernel_size =3, strides =2,  padding=’same ’))  31  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='add(Activation(tf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='nn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='leaky_relu))  32  33  return  model  34  35 def  build_discriminator (img_shape):  36  37  model = Sequential ()  38  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='add(Input(shape=img_shape))  39  40  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='add(  41  Conv2D (32,  42  kernel_size =3,  43  strides =2,  44  padding=’same ’))  45  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='add(LeakyReLU(alpha =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='01))  46  # 32 x32x32  > 16 x16x64  47  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='add(  48  Conv2D (64,  49  kernel_size =3,  50  strides =2,  51  padding=’same ’))  52  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='add(LeakyReLU(alpha =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='01))  53  # 16 x16x64  > 8x8x128  54  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='add(  36  CHAPTER 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Deep learning and Bayesian Inference  55  Conv2D (128,  56  kernel_size =3,  57  strides =2,  58  padding=’same ’))  59  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='add(LeakyReLU(alpha =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='01))  60  # 8x8x128  > 4x4x256  61  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='add(  62  Conv2D (256,  63  kernel_size =3,  64  strides =2,  65  padding=’same ’))  66  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='add(LeakyReLU(alpha =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='01))  67  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='add(Flatten ())  68  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='add(Dense (1, activation=’sigmoid ’))  69  70  return  model  71  72 def  build_gan(generator , discriminator):  73  74  model = Sequential ()  75  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='add(generator)  76  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='add(discriminator)  77  78  return  model  Listing 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3: The use of GAN with plasma equilibria: Define the GAN  architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  1 # d model  2 discriminator = build_discriminator (img_shape)  3 discriminator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='compile(loss=’binary_crossentropy ’,  4  optimizer=Adam (),  5  metrics =[’accuracy ’])  6 # g model  7 generator = build_generator (z_dim)  8 # let d be non -trainable  9 discriminator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='trainable = False  10 # g + d compile  37  CHAPTER 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Deep learning and Bayesian Inference  11 gan = build_gan(generator , discriminator)  12 gan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='compile(loss=’binary_crossentropy ’, optimizer=Adam ())  Listing 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4: The use of GAN with plasma equilibria: Compile the GAN defined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  1 train_history = defaultdict(list)  2 test_history = defaultdict(list)  3 nb_epochs = 100  4 batch_size = 100  5 latent_size = 100  6  7 real = np.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='ones (( batch_size , 1))  8 fake = np.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='zeros (( batch_size , 1))  9  10 for epoch in range(nb_epochs):  11  print(’Epoch {} of {}’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='format(epoch + 1, nb_epochs))  12  13  nb_batches = int(X_train.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='shape [0] / batch_size)  14  epoch_gen_loss = []  15  epoch_disc_loss = []  16  17  for index in range(nb_batches):  18  19  if index % 100 == 0:  20  print(’processed  {}/{}  batches ’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='format(index + 1,  nb_batches))  21  22  # generate a new batch of noise  23  noise = np.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='random.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='normal (0, 1, (batch_size , latent_size))  24  # get a batch of real  images  25  image_batch = X_train[index * batch_size :( index + 1) *  batch_size]  26  27  # generate a batch of fake images ,  28  # using the  generated  labels as a  29  # conditioner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We reshape  the  sampled  labels to be  30  # (batch_size , 1) so that we can feed them  31  # into the  embedding  38  CHAPTER 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Deep learning and Bayesian Inference  32  # layer as a length one  sequence  33  generated_images = generator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='predict(noise)  34  35  # see if the  discriminator  can figure  itself out .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  36  real_batch_loss = discriminator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' train_on_batch(  37  image_batch , real  38  )  39  40  # note that a given  batch  should  have  41  # either *only* real or *only* fake ,  42  # as we have both  minibatch  discrimination  43  # and batch  normalization , both  44  # of which  rely on batch  level  stats  45  fake_batch_loss = discriminator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' train_on_batch(  46  generated_images , fake  47  )  48  d_loss , accuracy =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5 * np.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='add(real_batch_loss ,  fake_batch_loss )  49  50  epoch_disc_loss .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='append(d_loss)  51  52  # we want to train the  genrator to trick  53  # the  discriminator  54  # For the generator , we want all the {fake , real} labels  55  # to say real  trick = np.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='ones(batch_size)  56  gen_losses = []  57  58  # we do this  twice  simply to match the number of batches  59  # per epoch  used to  60  # train the  discriminator  61  for _ in range (2):  62  noise = np.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='random.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='normal (0, 1, (batch_size ,  latent_size))  63  64  gen_losses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='append(gan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' train_on_batch(  65  noise ,  66  real  39  CHAPTER 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Deep learning and Bayesian Inference  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6: (a) Examples from the equilibrium database, (b) Examples of the  GAN results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  67  ))  Listing 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5: The use of GAN with plasma equilibria: Train the GAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  As one may have noticed, there are no physical constraints in this training  procedure although Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6 shows a great similarity between the prepared  database and the GAN results except wrinkled features in the GAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Of course,  this is a simple example but the cost function of GAN does not contain any  physical restrictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Therefore, applying our approach in the previous section  to a GAN may result in a physically constrained GAN result which might be  helpful to be used for simulations instead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3  Outlook  I have reviewed a part of constituents for learning physics via neural networks in  this thesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' I explain how the neural networks can be trained with not only their  output but also derivatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' From this perspective, we can gain insight into an  interesting paradigm that the networks can learn a physical system if the system  is governed by physical theories, then the networks can use the theories as their  40  CHAPTER 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Deep learning and Bayesian Inference  cost functions even if simulated data for the phenomenon is not prepared yet to  train the networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' It can be asserted that the network results can be more reli-  able than a usual training procedure since the networks literally understand the  physics theories based on the novel paradigm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' If the network results become more  credible, humans can trust the networks and entrust them to more tasks related  to the physical system (especially, tokamak operations).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Perhaps, this paradigm  might be regarded as a cornerstone of a pure autonomous tokamak control via  deep learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Anyhow, as a test bed, reconstructing plasma equilibria in the  field of magnetic confinement fusion is chosen to prove this idea.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Reconstruct-  ing plasma equilibria requires solving a second-order partial differential equation,  which will be introduced in the next chapter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  41  Chapter 4  Bayesian neural network in  fusion research  Here, Chapter 4 constitutes the main outcome of this thesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The findings listed  in this chapter are applications of the principles and methods that are described  in the previous chapters in order to reconstruct plasma equilibria as scientific  and practical usages of deep learning in nuclear fusion research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  With the Korea Superconducting Tokamak Advanced Research (KSTAR),  Article IV has been developed to show that a neural network can learn a plasma  ‘theory’ with the support of a database prepared from a numerical algorithm by  reconstructing plasma equilibria based on the Grad-Shafranov (GS) equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  This is a preliminary application for the network to provide the possibility of a  complete unsupervised learning for the reconstruction such that the neural net-  work can understand the GS equation itself, and the database from the numerical  algorithm is no longer required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This is described in Article V, providing how  a principle of the unsupervised learning works, and why this kind of network  is required for tokamak control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Article I, Article II and Article III have been  developed to preprocess KSTAR measurements used to inputs of our networks  since baseline increases of measured signals in time (signal drift), missing signals  due to mechanical issues and inconsistency between signals should be handled  to use our networks in any experimental circumstances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' From Bayesian neural  networks, our applications are able to quantify the epistemic uncertainty related  to the plasma theory by obtaining inference results of the GS equation as well  as plasma information such as positions and locations of the plasmas (which are  hard to be measured directly) in the KSTAR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Again, the principles and methods that I have used for the applications are  42  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  explained in the previous chapters, thus the reader who wants to take a look at  these is recommended to read chapter 2 and chapter 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  Article I: Signal drift correction  This approach deals with Bayesian based numerical method for real-time cor-  rection of signal drifts in magnetic measurements from tokamaks1, which is  largely taken from Ref [78], as a part of preprocessing magnetic measurements  via Bayesian inference and neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  This article is to model signal drift which is a phenomenon that baselines of  measured signals increase or decrease in time by using Bayesian inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Mag-  netic signals such as magnetic fields and fluxes typically measured from inductive  coils with analogue integrators can be obtained by integrating voltages induced  in the coils by time-varying magnetic fields from current sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' KSTAR usu-  ally has the poloidal field coils and the plasma as the current sources, and vessel  currents (induced current in KSTAR vessel structure) are often regarded as sig-  nificant current sources as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Besides, KSTAR measures the poloidal magnetic  fields and fluxes from magnetic pick-up coils and flux loops installed on the vac-  uum vessel wall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' When the voltages induced from the sources are integrated,  spurious offsets are also often accumulated, causing the magnetic signals to tend  to be increased (or decreased) over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This phenomenon should be compen-  sated properly to be used for various plasma analyses based on the magnetic  signals such as EFIT (plasma equilibrium fitting).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Thus, the Bayesian model for the KSTAR pick-up coils and flux loops are  suggested with information of initial magnetization stage which is a step that all  the poloidal field coils are being charged to be ready for tokamak discharges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In  this stage, currents of the poloidal field coils become a steady state after being  fully charged, meaning that the magnetic signals also have ideally no variance  1Reproduced from S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Joung et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' the Appendix in ’Deep neural network Grad–Shafranov  solver constrained with measured magnetic signals’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In: Nuclear Fusion, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1 (3rd Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  2019), page 016034, DOI:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1088/1741-4326/ab555f  43  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  3  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  R [m]  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  Z [m]  ←20  ←21  ←22  ←19  ←18  ←17  ←16  ←15  ←28  ←27  ←26  ←25  ←24  ←23  ← 6  FL 1→  FL12→  FL23→  FL34→  ←37  FL45→  ← 1  ← 2  ← 3  ← 4  ← 5  ← 7  ← 8  ← 9  ←11  ←12  ←13  ←14  ←29  ←30  ←31  ←32  ←33  ←34  ←35  ←36  ←38  ←39  ←40  ←41  ←42  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1: Configuration of magnetic diagnostics on a poloidal cross-section  of KSTAR at a certain toroidal position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Blue dots show the positions of both  MPn and MPt, and red open circles for the positions of the FLs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The black  thick line shows the first wall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Note that we only show five FL sensor numbers  out of 45 of them for simplicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  in time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, any variances in this phase can be considered as the signal drift  which is alleviated by our Bayesian model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' To model the signal drift, linearly  increased drift model is assumed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  This can reasonably handle the measured  signals from KSTAR short-pulse discharges (≤ 20 sec), while being required to  be improved for applications of KSTAR long-pulse discharges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nevertheless, this  method is quite effective in KSTAR discharges where the short-pulse discharges  account for the majority.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, Article II–V employs this development in order  to preprocess the signal drifts in the magnetic fields and fluxes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Note that this  article I is a long version of an appendix in Article IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  44  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  Introduction  Magnetic diagnostics (MDs) are one of the most fundamental and widely used  sensors installed in almost all (if not all) magnetic-confinement fusion devices,  for instance LHD [104], MAST [105], DIII-D [106], TCV [107], EAST [108],  JET [109], ITER [110] and KSTAR [2, 49].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Reference [111] also discusses mag-  netic diagnostics on TFTR, JET, JT-60 and DIII-D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Various magnetic signals  from MDs play significant roles in real-time plasma controls, detecting MHD  (magnetohydrodynamics) events [112–116] as well as reconstructing magnetic  equilibria [117–120], e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', EFIT [73].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Albeit such important roles, baselines of  the measured magnetic signals often suffer from drifts in time mainly due to ca-  pacitor leakage in analogue integrators [121] and possibly radiations [122].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This  phenomenon is typically called ‘signal drift’ whose error must be eliminated in  order to conform with required accuracy for EFIT [73], magnetic control [123]  and neural network applications [5,7,124].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In this paper, we propose a novel algo-  rithm that removes the signal drifts in real-time only based on the experimentally  measured data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Most of previous researches resolve the signal drifts by modifying hardware  systems [53, 61, 125–128] which is a good solution but more cumbersome than  having a simple numerical solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We develop a novel numerical method capa-  ble of inferring how much magnetic signals drift and correcting the signal drifts  in real-time that can work with existing MDs without any modification of the  hardware systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The method is based on Bayesian probability theory [86], and finds the slope  and the offset of the drift sequentially, thus a ‘two-step drift correction method,’  during the initial magnetization stage, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', before the plasma initiation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This  allows one to have not only more accurate magnetic signals for post-discharge  analyses but also to improve real-time monitoring and control systems such as  real-time EFIT [75].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We note that existing numerical algorithms to correct such  drifts require post discharge information [63,64,125,126] which inhibits real-time  application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  In this work, we first present a detailed description of the Bayesian based  45  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2: An example of temporal evolutions of (a) currents in the PF coils,  (b) normal and (c) tangential components of magnetic fields measured by an  MPn and an MPt, respectively, and (d) magnetic flux measured by an FL  during the initial magnetization stage, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', t < 0, for a typical KSTAR  discharge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Information from the time interval d1 (d2) is used to estimate am  i  (bm  i ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  real-time two-step correction method in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We, then, provide how the  method is applied to existing KSTAR experimental data and how effectively the  method removes the signal drifts from the magnetic measurements in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4,  followed by discussions of our proposed method on the short pulse discharge  (< 40 sec in terms of poloidal field (PF) coil operation time) and long pulse  discharge (> 40 sec) as well as abnormal magnetic signals in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Our  conclusions are stated in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  46  (a)  5000  d2  d1  A  0  5000  10000  15  10  5  0  (b)  E  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='04  Bn 06  B  0  15  10  5  0  (c)  0  E  Bt 27  B  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='06  15  10  5  0  (d)  [Wb]  0  FL 23  3  15  10  5  0  time [sec]CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  Real-time drift correction based on Bayesian infer-  ence  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1 shows the locations of the magnetic diagnostics (MDs) with the sensor  numbers [2] at a certain toroidal position of KSTAR [129].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The blue dots are  the magnetic probes (MPs) measuring both normal (Bn measured by MPn) and  tangential (Bt measrued by MPt) components of the magnetic fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Note that  MP #10 does not exist at this toroidal position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The red circles are the flux loops  (FLs) measuring magnetic fluxes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' There are total of 45 FLs on KSTAR, but we  only show five sensor numbers out of 45 of them in the figure for simplicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  In this work, we focus on correcting the signal drifts in real-time for the total  number of 127 magnetic signals, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', 2 × 41 MPs for both MPn and MPt and 45  FLs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3  Two-step drift correction method  To remove the signal drifts, we deem a priori that the signals drift linearly in  time [121,126,130], which we substantiate our assumption based on the measured  data obtained during actual plasma operations in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Therefore, we take  the drifting components of the signals (ym  i ) from various types of MDs to follow:  ym  i = am  i t + bm  i ,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1)  where t is the time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' am  i  and bm  i  are the slope and the offset, respectively, of a  drift signal for the ith magnetic sensor of a type m (MPn, MPt or FL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Then,  our goal simply becomes finding am  i  and bm  i  for all i and m of interests before  a plasma starts or the blip time (t = 0) so that ym  i  can be subtracted from the  measured magnetic signals in real-time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Here, we assume that am  i and bm  i do not  change over one plasma discharge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' One can consider such linearization in time  as taking up to the first order of Taylor expanded drifting signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Therefore, we  have to examine carefully our proposed method for long pulsed discharges with  large nonlinearities, which is discussed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  47  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3: Examples of the proposed two-step drift correction method for the  MDs of (a) MPn #6, (b) MPt #27 and (c) FL #45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Left and middle panels  show the posteriors of the slope and the offset for each MD where the red dots  depict the maximum a posterior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Right panel shows both the original magnetic  signals with the signal drifts (red) and the drift corrected signals (blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  We use two different time intervals during the initial magnetization stage for  every plasma discharge to find am  i and bm  i , sequentially, thus the name ‘two-step  drift correction method.’ Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2 shows an example of temporal evolutions of  currents in the poloidal field (PF) coils, Bn and Bt measured by an MPn and an  MPt, respectively, and magnetic flux by an FL up to the blip time (t = 0) of a  typical KSTAR discharge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  During the time interval d1 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2, all the magnetic signals must be  constant in time because there are no changes in currents of all the PF coils as  well as there are no plasmas yet that can change the magnetic signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Therefore,  any temporal changes in a magnetic signal during d1 can be regarded as due to  a non-zero am  i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' With the knowledge of am  i from d1 time interval, we obtain the  48  Slope Posterior  Offset Posterior  Correction result  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='06  Drifted Bn  (a)  Corrected Bn  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='04  6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6  0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6  E  g  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4  B 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  0  0  0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='7 -1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='68-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='66-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='64-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='62  10  0  10  ×104  ×10-3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='15  1  Drifted Bt  (b)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='8  Corrected Bt  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  b0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6  b0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6  E 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='05  g  g  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4  B  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='05  0  0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='85  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='05  10  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='95  3  0  10  ×10-4  ×10-3  2  Drifted flux  (c)  Corrected flux  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='8  b 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6  6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6  0  P 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4  P 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4  2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  3  0  0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='7  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='022  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='0214  10  0  10  slope  offset  ×10-3  time [sec]CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4: Histograms of the validation errors for randomly selected 297  KSTAR discharges before (left panel) and after (right panel) the two-step drift  correction for (a) m =MPn measuring Bn, (b) m =MPt measuring Bt, and (c)  m =FL measuring magnetic fluxes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' MD # in horizontal axes denote the MD  sensor numbers, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', subscript i in ϵm  i,s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Colors represent the relative occurrence  normalized to a unity for every sensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Non-existing magnetic signals are  displayed as white streaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  value of bm  i  using the fact that all the magnetic signals must be zeros during  the time interval d2 because there are no sources of magnetic fields, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', all the  currents in the PF coils are zeros.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Summarizing our procedure, (1) we first obtain the slopes am  i based on the  fact that all the magnetic signals must be constant in time during d1 time interval,  and then (2) find the offsets bm  i based on the fact that all the magnetic signals,  after the linear drifts in time are removed based on the knowledge of am  i , must  be zeros during d2 time interval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  49  (a)  MPn(drift)  MPn(TwoStepMethod)  20  20  MPn36  MPn36  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9  10  10  val  E  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='8  1  0  10  20  30  40  10  20  30  40  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='7  (q)  Normalized counts  MPt(drift)  MPt(TwoStepMethod)  20  20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6  10  10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  val  E  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4  0  0  10  20  30  40  10  20  30  40  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3  (c)  FL25  FL(drift)  FL(TwoStepMethod)  40  40  FL25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  FL01  FL35  20  FL23  FL35  20  FL34  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  E  FL01  FL23  FL34  0  0  10  20  30  40  10  20  30  40  MD #  MD #CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5: Averaged validation errors ⟨ϵm  i ⟩ for 297 KSTAR discharges for (a)  the normal (MPn) and (b) the tangential (MPt) components of magnetic  signals, and for (c) the flux loop (FL) measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Blue circles indicate the  validation errors after the two-step drift correction method, and red crosses  mean the validation errors before applying our correction method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Bayesian inference  Bayesian probability theory [86] has a general form of  p (W|D) = p (D|W) p (W)  p (D)  ,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2)  where W is a (set of) parameter(s) we wish to infer, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', am  i and bm  i for our case,  and D is the measured data, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', measured magnetic signals during the time  intervals of d1 and d2 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The posterior p (W|D) provides us probability  of having a certain value for W given the measured data D which is proportional  to a product of likelihood p (D|W) and prior p (W).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Then, we use the maximum  a posterior (MAP) to select the value of W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The evidence p (D) (or marginalized  likelihood) is typically used for a model selection and is irrelevant in this study  50  (a)  × MPn(drift) O MPn(TwoStepMethod)  10  xX  8  Ox  6+  XX  0  val  XX  E  08  1  08  0  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  10  20  30  40  (q)  X  MPt(drift)  MPt(TwoStepMethod)  10  X  8  X  val  区  x0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='8  ++  E  X  8  X  1  00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  10  20  30  40  (c)  × FL(drift) O FL(TwoStepMethod)  60  X  10  X  X 0 X  X  8  0808 8 0x000888  880.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='0  E  1  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  10  20  30  40  MD #CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  as we are only interested in estimating the parameter W, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', am  i and bm  i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  We estimate values of the slope am  i and the offset bm  i based on Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2) in  two steps as described in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3:  Step (1) : p(am  i | ⃗D  m  i,d1) ∝ p( ⃗Dm  i,d1|am  i )p(am  i ),  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3)  Step (2) : p(bm  i | ⃗D  m  i,d2, am∗  i ) ∝ p( ⃗Dm  i,d2|bm  i , am∗  i )p(bm  i ),  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4)  where ⃗D  m  i,d1 ( ⃗D  m  i,d2) are the time series data from the ith magnetic sensor of a type  m (MPn, MPt or FL) during the time intervals of d1 (d2) as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  am∗  i  is the MAP, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', the value of am  i maximizing the posterior p(am  i | ⃗D  m  i,d1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Since  we have no prior knowledge on am  i and bm  i , we take priors, p(am  i ) and p(bm  i ), to  be uniform allowing all the real numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We mention that the posterior for  bm  i  should, rigorously speaking, be obtained by marginalizing over all possible  am  i , i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', p(bm  i | ⃗D  m  i,d2) =  �  p(bm  i | ⃗D  m  i,d2, am  i )p(am  i | ⃗D  m  i,d1)dam  i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' However, as we are only  interested in MAP rather than obtaining full probability distribution of bm  i , we  omit the marginalization procedure and simply use am∗  i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Furthermore, as we are  interested in real-time application, we must consider the computation time as  well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  With Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1), we model likelihoods, p( ⃗Dm  i,d1|am  i ) and p( ⃗Dm  i,d2|bm  i , am∗  i ), as  Gaussian:  p( ⃗Dm  i,d1|am  i ) =  1  �  (2π)L|σm  i,d1|  ×exp  �  �  �  �  �−  L�  tl∈d1  �  am  i (tl − t0) −  �  Dm  i,d1(tl) −  �  Dm  i,d1(t0)  ���2  2(σm  i,d1)2  )  �  �  �  �  � ,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5)  51  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  p( ⃗Dm  i,d2|bm  i ,am∗  i ) =  1  �  (2π)K|σm  i,d2|  ×exp  �  �  �  �  �−  K  �  tk∈d2  �  bm  i −  �  Dm  i,d2(tk) − am∗  i tk  ��2  2(σm  i,d2)2  �  �  �  �  � ,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6)  which simply state that noises in the measured signals follow Gaussian distribu-  tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Here, σm  i,d1 and σm  i,d2 are the experimentally obtained noise levels for the  ith magnetic sensor of a type m (MPn, MPt or FL) during the time intervals of  d1 and d2 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' tl and tk define the actual time intervals of  d1 and d2, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', tl ∈ [−6, −1] sec and tk ∈ [−14, −13] sec with L and K being the  numbers of the data points in each time interval, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' t0 can be any value  within the d1 time interval, and we set t0 = −2 sec in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  �  Dm  i,d1(t0)  �  ,  removing the offset effect to obtain only the slope, is the time averaged value of  Dm  i,d1(t) for t ∈ [t0 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5, t0 +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5] sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We use the time averaged value to minimize  the effect of the noise in Dm  i,d1(t) at t = t0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  With our choice of uniform distributions for priors in Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4),  MAPs for am  i  and bm  i , which we denote them as am∗  i  and bm∗  i , coincide with  the maximum likelihoods which can be analytically obtained by maximizing Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6) with respect to am  i and bm  i , respectively:  am∗  i  =  L�  tl∈d1  ��  Dm  i,d1(tl) −  �  Dm  i,d1(t0)  ��  (tl − t0)  �  L�  tl∈d1  [tl − t0]2  ,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='7)  bm∗  i  = 1  K  K  �  tk∈d2  �  Dm  i,d2(tk) − am∗  i tk  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='8)  Now, we have attained simple algebraic equations based on Bayesian probability  theory which can provide us values of the slope am  i and the offset bm  i before the  blip time, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', before t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  52  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  20  25  30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='05  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='05  B [T]  (a) MPt#14 shot#:17016  20  25  30  time [sec]  0  5000  10000  IPF [A]  (c) shot#:17016 PFcoils  22  24  26  28  30  32  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='05  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='05  (b) MPt#14 shot#:9387  Raw signal  LinearFit  TwoStepMethod  DischargeEnd  22  24  26  28  30  32  time [sec]  0  5000  10000  (d) Shot#:9387 PFcoils  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6: Qualitative comparisons between a typical chi-square linear fitting  method (blue line) and our proposed two-step method (red line) with the raw  (before correction) signal (green line) in (a) KSTAR shot #17016 and (b)  #9387 for the tangential component of magnetic signal MPt #14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (c) and (d)  show temporal evolutions of currents through KSTAR PF coils, and vertical  dotted lines indicate the time where we expect all the magnetic signals return  to zeros if there were no signal drifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Note that the blue line in (b) is almost  overlapped with the red line, but it is slightly more off from the zero compared  to the red line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  As will be discussed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4, we find slopes and offsets for all 127 MDs  shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1 within ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2 sec (before the plasma starts for each shot) using  MATLAB on a typical laptop within of the order of 1% average validation errors,  except few abnormal events which are also discussed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This means  that we can correct the drifts of magnetic signals in real-time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4  Results with KSTAR experimental data  As examples of the results of the proposed two-step drift correction method  described in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3 shows posteriors of the slopes (left panel) and  the offsets (middle panel) of a few MDs: (a) MPn #6 for the normal component of  53  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='7: Histograms of the degree of corrections (DoC’s), where signal drift  corrections are performed based on a typical chi-square linear fitting method  (left panel) and our proposed two-step drift correction method (right panel) for  (a) MPn measuring Bn, (b) MPt measuring Bt, and (c) FL measuring magnetic  fluxes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' MD # in horizontal axes denote the MD sensor numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Colors  represent the relative occurrence normalized to a unity for every sensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Same  sets of magnetic signals used to generate Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4 are used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Non-existing  magnetic signals are displayed as white streaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  the magnetic field Bn, (b) MPt #27 for the tangential component of the magnetic  field Bt and (c) FL #45 for the poloidal magnetic flux from KSTAR shot #8775.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The right panel shows results of removing the signal drifts (blue lines) from the  original magnetic signals (red lines), where the slopes and the offsets are selected  as the values corresponding to the maximum a posterior (MAP), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', the values  with the maximum probabilities depicted as red dots in the left and middle panels  of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' It is indisputable how effectively the proposed method removes the  signal drifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  For the purpose of real-time correction during a plasma operation, it is not  54  (a)  MPn(LinearFit)  MPn(TwoStepMethod)  100  100  DoC [%]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='8  100  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='100  10  20  30  40  10  20  30  40  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='7  (q)  MPt(LinearFit)  MPt(TwoStepMethod)  Normalized counts  100  100  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6  DoC [%]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4  100  100  10  20  30  40  10  20  30  40  (c)  FL(LinearFit)  FL(TwoStepMethod)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3  100  100  DoC [%]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  100  10  20  30  40  10  20  30  40  MD #  MD #CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  necessary to generate full posteriors based on Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3)-(4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6), rather we can  simply calculate the MAPs of the slope and the offset using Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='7) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  For a post-discharge analysis, having full posteriors is beneficial as they provide  quantitative uncertainties of the estimated slopes and offsets which are required  information to perform a proper error propagation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  It is worthwhile to mention that ‘drift signals’ in this work are actually  “corrected” signals in some degrees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' KSTAR executes a 60-sec-long shot with the  predefined waveforms on the PF coils to calibrate (to obtain the slopes and the  offsets of) magnetic signals without plasmas every morning during a campaign.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  As right panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3 shows such calibration retains observable non-zero  values in correcting drift signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Our two-step drift correction method is applied  in these ‘corrected’ drift signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Validation error: How good is the two-step drift correction method?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  As a measure of merit of the proposed two-step drift correction method, we define  a validation error ϵm  i,s of a KSTAR shot number s for the ith sensor of a type m  (MPn, MPt or FL) as follow:  ϵm  i,s = 100 ×  δm  i,s  max  ���f m  i,s(t)  ���  flat-top  [%],  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9)  ⟨ϵm  i ⟩ = 1  N  �  s  ϵm  i,s,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='10)  where f m  i,s(t) is a magnetic signal of the KSTAR shot #s, and a max [|·|]flat-top  operator selects the maximum absolute value of the argument during the flat-top  phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' δm  i,s is the mean value of the f m  i,s(t) after all the currents of the KSTAR  PF coils are returned to zeros, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', we expect δm  i,s to be zero if signal drifts are  correctly removed (or if there were no signal drifts).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  N is the total number  of KSTAR shots we have used to estimate the average values of the validation  errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The validation error defined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9) quantifies how close δm  i,s is to zero  relative to the maximum magnetic signal during a flat-top plasma operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We  55  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='8: Averaged validation errors as in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5 before (red crosses) and  after the correction (blue circle) for (a) the normal component (MPn) and (b)  the tangential component (MPt) of magnetic signals and for (c) flux loop  measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Left panels show the results for the 286 short pulse discharges  (< 40 sec), while the right panels show the results for the 11 long pulse  discharges (> 40 sec).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Note the different scales for y-axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  normalize δm  i,s because its absolute value near zero is arbitrary, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', we cannot  quantify how close to zero is close enough in absolute sense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Therefore, this  validation error provides us quantitative measure of effectiveness of the proposed  two-step drift correction method as well as goodness of the assumptions that  signal drifts are linear in time, and the slopes and the offsets do not change  significantly over one plasma discharge 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4 shows histograms of the validation errors for (a) the normal (MPn)  and (b) the tangential (MPt) components of magnetic signals, and for (c) the  2If we have a large validation error, then we do not know whether the estimated slope and  offset are inaccurate, or the assumptions are not valid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' On the other hand, if we have a small  validation error, then it is likely that the assumptions are valid, AND the slope and the offset  are accurately estimated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  56  (a)  Short pulse MPn  Long pulse MPn  40  40  60  10  10  X  ++  0  XO  X  X  val  ×0×x  E  00  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  10  20  30  40  10  20  30  40  (b)  Short pulse MPt  Long pulse MPt  25  25  X  X  X  10  10  8  ox  0  80  8  08  val  αx  8  X  E  Q0X  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4  10  20  30  40  10  20  30  40  (c)  Short pulse FL  Long pulse FL  100  100  X  10  10  X0X  8  80080080  0,α0:00  E  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  10  20  30  40  10  20  30  40  MD #  TwoStepMethod  MD #  DriftCHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9: Temporal evolutions of the magnetic signals measured by MPn  #07 (blue) and MPn #36 (red) for (a) KSTAR shot #16051 (abnormal MPn  #36) and (b) #16447 (normal MPn #36).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' These two magnetic sensors are  located at the up-down symmetric positions as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1, and the  discrepancy between MPn #07 and #36 in (a) are too large compared to (b) to  be explained by the slight up-down asymmetry of the KSTAR plasmas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Vertical dotted lines indicate where all the currents through the PF coils are  returned to zeros.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  flux loop (FL) measurements;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' while left and right panels show before and after  the two-step drift correction, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' MD # (horizontal axes) indicate the  MD sensor numbers, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', subscript i in ϵm  i,s, and vertical axes are the validation  errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Colors representing the number of relative occurrence within a magnetic  sensor are normalized to a unity for every sensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We have randomly selected  297 KSTAR discharges from the 2013 KSTAR campaign to the 2017 campaign  with a constraint that magnetic signals must exist after all the currents of the  PF coils are returned to zeros 3 so that we can estimate the validation errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Non-existing magnetic signals are displayed as white streaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' It is evident that  large validation errors are suppressed by our proposed method as the widths of  the histograms are reduced to in the range of smaller values of the validation  errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  3Existence of the data after all the currents of the PF coils are returned to zeros is necessary  to estimate the validation error, but it is not required for real-time application of our two-step  drift correction method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  57  (a) Abnormal MPn36 case  (b) Normal MPn36 case  Shot#16051  Shot#16447  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='04  E  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='06  B  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='02  0  0  10  0  10  20  10  0  10  20  time [sec]  time [sec]  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='MPn07  MPn36CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='10: Temporal evolutions of the magnetic signals measured by (a) FL  #25 (KSTAR shot #14262), (b) FL #27 (KSTAR shot #17320) and (c) FL  #35 (KSTAR shot #16369).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' These signals are basically noises (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3(c)  as an example of working FL signal).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Vertical dotted lines indicate where all  the currents through the PF coils are returned to zeros.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  There are a few notable magnetic sensors indicated by red(MPn #36, FL  #25, FL #27 and FL #35) and green(FL #01, FL #23 and FL #34) arrows in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' As we discuss in more detail regarding these magnetic sensors in the  discussion section (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5), we just briefly mention that red arrowed magnetic  sensors correspond to a case where the two-step drift correction method does not  work, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', large validation errors (large drift) before the correction is not improved  by the proposed method, due to abnormal magnetic signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Contrarily, we assert  that our proposed method works well even on the sensors with large drifts as long  as magnetic signals are not abnormal as indicated by green arrows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Note that  there are many similar cases, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', large validation errors before the correction and  small validation errors after the correction, for MPn and MPt signals as attested  by the data in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5 shows the averaged validation errors ⟨ϵm  i ⟩ for N = 297 (same data  sets used to generate Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4), showing that the validation errors are indeed  reduced for MPn and MPt signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Note that the drift corrected signal of MPt  #20 is worse than the value before the correction, but we argue that this is not  so much a problem since the validation error is still less than the others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' MPn  #16 is also worse after the correction, but the difference in the validation error is  negligibly small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Our method is less effective for the FL measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' However,  58  (a) Abnormal FL25  (b) Abnormal FL27  (c) Abnormal FL35  Shot#14262  Shot#17320  Shot#16369  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='01  0  0  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='011  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='02  10  0  10  0  20  40  60  10  0  10  time [sec]  time [sec]  time [sec]CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  large errors such as FL #01, #23, #25, #27, #29 and #34 are certainly reduced  by our proposed method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Note that Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5 summarize all the 297 KSTAR discharges whose  pulse length (in terms of PF coil operation time) is less than 90 sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5, we break down our results into short (< 40 sec) and long (> 40 sec) pulses,  and discuss the appropriateness and limitations of our proposed method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Degree of Correction: Is the two-step drift correction method better  than a typical linear fitting method?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  We now turn our attention to show how good our proposed method is compared  to a typical chi-square linear fitting method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The slopes (am  i ) and the offsets  (bm  i ) in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1) are estimated simultaneously (rather than the two-step method  as proposed) using the magnetic data from the time interval of d2 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Since our method is proposed for a real-time control purpose, we must compare  with the existing method that can be applied to a real-time control as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  As qualitative comparisons, we show two cases in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6: (a) and (c) for  KSTAR shot #17016, and (b) and (d) for KSTAR shot #9387.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (a) and (b)  show tangential component of magnetic signal MPt #14;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' while (c) and (d) show  temporal evolutions of currents through the KSTAR PF coils.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Vertical dotted  lines indicate the time where we expect all the magnetic signals return to zeros  if there were no signal drifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6(a) shows a case where a typical chi-  square linear fitting method (blue line) makes the error worse compared to the  raw data (green line), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', before any correction, while our two-step method (red  line) makes the error much smaller, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', closer to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6(b) shows a case  where a typical chi-square linear fitting method (blue line) works well bringing  the magnetic signal closer to zero, but our proposed method (red line) is even  better.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  For more thorough and quantitative comparison, we define a degree of cor-  rection (DoC) as  DoC [%] =  �  δm  i,s  �  raw −  �  δm  i,s  �  corr  �  δm  i,s  �  raw  × 100,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='11)  59  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='11: Temporal evolutions of the magnetic signals measured by (a) FL  #01 (KSTAR shot #17321), (b) FL #23 (KSTAR shot #13366) and (c) FL  #34 (KSTAR shot #17039).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Blue (green) line is the signal after (before) the  correction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Vertical dotted lines indicate where all the currents through the PF  coils are returned to zeros.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  where  �  δm  i,s  �  has the same meaning as in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='(4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The subscript ‘raw’ means  before the correction, and ‘corr’ stands for after the correction using either a  typical chi-square linear fitting method (denoted as Linear Fit) or our proposed  two-step drift correction method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' If the DoC is 100 %, then the correction is  perfect, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=',  �  δm  i,s  �  corr = 0 bringing the magnetic signal back to zero after the cor-  rection;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' while 0 < DoC [%] < 100 means that the applied method has corrected  the signal in finite degrees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' However, DoC [%] ≤ 0 corresponds to a case where  applied method makes no correction or even worse than a before-correction case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='7 shows histograms of the DoC’s for (a) the normal (MPn) and (b)  the tangential (MPt) components of magnetic signals, and for (c) the flux loop  (FL) measurements;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' while the right (left) panels show the results based on our  proposed two-step method (a linear fitting method).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Here, same sets of magnetic  signals as in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4 are used, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', 297 KSTAR discharges, and horizontal axes  and color contours (normalized counts) represent same as in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The calculated DoC’s support that our proposed method, in general, brings  the magnetic signals closer to zeros, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', the values of DoC’s are typically within  0 to 100 %.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In addition, it works better than a typical chi-square linear fitting  method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Again, corrections on the FL signals are less effective (but still effective),  which can be anticipated from the results of the validation errors shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  60  (a) Strongly drifted FL01 case  (b) Strongly drifted FL23 case  (c) Strongly drifted FL34 case  Shot#17321  Shot#13366  Shot#17039  1  Drifted flux  4  4  Corrected flux  0  [Wb]  2  2  1  0  0  2  2  2  3  0  50  100  10  0  10  20  0  20406080  time [sec]  time [sec]  time [sec]CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  As we do not claim that our proposed method is a perfect solution (rather we  claim that it is an easy and better solution), we argue that our proposed method  is a meaningful and valid solution based on the measures of the validation error  and the degree of correction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  Discussions  There exist at least two questions that need to be addressed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' First, how good or  applicable is the assumption of linear model as in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1)?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Mathematically, this  is a Taylor expansion of the true drift signals neglecting higher order (nonlinear)  terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Therefore, it is evident that our proposed method will not work for long  pulse discharges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This is also true even if we are able to obtain the second order  term, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', nonlinear term forcing the drift model to be nonlinear, since it is still  an approximation neglecting even higher order terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, a valid question we  need to raise is: how long a discharge can be without a failure of our proposed  method?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Another question is on the issue of abnormal magnetic signals which is briefly  mentioned in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' How do abnormal magnetic signals affect our proposed  method?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' What good does our proposed method do for abnormal magnetic sig-  nals?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Short pulse vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Long pulse  We define a discharge pulse length based on the PF coil operation time in this  work rather than a usual plasma operation time since we need to be able to  estimate the validation error for quantitative judgement, and validation error  can only be estimated after all the currents through the PF coils are returned to  zeros.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We have examined 286 short pulse (< 40 sec) discharges and 11 long pulse  (> 40 sec) discharges, summing up to 297 KSTAR discharges from 2013 to 2017  campaigns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Notice that the number of long pulse discharges are much smaller  than the short pulse ones because smaller number of long pulse experiments have  been carried out, and we have randomly selected KSTAR discharges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  61  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='8 shows the averaged validation errors ⟨ϵm  i ⟩ (defined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='10)) as  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5 for (a) the normal component (MPn) and (b) the tangential component  (MPt) of magnetic signals and for (c) flux loop measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Left and right  panels show the results for the short and long pulse discharges, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' It is  clear that our proposed method performs reasonably good corrections on the drift  signals if a discharge pulse length is less than 40 sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We also have scrutinized the  validation errors with a ten-second step, such as 0 − 10 sec, 10 − 20 sec, 20 − 30  sec, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', and we have confirmed that 40 sec is an impartial and justifiable pulse  length limitation for our proposed method to work properly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  For the investigated long pulse discharges, the two-step drift correction  method is modestly working for MPn and MPt signals, whereas the corrections  on the flux loop measurements make the results worse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' If we take a careful look  on the results of the flux loop measurements in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='8(c), we notice that the  validation errors before the correction (red crosses) are smaller for the long pulse  discharges compared to the short pulse discharges, while levels of the validation  errors after the correction (blue circles) are similar for short and long pulse dis-  charges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Although not conclusive, such results can be explained if a slope of the  drift signal, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', am  i  in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1), changes its sign over a long pulse discharge,  certainly a nonlinear effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Having discussed on the limitation of our proposed method due to a finite  nonlinear effect, we enunciate that our two-step drift correction method do work  properly (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4) and better than a typical linear fitting method (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4)  at least for the pulse length less than 40 sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Existing magnetic confinement  devices such as tokamaks, stellarators, linear machines with non-superconducting  magnetic coils, in general, would not suffer from such a limitation as pulse lengths  tend to be shorter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Therefore, our proposed method can readily be used for those  existing devices without modifying any hardware systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  For future machines such as ITER, DEMO or even fusion power plants, this  limitation must be overcome for steady-state long pulse discharges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' One possible  numerical solution is based on the laws of physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We can conceive correcting  the drift signals using physics constrained Bayesian probability theory [86] and  62  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Gaussian processes [131] since the measured magnetic signals must conform with  Amp`ere’s law (∇ × ⃗B = µ0 ⃗J ignoring the displacement current term as usual)  and Gauss’s law for magnetism (∇ · ⃗B = 0) as has been done for imputation of  faulty magnetic sensors [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Needless to say, the best solution will be based on  the development of new kinds of hardwares.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Abnormal magnetic signals  As mentioned before (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4) some of the magnetic signals are not corrected  by our proposed method as indicated by the red arrows in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', MPn  #36, FL #25, FL #27 and FL #35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This is due to malfunction of the magnetic  sensors for the investigated KSTAR discharges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9 shows the temporal evolutions of MPn #7 and #36, where these  sensors are located at the up-down symmetric positions as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Slight up-down asymmetry of KSTAR plasmas cannot explain such large dis-  crepancy in these two signals shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' If the sensor were working  properly, we would expect that these two magnetic sensors output similar tem-  poral behaviour as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9(b) which is a case with normal MPn #36  signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Therefore, we conclude that abnormal MPn #36 signal has contributed  such a large validation error even after applying our proposed method to the  signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='10 shows examples of FL #25, FL #27 and FL #35 signals selected  from three different KSTAR discharges to substantiate that these sensors are  not working properly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' They just show features of random noises compared to a  proper flux loop measurement as shown in the right panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Notice  the scale difference of y-axes in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Again, we conclude that  abnormal FL #25, FL #27 and FL #35 signals have resulted in large validation  errors even after applying our proposed method to the signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Contrarily, we have many cases for MPn, MPt and FL signals where the  large validation errors before the corrections become noticeably smaller after the  corrections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Such examples are indicated by the green arrows in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4(c), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=',  FL #01, FL #23 and FL #34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This means that large drifts are well corrected  63  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  by our proposed method as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  With these observations that abnormal signals have the large validation  errors both before and after the correction while normal signals have the small  validation errors after the correction even if the validation errors are large before  the correction, we argue that the estimated average validation errors can be used  to detect flawed magnetic sensors automatically without scrutinizing hundreds  of magnetic signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6  Conclusions  Magnetic measurements with many kinds of magnetic probes and flux loops  are indispensable for preparing, operating and analyzing magnetically confined  plasmas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Yet, they suffer from the drifts in many cases, and many engineers  and scientists are required to provide non-trivial efforts to correct the obtained  signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  We have proposed the two-step drift correction method which resolves the  drift problem in real-time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The method is based on Bayesian probability the-  ory and obtains necessary information to correct the drifts before each plasma  discharge initiates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This means that we can correct the drifts in real-time and  provide more accurate information for real-time control of plasmas such as for  real-time EFIT reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Our method is capable of correcting the drifts  within of the order of 1% average validation errors at least for the pulse length  (in terms of PF coil operation time) less than 40 sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Furthermore, the av-  erage validation errors can be used to automatically detect defected magnetic  sensors without going through hundreds of magnetic signals one-by-one to find  such flawed ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Many real-time applications are developed or proposed based on neural net-  works these days.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' If one attempts to utilize neural networks with magnetic signals  as inputs to the networks, then our method can also be heavily used for such  applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  64  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  Article II: Imputation  This approach deals with the imputation of faulty magnetic sensors with coupled  Bayesian and Gaussian processes to reconstruct the magnetic equilibrium in real  time4, which is largely taken from Ref [3], as a part of preprocessing magnetic  measurements via Bayesian inference and neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  This article describes a Bayesian modelling of a magnetic diagnostic system  to infer one (or more) missing magnetic signals based on Maxwell’s equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  This Bayesian model has been applied to normal and tangential magnetic pick-  up coils at the Korea Superconducting Tokamak Advanced Research (KSTAR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  These pick-up coils measure the poloidal magnetic field, respectively, normal  and tangential to the vacuum vessel wall where the coils are installed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' As the  pick-up coils are subject to impairment during plasma operations, faulty plasma  operations and incorrect data analyses can be caused by the missing magnetic  fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, the normal pick-up coils are forward-modelled together by Gauss’s  law for magnetism, and Amp`ere’s law is used to build a forward model for the  tangential pick-up coils.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  We divide the missing magnetic signals from the measured signals while  forward-modelling the signals in order that the missing signals can be inferred  consistently with the measured magnetic signals as long as they satisfy Maxwell’s  equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' These models reasonably work when the number of missing signals is  only one although we obtain an infinite number of solutions from the maximum a  posteriori method if there are more than one unknown of the missing components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Thus, Gaussian processes assisted forward models are introduced to restrict the  solution spaces by arbitrarily relating the missing and the measured signals with  each other based on non-parametric Gaussian process regressions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Therefore, all  of the signals can be represented as a function of one arbitrary missing signal,  and after the selected missing signal is determined from the forward model, then  multiple signals can be subsequently inferred with the Gaussian processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This  4S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Joung, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kim, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kwak, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Park, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Hahn, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Han, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kim, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Bak, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Lee and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='-c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Ghim  Review of Scientific Instruments, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='10 (7th May 2018), DOI:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1063/ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5038938  65  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  approach, therefore, can infer the missing fields even if they are more than one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Note that the results of Article I have been used here in order to preprocess the  signal drift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  Introduction  Magnetic pick-up coils installed on magnetic confinement devices such as toka-  maks and stellarators in addition to Rogowski and flux loop coils provide mag-  netic information such that high temperature fusion-grade plasmas can be con-  trolled in real time and that magnetic equilibria can be reconstructed for data  analyses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Neural networks also have been developed to provide the positions  of X-point and plasma boundary in real time [5, 7] where input signals to the  networks are magnetic signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Therefore, integrity of the magnetic signals is of  paramount importance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' As magnetic probes are subject to impairment during  plasma operations, faulty plasma operations and incorrect data analyses can be  caused by missing magnetic signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' For the case of neural networks trained with  full sets of magnetic signals, even a single missing signal may cause the networks  not to work properly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' [132]  We present how one can numerically infer, thus impute, missing magnetic  signals in real time based on a Bayes’ model [86] coupled with the Gaussian  Process [131] (GP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Likelihood is constructed using Gauss’s law for magnetism  and Amp`ere’s law and ensuring the consistency with the measured data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  A  couple of algorithms to detect faulty magnetic sensors in real time have been  developed, [133,134] and an inference method for just one faulty signal has also  been proposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' [134] Our proposed method in this work is tested with up to nine  non-consecutive missing magnetic probe signals installed on KSTAR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' [129] We  find that the method infers the correct values in less than 1 msec on a typical  personal computer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Then, a full set of raw data, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', inferred ones together  with measured ones, can be passed for real-time EFIT reconstruction [73, 75]  and neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Detailed descriptions on how we generate the likelihood and estimate the  maximum a posteriori of the Bayes’ model and how well the model infers the  66  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='12: Schematics of (a) the Amperian loop (blue line connecting blue  dots) for ∇ × ⃗B = µ0 ⃗J and (b) the pancake-shaped Gaussian surface with three  surfaces s1, s2 and s3 for ∇ · ⃗B = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Blue dots with the numbers in (a) indicate  the magnetic probes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' [2]  missing values as well as its limitation are provided in section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The limita-  tion on the Bayes’ model motivates us to use the GP discussed in section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3  which also has a certain drawback.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4, we present improved perfor-  mance, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', resolving the defects of the Bayes’ model and the GP while retaining  their advantages, achieved by coupling the Bayes’ model with the GP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' To test  our proposed method we assume that the intact magnetic signals are missing  and compare the measured signals with the inferred values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Our conclusion is  presented in section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  Imputation Scheme: Based on Bayes’ model  Magnetic probes, [2] depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='12(a) as the blue dots with the probe  numbers, installed on KSTAR at a certain toroidal location measure tangential  (Bt) and normal (Bn) components of the magnetic fields with respect to the  wall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Missing tangential components are inferred using Amp`ere’s law with the  measured plasma currents by Rogowski coils, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', ∇× ⃗B = µ0 ⃗J neglecting ∂ ⃗E/∂t  term based on a usual magnetohydrodynamic assumption, [135] and missing  67  (a)1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  (b)  6  9  8  7  17  6  18  Z  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  924284  ns2  E  Plasma  0  current  Bt  N  ns3  39  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  38  25  37  R  1  36  35  8  34  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  29  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  3  R [m]CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Log-Posterior  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='01  Bt 16 [T]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='01  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='02  Bt 15 [T]  1200  1000  800  600  400  200  Prob  [a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=']  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='13: Log-posterior, ln[p(B∗  ⊕|B⊕, Ω⊕)], of the missing magnetic signals  inferred by the Bayes’ model with the Maxwell’s equations, when two  tangential components (Bt from MPs #15 and #16) of the magnetic signals are  missing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thick black line marks where the posterior is maximum indicating  that infinite number of solutions are possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Data are inferred for KSTAR  shot #9010 at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1 sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  normal components using Gauss’s law for magnetism, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', ∇ · ⃗B = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  With the Amperian loop, the blue line connecting the blue dots shown in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='12(a), the tangential components of the magnetic signals Bt must approx-  imately satisfy  µ0Ip  =  �  L  ⃗B · d⃗l ≈  �  L  �  BMP  t  − BPF  t  �  dl  ≈  � Nm  �  m=1  ∆l∗  m  �  B∗MP  t,m − B∗PF  t,m  �  +  Ni  �  i=1  ∆li  �  BMP  t,i − BPF  t,i  �  �  =  λ∗T �  B∗MP  t  − B∗PF  t  �  +  λT �  BMP  t  − BPF  t  �  ,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='12)  where Ip is the total plasma current assuming that the effect of transient eddy  currents is negligible [136] which, in general, is acceptable at least during a flat-  top phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' BMP  t  and BPF  t  are the tangential components of the magnetic fields  measured by the magnetic probes (MP) and induced by the poloidal field (PF)  coils, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Note that KSTAR has 14 PF coils, and their contributions  are not perfectly canceled out due to change of integral form to a summation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Therefore, we remove the PF coil contributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' m and i are the indices for the  68  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  missing and the intact magnetic signals;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' whereas Nm and Ni are the total num-  bers of the missing and the intact signals, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' ∆l, an approximation of  dl, denotes the segment distance between the magnetic probes, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', the distance  between the consecutive probe numbers in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='12(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' ∆l is different for dif-  ferent probes as can be seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='12(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Superscripted asterisk means the  missing magnetic signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The last line in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='12) is just a reformulation of the  second line using the vector notations, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', λ(∗) = {∆l(∗)  i(m)} and B(∗)  t  = {B(∗)  t,i(m)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Moret et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' [107] has used Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='12) to obtain plasma currents in TCV tokamak;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  whereas we apply the same idea to obtain the missing magnetic signals based on  the plasma currents measured by Rogowski coils.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  For the normal components of the magnetic signals, we utilize the pancake-  shaped Gaussian surface as depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='12(b) consisting of three surfaces  s1, s2 and s3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  We force the Gaussian surface to be flat enough, so that the  magnetic fluxes through the surfaces of ˆns1 and ˆns3 cancel each other as ˆns1·ˆns3 =  −1, where ˆn is a unit normal vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Then, ∇ · ⃗B = 0 can be written as  0 =  �  s1+s2+s3  ⃗B · d⃗S ≈  �  s2  Bn dA ≈ ∆w  �  L  Bn dl,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='13)  where dA (= ∆w dl) is the differential area normal to the surface s2 (parallel to  Bn) with ∆w being the thickness of the Gaussian surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' dl is the differential  length encompassing the minor radius (or the poloidal cross-section) and essen-  tially same as the blue line in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='12(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Since ∆w ̸= 0, we have, again with  the vector notations,  0  =  �  L  Bn dl ≈ λ∗TB∗  n + λTBn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='14)  Assuming that the noise in magnetic signals is Gaussian, the likelihood is  p(B⊕|B∗  ⊕, Ω⊕)  =  1  √  2πσ ×  exp  �  −  �  λ∗TB∗  ⊕ −  �  Ω⊕ − λTB⊕  ��2  2σ2  �  ,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='15)  where B(∗)  ⊕ is either B(∗)MP  t  − B(∗)PF  t  or B(∗)  n  depending on whether we are inter-  ested in the tangential or normal component, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Likewise, the value of  69  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Ω⊕ is µ0Ip for the tangential component or simply 0 for the normal component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  σ is the noise standard deviation based on the measured magnetic signals with  the uncertainty propagation, and measured to be O(10−4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Finally, we obtain posterior as  p(B∗  ⊕|B⊕, Ω⊕) ∝ p(B⊕|B∗  ⊕, Ω⊕) p(B∗  ⊕|Ω⊕),  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='16)  providing us inferred values of the missing magnetic signals (B∗  ⊕) consistent with  the measured signals (B⊕ and σ) and the Maxwell’s equations (Ω⊕) assuming  that p(Ω⊕) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' With a uniform prior p(B∗  ⊕|Ω⊕), it is obvious that we obtain  infinite number of solutions from maximum a posteriori (MAP) method if we  have more than one unknown of the same component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In simpler words, we have  only one equation for the tangential (Amp`ere’s law) or the normal (Gauss’s law  for magnetism) component;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' thus, more than one unknown of the same component  results in infinite number of solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='13 shows an estimated log-posterior  distribution, ln[p(B∗  ⊕|B⊕, Ω⊕)], where we have removed two Bt measurements,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', probe numbers #15 and #16, and confirms this effect clearly as depicted  by the thick black line corresponding to the MAPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This is the limitation of  the imputation scheme solely based on the Bayes’ model consistent with the  Maxwell’s equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3  Based on Gaussian Process  Motivated by the limitation of the Baye’s model with the Maxwell’s equations,  we introduce Gaussian Process [131] (GP) in our imputation scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We express  the probability distribution of B∗ (Nm × 1 column vector) given the measured  data B (Ni × 1 column vector) without any analytic expression of the data a  priori as described elsewhere [131,137]  p (B∗|B) = N  �  ¯¯K∗  ¯¯K−1B,  ¯¯K∗∗ −  ¯¯K∗  ¯¯K−1  ¯¯K∗T�  ,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='17)  70  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  10  20  30  40  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  B [T]  (a)  10  20  30  40  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  (b)  measured  GP-predicted  10  20  30  40  probe #  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='02  0  B [T]  (c)  10  20  30  40  probe #  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='02  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='02  (d)  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='14: Successful GP predictions (red crosses) compared with the actual  data (blue circles) for (a) Bt and (b) Bn at 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='70 sec of KSTAR shot #9010  where we remove nine non-consecutive signals (indicated by red arrows)  simultaneously to examine the proposed GP imputation scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' On the other  hand, if the magnetic signals are spatially varying fast such as (c) Bt of MPs  #15 and #16 and (d) Bn of MPs #17 and #18 at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='10 sec of the same shot,  the GP imputation scheme fails to infer the correct values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  with  ¯¯K ≡  ¯¯K (X, X) + σ2  n¯¯I,  (Ni × Ni matrix)  ¯¯K∗ ≡  ¯¯K (X∗, X) ,  (Nm × Ni matrix)  ¯¯K∗∗ ≡  ¯¯K (X∗, X∗) ,  (Nm × Nm matrix),  where N( , ) is the usual notation for a normal distribution, and  ¯¯I the iden-  tity matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' σ2  n ∼ O(10−4) is determined by treating it as a hyperparameter  for the numerical stability during matrix inversion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' [131, 138, 139] Recall that  Ni(Nm) is the total number of intact (missing) magnetic signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Here, X(∗) is  the 2×Ni(Nm) matrix containing the physical positions of all the intact (missing)  71  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  magnetic probes in two dimensional space, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', physical R and Z positions at a  fixed toroidal location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The ith and jth component of a covariance matrix  ¯¯K(∗ or ∗∗) is defined as  K(∗ or ∗∗)  ij  �  x(∗)  i , x(∗)  j  �  =  σ2  f exp  �  �−1  2  �  x(∗)  i  − x(∗)  j  �T  �  ℓ2  R  0  0  ℓ2  Z  �−1 �  x(∗)  i  − x(∗)  j  �  �  � ,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='18)  where x(∗)  i  is the ith column vector of the X(∗), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', 2×1 column vector containing  the physical positions of the ith magnetic probe in R and Z coordinate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Hyperpa-  rameters σ2  f, ℓR and ℓZ are the signal variance and the length scales in R and Z  directions, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' These hyperparameters govern the characteristic of the  Gaussian process, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='17), and we select the hyperparameters such that  the evidence p(B) is maximized [140] with an assumption [141] of ℓR = ℓZ for  simplicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' As searching for the hyperparameters may become time consuming,  thus not applicable for real-time control, one can obtain these values beforehand  using many existing plasma discharges as for the case of density reconstruc-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' [138] Once we have values for the hyperparameters, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', σf ∼ O(10−2) and  ℓR = ℓZ ∼ O(10−1) in this study, we use Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='17) to obtain the values of the  missing magnetic signals B∗, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', B∗ =  ¯¯K∗  ¯¯K−1B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='14(a) and (b) show that our proposed GP imputation scheme suc-  cessfully infers the missing magnetic signals both for (a) Bt and (b) Bn where the  red crosses are the inferred values and the blue circles are the measured (actual)  values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We have examined our scheme with up to nine non-consecutive missing  signals indicated by the red arrows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  We have also found that the GP imputation scheme fails to infer the correct  values if the magnetic signals are varying fast in space as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='14(c)  for Bt and (d) for Bn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This is the limitation of the GP-only imputation scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  72  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='15: (a) Bt from MPs #15 and #16 and (b) Bn from MPs #17 and  #18 from KSTAR shot #9010 at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1 sec as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='14(c) and (d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Green triangles obtained by the Bayes’ mode with the GP match the measured  values (blue circles) well, while the GP-only method (red crosses) fails to do so  as has been discussed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Comparisons of temporal evolutions for (c)  Bt from MP #15 and (d) Bn from MP #17 from KSTAR shot #9427 where  blue line is the measured values, red line for the GP-only and green line for the  Baye’s model with the GP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Green lines agree well with blue lines well  throughout the whole discharge including ramp-up and ramp-down phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4  Based on Bayes’ model coupled with Gaussian Pro-  cess  As we find the limitations of the Bayes’ model (infinite number of solutions  for more than one missing magnetic signal) and the GP (incorrect inference for  spatially fast-varying missing magnetic signals), we resolve such weaknesses by  combining the two schemes: for instance, if we have seven missing signals, we  select one missing signal among the seven.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Then, we use the GP to infer the non-  selected six missing ones based on the intact signals together with the selected  missing one which is inferred based on the Bayes’ model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  73  (h)0  GD  E-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='02  B  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='02  Q  10  20  30  40  10  20  30  4  probe #  probe #  (c)  (d)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  Bn17 (GP)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  (GP-Bayes)  E  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='05  (Measured)  0  B  Bt15 (GP)  0  (GP-Bayes)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='05  (Measured)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  0  2  4  6  0  2  4  6  time [sec]  time [sec]0CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Let us denote the selected missing magnetic signal as B∗  k, and define ˇX∗ to  contain the positions of R and Z for all the missing magnetic signals except the  ones corresponding to B∗  k resulting in 2 × (Nm − 1) matrix;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' while ˇX containing  those of B∗  k in addition to intact magnetic signals becoming 2 × (Ni + 1) matrix,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', concatenate those of B∗  k at the last column of X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' With ˇX∗ and ˇX our  covariance matrices become  ˇ  ¯¯K ≡ ˇ  ¯¯K  � ˇX, ˇX  �  + σ2  n¯¯I, ((Ni + 1) × (Ni + 1) matrix)  ˇ  ¯¯K∗ ≡ ˇ  ¯¯K  � ˇX∗, ˇX  �  ,  ((Nm − 1) × (Ni + 1) matrix)  ˇ  ¯¯K∗∗ ≡ ˇ  ¯¯K  � ˇX∗, ˇX∗�  ,  ((Nm − 1) × (Nm − 1) matrix).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  We separate out the last column of the (Nm − 1) × (Ni + 1) matrix of ˇ  ¯¯K∗ ˇ  ¯¯K−1  containing B∗  k information and denote this column vector as L and the rest of  the matrix, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', without the last column of ˇ  ¯¯K∗ ˇ  ¯¯K−1, be  ¯¯Λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Since we have found  that B∗ =  ¯¯K∗  ¯¯K−1B in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3, we obtain  ˇB∗  ⊕ =  ¯¯ΛB⊕ + LB∗  k⊕,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='19)  stating that once B∗  k is determined, then all the other missing magnetic signals  ˇB∗ are determined by the GP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We find the unknown B∗  k using the Bayes’ model  where it is perfectly applicable since we have only one missing signal as discussed  in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, λ∗TB∗  ⊕ in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='15) is  λ∗TB∗  ⊕  =  λ∗  kB∗  k⊕ + ˇλ∗T ˇB∗  ⊕  =  �  λ∗  k + ˇλ∗TL  �  B∗  k⊕ + ˇλ∗T  ¯¯ΛB⊕,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='20)  where λ∗  k and ˇλ∗ are the segment distances for the selected missing one B∗  k⊕ and  for the rest of the missing signals, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Slightly modifying Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='15) to include the GP scheme, our likelihood for  the Bayes’ model, then, becomes  p(B⊕|B∗  k⊕, Ω⊕)  =  1  √  2πσ exp  � 1  2σ2  ��  λ∗  k + ˇλ∗TL  �  B∗  k⊕  −  �  Ω⊕ − λTB⊕ − ˇλ∗T  ¯¯ΛB⊕  ��2�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='21)  74  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  The likelihood now contains only one unknown B∗  k, and all the rest of the missing  signals are treated as known ones using the GP, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='19).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  We construct the prior p(B∗  k⊕|Ω⊕) to follow a Gaussian distribution with  the mean of Bpair  k⊕ and the variance of σ2  prior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bpair  k⊕ is the signal of the magnetic  probe from the up-down symmetric position of the missing signal B∗  k⊕.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' MPs  #6 and #37, MPs #12 and #31, and MPs #19 and #24 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='12(a) are  examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We use such a paired magnetic signal as a prior mean of the missing  signal because KSTAR discharges are quite up-down symmetric, so that a typical  correlation between the paired signals is about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Regarding the prior variance  σ2  prior, to minimize possible biases we set it to be 500 which means that the prior  distribution is largely uniform since the actual values of the magnetic signals are  not much larger than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1 T as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  We finally obtain the posterior following Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='16) as  p(B∗  k⊕|B⊕, Ω⊕)  ∝  exp  �  ��−  �  B∗  k⊕ − B⋆  k⊕  �2  2σ2  GP  −  �  B∗  k⊕ − Bpair  k⊕  �2  2σ2  prior  �  �� ,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='22)  where  B⋆  k⊕  =  Ω⊕ − λTB⊕ − ˇλ∗T  ¯¯ΛB⊕  λ∗  k + ˇλ∗TL  σ2  GP  =  �  σ  λ∗  k + ˇλ∗TL  �2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Thus, maximum a posteriori (MAP) denoted as BMAP  k⊕  can be analytically esti-  mated and is  BMAP  k⊕  =  �  B⋆  k⊕  σ2  GP  + Bpair  k⊕  σ2  prior  � � 1  σ2  GP  +  1  σ2  prior  �−1  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='23)  with the posterior variance σ2  post = (1/σ2  GP + 1/σ2  prior)−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Once BMAP  k⊕  is found,  then all the other missing signals are determined by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='19).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This completes  the imputation process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  To validate our proposed imputation scheme based on the Bayes’ model  coupled with the GP, we take the same examples shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='14(c) and  75  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  (d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='15(a) Bt from MPs #15 and #16 and (b) Bn from MPs #17 and  #18 show considerable improvements where the green triangles inferred by the  Bayes’ model coupled with the GP are very close to the blue circles which are  the measured values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Again, the red crosses obtained only by the GP fails to do  so.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Fig 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='15(c) Bt from MP #15 and (d) Bn from MP #17 from KSTAR shot  #9427 show temporal evolutions of the inferred values where the blue line is the  measured values, the red line for the GP only and the green line for the Bayes’  model with the GP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Typically, the GP-only method fails largely during ramp-up  and ramp-down phases while it is not too bad during the flat-top phase;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' whereas  the Bayes’ model with the GP finds the correct values throughout the whole  discharge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='23) contains no unknowns which means that BMAP  k⊕  can be estimated  in real-time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In fact, our proposed method takes less than 1 msec on a typical  personal computer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The hyperparameters are prepared beforehand based on  many previous discharges, and missing or faulty signals can be identified [133,134]  in real-time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' What one requires to do is simply to perform the following three  steps in real-time: (1) select a missing signal (B∗  k⊕) among all the missing ones  (B∗  ⊕), (2) estimate noise levels (σ) of the measured signals and (3) apply Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='23) and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='19) to impute more than one missing magnetic signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Good  choice of a missing signal (B∗  k⊕) is from the ones that spatially vary fast if they  exist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In KSTAR such signals are Bt from MPs #15 and #16, and Bn from MP  #17 and #18 in almost all cases, if not all.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  Discussion and Conclusion  We have developed and presented a real-time inference scheme, thus imputation  scheme, for missing or faulty magnetic signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Our method, Bayes’ model with  the likelihood constructed based on Gauss’s law for magnetism and Amp`ere’s law,  coupled with the Gaussian process, allows one to infer the correct values even if  more than one missing signal that is spatially varying fast exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The coupled  method outperforms the Baye’s-only and the GP-only methods without losing  76  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  their own advantages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We have examined our method up to nine non-consecutive  missing magnetic signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The proposed method takes less than 1 msec on a typical personal computer,  so that the method can be applied to fusion-grade plasma operations where real-  time reconstruction of magnetic equilibria is crucial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' It can also be used for a  neural network trained with a complete set of magnetic signals without fearing  the possible loss of magnetic signals during plasma operations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  As a possible future work, developing a real-time searching algorithm for  the hyperparameters in the Gaussian process that optimizes the evidence will be  beneficial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Although results with the predetermined hyperparameters based on  many previous discharges can be satisfying, the hyperparameters specific to a  current discharge may provide much better plasma controls especially for those  discharges that we have not yet explored much.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In addition, including the effect  of eddy currents can improve the performance of our method especially during  the ramp-up and down phases and disruptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  77  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3  Article III: Preprocessing flux loop  This approach deals with A deep learning approach to recover hidden consis-  tency of KSTAR flux loop signals5, which is largely taken from Ref [142], as a  part of preprocessing magnetic measurements via Bayesian inference and neural  networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  This article describes a deep neural network applied to the KSTAR poloidal  flux loops to recover consistency between the measured flux signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The poloidal  magnetic signals are typically utilized to reconstruct a plasma equilibrium which  is a state when a plasma is assumed to be in an ideal magnetohydrodynamic  equilibrium state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The plasma equilibrium can be obtained by iteratively solv-  ing the Grad-Shafranov equation, together with the measured poloidal magnetic  fields and fluxes: first estimate toroidal current density from the Grad-Shafranov  equation by using assumed equilibrium;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' second, calculate magnetic signals from  the current density, and then update the current by comparing the calculated  signals with the measured signals based on the Grad-Shafranov equation;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' finally,  update the equilibrium, and repeat these procedure until the calculated signals  are close enough to the measured signals within a criterion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  However, the reconstruction procedure is often abortive when all of the  measured magnetic signals (the fields and the fluxes) are used simultaneously  although impaired signals are expelled from the reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Especially, the  intact signals measured from flux loops cannot be utilized at once since they yield  unreasonable reconstructions, making humans pick only a few of them meticu-  lously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The deep neural network is developed to compensate for the inconsistency  between the flux loops and generate cleaned fluxes as well as the missing fluxes  from its output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, the network generated fluxes can be used for the recon-  struction procedure at the same time, and the reconstruction results are quite  reasonable compared to existing equilibrium databases reconstructed by humans  with their careful decisions about selections of the magnetic signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Note that  5S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Joung, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kim, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Han, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bak and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='-c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Ghim  Scientific Reports, (2022), in preparation  78  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Article V employs this approach in order to reconstruct plasma equilibria solely  based on neural networks without depending on humans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  Introduction  Plasma is an ionized gas which is a fuel of thermonuclear fusion [37,38], a sus-  tainable and clean energy source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Tokamak is a device that confines the plasma  in the magnetic fields to help the fusion reactions continue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, it is impor-  tant to measure magnetic signals inside the tokamak generated from the magnet  coils as well as the plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' To this end, an induction coil-type diagnostics with  the integrator [48] are widely used for measuring the poloidal magnetic field,  the magnetic flux, and the plasma current in various magnetic confinement de-  vices [2,49,104–109,111] including ITER, the International Thermonuclear Ex-  perimental Reactor [110], which is built to prove the possibility for constructing  the fusion power plant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Basically, magnetic diagnostics are installed on the vacuum vessel wall of the  tokamak far away from the plasma since the plasma temperature can reach about  100 million degrees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, the magnetic data solely contains indirect information  about the internal properties of the plasma related to the plasma geometry or  large-scale magnetohydrodynamic (MHD) activities [73,112–120].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Here we focus  on real-time control of the plasma shape and position which are obtained from  the plasma reconstruction by solving the Grad-Shafranov (GS) equation [43,44]  where the GS equation is derived based on the MHD equation in equilibrium  state [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' To this end, KSTAR [1] has 84 magnetic probes and 45 flux loops  (FLs) which measure the poloidal magnetic fields and fluxes, respectively [2,49].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  However, compared with the probes, there are inconsistencies between the  magnetic fluxes hindering the plasma from being reconstructed reasonably, al-  though we can compensate impaired probes [3] as well as signal drifts (signals  tending to unintentionally increase or decrease over time) in magnetic measure-  ments [78] through Bayesian inference [86].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' These inconsistencies give rise to the  dependency on human expert knowledge which possibly causes biases to select  the specific signals for the reconstruction process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  79  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Thus, with tensorflow [103], we propose a method to recover the consistency  based on the capability of deep neural networks which are able to learn differ-  ential equations by themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Recently, this capability was used for various  research fields such as fluid dynamics [143–145], quantum mechanics [146–149],  and plasma physics [150].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' By means of differentiating neural networks analyti-  cally with respect to their inputs, we present that the network can produce the  consistent magnetic fluxes based on the measured magnetic fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Using the  network outputs, we also prove that reconstructing plasma equilibrium at the  level of the expert is plausible without relying on the expert knowledge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  Magnetic data collection  We collect 701 shots among the KSTAR 2020 year campaign experiments whose  discharge length is greater than or equal to 10 sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In each shot, the magnetic  signals from 200 msec to the half of the whole discharge length are collected  at intervals of ∼10 msec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, we extract a total of 369,610 time slices for  the magnetic probes, the flux loops, the plasma current, and the poloidal field  coil currents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' To train the neural network, we have a total of 13,675,570 (=  37×369, 610) magnetic fields normal to the wall, and 14,414,790 (= 39×369, 610)  magnetic fields tangential to the wall, and we also have a total of 11,827,520  magnetic fluxes obtained from 32 FLs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 90% of these collected signals are used  for the network training, 5% for the network validation, and the remaining 5%  for the test dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3  Domain knowledge regarding the poloidal magnetic  field  The magnetic fields normal and tangential to the wall where the probes are  installed can be converted into the R and Z components of the fields based on  the angle (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 1A, upper right) between the normal direction to the wall and the  80  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='16: Schematic diagram of FL recovery via a deep neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (A)  The positions of magnetic measurements on the KSTAR poloidal cross-section  where both Bn and Bt exist (blue dots), only Bn exists (pink dot), only Bt  exists (green dots), and FLs exist (red crosses).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (B) Schematics of the deep  neural network whose output stands for the flux function converted into BR  and BZ through analytic differentiation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (C) Temporal evolution of the plasma  current for KSTAR 24445 shot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (D–G) The network results (blue area) at the  red dotted lines in (C) are presented compared with the measured signals (red  dots).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' First row is for BR, second row is for BZ, and the last row is for FL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  R direction on the R–Z plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, we compute BR and BZ as shown below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  BR,i = Bt,icos(θi) − Bn,isin(θi)  BZ,i = Bt,isin(θi) + Bn,icos(θi)  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='24)  where the subscript i denotes the channel number of the probes, Bt is the tangen-  tial magnetic field, and Bn is the normal magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' From the Gauss’s law  for the magnetism, we can relate the BR and BZ with the poloidal flux function,  81  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  D  G  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  time [sec]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  Rm  FL Rocovory  Deep neural network  BrBz  BrIBz  DiffNN  @ref  NNCHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='17: Statistical analysis of the trained network with test dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (A)  Statistics of the coefficient of determination between the measured and the  network BR (left) and BZ (right) from the ramp-up phase, and (B) from the  flat-top phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (C) Distributions of the plasma current measured from the  Rogowski coil (purple line) and the network (purple area) of the ramp-up phase  (top) and the flat-top phase (bottom).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (D) Using 24445 shot, Statistics on the  difference between the measured ψ and the network ψa  rel of the ramp-up phase  (blue) and the flat-top phase (red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  ψ, based on the vector potential on the cylindrical coordinates, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=',  BR,i = − 1  R  dψ  dZi  BZ,i = 1  R  dψ  dRi  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='25)  where the subscript i denotes the channel number of the probes, Ri and Zi are  the position where the probe is on the R–Z domain, and ψ is the poloidal flux  function which is equal to the poloidal flux measured from the flux loop divided  by 2π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4  Modelling the network architecture  Based on the relationship between the magnetic field and the flux, we construct  the network architecture whose output is the flux function turning out to be BR  and BZ through the analytic differentiation of the network (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='16B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The  82  R2=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9997  R2=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9999  R2=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9988  R2=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9997CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  network is a 4-layer fully-connected network with 100 hidden neurons and one  bias per hidden layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The network weights are randomly initialized [151], and  the activation function is the swish function [152], i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=',  swish(x) = x × sigmoid(x) =  x  1 − exp (−x)  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='26)  The cost function for training the network is e = e1 + e2 where e1 is built with  BR and BZ from the probe positions having both the tangential and the normal  fields (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='16A, blue dots)  e1 = 1  N  N  �  i=1  �  BNN  R,i − BMD  R,i  �2 + 1  N  N  �  i=1  �  BNN  Z,i − BMD  Z,i  �2  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='27)  where N is 11,985,084 which is the total number of BR and BZ signals in the  training set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' On the other hand, e2 is for the normal (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='16A, pink dot) or  the tangential probes (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='16A, green dots) where there is no signals being  paired, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=',  e2 = 1  N2  N2  �  i=1  ��  αt(n),iBR,i + βt(n),iBZ,i  �NN − BMD  t(n),i  �2  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='28)  where the subscript i is the no-pair channel number of the probes, N2 is 1,330,596  which is the number of the no-pair signals in the training dataset, αt(n) is sin(θ)  (or cos(θ)), and βt(n) is cos(θ) (or −sin(θ)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The superscript NN stands for the  network results, and the superscript MD refers to the measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Addition-  ally, since the network output only learns the relative value for ψ, we process ψrel  to be the absolute value ψa  rel as follows,  ψa  rel,i = ψrel,i − 1  45  45  �  i=1  ψref,i + 1  32  32  �  i=1  ψFL,i  2π  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='29)  where the subscript i means the channel number of the flux loops, and ψFL is  the poloidal flux measured from the flux loops.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  83  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='18: Comparison of equilibrium reconstructions based on the network  (black), the expert (green) and the novice (orange).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (A) Left: comparison of  the equilibrium results at 498.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5 msec of 24445 shot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Right: a novice producing  equilibrium overlaid with the plasma boundaries from the network and the  expert (dotted lines).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (B) Spatial profiles of the plasma current density at Z=0  location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (C) Chi-square results of the ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (D-F) Same results with (A-C) at  2704.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3 msec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  Recovering flux loop consistency via the deep neural  network  To restore the consistency between magnetic fluxes, we apply the method using  the deep neural network in which the network output itself is learned by training  the derivatives of it [150].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' From the relationship between the magnetic fields and  the magnetic fluxes based on Maxwell’s equations, we can model the network  architecture (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='16B) whose output is the poloidal magnetic flux function,  ψ, which can be transformed into the poloidal magnetic fields in the R and Z  84  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  Current density (Z=0)  80  60  1  1  J [A/cm"]  40  20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5 [m]  20  0  0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='7  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  N  R [m]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='55  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  R [m]  R [m]  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  Current density (Z=0)  150  100  [A/cm′  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  50  [w]  0  0  0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='7  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3  N  R [m]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  R [m]  R [m]CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  direction, BR and BZ, via the analytic differentiation of the network ψ, while the  network is fed with the spatial positions R and Z, the magnetic fields, the plasma  current, and the poloidal field coil currents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Since the network ψrel trained from  its derivatives has no information about the absolute value, we turn ψrel into  ψa  rel to have the information by using the measured FL signals (see Methods  subsection ‘Domain knowledge regarding the poloidal magnetic field’).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Using 36 BR and 36 BZ signals at the blue dots in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='16A which are  computed based on the normal and tangential components of the poloidal mag-  netic fields with respect to the vessel wall where the probes are installed, we  generate the network results qualitatively based on KSTAR 24445 shot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Typi-  cally, the plasma current which is the induced current in the plasma starts being  discharged at 0 sec, reaches the flat-top phase where the current is approximately  in equilibrium state after passing through the ramp-up phase where the current  increases in time (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='16C, black line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' During the discharge, we choose four  different time slices (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='16C, red dotted lines) to generate the network results  with its uncertainties [153] (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='16D–G, blue areas) in comparison with the  measured magnetic data (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='16D–G, red dots).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The first and second rows in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='16D–G shows the spatial profiles of BR  and BZ where the x-axes stand for the probe channel numbers, while the figures  in the last row represent the spatial profiles of ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We can find that the measured  ψ are sporadically scattered, being laid within the network uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We  presume that this scatteredness is not due to the mechanical uncertainties of the  FLs since the uncertainty scale of the FL is about 10−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, this makes us  confirm that the scatteredness is elminated in the network results, meaning that  the network can recover the inconsistency between the FL signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6  Quantitative assessment of the network  So far, we have qualitatively demonstrated that the consistency between FLs  is reasonably recovered through the deep neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Here we show that  statistical approaches to evaluate the network quality by using the test dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  First, we use the R2 metric, the coefficient of determination [154], for validating  85  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  the network generality based on the training targets, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', BR and BZ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We present  that the network BR and BZ signals from the 36 probes each show a fairly linear  relation with those of the measurements for the ramp-up phase (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='17A;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Left:  R2 of BR = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9997, Right: R2 of BZ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Similarly, the R2 results for the  flat-top phase also show considerable linearity (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='17B;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Left: R2 of BR =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9988, Right: R2 of BZ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9997), indicating that our network can fully imitate  the test dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  To validate the network quality including the excluded BR and BZ signals  out of the 42 probes each, we estimate the plasma current from the poloidal  magnetic fields tangential to the vessel wall by computing the network BR and  BZ along with the Ampere’s law [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Compared with the distributions of the  measured plasma current at the ramp-up (top) and the flat-top phase (bottom)  (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='17C, purple lines), the network quite well picks up the features of the  plasma currents from various KSTAR discharges (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='17C, purple areas).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In  addition, we calculate the differences between the measured ψ and the network  ψa  rel over KSTAR 24445 shot for the ramp-up (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='17D, blue bars) and the  flat-top (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='17D, red bars) phases in order to indicate that the network can  produce a similar level of the ψa  rel with respect to the measurements over the  discharge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='7  Equilibrium reconstruction using the network mag-  netic flux  We now demonstrate that the use of the network can help the plasma be recon-  structed at the level of the expert without depending on the expert decisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Thus, we reconstruct the plasma equilibria using KSTAR 24445 shot based on  the network results, the expert selection, and a novice’s trial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Note that, in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='18, all the black colors refer to the network results, while the green colors are  for the expert, and the orange colors are related to the novice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' To reconstruct  the plasma, we use an algorithm called EFIT [73] which is a reconstruction code  widely used in various tokamaks [74,79,155–157], where we use all 45 recovered ψ  86  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  signals for the network case, but, the expert only uses 8 selected FL signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' For  mimicking the novice’s trial, we randomly choose 15 FL signals for the ramp-up  phase, and 21 FL signals for the flat-top phase which account for half of the total  number of the FL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Overall, we can find that the network helps to pick up the flux surfaces (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='18A and D) and the current density profiles (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='18B and E) comparable to  the expert’s reconstructions, while the novice creates unreasonable and signifi-  cantly different reconstruction results although the plasma boundaries are similar  with those of the network and the expert (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='18A and D, dotted lines).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This  indicates that the plasma reconstruction can be highly distorted by the recon-  struction attempts of the unskilled, which possibly gives an adverse impact to  the real-time control of the plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Furthermore, as a result of χ2 = ((ψEFIT − ψused)/σ)2 (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='18C and  F), we can clearly distinguish the reconstruction qualities such that the χ2 for  the novice’s trial is significantly higher than those of the expert as well as the  network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' It also would be noted that the total summation of the network χ2 for  the ramp-up case (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='18C) is 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='78 which is lower than the expert’s case, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=',  the total sum of χ2 = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='77 where only 8 signals participate in the reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  This informs that the expert-level of the reconstruction can be achieved by even  non-experts if the network results are utilized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, we can expect that we  can exclude the expert decision during the reconstruction so that a complete  automation of the process potentially comes true.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='8  Discussion  We have developed a method that recovers the flux loop consistency by means  of the network ability to be able to understand differential equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Based on  how the network output is learned by itself from its derivatives, we have applied  this approach to produce the poloidal flux function in order to remove its innate  scatteredness based on the poloidal magnetic fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Through the neural network,  the consistent flux signals are available to be used for the plasma reconstruction  where the expert-quality of the reconstruction can be attainable with no needs  87  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  to become proficient about magnetic diagnostics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In conclusion, we can expect  the fully automated reconstruction process can possibly be realized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  As future works, we deal with the other magnetic measurements installed  in KSTAR such as saddle loops measuring radial magnetic fluxes, Mirnov coils  detecting MHD activities, and a diamagnetic loop measuring a diamagnetic flux  by means of the deep neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Additionally, we expand our technique to  the long-pulse discharge sustaining the plasma over 300 sec where deterioration  in the magnetic signals are likely to occur, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', due to the signal drift with  assistance of Bayesian statistical analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  88  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4  Article IV: Preliminary result under super-  vised learning  This approach deals with deep neural network Grad–Shafranov solver constrained  with measured magnetic signals6, which is largely taken from Ref [158], as a part  of reconstruction of plasma equilibria via deep neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  This article describes a deep neural network approach to reconstruct plasma  equilibria in real time by using the existing equilibrium database.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  This also  proves that the solution of the Grad-Shafranov equation can be achieved by the  neural network although the network is trained based on a supervised learning  manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' As discussed in the synopsis of Article III, the equilibrium reconstruc-  tion requires the iterative estimation which takes time not to be suitable for a  real-time application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The reconstruction informs tokamak controllers of posi-  tions of the plasma, and thus the controllers regulate powers of the poloidal field  coils to manage the magnetic fields inside the tokamak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Therefore, to control  tokamak plasmas precisely, the reconstruction should be done in real time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  However, due to the iterative scheme, simplifying the original reconstruc-  tion algorithm is applied such as limiting the number of iterations or reusing  equilibria reconstructed previously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In this sense, the network trained based on  the database estimated by the original algorithm is suggested in order to take  advantage of the original-like (or off-line-EFIT-like) equilibrium in real time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  This network is fed with the poloidal magnetic fields and fluxes as its input,  and produces a solution of the Grad-Shafranov equation as its output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' To make  the network generate rigorous equilibria satisfying the Grad-Shafranov equation,  the equation itself is used as a cost function for the network training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Further-  more, This adopts the results of Article II in case of inferring missing inputs,  which guarantees the use of the network in any circumstances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Since this Article  proves that a neural network is able to encode rigorous plasma equilibria to its  6S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Joung, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kim, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kwak, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bak, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Lee, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Han, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kim, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Lee,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kwon and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='-c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Ghim  Nuclear Fusion, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1 (3rd Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 2019), DOI:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1088/1741-4326/ab555f  89  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  architecture, Article V is developed based on this approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  Introduction  Magnetic equilibrium is one of the most important information to understand  the basic behavior of plasmas in magnetically confined plasmas, and the off-line  EFIT [73] code has been extensively used to reconstruct such equilibria in toka-  maks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Its fundamentals are basically finding a solution to an ideal magnetohydro-  dynamic equilibrium with toroidal axisymmetry, known as the Grad-Shafranov  (GS) equation [42]:  ∆∗ψ ≡  �  R ∂  ∂R  1  R  ∂  ∂R + ∂2  ∂Z2  �  ψ  = −µ0Rjφ  = −µ0R2dp(ψ)  dψ  − F(ψ)dF(ψ)  dψ  ,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='30)  where ψ = ψ (R, Z) is the poloidal flux function, jφ = jφ (R, Z) the toroidal  current density function, p(ψ) the plasma pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' F(ψ) is related to the net  poloidal current.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Here, R, φ and Z denote the usual cylindrical coordinate sys-  tem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' As the ∆∗ is a two-dimensional nonlinear partial differential operator, the  off-line EFIT [73] finds a solution with many numerical iterations and has been  implemented in many tokamaks such as DIII-D [74], JET [157], NSTX [155],  EAST [156] and KSTAR [79] to name some as examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  With an aim of real-time control of tokamak plasmas, real-time EFIT (rt-  EFIT) [75] code is developed to provide a magnetic equilibrium fast enough whose  results are different from the off-line EFIT results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' As pulse lengths of tokamak  discharges become longer [159–165], demand on more elaborate plasma control  is ever increased.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Furthermore, some of the ITER relevant issues such as ELM  (edge localized mode) suppression with RMP (resonant magnetic perturbation)  coils [166] and the detached plasma scenarios [167, 168] require sophisticated  plasma controls, meaning that the more accurate magnetic equilibria we have in  real time, the better performance we can achieve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  90  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  1  2  3  R [m]  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  Z [m]  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='19: A poloidal cross-section of KSTAR with the first wall (blue  dotted line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Green dotted line indicates a Rogowski coil measuring the plasma  current (Ip).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Green open circles and crosses depict locations of the magnetic  pick-up coils measuring 32 normal (Bn) and 36 tangential (Bt) magnetic fields,  respectively, whereas green triangles represent 22 flux loops measuring poloidal  magnetic fluxes (ΨFL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Black asterisks (22 × 13 spatial positions) show  locations where we obtain the values of ψ from the off-line EFIT results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  There has been an attempt to satisfy such a requirement of acquiring a more  accurate, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', closer to the off-line EFIT results compared to the rt-EFIT results,  magnetic equilibrium in real-time using graphics processing units (GPUs) [76] by  parallelizing equilibrium reconstruction algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The GPU based EFIT (P-  EFIT) [76] enabled one to calculate a well-converged equilibrium in much less  time;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' however, the benchmark test showed similar results to the rt-EFIT rather  than the off-line results [169].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Thus, we propose a reconstruction algorithm based on a neural network that  satisfies the GS equation as well as the measured magnetic signals to obtain accu-  rate magnetic equilibrium in real time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We note that usage of neural networks in  fusion community is increasing rapidly, and examples are radiated power estima-  91  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  tion [170],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' identifying instabilities [171],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' estimating neutral beam effects [172],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  classifying confinement regimes [173],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' determination of scaling laws [174,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 175],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  disruption prediction [19,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 176,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 177],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' turbulent transport modelling [25–27,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 178],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  plasma tomography with the bolometer system [179,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='180],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' coil current prediction  with the heat load pattern in W7-X [181],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' filament detection on MAST-U [182],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  electron temperature profile estimation via SXR with Thomson scattering [183]  and equilibrium reconstruction [5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='7,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='13,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='124,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='184,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='185] together with an equilibrium  solver [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Most of previous works on the equilibrium reconstruction with neural  networks have paid attention to finding the poloidal beta, the plasma elongation,  positions of the X-points and plasma boundaries, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', last closed flux surface, and  gaps between plasmas and plasma facing components, rather than reconstructing  the whole internal magnetic structures we present in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The inputs to our developed neural networks consist of plasma current mea-  sured by a Rogowski coil, normal and tangential components of magnetic fields  by magnetic pick-up coils, poloidal magnetic fluxes by flux loops and a position  in (R, Z) coordinate system, where R is the major radius, and Z is the height as  shown in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The output of the neural networks is a value of poloidal  flux ψ at the specified (R, Z) position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' To train and validate the neural networks,  we have collected a total of 1, 118 KSTAR discharges from two consecutive cam-  paigns, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', 2017 and 2018 campaigns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We, in fact, generate three separate neural  networks which are NN2017, NN2018 and NN2017, 2018 where subscripts indicate the  year(s) of KSTAR campaign(s) that the training data sets are obtained from.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Ad-  ditional 163 KSTAR discharges (from the same two campaigns) are collected to  test the performance of the developed neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  We train the neural networks with the KSTAR off-line EFIT results, and let  them be accurate magnetic equilibria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Note that disputing on whether the off-  line EFIT results we use to train the networks are accurate or not is beyond the  scope of this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' If we find more accurate EFIT results, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', MSE(Motional  Stark Effect)-constrained EFIT or more sophisticated equilibrium reconstruction  algorithms that can cope with current-hole configurations (current reversal in  the core) [186–188], then we can always re-train the networks with new sets of  92  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='20: Before (blue) and after (red) the magnetic signal adjustments for  (a) normal and (b) tangential components of magnetic fields measured by the  magnetic pick-up coils, and (c) poloidal magnetic flux measured by one of the  flux loops.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The signals return closer to zeros after the adjustment when all the  external magnetic coils (except the toroidal field coils) are turned off at around  30 sec in this KSTAR discharge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  data as long as the networks follow the trained EFIT data with larger similarity  than the rt-EFIT results do.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This is because supervised neural networks are  limited to follow the training data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Hence, as a part of the training sets we  use the KSTAR off-line EFIT results as possible examples of accurate magnetic  equilibria to corroborate our developed neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  To calculate the output data a typical neural network requires the same  set of input data as it has been trained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Therefore, even a single missing input  (out of input data set) can result in a flawed output [132].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Such a case can  be circumvented by training the network with possible combinations of missing  inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' As a part of input data, we have 32 normal and 36 tangential magnetic  fields measured by the magnetic pick-up coils.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' If we wish to cover a case with  one missing input data, then we will need to repeat the whole training procedure  with 68 (32 + 36) different cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' If we wish to cover a case with two or three  missing input data, then we will need additional 2, 278 and 50, 116 different  cases to be trained on, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This number becomes large rapidly, and  it becomes formidable, if not impossible, to train the networks with reasonable  93  (a) Bn  (b) Bt  TI ()  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='05  5  0  0  E  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='01  0  B  2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='02  Before adjust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  After adjust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  5  0  20  0  20  0  20  time [sec]  time[sec  time [sec]CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  computational resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Since the magnetic pick-up coils are susceptible to  damages, we have developed our networks to be capable of inferring a few missing  signals of the magnetic pick-up coils in real-time by invoking an imputation  scheme [3] based on Bayesian probability [86] and Gaussian processes [131].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  In addition to reconstructing accurate magnetic equilibria in real-time, the  expected improvements with our neural networks compared to the previous stud-  ies are at least fourfold: (1) the network is capable of providing whole internal  magnetic topology, not limited to boundaries and locations of X-points and/or  magnetic axis;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (2) spatial resolution of reconstructed equilibria is arbitrarily ad-  justable within the first wall of KSTAR since (R, Z) position is a part of the  input data;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (3) the required training time and computational resources for the  networks are reduced by generating a coarse grid points also owing to (R, Z)  position being an input, and (4) the networks can handle a few missing signals  of the magnetic pick-up coils using the imputation method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  We, first, present how the data are collected to train the neural networks  and briefly discuss real-time preprocessing of the measured magnetic signals in  Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' For the readers who are interested in thorough description of the  real-time preprocessing, Article I provides the details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Then, we explain the  structure of our neural networks and how we train them in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4, we present the results of the developed neural network EFIT (nn-EFIT) in  four aspects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' First, we discuss how well the NN2017, 2018 network reproduces the  off-line EFIT results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Then, we make comparisons among the three networks,  NN2017, NN2018 and NN2017, 2018, by examining in-campaign and cross-campaign  performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Once the absolute performance qualities of the networks are estab-  lished, we compare relative performance qualities between nn-EFIT and rt-EFIT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Finally, we show how the imputation method support the networks when there  exist missing inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Our conclusions are presented in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  Collection and real-time preprocessing of data  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='19 shows locations where we obtain the input and the output data with  the first wall (blue dotted line) on a poloidal cross-section of KSTAR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The green  94  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1: Summary of the data samples to train and validate the networks  Parameter  Definition  Data size  No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' of samples  Ip  Plasma current  1  (Rogowski coil)  Bn  Normal magnetic field  32  (Magnetic pick-up coils)  217,820  Bt  Tangential magnetic field  36  (time slices)  (Magnetic pick-up coils)  ΨFL  Poloidal magnetic flux  22  (Flux loops)  R  Position in major radius  1  286  (22 × 13 grids)  Z  Position in height  1  Network Input size  93 (+1 for bias)  Total no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' of samples  62,296,520  dotted line indicates a Rogowski coil measuring the plasma current (Ip).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The  green open circles and crosses show locations of the magnetic pick-up coils mea-  suring 32 normal (Bn) and 36 tangential (Bt) components of magnetic fields, re-  spectively, whereas the green triangles show 22 flux loops measuring the poloidal  magnetic fluxes (ΨFL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' These magnetic signals are selectively chosen out of all  the magnetic sensors in KSTAR [2] whose performance has been demonstrated  for many years, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', less susceptible to damages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Although KSTAR calibrates the magnetic sensors (magnetic pick-up coils  and flux loops) regularly during a campaign to remove drifts in the magnetic  signals, it does not guarantee to fully eliminate such drifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, we preprocess  the signals to adjust the drifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='20 shows examples of before (blue) and  after (red) the drift adjustment for (a) normal and (b) tangential components of  magnetic fields measured by the magnetic pick-up coils and (c) poloidal magnetic  flux measured by one of the flux loops.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Here, a KSTAR discharge is sustained  95  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  until about 20 sec, and all the external magnetic coils (except the toroidal field  coils) are turned off at about 30 sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Therefore, we expect all the magnetic signals  to return to zeros at around 30 sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' If not, we envisage that there has been  residual drifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This means that we need to be able to preprocess the magnetic  signals in real-time so that the input signal characteristics for predictions are  similar to the trained ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Article I describes in detail how we preprocess the  magnetic signals in real-time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The black asterisks in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='19 show the 22 × 13 grid points where we  obtain the values of ψ from the off-line EFIT results as outputs of the networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  We note that the original off-line EFIT provides the values of ψ with 65 × 65  grid points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The 22×13 grid points are selected such that the distances between  the neighboring channels in R and Z directions are as similar as possible while  covering whole region within the first wall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' By generating such coarse grid points  we can decrease the number of samples to train the network, thus consuming less  amount of computational resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Nevertheless, we do not lose the spatial  resolution since (R, Z) position is an input, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', the network can obtain the  value of ψ at any position within the first wall (see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  With an additional input for the spatial position R and Z, each data sam-  ple contains 93 inputs (and yet another input for bias) and one output which  is a value of ψ at the specified (R, Z) location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We randomly collect a total  of 1, 118 KSTAR discharges from 2017 and 2018 campaigns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Since each dis-  charge can be further broken into many time slices, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', every 50 msec follow-  ing the temporal resolution of the off-line EFIT, we obtain 217, 820 time slices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  With a total of 286 value of ψ from 22 × 13 spatial points, we have a total of  62, 296, 520 (= 217, 820 × 286) samples to train and validate the networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 90%  of the samples are used to train the networks, while the other 10% are used to  validate the networks to avoid overfitting problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Note that an overfitting  problem can occur if a network is overly well trained to the training data follow-  ing the very details of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This inhibits generalization of the trained network  to predict unseen data, and such a problem can be minimized with the validation  data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' All the inputs except R and Z are normalized such that the maximum  96  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='21: An example of the two networks’ results trained with the cost  function (a) ϵ and (b) ϵnew for KSTAR shot# 17939 at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='950 sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Both  networks (red dashed line) reproduce the ψTarget (black line) well (left panels),  but only the network trained with ϵnew reproduces ∆∗ψTarget (right panels).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  and minimum values within the whole samples become 1 and −1, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  We use the actual values of R and Z in the unit of meters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1 summarizes the training and validation samples discussed in this  section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Additionally, we also have randomly collected another 163 KSTAR dis-  charges in the same way discussed here which are different from the 1, 118 KSTAR  discharges to test the performance of the networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3  Neural network model and training  Neural network model  We develop the neural networks that not only output a value of ψ but also satisfies  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='30), the GS equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' With the total of 94 input nodes (91 for a plasma  97  (a) KSTAR Shot#17939, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='950 sec (with E)  山  △*b  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0  0  N  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='8 2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='8 2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  △*b  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  E  0  0  N  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='8 2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='8 2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  R [m]  R [m]CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  current and magnetic signals, two for R and Z position, one for the bias) and  one output node for a value of ψ, each network has three fully connected hidden  layers with an additional bias node at each hidden layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Each layer contains  61 nodes including the bias node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The structure of our networks is selected by  examining several different structures by error and trials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Denoting the value of ψ calculated by the networks as ψNN, we have  ψNN =s0 +  60  �  l=1  sl  × f  �  ul0+  60  �  k=1  ulkf  �  vk0+  60  �  j=1  vkjf  �  wj0+  93  �  i=1  wjixi  ���  ,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='31)  where xi is the ith input value with i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' , 93, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', 91 measured values with the  various magnetic diagnostics and two for R and Z positions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' wji is an element in  a 61×94 matrix, whereas vkj and ulk are elements in 61×61 matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' sl connects  the lth node of the third (last) hidden layer to the output node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' w, v, u and s  are the weighting factors that need to be trained to achieve our goal of obtaining  accurate ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' wj0, vk0, ul0 and s0 are the weighting factors connecting the biases,  where values of all the biases are fixed to be unity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We use a hyperbolic tangent  function as the activation function f giving the network non-linearity [189]:  f(t) = tanh(t) =  2  1 + e−2t − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='32)  The weighting factors are initialized as described in [151] so that a good  training can be achieved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' They are randomly selected from a normal distribution  whose mean is zero with the variance set to be an inverse of total number of  connecting nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' For instance, our weighting factor w connects the input layer  (94 nodes with bias) and the first hidden layer (61 nodes with bias), therefore  the variance is set to be 1/(94 + 61).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Likewise, the variances for v, u and s are  1/(61 + 61), 1/(61 + 61) and 1/(61 + 1), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Training  With the aforementioned network structure, training (or optimizing) the weight-  ing factors to predict the correct value of ψ highly depends on a choice of the  98  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='22: The descending feature of training (blue line) and validation (red  dashed line) errors as a function of iterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Shaded areas represent standard  deviation of the errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  cost function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' A typical choice of such cost function would be:  ϵ = 1  N  N  �  i=1  �  ψNN  i  − ψTarget  i  �2  ,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='33)  where ψTarget is the target value, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', the value of ψ from the off-line EFIT results  in our case, and N the number of data sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  As will be shown shortly, minimizing the cost function ϵ does not guarantee  to satisfy the GS equation (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='30)) even if ψNN and ψTarget matches well, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=',  the network is well trained with the given optimization rule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Since ∆∗ψ provides  information on the toroidal current density directly, it is important that ∆∗ψNN  matches ∆∗ψTarget as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We have an analytic form representing ψNN as in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='31);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' therefore, we can analytically differentiate ψNN with respect to R and  Z, meaning that we can calculate ∆∗ψNN during the training stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, we  introduce another cost function:  ϵnew = 1  N  N  �  i=1  �  ψNN  i  − ψTarget  i  �2  + 1  N  N  �  i=1  �  ∆∗ψNN  i  − ∆∗ψTarget  i  �2  ,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='34)  where we obtain the value of ∆∗ψTarget from the off-line EFIT results as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  To acknowledge difference between the two cost functions ϵ and ϵnew, we first  discuss the results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='21 shows the outputs of the two trained networks  99  10~2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  +.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  一Training error  -Validation error  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='.  +.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='.  +.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='.  10  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  One epoch  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='.  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  Training iteration  ×10CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  with the cost function (a) ϵ and (b) ϵnew.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' It is evident that in both cases the  network output ψNN (red dashed line) reproduces the off-line EFIT ψTarget (black  line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' However, only the network trained with the cost function ϵnew reproduces  the off-line EFIT ∆∗ψTarget.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Both networks are trained well, but the network  with the cost function ϵ does not achieve our goal, that is correctly predicting  ψTarget and ∆∗ψTarget.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Since our goal is to develop a neural network that solves the GS equation,  we choose the cost function to be ϵnew to train the networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We optimize the  weighting factors by minimizing ϵnew with the Adam [190] which is one of the  gradient-based optimization algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' With 90% and 10% of the total data  samples for training and validation of the networks, respectively, we stop training  the networks with a fixed number of iterations that is large enough but not too  large such that the validation errors do not increase, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', to avoid overfitting  problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The whole workflow is carried out with Python and Tensorflow [103].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  With the selected cost function we create three different networks that differ  only by the training data sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  NN2017, NN2018 and NN2017, 2018 refer to the  three networks trained with the data sets from only 2017 (744 discharges), from  only 2018 (374 discharges) and from both 2017 and 2018 (744 + 374 discharges)  campaigns, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The descending feature of the cost function ϵnew as a function of the training  iteration for NN2017,2018 network is shown in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Both the training errors  (blue line) and validation errors (red dashed line) decrease together with similar  values which means that the network is well generalized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Furthermore, since  the validation errors do not increase, the network does not have an overfitting  problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Note that fluctuations in the errors, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', standard deviation of the  errors, are represented as shaded areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Small undulations repeated over the iterations in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='22 are due to the  mini-batch learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Contrary to the batch learning, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', optimizing the network  with the entire training set in one iteration, the mini-batch learning divides the  training set into some number of small subsets (1, 000 subsets for our case) to  optimize the networks sequentially.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' One cycle that goes through all the subsets  100  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='23: Performance tests of the NN2017,2018 network on the unseen  KSTAR discharges from (a)(b) 2017 campaign and (c)(d) 2018 campaign.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The  values of R2 and histograms of (a)(c) ψNN vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' ψTarget and (b)(d) ∆∗ψNN vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  ∆∗ψTarget with colors representing number of counts manifest goodness of the  NN2017,2018 network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Red dashed line is the y = x line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  once is called an epoch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The mini-batch learning helps to escape from local  minima in the weighting factor space [191] via the stochastic gradient descent  scheme [192].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4  Performance of the developed neural networks: Bench-  mark tests  In this section, we present how well the developed networks perform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Main  figures of merit we use are peak signal-to-noise ratio (PSNR) and mean structural  similarity (MSSIM) as have been used perviously [179] in addition to the usual  statistical quantity R2, coefficient of determination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We note that obtaining full  flux surface information ψ (R, Z) on 22 × 13 or 65 × 65 spatial grids with our  networks takes less than 1 msec on a typical personal computer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  First, we discuss the benchmark results of the NN2017,2018 network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Then,  101  ×105  ×104  10  2  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  R2=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='998  8  Counts  R2=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='999  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  2  NN  NN  6  0  1  4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  6  2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  6 -4 -2 0  ×104  ×104  12  0  R2=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='999  5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  Counts  10  R?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='997  Counts  2  4  8  NN  3  9  4  2  4  2  9-  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  6 -4 -2  0  EFITCHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='24: The actual reconstruction results for the KSTAR shot#18057,  comparing the network results and off-line EFIT reconstructions for ramp-up  ((b) and (c)), flat-top ((d) and (e)), ramp-down ((f) and (g)) phases following  (a) the plasma current evolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Black lines indicate the flux surfaces from the  off-line EFIT, overlaid with the red dotted lines which stand for the NN  reconstructions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' As a figure of merit, magnitudes of PSNR metric are written  on each figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  we compare the performance of NN2017, NN2018 and NN2017,2018 networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Here,  we also investigate cross-year performance, for instance, applying the NN2017  network to predict the discharges obtained from 2018 campaign and vice versa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Then, we evaluate the performance of the networks against the rt-EFIT results  to examine possibility of supplementing or even replacing the rt-EFIT with the  networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Finally, we show how the imputation scheme supports the networks’  performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Here, all the tests are performed with the unseen (to all three  networks, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', NN2017, NN2018 and NN2017,2018) KSTAR discharges which are 88  and 75 KSTAR discharges from 2017 and 2018 campaigns, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  102  (a) Plasma current (KSTAR Shot#18057)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='8  (b) :  (c)i  (d)  A0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6  M  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  (e)i  (f)i  (g)  0  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  3  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  4  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  5  time [sec]  (b) Ramp-up 1  (c) Ramp-up 2  @EFIT  NN)  (d) Flat-top 1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  PSNR55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  PSNR33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6  PSNR58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4  PSNR 39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='8  PSNR 55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  PSNR34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1  1  1  1  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  E  0  0  0  0  0  0  N  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1  1  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='62  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6  2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='62  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='62  2  (e) Flat-top 2  (f) Ramp-down 1  (g) Ramp-down 2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  PSNR51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  PSNR37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4  VPSNR54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='7  PSNR 35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='7  PSNR46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  PSNR26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6  1  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  E  0  0  0  0  0  0  N  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='62  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='62  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6  2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6 2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='62  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6  R [m]  R [m]  R [m]  R [m]  R [m]  R [m]CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='25: Same as Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='23 for the the NN2017 network, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', trained with  the data sets from 2017 campaign.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Benchmark results of the NN2017,2018 network  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='23 show the benchmark results of the NN2017,2018 network, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', network  trained with the data sets from both 2017 and 2018 campaigns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (a) and (b)  show the results with the test discharges from 2017 campaign;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' while (c) and (d)  present the results with the test discharges from 2018 campaign.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Histograms of  (a)(c) ψNN vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' ψTarget and (b)(d) ∆∗ψNN vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' ∆∗ψTarget are shown with colors  representing the number of counts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' For instance, there is a yellow colored point  in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='23(a) around (−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1, −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1)±ε, where ε is a bin size for the histogram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Since yellow represents about 2 × 105 counts, there are approximately 2 × 105  data whose neural network values and EFIT values are −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1 ± ε simultaneously  within our test data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Note that each KSTAR discharge contains numerous  time slices whose number depends on the actual pulse length of a discharge, and  each time slice generates the total of 22 × 13 = 286 data points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The values of  ψTarget and ∆∗ψTarget are obtained from the off-line EFIT results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' It is clear that  the network predicts the target values well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  103  ×104  ×104  0  R2=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='996  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  R²=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='999  Counts  15  2  8  NN  10  6  4  4  5  2  6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  6 -4 -2  0  ×104  X104  6  R²=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='999  12  0  R?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='996  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  Counts  Counts  10  4  。' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  8  NN  6  4  2  4  2  6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  6  4-2  0  EFIT  EFITCHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='26: Same as Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='23 for the the NN2018 network, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', trained with  the data sets from 2018 campaign.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  As a figure of merit, we introduce the R2 metric (coefficient of determination)  defined as  R2 = 1 −  �L  i=1  �  yTarget  i  − yNN  i  �2  �L  i=1  �  yTarget  i  − 1  L  �L  j=1 yTarget  j  �2,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='35)  where y takes either ψ or ∆∗ψ, and L is the number of test data sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The  calculated values are written in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='23, and they are indeed close to unity,  implying the existence of very strong linear correlations between the predicted  (from the network) and target (from the off-line EFIT) values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Note that R2 = 1  means the perfect prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The red dashed lines on the figures are the y = x  lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='24 is an example of reconstructed magnetic equilibria using KSTAR  shot #18057 from 2017 campaign.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (a) shows the evolution of the plasma current.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The vertical dashed lines indicate the time points where we show and compare  the equilibria obtained from the network (red) and the off-line EFIT (black)  which is our target.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (b) and (c) are taken during the ramp-up phase, (d) and (e)  104  ×104  ×104  0  R2=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='998  6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  R?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content="999  15  Counts  'ount  NN  4  NN  10  4  5  2  6  0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  6 -4  2  0  ×104  ×104  12  R2=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='998  R?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='999  0  6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  10  punts  2  8  4  NN  6  4  4  2  C  2  6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  6  4  2  0  EFIT  EFITCHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  during the flat-top phase, and (f) and (g) during the ramp-down phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In each  sub-figure from (b) to (g), left panels compare ψ, and right panels are for ∆∗ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  We mention that the equilibria in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='24 are reconstructed with 65×65 grid  points even though the network is trained with 22×13 grid points demonstrating  how spatial resolution is flexible in our networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  For a quantitative assessment of the network, we use an image relevant figure  of merit that is peak signal-to-noise ratio (PSNR) [193] originally developed  to estimate a degree of artifacts due to an image compression compared to an  original image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Typical PSNR range for the JPEG image, which preserves the  original quality with a reasonable degree, is generally in 30–50 dB [179,194].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' For  our case, the networks errors relative to the off-line EFIT results can be treated  as artifacts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' As listed on Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='24(b)-(g), PSNR for ψ is very good, while we  achieve acceptable values for ∆∗ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The NN2017, NN2018 and NN2017,2018 networks  Similar to shown in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='23, we show the benchmark results of the NN2017  (trained with the data sets from 2017 campaign) and the NN2018 (trained with the  data sets from 2018 campaign) in Figures 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='25 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='26, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' R2 metric  is also provided on the figures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Again, overall performance of the networks are  good.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The NN2017 and NN2018 networks are trained with only in-campaign data  sets, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', NN2018 with the data sets from only 2018 campaign, and we find  slightly worse results, but still good, on predicting cross-campaign magnetic  equilibria, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  NN2018 predicting equilibria for 2017 campaign.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Notice that  the NN2017 seems to predict cross-campaign equilibria better than in-campaign  ones by comparing Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='25(a) and (c) which contradicts our intuition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Al-  though the histogram in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='25(c) seems tightly aligned with the y = x line  (red dashed line), close inspection reveals that the NN2017 network, in general,  underestimates the off-line EFIT results from 2018 campaign marginally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This  will be evident when we compare image qualities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Mean structural similarity (MSSIM) [195] is another image relevant figure  105  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='27: Histograms of MSSIM (left panel) and PSNR (right panel) for  (a) NN2017, (b) NN2018 and (c) NN2017,2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Red (green) line indicates the test  results on the data sets from 2017 (2018) campaign.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In each sub-figure, top  (bottom) panel show the results for ψ (∆∗ψ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The off-line EFIT results are  used as reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  106  (a) NN201z test results  Test set from 2018  Counts  Testsetfrom2017  500  102  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='94  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='96  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='98  1  20  40  60  500  山  山  Counts  102  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='94  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='96  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='98  20  40  60  MSSIM  PSNR  (b) NN2018 test results  ITest set from2018  山  500  山  Test set from 2017  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='94  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='96  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='98  1  20  40  60  400  △*山 Counts  102  200  5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='94  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='96  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='98  1  20  40  60  MSSIM  PSNR  (c) NN2017,2018 test results  ITest set from 2018  山  山  Counts  Testsetfrom2017  500  102  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='94  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='96  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='98  1  20  40  60  △*山  400 Counts  102  200  100  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='94  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='96  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='98  1  20  40  60  MSSIM  PSNRCHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  of merit used to estimate perceptual similarity (or perceived differences) between  the true and reproduced images based on inter-dependence of adjacent spatial  pixels in the images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' MSSIM ranges from zero to one, where the closer to unity  the better the reproduced image is.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Together with PSNR, Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='27 shows MSSIM for (a) NN2017, (b) NN2018  and (c) NN2017,2018 where the off-line EFIT results are used as reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Notice  that counts in all the histograms of MSSIM and PSNR in this work correspond  to the number of reconstructed magnetic equilibria (or a number of time slices)  since we obtain a single value of MSSIM and PSNR from one equilibrium;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' whereas  counts in Figures 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='23, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='25 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='26 are much bigger since 286(= 22 × 13) data  points are generated from each time slice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Red (green) line indicates the test  results on the data sets from 2017 (2018) campaign.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In general, whether the test  data sets are in-campaign or cross-campaign, image reproducibility of all three  networks, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', predicting the off-line EFIT results, is good as attested by the fact  that MSSIM is quite close to unity and PSNR for ψ (∆∗ψ) ranges approximately  40 to 60 (20 to 40).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' It is easily discernible that in-campaign results are better  for both NN2017 and NN2018 unlike what we noted in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='25(a) and (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Not  necessarily guaranteed, we find that the NN2017,2018 network works equally well  for both campaigns as shown in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='27(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Comparisons among nn-EFIT, rt-EFIT and off-line EFIT  It is widely recognized that rt-EFIT results and off-line results are different from  each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' If we allow the off-line EFIT results used to train the networks to  be accurate ones, then the reconstruction of equilibria with the neural networks  (nn-EFIT) must satisfy the following criterion: nn-EFIT results must be more  similar to the off-line EFIT results than rt-EFIT results are to the off-line EFIT  as mentioned in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Once this criterion is satisfied, then we can always  improve the nn-EFIT as genuinely more accurate EFIT results are collected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  For this reason, we make comparisons among the nn-EFIT, rt-EFIT and off-line  EFIT results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='28 shows an example of reconstructed magnetic equilibria for (a)  107  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='28: An example of reconstructed ψ (R, Z) (left panel) and  ∆∗ψ (R, Z) (right panel) for KSTAR shot #17975 at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='7 sec comparing (a)  rt-EFIT (green) and off-line EFIT (black) and (b) nn-EFIT (NN2017,2018) (red)  and off-line EFIT (black).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  rt-EFIT vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' off-line EFIT and (b) nn-EFIT (the NN2017,2018 network) vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' off-  line EFIT for KSTAR shot #17975 at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='7 sec with ψ (left panel) and ∆∗ψ  (right panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Green, red and black lines indicate rt-EFIT, nn-EFIT and off-line  EFIT results, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This simple example shows that the nn-EFIT is more  similar to the off-line EFIT than the rt-EFIT is to the off-line EFIT, satisfying  the aforementioned criterion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  To validate the criterion statistically, we generate histograms of MSSIM  and PSNR for the nn-EFIT and the rt-EFIT with reference to the off-line EFIT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  This is shown in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='29 as histograms, where MSSIM (left panel) and PSNR  (right panel) of ψ (top) and ∆∗ψ (bottom) are compared between the nn-EFIT  (black) and the rt-EFIT (green).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Here, the nn-EFIT results are obtained with  the NN2017,2018 network on the test data sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  We confirm that the criterion  108  △*  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  E  0  0  N  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='822.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='8 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='8 2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  R [m]  R [m]CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='29: Histograms of MSSIM (left panel) and PSNR (right panel) of ψ  (top) and ∆∗ψ (bottom) calculated by the nn-EFIT (black) and the rt-EFIT  (green), where the nn-EFIT is the NN2017,2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' For both the nn-EFIT and the  rt-EFIT, the off-line EFIT is treated as reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  is satisfied with the NN2017,2018 network as the histograms in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='29 are  in favour of the nn-EFIT, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', larger MSSIM and PSNR are obtained by the  nn-EFIT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This is more conspicuous for ∆∗ψ than ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  We perform the similar statistical analyses for the other two networks,  NN2017 and NN2018, which are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='30 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Since these two  networks are trained with the data sets from only one campaign, we show the  results where the test data sets are prepared from (a) 2017 campaign or (b) 2018  campaign so that in-campaign and cross-campaign effects can be assessed sepa-  rately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We find that whether in- or cross-campaign, the criterion is fulfilled for  both ψ and ∆∗ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The NN2017,2018 network with the imputation scheme  If one or a few magnetic pick-up coils which are a part of the inputs to the  nn-EFIT are impaired, then we will have to re-train the network without the  damaged ones or hope that the network will reconstruct equilibria correctly by  padding a fixed value, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', zero-padding, to the broken ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Of course, one can  anticipate training the network by considering possible combinations of impaired  109  (Test set from 2017, 2018)  104  INN2017,2018  Counts  rt-EFIT  200  102  100  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9  1  20  40  60  104  心  △*山  △*山  200  Counts  102  100  100  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9  1  20  40  60  MSSIM  PSNRCHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='30: Same as Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='29 with the NN2017 as the nn-EFIT where the  test data sets are obtained from (a) 2017 campaign and (b) 2018 campaign.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  magnetic pick-up coils.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' With the total number of 68 signals from the magnetic  pick-up coils being inputs to the network in our case, we immediately find that  the number of possible combinations increases too quickly to consider it as a  solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Since inferring the missing values is better than the null replacement [132],  we resolve the issue by using the recently proposed imputation method [3] based  on Gaussian processes (GP) [131] and Bayesian inference [86], where the likeli-  hood is constructed based on Maxwell’s equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The imputation method infers  the missing values fast enough, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', less than 1 msec to infer at least up to nine  missing values on a typical personal computer;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' thus, we can apply the method  during a plasma discharge by replacing the missing values with the real-time  inferred values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  110  (a) NN2017 and rt-EFIT  (Test set from 2017)  104  JNN2017  山  200  Counts  Irt-EFIT  102  100  100  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9  1  20  40  60  104  200  △*山  △*  Counts  102  100  100  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9  1  20  40  60  MSSIM  PSNR  (b) NN2017 and rt-EFIT  (Test set from 2018)  104  150  JNN2017  Counts  Irt-EFIT  100  102  50  100  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9  1  20  40  60  104  150  △* Counts  100  102  50  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9  1  20  40  60  MSSIM  PSNRCHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='31: Same as Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='29 with the NN2018 as the nn-EFIT where the  test data sets are obtained from (a) 2017 campaign and (b) 2018 campaign.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  We have applied the imputation method to KSTAR shot #20341 at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  sec for the normal (Bn) and tangential (Bt) components of the magnetic pick-  up coils as an example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We have randomly chosen nine signals from the 32 Bn  measurements and another nine from the 36 Bt measurements and pretended that  all of them (9 + 9) are missing simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='32 shows the measured  (blue open circles) and the inferred (red crosses with their uncertainties) values  for (a) Bn and (b) Bt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Probe # on the horizontal axis is used as an identification  index of the magnetic pick-up coils.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2 provides the actual values of the  measured and inferred ones for better comparisons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We find that the imputation  method infers the correct (measured) values very well except Probe #37 of Bn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Inferred (missing) probes are Probe #3, 4, 6, 14, 18, 24, 30, 35, 37 for Bn and  Probe #4, 6, 8, 11, 17, 29, 30, 32, 35 for Bt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Here, we provide all the Probe #’s  111  (a) NN2018 and rt-EFIT  (Test set from 2017)  104  INN2018  山  200  Counts  Irt-EFIT  102  100  100  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9  1  20  40  60  104  200  △*山 Counts  102  100  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9  1  20  40  60  MSSIM  PSNR  (b) NN2018 and rt-EFIT  (Test set from 2018)  104  200  INN2018  山  Counts  rt-EFIT  102  100  100  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9  1  20  40  60  104  150 △*  Counts  100  102  50  100  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9  1  20  40  60  MSSIM  PSNRCHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='32: Measured (blue open circles) and inferred with the imputation  method [3] (red crosses with their uncertainties) values for (a) Bn and (b) Bt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Probe # on the horizontal axis is used as an identification index of magnetic  pick-up coils.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Inferred probes are Probe #3, 4, 6, 14, 18, 24, 30, 35, 37 for Bn  and Probe #4, 6, 8, 11, 17, 29, 30, 32, 35 for Bt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  used for the neural network: Bn Probe #[2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' , 6, 8, 9, 11, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' , 15, 17, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' , 20,  23, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' , 26, 28, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' , 32, 34, 35, 37, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' , 41] (a total of 32) and Bt Probe #[2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' ,  6, 8, 9, 11, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' , 32, 34, 35, 37, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' , 41] (a total of 36).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Comparisons between the nn-EFIT without any missing values, which we  treat as reference values, and the nn-EFIT with the imputation method or with  the zero-padding method are made.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Here, nn-EFIT results are obtained using the  NN2017,2018 network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Top panel of Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='33 shows ψ (R, Z) obtained from the  nn-EFIT without any missing values (black line) and from the nn-EFIT with the  two missing values replaced with the inferred values (green line), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', imputation  method, or with zeros (pink dashed line), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', zero-padding method for (a) Bn  (left panel) and (b) Bt (right panel) at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1 sec of KSTAR shot #20341.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Probe #14  and 30 for Bn and Probe #4 and 8 for Bt are treated as the missing ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bottom  panels compare histograms of MSSIM and PSNR using the imputation method  (green) and the zero-padding method (pink) for all the equilibria obtained from  KSTAR shot #20341.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  112  (a) Bn  (b) Bt  @-measured  X inferred  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='06  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='02  E  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  B  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='25  20  40  20  40  probe #  probe #CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='33: Top panel: nn-EFIT (NN2017,2018 network) reconstructed  equilibria without any missing values (black line), and with two missing values  replaced with the inferred values using the imputation method (green line) or  with the zeros using the zero-padding method (pink dashed line), where the  missing values are (a) Bn Probe #14 and 30 (left panel) and (b) Bt Probe #4  and 8 (right panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bottom panels: histograms of MSSIM and PSNR using the  imputation method (green) and the zero-padding method (pink) for all the  equilibria obtained from KSTAR shot #20341, where the reference values are  those obtained using nn-EFIT without any missing values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Note that there are  many more counts less than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9 for MSSIM with the zero-padding method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  113  KSTAR Shot #20341  a) Bn: 2 probes  (b) Bt: 2 probes  w/o 14th, 30th probes  w/o 4th, 8th probes  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1 sec  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1 sec  [u]  0  0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='62  R [m]  R [m]  15  Counts  10  IMP  4  ZEROS  2  5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='95  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='95  1  1  MSSIM  MSSIM  30  30  Counts  20  20  10  10  0  0  20  4060  20  40  60  PSNR  PSNRCHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2: The imputation results shown in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='32 with KSTAR shot  #20341 at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1 sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Bn [T] ×10−2  Bt [T] ×10−2  No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Measured  Inferred  No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Measured  Inferred  3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='45  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='88±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='22  4  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='69  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='97±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='47  4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='72  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='31±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='24  6  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='38  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='42±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='97  6  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='62  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='45±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='65  8  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='82  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='88±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='67  14  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='13  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='36±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='27  11  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='15  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='22±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='65  18  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='27  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='11±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='48  17  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='30±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='52  24  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='86  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='65±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='30  29  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='84  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='65±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='64  30  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='52  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='19±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='18  30  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='49±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='61  35  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='93  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='08±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='65  32  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='65  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='11±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='62  37  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='27  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='41±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='93  35  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='07  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='87±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='55  It is clear that nn-EFIT with the imputation method (green line) is not only  much better than that with the zero-padding method (pink dashed line) but it  also reconstructs the equilibrium close to the reference (black).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In fact, the zero-  padding method is too far off from the reference (black line) to be relied on for  plasma controls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Motivated by such a successful result of the nn-EFIT with the imputation  method on the two missing values, we have increased number of missing values as  shown in Figures 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='34 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='35 for the same KSTAR discharge, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', KSTAR shot  #20341.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Let us first discuss Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='34 which are with (a) the eight (except only  Probe #6) and (b) nine (all) missing values of Bt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Color codes are same as in  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='33, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', the reference is black, and nn-EFIT with the imputation method  green or with the zero-padding method pink.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' It is evident that the nn-EFIT with  the imputation method performs well at least up to nine missing values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Such a  result is, in fact, expected since the imputation method has inferred the missing  values well as shown in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='32(b) in addition to the fact that a well-trained  neural network typically has a reasonable degree of resistance on noises.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Again,  the nn-EFIT with the zero-padding method is not reliable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='35 (a) and (b) are results with the eight (except only Probe #37)  and nine (all) missing values of Bn, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Color codes are same as in Figure  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We find that the nn-EFIT with the eight missing values reconstructs the  equilibrium similar to the reference one, while the reconstruction quality becomes  114  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='34: Same color code as in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Missing values are (a) eight  Bt (except only Probe #6) and (b) all nine Bt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  notably worse for nine missing values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This is caused mostly due to poor inference  of Probe #37 by the imputation method (see Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='32(a)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Nevertheless,  the result is still better than the zero-padding method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='36 shows the  reconstruction results with the same color codes as in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='33 when we have  (a) 4+4 and (b) 9+9 combinations of Bn and Bt missing values simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  All these results suggest that the nn-EFIT with the imputation method re-  constructs equilibria reasonably well except when the imputation infers the true  value poorly, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', Bn Probe #37 in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='32(a) and Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In fact, the  suggested imputation method [3] infers the missing values based on the neigh-  boring intact values (using Gaussian processes) while satisfying the Maxwell’s  equations (using Bayesian probability theory).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Consequently, such a method be-  comes less accurate if (1) the neighboring channels are also missing AND (2)  115  KSTAR Shot #20341  a) Bt: 8 probes  (b) Bt: 9 probes  except 6th probe  w/o all  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1 sec  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1 sec  [w]  0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='62  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 2  R [m]  R [m]  15  15  Counts  IMP  10  10  ZEROS  5  5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='95  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='95  1  MSSIM  MSSIM  40  40  Counts  20  20  0  0  30 40 50  30 40 50  PSNR  PSNRCHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='35: Same color code as in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Missing values are (a) eight  Bn (except only Probe #37), (b) all nine Bn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  the true values change fast from the neighboring values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In fact, Bn Probe #37  happens to satisfy these two conditions, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', Probe #35 is also missing, and the  true values of Probe #35, #37 and #38 are changing fast as one can discern  from Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='32(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  Discussions and Conclusions  We have developed and presented the neural network based Grad-Shafranov  solver constrained with the measured magnetic signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The networks take the  plasma current from a Rogowski coil, 32 normal and 36 tangential components  of the magnetic fields from the magnetic pick-up coils, 22 poloidal fluxes from  the flux loops, and (R, Z) position of the interest as inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' With three fully  connected hidden layers consisting of 61 nodes each layer, the network outputs  116  KSTAR Shot #20341  (a) Bn: 8 probes  (b) Bn: 9 probes  except 37th probe  w/o all  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1 sec  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1 sec  E  0  0  N  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='62  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6  2  R [m]  R [m]  20  20  IMP  Counts  10  ZEROS  10  0  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1  MSSIM  MSSIM  30  30  Counts  20  20  10  10  0  0  20  40  60  20  40  60  PSNR  PSNRCHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='36: Same color code as in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Combinations of missing Bn  and Bt are examined: (a) four missing Bn and four mssing Bt case and (b) nine  missing Bn and nine missing Bt case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  a value of poloidal flux ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We set the cost function used to train the networks  to be a function of not only the poloidal flux ψ but also the Grad-Shafranov  equation ∆∗ψ itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The networks are trained and validated with 1, 118 KSTAR  discharges from 2017 and 2018 campaigns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Treating the off-line EFIT results as accurate magnetic equilibria to train  the networks, our networks fully reconstruct magnetic equilibria, not limited to  obtaining selected information such as positions of magnetic axis, X-points or  plasma boundaries, more similar to the off-line EFIT results than the rt-EFIT  is to the off-line EFIT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Owing to the fact that (R, Z) position is a part of the  input, our networks have adjustable spatial resolution within the first wall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The  imputation method supports the networks to obtain the nn-EFIT results even if  117  KSTAR Shot #20341  a)Bn:4,Bt:4 probes  (b)Bn:9,Bt:9 probes  Bn: w/o 3rd,6th.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='18th,24th  Bn: w/o all  Bt: w/o 4th,8th,17th,29th  Bt: w/o all  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1 sec  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1 sec  E  0  0  N  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='62  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6  R [m]  R [m]  10  IMP  6  Counts  ZEROS  5  4  2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='95  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  MSSIM  MSSIM  Counts  20  20  0  0  20  40  20  40  PSNR  PSNRCHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  there exist a few missing inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  As all the necessary computation time is approximately 1 msec, the networks  have potential to be used for real-time plasma control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In addition, the networks  can be used to provide large number of automated EFIT results fast for many  other data analyses requiring magnetic equilibria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  118  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  Article V: Plasma reconstruction via unsu-  pervised learning  This approach deals with GS-DeepNet: Mastering tokamak plasma equilibria  with deep neural networks and the Grad-Shafranov equation7, which is largely  taken from Ref [150], as a part of reconstruction of plasma equilibria via deep  neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  This article embodies the essence of this thesis, taking advantage of all  the principles and methods described previously, in order to reconstruct plasma  equilibria in a magnetic confinement fusion experiment via deep neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  KSTAR serves as a test bed for an application of this approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' As the networks  demonstrated the fact that the plasma equilibrium can be encoded in the network  architecture, this article taking one step forward brings up a question that neural  networks can directly solve plasma equilibria by themselves unlike Article IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Here, solving plasma equilibria denotes obtaining plasma equilibria by solv-  ing the Grad-Shafranov equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Since this approach does not rely on training  database containing solutions of the Grad-Shafranov equation, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', the EFIT  database used in Article IV, a large number of different measurement data em-  ployed in current reconstruction algorithms are collected for the networks such as  the magnetic pick-up coils, the poloidal flux loops, KSTAR Thomson scattering  system and KSTAR Charge exchange spectroscopy system as well as Motional  Stark Effect system (albeit not being introduced).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Since the Grad-Shafranov  equation is derived from both the plasma force equation with equilibrium as-  sumption and Maxwell’s equations, two neural network architectures take charge  of each contribution for reasonably solving the whole equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Furthermore,  two additional modules are introduced to determine a plasma boundary (dividing  a plasma region from a vacuum area) since solving the Grad-Shafranov equation  is a free-boundary problem, and using only the networks is not enough to resolve  it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' From the modelling for the relations between tokamak current sources and  7S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Joung, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='-c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Ghim, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kim, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kwak, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Lee, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kwon, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kim, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bak  Science Advances, (2022), in preparation  119  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  the measured magnetic signals, the networks can learn various plasma equilibria  via unsupervised learning manner and the gradient descent, meanwhile kinetic  profiles of plasmas are optimally found by the network themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' After the  training is done, the networks can produce plasma equilibria in real time which  can be used for tokamak operations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Note that Article V applies all the tech-  niques suggested in Article I–IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1  Introduction  The ultimate goal of scientific and engineering research in the field of nuclear fu-  sion is to build a power plant producing sustainable and clean electricity through  fusion reactions from a confined plasma heated up to ∼100 million degrees in Cel-  sius [37,38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' A tokamak is a torus-shape vacuum vessel within which the plasma is  confined by magnetic fields directed along the long (toroidal) and short (poloidal)  way around the torus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In order to maintain such a high-temperature plasma for  a long period of time (for instance, more than 400 seconds [196]), it is necessary  to balance the plasma pressure and the Lorentz force within the entire plasma  volume [42] during a tokamak operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This means that spatial structures of  plasma pressure and magnetic fields must be known in real time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  It is often hard to make direct in situ measurements of the plasma structures  due to its harsh environments, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', high temperature and radiation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Although  there are some optics systems directly measuring internal information such as  electron temperature and density [197] and magnetic pitch-angle [71], these mea-  surements are spatially localized and require a magnetic field structure for the  measured data to be mapped onto a whole plasma volume.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Hence, a suite of mag-  netic diagnostics [48], fundamental measurement devices installed on a tokamak  wall far from the plasma, are used to obtain the magnetic field structures indi-  rectly by solving the Grad-Shafranov (GS) equation [43, 44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The GS equation  describes a force balanced plasma state conforming to Maxwell’s equations with  a toroidal axisymmetry assumption, thus finding a solution to the GS equation  is regarded as reconstructing the magnetohydrodynamic (MHD) equilibrium of  a toroidal plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  120  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  The GS equation, resembling the Hicks equation [198] which describes ax-  isymmetric inviscid fluid, is a two-dimensional (poloidal cross-section), nonlinear,  elliptic partial differential equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Owing to its nonlinearity, finding a solution  to the GS equation typically requires an iterative numerical approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Compli-  cating the problem even further, it is an inverse and free boundary problem as  only external measurements of magnetic fields are often only available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' These  difficulties hinder a real-time application of the GS equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Of course, a simple  resolution for the real-time application is to sacrifice accuracy of the solution as  in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' [75].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' But, even if accuracy is eschewed, there exist human expert choices  for numerical convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Current numerical algorithms of the reconstruction,  chiefly EFIT [73], often require decisions made by human experts in manually  choosing measured magnetic data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Those neglected data do not participate in re-  constructing a plasma equilibrium, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', in finding a solution to the GS equation,  as they tend to obstruct finding a converged numerical solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  There have been attempts to parallelize the numerical algorithms based on  GPUs [76,199] or to use a supervised deep neural network [78], which fulfil real-  time demand but human decisions as they are all based on the EFIT algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Contrarily, reconstruction methods using Bayesian inference [200–202] were in-  troduced to eliminate (or at least explicitly articulate) manual selections, but  they are unlikely to be used for real-time purpose due to their required heavy  computational time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We note that reconstructing more detailed plasma equilibria  in real time using internal information is also an active research area [14,77].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  As recent scientific computing is highly supported by deep learning [203],  there have been various approaches for neural networks to learn physics-based  differential equations such as solving the many-electron Schr¨odinger equation  [146, 204], the Navier-Stokes equation [145] and an atmospheric model for cli-  mate modelling [205].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Other examples include interpolating partial differential  equations [8, 144, 206] and regularizing neural networks with the Kohn-Sham  equations [149].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' These previous works require actual solutions [144, 206], prior  knowledge on some of the unknown parameters [8, 145, 205], or approximated  solution states [146,149, 204] of the target governing equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' There were at-  121  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  tempts of solving the GS equation using neural networks [8,207];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' however, they  work only if entire internal profiles over a plasma volume are given with a fixed  boundary condition, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', from a numerical code, VMEC [8, 208], or prescribed  polynomial-based functions [207], which may not be applicable for many of ex-  isting tokamaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Besides, there was an approach [209] for neural networks to  solve a Stefan problem [210] which is a free-boundary problem and describes a  phase-change between a liquid and a solid state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' However, the method assumed  that a boundary of the phase-change between the states is already known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  We propose an algorithm, Grad-Shafranov Deep Neural Networks (GS-DeepNet),  that learns plasma equilibria solely via unsupervised learning without existing  numerical algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' GS-DeepNet does not depend on several aspects in both  current reconstruction methods and other neural networks solving differential  equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' First and foremost, it is trained by self-teaching unsupervised learn-  ing, without use of any guess of solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Only known information is the GS  equation and externally (and locally) measured data with no manual selections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Second, it uses typical fully-connected neural networks known as retaining real-  time plausibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Finally, it uses an auxiliary module that detects boundary in-  formation based solely on network outputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' To reach these outcomes, we develop  neural networks that are capable of solving a nonlinear elliptic partial differential  equation in a free-boundary and inverse condition, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', the GS equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' As a  simple survey, we introduce that a neural network can solve a first-order linear  differential equation, which is discussed in Appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2  Modelling Grad-Shafranov Deep Neural Networks  Our novel algorithm GS-DeepNet has two deep neural networks NN 1  Θ and NN 2  θ  with parameters Θ and θ, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The goal of it is to discover the poloidal  flux function, ψ, a solution of the GS equation on the spatial positions shown in  Fig 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='37B under a given measurement state as its input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='37B shows 41 × 41 grid points where a plasma potentially exists  and the positions of the magnetic diagnostics which obtains radial and axial  components of the poloidal magnetic field (BR and BZ) and the poloidal magnetic  122  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='37: Self-teaching unsupervised learning scheme in  GS-DeepNet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (A) The locations and sensor numbers of the KSTAR magnetic  diagnostics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Colors represent the magnitude of the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (B) 41 × 41 grid  points where the plasmas are potentially generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (C) Schematic  representation of GS-DeepNet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We call the bundle of NN 1  Θ and Diff A the  Maxwell-Net, and NN 2  θ is named as the Force-Balance (FB) Net.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (D–E) The  three-dimensional configurations of ∆∗ψ and ψ from GS-DeepNet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' KSTAR  poloidal field coils (gray), the vacuum vessel wall (orange) and the plasma  facing components (blue) are also shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  123  leasured magnetic signals  sianas  Bz signals  r signals  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  FL12-  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  [w]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0  FL23-  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  [w]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  826  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  15  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  15*  FL34  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  100  R [m]  [m]  R [m]  Grad-Shafranov Deep neural networks (GS-DeepNet)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  Network structure  μoR?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='p\'-ff"  1  BR  DiffA  R  Bz  MD =[BMD,BD,MP]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  FL  Z  NN1  [m]  0  MD  N  NN?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content="  R  MD = [BMD,BD,MD]  p'  0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1  Auxiliary Modules  Boundary  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='04 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Measuredthermal pressures  Detection  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  R[m]  _6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='02 -  100  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2°  500  R [m]  Feature #  D  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Inferred  Inferred △*  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  1 、  0  N  1、  2 、  3 、  4  2  y [m]  0  0  2  2  4  x [m]CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  flux (ψFL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Taking a single spatial point (R, Z) among the spatial positions and  a set of the magnetic data −−→  MD = ( ⃗BR, ⃗BZ, ⃗ψFL) as an input, NN 1  Θ outputs a flux  function, ψ = NN 1  Θ(R, Z, −−→  MD).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The vector of ⃗B(R(Z)) (or ψFL) means a feature  of all obtained ⃗B(R(Z)) (or ψFL) from its measurement locations at a single time  slice during a tokamak operation (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='37A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This network output is fed into  NN 2  θ which outputs both a plasma pressure gradient and a quantity related to  the toroidal magnetic field, (dp/dψ, fdf/dψ) = (p′, ff ′) = NN 2  θ (ψ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Here, p  represents the plasma pressure, and the toroidal field Bφ can turn into f = RBφ  which is related to the poloidal plasma current.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (p′, ff ′) is the variables of the GS  equation (see equation 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Both neural networks have multiple fully-connected  layers [203] with dropout [211] and swish nonlinear activation functions [152]  (See Materials and Methods).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Since we do not depend on existing numerical algorithms, there are not any  guesses of the solution ψ to train NN 1  Θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Instead, GS-DeepNet teaches itself by  an unsupervised learning algorithm following the GS equation and the magnetic  measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' With a given measurement set −−→  MD, NN 1  Θ generates ψ all over  the spatial positions (R, Z) where ψ is the vector representation of ψ consistent  with the vector (R, Z), and (R, Z) is the vector representation for all the points  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='37B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Passing through the automatic differential operator [212, 213]  (Diff A in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='37C), the flux functions ψ turn into BR(= −1/R · ∂ψ/∂Z),  BZ(= 1/R · ∂ψ/∂R) and ∆∗ψ{= (∂2/∂R2 + ∂2/∂Z2 − 1/R · ∂/∂R)ψ} based on  Maxwell’s equations, where the symbol · represents the element-wise product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  A plasma is usually placed inside a boundary called the plasma bound-  ary (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='37B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This boundary dividing the plasma region from the vacuum  area cannot be defined until the solution ψ is prepared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The pressure p and the  poloidal current function f of the plasma are ideally defined within the plasma re-  gion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, after locating the boundary through an auxiliary module for bound-  ary detection (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='37C) based on (BR, BZ, ψ), NN 2  θ generates (p′, ff ′) by  using the flux functions inside the plasma, ψin, where (p′, ff ′) is also the vector  representations for (p′, ff ′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Then, (p′, ff ′) forms −µ0R2 · p′ − ff ′(= ∆∗ψin)  based on the force balance equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This is also related to the toroidal plasma  124  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  current density Jφ = −∆∗ψ/(µ0R) where µ0 is the vacuum permeability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Since  −µ0R2 ·p′ −ff ′ is constrained with the given magnetic data −−→  MD via a response  matrix ¯¯R estimated based on the Biot-Savart law, it may be viewed as a potential  guess of the GS equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, the main concept of the unsupervised learning  algorithm is that NN 1  Θ is repeatedly taught by NN 2  θ which takes ψ from NN 1  Θ  as an input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We call the bundle of NN 1  Θ and the differential operator Diff A the  Maxwell-Net, and NN 2  θ is named as the Force-Balance (FB) Net.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The networks’ parameters are updated to keep their ∆∗ψ matched with  each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Since we theoretically have a vacuum on the outside of the plasma  boundary, NN 1  Θ is updated to have null current densities for ∆∗ψout estimated  from ψout, the flux functions outside the plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Furthermore, the Maxwell-Net  outputs corresponding to the measurement locations, (BR, BZ, ψ)md, are trained  to match −−→  MD as the initial value of a differential equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The pipeline of this  self-teaching procedure is presented in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='37C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The Biot-Savart law explains a relationship between a magnetic field (or  flux) and its corresponding current source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This relationship can depend on a  single independent variable, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', a magnitude of the current source in Ampere  if the locations of the magnetic field (or flux) and current source are fixed, and  the source carries a constant current at a certain time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Thus, we treat the  toroidal current density Jφ of the plasma as a constant current source, and each  Jφ on a single R-Z grid position is modelled with an arbitrary three-dimensional  volumetric current beam having rectangular cross-section (See fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' S4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus,  we can pre-calculate a contribution of Jφ generating a magnetic field (or flux) at  a measurement position as rij where the subscript i and j represent the indices  of the magnetic sensor locations and J φ over all 41×41 grid points, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  We estimate rij for all grids at first due to undefined plasma boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This  contribution rij can be contained in a matrix called the response matrix for the  plasma, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', ¯¯Rp whose matrix size is Nmd × 412 where Nmd is the size of −−→  MD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  After the boundary is detected via the auxiliary module, the matrix ¯¯Rp is reduced  to ¯¯Rp,in whose size is Nmd×Nin where Nin is the number of the grid points inside  the boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  125  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  A tokamak has external field coils that we control to generate the poloidal  magnetic field (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='37D–E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' With the identical procedure with the plasma,  we pre-calculate the contributions of the external coils as ¯¯Rext.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We also pre-  estimate the contributions of the vessel currents (currents induced in tokamak  structures such as the vacuum vessel wall) which cannot be negligible [214,215]  as ¯¯RV V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Therefore, we can relate −−→  MD with every current source in the tokamak,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', −−→  MD = ¯¯R¯¯Iφ where ¯¯R = ( ¯¯Rp,in, ¯¯Rext, ¯¯RV V ) with ¯¯Iφ containing Jφ, Jext and  JV V as a column vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The current densities of the external coils Jext are  known, while the vessel currents JV V are required to be inferred [216] during  the unsupervised training procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Further technical details are described in  Materials and Methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  GS-DeepNet includes two auxiliary modules for plasma boundary detection  and locally measured plasma pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Because solving the GS equation is a  free-boundary problem, the plasma boundary cannot be determined until the flux  function ψ is defined all over the grid points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The boundary can be regarded as an  outermost line which connects R-Z positions whose flux functions are identical  to one another as well as encloses a whole plasma area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, the boundary  module detects the R-Z positions by searching ψ at the boundary spots based  on the Maxwell-Net outputs (see Methods for details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  As explained before, the FB-Net outputs (p′, ff ′) by taking ψin, and its  parameters are updated based on the magnetic data −−→  MD by forming −µ0R2p′ −  ff ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We came up with this update procedure in case that measured data to train  the network outputs directly is not available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, the pressure module is used  when measured plasma pressure pm is available although it is spatially localized  in the fixed R-Z positions (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='37B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' To use the measured pressure pm in  order to train the FB-Net p′, the module performs Gaussian process regressions  [131] (a non-parametric regression) to the measured pressure pm [90, 92] and  subsequently estimates derivatives of the regressed pressure pm,GP with respect  to ψ which is given by the Maxwell-Net.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Similarly, the poloidal current function f  can be deduced from measurements for the local pitch angle between the toroidal  and the poloidal magnetic fields [71], which can be used to train the FB-Net ff ′  126  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  with using Gaussian process regressions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This is left as future works since we  here consider a way how to use spatially localized data in GS-DeepNet, and it is  presumably sufficient to show the method for the measured pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The neural networks in GS-DeepNet are trained by the self-teaching unsu-  pervised training algorithm fundamentally based on the GS equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' First and  foremost, we initialize both networks with random parameters, Θ0 and θ0, re-  spectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' At every iteration i ≥ 1 and each feature t, a guess of the solution  ψ = NN 1  Θi−1(R, Z, −−→  MDt) is generated, and (BR,t, BZ,t, ψt, ∆∗ψt) is estimated  using the automatic differential operator Diff A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' After a plasma boundary is  determined (as well as preprocessing of pm  t is done), (p′  t, ff ′  t) = NN 2  θi−1(ψin,t) is  generated, and (−µ0R2·p′  t−ff ′  t, ¯¯Iφ,t, p′  t) is prepared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' With a randomly sampled  feature from the total feature space, renewed network parameters Θi are trained  by (BR, BZ, ψ, ∆∗ψ) compared to (−−→  MD, −µ0R2 · p′ − ff ′(ornulls)), while new  network parameters θi are updated by (−µ0R2 · p′ − ff ′, ¯¯Iφ, p′) compared to  (−−→  MD, pm,GP) using the response matrix ¯¯R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We use gradient descent for training  the parameters Θ and θ by means of loss functions l1:  l1 =  �  (BR, BZ, ψ)md − −−→  MD  �2  + (∆∗ψin + µ0R2p′ + ff ′)2 + (∆∗ψout)2 + c1||Θ||2  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='36)  and l2, respectively:  l2 = ( ¯¯R¯¯Iφ−−−→  MD)2+  �  α  Nin  �  i=1  �  Rip′  i− ff ′  i  Riµ0  �  −Im  P  �2  +c2|θ|+(p′−pm,GP)2 (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='37)  where l1 and l2 are averaged over the mean-squared errors, c1 and c2 are the  coefficients for L2 and L1 weight regularizations, respectively, to avoid overfit-  ting, and α �Nin  i=1(Rip′  i − ff ′  i/Riµ0) is the sum of the toroidal current densities  multiplied by the area of the rectangular cross-section α, which turns out to be  the total plasma current IP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Im  P is the measured total plasma current by the  Rogowski coil [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The last term of l2 are only used when the measured pressure  pm is usable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  As an example, three-dimensional configurations of ∆∗ψ and ψ from the  Maxwell-Net are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='37D and E, respectively, with some tokamak  127  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='38: Statistical evaluation of GS-DeepNet training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (A) Blue  box: the comparison of the initial values of the Maxwell-Net with the magnetic  dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Red box: the comparison of the Maxwell-Net ∆∗ψ with the FB-Net  ∆∗ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (B–D) The Maxwell-Net BR, BZ and ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (E–F) Left: the configurations of  the Maxwell-Net ∆∗ψ for a limited and diverted plasmas, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Right:  the uncertainty configurations of the Maxwell-Net ∆∗ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' They show their  structural consistencies with ∆∗ψ such that if ∆∗ψ increases, then uncertainty  increases with it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (G) R2 for ∆∗ψ between the Maxwell-Net (x-axis) and the  FB-Net (y-axis).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  structures of the KSTAR [45], one of the first research tokamaks with fully su-  perconducting magnets in the world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  128  Network structure  A*+  μoR"p\' -ff"  BR  DiffA  Bz  MD = [BMD,BD,M]  MAG NN: R2=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9876  MD =[BMD,BD,MP]  MAG NN  MD  R2=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9958  MAG NN  MD  MAG NN  R2=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9944  MD  R2=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9848CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3  Statistical analysis of GS-DeepNet training  Our unsupervised training scheme was performed to train our algorithm GS-  DeepNet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' From the completely random network parameters, the training con-  tinued until it was terminated by the early stopping method (a regularization  method to avoid losing generalization for unseen features) [217], which approxi-  mately took a day.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  We collected 50 experimental plasma discharges of the KSTAR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' A plasma  discharge (fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' S2A–E) represents a series of experimental procedures: first, the  external magnetic field from the external coils is built up;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' then, a plasma is  initiated (or discharged) and controlled by the external magnetic field until it  is eventually disappeared due to mechanical and physical reasons such as the  maximum limit of coil currents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' A typical discharge length of the KSTAR is  of the order of 101-2 seconds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Among all time-steps of 50 discharges, we chose  ∼ 104 time slices (features) for the magnetic and pressure measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' With  approximate 2 × 102 spatial R-Z positions, network parameters were dealt with  about 2 × 106(= 2 × 102 × 104) dataset for covering combination of the total  features as well as all the R-Z points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 80%, 5% and 15% of the dataset went to  the training, validation and test datasets, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='38 shows the statistical evaluations of GS-DeepNet training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We  did not use solutions of the GS equation calculated from an existing numerical  algorithm to train the networks, rather we used the magnetic measurements  to constrain the initial values of the network solutions and the self-teaching  unsupervised learning for the networks to acquire the knowledge of the GS  equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Thus, as instructed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='38A, we compared the Maxwell-Net  (BR, BZ, ψ)md and ∆∗ψ with the obtained magnetic data −−→  MD and the FB-Net  ∆∗ψ(= −µ0R2 · p′ − ff ′), respectively, to prove whether GS-DeepNet has good  understanding for both the initial values and the GS equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Here, we did not  use the measured plasma pressure, meaning that the last term of the loss func-  tion l2 constraining the form of the pressure gradient did not participate during  the self-teaching unsupervised learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='38B–D show the comparisons of the Maxwell-Net (BR, BZ, ψ)md  129  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  and −−→  MD over the test dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' KSTAR has 42 magnetic pick-coil coils each  for ⃗BR and ⃗BZ, and 45 flux loops for ⃗ψFL [65] (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='37A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Among them,  31 intact pick-up coils each were selected, while 45 flux loops were used after  their intactness was inferred based on both a deep neural network and the intact  pick-up coils [142].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' It is worth to mention that, often, some of the magnetic  measurements are impaired since they are susceptible to damage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The funda-  mental difference between our GS-DeepNet and an existing numerical algorithm  is that we used every magnetic measurement except the one that is fully out  of order such that only null signals are measured, while an existing numerical  algorithm yet requires human selections among those intact data for its numerial  convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Moreover, we can also cover the flawed data by invoking an impu-  tation scheme [3] that estimates the missing magnetic data based on Bayesian  inference [86].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  As an example, the left column in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='38B–D shows the initial values of  the network compared to their corresponding −−→  MD where they qualitatively well  agree with each other within one standard deviation (1-σ) uncertainties of the  network given by Monte Carlo (MC) dropout [153].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In addition, with the use of  the coefficient of determination R2 [154] (BR, R2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9876;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' BZ, R2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9958;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  ψFL, R2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9944), these suggest that GS-DeepNet may achieve proper initial  values for solutions ψ of the GS equation which were also used as its input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  We presented the examples of configurations of the Maxwell-Net ∆∗ψ under  certain features as inputs with their determined plasma boundaries using the  boundary module (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='38E–F).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We have fundamentally two kinds of plasma  boundaries in a tokamak [218]: a limited plasma boundary where the plasma is  ‘limited’ by hitting a solid wall (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='38E);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' a diverted plasma boundary where  a magnetic X-point, a null point whose poloidal magnetic field is zero, is created,  and only a leg extended from the X-point touches the wall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='38F shows  the X-point (the point where the red line crosses) with two legs extended from it  in the lower left corner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Note that the uncertainty configurations of the Maxwell-  Net show their structural consistencies with ∆∗ψ configurations such that large  uncertainty happens around large ∆∗ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  130  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='39: Equilibrium knowledge learned by GS-DeepNet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (A) The  physical knowledge discovered by GS-DeepNet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (B) The limited and diverted  plasma equilibria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (C) The histograms of plasma parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (D) The  comparison of the plasma pressure from the FB-Net with the measured one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  (E) Left: the measured tan γ (red), the estimated tan γ from GS-DeepNet  without the kinetic constraints (green) and that from GS-DeepNet with the  kinetic constraints (blue) are presented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Right: the comparison of RMSE of  tan γ between GS-DeepNet with (y-axis) and without (x-axis) the kinetic  constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Colors represent the histogram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  To assess whether the GS equation was properly learned, we compared the  Maxwell-Net ∆∗ψ (the left hand side of the GS equation) with the FB-Net ∆∗ψ  (the right hand side of the GS equation) in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 2G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Namely, the Maxwell-Net  ∆∗ψ is required to be comparable with the FB-Net ∆∗ψ generated from taking  the Maxwell-Net ψ as the network inputs if the self-teaching training reasonably  worked.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' With the coefficient of determination R2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9848 estimated with the  test dataset, this proposes that GS-DeepNet may achieve the knowledge of the  GS equation with its solutions ψ as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' It is worth mentioning that an example  of comparing the FB-Net ¯¯R¯¯Iφ with −−→  MD)2 can be found in Supplementary section  S3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  131 HoR"p\' -ff"  BR  MD =[BD,BD,iMP]  MD  MD =[BMD, yD,MP]  EFIT  EFIT  EFIT  MAG NN  MAG NN  MAG NN  MAG NN  RMSEpres = RMSEMag  tan yMag  pot =peN + ppred  tan ypres  PtoN = 2pAN  tan Ym  pmCHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='40: Performance of GS-DeepNet with local pressure  constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (A) The Maxwell-Net ∆∗ψ with the kinetic constraints is shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Compared to Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='38F, the configuration become noticeably changed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (B) R2  for BR, BZ, ψFL and ∆∗ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (C) Two plasma equilibria with (colored) and  without (black) the kinetic constraints is shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (D) The histograms of the  plasma parameters from EFIT (green), GS-DeepNet with (orange) and without  (purple) the kinetic constraints are shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4  Physical knowledge learned by GS-DeepNet  GS-DeepNet understood the knowledge of the GS equation conforming to Maxwell’s  equations as well as the force balance from its self-teaching training procedure  with the measurement constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Here, we presented that GS-DeepNet also  discovered the physical knowledge within the GS equation from the Maxwell-  Net ψ and the FB-Net (p′  t, ff ′  t) (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='39A) which were trained indirectly (or  partially directly).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='39B shows two plasma equilibria (the solutions ψ) discovered by  the Maxwell-Net corresponding to the configurations of the Maxwell-Net ∆∗ψ  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='38E–F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We compared these solutions with equilibria reconstructed  from an existing numerical algorithm, EFIT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Note that we cannot argue whether  or not the plasma equilibria from EFIT are the accurate solutions of the GS  equation since they have human decisions for numerical convergence, and most  132  R2=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9985  R2=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9979  R2=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9651  R2=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9936  BR  Bz  FL  △*山  MAG NN  EFIT  EFIT  EFIT  EFIT  KIN NN  MAG NN  MAG NN  MAG NN  MAG NN  KIN NN  KIN NN  KIN NN  KIN NNCHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  importantly there are no means to measure the equilibria directly to compare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' At  least, what we may be able to argue is that EFIT is commonly used to reconstruct  equilibria in the field of nuclear fusion, and GS-DeepNet is capable of providing  such equilibria without influence on several aforementioned aspects in numerical  algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In the right corners of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='39B, we presented the uncertainty  configurations for the Maxwell-Net ψ that show larger uncertainty at the center  region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  For further statistical comparison, we presented the histograms of plasma pa-  rameters (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 3C) such as minor radius a (half distance between innermost and  outermost R positions), major radius R0 (R at the central axis of an equilibrium),  elongation κ (ratio of vertical to horizontal sizes of a plasma) and triangularity  δ (degree of shape closeness to triangle) (see fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' S2G in Supplementary section  S2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Furthermore, we named and related the FB-Net outputs with the plasma  pressure gradient p′ and the toroidal magnetic field Bφ = f/R, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Thus, we presented the suitability of their terminologies compared with their  corresponding measured data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='39D shows the plasma pressure from the FB-Net compared with  the measured one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The plasma pressure p is generally estimated based on the  ideal gas law [219], i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', p = nT where n is the plasma density, and T is the  plasma temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' A plasma is an ionized gas that contains charged particles:  ions and electrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This plasma is mainly heated up by using its own electrical  resistivity [220], externally injected energetic ions (whose temperature is greater  than the plasma) [221] and external injection of electromagnetic waves [222].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Therefore, to assess the plasma pressure completely, it is required to know the  electron pressure neTe, the ion pressure niTi as well as the pressure of externally  injected energetic ions pext, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', p = neTe + niTi + pext.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The electron pressure neTe can be measured by the Thomson Scattering  (TS) system [65, 197] using the scattered and Doppler-shifted photons from an  interaction between high-power laser photons and the plasma electrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Since  the plasma is known as having quasi-neutrality (ne ≈ ni) [38], the ion pressure  133  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  niTi can be estimated with the quasi-neutrality and measuring Ti based on the  energetic ion injection called the Charge Exchange Spectroscopy (CES) system  [66] by capturing the Doppler line width and deviation of a spectrum emitted  from an interaction between the energetic and the plasma ions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Unfortunately,  measurement systems for pext still need to be developed further [68–70], meaning  that we cannot measure pext yet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Thus, to check whether or not GS-DeepNet is able to contain the physical  knowledge for the FB-Net p′, we presented the plasma heated up by solely the  plasma resistivity, meaning that there were no externally injected energetic ions  to be considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' But, this fact also made measuring Ti unavailable, thus the  pressure was estimated with an assumption that the electron temperature came  into a thermal equilibrium with the ion temperature, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', p = neTe + niTi =  2neTe (this assumption has commonly been made in the field of nuclear fusion  [223–225]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Here, we devised two different ways of the verification: first, the  measured pressure is known by p = 2neTe which is used to train the FB-Net p′  based on equation 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' second, the electron pressure is only known, and the FB-Net  p′ is in charge of inferring the ion pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, the plasma pressure p turns  out to be p = neTe + pNN  pred where pNN  pred is inferred by the FB-Net.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' To this end,  we trained a neural network (using the same architecture of the FB-Net except  the output ff ′) with respect to the electron pressure pe = neTe by only using  the last term of equation 2, while the rest of equation 2 was used to train the  FB-Net.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Both ways of the verification yielded the total plasma pressures consistent  with each other within their uncertainties (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='39D) although they are not  perfectly matched with each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This suggests that the FB-Net p′ may capture  some knowledge of the pressure gradient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' These uncertainties are quantified via  MC dropout.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  As mentioned before, the FB-Net ff ′ can be constrained with a magnetic  pitch angle measurement which is called the Motional Stark Effect (MSE) system  [71,72] measuring local pitch angles using the polarization of the motional Stark  effect emission signals by the energetic ion injection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Although we left this to  134  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  future works, we presented the comparison between the FB-Net ff ′ and the MSE  measurements in order to verify the knowledge learned by the FB-Net ff ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  KSTAR MSE system [72] has 25 channels, and each channel measures the lo-  cal pitch angle γ given by tan γ ∼= A1BZ/(A2Bφ+A3BR) where the A coefficients  are the fixed values related to the geometry information of the measurement sys-  tem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We prepared GS-DeepNet results trained with and without using the last  term of equation 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Here, we collected the measured tan γ and neTe as well as  Ti from 50 KSTAR discharges and let the FB-Net take charge of inferring pext.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The FB-Net was used to generate f(= R · Bφ), and the Maxwell-Net was used  to generate (BR, BZ) to estimate the tan γ formula.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Note that the density and  temperature data are often called the kinetic data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Both GS-DeepNet results with and without using the kinetic information  qualitatively show the similarity to the measured pitch angle, tan γm, in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='39E even though their poloidal current functions f were trained indirectly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='39E also shows the histogram of Root Mean Square Error (RMSE) of  tan γ, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', RMSE = {�n  i=1(tan γGS,i−tan γm,i)2/n}0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5 for each feature in the test  dataset where n is the total channel number of the MSE system (n = 25), and  tan γGS,i is the local pitch angle estimated from GS-DeepNet results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Although  some of the RMSE results constrained with the kinetic data, RMSEPres, are  greater than those using the magnetic data only, RMSEMag, most of RMSEPres  are smaller than RMSEMag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This is presumably due to the fact that RMSEPres  can contain the internal information of the plasmas even if it is localized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' It is  worth to mention that the tan γGS profiles in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='39E have RMSEPres = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='023  and RMSEMag = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='024, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5  Final performance of GS-DeepNet with the kinetic  constraints  As mentioned earlier, we applied the kinetic measurement constraints to GS-  DeepNet via our unsupervised learning scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Since we used the localized  internal measurements to train the FB-Net p′, the Maxwell-Net ψ and ∆∗ψ were  135  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  qualitatively altered, compared to Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='38F–G and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='39B–C whose results  depended only on the magnetic measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='40A shows that the Maxwell-Net ∆∗ψ with the kinetic constraints  became noticeably varied compared to Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='38F where they used the same input  feature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' But of course, GS-DeepNet caught the initial values for its solutions well  enough with the coefficient of determination R2 of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9936, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9985 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9979  for BR, BZ and ψFL, respectively, in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='40B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The result of comparing the  Maxwell-Net ∆∗ψ with the FB-Net ∆∗ψ shows the coefficient of determination  R2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9651 which slightly diminishes compared to Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='38G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We presume  that this might happen because we kept using the same network architecture  and the coefficients for L2 and L1 weight regularizations although the shapes  of 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='38 became more complex when we adopted the kinetic constraints to the  unsupervised training procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, increasing complexity of the networks  (in other words, decreasing the coefficients for the regularizations for instance)  can possibly improve the network performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In addition, we also expect that  using the MSE measurements to constrain the FB-Net ff ′ directly may help the  performance improved, which might bring the histogram of RMSE of tan γ in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='39E much closer to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='40C shows the comparison of two plasma equilibria corresponding to  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='40A and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='38F, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Unlike the significant structural change  in ∆∗ψ, there were seemingly slight variation depending on the constraints used  in GS-DeepNet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nevertheless, this slight change made notable difference in ∆∗ψ  followed by the GS equation, meaning that careful acquirement of solutions of the  GS equation might be required for those who would like to have more complex  structures of plasma equilibria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We also prepared the histograms of the plasma  parameters (minor radius a, major radius R0, elongation κ and triangularity δ)  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='40D for additional statistical comparisons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  136  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6  Materials and Methods  Domain knowledge  The plasma force-balance equation can be regarded as the well-known incom-  pressible Navier-Stokes equations [226] under assumptions of the steady-state  and no viscosity conditions, together with the Lorentz force as the external force  instead of the gravitational force, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=',  −∇p + ⃗J × ⃗B = 0  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='38)  where p is the plasma pressure, ⃗J is the current density, and ⃗B is the mag-  netic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' From this force-balance equation, we can derive the GS equation [42]  (which can be explained in a form of the Hicks equation) with the toroidal sym-  metry assumption in the cylindrical coordinates (R, φ, Z) by taking advantage of  Maxwell’s equations as shown below:  ∆∗ψ ≡  �  R ∂  ∂R  1  R  ∂  ∂R + ∂2  ∂Z2  �  ψ  = −µ0RJt  = −R2µ0  dp(ψ)  dψ  − f(ψ)df(ψ)  dψ  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='39)  where combining Maxwell’s equations, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', the Gauss’s law for magnetism, ∇ ·  ⃗B = 0, and the Ampere’s law, ∇× ⃗B = µ0 ⃗J, together derives the first two lines of  the equation, R ∂  ∂R  1  R  ∂ψ  ∂R+ ∂2ψ  ∂Z2 = −µ0RJφ, and the force balance equation is used to  derive the second to third lines of the equation above, −R2µ0  dp  dψ −f df  dψ = −µ0RJφ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Here, ψ is the poloidal flux function, Jφ is the toroidal current density, µ0 is the  vacuum permeability, p(ψ) is the plasma pressure as a function of ψ, and f(ψ)  is the poloidal current function as a function of ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The poloidal current function  f has the relation with the toroidal magnetic field Bφ such that f = RBφ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Technically, the toroidal current density Jφ is required to be known over the  whole tokamak area in order to solve the GS equation, which is barely achiev-  able due to the harsh environment of the plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Instead, the external magnetic  measurements (and the spatially localized pressure measurements) are the only  137  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  information for the GS equation, which causes an inverse problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In addition,  since we only have ∼ 102 number of the measurement data to be used for dis-  covering solutions of the GS equation on the 41 × 41(∼= 103) spatial grids for a  certain during a tokamak operation (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='37B), this results in an ill-posed  problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Finally, the plasma boundary which divides the plasma region from the  vacuum region can be determined after the solution ψ is found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This corresponds  to the definition of a free-boundary problem since a boundary is unknown until  we solve the GS equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Therefore, solving the GS equation is a free-boundary  and ill-posed inverse problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Again, we tackled this problem by developing the Maxwell-Net, the FB-Net  and the auxiliary modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Starting from scratch, the Maxwell-Net generates a  solution ψ of the GS equation and achieves initial values of the solution from  the prepared magnetic data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This Maxwell-Net solution is used to determine a  plasma boundary via the auxiliary module for boundary detection, and the FB-  Net generates a toroidal current density Jφ given by the Maxwell-Net solution as  well as the boundary information from the module, constrained with the mag-  netic data using the response matrix ¯¯R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Therefore, the Maxwell-Net is taught  by the FB-Net output under our self-teaching unsupervised learning algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  In case that we can use the local pressure measurements to train the FB-Net,  we prepare the auxiliary module for plasma pressure which performs Gaussian  process regressions to the measured pressure and takes the derivative of it with  respect to the Maxwell-Net ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, our GS-DeepNet is capable of solving the  GS equation, starting tabula rasa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Data acquisition and preprocessing  From 50 KSTAR experimental discharges that we collect, the measured data  from the magnetic pick-up coils, the flux loops and the Rogowski coils for the  plasma and external coil currents (the poloidal field coils and in-vessel coils [45])  as well as the TS, CES and MSE systems is used for training, validation and  testing our GS-DeepNet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The magnetic pick-up coils, in fact, measure the poloidal magnetic field  138  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  normal and tangential to the vessel wall, Bn and Bt, where the measurements  are installed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Thus, we transform Bn and Bt into BR and BZ based on the  following coordinate transformations:  BR = −Bn sin ξ + Bt cos ξ  BZ = Bn cos ξ + Bt sin ξ  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='40)  where ξ is the angle between the direction normal to the wall and the radial  direction (see fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' S5 in Supplementary section S5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  A noise reduction technique is applied to the magnetic pick-up coils, the flux  loops and the Rogowski coils based on the boxcar average with a time scale of  1 msec which is smaller scale than a typical time scale of KSTAR equilibrium  reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Furthermore, we preprocess the signal drifts in the magnetic  measurements [78] based on Bayesian inference since the magnetic data tends to  suffer from the signal drift in time such that the baseline of the data increases or  decreases over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Response matrix  Following a previous approach [117] that models the plasma and external coils  as toroidal current beams with rectangular cross sections [47], we estimate the  response matrix ¯¯R with the following expressions for a matrix component rij  where the subscript i is the index for the magnetic measurements:  r(BR)  ij  = µ0  2π  � Zj,2  Zj,1  � Rj,2  Rj,1  dRdZ Zi − Z  Ri  �  k  4RRi  �  K(k)+ R2 + R2  i + (Zi − Z)2  (R − Ri)2 + (Zi − Z)2E(k)  �  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='41)  where r(BR)  ij  is the component for BR, and the subscript i is set to 1 ≤ i ≤ 31,  r(BZ)  ij  = µ0  2π  � Zj,2  Zj,1  � Rj,2  Rj,1  dRdZ  �  k  4RRi  �  K(k) + R2 − R2  i − (Zi − Z)2  (R − Ri)2 + (Zi − Z)2E(k)  �  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='42)  where r(BZ)  ij  is the component for BZ, and the subscript i is set to 32 ≤ i ≤ 62,  r(ψF L)  ij  = 2µ0  � Zj,2  Zj,1  � Rj,2  Rj,1  dRdZ  �  R  Ri  1  √  k  ��  1 − 1  2k  �  K(k) − E(k)  �  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='43)  139  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  where r(ψF L)  ij  is the component for ψFL, and the subscript i is set to 63 ≤ i ≤  107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Here, k is the elliptic modulus k =  4RRi  (R+Ri)2+(Zi−Z)2, (Ri, Zi) is the location  of the magnetic measurement, and (Rj,1, Rj,2, Zj,3, Zj,4) represents the location  of the rectangular cross section of the toroidal current beam (see fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  S4 in  Supplementary section S4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The subscript j is set to 1 ≤ j ≤ 412(= 1,681)  for ¯¯Rp, 1 ≤ j ≤ 30(= 14 + 16) for ¯¯Rext and 1 ≤ j ≤ 18 for ¯¯RV V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The  KSTAR has 14 poloidal field coils and 16 segments of the in-vessel coils as the  external magnetic coils.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  We divide the tokamak vessel wall into 18 current-  carrying segments, following a previous approach used in the KSTAR [227].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  In the equations above, K(k) and E(k) are the complete elliptic integral of  the first and the second kinds, respectively, as defined below:  K(k) =  �  π  2  0  dθ  1  �  1 − k2 sin2 θ  ,  E(k) =  �  π  2  0  dθ  �  1 − k2 sin2 θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='44)  The vessel currents JV V are treated as free-parameters [117] which are optimized  during the network optimization process based on an approach [216] suggesting  that the vessel currents can be reasonably inferred even though actual conducting  structures are not precisely identified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Auxiliary module: boundary and pressure modules  A fundamental concept to determine a plasma boundary is finding a X-point  by using the fact that the poloidal magnetic field at the X-point is ideally zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Since a plasma boundary is a connected line of R-Z positions enclosing the  plasma area where flux functions on the R-Z positions are all the same, we  estimate a flux function ψ at the X-point and use it to determine a location of  the boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, the auxiliary module for boundary detection performs the  following procedure: first, the module receives the Maxwell-Net (ψ, BR, BZ) over  the spatial grids and estimate magnitudes of the poloidal magnetic field, BP, via  BP =  �  B2  R + B2  R;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' second, the module searches a R-Z point where magnitude  of its BP is the smallest;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' third, by feeding the R-Z point into the Maxwell-Net  140  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  again, the module can obtain the flux function ψ at the X-point, ψb, and use it  to find R-Z positions whose flux functions are identical to ψb;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' finally, in case that  the plasma is limited, the module compares ψb with flux functions on locations of  the solid wall by using the Maxwell-Net.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' If some of the R-Z positions possessing  ψb are out of the wall, then the module defines that the plasma is limited or vice  versa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' It is worth to mention that the plasma boundary is always changed during  a tokamak operation (fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' S2F).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The major role of the auxiliary module for plasma pressure module is to  perform Gaussian process regression (GPR) to the measured plasma pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  As mentioned before, this module takes the derivative of the GPR-regressed  pressure with respect to the Maxwell-Net ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Here, we use a finite difference  method to calculate the regressed pressure gradient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Optimization  Our neural networks NN 1  Θi and NN 2  θi are trained via TensorFlow [103] with one  GPU worker and 20 CPU cores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' We pass one randomly selected measurement  feature to the optimization process at a time, meaning that the batch-size is  412 + 107 = 1,788 corresponding to the grid points and the locations of the mag-  netic measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' A total mini-batch size is approximately 8,000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Stochastic  gradient descent is used to optimized out network parameters with the loss func-  tions in equations 1 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The coefficients for the L2 and L1 regularizations  used in the loss functions are set to c1 = 10−3 and c2 = 10−2, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' At  every iteration, a new checkpoint is saved and used to estimate the validation  loss for the early stopping method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Neural network architectures  The network NN 1  Θ uses 31 BR, 31 BZ, 45 ψFL from a certain time slice, and a  single R-Z point as its input whose size is 1 × 109(= 31 + 31 + 45 + 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This  input passes through three fully connected layers with the swish nonlinearities  and a fully connected linear layer, then turns into a scalar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Each layers have 100  hidden neurons and a bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The output scalar is treated as a solution ψ on the  141  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  R-Z position, and processed by the automatic differential operator Diff A that  produces BR, BZ and ∆∗ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Dropout with a rate of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='05 is applied to all the fully  connected layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Similarly, the network NN 2  θ has a fully connected layer with the swish non-  linearity and a fully connected linear layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Each layer has 60 and five neurons,  respectively, and applies dropout with a rate of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='10 as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Taking a scalar (a  solution ψ from the network NN 1  Θ) as an input, this network outputs a vector of  size 2, corresponding to the pressure gradient p′ and the poloidal current related  variable ff ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  These networks are initialized to random weights based on Glorot (or Xavier)  initialization [151].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='7  Discussion  Our results reasonably demonstrate that a self-teaching unsupervised learning  scheme is applicable for deep neural networks to learn a second-order nonlinear  differential equation such as the GS equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Without using any guess or pre-  calculated solutions of the GS equation, we prove that it is possible to train deep  neural networks to acquire knowledge of the solution of the GS equation which  is a free-boundary and inverse problem required numerical algorithms in general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Since our approach do not depend on existing numerical algorithms (or existing  reconstruction methods), GS-DeepNet is unfettered with the challenges raised in  the existing methods as mentioned earlier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Furthermore, our approach is possible  to include not only external measurement constraints but also both external and  internal (but localized) measurement constraints in the unsupervised training  procedure without any significant changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  We introduce the method to solve a differential equation via neural networks,  and leave using various measurements to constrain the network training as future  works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, we plan training neural networks with our unsupervised learning  scheme by including other plasma measurements such as the MSE pitch angle  measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Furthermore, we have plans to search the most suitable architec-  ture of a neural network to improve its performance when internal constraints  142  CHAPTER 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural network in fusion research  are involved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Most physical phenomena can be, in general, expressed in differential equa-  tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, our work might be helpful for other engineering and science fields to  support solving their differential equations, starting from scratch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Furthermore,  previous researches using GAN [96] to simulate complex physical systems such as  accelerators [98–100] are likely to be improved based on our approach by giving  physical knowledge to them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  143  Chapter 5  Conclusions  “Farewell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' My brave Hobbits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' My work is now  finished.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Here at last, on the shores of the  sea.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='comes the end of our Fellowship.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' I will not  say “Do not weep”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='for not all tears are an evil.”  — Gandalf the White,  The Lord of the Rings  So far, we – me and the readers of this thesis – have had a journey with the neu-  ral networks which proved the fact that they are really able to solve a governing  equation, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', the Grad-Shafranov equation in our case which is a second-order  non-linear and elliptic partial differential equation for a two-dimensional plasma,  by themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Here again, I would like to emphasize that the way that the  networks solve the Grad-Shafranov equation is indeed general and applicable to  many other governing equations in various scientific problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Only tedious part  that one needs to do is switching the Grad-Shafranov equation with other differ-  ential equations, then modifying the network architectures slightly to be suitable  for their own problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' As we have shown together previously, I have defined  the differential equations as the cost functions of the networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Namely, given  measurement data and their corresponding governing equations, the networks  are trained automatically based on gradient descents of the cost functions and  capture physical behaviors of interest without taking a glance at any man-made  solutions of the problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Furthermore, one can reflect the principle of Occam’s  razor to the networks by appropriately modifying forms of the cost functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  This thesis has showed that the neural networks are able to produce plasma  equilibria whose quality is equivalent to EFIT results, which are regarded as well-  144  CHAPTER 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Conclusions  converged solutions of the GS equation, in real time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In addition, the consistent  flux signals can be fitted by the neural networks, which can be available for the  plasma reconstruction whose quality is as reasonable as the plasma equilibria  attained by selecting some of the measurements arbitrarily based on human (ex-  pert) decisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian neural networks applied in fusion research have showed  that we can quantify the uncertainty of the network models which solve a free-  boundary and inverse problem to generate plasma equilibria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Of course, this  thesis still needs to show applicability to long pulse discharges of tokamaks, and  thorough consistency with the MSE diagnostic system, which is future works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Applying the methods used in this thesis to a method such as GAN that may  complement existing physics simulations is also planned to be conducted for  tokamak plasmas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  However, we should think about this, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', what is better about solving dif-  ferential equations with neural networks than with conventional methods such as  finite difference method?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' There are numerous conventional methods that exist  already to solve differential equations, and these methods also proved that they  can be quantitatively evaluated and provide reasonable outcomes of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In  other words, good (sometimes fantastic) solutions of differential equations can be  already obtained by the existing algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' At this moment, what I can men-  tion about neural networks is that a lot of trends have appeared and disappeared  in the field of neural networks over the past decades, and the method of solving  differential equations via networks may also be one of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Of course, I want  to note that networks are powerful to calculate derivatives really conveniently  through the back-propagation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Nevertheless, let me suppose that neural networks are trained only with pre-  pared solutions of governing equations of interests through supervised learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The results of the trained networks, of course, will be really similar to the so-  lutions used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' However, can we affirm that the network results truly satisfy the  governing equations used to prepare the solutions?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' I would say, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' I have con-  firmed through my findings that this may not be true.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' As dealt with previously,  I trained the network with the solutions of the Grad-Shafranov equation calcu-  145  CHAPTER 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Conclusions  lated from EFIT, but the network results did not follow the equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, I  would argue that if networks are needed to be used for rigorous physics, they  should obviously produce physically rigorous results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' I would like to emphasize  that attempts to learn differential equations through networks can be a stepping  stone for neural networks to be able to be used strictly in the field of physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Finally, I would also like to add that we need to find a way for networks to  collaborate with the existing methods rather than persisting in the use of neural  networks only as a perspective of taking advantage of each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  As one may have noticed, I did not answer the question, “Why is it better  to use neural networks than the conventional methods?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' A persuasive answer  to this question will be very subjective (at this moment I guess), and I would  like to leave it as a future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' So, let us simply enjoy our journey now  and beyond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' It is unknown what will happen next, but at least it is really  fascinating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  146  Chapter A  Bayesian Deep Learning: Model  uncertainty  Bayesian neural networks (BNNs) was first suggested in the 1990s [228,229] where  a brief history can be found elsewhere [95].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' These networks set prior distributions  for their weights, offering a probabilistic interpretation of their models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' While  their formulations are relatively easy, the probabilistic inference is quite tricky.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Thus, we would like to approximate p  �  ω|X, Y  �  by means of VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This approxi-  mate BNN inference comes out with stochastic regularization techniques (SRTs)  like dropout used in VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This approach is largely taken from Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' [95].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  To approximate the BNN inference, we would like to approximate p  �  ω|X, Y  �  in light of VI, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=',  LV I(θ) ≡ −  N  �  i=1  �  qθ(ω) log p  �  yi|f ω(Xi)  �  dω + KL  �  qθ(ω)  ����p(ω)  �  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1)  where f ω is the function parameterized by ω, and the subscript i is the row or  column of a matrix denoted in boldface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This stands for an average (or integra-  tion) over the entire dataset, which costs heavy computations for large N, thus  we apply the mini-batch approach to approximate it as:  ˆLV I(θ) ≡ − N  M  �  i∈S  �  qθ(ω) log p  �  yi|f ω(Xi)  �  dω + KL  �  qθ(ω)  ����p(ω)  �  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2)  where S is the random index set of size M, and Monte Carlo (MC) integration has  been applied to this.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The data sub-sampling also gives us an optimum [230,231].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  After reparameterizing qθ(ω) and ω as p(ϵ) and g(θ, ϵ), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', using the path-  wise derivative estimator (the reparametrization trick, infinitesimal perturbation  analysis, and stochastic backpropagation [232–234]) which assumes that qθ(ω)  147  CHAPTER A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian Deep Learning: Model uncertainty  can be re-parameterized as a parameter-free distribution p(ϵ) with a determinis-  tic differentiable bivariate transformation g, we rewrite the sub-sampling VI as:  ˆLV I(θ) = − N  M  �  i∈S  �  p(ϵ) log p  �  yi|f g(θ,ϵ)(Xi)  �  dϵ + KL  �  qθ(ω)  ����p(ω)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3)  This expression turns out to be the form below:  ˆLMC(θ) = − N  M  �  i∈S  log p  �  yi|f g(θ,ϵ)(Xi)  �  + KL  �  qθ(ω)  ����p(ω)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4)  where the log likelihood is replaced with its stochastic estimator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This is a new  MC estimator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Now, we can optimize ˆLMC(θ) with respect to θ following a sequence for  inference:  �  ∆θ ← − N  M  �  i∈S  ∂  ∂θ log p  �  yi|f g(θ,ˆϵi)(Xi)  �  + ∂  ∂θKL  �  qθ(ω)  ����p(ω)  �  θ ← θ + η �  ∆θ  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5)  where η is the learning rate, ˆϵi p(ϵ) is M random variables, and θ is initialized  randomly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  From now on, we relate the approximate inference above to SRTs used in  deep learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Dropout [211,235] is the most popular SRT which is easily appli-  cable to any neural networks and used to avoid over-fitting issues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, let us  focus mainly on dropout.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Suppose that there is a neural network having a single hidden layer, dropout  applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' When we start to estimate the network’s outputs through dropout, two  binary vectors �ϵ1 and �ϵ2 whose dimension corresponds to the input and the hidden  layer, respectively, are sampled to be assigned with value 0 with probability  0 ≤ p1(or 2) ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Then, we multiply given input x with �ϵ1 like �x = x ⊙ �ϵ1  making some inputs to zero (turn off activation of some input nodes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' ⊙ is the  element-wise product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Similarly, some hidden nodes h are turned off through  �h = h⊙�ϵ2 where h = f(�xM 1 +b) and f is an activation function, and therefore  the network’s output with given dropout �y = �hM 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Here, M 1 and M 2 are the  148  CHAPTER A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian Deep Learning: Model uncertainty  deterministic matrix for the network weights for the input and the hidden layer,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  A stark difference between BNNs and dropout is that BNNs quantify their  uncertainty over their model parameters while dropout injects its noise into the  feature space, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', x and h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, let us treat the dropout noise as the parameter  space noise from the feature space noise as shown below:  �y = �hM 2  = (h ⊙ �ϵ2)M 2  = (h · diag(�ϵ2))M 2  = h(diag(�ϵ2)M 2)  = f  �  �xM 1 + b  �  (diag(�ϵ2)M 2)  = f  �  (x ⊙ �ϵ1)M 1 + b  �  (diag(�ϵ2)M 2)  = f  �  x  �  diag(�ϵ1)M 1  �  + b  �  (diag(�ϵ2)M 2)  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6)  where we define �  W 1 ≡ diag(�ϵ1)M 1 and �  W 2 ≡ diag(�ϵ2)M 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' �  W is a realization  of W , i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', a random variable defined over the set of real matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This turns  out to be:  �y = f  �  x�  W 1 + b  �  �  W 2 ≡ F  �  W 1,�  W 2,b(x)  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='7)  where we define �ω = {�  W 1, �  W 2, b}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Therefore, we can optimize this dropout network based on:  Ldropout(M 1, M 2, b) ≡ 1  M  �  i∈S  E  �  W  i  1,�  W  i  2,b�  xi, yi  �  +λ1||M 1||2+λ2||M 2||2+λ3||b||2  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='8)  where �  W  i  1 and �  W  i  2 are the contributions of �ϵi  1 and �ϵi  2 sampled from each data  point i to the matrix M 1or 2, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The mini-batch approach is applied  here to sub-sample a random index set S whose size is M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  We can rewrite EM1,M2,b(x, y) as follows [236]:  EM1,M2,b(x, y) = 1  2||y − F M1,M2,b(x)||2  = −1  τ log p(y|F M1,M2,b(x)) + const  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9)  149  CHAPTER A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian Deep Learning: Model uncertainty  where this is a form of the negative log-likelihood with an offset (constant), and  p(y|F M1,M2,b(x)) = N(y;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' F M1,M2,b(x), τ −1I) with observation noise τ −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  For the data point i in the range of 1 ≤ i ≤ N, we can also rewrite �ω as  follows:  �ωi = {�  W  i  1, �  W  i  2, b} = {diag(ˆϵi  1)M 1, diag(ˆϵi  2)M 2, b}  ≡ g(θ, ˆϵi)  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='10)  if we define θ = {M 1, M 2, b}, and �ϵi  1 and �ϵi  2 are approximately p(ϵ1) and  p(ϵ2) where p(ϵ1(or 2)) is products of Bernoulli distributions with probabilities  1 − p1(or 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Finally, we can re-define Ldropout(M 1, M 2, b) as follows:  ˆLdropout(M 1, M 2, b) = −  1  Mτ  �  i∈S  log p(y|F g(θ,ˆϵi)(x))  + λ1||M 1||2 + λ2||M 2||2 + λ3||b||2  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='11)  where ˆϵ is the realization of ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, taking a differentiation of this with respect  to θ is shown as:  ∂  ∂θ  ˆLdropout(θ) = −  1  Mτ  �  i∈S  ∂  ∂θ log p(y|F g(θ,ˆϵi)(x))  + ∂  ∂θ  �  λ1||M 1||2 + λ2||M 2||2 + λ3||b||2�  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='12)  Now, we can optimize ˆLdropout(θ) through the sequence below for inference:  �  ∆θ ← − 1  Mτ  �  i∈S  ∂  ∂θ log p(y|F g(θ,ˆϵi)(x)) + ∂  ∂θ  �  λ1||M 1||2 + λ2||M 2||2 + λ3||b||2�  θ ← θ + η �  ∆θ  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='13)  where η is the learning rate, ˆϵi p(ϵ) is M random variables, and θ is initialized  randomly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' As can be easily noticed, except a constant scale of 1/Nτ, this is  greatly identical to the approximate inference of a BNN if we let KL(qθ(ω)||p(ω))  become:  ∂  ∂θKL  �  qθ(ω)  ����p(ω)  �  = ∂  ∂θNτ  �  λ1||M 1||2 + λ2||M 2||2 + λ3||b||2�  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='14)  150  CHAPTER A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian Deep Learning: Model uncertainty  toward the optimization as follows:  ∂  ∂θ  ˆLdropout(θ) =  1  Nτ  ∂  ∂θ  ˆLMC(θ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='15)  This result shows that if we optimize a network’s weights by means of  dropout, this optimization process is exactly identical to the variational opti-  mization of a Bayesian neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, this dropout neural network is the  Bayesian neural network, allowing us to express the network uncertainty quanti-  tatively with given observed data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' I would like to stress that we now possess the  tool to construct a reliable neural network being able to provide its confidence  to given inputs, which is tested with the typical sine regressions again in chapter  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  151  Chapter B  Neural Network Differentiation  In this chapter, I would like to introduce a method to learn physical theories by a  neural network itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Theories are generally represented in the form of differential  equations, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', differentiable physics, thus, if I can show that the network is able  to learn differential equations, then it would become true that the network can  be trained with the theories directly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Learning differential equations is eventually  related to setting cost functions in terms of those equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Therefore, we will  confirm how to model a cost function with a differential equation through taking  derivatives of the neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' To this end, suppose that we have a simple  neural network where this has only a single hidden layer with a single input and  output node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Figure B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1 shows the structure of the basic neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' With two nodes  in the hidden layer, there are biases in the input and the hidden layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This is  expressed as a basic algebra as follows:  y = v0 +  �  v1f  �  w10 + w1x  �  + v2f  �  w20 + w2x  ��  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1)  where it is worth to note that there should be b1 and b2 multiplied to w10 and  w20, respectively, in the equation above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Instead, I simply prescribe unity to the  biases in order to ignore the explicit expressions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' I set an activation function in  the hidden layer to the linear function for simplicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  From the fact that the network can be represented analytically, this then  gives us the ability to express a derivative of the network outputs with respect  to the input x, together with an arbitrary activation function, f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Therefore, if  one take first order derivative of the network, this can be represented as follows:  ∂y  ∂x = v1w1f ′�  w10 + w1x  �  + v2w2f ′�  w20 + w2x  �  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2)  152  CHAPTER B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Neural Network Differentiation  Figure B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1: A simple neural network having only one input node (except the  input bias), hidden layer and output node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' There are two nodes in the hidden  layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  where f ′(X, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=') refers to the first order partial derivative of the function f with  respect to X, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', ∂f(X, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=')/∂X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  This shows how the network output changes according to the input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Note  that there are no restrictions for this input and output to be any quantities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This  means that those can be any physical parameters of interest being able to be ex-  pressed in the analytic expression through the network derivative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Namely, if  optimal weights of the network can be found to explain related physical phenom-  ena appropriately, then we are now capable of calculating all possible changes of  the phenomena in, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', time and space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This is quite powerful since we treat the  network as solutions of physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' However, an important issue left is how we can  obtain the proper weights for the physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Here, this can be simply resolved if a  cost function of the network contains the differential equations themselves with  a given training dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  For instance, suppose that we are interested in a simple differential equation  below:  dˆt  dx − 14π cos (14πx) = 0  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3)  where 14π cos (14πx) is the observed quantity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' If we replace ˆt with y, the network  output, in the equation and use the equation itself as a cost function with given  14π cos (14πx), then we can eventually acquire the network whose output satisfies  the equation above such that the output y = sin (14πx), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', the solution ˆt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  153  W1  V1  W10  x  W2  V2  b1  W20  o  b2CHAPTER B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Neural Network Differentiation  Likewise, we can generalize the cost function as follows:  ϵ =  �∂yi  ∂xi  − ti  �2  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='4)  where subscript i refers to an arbitrary feature to be used for training the network,  and t is a single training data point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Therefore, the training of the network is possible through the gradient de-  scent method with the cost function above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  From this, the gradients of the  weights in the hidden layer are expressed as follows:  ∂ϵ  ∂v1  =  ∂  ∂v1  �∂yi  ∂xi  − ti  �2  = 2√ϵ  ∂  ∂v1  �  v1w1f ′�  w10 + w1xi  �  + v2w2f ′�  w20 + w2xi  �  − ti  �  = 2√ϵ w1f ′�  w10 + w1xi  �  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5)  ∂ϵ  ∂v2  = 2√ϵ w2f ′�  w20 + w2xi  �  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6)  where v1 and v2 are the weights between the hidden and the output layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Note  that the cost function (Equation B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2) does not have v0 dependency, meaning  that prescribed v0 cannot be trained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Thus, one can see an error message while  training a neural network with a bias in the last hidden layer, together with the  cost function defined before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Similarly, we can analytically represent the gradients of the weights between  the input and the hidden layer as follows:  ∂ϵ  ∂w1  = 2√ϵ v1  �  f ′�  w10 + w1xi  �  + w1xif ′′�  w10 + w1xi  ��  ∂ϵ  ∂w2  = 2√ϵ v2  �  f ′�  w20 + w2xi  �  + w2xif ′′�  w20 + w2xi  ��  ∂ϵ  ∂w10  = 2√ϵ v1w1f ′′�  w10 + w1xi  �  ∂ϵ  ∂w20  = 2√ϵ v2w2f ′′�  w20 + w2xi  �  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='7)  where it is worth to mention that f ′′(X) stands for the second order partial  derivative of the function f with respect to X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In contrast to v0, the cost function  ϵ is a function of wi0 which is updated during the process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  154  CHAPTER B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Neural Network Differentiation  So far, we have identified how the first order derivative of the network with  respect to the input can be trained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' To check a tendency of high order derivatives  with respect to the input, I introduce the second order derivatives regarding the  input and show corresponding training procedure as an example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The following  equation is the second order derivative:  ∂2y  ∂x2 = ∂  ∂x  �  v1w1f ′�  w10 + w1x  �  + v2w2f ′�  w20 + w2x  ��  = v1w2  1f ′′�  w10 + w1x  �  + v2w2  2f ′′�  w20 + w2x  �  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='8)  where the only difference with the first order derivative is that we now have the  square terms of w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' From the cost function for the second order derivative, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=',  ϵ2 =  �∂2yi  ∂x2  i  − ti  �2  ,  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='9)  the gradients of the neural network weights can be expressed as follows:  ∂ϵ2  ∂v1  = 2√ϵ2 w2  1f ′′�  w10 + w1xi  �  ∂ϵ2  ∂v2  = 2√ϵ2 w2  2f ′�  w20 + w2xi  �  ∂ϵ2  ∂w1  = 2√ϵ2 v1  �  2W1f ′′�  w10 + w1xi  �  + w3  1xif ′′′�  w10 + w1xi  ��  ∂ϵ2  ∂w2  = 2√ϵ2 v2  �  2W2f ′′�  w20 + w2xi  �  + w3  2xif ′′′�  w20 + w2xi  ��  ∂ϵ2  ∂w10  = 2√ϵ2 v1w2  1f ′′�  w10 + w1xi  �  ∂ϵ2  ∂w20  = 2√ϵ2 v2w2  2f ′′�  w20 + w2xi  �  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='10)  where v0 is also not updated at all during the training, and we can train the  network output according to the second (or high) order changes in space (or  time) of certain physical phenomena that we are concerned with.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' I collect the  simple formulas for the neural network output, the first order, and the second  order derivatives as shown below:  y = v0 +  �  v1f  �  w10 + w1x  �  + v2f  �  w20 + w2x  ��  ∂y  ∂x = v1w1f ′�  w10 + w1x  �  + v2w2f ′�  w20 + w2x  �  ∂2y  ∂x2 = v1w2  1f ′′�  w10 + w1x  �  + v2w2  2f ′′�  w20 + w2x  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='11)  155  CHAPTER B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Neural Network Differentiation  Figure B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2: A simple neural network having two input nodes, two hidden  layers and one output node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' There are two nodes in each hidden layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Could one argue that what if the activation function f is an exponential  function?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  If the function f(X) is exp (X) where X is a certain variable, all  the derivatives of the function f will be identical, leading us to estimate high  order derivatives of the network easily.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Then, one can raise a question like “is  exp (X) able to play a role of non-linearity of the neural network as the sigmoid  function, tanh and ReLU?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The answer is yes, however, I would like to leave  this fact that exp (exp (exp (exp (1)))) ≈ e3814279.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This means that the output  given by exp (X) will be literally exponentially skyrocketing, making the training  procedure unstable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Then what if we simplify w to be unity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The major difference in Equation  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='11 is the power of w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Furthermore, it is reasonable that although w is fixed,  non-linearity of the network can be achievable from the hidden layer as well as  a non-linear activation function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' I would like to leave this argument as a future  work, however it is clear that if we can find proper weights, then derivatives may  easily be estimated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Here, I would like to introduce an excursion into the topic that a network has  more than one hidden layer with more input nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Let me take a look at what  kind of complexity occurs when I add another hidden layer to the network used  before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' For simplicity, the hidden layers contain two hidden nodes each with  one bias, and there are two input nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The functional form of the network  156  W11  V11  R  h2)  W12  V12  u  W21  V21  W22  V22  U2  Z  h12  h22  b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  b5CHAPTER B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Neural Network Differentiation  displayed in Figure B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='2 is presented as follows:  h11 = f  �  w11R + w21Z + b1  �  h12 = f  �  w12R + w22Z + b2  �  h21 = f  �  v11h11 + v21h12 + b3  �  h22 = f  �  v12h11 + v22h12 + b4  �  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='12)  where b is the bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Based on the expressions above, the output of the network  can be expressed as follows:  y = u1h21 + u2h22 + b5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='13)  I would like to present here ∂y/∂R only for instance, which is  ∂y  ∂R = u1  ∂h21  ∂R + u2  ∂h22  ∂R  = u1  �  v11w11 f ′�  w11R + w21Z + b1  �  + v21w12 f ′�  w12R + w22Z + b2  ��  f ′�  v11h11 + v21h12 + b3  �  + u2  �  v12w11 f ′�  (w11R + w21Z + b1  �  + v22w12 f ′�  w12R + w22Z + b2  ��  f ′�  v12h11 + v22h12 + b4  �  ≡ u1  �  v11w11 ˜h11 + v21w12 ˜h12  �  ˜h21 + u2  �  v12w11 ˜h11 + v22w12 ˜h12  �  ˜h22  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='14)  The derivatives of the network look like becoming more complex than those of  the previous network which has one hidden layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' However, if we define ∆21 ≡  v11 ˜h11 + v21 ˜h12 and ∆22 ≡ v12 ˜h11 + v22 ˜h12 with w ≡ w11 = w12 assumption and  assume h = ˜h by using exp (X) as the activation function, then the first order  derivative turns out to be:  ∂y  ∂R ≈ u1 w∆21h21 + u2 w∆22h22  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='15)  where this is somewhat identical to Equation B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='11 if we make such strict con-  straints, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', ∆ should be unity, meaning that stacking more layers is futile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  157  CHAPTER B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Neural Network Differentiation  We have seen so far the fact that how we train a neural network holds a  differential equation itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Recall that a differential equation is a fundamen-  tal representative of a physical phenomenon, which is often called differentiable  physics as well, and inculcating that kind of equation in the network through the  procedures above means that we possibly think that the network have knowledge  of corresponding physics that we are interested in.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' This might lead us to step  forward to believe the network can be used for the scientific fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In section  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='3, I show practical results of this scheme with the usual sine function problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  158  Bibliography  [1] GS Lee, M Kwon, CJ Doh, BG Hong, K Kim, MH Cho, W Namkung,  Choong-Seock Chang, YC Kim, JY Kim, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Design and construction of  the KSTAR tokamak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion, 41(10):1515, 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [2] S G Lee, J G Bak, E M Ka, J H Kim, and S H Hahn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Magnetic diag-  nostics for the first plasma operation in Korea Superconducting Tokamak  Advanced Research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Review of Scientific Instruments, 79(10):10F117–4,  2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [3] Semin Joung, Jaewook Kim, Sehyun Kwak, Kyeo-reh Park, S H Hahn,  H S Han, H S Kim, J G Bak, S G Lee, and Y c Ghim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Imputation of  faulty magnetic sensors with coupled Bayesian and Gaussian processes to  reconstruct the magnetic equilibrium in real time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Review of Scientific  Instruments, 89(10):10K106, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [4] Jonathan B Lister, HARRY Schnurrenberger, and Ph Marmillod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Imple-  mentation of a multi-layer perceptron for a non-linear control problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Technical report, LRP 398/90, CRPP-Lausanne, 1990.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [5] J B Lister and H Schnurrenberger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Fast non-linear extraction of plasma  equilibrium parameters using a neural network mapping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion,  31(7):1291–1300, 1991.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [6] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' LAGIN, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' BELL, S DAVIS, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' ECK, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' JARDIN, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' KESSEL,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' MCENERNEY, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' OKABAYASHI, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' POPYACK, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' SAUTHOFF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  APPLICATION OF NEURAL NETWORKS FOR REAL-TIME CALCU-  LATIONS OF PLASMA EQUILIBRIUM PARAMETERS FOR PBX-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  In C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' FERRO, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' GASPAROTTO, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' KNOEPFEL, editors, Fusion  Technology 1992, pages 1057–1061.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' North-Holland, Oxford, 1993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  159  BIBLIOGRAPHY  [7] E Coccorese, C Morabito, and R Martone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Identification of noncircu-  lar plasma equilibria using a neural network approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion,  34(10):1349–1363, 1994.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [8] B Ph van Milligen, V Tribaldos, and J A Jim´enez.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Neural Network Differ-  ential Equation and Plasma Equilibrium Solver.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Physical Review Letters,  75(20):3594–3597, 1995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [9] Chris M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bishop, Paul S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Haynes, Mike E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Smith, Tom N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Todd, and  David L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Trotman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Real-Time Control of a Tokamak Plasma Using Neural  Networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Neural Computation, 7(1):206–217, 01 1995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [10] Colin George Windsor, Thomas Noel Todd, David Leonard Trotman, and  Michael Edward Underhill Smith.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Real-time electronic neural networks for  iter-like multiparameter equilibrium reconstruction and control in compass-  d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Fusion technology, 32(3):416–430, 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [11] Patrick J Mc Carthy and Francesco C Morabito.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Realtime Identification  of Plasma Shape and Position on ITER Using an Equilibrium Database.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  In Diagnostics for Experimental Thermonuclear Fusion Reactors 2, pages  541–544.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Springer, 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [12] Chris M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bishop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Neural networks and their applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Review of Sci-  entific Instruments, 65(6):1803–1832, 1994.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [13] Bo Wang, Bingjia Xiao, Jiangang Li, Yong Guo, and Zhengping Luo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Ar-  tificial Neural Networks for Data Analysis of Magnetic Measurements on  East.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Journal of Fusion Energy, 35(2):390–400, Apr 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [14] F Carpanese, F Felici, C Galperti, A Merle, JM Moret, O Sauter, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  First demonstration of real-time kinetic equilibrium reconstruction on TCV  by coupling LIUQE and RAPTOR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion, 60(6):066020, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [15] Jonas Degrave, Federico Felici, Jonas Buchli, Michael Neunert, Brendan  Tracey, Francesco Carpanese, Timo Ewalds, Roland Hafner, Abbas Abdol-  160  BIBLIOGRAPHY  maleki, Diego de Las Casas, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Magnetic control of tokamak plasmas  through deep reinforcement learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nature, 602(7897):414–419, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [16] JT Wai, MD Boyer, and E Kolemen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Neural net modeling of equilibria in  NSTX-U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' arXiv preprint arXiv:2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='13915, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [17] Markus Svens´en.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Neural network prediction of disruptions in a tokamak  plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Master’s thesis, Aston University, 1994.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [18] CG Windsor, G Pautasso, C Tichmann, RJ Buttery, TC Hender,  JET EFDA Contributors, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' A cross-tokamak neural network disrup-  tion predictor for the JET and ASDEX Upgrade tokamaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear fusion,  45(5):337, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [19] Kates-Harbeck, Julian, Svyatovskiy, Alexey, and Tang, William.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Predict-  ing disruptive instabilities in controlled fusion plasmas through deep learn-  ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nature, 568(7753):526–531, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [20] JV Hernandez, A Vannucci, T Tajima, Z Lin, W Horton, and SC McCool.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Neural network prediction of some classes of tokamak disruptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear  fusion, 36(8):1009, 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [21] D Wroblewski, GL Jahns, and JA Leuer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Tokamak disruption alarm  based on a neural network model of the high-beta limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion,  37(6):725, 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [22] G Tresset, CD Challis, X Garbet, X Litaudon, M Mantsinen, D Mazon, and  D Moreau.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Transport identification by neural network in jet itb regimes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  In Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 29th EPS Conference on Controlled Fusion and Plasma Physics  P, volume 2, page 039, 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [23] Arimitsu Wakasa, Sadayoshi MURAKAMI, Hiroshi YAMADA, Masayuki  YOKOYAMA,  Hening  MAASSBERG,  Craig  BEIDLER,  Kiyomasa  WATANABE, and Shun-ichi OIKAWA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Development of a neoclassical  transport database by neural network fitting in lhd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Plasma Fusion  Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' SERIES, 6:203, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  161  BIBLIOGRAPHY  [24] Arimitsu Wakasa, Sadayoshi Murakami, and Shun-ichi Oikawa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Study of  neoclassical transport in lhd plasmas by applying the dcom/nnw neoclas-  sical transport database.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Plasma and Fusion Research, 3:S1030–S1030,  2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [25] Meneghini, O, Luna, C J, Smith, S P, and Lao, L L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Modeling of transport  phenomena in tokamak plasmas with neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Physics of Plasmas,  21(6):060702–5, June 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [26] Citrin, J, Breton, S, Felici, F, Imbeaux, F, Aniel, T, Artaud, J F, Baioc-  chi, B, Bourdelle, C, Camenen, Y, and Garcia, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Real-time capable first  principle based modelling of tokamak turbulent transport.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion,  55(9):092001–7, July 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [27] O Meneghini, S P Smith, P B Snyder, G M Staebler, J Candy, E Belli,  L Lao, M Kostuk, T Luce, T Luda, J M Park, and F Poli.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Self-consistent  core-pedestal transport simulations with neural network accelerated mod-  els.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion, 57(8):086034, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [28] Karel Lucas van de Plassche, Jonathan Citrin, Clarisse Bourdelle, Yann  Camenen, Francis J Casson, Victor I Dagnelie, Federico Felici, Aaron Ho,  Simon Van Mulders, and JET Contributors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Fast modeling of turbulent  transport in fusion plasmas using neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Physics of Plasmas,  27(2):022310, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [29] Carl Friedrich Gauss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Theoria motus corporum coelestium in sectionibus  conicis solem ambientium, volume 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' FA Perthes, 1877.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [30] Christopher M Bishop and Nasser M Nasrabadi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Pattern recognition and  machine learning, volume 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Springer, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [31] David E Rumelhart, Geoffrey E Hinton, and Ronald J Williams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Learning  internal representations by error propagation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Technical report, California  Univ San Diego La Jolla Inst for Cognitive Science, 1985.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  162  BIBLIOGRAPHY  [32] Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Imagenet clas-  sification with deep convolutional neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Advances in neural  information processing systems, 25, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [33] Christian Szegedy, Wei Liu, Yangqing Jia, Pierre Sermanet, Scott Reed,  Dragomir Anguelov, Dumitru Erhan, Vincent Vanhoucke, and Andrew Ra-  binovich.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Going deeper with convolutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  In Proceedings of the IEEE  conference on computer vision and pattern recognition, pages 1–9, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [34] Nal Kalchbrenner and Phil Blunsom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Recurrent continuous translation  models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  In Proceedings of the 2013 conference on empirical methods in  natural language processing, pages 1700–1709, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [35] Martin Sundermeyer, Ralf Schl¨uter, and Hermann Ney.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Lstm neural net-  works for language modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In Thirteenth annual conference of the inter-  national speech communication association, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [36] Tomas Mikolov, Martin Karafi´at, Lukas Burget, Jan Cernock`y, and San-  jeev Khudanpur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Recurrent neural network based language model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  In  Interspeech, volume 2, pages 1045–1048.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Makuhari, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [37] Bart Verberck and Andrea Taroni.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Nuclear fusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Nature Physics,  12(5):383–383, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [38] Francis F Chen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' An Indispensable Truth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' How Fusion Power Can Save the  Planet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Springer, apr 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [39] G Federici, L Boccaccini, F Cismondi, M Gasparotto, Y Poitevin, and  I Ricapito.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' An overview of the EU breeding blanket design strategy as an  integral part of the DEMO design effort.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Fusion Engineering and Design,  141:30–42, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [40] Yeong-Kook Oh, WC Kim, KR Park, MK Park, HL Yang, YS Kim, Y Chu,  YO Kim, JG Bak, EN Baang, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Commissioning and initial operation of  KSTAR superconducting tokamak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Fusion Engineering and Design, 84(2-  6):344–350, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  163  BIBLIOGRAPHY  [41] H Han, SJ Park, C Sung, J Kang, YH Lee, J Chung, TS Hahm, B Kim, J-K  Park, JG Bak, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' A sustained high-temperature fusion plasma regime  facilitated by fast ions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nature, 609(7926):269–275, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [42] Jeffrey P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Freidberg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Ideal Magnetohydrodynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Plenum Press, New  York, 1987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [43] Harold Grad and Hanan Rubin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Hydromagnetic equilibria and force-free  fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Journal of Nuclear Energy (1954), 7(3-4):284–285, 1958.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [44] VD Shafranov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Plasma equilibrium in a magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Reviews of plasma  physics, 2:103, 1966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [45] HK Kim, HL Yang, GH Kim, Jin-Yong Kim, Hogun Jhang, JS Bak, and  GS Lee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Design features of the KSTAR in-vessel control coils.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Fusion  Engineering and Design, 84(2-6):1029–1032, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [46] K Kim, HK Park, KR Park, BS Lim, SI Lee, Y Chu, WH Chung, YK Oh,  SH Baek, SJ Lee, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Status of the KSTAR superconducting magnet  system development.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion, 45(8):783, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [47] Laxmikant Urankar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Vector potential and magnetic field of current-carrying  finite arc segment in analytical form, Part III: Exact computation for rect-  angular cross section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' IEEE Transactions on Magnetics, 18(6):1860–1867,  1982.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [48] E J Strait, E D Fredrickson, and Takechi M Moret, J M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Chapter 2:  Magnetic diagnostics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Fusion Science and Technology, 53:304, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [49] S G Lee and J G Bak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Magnetic diagnostics for Korea superconducting  tokamak advanced research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Review of Scientific Instruments, 72(1):439–4,  2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [50] JG Bak and SG Lee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Performance test of sample coils in the Korea super-  conducting tokamak advanced research magnetic diagnostics test chamber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Review of Scientific Instruments, 72(1):435–438, 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  164  BIBLIOGRAPHY  [51] JG Bak, SG Lee, KSTAR Project Team, and DeRac Son.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Performance of  the magnetic sensor and the integrator for the KSTAR magnetic diagnos-  tics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Review of scientific instruments, 75(10):4305–4307, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [52] SG Lee and JG Bak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Fabrication details, calibrations, and installation ac-  tivities of magnetic diagnostics for Korea Superconducting Tokamak Ad-  vanced Research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Review of scientific instruments, 77(10):10E306, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [53] Bak, J G, Lee, S G, Son, D, and Ga, E M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Analog integrator for the Korea  superconducting tokamak advanced research magnetic diagnostics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Review  of Scientific Instruments, 78(4):043504–6, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [54] JG Bak, SG Lee, and EM Ka.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Diamagnetic loop for the first plasma in the  KSTAR machine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Review of Scientific Instruments, 79(10):10F118, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [55] JG Bak, SG Lee, and HS Kim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Diamagnetic loop measurement in korea  superconducting tokamak advanced research machine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Review of Scientific  Instruments, 82(6):063504, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [56] JH Lee, HK Na, SG Lee, JG Bak, DC Seo, SH Seo, ST Oh, WH Ko,  J Chung, YU Nam, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Diagnostics for first plasma and development  plan on KSTAR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Review of Scientific Instruments, 81(6):063502, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [57] Heung-Su Kim, Jun-Gyo Bak, and Sang-hee Hahn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Improvements of mag-  netic measurements for plasma control in KSTAR tokamak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Fusion Engi-  neering and Design, 123:641–645, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [58] S Ali-Arshad and L De Kock.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Long-pulse analog integration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Review of  scientific instruments, 64(9):2679–2682, 1993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [59] EJ Strait, JD Broesch, RT Snider, and ML Walker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' A hybrid digital–analog  long pulse integrator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Review of scientific instruments, 68(1):381–384, 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [60] Andreas Werner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' W7-X magnetic diagnostics: Performance of the digital  integrator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Review of scientific instruments, 77(10):10E307, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  165  BIBLIOGRAPHY  [61] Seong-Heon Seo, Andreas Werner, and M Marquardt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Development of a  digital integrator for the KSTAR device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Review of Scientific Instruments,  81(12):123507, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [62] Y Wang, ZS Ji, GJ Xu, F Wang, S Li, XY Sun, and ZC Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' A digital  long pulse integrator for EAST Tokamak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Fusion Engineering and Design,  89(5):618–622, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [63] Seong-Heon Seo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Plasma current position measurements in the Korea Su-  perconducting Tokamak Advanced Research device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Physics of Plasmas,  16(3):032501, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [64] Moreau, Ph, Saint-Laurent, F, and Lister, J B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Drift-free magnetic equi-  librium reconstruction using the response to plasma position modulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Fusion Engineering and Design, 84(7-11):1339–1343, June 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [65] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Lee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Oh, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Wi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Development of KSTAR Thomson  scattering system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Review of Scientific Instruments, 81(10):10D528, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [66] Won-Ha Ko, Hyungho Lee, Dongcheol Seo, and Myeun Kwon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Charge  exchange spectroscopy system calibration for ion temperature measurement  in KSTAR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Review of Scientific Instruments, 81(10):10D740, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [67] YS Bae, YM Park, JS Kim, WS Han, SW Kwak, YB Chang, HT Park,  NH Song, HL Yang, SW Yoon, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Commissioning of the first KSTAR  neutral beam injection system and beam experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Fusion Engineering  and Design, 87(9):1597–1610, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [68] S Sarwar, HK Na, and JM Park.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Effective ion charge (Zeff) measure-  ments and impurity behavior in KSTAR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Review of Scientific Instruments,  89(4):043504, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [69] Junghee Kim, Jun Young Kim, SW Yoon, M Garc´ıa-Mu˜noz, M Isobe, and  WC Kim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Initial measurements of fast ion loss in KSTAR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Review of  Scientific Instruments, 83(10):10D305, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  166  BIBLIOGRAPHY  [70] JW Yoo, Junghee Kim, MW Lee, J Kang, W-H Ko, SG Oh, J Ko, JH Lee,  YU Nam, L Jung, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Fast-ion Dα spectroscopy diagnostic at KSTAR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Review of Scientific Instruments, 92(4):043504, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [71] FM Levinton, RJ Fonck, GM Gammel, R Kaita, HW Kugel, ET Pow-  ell, and DW Roberts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Magnetic field pitch-angle measurments in the  PBX-M tokamak using the motional Stark effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Physical review letters,  63(19):2060, 1989.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [72] J Ko, J Chung, AGG Lange, and MFM De Bock.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Polarimetric spectra anal-  ysis for tokamak pitch angle measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Journal of Instrumentation,  8(10):C10022, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [73] L L Lao, H St John, R D Stambaugh, A G Kellman, and W Pfeiffer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Re-  construction of current profile parameters and plasma shapes in tokamaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Nuclear Fusion, 25(11):1611–1622, 1985.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [74] L L Lao, H E St John, Q Peng, and J R Ferron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  MHD Equilibrium  Reconstruction in the DIII-D Tokamak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Fusion Science and Technology,  48(2):968–977, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [75] J R Ferron, M L Walker, L L Lao, H E St John, D A Humphreys, and J A  Leuer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Real time equilibrium reconstruction for tokamak discharge control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Nuclear Fusion, 38(7):1055–1066, May 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [76] Yue, X N, Xiao, B J, Luo, Z P, and Guo, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Fast equilibrium reconstruc-  tion for tokamak discharge control based on GPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Plasma Physics and  Controlled Fusion, 55(8):085016–10, June 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [77] JW Berkery, SA Sabbagh, L Kogan, D Ryan, JM Bialek, Y Jiang,  DJ Battaglia, S Gibson, and C Ham.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kinetic equilibrium reconstructions  of plasmas in the MAST database and preparation for reconstruction of the  first plasmas in MAST upgrade.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Plasma Physics and Controlled Fusion,  63(5):055014, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  167  BIBLIOGRAPHY  [78] Semin Joung, Jaewook Kim, Sehyun Kwak, JG Bak, SG Lee, HS Han,  HS Kim, Geunho Lee, Daeho Kwon, and Y-C Ghim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Deep neural net-  work Grad–Shafranov solver constrained with measured magnetic signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Nuclear Fusion, 60(1):016034, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [79] Y S Park, S A Sabbagh, J W Berkery, J M Bialek, Y M Jeon, S H Hahn,  N Eidietis, T E Evans, S W Yoon, J W Ahn, J Kim, H L Yang, K I You,  Y S Bae, J Chung, M Kwon, Y K Oh, W C Kim, J Y Kim, S G Lee, H K  Park, H Reimerdes, J Leuer, and M Walker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' KSTAR equilibrium operating  space and projected stabilization at high normalized beta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion,  51(5):053001, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [80] Warren S McCulloch and Walter Pitts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  A logical calculus of the ideas  immanent in nervous activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The bulletin of mathematical biophysics,  5(4):115–133, 1943.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [81] Donald Olding Hebb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The organization of behavior: a neuropsychological  theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Science editions, 1949.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [82] Frank Rosenblatt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The perceptron: a probabilistic model for information  storage and organization in the brain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Psychological review, 65(6):386, 1958.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [83] Marvin Minsky and Oliver G Selfridge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Learning in random nets, vol-  ume 46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' MIT Lincoln Laboratory, 1960.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [84] Marvin Minsky and Seymour Papert.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Perceptrons an introduction to com-  putational geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' MIT Press, 1969.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [85] Marvin Minsky and Seymour Papert.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Perceptrons: expanded edition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' MIT  press, 1988.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [86] D S Sivia and J Skilling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Data Analysis: A Bayesian Tutorial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Oxford:  Oxford University Press, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  168  BIBLIOGRAPHY  [87] Sehyun Kwak, J Svensson, M Brix, Y-c Ghim, and JET Contributors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Bayesian electron density inference from JET lithium beam emission spec-  tra using Gaussian processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion, 57(3):036017, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [88] Sehyun Kwak, Jakob Svensson, S Bozhenkov, Joanne Flanagan, Mark  Kempenaars, Alexandru Boboc, Y-C Ghim, and JET Contributors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Bayesian modelling of Thomson scattering and multichannel interferom-  eter diagnostics using Gaussian processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion, 60(4):046009,  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [89] Sehyun Kwak, U Hergenhahn, U H¨ofel, M Krychowiak, A Pavone, J Svens-  son, O Ford, R K¨onig, S Bozhenkov, G Fuchert, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian inference of  spatially resolved Z eff profiles from line integrated Bremsstrahlung spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Review of Scientific Instruments, 92(4):043505, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [90] MA Chilenski, M Greenwald, Y Marzouk, NT Howard, AE White, JE Rice,  and JR Walk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Improved profile fitting and quantification of uncertainty in  experimental measurements of impurity transport coefficients using Gaus-  sian process regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion, 55(2):023012, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [91] MA Chilenski, MJ Greenwald, AE Hubbard, JW Hughes, JP Lee, YM Mar-  zouk, JE Rice, and AE White.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Experimentally testing the dependence of  momentum transport on second derivatives using Gaussian process regres-  sion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion, 57(12):126013, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [92] Aaron Ho, Jonathan Citrin, Fulvio Auriemma, Clarisse Bourdelle, Francis J  Casson, Hyun-Tae Kim, Pierre Manas, Gabor Szepesi, Henri Weisen, and  JET Contributors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Application of Gaussian process regression to plasma  turbulent transport model validation via integrated modelling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Nuclear  fusion, 59(5):056007, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [93] O Linder, J Citrin, GMD Hogeweij, C Angioni, Clarisse Bourdelle, Fran-  cis J Casson, E Fable, A Ho, Florian Koechl, M Sertoli, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Flux-driven  integrated modelling of main ion pressure and trace tungsten transport in  ASDEX Upgrade.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion, 59(1):016003, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  169  BIBLIOGRAPHY  [94] Jarrod Leddy, Sandeep Madireddy, Eric Howell, and Scott Kruger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Single  Gaussian Process Method for Arbitrary Tokamak Regimes with a Statisti-  cal Analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' arXiv preprint arXiv:2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='11557, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [95] Yarin Gal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Uncertainty in deep learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' PhD thesis, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [96] Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David  Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Gener-  ative adversarial nets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Advances in neural information processing systems,  27, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [97] Antonia Creswell, Tom White, Vincent Dumoulin, Kai Arulkumaran,  Biswa Sengupta, and Anil A Bharath.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Generative adversarial networks:  An overview.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' IEEE Signal Processing Magazine, 35(1):53–65, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [98] Luke de Oliveira, Michela Paganini, and Benjamin Nachman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Learning par-  ticle physics by example: location-aware generative adversarial networks  for physics synthesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Computing and Software for Big Science, 1(1):1–24,  2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [99] Michela Paganini, Luke de Oliveira, and Benjamin Nachman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Calogan:  Simulating 3d high energy particle showers in multilayer electromagnetic  calorimeters with generative adversarial networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Physical Review D,  97(1):014021, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [100] Michela Paganini, Luke de Oliveira, and Benjamin Nachman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Accelerating  science with generative adversarial networks: an application to 3d particle  showers in multilayer calorimeters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Physical review letters, 120(4):042003,  2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [101] Sungwon Kim, Juhwan Noh, Geun Ho Gu, Alan Aspuru-Guzik, and  Yousung Jung.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Generative adversarial networks for crystal structure pre-  diction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' ACS central science, 6(8):1412–1420, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  170  BIBLIOGRAPHY  [102] Baekjun Kim, Sangwon Lee, and Jihan Kim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Inverse design of porous  materials using artificial neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Science advances, 6(1):eaax9324,  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [103] Mart´ın Abadi, Ashish Agarwal, Paul Barham, Eugene Brevdo, Zhifeng  Chen, Craig Citro, Greg S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Corrado,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Andy Davis,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Jeffrey Dean,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Matthieu  Devin,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Sanjay Ghemawat,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Ian Goodfellow,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Andrew Harp,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Geoffrey Irving,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Michael Isard,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Yangqing Jia,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Rafal Jozefowicz,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Lukasz Kaiser,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Manjunath  Kudlur,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Josh Levenberg,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Dandelion Man´e,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Rajat Monga,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Sherry Moore,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Derek Murray,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Chris Olah,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Mike Schuster,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Jonathon Shlens,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Benoit Steiner,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Ilya Sutskever,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kunal Talwar,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Paul Tucker,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Vincent Vanhoucke,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Vijay Va-  sudevan,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Fernanda Vi´egas,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Oriol Vinyals,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Pete Warden,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Martin Watten-  berg,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Martin Wicke,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Yuan Yu,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' and Xiaoqiang Zheng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' TensorFlow: Large-  scale machine learning on heterogeneous systems, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Software available  from tensorflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='org.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [104] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Sakakibara, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Yamada, and LHD Experiment Group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Magnetic mea-  surements in lhd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Fusion Science and Technology, 58(1):471–481, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [105] Edlington, T, Martin, R, and Pinfold, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' MAST magnetic diagnostics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Review of Scientific Instruments, 72(1):421–6, 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [106] Strait, E J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Magnetic diagnostic system of the DIII-D tokamak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Review of  Scientific Instruments, 77(2):023502–15, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [107] J M Moret, F Buhlmann, D Fasel, F Hofmann, and G Tonetti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Magnetic  measurements on the TCV Tokamak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Review of Scientific Instruments,  69(6):2333–17, 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [108] Liu, G J, Wan, B N, Sun, Y W, Xiao, B J, Wang, Y, Luo, Zh P, Qian,  J P, and Liu, D M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Analysis of uncertainty in equilibrium reconstruction  in the EAST superconducting tokamak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Review of Scientific Instruments,  84(7):073502–7, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  171  BIBLIOGRAPHY  [109] Simone Peruzzo, Raffaele Albanese, Giovanni Artaserse, Vincenzo Coc-  corese, Sergei Gerasimov, Norman Lam, Francesco Maviglia, Ian Pearson,  Phil Prior, Antonio Quercia, and Luca Zabeo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Installation and commis-  sioning of the JET-EP magnetic diagnostic system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Fusion Engineering  and Design, 84(7-11):1495–1498, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [110] R Chavan, G Chitarin, R S Delogu, A Encheva, A Gallo, E R Hodgson,  L C Ingesson, A Le-Luyer, J B Lister, Ph Moreau, J M Moret, S Peruzzo,  J Romero, D S Testa, M Toussaint, G Vayakis, and R Vila.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The magnetics  diagnostic set for ITER.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Fusion Engineering and Design, 84(2-6):295–299,  June 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [111] D V Orlinskij and G Magyar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Plasma diagnostics on large Tokamaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Nuclear Fusion, 28(JET-P-88-33):611–697, 1988.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [112] D Shiraki, N Commaux, L R Baylor, N W Eidietis, E M Hollmann, V A  Izzo, R A Moyer, and C Paz-Soldan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Characterization of MHD activity  and its influence on radiation asymmetries during massive gas injection in  DIII-D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion, 55(7):073029, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [113] J A Snipes, D J Campbell, P S Haynes, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Large amplitude quasi-  stationary MHD modes in JET.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion, 28(6):1085–1097, 1988.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [114] S N Gerasimov, T C Hender, J Morris, V Riccardo, L E Zakharov, and  JET EFDA Contributors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Plasma current asymmetries during disruptions  in JET.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion, 54(7):073009, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [115] R J Buttery, O Sauter, R Akers, M Gryaznevich, R Martin, C D Warrick,  H R Wilson, and the MAST Team.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Neoclassical Tearing Physics in the  Spherical Tokamak MAST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Physical Review Letters, 88(12), 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [116] Y S Park, S A Sabbagh, J M Bialek, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Investigation of MHD insta-  bilities and control in KSTAR preparing for high beta operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear  Fusion, 53(8):083029, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  172  BIBLIOGRAPHY  [117] Svensson, J, Werner, A, and JET EFDA Contributors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Current tomog-  raphy for axisymmetric plasmas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Plasma Physics and Controlled Fusion,  50(8):085002–26, May 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [118] S A Lazerson and the DIII-D Team.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Three-dimensional equilibrium recon-  struction on the DIII-D device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion, 55(2):023009, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [119] Romero, J A and Svensson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Optimization of out-vessel magnetic diag-  nostics for plasma boundary reconstruction in tokamaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion,  53(3):033009–26, February 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [120] J P Qian, L L Lao, C T Holcomb, B N Wan, Y W Sun, D Moreau, E Li,  L Zeng, K Hanada, A M Garofalo, X Z Gong, B Shen, and B J Xiao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' An  efficient technique for magnetic equilibrium reconstruction with q profile  constraints and its application on the EAST tokamak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion,  57(8):084001, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [121] Xia, Yu-Jun, Zhang, Zhong-Dian, Xia, Zhen-Xin, Zhu, Shi-Liang, and  Zhang, Rui.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  A precision analogue integrator system for heavy current  measurement in MFDC resistance spot welding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Measurement Science and  Technology, 27(2):025104–12, December 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [122] T Shikama, T Nishitani, T Kakuta, S Yamamoto, S Kasai, M Narui,  E Hodgson, R Reichle, B Brichard, A Krassilinikov, R Snider, G Vayakis,  A Costley, S Nagata, B Tsuchiya, and K Toh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Irradiation test of diagnostic  components for ITER application in the Japan Materials Testing Reactor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Nuclear Fusion, 43(7):517–521, 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [123] Marco Ariola and Alfredo Pironti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Magnetic Control of Tokamak Plasmas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Springer, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [124] Chris M Bishop, Paul S Haynes, Mike E U Smith, Tom N Todd, and  David L Trotman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Fast feedback control of a high temperature fusion  plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Neural Computing & Applications, 2(3):148–159, 1994.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  173  BIBLIOGRAPHY  [125] S Ali Arshad and L de Kock.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Long-pulse analog integration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Review of  Scientific Instruments, 64(9):2679–2682, 1993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [126] E J Strait, J D Broesch, R T Snider, and M L Walker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  A hybrid  digital–analog long pulse integrator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Review of Scientific Instruments,  68(1):381–5, 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [127] Werner, Andreas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' W7-X magnetic diagnostics: Performance of the digital  integrator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Review of Scientific Instruments, 77(10):10E307–6, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [128] Y Wang, Z S Ji, G J Xu, F Wang, S Li, X Y Sun, and Z C Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' A  digital long pulse integrator for EAST Tokamak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Fusion Engineering and  Design, 89(5):618–622, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [129] M Kwon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Overview of KSTAR initial operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion,  51(9), September 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [130] Ka, E M, Lee, S G, Bak, J G, and Son, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Performance test of the in-  tegrator system for magnetic diagnostics in KSTAR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Review of Scientific  Instruments, 79(10):10F119–4, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [131] C E Rasmussen and C K I Williams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Gaussian Processes for Machine  Learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The MIT Press, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [132] J W C van Lint, S P Hoogendoorn, and H J van Zuylen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Accurate freeway  travel time prediction with state-space neural networks under missing data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Transportation Research Part C: Emerging Technologies, 13(5-6):347–369,  October 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [133] Andre C Neto, Diogo Alves, Bernardo B Carvalho, Gianmaria De Tommasi,  Robert Felton, Horacio Fernandes, Peter J Lomas, Francesco Maviglia,  Fernanda G Rimini, Filippo Sartori, Adam V Stephen, Daniel F Valcarcel,  and Luca Zabeo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' A Real-Time Architecture for the Identification of Faulty  Magnetic Sensors in the JET Tokamak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' IEEE Transactions on Nuclear  Science, 61(3):1228–1235, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  174  BIBLIOGRAPHY  [134] R´emy Nouailletas, Philippe Moreau, and Sylvain Bremond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  A generic  method for real time detection of magnetic sensor failure on tokamaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Fusion Engineering and Design, 87(3):289–297, March 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [135] Jeffrey Freidberg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Ideal MHD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Cambridge University Press, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [136] S Tsaun and Hogun Jhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Real-time plasma boundary reconstruction in  the KSTAR tokamak using finite element method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Fusion Engineering and  Design, 82(2):163–174, February 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [137] R von Mises.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Mathematical Theory of Probability and Statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Academic  Press, 1964.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [138] Sehyun Kwak, J Svensson, M Brix, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='-c Ghim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Bayesian electron  density inference from JET lithium beam emission spectra using Gaussian  processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion, 57(3), March 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [139] Leslie Foster et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Stable and Efficient Gaussian Process Calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Journal of Machine Learning Research, 10:857, April 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [140] Sehyun Kwak, J Svensson, M Brix, Y c Ghim, and JET Contributors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Bayesian modelling of the emission spectrum of the Joint European Torus  Lithium Beam Emission Spectroscopy system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Review of Scientific Instru-  ments, 87(2):023501, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [141] Dong Li, J Svensson, H Thomsen, F Medina, A Werner, and R Wolf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Bayesian soft X-ray tomography using non-stationary Gaussian Processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Instrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', 84:083506, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [142] Semin Joung, Jaewook Kim, HS Kim, JG Bak, and Y-C Ghim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' A deep  learning approach to recover hidden consistency of kstar flux loop signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  arXiv, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [143] Steven G Worswick,  James A Spencer,  Gunnar Jeschke,  and Ilya  Kuprov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Deep neural network processing of deer data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Science advances,  4(8):eaat5218, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  175  BIBLIOGRAPHY  [144] Yohai Bar-Sinai, Stephan Hoyer, Jason Hickey, and Michael P Brenner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Learning data-driven discretizations for partial differential equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Pro-  ceedings of the National Academy of Sciences, 116(31):15344–15349, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [145] Maziar Raissi, Alireza Yazdani, and George Em Karniadakis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Hidden fluid  mechanics: Learning velocity and pressure fields from flow visualizations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Science, 367(6481):1026–1030, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [146] David  Pfau,  James  S  Spencer,  Alexander  GDG  Matthews,  and  W Matthew C Foulkes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Ab initio solution of the many-electron  schr¨odinger equation with deep neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Physical Review Research,  2(3):033429, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [147] Kyle Mills, Michael Spanner, and Isaac Tamblyn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Deep learning and the  schr¨odinger equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Physical Review A, 96(4):042113, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [148] Giacomo Torlai, Guglielmo Mazzola, Juan Carrasquilla, Matthias Troyer,  Roger Melko, and Giuseppe Carleo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Neural-network quantum state tomog-  raphy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nature Physics, 14(5):447–450, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [149] Li Li, Stephan Hoyer, Ryan Pederson, Ruoxi Sun, Ekin D Cubuk, Patrick  Riley, Kieron Burke, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kohn-sham equations as regularizer: Build-  ing prior knowledge into machine-learned physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Physical review letters,  126(3):036401, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [150] Semin Joung and Y-C Ghim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Mastering plasma equilibria with deep neural  networks and grad-shafranov equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Science Advances, 2022, submitted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [151] Xavier Glorot and Yoshua Bengio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Understanding the difficulty of training  deep feedforward neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  In Yee Whye Teh and Mike Titter-  ington, editors, Proceedings of the Thirteenth International Conference on  Artificial Intelligence and Statistics, volume 9 of Proceedings of Machine  Learning Research, pages 249–256, Chia Laguna Resort, Sardinia, Italy,  13–15 May 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' PMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  176  BIBLIOGRAPHY  [152] Prajit Ramachandran, Barret Zoph, and Quoc V Le.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Searching for activa-  tion functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' arXiv preprint arXiv:1710.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='05941, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [153] Yarin Gal and Zoubin Ghahramani.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Dropout as a bayesian approxima-  tion: Representing model uncertainty in deep learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In international  conference on machine learning, pages 1050–1059.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' PMLR, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [154] Calyampudi Radhakrishna Rao, Calyampudi Radhakrishna Rao, Math-  ematischer Statistiker, Calyampudi Radhakrishna Rao, and Calyam-  pudi Radhakrishna Rao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Linear statistical inference and its applications,  volume 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Wiley New York, 1973.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [155] S A Sabbagh, S M Kaye, J Menard, F Paoletti, M Bell, R E Bell, J M  Bialek, M Bitter, E D Fredrickson, D A Gates, A H Glasser, H Kugel,  L L Lao, B P LeBlanc, R Maingi, R J Maqueda, E Mazzucato, D Mueller,  M Ono, S F Paul, M Peng, C H Skinner, D Stutman, G A Wurden, W Zhu,  and NSTX Research Team.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Equilibrium properties of spherical torus plas-  mas in NSTX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion, 41(11):1601–1611, 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [156] Qian Jinping, Wan Baonian, L L Lao, Shen Biao, S A Sabbagh, Sun  Youwen, Liu Dongmei, Xiao Bingjia, Ren Qilong, Gong Xianzu, and  Li Jiangang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Equilibrium Reconstruction in EAST Tokamak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Plasma Sci-  ence and Technology, 11(2):142–145, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [157] D P O’Brien, L L Lao, E R Solano, M Garribba, T S Taylor, J G Cordey,  and J J Ellis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Equilibrium analysis of iron core tokamaks using a full domain  method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion, 32(8):1351–1360, 1992.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [158] Semin Joung and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='-c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Ghim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian based real-time numerical method  to correct signal drifts in magnetic measurements from tokamaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  unpublished.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [159] D Van Houtte and Equipe TORE SUPRA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' One minute pulse operation in  the Tore Supra Tokamak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion, 33(1):137–141, 1993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  177  BIBLIOGRAPHY  [160] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Ekedahl, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Delpech, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Goniche, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Guilhem, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Hillairet, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Prey-  nas, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Sharma, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Achard, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bae, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bai, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Balorin, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Baranov,  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Basiuk, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' B´ecoulet, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Belo, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Berger-By, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Br´emond, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Castaldo,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Ceccuzzi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Cesario, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Corbel, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Courtois, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Decker, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Delmas,  X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Ding, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Douai, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Goletto, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Gunn, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Hertout, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Hoang, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Im-  beaux, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kirov, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Litaudon, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Magne, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Mailloux, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Mazon, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Mi-  rizzi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Mollard, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Moreau, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Oosako, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Petrzilka, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Peysson, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Poli,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Prou, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Saint-Laurent, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Samaille, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Saoutic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Validation of the  ITER-relevant passive-active-multijunction LHCD launcher on long pulses  in tore supra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion, 50(11):112002, sep 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [161] S Itoh, K N Sato, K Nakamura, H Zushi, M Sakamoto, K Hanada, E Jotaki,  K Makino, S Kawasaki, H Nakashima, and A Iyomasa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Recent progress in  the superconducting tokamak TRIAM-1m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Plasma Physics and Controlled  Fusion, 41(3A):A587–A594, jan 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [162] H Zushi,  S Itoh,  K Hanada,  K Nakamura,  M Sakamoto,  E Jo-  taki, M Hasegawa, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='D Pan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='V Kulkarni, A Iyomasa, S Kawasaki,  H Nakashima, N Yoshida, K Tokunaga, T Fujiwara, M Miyamoto,  H Nakano, M Yuno, A Murakami, S Nakamura, N Sakamoto, K Shinoda,  S Yamazoe, H Akanishi, K Kuramoto, Y Matsuo, A Iwamae, T Fuijimoto,  A Komori, T Morisaki, H Suzuki, S Masuzaki, Y Hirooka, Y Nakashima,  and O Mitarai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Overview of steady state tokamak plasma experiments in  TRIAM-1m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion, 43(12):1600–1609, dec 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [163] B Saoutic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Status of long pulse experiments in magnetic fusion devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Plasma Physics and Controlled Fusion, 44(12B):B11–B22, nov 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [164] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Park, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Choi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Hong, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Jeon, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Ko, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Ko,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kwak, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kwon, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Lee, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Lee, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nam, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Oh, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Park, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Park, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Park, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Wang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Yoo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Yoon, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bak, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Chang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Choe, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Chu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Chung, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Eidietis, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Han, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Hahn,  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Jhang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Juhn, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kim, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kim, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Loarte, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Lee, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Lee,  178  BIBLIOGRAPHY  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Mueller, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Na, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nam, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Park, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Park, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Pitts, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Sabbagh, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Yun and.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Overview of KSTAR research progress and  future plans toward ITER and k-DEMO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion, 59(11):112020,  jul 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [165] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Wan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Liang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Gong, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Xiang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Xu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Sun, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Wang,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Qian, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Liu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Zeng, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Zhang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Zhang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Ding, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Zang,  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Lyu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Garofalo, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Ekedahl, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Li, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Ding, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Ding, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Du,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kong, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Yu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Yang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Luo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Huang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Zhang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Li, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Xia, and and.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Recent advances in EAST physics experiments in  support of steady-state operation for ITER and CFETR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion,  59(11):112003, jun 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [166] Jong-Kyu Park, YoungMu Jeon, Yongkyoon In, Joon-Wook Ahn, Raffi  Nazikian, Gunyoung Park, Jaehyun Kim, HyungHo Lee, WonHa Ko, Hyun-  Seok Kim, Nikolas C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Logan, Zhirui Wang, Eliot A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Feibush, Jonathan E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Menard, and Michael C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Zarnstroff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 3d field phase-space control in tokamak  plasmas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nature Physics, 14:1223, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [167] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Reimold, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Wischmeier, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bernert, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Potzel, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kallenbach, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  M˜AŒller, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Sieglin, and U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Stroth and.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Divertor studies in nitrogen  induced completely detached h-modes in full tungsten ASDEX upgrade.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Nuclear Fusion, 55(3):033004, feb 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [168] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Jaervinen, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Giroud, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Groth, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Belo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Brezinsek, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Beurskens,  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Corrigan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Devaux, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Drewelow, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Harting, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Huber, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Jach-  mich, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Lawson, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Lipschultz, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Maddison, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Maggi, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Marchetto,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Marsen, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Matthews, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Meigs, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Moulton, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Sieglin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Stamp, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Wiesen and.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Comparison of h-mode plasmas in JET-  ILW and JET-c with and without nitrogen seeding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Nuclear Fusion,  56(4):046012, mar 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  179  BIBLIOGRAPHY  [169] Yao Huang, BJ Xiao, ZP Luo, QP Yuan, XF Pei, and XN Yue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Implemen-  tation of gpu parallel equilibrium reconstruction for plasma control in east.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Fusion Engineering and Design, 112:1019–1024, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [170] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Barana, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Murari, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Franz, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Ingesson, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Manduchi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Neural  networks for real time determination of radiated power in jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Review of  Scientific Instruments, 73(5):2038–2043, 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [171] Murari, A, Arena, P, Buscarino, A, Fortuna, L, Iachello, M, and contribu-  tors, JET-EFDA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' On the identification of instabilities with neural networks  on JET.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Inst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' and Methods in Physics Research, A, 720(C):2–6,  August 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [172] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Boyer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kaye, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Erickson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Real-time capable modeling of  neutral beam injection on NSTX-u using neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion,  59(5):056008, mar 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [173] Andrea Murari, Didier Mazon, N Martin, Guido Vagliasindi, and Michela  Gelfusa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Exploratory Data Analysis Techniques to Determine the Dimen-  sionality of Complex Nonlinear Phenomena: The L-to-H Transition at JET  as a Case Study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' IEEE Transactions on Plasma Science, 40(5):1386–1394,  April 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [174] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Murari, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Vega, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Mazon, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Patan, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Vagliasindi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Arena, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Mar-  tin, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Martin, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Ratt, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Caloone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Machine learning for the  identification of scaling laws and dynamical systems directly from data in  fusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Instruments and Methods in Physics Research Section A,  623(2):850 – 854, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [175] P Gaudio, A Murari, M Gelfusa, I Lupelli, and J Vega.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' An alternative  approach to the determination of scaling law expressions for the l–h transi-  tion in tokamaks utilizing classification tools instead of regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Plasma  Physics and Controlled Fusion, 56(11):114002, oct 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  180  BIBLIOGRAPHY  [176] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Cannas, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Fanni, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Pautasso, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Sias, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Sonato.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  An adap-  tive real-time disruption predictor for ASDEX upgrade.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion,  50(7):075004, jun 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [177] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Pau, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Fanni, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Carcangiu, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Cannas, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Sias, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Murari, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Ri-  mini and.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' A machine learning approach based on generative topographic  mapping for disruption prevention and avoidance at JET.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion,  59(10):106017, aug 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [178] F Felici, J Citrin, A A Teplukhina, J Redondo, C Bourdelle, F Imbeaux,  O Sauter, JET Contributors, and the EUROfusion MST1 Team.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Real-time-  capable prediction of temperature and density profiles in a tokamak using  RAPTOR and a first-principle-based transport model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Nuclear Fusion,  58(9):096006, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [179] Matos, Francisco A, Ferreira, Diogo R, and Carvalho, Pedro J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Deep learn-  ing for plasma tomography using the bolometer system at JET.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Fusion  Engineering and Design, 114:18–25, January 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [180] Diogo R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Ferreira, Pedro J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Carvalho, Horcio Fernandes, and JET Contrib-  utors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Full-pulse tomographic reconstruction with deep neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Fusion Science and Technology, 74(1-2):47–56, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [181] Daniel B¨ockenhoff, Marko Blatzheim, Hauke H¨olbe, Holger Niemann, Fabio  Pisano, Roger Labahn, Thomas Sunn Pedersen, and The W7-X Team.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Reconstruction of magnetic configurations in W7-X using artificial neural  networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion, 58(5):056009, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [182] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Cannas, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Carcangiu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Fanni, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Farley, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Militello, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Montisci,  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Pisano, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Sias, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Walkden.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Towards an automatic filament detec-  tor with a faster r-cnn on mast-u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Fusion Engineering and Design, 146:374  – 377, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [183] Clayton, D J, Tritz, K, Stutman, D, Bell, R E, Diallo, A, LeBlanc, B P,  and Podest`a, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Electron temperature profile reconstructions from multi-  181  BIBLIOGRAPHY  energy SXR measurements using neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Plasma Physics and  Controlled Fusion, 55(9):095015–9, August 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [184] Cacciola, Matteo, Greco, Antonino, Morabito, Francesco Carlo, and Ver-  saci, Mario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' An Exhaustive Employment of Neural Networks to Search  the Better Configuration of Magnetic Signals in ITER Machine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In Neural  Information Processing, pages 353–360.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Springer Berlin Heidelberg, Berlin,  Heidelberg, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [185] Young-Mu Jeon, Yong-Su Na, Myung-Rak Kim, and Y S Hwang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Newly  developed double neural network concept for reliable fast plasma position  control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Review of Scientific Instruments, 72(1):513–5, 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [186] Paulo Rodrigues and Jo˜ao P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bizarro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Grad-shafranov equilibria with  negative core toroidal current in tokamak plasmas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=',  95:015001, Jun 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [187] Paulo Rodrigues and Jo˜ao P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bizarro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Tokamak equilibria with toroidal-  current reversal in the plasma core consistent with experimental data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=', 99:125001, Sep 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [188] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Ludwig, Paulo Rodrigues, and Jo˜ao P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bizarro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Tokamak equilibria  with strong toroidal current density reversal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion, 53(5):053001,  apr 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [189] Simon Haykin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Neural Networks and Learning Machines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Pearson, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [190] Diederik P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kingma and Jimmy Ba.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Adam: A method for stochastic opti-  mization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' CoRR, abs/1412.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6980, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [191] Rong Ge, Furong Huang, Chi Jin, and Yang Yuan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Escaping from sad-  dle points - online stochastic gradient for tensor decomposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' CoRR,  abs/1503.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='02101, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [192] L´eon Bottou.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Large-scale machine learning with stochastic gradient de-  scent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In Proceedings of COMPSTAT’2010, pages 177–186.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Springer, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  182  BIBLIOGRAPHY  [193] Q Huynh-Thu and M Ghanbari.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Scope of validity of PSNR in image/video  quality assessment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Electronics Letters, 44(13):800, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [194] JPEG vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' JPEG 2000: an objective comparison of image encoding quality,  2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [195] Z Wang, A C Bovik, H R Sheikh, and E P Simoncelli.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Image Quality  Assessment: From Error Visibility to Structural Similarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' IEEE Trans-  actions on Image Processing, 13(4):600–612, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [196] R Aymar, P Barabaschi, and Y Shimomura.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The iter design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Plasma  physics and controlled fusion, 44(5):519, 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [197] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' PEACOCK, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' ROBINSON, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' FORREST, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' WILCOCK,  and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' SANNIKOV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Measurement of the electron temperature by thom-  son scattering in tokamak t3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nature, 224(5218):488–490, 1969.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [198] William Mitchinson Hicks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Ii.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' researches in vortex motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='—part iii.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' on  spiral or gyrostatic vortex aggregates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Philosophical Transactions of the  Royal Society of London.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Series A, Containing Papers of a Mathematical  or Physical Character, (192):33–99, 1899.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [199] Y Huang, ZP Luo, BJ Xiao, LL Lao, A Mele, A Pironti, M Mattei, G Am-  brosino, QP Yuan, YH Wang, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Gpu-optimized fast plasma equilibrium  reconstruction in fine grids for real-time control and data analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear  Fusion, 60(7):076023, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [200] GT Von Nessi, MJ Hole, MAST team, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' A unified method for infer-  ence of tokamak equilibria and validation of force-balance models based  on bayesian analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Journal of Physics A: Mathematical and Theoretical,  46(18):185501, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [201] JA Romero, SA Dettrick, E Granstedt, T Roche, and Y Mok.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Inference  of field reversed configuration topology and dynamics during alfvenic tran-  sients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nature communications, 9(1):1–10, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  183  BIBLIOGRAPHY  [202] Sehyun Kwak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian modelling of nuclear fusion experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' PhD  thesis, Technische Universit¨at Berlin, Berlin, Germany, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [203] Yann LeCun, Yoshua Bengio, and Geoffrey Hinton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Deep learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' nature,  521(7553):436–444, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [204] Jan Hermann, Zeno Sch¨atzle, and Frank No´e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Deep-neural-network solution  of the electronic schr¨odinger equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nature Chemistry, 12(10):891–897,  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [205] Tom Beucler, Michael Pritchard, Stephan Rasp, Jordan Ott, Pierre Baldi,  and Pierre Gentine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Enforcing analytic constraints in neural networks em-  ulating physical systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Physical Review Letters, 126(9):098302, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [206] Dmitrii Kochkov, Jamie A Smith, Ayya Alieva, Qing Wang, Michael P  Brenner, and Stephan Hoyer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Machine learning–accelerated computational  fluid dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Proceedings of the National Academy of Sciences, 118(21),  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [207] DA Kaltsas and GN Throumoulopoulos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Neural network tokamak equilibria  with incompressible flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Physics of Plasmas, 29(2):022506, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [208] Steven P Hirshman and JC Whitson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Steepest-descent moment method for  three-dimensional magnetohydrodynamic equilibria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The Physics of fluids,  26(12):3553–3568, 1983.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [209] Sifan Wang and Paris Perdikaris.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Deep learning of free boundary and stefan  problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Journal of Computational Physics, 428:109914, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [210] Johan Stefan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' ¨Uber die theorie der eisbildung, insbesondere ¨uber die eis-  bildung im polarmeere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Annalen der Physik, 278(2):269–286, 1891.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [211] Nitish Srivastava, Geoffrey Hinton, Alex Krizhevsky, Ilya Sutskever, and  Ruslan Salakhutdinov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Dropout: a simple way to prevent neural networks  from overfitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' The journal of machine learning research, 15(1):1929–  1958, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  184  BIBLIOGRAPHY  [212] Adam Paszke, Sam Gross, Soumith Chintala, Gregory Chanan, Edward  Yang, Zachary DeVito, Zeming Lin, Alban Desmaison, Luca Antiga, and  Adam Lerer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Automatic differentiation in pytorch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' NIPS Workshop, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [213] Atilim Gunes Baydin, Barak A Pearlmutter, Alexey Andreyevich Radul,  and Jeffrey Mark Siskind.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Automatic differentiation in machine learning:  a survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Journal of Marchine Learning Research, 18:1–43, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [214] SG Lee, JG Bak, EM Ka, JH Kim, and SH Hahn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Magnetic diagnostics  for the first plasma operation in korea superconducting tokamak advanced  research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Review of Scientific Instruments, 79(10):10F117, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [215] YS Park, SA Sabbagh, JW Berkery, JM Bialek, YM Jeon, SH Hahn, N Ei-  dietis, TE Evans, SW Yoon, J-W Ahn, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kstar equilibrium operating  space and projected stabilization at high normalized beta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion,  51(5):053001, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [216] H Urano, Y Miyata, T Suzuki, and K Kurihara.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Breakdown optimiza-  tion method based on inverse reconstruction of magnetic fluxes in jt-60sa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Nuclear Fusion, 60(6):066002, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [217] Nelson Morgan and Herv´e Bourlard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Generalization and parameter esti-  mation in feedforward nets: Some experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Advances in neural infor-  mation processing systems, 2, 1989.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [218] Alessandro Beghi and Angelo Cenedese.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Advances in real-time plasma  boundary reconstruction: From gaps to snakes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  IEEE Control Systems  Magazine, 25(5):44–64, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [219] ´Emile Clapeyron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' M´emoire sur la puissance motrice de la chaleur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Journal  de l’´Ecole polytechnique, 14:153–190, 1834.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [220] B Coppi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Compact experiments for o-particle heating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Tokamak Reactors  for Breakeven: A Critical Study of the Near-Term Fusion Reactor Program,  page 303, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  185  BIBLIOGRAPHY  [221] DR Sweetman, JG Cordey, and TS Green.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Heating and plasma interactions  with beams of energetic neutral atoms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Philosophical Transactions of the  Royal Society of London.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Series A, Mathematical and Physical Sciences,  300(1456):589–598, 1981.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [222] RA Cairns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Radiofrequency heating of plasmas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' CRC Press, 1991.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [223] Robert James Goldston.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Heuristic drift-based model of the power scrape-  off width in low-gas-puff h-mode tokamaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion, 52(1):013009,  2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [224] Hyun-Tae Kim, ACC Sips, M Romanelli, CD Challis, F Rimini, L Garzotti,  E Lerche, J Buchanan, X Yuan, S Kaye, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' High fusion performance at  high ti/te in jet-ilw baseline plasmas with high nbi heating power and low  gas puffing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion, 58(3):036020, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [225] Baptiste Jimmy Frei, Rog´erio Jorge, and Paolo Ricci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' A gyrokinetic model  for the plasma periphery of tokamak devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Journal of Plasma Physics,  86(2), 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [226] G K Batchelor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' An introduction to fluid dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Cambridge university  press, 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [227] YS Park, SA Sabbagh, JM Bialek, JW Berkery, SG Lee, WH Ko, JG Bak,  YM Jeon, JK Park, J Kim, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Investigation of mhd instabilities  and control in kstar preparing for high beta operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Nuclear Fusion,  53(8):083029, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [228] David JC MacKay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' A practical bayesian framework for backpropagation  networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Neural computation, 4(3):448–472, 1992.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [229] RM Neal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bayesian learning for neural networks [phd thesis].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Toronto,  Ontario, Canada: Department of Computer Science, University of Toronto,  1995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  186  BIBLIOGRAPHY  [230] Herbert Robbins and Sutton Monro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' A stochastic approximation method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  The annals of mathematical statistics, pages 400–407, 1951.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [231] Matthew D Hoffman, David M Blei, Chong Wang, and John Paisley.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Stochastic variational inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Journal of Machine Learning Research,  2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [232] Paul Glasserman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Monte Carlo methods in financial engineering, vol-  ume 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Springer, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [233] Diederik P Kingma and Max Welling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Auto-encoding variational bayes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  arXiv preprint arXiv:1312.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='6114, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [234] Michalis Titsias and Miguel L´azaro-Gredilla.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Doubly stochastic variational  bayes for non-conjugate inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In International conference on machine  learning, pages 1971–1979.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' PMLR, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [235] Geoffrey E Hinton, Nitish Srivastava, Alex Krizhevsky, Ilya Sutskever, and  Ruslan R Salakhutdinov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Improving neural networks by preventing co-  adaptation of feature detectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' arXiv preprint arXiv:1207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='0580, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  [236] Naftali Tishby, Esther Levin, and Sara A Solla.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Consistent inference of  probabilities in layered networks: Predictions and generalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In Inter-  national Joint Conference on Neural Networks, volume 2, pages 403–409.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  IEEE New York, 1989.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  187  Acknowledgments in Korean  감사했던 분들의 성함은 다 적지 못할까 염려되어 선뜻 남기기 어려웠습니다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 그  럼에도 이야기하고자 합니다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 지난 2015년 1월을 시작으로 제가 감히 이해할 수  없는 마음으로 여러 가르침을 주신 김영철 교수님께 감사드립니다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 아직 더 배  움이 필요함에도 불구하고 미숙한 저의 학위 심사에 참여해주시고 많은 가르침을  주셨던 최원호 교수님, 윤시우 박사님, 성충기 교수님, 미숙한 석사과정 학생에  불과했던 저에게 여러 가르침과 격려를 해주셨던 김현석 박사님께 감사드립니다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  연구의 시작점이며 방향이 되었던 곽세현 박사님께 감사드립니다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 언제나 말도  안 되는 이야기와 주장을 해도 깊은 이해로 진지하게 받아주셨던 김재욱 박사님께  도 감사드립니다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 좌충우돌 어디로 튈지 저 조차도 모르던 미숙함을 언제나 높은  마음으로 이해해주셨던 김건희, 때로는 본이 되는 연구자로서 때로는 깊은 토론  을 할 수 있는 동료로서 때로는 함께 즐길 수 있는 친구며 동생이 되어준 오태석,  마찬가지로 깊은 연구 토론과 때로는 삶을 공유할 수 있었던 임예건, 언제나 여  러 힘이 되어준 권대호, 미숙한 모습에도 내색없이 바라봐주었던 이정진, 정충순,  해준 것 없는 데도 많은 도움을 주었던 유용성, 이원준, 박사 마지막 시기에 많은  도움이 되었던 김동욱, 연구에 영어에 많은 도움을 준 Alvin 모두 다 감사드립니  다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 언제나 저를 어여삐 여겨주신 Scott, Mandy, SeongOk, Kidoo 그리고 힘든  시기 도움이 되어주신 여러 선생님들, 학교에서 까지 의지할 곳이 되어준 이신의  모두 감사드립니다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 언제나 툴툴대고 선택 못 하고 하고 싶은 말이 아니라 감정에  치우친 말이 나와도 이해해주었던 신찰범 고맙습니다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 혹여 급히 작성하느라 미처  다 언급하지 못한 분들 및 연구실 일원들에게도 깊은 감사드립니다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  지난 날을 되돌아 보면 기억은 빛을 바래도 추억은 보다 더 또렷해지는 순  간들이 있습니다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  이미 한참 지났지만 성남 구 시가지에서 친구들과 뛰어놀던  기억에 더욱 추억이 깊습니다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 그리고 아쉽습니다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 흐려져 가는 기억들이 아깝습  니다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 일기라도 적어놓을 것 그랬습니다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 어찌 하다보니 지금 이 순간을 맞이하게  되었습니다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 어렸을 때의 저는 이런 공부를 하는 제가 되리라고는 전혀 생각도  못 했었겠지요.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 돌아보니 석사 졸업 시기와는 사뭇 다른 감정을 지금은 느끼는 것  188  BIBLIOGRAPHY  같습니다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 보다 명확해진 점은 이전에는 제가 제 길을 만들려고 부단히 애를 썼지  만 지금은 이끄시는 대로 그저 따라 가려 합니다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 이미 많이 미숙했기에 앞으로  성숙해질 것만이 남아 있다는 점은 참 감사하게 여겨집니다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 그래서 어느 방향의  길이든 그 끝은 다 감사하지 않을까 생각합니다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 지금 이 순간도 후에 돌아보면  기억은 바랬지만 추억은 보다 살아남아 있을 것이라 생각합니다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 언제나 제 삶을  지지해주시는 아버지 어머니 감사드립니다 동생들도 미안하고 사랑합니다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 마지  막으로 혜린아 고생 정말 많았어요, 덕분에 나무 아래 누워 쉬던 날에서 일어나  걸을 수 있었습니다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 잡은 손 놓지 않겠습니다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 감사합니다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 내 그대를 생각함은 항상 그대가 앉아 있는 배경에서 해가 지고 바람이  부는 일처럼 사소한 일일 것이나 언젠가 그대가 한없이 괴로움 속을 헤매일 때에  오랫동안 전해오던 그 사소함으로 그대를 불러보리라.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' // 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 진실로 진실로 내  가 그대를 사랑하는 까닭은 내 나의 사랑을 한없이 잇닿은 그 기다림으로 바꾸어  버린 데 있었다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 밤이 들면서 골짜기엔 눈이 퍼붓기 시작했다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 내 사랑도 어디쯤  에선 반드시 그칠 것을 믿는다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 다만 그때 내 기다림의 자세를 생각하는 것뿐이다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  그 동안에 눈이 그치고 꽃이 피어나고 낙엽이 떨어지고 또 눈이 퍼붓고 할 것을  믿는다.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' (황동규, ‘즐거운 편지’, 현대문학, 1958)  189  Curriculum Vitae  Name  :  정 세 민 (SEMIN JOUNG)  E-mail  :  smjoung@kaist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='kr, smjoungsemail@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='com  Educations  2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' – 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  KAIST (Korea Advanced Institute of Science and Technology)  Department of Nuclear and Quantum Engineering (PhD)  2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' – 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  KAIST  Department of Nuclear and Quantum Engineering (MS)  2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' – 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  KYUNG HEE University  Department of Nuclear Engineering (Bachelor’s degree)  Publications  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Joung, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='-c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Ghim, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kim, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kwak, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Lee, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kwon, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Kim and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' ‘GS-DeepNet: Mastering tokamak plasma equilibria  with deep neural networks and the Grad-Shafranov equation’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In: Science  Advances, (2022), In preparation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Joung, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kim, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Han, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bak and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='-c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Ghim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' ‘A deep learning  approach to recover hidden consistency of KSTAR flux loop signals’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In:  Scientific Reports, (2022), In preparation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Joung, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kim, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kwak, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bak, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Lee, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Han, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kim,  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Lee, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kwon and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='-c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Ghim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' ‘Deep neural network Grad–Shafranov  solver constrained with measured magnetic signals’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In: Nuclear Fusion,  Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1 (3rd Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 2019), DOI:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1088/1741-4326/ab555f  190  BIBLIOGRAPHY  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Joung, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kim, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kwak, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Park, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Hahn, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Han, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kim,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bak, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Lee and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='-c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Ghim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' ‘Imputation of faulty magnetic  sensors with coupled Bayesian and Gaussian processes to reconstruct the  magnetic equilibrium in real time’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' In: Review of Scientific Instruments,  Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='10 (7th May 2018), DOI:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='1063/ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='5038938  Talks  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Joung, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kim, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kwak, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kim, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kim, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bak and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='-c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Ghim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' ‘Learning plasma equilibria from scratch with deep neural network  Grad-Shafranov solver’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 63rd Annual Meeting of the APS Division of Plasma  Physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Pittsburgh, PA, USA, 8th Nov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Jiheon Song, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Joung, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='-c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Ghim, Jungpyo and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Hahn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' ‘Implement  of machine learning U-net model for automatic ELM-burst detection in the  KSTAR tokamak’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Korean Physical Society Fall Conference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Remote e-  conference, 20th Oct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Joung, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kim, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kwak, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Han, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kim, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bak, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Lee and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='-c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Ghim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' ‘Learning tokamak equilibria from scratch with deep  neural network Grad-Shafranov solver’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  3rd International Conference on  Data Driven Plasma Science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Remote e-conference, 29th May 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Joung, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kim, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kwak, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Jeon, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Hahn, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kim, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Han, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bak, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Lee, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Lee, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kwon and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='-c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Ghim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' ‘Data-  driven Grad-Shafranov solver with KSTAR EFIT data based on neural net-  work and Bayesian inference’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 3rd IAEA Technical Meeting on Fusion Data  Processing, Validation and Analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Vienna, Austria, 27th May 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='-c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Ghim, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kim, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kwak and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Joung.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' ‘Bayesian based data analy-  sis to infer plasma parameters and to generate synthetic data in tokamaks’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Korean Physical Society Fall Conference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Changwon, South Korea, 24th  Oct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Joung, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kwak, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Jeon, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Hahn, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kim, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Han, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Bak, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Lee and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='-c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Ghim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' ‘Neural network magnetic equilibrium  191  BIBLIOGRAPHY  reconstruction with Bayesian based preprocessor in KSTAR’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 11th IAEA  Technical Meeting on Control, Data Acquisition, and Remote Participation  for Fusion Research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Greifswald, Germany, 8th May 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Posters  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Joung, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kim and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='-c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Ghim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' ‘Bayesian modelling of magnetic pick-  up coils and flux loops using Gaussian processes for real-time control of  plasmas’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 23rd Topical Conference on High Temperature Plasma Diagnos-  tics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Remote e-conference, 13th Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Joung, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kim and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='-c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Ghim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' ‘Real-time compensation of KSTAR  magnetic signal drifts based on Bayesian inference’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  KSTAR Conference  2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' COEX, Seoul, South Korea, 20th Feb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Joung, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kim, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kwak, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Park, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Jeon, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Hahn, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Han, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kim, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Bak, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Lee and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='-c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Ghim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' ‘Bayesian based  missing input imputation scheme for neural network reconstructing mag-  netic equilibria in real time’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 22nd Topical Conference on High Temperature  Plasma Diagnostics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' San Diego, CA, USA, 16th Apr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Joung, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kwak, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Jeon, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Hahn, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kim, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Han, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  Bak, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Lee and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='-c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Ghim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' ‘Neural network based real-time recon-  struction of KSTAR magnetic equilibria with Bayesian-based preprocessing’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  59th Annual Meeting of the APS Division of Plasma Physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Milwaukee,  WI, USA, 22nd Oct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Joung, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Kwak and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='-c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Ghim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' ‘Plasma equilibrium reconstruction  for real-time control using artificial neural network in KSTAR’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' KSTAR  Conference 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' Daejeon, South Korea, 24th Feb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content=' 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
+page_content='  192' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFJT4oBgHgl3EQffCyN/content/2301.11555v1.pdf'}
diff --git a/vdFPT4oBgHgl3EQfOTSJ/vector_store/index.faiss b/vdFPT4oBgHgl3EQfOTSJ/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..a6788256274d9a5c161c0b73b8e22215ace4fa1b
--- /dev/null
+++ b/vdFPT4oBgHgl3EQfOTSJ/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:57b62fa1355a4b703bfe31657bd29ba6d99518ac3e34a2543d9e183125bc139f
+size 6553645
diff --git a/y9AyT4oBgHgl3EQfbPc2/content/2301.00257v1.pdf b/y9AyT4oBgHgl3EQfbPc2/content/2301.00257v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..3682e65386c3058da5e01995d5a839f8f607c66f
--- /dev/null
+++ b/y9AyT4oBgHgl3EQfbPc2/content/2301.00257v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:436846d5f44e91d3b287b998f4c497e25900bde36a24657466df66f227e4a568
+size 2413458
diff --git a/y9AyT4oBgHgl3EQfbPc2/vector_store/index.faiss b/y9AyT4oBgHgl3EQfbPc2/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..df1168f02b3156a923c3329127fd6abf2ef72e1f
--- /dev/null
+++ b/y9AyT4oBgHgl3EQfbPc2/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5caf9c89029c39dc204d2ce082c7aeb40658ab9bab6d1bb10d7b65ab417f67aa
+size 4849709
diff --git a/y9AyT4oBgHgl3EQfbPc2/vector_store/index.pkl b/y9AyT4oBgHgl3EQfbPc2/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..f034cd22118185baaec51be2e7827c239d7dea55
--- /dev/null
+++ b/y9AyT4oBgHgl3EQfbPc2/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1fd680ee0b7f2bd42534a9e3b3cee9f6ec3743f222d578f6b60501e7f6e910da
+size 184977
diff --git a/ytAzT4oBgHgl3EQfCvqr/content/2301.00965v1.pdf b/ytAzT4oBgHgl3EQfCvqr/content/2301.00965v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..7bded3da5df329cd5537fc92d1098fe1236b9a38
--- /dev/null
+++ b/ytAzT4oBgHgl3EQfCvqr/content/2301.00965v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3a5425a092ebb4291086e7462187aeb5a15e14eb954d4922ad7d4939ab8fb672
+size 2439267
diff --git a/ytAzT4oBgHgl3EQfCvqr/vector_store/index.faiss b/ytAzT4oBgHgl3EQfCvqr/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..e9440a3acbcbfca65274fe54bbb09f0ac5dcd1a2
--- /dev/null
+++ b/ytAzT4oBgHgl3EQfCvqr/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c5ec22370bfb96a5262bd03c6c13a51b145bc3ece9d45690d0361d596afbadf2
+size 3801133
diff --git a/ytAzT4oBgHgl3EQfCvqr/vector_store/index.pkl b/ytAzT4oBgHgl3EQfCvqr/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..341301823bf3a8ee0795c06f5a9536875eca61a8
--- /dev/null
+++ b/ytAzT4oBgHgl3EQfCvqr/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:edaa77f62c69eb51e778d5beb96370bfc6f6f3b7ed0aecf9130cc375e5b9ef6e
+size 138046
diff --git a/z9AzT4oBgHgl3EQfRPsg/vector_store/index.faiss b/z9AzT4oBgHgl3EQfRPsg/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..0778170663cfc10c6a04b42fb336589cf6a16502
--- /dev/null
+++ b/z9AzT4oBgHgl3EQfRPsg/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:16da3de54e41005039e63f765f7a72805e1982c79ea2e30454b824e4d782b4fb
+size 8650797